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tech / sci.math / Re: Unity and its interpretation

SubjectAuthor
* Unity and its interpretationTimothy Golden
+* Re: Unity and its interpretationsergio
|`- Re: Unity and its interpretationmitchr...@gmail.com
+* Re: Unity and its interpretationTimothy Golden
|+- Re: Unity and its interpretationsergio
|`* Re: Unity and its interpretationTimothy Golden
| +- Re: Unity and its interpretationsergio
| `* Re: Unity and its interpretationTimothy Golden
|  `* Re: Unity and its interpretationTimothy Golden
|   `* Re: Unity and its interpretationsergio
|    `* Re: Unity and its interpretationTimothy Golden
|     `- Re: Unity and its interpretationsergio
+- Re: Unity and its interpretationzelos...@gmail.com
+* Re: Unity and its interpretationFromTheRafters
|+- Re: Unity and its interpretationRoss A. Finlayson
|`* Re: Unity and its interpretationTimothy Golden
| +- Re: Unity and its interpretationsergi o
| `* Re: Unity and its interpretationzelos...@gmail.com
|  `* Re: Unity and its interpretationTimothy Golden
|   +- Re: Unity and its interpretationsergi o
|   `- Re: Unity and its interpretationzelos...@gmail.com
`* Re: Unity and its interpretationTimothy Golden
 `* Re: Unity and its interpretationzelos...@gmail.com
  +- Re: Unity and its interpretationTimothy Golden
  `- Re: Unity and its interpretationRoss A. Finlayson

1
Unity and its interpretation

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Subject: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Tue, 10 May 2022 13:13 UTC

It seems uncontroversial at first.
Discern unity on the continuum
versus unity in discrete terms.
The problem opens up considerably.
That these two take the same representation '1' within our numerical representation is problematic.

Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?

Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?

Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.

Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator.. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.

The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.

That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.

Re: Unity and its interpretation

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From: inva...@invalid.com (sergio)
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Subject: Re: Unity and its interpretation
Date: Tue, 10 May 2022 09:03:38 -0500
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 by: sergio - Tue, 10 May 2022 14:03 UTC

On 5/10/2022 8:13 AM, Timothy Golden wrote:
> It seems uncontroversial at first.

to main stream journalists

> Discern unity on the continuum
> versus unity in discrete terms.

mush.

> The problem opens up considerably.

more mush.

> That these two take the same representation '1' within our numerical representation is problematic.

subject change from mush 1 to mush '1'

<snip crap>

Re: Unity and its interpretation

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 by: mitchr...@gmail.com - Tue, 10 May 2022 18:27 UTC

..999 repeating becomes 1 after an infinitely small is added.

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Wed, 11 May 2022 17:09 UTC

On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> It seems uncontroversial at first.
> Discern unity on the continuum
> versus unity in discrete terms.
> The problem opens up considerably.
> That these two take the same representation '1' within our numerical representation is problematic.
>
> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
>
> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
>
> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
>
> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
>
> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
>
> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.

Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.

No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.

As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.

Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?

Re: Unity and its interpretation

<t5gr1b$1bin$1@gioia.aioe.org>

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Subject: Re: Unity and its interpretation
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 by: sergio - Wed, 11 May 2022 17:16 UTC

On 5/11/2022 12:09 PM, Timothy Golden wrote:
> On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
>> It seems uncontroversial at first.
>> Discern unity on the continuum
>> versus unity in discrete terms.
>> The problem opens up considerably.
>> That these two take the same representation '1' within our numerical representation is problematic.
>>
>> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
>>
>> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
>>
>> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
>>
>> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
>>
>> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
>>
>> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
>
> Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
>
> No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
>
> As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
>
> Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?

and....

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Thu, 12 May 2022 15:35 UTC

On Wednesday, May 11, 2022 at 1:09:32 PM UTC-4, Timothy Golden wrote:
> On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> > It seems uncontroversial at first.
> > Discern unity on the continuum
> > versus unity in discrete terms.
> > The problem opens up considerably.
> > That these two take the same representation '1' within our numerical representation is problematic.
> >
> > Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
> >
> > Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
> >
> > Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
> >
> > Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
> >
> > The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
> >
> > That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
> Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
>
> No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
>
> As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
>
> Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?

If we accept the logic that rejects the rational value as fundamental based upon its embedded operator we land in the evaluated form of those values, for instance 3/5= 0.6, and we see that but for the decimal point the representation is fully back to a modulo ten natural value. The decimal place is indicating the unity position of the decimal value. In other words (confusion here: base 10 versus the secondary unital mark) the regard of the decimal number as a natural number is not within the ordinary interpretations yet mechanistically it holds. Computations such as sum and product will carry out on these values as natural values. Division as a reverse operator need not be burdensome.

As we come to regard this format as the working format on the continuum it is because of its adjustable resolution that it is so. This is epsilon/delta theory playing out as digit chasing. This same awareness put the irrational values on the real line according to Dedekind et al. That this same applies to the rational values: here is a substantial change. Of course having just rejected the rational number what right do I have bringing it back in here? In its just form the instance above 3/5 becomes 3.0/5.0, and here of course the precision is quite limited, but the type of the numbers has brought closure. Natural values do not so easily creep into the continuum other than through the careful interpretation as I've laid it out here. Certainly with a pair of dividers and a straight edge one can develop the intervals needed with geometry on paper, but all will concede that their perfection is an assumption that does not hold true. I would think without too much effort accuracy to 0.01 might be possible but not to 0.001. Well is this mathematics or physics? Doesn't geometry actually lay between the two? The logic of the continuum as I am laying it out here is consistent with geometrical works on paper. 6.67430(15)×10−11: physicists would like to do better than this. Always this will be true.

The invalid assumption of mathematicians is that three can exist as 3.000.... in perfection. Why this value is invalid is because the natural value 3000... is invalid. No computation can be done on this form. This is because computation is actually done on natural values. Strange though it is for I who originally thought that I could grant the continuous magnitude as a pure concept without ever looking back; yes, polysign does work out this way on the side of sign... but as we go through the gyrations of mathematics from abstract algebra (rather high on the heap) back down into operator theory (which is actually a fairly direct course down to the bottom) the ambiguities that have accrued in mathematics do make themselves felt. The lack of regard for type sensitivity has been enforced on mathematicians under threat of failure. And this as they pay for the way of their teachers and institutions. Mimicry is one of the human's finest capabilities, but if ever there were a place that it ought to have been challenged it is in this subject. Of course there is a necessary tension: without the prior works we would have little to go upon and the gains to be had are quite slow in surfacing. As to how many gems we have still failed to uncover: I happily declare polysign numbers to be one of these gems and expose that polysign acts as a surrogate. I find it bizarre that those amazing minds who have come before did not find it and that I who really do not have so much ability did find them. That they could lead me all the way through to here back in the bowels of simple number theory; rather they empower me to treat this space as open. This notion of openness perhaps is the most threatening thing of all for it lays the professor and the student flat.


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Re: Unity and its interpretation

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 by: sergio - Thu, 12 May 2022 15:39 UTC

On 5/12/2022 10:35 AM, Timothy Golden wrote:
> On Wednesday, May 11, 2022 at 1:09:32 PM UTC-4, Timothy Golden wrote:
>> On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
>>> It seems uncontroversial at first.
>>> Discern unity on the continuum
>>> versus unity in discrete terms.
>>> The problem opens up considerably.
>>> That these two take the same representation '1' within our numerical representation is problematic.
>>>
>>> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
>>>
>>> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
>>>
>>> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
>>>
>>> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
>>>
>>> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
>>>
>>> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
>> Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
>>
>> No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
>>
>> As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
>>
>> Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?
>
> If we accept the logic that rejects the rational value as fundamental based upon its embedded operator we land in the evaluated form of those values, for instance 3/5= 0.6, and we see that but for the decimal point the representation is fully back to a modulo ten natural value. The decimal place is indicating the unity position of the decimal value. In other words (confusion here: base 10 versus the secondary unital mark) the regard of the decimal number as a natural number is not within the ordinary interpretations yet mechanistically it holds. Computations such as sum and product will carry out on these values as natural values. Division as a reverse operator need not be burdensome.
>
> As we come to regard this format as the working format on the continuum it is because of its adjustable resolution that it is so. This is epsilon/delta theory playing out as digit chasing. This same awareness put the irrational values on the real line according to Dedekind et al. That this same applies to the rational values: here is a substantial change. Of course having just rejected the rational number what right do I have bringing it back in here? In its just form the instance above 3/5 becomes 3.0/5.0, and here of course the precision is quite limited, but the type of the numbers has brought closure. Natural values do not so easily creep into the continuum other than through the careful interpretation as I've laid it out here. Certainly with a pair of dividers and a straight edge one can develop the intervals needed with geometry on paper, but all will concede that their perfection is an assumption that does not hold true. I would think without too much effort accuracy to 0.01 might be possible but not to 0.001. Well is this mathematics or physics? Doesn't geometry actually lay between the two? The logic of the continuum as I am laying it out here is consistent with geometrical works on paper. 6.67430(15)×10−11: physicists would like to do better than this. Always this will be true.
>
> The invalid assumption of mathematicians is that three can exist as 3.000... in perfection. Why this value is invalid is because the natural value 3000... is invalid. No computation can be done on this form. This is because computation is actually done on natural values. Strange though it is for I who originally thought that I could grant the continuous magnitude as a pure concept without ever looking back; yes, polysign does work out this way on the side of sign... but as we go through the gyrations of mathematics from abstract algebra (rather high on the heap) back down into operator theory (which is actually a fairly direct course down to the bottom) the ambiguities that have accrued in mathematics do make themselves felt. The lack of regard for type sensitivity has been enforced on mathematicians under threat of failure. And this as they pay for the way of their teachers and institutions. Mimicry is one of the human's finest capabilities, but if ever there were a place that it ought to have been challenged it is in this subject. Of course there is a necessary tension: without the prior works we would have little to go upon and the gains to be had are quite slow in surfacing. As to how many gems we have still failed to uncover: I happily declare polysign numbers to be one of these gems and expose that polysign acts as a surrogate. I find it bizarre that those amazing minds who have come before did not find it and that I who really do not have so much ability did find them. That they could lead me all the way through to here back in the bowels of simple number theory; rather they empower me to treat this space as open. This notion of openness perhaps is the most threatening thing of all for it lays the professor and the student flat.
>
> This principle of openness is in some ways forgotten by me. I do remember back when I thought that the internet could yield it. The open system is not one ruled by a government in secrecy. Obviously the governments will have to practice openness. Whether it can be done in a way that the wrenches in the gears that corrupt capitalists will throw their way: yes, I suppose so. I hope so.

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Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
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 by: Timothy Golden - Thu, 12 May 2022 19:16 UTC

