Timothy Golden <timbandtech@gmail.com> writes:
>What it means to a mathematician 'to exist' is
>quite a controversial problem

"To exist" means that it may be given a name, and that one
may speak about it in statements or formulas or use it in
a term to denote something.

For example, one might choose to assume that the solution
of "x+1=0" exists.

Then one might give it a name. Let's do this. I call it "E".

I may speak about it in a statement: "E is a value.".

I may use it in a formula: "E < 0".

I may use it in a term: "2*E".

måndag 28 augusti 2023 kl. 19:55:42 UTC+2 skrev Timothy Golden:
> On Sunday, August 27, 2023 at 6:07:42 AM UTC-4, Phil Carmody wrote:
> > FromTheRafters <F...@nomail.afraid.org> writes:
> > > on 8/25/2023, Chris M. Thomasson supposed :
> > >> On 8/25/2023 1:34 PM, FromTheRafters wrote:
> > >>> Kevin S brought next idea :
> > >>>> On Friday, August 25, 2023 at 8:11:12 PM UTC+2, mitchr...@gmail.com wrote:
> > >>>>> there is no negative 1.
> > >>>>> Mitchell Raemsch
> > >>>>
> > >>>> Yeah there is.
> > >>>
> > >>> Indeed, since we have integers. One could claim that there is no
> > >>> minus one though.
> > >>
> > >> Not exactly sure what you mean.
> > >
> > > One could claim...
> > >
> > > The integers form a ring, instead of subtraction of naturals (a
> > > partial function for them) we have addition of integers. The binary
> > > operator 'minus' (a-b) is essentially gone and we add a negative
> > > integer (a+(-b)) instead.
> > That X can be defined in terms of Y, where Y is known to exist, does not
> > mean that X does not exist. One might even say it's pretty good proof
> > that X does exist.
> >
> > Phil
> > --
> > We are no longer hunters and nomads. No longer awed and frightened, as we have
> > gained some understanding of the world in which we live. As such, we can cast
> > aside childish remnants from the dawn of our civilization.
> > -- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
> What it means to a mathematician 'to exist' is quite a controversial problem, especially when physical correspondence is cast aside as irrelevant, and what would be next to cast aside but philosophy? Certainly the quantum physicists have done exactly this, and as if these broad divides were even accurate in the third place, and which deserves the first place: each will claim it for their own, right?
>
> If, on the other hand, we dismiss these status quo assumptions, and witness these divides as false, then we ought to reflect a bit deeper upon the negative integer. Of course sensibility is lost as regards sheep in a field, whereby no physical correspondence can be laid by -5 sheep. A discussion of inverse sheep I suppose could ensue, and in some cases this argument does take physical relevance going over to antimatter, landing in an open puzzle as to how such an imbalance has occurred as we seem to observe. The hope that we will one day unwind this problem and land in fertile mathematics which provides physical correspondence is obviously where many would like to land.
>
> A broader treatment of sign will disentangle the confusion between sign and inversion; the conflict that exists as an operator versus a value in the discrete symbol '-' is an ambiguity within our notation. If anyone ought to abhor such ambiguity would it be the mathematician? The philosopher? The physicist? As to whose burden this one is; that is pretty easy to pinpoint. This is mathematics. As to who ought to be concerned about it: we all should.
>
> Operator theory itself seems to contain additional quagmire. The idea that an operator will map SxS onto S is a functional blunder. To some all is a function apparently, and yet will you even be able to use addition within your function? Where is the need for this Cartesian product? To sum three elements we'll be needing SxSxS? I'm sorry but one S will do very nicely, thank you. As if closure didn't even mean closure in the first place, certainly it doesn't mean it in the second place, and by the time you've gone three-dimensional on the thing to call this closure any more is just an abuse of the human mind. That we all could buy into such clap-trap at the base of mathematics is a sad citing of modernity.
Something exists mathematically if it is logically self-consistent.