On Thursday, May 12, 2022 at 11:35:15 AM UTC-4, Timothy Golden wrote:
> On Wednesday, May 11, 2022 at 1:09:32 PM UTC-4, Timothy Golden wrote:
> > On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> > > It seems uncontroversial at first.
> > > Discern unity on the continuum
> > > versus unity in discrete terms.
> > > The problem opens up considerably.
> > > That these two take the same representation '1' within our numerical representation is problematic.
> > >
> > > Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
> > >
> > > Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
> > >
> > > Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
> > >
> > > Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
> > >
> > > The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
> > >
> > > That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
> > Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
> >
> > No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
> >
> > As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
> >

https://www.youtube.com/watch?v=bhj8xTRjFA0

> > Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?
> If we accept the logic that rejects the rational value as fundamental based upon its embedded operator we land in the evaluated form of those values, for instance 3/5= 0.6, and we see that but for the decimal point the representation is fully back to a modulo ten natural value. The decimal place is indicating the unity position of the decimal value. In other words (confusion here: base 10 versus the secondary unital mark) the regard of the decimal number as a natural number is not within the ordinary interpretations yet mechanistically it holds. Computations such as sum and product will carry out on these values as natural values. Division as a reverse operator need not be burdensome.
>
> As we come to regard this format as the working format on the continuum it is because of its adjustable resolution that it is so. This is epsilon/delta theory playing out as digit chasing. This same awareness put the irrational values on the real line according to Dedekind et al. That this same applies to the rational values: here is a substantial change. Of course having just rejected the rational number what right do I have bringing it back in here? In its just form the instance above 3/5 becomes 3.0/5.0, and here of course the precision is quite limited, but the type of the numbers has brought closure. Natural values do not so easily creep into the continuum other than through the careful interpretation as I've laid it out here. Certainly with a pair of dividers and a straight edge one can develop the intervals needed with geometry on paper, but all will concede that their perfection is an assumption that does not hold true. I would think without too much effort accuracy to 0.01 might be possible but not to 0.001. Well is this mathematics or physics? Doesn't geometry actually lay between the two? The logic of the continuum as I am laying it out here is consistent with geometrical works on paper. 6.67430(15)×10−11: physicists would like to do better than this. Always this will be true.
>
> The invalid assumption of mathematicians is that three can exist as 3.000.... in perfection. Why this value is invalid is because the natural value 3000... is invalid. No computation can be done on this form. This is because computation is actually done on natural values. Strange though it is for I who originally thought that I could grant the continuous magnitude as a pure concept without ever looking back; yes, polysign does work out this way on the side of sign... but as we go through the gyrations of mathematics from abstract algebra (rather high on the heap) back down into operator theory (which is actually a fairly direct course down to the bottom) the ambiguities that have accrued in mathematics do make themselves felt. The lack of regard for type sensitivity has been enforced on mathematicians under threat of failure. And this as they pay for the way of their teachers and institutions. Mimicry is one of the human's finest capabilities, but if ever there were a place that it ought to have been challenged it is in this subject. Of course there is a necessary tension: without the prior works we would have little to go upon and the gains to be had are quite slow in surfacing. As to how many gems we have still failed to uncover: I happily declare polysign numbers to be one of these gems and expose that polysign acts as a surrogate. I find it bizarre that those amazing minds who have come before did not find it and that I who really do not have so much ability did find them. That they could lead me all the way through to here back in the bowels of simple number theory; rather they empower me to treat this space as open. This notion of openness perhaps is the most threatening thing of all for it lays the professor and the student flat.
>
> This principle of openness is in some ways forgotten by me. I do remember back when I thought that the internet could yield it. The open system is not one ruled by a government in secrecy. Obviously the governments will have to practice openness. Whether it can be done in a way that the wrenches in the gears that corrupt capitalists will throw their way: yes, I suppose so. I hope so.


Click here to read the complete article
Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Thu, 12 May 2022 19:34 UTC

On Thursday, May 12, 2022 at 3:16:58 PM UTC-4, Timothy Golden wrote:
> On Thursday, May 12, 2022 at 11:35:15 AM UTC-4, Timothy Golden wrote:
> > On Wednesday, May 11, 2022 at 1:09:32 PM UTC-4, Timothy Golden wrote:
> > > On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> > > > It seems uncontroversial at first.
> > > > Discern unity on the continuum
> > > > versus unity in discrete terms.
> > > > The problem opens up considerably.
> > > > That these two take the same representation '1' within our numerical representation is problematic.
> > > >
> > > > Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
> > > >
> > > > Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
> > > >
> > > > Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
> > > >
> > > > Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed..
> > > >
> > > > The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
> > > >
> > > > That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
> > > Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting.. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
> > >
> > > No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
> > >
> > > As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
> > >
> https://www.youtube.com/watch?v=bhj8xTRjFA0
> > > Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?
> > If we accept the logic that rejects the rational value as fundamental based upon its embedded operator we land in the evaluated form of those values, for instance 3/5= 0.6, and we see that but for the decimal point the representation is fully back to a modulo ten natural value. The decimal place is indicating the unity position of the decimal value. In other words (confusion here: base 10 versus the secondary unital mark) the regard of the decimal number as a natural number is not within the ordinary interpretations yet mechanistically it holds. Computations such as sum and product will carry out on these values as natural values. Division as a reverse operator need not be burdensome.
> >
> > As we come to regard this format as the working format on the continuum it is because of its adjustable resolution that it is so. This is epsilon/delta theory playing out as digit chasing. This same awareness put the irrational values on the real line according to Dedekind et al. That this same applies to the rational values: here is a substantial change. Of course having just rejected the rational number what right do I have bringing it back in here? In its just form the instance above 3/5 becomes 3.0/5.0, and here of course the precision is quite limited, but the type of the numbers has brought closure. Natural values do not so easily creep into the continuum other than through the careful interpretation as I've laid it out here. Certainly with a pair of dividers and a straight edge one can develop the intervals needed with geometry on paper, but all will concede that their perfection is an assumption that does not hold true. I would think without too much effort accuracy to 0.01 might be possible but not to 0.001. Well is this mathematics or physics? Doesn't geometry actually lay between the two? The logic of the continuum as I am laying it out here is consistent with geometrical works on paper. 6.67430(15)×10−11: physicists would like to do better than this. Always this will be true.
> >
> > The invalid assumption of mathematicians is that three can exist as 3.000... in perfection. Why this value is invalid is because the natural value 3000... is invalid. No computation can be done on this form. This is because computation is actually done on natural values. Strange though it is for I who originally thought that I could grant the continuous magnitude as a pure concept without ever looking back; yes, polysign does work out this way on the side of sign... but as we go through the gyrations of mathematics from abstract algebra (rather high on the heap) back down into operator theory (which is actually a fairly direct course down to the bottom) the ambiguities that have accrued in mathematics do make themselves felt. The lack of regard for type sensitivity has been enforced on mathematicians under threat of failure. And this as they pay for the way of their teachers and institutions. Mimicry is one of the human's finest capabilities, but if ever there were a place that it ought to have been challenged it is in this subject. Of course there is a necessary tension: without the prior works we would have little to go upon and the gains to be had are quite slow in surfacing.. As to how many gems we have still failed to uncover: I happily declare polysign numbers to be one of these gems and expose that polysign acts as a surrogate. I find it bizarre that those amazing minds who have come before did not find it and that I who really do not have so much ability did find them. That they could lead me all the way through to here back in the bowels of simple number theory; rather they empower me to treat this space as open. This notion of openness perhaps is the most threatening thing of all for it lays the professor and the student flat.
> >
> > This principle of openness is in some ways forgotten by me. I do remember back when I thought that the internet could yield it. The open system is not one ruled by a government in secrecy. Obviously the governments will have to practice openness. Whether it can be done in a way that the wrenches in the gears that corrupt capitalists will throw their way: yes, I suppose so. I hope so.


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Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
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 by: sergio - Thu, 12 May 2022 19:55 UTC

On 5/12/2022 2:34 PM, Timothy Golden wrote:
> On Thursday, May 12, 2022 at 3:16:58 PM UTC-4, Timothy Golden wrote:
>> On Thursday, May 12, 2022 at 11:35:15 AM UTC-4, Timothy Golden wrote:
>>> On Wednesday, May 11, 2022 at 1:09:32 PM UTC-4, Timothy Golden wrote:
>>>> On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
>>>>> It seems uncontroversial at first.
>>>>> Discern unity on the continuum
>>>>> versus unity in discrete terms.
>>>>> The problem opens up considerably.
>>>>> That these two take the same representation '1' within our numerical representation is problematic.
>>>>>
>>>>> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
>>>>>
>>>>> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
>>>>>
>>>>> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
>>>>>
>>>>> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
>>>>>
>>>>> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
>>>>>
>>>>> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
>>>> Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
>>>>
>>>> No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
>>>>
>>>> As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
>>>>
>> https://www.youtube.com/watch?v=bhj8xTRjFA0
>>>> Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?
>>> If we accept the logic that rejects the rational value as fundamental based upon its embedded operator we land in the evaluated form of those values, for instance 3/5= 0.6, and we see that but for the decimal point the representation is fully back to a modulo ten natural value. The decimal place is indicating the unity position of the decimal value. In other words (confusion here: base 10 versus the secondary unital mark) the regard of the decimal number as a natural number is not within the ordinary interpretations yet mechanistically it holds. Computations such as sum and product will carry out on these values as natural values. Division as a reverse operator need not be burdensome.
>>>
>>> As we come to regard this format as the working format on the continuum it is because of its adjustable resolution that it is so. This is epsilon/delta theory playing out as digit chasing. This same awareness put the irrational values on the real line according to Dedekind et al. That this same applies to the rational values: here is a substantial change. Of course having just rejected the rational number what right do I have bringing it back in here? In its just form the instance above 3/5 becomes 3.0/5.0, and here of course the precision is quite limited, but the type of the numbers has brought closure. Natural values do not so easily creep into the continuum other than through the careful interpretation as I've laid it out here. Certainly with a pair of dividers and a straight edge one can develop the intervals needed with geometry on paper, but all will concede that their perfection is an assumption that does not hold true. I would think without too much effort accuracy to 0.01 might be possible but not to 0.001. Well is this mathematics or physics? Doesn't geometry actually lay between the two? The logic of the continuum as I am laying it out here is consistent with geometrical works on paper. 6.67430(15)×10−11: physicists would like to do better than this. Always this will be true.
>>>
>>> The invalid assumption of mathematicians is that three can exist as 3.000... in perfection. Why this value is invalid is because the natural value 3000... is invalid. No computation can be done on this form. This is because computation is actually done on natural values. Strange though it is for I who originally thought that I could grant the continuous magnitude as a pure concept without ever looking back; yes, polysign does work out this way on the side of sign... but as we go through the gyrations of mathematics from abstract algebra (rather high on the heap) back down into operator theory (which is actually a fairly direct course down to the bottom) the ambiguities that have accrued in mathematics do make themselves felt. The lack of regard for type sensitivity has been enforced on mathematicians under threat of failure. And this as they pay for the way of their teachers and institutions. Mimicry is one of the human's finest capabilities, but if ever there were a place that it ought to have been challenged it is in this subject. Of course there is a necessary tension: without the prior works we would have little to go upon and the gains to be had are quite slow in surfacing. As to how many gems we have still failed to uncover: I happily declare polysign numbers to be one of these gems and expose that polysign acts as a surrogate. I find it bizarre that those amazing minds who have come before did not find it and that I who really do not have so much ability did find them. That they could lead me all the way through to here back in the bowels of simple number theory; rather they empower me to treat this space as open. This notion of openness perhaps is the most threatening thing of all for it lays the professor and the student flat.
>>>
>>> This principle of openness is in some ways forgotten by me. I do remember back when I thought that the internet could yield it. The open system is not one ruled by a government in secrecy. Obviously the governments will have to practice openness. Whether it can be done in a way that the wrenches in the gears that corrupt capitalists will throw their way: yes, I suppose so. I hope so.
>
> https://www.youtube.com/watch?v=Kfe1Slac6W0

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Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Fri, 13 May 2022 17:48 UTC

On Thursday, May 12, 2022 at 3:55:34 PM UTC-4, sergio wrote:
> On 5/12/2022 2:34 PM, Timothy Golden wrote:
> > On Thursday, May 12, 2022 at 3:16:58 PM UTC-4, Timothy Golden wrote:
> >> On Thursday, May 12, 2022 at 11:35:15 AM UTC-4, Timothy Golden wrote:
> >>> On Wednesday, May 11, 2022 at 1:09:32 PM UTC-4, Timothy Golden wrote:
> >>>> On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> >>>>> It seems uncontroversial at first.
> >>>>> Discern unity on the continuum
> >>>>> versus unity in discrete terms.
> >>>>> The problem opens up considerably.
> >>>>> That these two take the same representation '1' within our numerical representation is problematic.
> >>>>>
> >>>>> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
> >>>>>
> >>>>> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
> >>>>>
> >>>>> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
> >>>>>
> >>>>> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed..
> >>>>>
> >>>>> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
> >>>>>
> >>>>> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
> >>>> Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
> >>>>
> >>>> No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
> >>>>
> >>>> As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
> >>>>
> >> https://www.youtube.com/watch?v=bhj8xTRjFA0
> >>>> Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?
> >>> If we accept the logic that rejects the rational value as fundamental based upon its embedded operator we land in the evaluated form of those values, for instance 3/5= 0.6, and we see that but for the decimal point the representation is fully back to a modulo ten natural value. The decimal place is indicating the unity position of the decimal value. In other words (confusion here: base 10 versus the secondary unital mark) the regard of the decimal number as a natural number is not within the ordinary interpretations yet mechanistically it holds. Computations such as sum and product will carry out on these values as natural values. Division as a reverse operator need not be burdensome.
> >>>
> >>> As we come to regard this format as the working format on the continuum it is because of its adjustable resolution that it is so. This is epsilon/delta theory playing out as digit chasing. This same awareness put the irrational values on the real line according to Dedekind et al. That this same applies to the rational values: here is a substantial change. Of course having just rejected the rational number what right do I have bringing it back in here? In its just form the instance above 3/5 becomes 3.0/5.0, and here of course the precision is quite limited, but the type of the numbers has brought closure. Natural values do not so easily creep into the continuum other than through the careful interpretation as I've laid it out here. Certainly with a pair of dividers and a straight edge one can develop the intervals needed with geometry on paper, but all will concede that their perfection is an assumption that does not hold true. I would think without too much effort accuracy to 0.01 might be possible but not to 0.001. Well is this mathematics or physics? Doesn't geometry actually lay between the two? The logic of the continuum as I am laying it out here is consistent with geometrical works on paper. 6.67430(15)×10−11: physicists would like to do better than this. Always this will be true.
> >>>
> >>> The invalid assumption of mathematicians is that three can exist as 3..000... in perfection. Why this value is invalid is because the natural value 3000... is invalid. No computation can be done on this form. This is because computation is actually done on natural values. Strange though it is for I who originally thought that I could grant the continuous magnitude as a pure concept without ever looking back; yes, polysign does work out this way on the side of sign... but as we go through the gyrations of mathematics from abstract algebra (rather high on the heap) back down into operator theory (which is actually a fairly direct course down to the bottom) the ambiguities that have accrued in mathematics do make themselves felt. The lack of regard for type sensitivity has been enforced on mathematicians under threat of failure. And this as they pay for the way of their teachers and institutions. Mimicry is one of the human's finest capabilities, but if ever there were a place that it ought to have been challenged it is in this subject. Of course there is a necessary tension: without the prior works we would have little to go upon and the gains to be had are quite slow in surfacing. As to how many gems we have still failed to uncover: I happily declare polysign numbers to be one of these gems and expose that polysign acts as a surrogate. I find it bizarre that those amazing minds who have come before did not find it and that I who really do not have so much ability did find them. That they could lead me all the way through to here back in the bowels of simple number theory; rather they empower me to treat this space as open. This notion of openness perhaps is the most threatening thing of all for it lays the professor and the student flat.
> >>>
> >>> This principle of openness is in some ways forgotten by me. I do remember back when I thought that the internet could yield it. The open system is not one ruled by a government in secrecy. Obviously the governments will have to practice openness. Whether it can be done in a way that the wrenches in the gears that corrupt capitalists will throw their way: yes, I suppose so. I hope so.
> >
> > https://www.youtube.com/watch?v=Kfe1Slac6W0
>
>
> what happened after that ?


Click here to read the complete article
Re: Unity and its interpretation

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 by: sergio - Fri, 13 May 2022 18:17 UTC

On 5/13/2022 12:48 PM, Timothy Golden wrote:
> On Thursday, May 12, 2022 at 3:55:34 PM UTC-4, sergio wrote:
>> On 5/12/2022 2:34 PM, Timothy Golden wrote:
>>> On Thursday, May 12, 2022 at 3:16:58 PM UTC-4, Timothy Golden wrote:
>>>> On Thursday, May 12, 2022 at 11:35:15 AM UTC-4, Timothy Golden wrote:
>>>>> On Wednesday, May 11, 2022 at 1:09:32 PM UTC-4, Timothy Golden wrote:
>>>>>> On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
>>>>>>> It seems uncontroversial at first.
>>>>>>> Discern unity on the continuum
>>>>>>> versus unity in discrete terms.
>>>>>>> The problem opens up considerably.
>>>>>>> That these two take the same representation '1' within our numerical representation is problematic.
>>>>>>>
>>>>>>> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
>>>>>>>
>>>>>>> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
>>>>>>>
>>>>>>> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
>>>>>>>
>>>>>>> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
>>>>>>>
>>>>>>> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
>>>>>>>
>>>>>>> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.
>>>>>> Unity in discrete terms can be represented without even uttering our usual sense of number. Any glyph will do to represent a concept such as a count of sheep in a flock; a practical instance of early need for accounting. A leather bag containing pebbles would suffice. On a clean piece of bark a series of blobs or tics made with a piece of carbon from the fire. These early marks are unital in nature. Their value as a transcribable record is complete. So long as no ellipses are used the mapping of a modulo ten value (though here some ambiguity creeps in) is possible, which is our usually presumed representation as say '14 sheep' being bbbbbbbbbbbbbb, the 'b' arbitrarily chosen.
>>>>>>
>>>>>> No geometrical significance is had in this sense of number. We do however witness that every practical instance that can be discussed and verified does occur in spacetime. In this regard the continuum is acting as a basis for the analysis and for the representation. The notion that we will somehow build off of this discrete form to recover the continuum cannot gain theoretical support under this awareness.
>>>>>>
>>>>>> As works in geometry progress and the appreciation of the line as defined by two positions in space (and here should we engage time?) we can eventually work up to this line as a concept of 'dimension' and with the use of the Cartesian product beget the three dimensional representation of the continuum. Frozen depictions on a piece of paper have sufficed and now we all do have the ability to animate a pixelated version on these displays. Still though our perception is not truly three dimensional. We do not see any galaxies beyond the tree. Not even a mountain. We have an occluded form of vision based on ray tracing. We should all be able to point to Hawaii and convey thanks to Tulsi and hope she does not get swallowed by the machine.
>>>>>>
>>>> https://www.youtube.com/watch?v=bhj8xTRjFA0
>>>>>> Meanwhile the orthogonal real valued approach leads to 4D spacetime, three dimensions of which are pulled out of a hat for the sake of physical correspondence and the other bidirectional in direct conflict with its properties as unidirectional. All the while one might ask how a zero dimensional point actually requires four dimensions to address... or was it three actually? This awareness leads to some concept of collapsing systems but also the care with which we could scrutinize existing theory as fictitious. In that modern mathematics has failed to yield an emergent spacetime candidate then its usage as a basis for physics is suspect. This is a fine position to land in, except for the fact that the openings are not well declared. We are engaged in a progression. Existing theory needn't be perfect, but as well it needn't be presented that way either. As we entrain ourselves on the works that came before; as we struggle to repeat their results; to what degree do we blind ourselves?
>>>>> If we accept the logic that rejects the rational value as fundamental based upon its embedded operator we land in the evaluated form of those values, for instance 3/5= 0.6, and we see that but for the decimal point the representation is fully back to a modulo ten natural value. The decimal place is indicating the unity position of the decimal value. In other words (confusion here: base 10 versus the secondary unital mark) the regard of the decimal number as a natural number is not within the ordinary interpretations yet mechanistically it holds. Computations such as sum and product will carry out on these values as natural values. Division as a reverse operator need not be burdensome.
>>>>>
>>>>> As we come to regard this format as the working format on the continuum it is because of its adjustable resolution that it is so. This is epsilon/delta theory playing out as digit chasing. This same awareness put the irrational values on the real line according to Dedekind et al. That this same applies to the rational values: here is a substantial change. Of course having just rejected the rational number what right do I have bringing it back in here? In its just form the instance above 3/5 becomes 3.0/5.0, and here of course the precision is quite limited, but the type of the numbers has brought closure. Natural values do not so easily creep into the continuum other than through the careful interpretation as I've laid it out here. Certainly with a pair of dividers and a straight edge one can develop the intervals needed with geometry on paper, but all will concede that their perfection is an assumption that does not hold true. I would think without too much effort accuracy to 0.01 might be possible but not to 0.001. Well is this mathematics or physics? Doesn't geometry actually lay between the two? The logic of the continuum as I am laying it out here is consistent with geometrical works on paper. 6.67430(15)×10−11: physicists would like to do better than this. Always this will be true.
>>>>>
>>>>> The invalid assumption of mathematicians is that three can exist as 3.000... in perfection. Why this value is invalid is because the natural value 3000... is invalid. No computation can be done on this form. This is because computation is actually done on natural values. Strange though it is for I who originally thought that I could grant the continuous magnitude as a pure concept without ever looking back; yes, polysign does work out this way on the side of sign... but as we go through the gyrations of mathematics from abstract algebra (rather high on the heap) back down into operator theory (which is actually a fairly direct course down to the bottom) the ambiguities that have accrued in mathematics do make themselves felt. The lack of regard for type sensitivity has been enforced on mathematicians under threat of failure. And this as they pay for the way of their teachers and institutions. Mimicry is one of the human's finest capabilities, but if ever there were a place that it ought to have been challenged it is in this subject. Of course there is a necessary tension: without the prior works we would have little to go upon and the gains to be had are quite slow in surfacing. As to how many gems we have still failed to uncover: I happily declare polysign numbers to be one of these gems and expose that polysign acts as a surrogate. I find it bizarre that those amazing minds who have come before did not find it and that I who really do not have so much ability did find them. That they could lead me all the way through to here back in the bowels of simple number theory; rather they empower me to treat this space as open. This notion of openness perhaps is the most threatening thing of all for it lays the professor and the student flat.
>>>>>
>>>>> This principle of openness is in some ways forgotten by me. I do remember back when I thought that the internet could yield it. The open system is not one ruled by a government in secrecy. Obviously the governments will have to practice openness. Whether it can be done in a way that the wrenches in the gears that corrupt capitalists will throw their way: yes, I suppose so. I hope so.
>>>
>>> https://www.youtube.com/watch?v=Kfe1Slac6W0
>>
>>
>> what happened after that ?
>
> You could try: https://www.youtube.com/watch?v=kfMwXsWbvuk
>
> When was the cold war with Russia reignited? 2016 begins an era.
>
> On the numerical front: Values such as 0.333... seem to be accepted by mathematicians while a value such as 333... is not accepted by mathematicians. As to why the addition of a decimal point makes one more acceptable than the other: here I believe my meanderings have come into a new crux. Of course the side effects are many, and this is but one vector of awareness. Still, computationally this arguments holds up very well. That modern mathematics is soaked in ambiguity I find provable.
>
> That epsilon delta theory has enough in it to handle the irrational value suggests that we simply apply it to all values unconditionally. This then exposes our representation of the continuum as gray in nature. The discrete and the continuous each take their representation through the natural value but their meanings, and the added complexity of a floating unit position, differentiates them. Sufficient versus perfection could be a loose form of the discussion, and of course the mathematician as more perfect than any other is a sort of aesthetic that draws certain types to the subject. They are purists. We like that, but still, when the perfection is not attainable some concession has to be made.

Click here to read the complete article

Re: Unity and its interpretation

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 by: zelos...@gmail.com - Mon, 16 May 2022 08:39 UTC

tisdag 10 maj 2022 kl. 15:13:35 UTC+2 skrev timba...@gmail.com:
> It seems uncontroversial at first.
> Discern unity on the continuum
> versus unity in discrete terms.
> The problem opens up considerably.
> That these two take the same representation '1' within our numerical representation is problematic.
>
> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
>
> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
>
> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
>
> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
>
> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
>
> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.

1 is used for the multiplicative identity element in rings.

Was that so fucking hard?

Re: Unity and its interpretation

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 by: FromTheRafters - Mon, 16 May 2022 09:41 UTC

Timothy Golden wrote on 5/10/2022 :
> It seems uncontroversial at first.
> Discern unity on the continuum
> versus unity in discrete terms.
> The problem opens up considerably.
> That these two take the same representation '1' within our numerical
> representation is problematic.
>
> Set theory is supposed to address this, yet the natural values are formally a
> subset of the real values. This has been vetted by eons of mathematicians,
> right?

Actually, it has been pointed out many times that they are embeddings
not strictly speaking always 'subsets'.

Funny that we seem to have started discrete with naturals and integers
and then fractions of wholes where they can be symbolized as ratios of
these discrete naturals or integers, then on to our continuous reals
after discovering gaps or holes between the discrete fractions where
irrational numbers can be envisioned to reside.

Then we find the actual physical reality is more likely discrete and
probabilistic in nature, perhaps making calculus take a back seat to
number theory and probability theory when dealing with very small
realities.

Re: Unity and its interpretation

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 by: Ross A. Finlayson - Mon, 16 May 2022 15:51 UTC

On Monday, May 16, 2022 at 2:42:07 AM UTC-7, FromTheRafters wrote:
> Timothy Golden wrote on 5/10/2022 :
> > It seems uncontroversial at first.
> > Discern unity on the continuum
> > versus unity in discrete terms.
> > The problem opens up considerably.
> > That these two take the same representation '1' within our numerical
> > representation is problematic.
> >
> > Set theory is supposed to address this, yet the natural values are formally a
> > subset of the real values. This has been vetted by eons of mathematicians,
> > right?
> Actually, it has been pointed out many times that they are embeddings
> not strictly speaking always 'subsets'.
>
> Funny that we seem to have started discrete with naturals and integers
> and then fractions of wholes where they can be symbolized as ratios of
> these discrete naturals or integers, then on to our continuous reals
> after discovering gaps or holes between the discrete fractions where
> irrational numbers can be envisioned to reside.
>
> Then we find the actual physical reality is more likely discrete and
> probabilistic in nature, perhaps making calculus take a back seat to
> number theory and probability theory when dealing with very small
> realities.