On Tuesday, August 29, 2023 at 9:50:08 AM UTC+3, markus...@gmail.com wrote:
> måndag 28 augusti 2023 kl. 19:55:42 UTC+2 skrev Timothy Golden:
> > On Sunday, August 27, 2023 at 6:07:42 AM UTC-4, Phil Carmody wrote:
> > > FromTheRafters <F...@nomail.afraid.org> writes:
> > > > on 8/25/2023, Chris M. Thomasson supposed :
> > > >> On 8/25/2023 1:34 PM, FromTheRafters wrote:
> > > >>> Kevin S brought next idea :
> > > >>>> On Friday, August 25, 2023 at 8:11:12 PM UTC+2, mitchr....@gmail.com wrote:
> > > >>>>> there is no negative 1.
> > > >>>>> Mitchell Raemsch
> > > >>>>
> > > >>>> Yeah there is.
> > > >>>
> > > >>> Indeed, since we have integers. One could claim that there is no
> > > >>> minus one though.
> > > >>
> > > >> Not exactly sure what you mean.
> > > >
> > > > One could claim...
> > > >
> > > > The integers form a ring, instead of subtraction of naturals (a
> > > > partial function for them) we have addition of integers. The binary
> > > > operator 'minus' (a-b) is essentially gone and we add a negative
> > > > integer (a+(-b)) instead.
> > > That X can be defined in terms of Y, where Y is known to exist, does not
> > > mean that X does not exist. One might even say it's pretty good proof
> > > that X does exist.
> > >
> > > Phil
> > > --
> > > We are no longer hunters and nomads. No longer awed and frightened, as we have
> > > gained some understanding of the world in which we live. As such, we can cast
> > > aside childish remnants from the dawn of our civilization.
> > > -- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
> > What it means to a mathematician 'to exist' is quite a controversial problem, especially when physical correspondence is cast aside as irrelevant, and what would be next to cast aside but philosophy? Certainly the quantum physicists have done exactly this, and as if these broad divides were even accurate in the third place, and which deserves the first place: each will claim it for their own, right?
> >
> > If, on the other hand, we dismiss these status quo assumptions, and witness these divides as false, then we ought to reflect a bit deeper upon the negative integer. Of course sensibility is lost as regards sheep in a field, whereby no physical correspondence can be laid by -5 sheep. A discussion of inverse sheep I suppose could ensue, and in some cases this argument does take physical relevance going over to antimatter, landing in an open puzzle as to how such an imbalance has occurred as we seem to observe. The hope that we will one day unwind this problem and land in fertile mathematics which provides physical correspondence is obviously where many would like to land.
> >
> > A broader treatment of sign will disentangle the confusion between sign and inversion; the conflict that exists as an operator versus a value in the discrete symbol '-' is an ambiguity within our notation. If anyone ought to abhor such ambiguity would it be the mathematician? The philosopher? The physicist? As to whose burden this one is; that is pretty easy to pinpoint. This is mathematics. As to who ought to be concerned about it: we all should.
> >
> > Operator theory itself seems to contain additional quagmire. The idea that an operator will map SxS onto S is a functional blunder. To some all is a function apparently, and yet will you even be able to use addition within your function? Where is the need for this Cartesian product? To sum three elements we'll be needing SxSxS? I'm sorry but one S will do very nicely, thank you. As if closure didn't even mean closure in the first place, certainly it doesn't mean it in the second place, and by the time you've gone three-dimensional on the thing to call this closure any more is just an abuse of the human mind. That we all could buy into such clap-trap at the base of mathematics is a sad citing of modernity.
> Something exists mathematically if it is logically self-consistent.