Probabilities vanish, our "best guess" is probabilistic while still
it's all as continuous with the limits of information and dissipation.

When I learned about atoms it wasn't until much later that
I learned about superstrings: as much smaller than atoms as
atoms are smaller that us: about 25 orders of magnitude.
This was after having learned about atoms, then also about the
particle/wave duality and Schroedinger and why there are
probabilistic interpretations of otherwise the "terms" of quantum
mechanics - where there are "quantum" mechanics besides "continuum"
mechanics at all to define whatever are emmanent properties.

Then, in the particle/wave, and, wave/resonance theories that
there are, it's almost always assumed these are "continuous
manifolds", as according their field numbers (numbers at each
lattice point at space-time, with probabilistic interpretations
according only to indeterminacy).

That the atom is a discrete point while the meter is continuous,
or infinitely divisible, helps explain for physics why it is quantum
mechanics, of the quantized atom and quantizing meter,
of continuum mechanics.

This way then mathematics is mostly mathematics of the
continuous and discrete.

Here it was a requirement to "derive" thermo 2'nd law.
(In the statistical ensemble.)

Lots of quantum mechanics is "the interface of continuous
resonances".

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Tue, 17 May 2022 17:21 UTC

On Monday, May 16, 2022 at 5:42:07 AM UTC-4, FromTheRafters wrote:
> Timothy Golden wrote on 5/10/2022 :
> > It seems uncontroversial at first.
> > Discern unity on the continuum
> > versus unity in discrete terms.
> > The problem opens up considerably.
> > That these two take the same representation '1' within our numerical
> > representation is problematic.
> >
> > Set theory is supposed to address this, yet the natural values are formally a
> > subset of the real values. This has been vetted by eons of mathematicians,
> > right?
> Actually, it has been pointed out many times that they are embeddings
> not strictly speaking always 'subsets'.

This distinction to embedding still does not hold up.
Unity represented in the discrete form is not controversial.
Unity upon the continuum is arbitrarily selected, from which discrete intervals can extend.
However, for instance, the meter versus the foot as embeddings expose that the discrete value '3' takes different positions.
Clearly the geometrical representation of the real line lacks the clarity that a discrete representation had.
bbb is uncontroversially the discrete three using b as a unit. No real line representation provides this level of clarity.
As well the marks along the real line as a geometer makes them, say with a pair of dividers, will contain some error.
The disconnect between the discrete and the continuous creeps even wider.

As to who is strict and who is not strict: I believe it is safe to say that I am being quite strict here while the mathematician and his curriculum is not so strict. It should be the other way around, but it is true that the modern engineer has suffered the C compiler and its attention to structured data. Furthermore the notion of an operator as something which actually does work and yields a result; rather than something that can always be embedded as if it is already a pure value: here we have to land in the decimal value to make sense of the rational value. Here we have to land early on epsilon/delta as something that can apply to every value in the continuum. This notion even applies to the geometers who do careful works with the best of materials. Physical correspondence between the discrete and the continuous is lacking and yet the decimal number does provide for it.
This same decimal number takes a natural valued interpretation merely be removing a little dot. How can I land in such a simplification while others cannot admit it? Congruent with computation and hardware implementation of the basic operations? Yes.

Within the discrete there is as well the modulo branch. And again there is a structural form within the real value which is not appreciated. It is the sign of the real value. It's modulo two character is perfectly supported. The structural option to generalize this is the biggest blunder of modern mathematics. From this bud the complex numbers and the real numbers are siblings of series P2 and P3. From this bud a unidirectional form P1 whose zero dimensional character exactly matches that of time goes under appreciated.. P4, P5, and so forth all work fine, though some surprises do occur. As importantly the geometrical rendering of these types comes as fundamental character of their balance amongst the signs as for instance in a P4 value we will have -z+z*z#z=0 just as in P2 we had -z+z=0. P2 as fundamental is a fraud. It is just early along the way.

Taking sx where s is sign and x is continuous magnitude the next step takes the decimal value more seriously and places the little dot within the structure we could land with sxe numbers with s as sign, x as a natural value, and e being another natural valued being marking the position of the decimal point. This is different only slightly from scientific notation. These are all values. There are no operators embedded. These numbers are of unique types and so as a product these simply preserve their place. When operations take place upon them as elements z in Pn they are each involved in the computation. If this representation is fundamental it is interesting that it has three components. Still, physical correspondence is found more in the progression P1P2P3|P4P5... with its natural breakpoint.

It's odd that these values do come with a sense of unital scale though it is not at all like a selection of feet or meters. In effect I am suffering my original complaint but still do come closer in physical correspondence to the notion of the continuum, all the while claiming that the natural value is at the root of the structure. It's a strange turn. And we've barely modified anything. It is merely an interpretation.

>
> Funny that we seem to have started discrete with naturals and integers
> and then fractions of wholes where they can be symbolized as ratios of
> these discrete naturals or integers, then on to our continuous reals
> after discovering gaps or holes between the discrete fractions where
> irrational numbers can be envisioned to reside.
>
> Then we find the actual physical reality is more likely discrete and
> probabilistic in nature, perhaps making calculus take a back seat to
> number theory and probability theory when dealing with very small
> realities.

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
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 by: sergi o - Tue, 17 May 2022 17:26 UTC

On 5/17/2022 12:21 PM, Timothy Golden wrote:
> On Monday, May 16, 2022 at 5:42:07 AM UTC-4, FromTheRafters wrote:
>> Timothy Golden wrote on 5/10/2022 :
>>> It seems uncontroversial at first.
>>> Discern unity on the continuum
>>> versus unity in discrete terms.
>>> The problem opens up considerably.
>>> That these two take the same representation '1' within our numerical
>>> representation is problematic.
>>>
>>> Set theory is supposed to address this, yet the natural values are formally a
>>> subset of the real values. This has been vetted by eons of mathematicians,
>>> right?
>> Actually, it has been pointed out many times that they are embeddings
>> not strictly speaking always 'subsets'.
>
> This distinction to embedding still does not hold up.
> Unity represented in the discrete form is not controversial.
> Unity upon the continuum is arbitrarily selected, from which discrete intervals can extend.
> However, for instance, the meter versus the foot as embeddings expose that the discrete value '3' takes different positions.
> Clearly the geometrical representation of the real line lacks the clarity that a discrete representation had.
> bbb is uncontroversially the discrete three using b as a unit. No real line representation provides this level of clarity.
> As well the marks along the real line as a geometer makes them, say with a pair of dividers, will contain some error.
> The disconnect between the discrete and the continuous creeps even wider.
>
> As to who is strict and who is not strict: I believe it is safe to say that I am being quite strict here while the mathematician and his curriculum is not so strict. It should be the other way around, but it is true that the modern engineer has suffered the C compiler and its attention to structured data. Furthermore the notion of an operator as something which actually does work and yields a result; rather than something that can always be embedded as if it is already a pure value: here we have to land in the decimal value to make sense of the rational value. Here we have to land early on epsilon/delta as something that can apply to every value in the continuum. This notion even applies to the geometers who do careful works with the best of materials. Physical correspondence between the discrete and the continuous is lacking and yet the decimal number does provide for it.
> This same decimal number takes a natural valued interpretation merely be removing a little dot. How can I land in such a simplification while others cannot admit it? Congruent with computation and hardware implementation of the basic operations? Yes.
>
> Within the discrete there is as well the modulo branch. And again there is a structural form within the real value which is not appreciated. It is the sign of the real value. It's modulo two character is perfectly supported. The structural option to generalize this is the biggest blunder of modern mathematics. From this bud the complex numbers and the real numbers are siblings of series P2 and P3. From this bud a unidirectional form P1 whose zero dimensional character exactly matches that of time goes under appreciated. P4, P5, and so forth all work fine, though some surprises do occur. As importantly the geometrical rendering of these types comes as fundamental character of their balance amongst the signs as for instance in a P4 value we will have -z+z*z#z=0 just as in P2 we had -z+z=0. P2 as fundamental is a fraud. It is just early along the way.
>
> Taking sx where s is sign and x is continuous magnitude the next step takes the decimal value more seriously and places the little dot within the structure we could land with sxe numbers with s as sign, x as a natural value, and e being another natural valued being marking the position of the decimal point. This is different only slightly from scientific notation. These are all values. There are no operators embedded. These numbers are of unique types and so as a product these simply preserve their place. When operations take place upon them as elements z in Pn they are each involved in the computation. If this representation is fundamental it is interesting that it has three components. Still, physical correspondence is found more in the progression P1P2P3|P4P5... with its natural breakpoint.
>
> It's odd that these values do come with a sense of unital scale though it is not at all like a selection of feet or meters. In effect I am suffering my original complaint but still do come closer in physical correspondence to the notion of the continuum, all the while claiming that the natural value is at the root of the structure. It's a strange turn. And we've barely modified anything. It is merely an interpretation.
>

not under all conditions...

>
>>
>> Funny that we seem to have started discrete with naturals and integers
>> and then fractions of wholes where they can be symbolized as ratios of
>> these discrete naturals or integers, then on to our continuous reals
>> after discovering gaps or holes between the discrete fractions where
>> irrational numbers can be envisioned to reside.
>>
>> Then we find the actual physical reality is more likely discrete and
>> probabilistic in nature, perhaps making calculus take a back seat to
>> number theory and probability theory when dealing with very small
>> realities.

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Wed, 18 May 2022 05:23 UTC

tisdag 17 maj 2022 kl. 19:21:21 UTC+2 skrev timba...@gmail.com:
> On Monday, May 16, 2022 at 5:42:07 AM UTC-4, FromTheRafters wrote:
> > Timothy Golden wrote on 5/10/2022 :
> > > It seems uncontroversial at first.
> > > Discern unity on the continuum
> > > versus unity in discrete terms.
> > > The problem opens up considerably.
> > > That these two take the same representation '1' within our numerical
> > > representation is problematic.
> > >
> > > Set theory is supposed to address this, yet the natural values are formally a
> > > subset of the real values. This has been vetted by eons of mathematicians,
> > > right?
> > Actually, it has been pointed out many times that they are embeddings
> > not strictly speaking always 'subsets'.
> This distinction to embedding still does not hold up.
> Unity represented in the discrete form is not controversial.
> Unity upon the continuum is arbitrarily selected, from which discrete intervals can extend.
> However, for instance, the meter versus the foot as embeddings expose that the discrete value '3' takes different positions.
> Clearly the geometrical representation of the real line lacks the clarity that a discrete representation had.
> bbb is uncontroversially the discrete three using b as a unit. No real line representation provides this level of clarity.
> As well the marks along the real line as a geometer makes them, say with a pair of dividers, will contain some error.
> The disconnect between the discrete and the continuous creeps even wider.
>
> As to who is strict and who is not strict: I believe it is safe to say that I am being quite strict here while the mathematician and his curriculum is not so strict. It should be the other way around, but it is true that the modern engineer has suffered the C compiler and its attention to structured data. Furthermore the notion of an operator as something which actually does work and yields a result; rather than something that can always be embedded as if it is already a pure value: here we have to land in the decimal value to make sense of the rational value. Here we have to land early on epsilon/delta as something that can apply to every value in the continuum. This notion even applies to the geometers who do careful works with the best of materials. Physical correspondence between the discrete and the continuous is lacking and yet the decimal number does provide for it.
> This same decimal number takes a natural valued interpretation merely be removing a little dot. How can I land in such a simplification while others cannot admit it? Congruent with computation and hardware implementation of the basic operations? Yes.
>
> Within the discrete there is as well the modulo branch. And again there is a structural form within the real value which is not appreciated. It is the sign of the real value. It's modulo two character is perfectly supported.. The structural option to generalize this is the biggest blunder of modern mathematics. From this bud the complex numbers and the real numbers are siblings of series P2 and P3. From this bud a unidirectional form P1 whose zero dimensional character exactly matches that of time goes under appreciated. P4, P5, and so forth all work fine, though some surprises do occur. As importantly the geometrical rendering of these types comes as fundamental character of their balance amongst the signs as for instance in a P4 value we will have -z+z*z#z=0 just as in P2 we had -z+z=0. P2 as fundamental is a fraud. It is just early along the way.
>
> Taking sx where s is sign and x is continuous magnitude the next step takes the decimal value more seriously and places the little dot within the structure we could land with sxe numbers with s as sign, x as a natural value, and e being another natural valued being marking the position of the decimal point. This is different only slightly from scientific notation. These are all values. There are no operators embedded. These numbers are of unique types and so as a product these simply preserve their place. When operations take place upon them as elements z in Pn they are each involved in the computation. If this representation is fundamental it is interesting that it has three components. Still, physical correspondence is found more in the progression P1P2P3|P4P5... with its natural breakpoint.
>
> It's odd that these values do come with a sense of unital scale though it is not at all like a selection of feet or meters. In effect I am suffering my original complaint but still do come closer in physical correspondence to the notion of the continuum, all the while claiming that the natural value is at the root of the structure. It's a strange turn. And we've barely modified anything. It is merely an interpretation.
> >
> > Funny that we seem to have started discrete with naturals and integers
> > and then fractions of wholes where they can be symbolized as ratios of
> > these discrete naturals or integers, then on to our continuous reals
> > after discovering gaps or holes between the discrete fractions where
> > irrational numbers can be envisioned to reside.
> >
> > Then we find the actual physical reality is more likely discrete and
> > probabilistic in nature, perhaps making calculus take a back seat to
> > number theory and probability theory when dealing with very small
> > realities.

No, 1 and units have strict definitions.

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Thu, 19 May 2022 14:51 UTC

On Wednesday, May 18, 2022 at 1:23:20 AM UTC-4, zelos...@gmail.com wrote:
> tisdag 17 maj 2022 kl. 19:21:21 UTC+2 skrev timba...@gmail.com:
> > On Monday, May 16, 2022 at 5:42:07 AM UTC-4, FromTheRafters wrote:
> > > Timothy Golden wrote on 5/10/2022 :
> > > > It seems uncontroversial at first.
> > > > Discern unity on the continuum
> > > > versus unity in discrete terms.
> > > > The problem opens up considerably.
> > > > That these two take the same representation '1' within our numerical
> > > > representation is problematic.
> > > >
> > > > Set theory is supposed to address this, yet the natural values are formally a
> > > > subset of the real values. This has been vetted by eons of mathematicians,
> > > > right?
> > > Actually, it has been pointed out many times that they are embeddings
> > > not strictly speaking always 'subsets'.
> > This distinction to embedding still does not hold up.
> > Unity represented in the discrete form is not controversial.
> > Unity upon the continuum is arbitrarily selected, from which discrete intervals can extend.
> > However, for instance, the meter versus the foot as embeddings expose that the discrete value '3' takes different positions.
> > Clearly the geometrical representation of the real line lacks the clarity that a discrete representation had.
> > bbb is uncontroversially the discrete three using b as a unit. No real line representation provides this level of clarity.
> > As well the marks along the real line as a geometer makes them, say with a pair of dividers, will contain some error.
> > The disconnect between the discrete and the continuous creeps even wider.
> >
> > As to who is strict and who is not strict: I believe it is safe to say that I am being quite strict here while the mathematician and his curriculum is not so strict. It should be the other way around, but it is true that the modern engineer has suffered the C compiler and its attention to structured data. Furthermore the notion of an operator as something which actually does work and yields a result; rather than something that can always be embedded as if it is already a pure value: here we have to land in the decimal value to make sense of the rational value. Here we have to land early on epsilon/delta as something that can apply to every value in the continuum. This notion even applies to the geometers who do careful works with the best of materials. Physical correspondence between the discrete and the continuous is lacking and yet the decimal number does provide for it.
> > This same decimal number takes a natural valued interpretation merely be removing a little dot. How can I land in such a simplification while others cannot admit it? Congruent with computation and hardware implementation of the basic operations? Yes.
> >
> > Within the discrete there is as well the modulo branch. And again there is a structural form within the real value which is not appreciated. It is the sign of the real value. It's modulo two character is perfectly supported. The structural option to generalize this is the biggest blunder of modern mathematics. From this bud the complex numbers and the real numbers are siblings of series P2 and P3. From this bud a unidirectional form P1 whose zero dimensional character exactly matches that of time goes under appreciated. P4, P5, and so forth all work fine, though some surprises do occur. As importantly the geometrical rendering of these types comes as fundamental character of their balance amongst the signs as for instance in a P4 value we will have -z+z*z#z=0 just as in P2 we had -z+z=0. P2 as fundamental is a fraud. It is just early along the way.
> >
> > Taking sx where s is sign and x is continuous magnitude the next step takes the decimal value more seriously and places the little dot within the structure we could land with sxe numbers with s as sign, x as a natural value, and e being another natural valued being marking the position of the decimal point. This is different only slightly from scientific notation. These are all values. There are no operators embedded. These numbers are of unique types and so as a product these simply preserve their place. When operations take place upon them as elements z in Pn they are each involved in the computation. If this representation is fundamental it is interesting that it has three components. Still, physical correspondence is found more in the progression P1P2P3|P4P5... with its natural breakpoint.
> >
> > It's odd that these values do come with a sense of unital scale though it is not at all like a selection of feet or meters. In effect I am suffering my original complaint but still do come closer in physical correspondence to the notion of the continuum, all the while claiming that the natural value is at the root of the structure. It's a strange turn. And we've barely modified anything. It is merely an interpretation.
> > >
> > > Funny that we seem to have started discrete with naturals and integers
> > > and then fractions of wholes where they can be symbolized as ratios of
> > > these discrete naturals or integers, then on to our continuous reals
> > > after discovering gaps or holes between the discrete fractions where
> > > irrational numbers can be envisioned to reside.
> > >
> > > Then we find the actual physical reality is more likely discrete and
> > > probabilistic in nature, perhaps making calculus take a back seat to
> > > number theory and probability theory when dealing with very small
> > > realities.
> No, 1 and units have strict definitions.

Ah, the foot and the meter have physical definitions and as units they are unique. But the conjunction of one foot and the definition of the foot are one and the same. If you could differentiate that I'd be impressed. Dimensional analysis does ensue here in terms of physical correspondence. I think that context is more appropriate but that is filling out the picture rather than falsifying it. We've been taught that a line on a piece of paper is fundamental somehow. Two of those lines at right angles develops the geometry of the paper somehow. Meanwhile the point is zero dimensional yet requires two dimensions to locate it on the paper somehow. We are dealing in interdimensional systems somehow. The care that has been taken and the habits formed and enforced upon us by our predecessors are merely ensuring our coherence to their rules. Breaking out of such a straight jacket is not so easy as we'd like to believe. How the simplest things can go undetected by the human mind: how we fail to cover the ground; this explains much of the lies. The human as a two-signed moron will have to live on a few more generations perhaps.

Did topology open the puzzle up better somehow? I didn't find that to be the case. Nor for abstract algebra. Possibly, and it does run in my head as an abstract thing that is actually a bit unpleasant, but possibly the proper zero dimensional point realization is the collapse of the universe to a point. Thence the line properly formed is the collapse of the universe to the line. This does somehow embody some sort of order that gets lost upward in three dimensions, where the apparent actual order is obtained, at least according to standard theory. As to why this three dimensional (a term somewhat corrupted by me though it still works somewhat) order holds up nobody has a clue. Obviously if theory can land this then physics could ensue in a pure theoretical form. To accept that our position in this progression is far closer to apes than the refinement level that we presume is known as the leading edge. We all are attempting to establish some flow there. At least I would hope that you count yourself in that group.

As destructive as my works and words may seem in them lays the openings and hopefully the proof that things are still open; that the progression still has some way to go. Within this large level of reasoning there comes a time when we accept that things that do not make sense to us are not sensible. We may be able to mimic them so as to pass through the system, but to take a strong mind and make it a weak one: this is the greatest fail of the academic system. I am fairly certain it is being done a thousand and a million times over. As some pledge some sort of salute to books or to academia... it's a bit religious, really. The tentacles and politics of every niche in that system are suspect. Still, we have to admit that without it there would be little to work from. The tension is necessary I suppose. Whatever, if you grant no room to work from there will be no work that can be done. Therefor we must keep things a bit open, yeah?

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
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 by: sergi o - Thu, 19 May 2022 17:51 UTC

On 5/19/2022 9:51 AM, Timothy Golden wrote:
> On Wednesday, May 18, 2022 at 1:23:20 AM UTC-4, zelos...@gmail.com wrote:
>> tisdag 17 maj 2022 kl. 19:21:21 UTC+2 skrev timba...@gmail.com:
>>> On Monday, May 16, 2022 at 5:42:07 AM UTC-4, FromTheRafters wrote:
>>>> Timothy Golden wrote on 5/10/2022 :
>>>>> It seems uncontroversial at first.
>>>>> Discern unity on the continuum
>>>>> versus unity in discrete terms.
>>>>> The problem opens up considerably.
>>>>> That these two take the same representation '1' within our numerical
>>>>> representation is problematic.
>>>>>
>>>>> Set theory is supposed to address this, yet the natural values are formally a
>>>>> subset of the real values. This has been vetted by eons of mathematicians,
>>>>> right?
>>>> Actually, it has been pointed out many times that they are embeddings
>>>> not strictly speaking always 'subsets'.
>>> This distinction to embedding still does not hold up.
>>> Unity represented in the discrete form is not controversial.
>>> Unity upon the continuum is arbitrarily selected, from which discrete intervals can extend.
>>> However, for instance, the meter versus the foot as embeddings expose that the discrete value '3' takes different positions.
>>> Clearly the geometrical representation of the real line lacks the clarity that a discrete representation had.
>>> bbb is uncontroversially the discrete three using b as a unit. No real line representation provides this level of clarity.
>>> As well the marks along the real line as a geometer makes them, say with a pair of dividers, will contain some error.
>>> The disconnect between the discrete and the continuous creeps even wider.
>>>
>>> As to who is strict and who is not strict: I believe it is safe to say that I am being quite strict here while the mathematician and his curriculum is not so strict. It should be the other way around, but it is true that the modern engineer has suffered the C compiler and its attention to structured data. Furthermore the notion of an operator as something which actually does work and yields a result; rather than something that can always be embedded as if it is already a pure value: here we have to land in the decimal value to make sense of the rational value. Here we have to land early on epsilon/delta as something that can apply to every value in the continuum. This notion even applies to the geometers who do careful works with the best of materials. Physical correspondence between the discrete and the continuous is lacking and yet the decimal number does provide for it.
>>> This same decimal number takes a natural valued interpretation merely be removing a little dot. How can I land in such a simplification while others cannot admit it? Congruent with computation and hardware implementation of the basic operations? Yes.
>>>
>>> Within the discrete there is as well the modulo branch. And again there is a structural form within the real value which is not appreciated. It is the sign of the real value. It's modulo two character is perfectly supported. The structural option to generalize this is the biggest blunder of modern mathematics. From this bud the complex numbers and the real numbers are siblings of series P2 and P3. From this bud a unidirectional form P1 whose zero dimensional character exactly matches that of time goes under appreciated. P4, P5, and so forth all work fine, though some surprises do occur. As importantly the geometrical rendering of these types comes as fundamental character of their balance amongst the signs as for instance in a P4 value we will have -z+z*z#z=0 just as in P2 we had -z+z=0. P2 as fundamental is a fraud. It is just early along the way.
>>>
>>> Taking sx where s is sign and x is continuous magnitude the next step takes the decimal value more seriously and places the little dot within the structure we could land with sxe numbers with s as sign, x as a natural value, and e being another natural valued being marking the position of the decimal point. This is different only slightly from scientific notation. These are all values. There are no operators embedded. These numbers are of unique types and so as a product these simply preserve their place. When operations take place upon them as elements z in Pn they are each involved in the computation. If this representation is fundamental it is interesting that it has three components. Still, physical correspondence is found more in the progression P1P2P3|P4P5... with its natural breakpoint.
>>>
>>> It's odd that these values do come with a sense of unital scale though it is not at all like a selection of feet or meters. In effect I am suffering my original complaint but still do come closer in physical correspondence to the notion of the continuum, all the while claiming that the natural value is at the root of the structure. It's a strange turn. And we've barely modified anything. It is merely an interpretation.
>>>>
>>>> Funny that we seem to have started discrete with naturals and integers
>>>> and then fractions of wholes where they can be symbolized as ratios of
>>>> these discrete naturals or integers, then on to our continuous reals
>>>> after discovering gaps or holes between the discrete fractions where
>>>> irrational numbers can be envisioned to reside.
>>>>
>>>> Then we find the actual physical reality is more likely discrete and
>>>> probabilistic in nature, perhaps making calculus take a back seat to
>>>> number theory and probability theory when dealing with very small
>>>> realities.
>> No, 1 and units have strict definitions.
>
> Ah, the foot and the meter have physical definitions and as units they are unique. But the conjunction of one foot and the definition of the foot are one and the same. If you could differentiate that I'd be impressed. Dimensional analysis does ensue here in terms of physical correspondence. I think that context is more appropriate but that is filling out the picture rather than falsifying it. We've been taught that a line on a piece of paper is fundamental somehow. Two of those lines at right angles develops the geometry of the paper somehow. Meanwhile the point is zero dimensional yet requires two dimensions to locate it on the paper somehow. We are dealing in interdimensional systems somehow. The care that has been taken and the habits formed and enforced upon us by our predecessors are merely ensuring our coherence to their rules. Breaking out of such a straight jacket is not so easy as we'd like to believe. How the simplest things can go undetected by the human mind: how we fail to cover the ground; this explains much of the lies. The human as a two-signed moron will have to live on a few more generations perhaps.
>
> Did topology open the puzzle up better somehow? I didn't find that to be the case. Nor for abstract algebra. Possibly, and it does run in my head as an abstract thing that is actually a bit unpleasant, but possibly the proper zero dimensional point realization is the collapse of the universe to a point. Thence the line properly formed is the collapse of the universe to the line. This does somehow embody some sort of order that gets lost upward in three dimensions, where the apparent actual order is obtained, at least according to standard theory. As to why this three dimensional (a term somewhat corrupted by me though it still works somewhat) order holds up nobody has a clue. Obviously if theory can land this then physics could ensue in a pure theoretical form. To accept that our position in this progression is far closer to apes than the refinement level that we presume is known as the leading edge. We all are attempting to establish some flow there. At least I would hope that you count yourself in that group.
>
> As destructive as my works and words may seem in them lays the openings and hopefully the proof that things are still open; that the progression still has some way to go. Within this large level of reasoning there comes a time when we accept that things that do not make sense to us are not sensible. We may be able to mimic them so as to pass through the system, but to take a strong mind and make it a weak one: this is the greatest fail of the academic system. I am fairly certain it is being done a thousand and a million times over. As some pledge some sort of salute to books or to academia... it's a bit religious, really. The tentacles and politics of every niche in that system are suspect. Still, we have to admit that without it there would be little to work from. The tension is necessary I suppose. Whatever, if you grant no room to work from there will be no work that can be done. Therefor we must keep things a bit open, yeah?
>
>
do you think that way ?