Actually, there isn’t anything consistent with those illegal immaginary numbers, since they were Created by human false decisions they usually call it proper definition

I.e they aren't any true discovery but on the contrary, they are absolutely the most dumb & Trolish math ever made by humans where there are many public published refutationS not only by modest self but by many other Outstanding members I think

Should I repeat the many old numerical counter exampleS to every one alone to understand this unbelievable human Brain bird 🧠 fart ? No wonder!
But we do understand why human mathematickers usually love those bird brains numbers 😉, it is the free & huge worthless buissness & the utter beliefs for sure

BKK 🔊

tisdag 29 augusti 2023 kl. 16:14:16 UTC+2 skrev bassam karzeddin:
> On Tuesday, August 29, 2023 at 9:50:08 AM UTC+3, markus...@gmail.com wrote:
> > måndag 28 augusti 2023 kl. 19:55:42 UTC+2 skrev Timothy Golden:
> > > On Sunday, August 27, 2023 at 6:07:42 AM UTC-4, Phil Carmody wrote:
> > > > FromTheRafters <F...@nomail.afraid.org> writes:
> > > > > on 8/25/2023, Chris M. Thomasson supposed :
> > > > >> On 8/25/2023 1:34 PM, FromTheRafters wrote:
> > > > >>> Kevin S brought next idea :
> > > > >>>> On Friday, August 25, 2023 at 8:11:12 PM UTC+2, mitchr....@gmail.com wrote:
> > > > >>>>> there is no negative 1.
> > > > >>>>> Mitchell Raemsch
> > > > >>>>
> > > > >>>> Yeah there is.
> > > > >>>
> > > > >>> Indeed, since we have integers. One could claim that there is no
> > > > >>> minus one though.
> > > > >>
> > > > >> Not exactly sure what you mean.
> > > > >
> > > > > One could claim...
> > > > >
> > > > > The integers form a ring, instead of subtraction of naturals (a
> > > > > partial function for them) we have addition of integers. The binary
> > > > > operator 'minus' (a-b) is essentially gone and we add a negative
> > > > > integer (a+(-b)) instead.
> > > > That X can be defined in terms of Y, where Y is known to exist, does not
> > > > mean that X does not exist. One might even say it's pretty good proof
> > > > that X does exist.
> > > >
> > > > Phil
> > > > --
> > > > We are no longer hunters and nomads. No longer awed and frightened, as we have
> > > > gained some understanding of the world in which we live. As such, we can cast
> > > > aside childish remnants from the dawn of our civilization.
> > > > -- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
> > > What it means to a mathematician 'to exist' is quite a controversial problem, especially when physical correspondence is cast aside as irrelevant, and what would be next to cast aside but philosophy? Certainly the quantum physicists have done exactly this, and as if these broad divides were even accurate in the third place, and which deserves the first place: each will claim it for their own, right?
> > >
> > > If, on the other hand, we dismiss these status quo assumptions, and witness these divides as false, then we ought to reflect a bit deeper upon the negative integer. Of course sensibility is lost as regards sheep in a field, whereby no physical correspondence can be laid by -5 sheep. A discussion of inverse sheep I suppose could ensue, and in some cases this argument does take physical relevance going over to antimatter, landing in an open puzzle as to how such an imbalance has occurred as we seem to observe. The hope that we will one day unwind this problem and land in fertile mathematics which provides physical correspondence is obviously where many would like to land.
> > >
> > > A broader treatment of sign will disentangle the confusion between sign and inversion; the conflict that exists as an operator versus a value in the discrete symbol '-' is an ambiguity within our notation. If anyone ought to abhor such ambiguity would it be the mathematician? The philosopher? The physicist? As to whose burden this one is; that is pretty easy to pinpoint. This is mathematics. As to who ought to be concerned about it: we all should.
> > >
> > > Operator theory itself seems to contain additional quagmire. The idea that an operator will map SxS onto S is a functional blunder. To some all is a function apparently, and yet will you even be able to use addition within your function? Where is the need for this Cartesian product? To sum three elements we'll be needing SxSxS? I'm sorry but one S will do very nicely, thank you. As if closure didn't even mean closure in the first place, certainly it doesn't mean it in the second place, and by the time you've gone three-dimensional on the thing to call this closure any more is just an abuse of the human mind. That we all could buy into such clap-trap at the base of mathematics is a sad citing of modernity.
> > Something exists mathematically if it is logically self-consistent.
> Actually, there isn’t anything consistent with those illegal immaginary numbers, since they were Created by human false decisions they usually call it proper definition
>
> I.e they aren't any true discovery but on the contrary, they are absolutely the most dumb & Trolish math ever made by humans where there are many public published refutationS not only by modest self but by many other Outstanding members I think
>
> Should I repeat the many old numerical counter exampleS to every one alone to understand this unbelievable human Brain bird 🧠 fart ? No wonder!
> But we do understand why human mathematickers usually love those bird brains numbers 😉, it is the free & huge worthless buissness & the utter beliefs for sure
>
> BKK 🔊
What's inconsistent about complex numbers?