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Mon, 23 May 2022 06:54 UTC

torsdag 19 maj 2022 kl. 16:51:42 UTC+2 skrev timba...@gmail.com:
> On Wednesday, May 18, 2022 at 1:23:20 AM UTC-4, zelos...@gmail.com wrote:
> > tisdag 17 maj 2022 kl. 19:21:21 UTC+2 skrev timba...@gmail.com:
> > > On Monday, May 16, 2022 at 5:42:07 AM UTC-4, FromTheRafters wrote:
> > > > Timothy Golden wrote on 5/10/2022 :
> > > > > It seems uncontroversial at first.
> > > > > Discern unity on the continuum
> > > > > versus unity in discrete terms.
> > > > > The problem opens up considerably.
> > > > > That these two take the same representation '1' within our numerical
> > > > > representation is problematic.
> > > > >
> > > > > Set theory is supposed to address this, yet the natural values are formally a
> > > > > subset of the real values. This has been vetted by eons of mathematicians,
> > > > > right?
> > > > Actually, it has been pointed out many times that they are embeddings
> > > > not strictly speaking always 'subsets'.
> > > This distinction to embedding still does not hold up.
> > > Unity represented in the discrete form is not controversial.
> > > Unity upon the continuum is arbitrarily selected, from which discrete intervals can extend.
> > > However, for instance, the meter versus the foot as embeddings expose that the discrete value '3' takes different positions.
> > > Clearly the geometrical representation of the real line lacks the clarity that a discrete representation had.
> > > bbb is uncontroversially the discrete three using b as a unit. No real line representation provides this level of clarity.
> > > As well the marks along the real line as a geometer makes them, say with a pair of dividers, will contain some error.
> > > The disconnect between the discrete and the continuous creeps even wider.
> > >
> > > As to who is strict and who is not strict: I believe it is safe to say that I am being quite strict here while the mathematician and his curriculum is not so strict. It should be the other way around, but it is true that the modern engineer has suffered the C compiler and its attention to structured data. Furthermore the notion of an operator as something which actually does work and yields a result; rather than something that can always be embedded as if it is already a pure value: here we have to land in the decimal value to make sense of the rational value. Here we have to land early on epsilon/delta as something that can apply to every value in the continuum. This notion even applies to the geometers who do careful works with the best of materials. Physical correspondence between the discrete and the continuous is lacking and yet the decimal number does provide for it.
> > > This same decimal number takes a natural valued interpretation merely be removing a little dot. How can I land in such a simplification while others cannot admit it? Congruent with computation and hardware implementation of the basic operations? Yes.
> > >
> > > Within the discrete there is as well the modulo branch. And again there is a structural form within the real value which is not appreciated. It is the sign of the real value. It's modulo two character is perfectly supported. The structural option to generalize this is the biggest blunder of modern mathematics. From this bud the complex numbers and the real numbers are siblings of series P2 and P3. From this bud a unidirectional form P1 whose zero dimensional character exactly matches that of time goes under appreciated. P4, P5, and so forth all work fine, though some surprises do occur. As importantly the geometrical rendering of these types comes as fundamental character of their balance amongst the signs as for instance in a P4 value we will have -z+z*z#z=0 just as in P2 we had -z+z=0. P2 as fundamental is a fraud. It is just early along the way.
> > >
> > > Taking sx where s is sign and x is continuous magnitude the next step takes the decimal value more seriously and places the little dot within the structure we could land with sxe numbers with s as sign, x as a natural value, and e being another natural valued being marking the position of the decimal point. This is different only slightly from scientific notation. These are all values. There are no operators embedded. These numbers are of unique types and so as a product these simply preserve their place. When operations take place upon them as elements z in Pn they are each involved in the computation. If this representation is fundamental it is interesting that it has three components. Still, physical correspondence is found more in the progression P1P2P3|P4P5... with its natural breakpoint.
> > >
> > > It's odd that these values do come with a sense of unital scale though it is not at all like a selection of feet or meters. In effect I am suffering my original complaint but still do come closer in physical correspondence to the notion of the continuum, all the while claiming that the natural value is at the root of the structure. It's a strange turn. And we've barely modified anything. It is merely an interpretation.
> > > >
> > > > Funny that we seem to have started discrete with naturals and integers
> > > > and then fractions of wholes where they can be symbolized as ratios of
> > > > these discrete naturals or integers, then on to our continuous reals
> > > > after discovering gaps or holes between the discrete fractions where
> > > > irrational numbers can be envisioned to reside.
> > > >
> > > > Then we find the actual physical reality is more likely discrete and
> > > > probabilistic in nature, perhaps making calculus take a back seat to
> > > > number theory and probability theory when dealing with very small
> > > > realities.
> > No, 1 and units have strict definitions.
> Ah, the foot and the meter have physical definitions and as units they are unique.

No, not measurement units, mathematical units you imbecile.

>But the conjunction of one foot and the definition of the foot are one and the same. If you could differentiate that I'd be impressed. Dimensional analysis does ensue here in terms of physical correspondence. I think that context is more appropriate but that is filling out the picture rather than falsifying it. We've been taught that a line on a piece of paper is fundamental somehow. Two of those lines at right angles develops the geometry of the paper somehow. Meanwhile the point is zero dimensional yet requires two dimensions to locate it on the paper somehow. We are dealing in interdimensional systems somehow.

blah blah blah shit irrelevant.

>The care that has been taken and the habits formed and enforced upon us by our predecessors are merely ensuring our coherence to their rules. Breaking out of such a straight jacket is not so easy as we'd like to believe. How the simplest things can go undetected by the human mind: how we fail to cover the ground; this explains much of the lies. The human as a two-signed moron will have to live on a few more generations perhaps.

Yeah "two sign" stuff, as you go on, means you just do not fucking understand mathematics, rings, ordering, groups or really anything.

>
> Did topology open the puzzle up better somehow? I didn't find that to be the case. Nor for abstract algebra. Possibly, and it does run in my head as an abstract thing that is actually a bit unpleasant, but possibly the proper zero dimensional point realization is the collapse of the universe to a point. Thence the line properly formed is the collapse of the universe to the line. This does somehow embody some sort of order that gets lost upward in three dimensions, where the apparent actual order is obtained, at least according to standard theory. As to why this three dimensional (a term somewhat corrupted by me though it still works somewhat) order holds up nobody has a clue. Obviously if theory can land this then physics could ensue in a pure theoretical form. To accept that our position in this progression is far closer to apes than the refinement level that we presume is known as the leading edge. We all are attempting to establish some flow there. At least I would hope that you count yourself in that group.
>
> As destructive as my works and words may seem in them lays the openings and hopefully the proof that things are still open; that the progression still has some way to go. Within this large level of reasoning there comes a time when we accept that things that do not make sense to us are not sensible. We may be able to mimic them so as to pass through the system, but to take a strong mind and make it a weak one: this is the greatest fail of the academic system. I am fairly certain it is being done a thousand and a million times over. As some pledge some sort of salute to books or to academia.... it's a bit religious, really. The tentacles and politics of every niche in that system are suspect. Still, we have to admit that without it there would be little to work from. The tension is necessary I suppose. Whatever, if you grant no room to work from there will be no work that can be done. Therefor we must keep things a bit open, yeah?

Re: Unity and its interpretation

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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Thu, 26 May 2022 15:24 UTC

There is a sort of convergence that occurs at unity.
This is a matter of physical correspondence, philosophy, and mathematics.
To unify is to make one.
To unite is to join together.
We see that mathematics has done this but that this junction has to be kept tender.
How is this?
We reuse the same numerical format to represent the continuum that was used to represent discrete concepts.
This is done not only by choice but out of necessity. There is but one difference between the two and that is the decimal point.
This little dot marks a new unity reference. It comes at the convenience of the digits in distinction to the geometer's way of simply fixing his dividers at a handy workable span for the amount of material he has to work upon.. The little dot does nothing in these physical terms. Yet it establishes the ability to work arithmetically upon the continuum. It does reuse the natural value with the slightest augmentation. Other than this augmentation, however, there is nothing left but a natural value. This interpretation is starkly different than the standard one which leans upon the elderly rational value. There lays a fault. The simplicity of the structural interpretation is exposed. It is a superior format in that its simplicity is intact without the complications that rational analysis requires, some of which is dubious at best.

To me a source of conviction is ultimately to go back to primitive forms. Above is a digital analysis on the reuse of the modulo-10 value. Few are attracted to those sorts of arguments,though their work will be done in those terms should instantiation be called upon. Yielding back to the primitive form we will see that the continuum ultimately asks for direct graphical transcription. In other words the concept of representation by this form actually lacks any unit other than the value itself, which cannot really even be called a value at this primitive stage. Giving up as much technology as possible a piece of twine cut to the length of say the length of a pole in order to transcribe that pole length could stand as a reference to be copied or transferred say to groups of men who are to cut such poles from the woods. As to how many poles each group should cut: this is a discrete figure, and each group could be given a number of pebbles in a bag along with the string to account for what is asked of them. Of course other figures could be augmented, but this is a simplistic example explaining the distinction between the discrete and the continuous. As the man in charge of the bag fumbles through the stones and sees that there are some left to go to what degree did he just bump into the rational value without ever encountering division? Here we see the dirty reradixer in primitive form. This sense of the modulo exception is perhaps not even perceived by the reader here. If there were five stones in the bag then the work is honestly done in fifths. No division was necessary; no five was uttered; yet it occurred as an exception, and then they hauled the logs to the work site.

That these two distinct forms happen to overlap in our numerical representation is a tender point. It is as false as it is true. As to what the unit is upon the continuum that affords such a number: here physical correspondence is done away with by the mathematician in modernity. In a time when physics is stumbling and mathematics contains provable ambiguities within its base; as to why the subjects were trifurcated in the first place when many of the best practiced all three as if they were one; I see that we are engaged in a progression; that humans really do have a very difficult time finding the truth. We do in fact start from a blank slate and rely upon the transfer of previous generations of knowledge which we habituate into in order to proceed along a path. So long as ambiguity has been absorbed and even enforced under threat of failure the necessary tension has us shooting ourselves not just in the foot, but in the head. Somehow we survive the wound and keep trying, but progress is minimal.