Le 29/08/2023 à 19:10, markus...@gmail.com a écrit :
> tisdag 29 augusti 2023 kl. 16:14:16 UTC+2 skrev bassam karzeddin:
>> On Tuesday, August 29, 2023 at 9:50:08 AM UTC+3, markus...@gmail.com wrote:
>>> måndag 28 augusti 2023 kl. 19:55:42 UTC+2 skrev Timothy Golden:
>>>> On Sunday, August 27, 2023 at 6:07:42 AM UTC-4, Phil Carmody wrote:
>>>>> FromTheRafters <F...@nomail.afraid.org> writes:
>>>>>> on 8/25/2023, Chris M. Thomasson supposed :
>>>>>>> On 8/25/2023 1:34 PM, FromTheRafters wrote:
>>>>>>>> Kevin S brought next idea :
>>>>>>>>> On Friday, August 25, 2023 at 8:11:12 PM UTC+2, mitchr...@gmail.com wrote:
>>>>>>>>>> there is no negative 1.
>>>>>>>>>> Mitchell Raemsch
>>>>>>>>>
>>>>>>>>> Yeah there is.
>>>>>>>>
>>>>>>>> Indeed, since we have integers. One could claim that there is no
>>>>>>>> minus one though.
>>>>>>>
>>>>>>> Not exactly sure what you mean.
>>>>>>
>>>>>> One could claim...
>>>>>>
>>>>>> The integers form a ring, instead of subtraction of naturals (a
>>>>>> partial function for them) we have addition of integers. The binary
>>>>>> operator 'minus' (a-b) is essentially gone and we add a negative
>>>>>> integer (a+(-b)) instead.
>>>>> That X can be defined in terms of Y, where Y is known to exist, does not
>>>>> mean that X does not exist. One might even say it's pretty good proof
>>>>> that X does exist.
>>>>>
>>>>> Phil
>>>>> --
>>>>> We are no longer hunters and nomads. No longer awed and frightened, as we have
>>>>> gained some understanding of the world in which we live. As such, we can cast
>>>>> aside childish remnants from the dawn of our civilization.
>>>>> -- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
>>>> What it means to a mathematician 'to exist' is quite a controversial problem, especially when physical correspondence is cast aside as irrelevant, and what would be next to cast aside but philosophy? Certainly the quantum physicists have done exactly this, and as if these broad divides were even accurate in the third place, and which deserves the first place: each will claim it for their own, right?
>>>>
>>>> If, on the other hand, we dismiss these status quo assumptions, and witness these divides as false, then we ought to reflect a bit deeper upon the negative integer. Of course sensibility is lost as regards sheep in a field, whereby no physical correspondence can be laid by -5 sheep. A discussion of inverse sheep I suppose could ensue, and in some cases this argument does take physical relevance going over to antimatter, landing in an open puzzle as to how such an imbalance has occurred as we seem to observe. The hope that we will one day unwind this problem and land in fertile mathematics which provides physical correspondence is obviously where many would like to land.
>>>>
>>>> A broader treatment of sign will disentangle the confusion between sign and inversion; the conflict that exists as an operator versus a value in the discrete symbol '-' is an ambiguity within our notation. If anyone ought to abhor such ambiguity would it be the mathematician? The philosopher? The physicist? As to whose burden this one is; that is pretty easy to pinpoint. This is mathematics. As to who ought to be concerned about it: we all should.
>>>>
>>>> Operator theory itself seems to contain additional quagmire. The idea that an operator will map SxS onto S is a functional blunder. To some all is a function apparently, and yet will you even be able to use addition within your function? Where is the need for this Cartesian product? To sum three elements we'll be needing SxSxS? I'm sorry but one S will do very nicely, thank you. As if closure didn't even mean closure in the first place, certainly it doesn't mean it in the second place, and by the time you've gone three-dimensional on the thing to call this closure any more is just an abuse of the human mind. That we all could buy into such clap-trap at the base of mathematics is a sad citing of modernity.
>>> Something exists mathematically if it is logically self-consistent.
>> Actually, there isn’t anything consistent with those illegal immaginary numbers, since they were Created by human false decisions they usually call it proper definition
>>
>> I.e they aren't any true discovery but on the contrary, they are absolutely the most dumb & Trolish math ever made by humans where there are many public published refutationS not only by modest self but by many other Outstanding members I think
>>
>> Should I repeat the many old numerical counter exampleS to every one alone to understand this unbelievable human Brain bird 🧠 fart ? No wonder!
>> But we do understand why human mathematickers usually love those bird brains numbers 😉, it is the free & huge worthless buissness & the utter beliefs for sure
>>
>> BKK 🔊
> What's inconsistent about complex numbers?

BKK (the piece of shit) considers Real Numbers as inconsistent
(he's wrong of course), so we could ask him also if Q[i] i.e.
Q[X]/(X^2+1) which is a set of sets of polynomials with rational
coefficients is inconsistent too?

Do you think he could understand the question? Go figure! No,
for SURE, SURER, SUREST!!!

On Monday, August 28, 2023 at 11:50:08 PM UTC-7, markus...@gmail.com wrote:
> måndag 28 augusti 2023 kl. 19:55:42 UTC+2 skrev Timothy Golden:
> > On Sunday, August 27, 2023 at 6:07:42 AM UTC-4, Phil Carmody wrote:
> > > FromTheRafters <F...@nomail.afraid.org> writes:
> > > > on 8/25/2023, Chris M. Thomasson supposed :
> > > >> On 8/25/2023 1:34 PM, FromTheRafters wrote:
> > > >>> Kevin S brought next idea :
> > > >>>> On Friday, August 25, 2023 at 8:11:12 PM UTC+2, mitchr....@gmail.com wrote:
> > > >>>>> there is no negative 1.
> > > >>>>> Mitchell Raemsch
> > > >>>>
> > > >>>> Yeah there is.
> > > >>>
> > > >>> Indeed, since we have integers. One could claim that there is no
> > > >>> minus one though.
> > > >>
> > > >> Not exactly sure what you mean.
> > > >
> > > > One could claim...
> > > >
> > > > The integers form a ring, instead of subtraction of naturals (a
> > > > partial function for them) we have addition of integers. The binary
> > > > operator 'minus' (a-b) is essentially gone and we add a negative
> > > > integer (a+(-b)) instead.
> > > That X can be defined in terms of Y, where Y is known to exist, does not
> > > mean that X does not exist. One might even say it's pretty good proof
> > > that X does exist.
> > >
> > > Phil
> > > --
> > > We are no longer hunters and nomads. No longer awed and frightened, as we have
> > > gained some understanding of the world in which we live. As such, we can cast
> > > aside childish remnants from the dawn of our civilization.
> > > -- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
> > What it means to a mathematician 'to exist' is quite a controversial problem, especially when physical correspondence is cast aside as irrelevant, and what would be next to cast aside but philosophy? Certainly the quantum physicists have done exactly this, and as if these broad divides were even accurate in the third place, and which deserves the first place: each will claim it for their own, right?
> >
> > If, on the other hand, we dismiss these status quo assumptions, and witness these divides as false, then we ought to reflect a bit deeper upon the negative integer. Of course sensibility is lost as regards sheep in a field, whereby no physical correspondence can be laid by -5 sheep. A discussion of inverse sheep I suppose could ensue, and in some cases this argument does take physical relevance going over to antimatter, landing in an open puzzle as to how such an imbalance has occurred as we seem to observe. The hope that we will one day unwind this problem and land in fertile mathematics which provides physical correspondence is obviously where many would like to land.
> >
> > A broader treatment of sign will disentangle the confusion between sign and inversion; the conflict that exists as an operator versus a value in the discrete symbol '-' is an ambiguity within our notation. If anyone ought to abhor such ambiguity would it be the mathematician? The philosopher? The physicist? As to whose burden this one is; that is pretty easy to pinpoint. This is mathematics. As to who ought to be concerned about it: we all should.
> >
> > Operator theory itself seems to contain additional quagmire. The idea that an operator will map SxS onto S is a functional blunder. To some all is a function apparently, and yet will you even be able to use addition within your function? Where is the need for this Cartesian product? To sum three elements we'll be needing SxSxS? I'm sorry but one S will do very nicely, thank you. As if closure didn't even mean closure in the first place, certainly it doesn't mean it in the second place, and by the time you've gone three-dimensional on the thing to call this closure any more is just an abuse of the human mind. That we all could buy into such clap-trap at the base of mathematics is a sad citing of modernity.
> Something exists mathematically if it is logically self-consistent.