The obvious answer is to break the old rules and reject the old rulers. They filtered out the best who challenged their false paradigms. Rejection is done that easily. The notion that something else quite fundamental remains to be exposed by humans or possibly our offspring AI; something that humans' linguistic abilities simply cannot muster; this would be the greatest hope and yet the simplest explanation as to why physics flounders and mathematics continues its burgeoning accumulation.

I've already offered up polysign numbers as an instance of overlooked mathematics. They do beget their own version of emergent spacetime with unidirectional time through the family
P1 P2 P3 | P4 P5 ...
thanks to a natural breakpoint in the product behavior.

Time has been cast as an open problem. Polysign does indeed have something to say about it as well. To what degree is time embedded within mathematical argumentation may be a workable problem. Under this guise concerns that all our work actually takes place in the physical continuum will have to be a basic concession of all of mathematics. A lack of physical correspondence is problematic. Mathematics thus far has failed to recover the spacetime continuum. In that this is the basis that is under discussion is it appropriate to burden mathematics rather than physics with its development? By definition a basis is that primitive. It is that which we work from. In other words physics is to take place upon a continuum that is mathematical in nature. This is the ideal form that we all seek. As objects in or of the basis we cannot hope to gain direct access to its developing parts or mechanisms as we are built out of those things. As we work with intangibles the guessing game ensues.

While I don't see polysign numbers as the end of the progression I do realize that they are a necessary step along the way. They fly in the face of the first cosmological principle; isotropy; and expose that spacetime is in fact structured. In the marriage of continuous and discrete entities something may be left to construct still. This is the ideal situation, and I am attempting to give it away here, so to speak. Could you stew on a mixed modulo augmentation to the progression so that not only the sign of P1 is modulo one but that the component value is as well? Likewise the modulo two nature of P2 then extends into its magnitude, and so forth up the chain. What is different? Certainly P1 does come out discretely as its decimal point is not operative. It can exist, but it does nothing to the first interpretation of its value. In some ways this is congruent with our computers and even our writings which come out discretely.

This is possibly a view of the natural value as P1. P2 certainly does go continuous as well. Strangely this modulo interpretation comes out fairly consistent with existing mathematics. Perhaps then we can come around to the P2 as a two component value differently? It does seem like a more unified value. Almost as if they are more free-standing entities; individuated entities, but that is just a gross sensitivity. A P3 value is three all the way under this intepretation. Its three components modulo three and three signs.... is it simply a triplicate numerical format? There is nothing new there; just that they are right on top of each other. Far be it for me to handle this level of complexity. Call in the mathematicians!

On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> It seems uncontroversial at first.
> Discern unity on the continuum
> versus unity in discrete terms.
> The problem opens up considerably.
> That these two take the same representation '1' within our numerical representation is problematic.
>
> Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
>
> Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
>
> Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
>
> Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
>
> The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
>
> That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.


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Subject: Re: Unity and its interpretation
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 by: zelos...@gmail.com - Fri, 27 May 2022 04:52 UTC

torsdag 26 maj 2022 kl. 17:24:48 UTC+2 skrev timba...@gmail.com:
> There is a sort of convergence that occurs at unity.
> This is a matter of physical correspondence, philosophy, and mathematics.

Mathematics do not care about physical correspondence, that is for physicists

> To unify is to make one.
> To unite is to join together.
> We see that mathematics has done this but that this junction has to be kept tender.
> How is this?
> We reuse the same numerical format to represent the continuum that was used to represent discrete concepts.
> This is done not only by choice but out of necessity. There is but one difference between the two and that is the decimal point.
> This little dot marks a new unity reference. It comes at the convenience of the digits in distinction to the geometer's way of simply fixing his dividers at a handy workable span for the amount of material he has to work upon. The little dot does nothing in these physical terms. Yet it establishes the ability to work arithmetically upon the continuum. It does reuse the natural value with the slightest augmentation. Other than this augmentation, however, there is nothing left but a natural value. This interpretation is starkly different than the standard one which leans upon the elderly rational value. There lays a fault. The simplicity of the structural interpretation is exposed. It is a superior format in that its simplicity is intact without the complications that rational analysis requires, some of which is dubious at best.
>
> To me a source of conviction is ultimately to go back to primitive forms. Above is a digital analysis on the reuse of the modulo-10 value. Few are attracted to those sorts of arguments,though their work will be done in those terms should instantiation be called upon. Yielding back to the primitive form we will see that the continuum ultimately asks for direct graphical transcription. In other words the concept of representation by this form actually lacks any unit other than the value itself, which cannot really even be called a value at this primitive stage. Giving up as much technology as possible a piece of twine cut to the length of say the length of a pole in order to transcribe that pole length could stand as a reference to be copied or transferred say to groups of men who are to cut such poles from the woods. As to how many poles each group should cut: this is a discrete figure, and each group could be given a number of pebbles in a bag along with the string to account for what is asked of them. Of course other figures could be augmented, but this is a simplistic example explaining the distinction between the discrete and the continuous. As the man in charge of the bag fumbles through the stones and sees that there are some left to go to what degree did he just bump into the rational value without ever encountering division? Here we see the dirty reradixer in primitive form. This sense of the modulo exception is perhaps not even perceived by the reader here. If there were five stones in the bag then the work is honestly done in fifths. No division was necessary; no five was uttered; yet it occurred as an exception, and then they hauled the logs to the work site.
>
> That these two distinct forms happen to overlap in our numerical representation is a tender point. It is as false as it is true. As to what the unit is upon the continuum that affords such a number: here physical correspondence is done away with by the mathematician in modernity. In a time when physics is stumbling and mathematics contains provable ambiguities within its base; as to why the subjects were trifurcated in the first place when many of the best practiced all three as if they were one; I see that we are engaged in a progression; that humans really do have a very difficult time finding the truth. We do in fact start from a blank slate and rely upon the transfer of previous generations of knowledge which we habituate into in order to proceed along a path. So long as ambiguity has been absorbed and even enforced under threat of failure the necessary tension has us shooting ourselves not just in the foot, but in the head. Somehow we survive the wound and keep trying, but progress is minimal.
>
> The obvious answer is to break the old rules and reject the old rulers. They filtered out the best who challenged their false paradigms. Rejection is done that easily. The notion that something else quite fundamental remains to be exposed by humans or possibly our offspring AI; something that humans' linguistic abilities simply cannot muster; this would be the greatest hope and yet the simplest explanation as to why physics flounders and mathematics continues its burgeoning accumulation.
>
> I've already offered up polysign numbers as an instance of overlooked mathematics. They do beget their own version of emergent spacetime with unidirectional time through the family
> P1 P2 P3 | P4 P5 ...
> thanks to a natural breakpoint in the product behavior.
>
> Time has been cast as an open problem. Polysign does indeed have something to say about it as well. To what degree is time embedded within mathematical argumentation may be a workable problem. Under this guise concerns that all our work actually takes place in the physical continuum will have to be a basic concession of all of mathematics. A lack of physical correspondence is problematic. Mathematics thus far has failed to recover the spacetime continuum. In that this is the basis that is under discussion is it appropriate to burden mathematics rather than physics with its development? By definition a basis is that primitive. It is that which we work from. In other words physics is to take place upon a continuum that is mathematical in nature. This is the ideal form that we all seek. As objects in or of the basis we cannot hope to gain direct access to its developing parts or mechanisms as we are built out of those things. As we work with intangibles the guessing game ensues.
>
> While I don't see polysign numbers as the end of the progression I do realize that they are a necessary step along the way. They fly in the face of the first cosmological principle; isotropy; and expose that spacetime is in fact structured. In the marriage of continuous and discrete entities something may be left to construct still. This is the ideal situation, and I am attempting to give it away here, so to speak. Could you stew on a mixed modulo augmentation to the progression so that not only the sign of P1 is modulo one but that the component value is as well? Likewise the modulo two nature of P2 then extends into its magnitude, and so forth up the chain. What is different? Certainly P1 does come out discretely as its decimal point is not operative. It can exist, but it does nothing to the first interpretation of its value. In some ways this is congruent with our computers and even our writings which come out discretely.
>
> This is possibly a view of the natural value as P1. P2 certainly does go continuous as well. Strangely this modulo interpretation comes out fairly consistent with existing mathematics. Perhaps then we can come around to the P2 as a two component value differently? It does seem like a more unified value. Almost as if they are more free-standing entities; individuated entities, but that is just a gross sensitivity. A P3 value is three all the way under this intepretation. Its three components modulo three and three signs... is it simply a triplicate numerical format? There is nothing new there; just that they are right on top of each other. Far be it for me to handle this level of complexity. Call in the mathematicians!
> On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> > It seems uncontroversial at first.
> > Discern unity on the continuum
> > versus unity in discrete terms.
> > The problem opens up considerably.
> > That these two take the same representation '1' within our numerical representation is problematic.
> >
> > Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
> >
> > Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
> >
> > Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
> >
> > Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
> >
> > The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
> >
> > That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.


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Subject: Re: Unity and its interpretation
From: timbandt...@gmail.com (Timothy Golden)
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 by: Timothy Golden - Wed, 7 Sep 2022 14:03 UTC

On Friday, May 27, 2022 at 12:52:49 AM UTC-4, zelos...@gmail.com wrote:
> torsdag 26 maj 2022 kl. 17:24:48 UTC+2 skrev timba...@gmail.com:
> > There is a sort of convergence that occurs at unity.
> > This is a matter of physical correspondence, philosophy, and mathematics.
> Mathematics do not care about physical correspondence, that is for physicists

Indeed: it seems that when physical correspondence smacks a mathematician in the head he will look the other way.
That the physicist rests his case on the supposedly pristine real number only places the physicist that much farther away from the puzzle.

> > To unify is to make one.
> > To unite is to join together.
> > We see that mathematics has done this but that this junction has to be kept tender.
> > How is this?
> > We reuse the same numerical format to represent the continuum that was used to represent discrete concepts.
> > This is done not only by choice but out of necessity. There is but one difference between the two and that is the decimal point.
> > This little dot marks a new unity reference. It comes at the convenience of the digits in distinction to the geometer's way of simply fixing his dividers at a handy workable span for the amount of material he has to work upon. The little dot does nothing in these physical terms. Yet it establishes the ability to work arithmetically upon the continuum. It does reuse the natural value with the slightest augmentation. Other than this augmentation, however, there is nothing left but a natural value. This interpretation is starkly different than the standard one which leans upon the elderly rational value. There lays a fault. The simplicity of the structural interpretation is exposed. It is a superior format in that its simplicity is intact without the complications that rational analysis requires, some of which is dubious at best.
> >
> > To me a source of conviction is ultimately to go back to primitive forms. Above is a digital analysis on the reuse of the modulo-10 value. Few are attracted to those sorts of arguments,though their work will be done in those terms should instantiation be called upon. Yielding back to the primitive form we will see that the continuum ultimately asks for direct graphical transcription. In other words the concept of representation by this form actually lacks any unit other than the value itself, which cannot really even be called a value at this primitive stage. Giving up as much technology as possible a piece of twine cut to the length of say the length of a pole in order to transcribe that pole length could stand as a reference to be copied or transferred say to groups of men who are to cut such poles from the woods. As to how many poles each group should cut: this is a discrete figure, and each group could be given a number of pebbles in a bag along with the string to account for what is asked of them. Of course other figures could be augmented, but this is a simplistic example explaining the distinction between the discrete and the continuous. As the man in charge of the bag fumbles through the stones and sees that there are some left to go to what degree did he just bump into the rational value without ever encountering division? Here we see the dirty reradixer in primitive form. This sense of the modulo exception is perhaps not even perceived by the reader here. If there were five stones in the bag then the work is honestly done in fifths. No division was necessary; no five was uttered; yet it occurred as an exception, and then they hauled the logs to the work site.
> >
> > That these two distinct forms happen to overlap in our numerical representation is a tender point. It is as false as it is true. As to what the unit is upon the continuum that affords such a number: here physical correspondence is done away with by the mathematician in modernity. In a time when physics is stumbling and mathematics contains provable ambiguities within its base; as to why the subjects were trifurcated in the first place when many of the best practiced all three as if they were one; I see that we are engaged in a progression; that humans really do have a very difficult time finding the truth. We do in fact start from a blank slate and rely upon the transfer of previous generations of knowledge which we habituate into in order to proceed along a path. So long as ambiguity has been absorbed and even enforced under threat of failure the necessary tension has us shooting ourselves not just in the foot, but in the head. Somehow we survive the wound and keep trying, but progress is minimal.
> >
> > The obvious answer is to break the old rules and reject the old rulers. They filtered out the best who challenged their false paradigms. Rejection is done that easily. The notion that something else quite fundamental remains to be exposed by humans or possibly our offspring AI; something that humans' linguistic abilities simply cannot muster; this would be the greatest hope and yet the simplest explanation as to why physics flounders and mathematics continues its burgeoning accumulation.
> >
> > I've already offered up polysign numbers as an instance of overlooked mathematics. They do beget their own version of emergent spacetime with unidirectional time through the family
> > P1 P2 P3 | P4 P5 ...
> > thanks to a natural breakpoint in the product behavior.
> >
> > Time has been cast as an open problem. Polysign does indeed have something to say about it as well. To what degree is time embedded within mathematical argumentation may be a workable problem. Under this guise concerns that all our work actually takes place in the physical continuum will have to be a basic concession of all of mathematics. A lack of physical correspondence is problematic. Mathematics thus far has failed to recover the spacetime continuum. In that this is the basis that is under discussion is it appropriate to burden mathematics rather than physics with its development? By definition a basis is that primitive. It is that which we work from. In other words physics is to take place upon a continuum that is mathematical in nature. This is the ideal form that we all seek. As objects in or of the basis we cannot hope to gain direct access to its developing parts or mechanisms as we are built out of those things. As we work with intangibles the guessing game ensues.
> >
> > While I don't see polysign numbers as the end of the progression I do realize that they are a necessary step along the way. They fly in the face of the first cosmological principle; isotropy; and expose that spacetime is in fact structured. In the marriage of continuous and discrete entities something may be left to construct still. This is the ideal situation, and I am attempting to give it away here, so to speak. Could you stew on a mixed modulo augmentation to the progression so that not only the sign of P1 is modulo one but that the component value is as well? Likewise the modulo two nature of P2 then extends into its magnitude, and so forth up the chain. What is different? Certainly P1 does come out discretely as its decimal point is not operative. It can exist, but it does nothing to the first interpretation of its value. In some ways this is congruent with our computers and even our writings which come out discretely.