Not if is the formula has no solution.
That is why it is only the imaginary.
Math got the name right. But wants
something more out of it that
never belonged.

Mitchell Raemsch

On Tuesday, August 29, 2023 at 1:39:38 PM UTC-4, mitchr...@gmail.com wrote:
> On Monday, August 28, 2023 at 11:50:08 PM UTC-7, markus...@gmail.com wrote:
> > måndag 28 augusti 2023 kl. 19:55:42 UTC+2 skrev Timothy Golden:
> > > On Sunday, August 27, 2023 at 6:07:42 AM UTC-4, Phil Carmody wrote:
> > > > FromTheRafters <F...@nomail.afraid.org> writes:
> > > > > on 8/25/2023, Chris M. Thomasson supposed :
> > > > >> On 8/25/2023 1:34 PM, FromTheRafters wrote:
> > > > >>> Kevin S brought next idea :
> > > > >>>> On Friday, August 25, 2023 at 8:11:12 PM UTC+2, mitchr....@gmail.com wrote:
> > > > >>>>> there is no negative 1.
> > > > >>>>> Mitchell Raemsch
> > > > >>>>
> > > > >>>> Yeah there is.
> > > > >>>
> > > > >>> Indeed, since we have integers. One could claim that there is no
> > > > >>> minus one though.
> > > > >>
> > > > >> Not exactly sure what you mean.
> > > > >
> > > > > One could claim...
> > > > >
> > > > > The integers form a ring, instead of subtraction of naturals (a
> > > > > partial function for them) we have addition of integers. The binary
> > > > > operator 'minus' (a-b) is essentially gone and we add a negative
> > > > > integer (a+(-b)) instead.
> > > > That X can be defined in terms of Y, where Y is known to exist, does not
> > > > mean that X does not exist. One might even say it's pretty good proof
> > > > that X does exist.
> > > >
> > > > Phil
> > > > --
> > > > We are no longer hunters and nomads. No longer awed and frightened, as we have
> > > > gained some understanding of the world in which we live. As such, we can cast
> > > > aside childish remnants from the dawn of our civilization.
> > > > -- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
> > > What it means to a mathematician 'to exist' is quite a controversial problem, especially when physical correspondence is cast aside as irrelevant, and what would be next to cast aside but philosophy? Certainly the quantum physicists have done exactly this, and as if these broad divides were even accurate in the third place, and which deserves the first place: each will claim it for their own, right?
> > >
> > > If, on the other hand, we dismiss these status quo assumptions, and witness these divides as false, then we ought to reflect a bit deeper upon the negative integer. Of course sensibility is lost as regards sheep in a field, whereby no physical correspondence can be laid by -5 sheep. A discussion of inverse sheep I suppose could ensue, and in some cases this argument does take physical relevance going over to antimatter, landing in an open puzzle as to how such an imbalance has occurred as we seem to observe. The hope that we will one day unwind this problem and land in fertile mathematics which provides physical correspondence is obviously where many would like to land.
> > >
> > > A broader treatment of sign will disentangle the confusion between sign and inversion; the conflict that exists as an operator versus a value in the discrete symbol '-' is an ambiguity within our notation. If anyone ought to abhor such ambiguity would it be the mathematician? The philosopher? The physicist? As to whose burden this one is; that is pretty easy to pinpoint. This is mathematics. As to who ought to be concerned about it: we all should.
> > >
> > > Operator theory itself seems to contain additional quagmire. The idea that an operator will map SxS onto S is a functional blunder. To some all is a function apparently, and yet will you even be able to use addition within your function? Where is the need for this Cartesian product? To sum three elements we'll be needing SxSxS? I'm sorry but one S will do very nicely, thank you. As if closure didn't even mean closure in the first place, certainly it doesn't mean it in the second place, and by the time you've gone three-dimensional on the thing to call this closure any more is just an abuse of the human mind. That we all could buy into such clap-trap at the base of mathematics is a sad citing of modernity.
> > Something exists mathematically if it is logically self-consistent.
> Not if is the formula has no solution.
> That is why it is only the imaginary.
> Math got the name right. But wants
> something more out of it that
> never belonged.
>
>
> Mitchell Raemsch