This particular idea: of allowing the mod-3 P3 to carry a modulo-3 triple of values has a sense of 'parity' about it, though the new term would be more like 'triality', and so forth in the chain. At some level all that we are speaking of is a value (a,b,c) and yet encoding is or can be part of the game.
I don't mean to trivialize this option but to follow it through here. Several forms come along rather quickly so that
( 102.1, 101.2, 0.1 )
is a very 'real' possibility, though the real number is nowhere to be found here. I am even worrying about the parentheses in this statement, yet as bounds they suggest that we should do away with them in our focus as they are a containment strategy. Let's then do away with them since nothing else exists on that line:
102.1,101.2,0.1
Then of course comes the balance and its cancellation effect:
102.0,101.1,0.0
Already we know of the savings informationally over the Cartesian form as a gain in bits over sign coding. We send two values; they send two values;
yet in mod-3 we can see that our signs can be internal to our values and that this form of coding already takes place within our computers in the modulo-two form and the mechanics of the two's complement value. That mod-2 version fits the sum and it doesn't seem to work out on our mod-3 version. Then again, who has worked out three's complement logic yet? Perhaps it should be said that if hardware likes it then that is enough, for the sensibilities of the human mind are frail these days.

The discussion above is actually breaking with the sx interpretation. It is stating that s is encoded within x. It is pretty in that all the modulo forms are in use not in general, but in specificity. The line becomes mod-2. The plane becomes mod-3. Volume becomes mod-4, and so on. That time is mod-1, well, certainly, sir. That mod-1 has serious limitations in its decimal representation; yes, sir. And yet the decimal point remains. Well to trouble over P1 is small potatoes. It's like asking: "did you mean 0.0011 or not?" In this way that this early form converges with the other qualities is apparent and as paradoxical. In polysign P1 is already recognized as zero dimensional along with its unidirectional nature. Here I feel as though the pivotal detail is whether we are on a continuum or in a discrete way, and yet the natural valued realization somewhat has already done away with that. That the decimal place has lost its meaning too is convergent to these concerns rather than divergent to them. The invalidity of the value 0.0011 in mod-1 is in some regards a futuristic problem. It is a good breakdown rather than a fraudulent breakdown. I understand that will take some getting used to.
Already at mod-2 the cessation of those tensions ends, and it should be recognized that the continuum representation is plenty good mod-2. To claim that the representation of the continuum mod-3 now is better by the third is not quite the factor, since now we be jumping dimensionally. Of course the same should have been said at mod-2, but then mod-1 as a jump-point feels stark. In that these numerical types are self-segregating perhaps their personage can remain a mystery, as if a series:
p1 p2 p3 p4 p5 p6 p7 ...
of little polysign blips would fill out a tatrix over time. These p would be indexed only with their mod encoded within. That is a strange form to proceed upon, yet the first and most obvious measure is the stature of p so that were p7 a mod-3 fPn(p7) would have n=3 whereas its actual sign and value are TBD by this nomenclature. Not feeling good about the notation here. This perhaps forms a neat statement on human convention: when a new concept emerges and the notation looks wrong it makes the concept look wrong too. There is a whole lot of notation on the books that I am not comfortable with, by the way. I am not one who adapts so easily. I suppose simply presenting the tatrix in its full triangular form alleviates the distress here:
a10
a20 a21
a30 a31 a32
a40 a41 a42 a43
...
Suffice it to say that every entry of that series pn fits one of these. Little deltas, so to speak. Maybe not so little. Not generally.
We wish we had streams of such data to process. Thence does it render graphically? In following with the Cartesian dillemma to what degree do I have the right to pronounce P2 orthogonal to P3? It seems natural to the Cartesian thinker to do so, yet were they each their own and why do they mix? Certainly they are geometric forms. Certainly so, sir.


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Date: Wed, 7 Sep 2022 08:56:17 -0700 (PDT)
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Subject: Re: Unity and its interpretation
From: ross.fin...@gmail.com (Ross A. Finlayson)
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 by: Ross A. Finlayson - Wed, 7 Sep 2022 15:56 UTC

On Thursday, May 26, 2022 at 9:52:49 PM UTC-7, zelos...@gmail.com wrote:
> torsdag 26 maj 2022 kl. 17:24:48 UTC+2 skrev timba...@gmail.com:
> > There is a sort of convergence that occurs at unity.
> > This is a matter of physical correspondence, philosophy, and mathematics.
> Mathematics do not care about physical correspondence, that is for physicists
> > To unify is to make one.
> > To unite is to join together.
> > We see that mathematics has done this but that this junction has to be kept tender.
> > How is this?
> > We reuse the same numerical format to represent the continuum that was used to represent discrete concepts.
> > This is done not only by choice but out of necessity. There is but one difference between the two and that is the decimal point.
> > This little dot marks a new unity reference. It comes at the convenience of the digits in distinction to the geometer's way of simply fixing his dividers at a handy workable span for the amount of material he has to work upon. The little dot does nothing in these physical terms. Yet it establishes the ability to work arithmetically upon the continuum. It does reuse the natural value with the slightest augmentation. Other than this augmentation, however, there is nothing left but a natural value. This interpretation is starkly different than the standard one which leans upon the elderly rational value. There lays a fault. The simplicity of the structural interpretation is exposed. It is a superior format in that its simplicity is intact without the complications that rational analysis requires, some of which is dubious at best.
> >
> > To me a source of conviction is ultimately to go back to primitive forms. Above is a digital analysis on the reuse of the modulo-10 value. Few are attracted to those sorts of arguments,though their work will be done in those terms should instantiation be called upon. Yielding back to the primitive form we will see that the continuum ultimately asks for direct graphical transcription. In other words the concept of representation by this form actually lacks any unit other than the value itself, which cannot really even be called a value at this primitive stage. Giving up as much technology as possible a piece of twine cut to the length of say the length of a pole in order to transcribe that pole length could stand as a reference to be copied or transferred say to groups of men who are to cut such poles from the woods. As to how many poles each group should cut: this is a discrete figure, and each group could be given a number of pebbles in a bag along with the string to account for what is asked of them. Of course other figures could be augmented, but this is a simplistic example explaining the distinction between the discrete and the continuous. As the man in charge of the bag fumbles through the stones and sees that there are some left to go to what degree did he just bump into the rational value without ever encountering division? Here we see the dirty reradixer in primitive form. This sense of the modulo exception is perhaps not even perceived by the reader here. If there were five stones in the bag then the work is honestly done in fifths. No division was necessary; no five was uttered; yet it occurred as an exception, and then they hauled the logs to the work site.
> >
> > That these two distinct forms happen to overlap in our numerical representation is a tender point. It is as false as it is true. As to what the unit is upon the continuum that affords such a number: here physical correspondence is done away with by the mathematician in modernity. In a time when physics is stumbling and mathematics contains provable ambiguities within its base; as to why the subjects were trifurcated in the first place when many of the best practiced all three as if they were one; I see that we are engaged in a progression; that humans really do have a very difficult time finding the truth. We do in fact start from a blank slate and rely upon the transfer of previous generations of knowledge which we habituate into in order to proceed along a path. So long as ambiguity has been absorbed and even enforced under threat of failure the necessary tension has us shooting ourselves not just in the foot, but in the head. Somehow we survive the wound and keep trying, but progress is minimal.
> >
> > The obvious answer is to break the old rules and reject the old rulers. They filtered out the best who challenged their false paradigms. Rejection is done that easily. The notion that something else quite fundamental remains to be exposed by humans or possibly our offspring AI; something that humans' linguistic abilities simply cannot muster; this would be the greatest hope and yet the simplest explanation as to why physics flounders and mathematics continues its burgeoning accumulation.
> >
> > I've already offered up polysign numbers as an instance of overlooked mathematics. They do beget their own version of emergent spacetime with unidirectional time through the family
> > P1 P2 P3 | P4 P5 ...
> > thanks to a natural breakpoint in the product behavior.
> >
> > Time has been cast as an open problem. Polysign does indeed have something to say about it as well. To what degree is time embedded within mathematical argumentation may be a workable problem. Under this guise concerns that all our work actually takes place in the physical continuum will have to be a basic concession of all of mathematics. A lack of physical correspondence is problematic. Mathematics thus far has failed to recover the spacetime continuum. In that this is the basis that is under discussion is it appropriate to burden mathematics rather than physics with its development? By definition a basis is that primitive. It is that which we work from. In other words physics is to take place upon a continuum that is mathematical in nature. This is the ideal form that we all seek. As objects in or of the basis we cannot hope to gain direct access to its developing parts or mechanisms as we are built out of those things. As we work with intangibles the guessing game ensues.
> >
> > While I don't see polysign numbers as the end of the progression I do realize that they are a necessary step along the way. They fly in the face of the first cosmological principle; isotropy; and expose that spacetime is in fact structured. In the marriage of continuous and discrete entities something may be left to construct still. This is the ideal situation, and I am attempting to give it away here, so to speak. Could you stew on a mixed modulo augmentation to the progression so that not only the sign of P1 is modulo one but that the component value is as well? Likewise the modulo two nature of P2 then extends into its magnitude, and so forth up the chain. What is different? Certainly P1 does come out discretely as its decimal point is not operative. It can exist, but it does nothing to the first interpretation of its value. In some ways this is congruent with our computers and even our writings which come out discretely.
> >
> > This is possibly a view of the natural value as P1. P2 certainly does go continuous as well. Strangely this modulo interpretation comes out fairly consistent with existing mathematics. Perhaps then we can come around to the P2 as a two component value differently? It does seem like a more unified value. Almost as if they are more free-standing entities; individuated entities, but that is just a gross sensitivity. A P3 value is three all the way under this intepretation. Its three components modulo three and three signs... is it simply a triplicate numerical format? There is nothing new there; just that they are right on top of each other. Far be it for me to handle this level of complexity. Call in the mathematicians!
> > On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> > > It seems uncontroversial at first.
> > > Discern unity on the continuum
> > > versus unity in discrete terms.
> > > The problem opens up considerably.
> > > That these two take the same representation '1' within our numerical representation is problematic.
> > >
> > > Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
> > >
> > > Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
> > >
> > > Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
> > >
> > > Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
> > >
> > > The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
> > >
> > > That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.


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