There is another aspect to attack the system from, and that is the introduction of additional symbols. Firstly though, I doubt any here deny the utility of the complex number. It does make its way into physics and engineering rapidly. True complex functions; even just in their polynomial form; become four dimensional in nature, and so we cannot manage to visualize them. What is most entertaining is that much more work and dimensional freedom lays this way if we handle the details correctly. People have struggled over the three dimensional counterpart that follows in the progression of the reals as 1D, the complex numbers as 2D, and from there all have faltered until the polysign form was found. The result is in some ways less impressive that some would like. For instance a 3D Mandelbrot set is merely an extruded form of the 2D Mandelbrot set, owing to the RxC nature of the 3D system, just as predicted from associative algebra, though I have not honestly come to understand the theorem. Instead I find trouble in the tenets of abstract algebra, and even in simpler mathematics.

As we discuss numbers, initially we simply have a string of digits, and this adequately defines a natural value once the presumed radix and sequence of digits, and I suppose even an agreement to read left to right and then top to bottom. These unstated assumptions could actually become relevant as we face the fact of a 2D substrate for our work (paper and pencil) and as academia barely will let in animated graphics as they are not printable media.. We should perhaps stop for a moment and confess that our tools that we deal with may be interfering with pure theory.

Upon introducing a little dot into our string of digits have we magically gone out of the discrete form and entered a pure continuum? Do we really have to ponder things like 1/3 as a pure value, though it is composed of two pure values and one nonfundamental operator, and leads to another representation 0.333...? Leaving such paltry issues behind, there are more serious details to discuss within the symbology of number, and the next we encounter is sign, which for some is either positive or negative, and which achieves a discrete binary appendage to what just became a continuous value. Then in a grand culmination yet another unique appendage connected to sign as ii=-1, and lo and behold a 2D continuum form with algebraic properties was born with the form z=a+bi.

That 'number' has come to handle this many appendages suggests we make some more, no? Is this the art of mathematics? Well, yes, we can, and probably we should be encouraged in covering such ground, though the results that are coherent may be quite thin. The very fact that polysign numbers have waited until now to be recognized is a proof that exceeds mathematics and enters philosophy and physics. Indeed, as to why sign would be so committed to a binary form and never yield the possibility of a triple or a quadruple form has only been discussed marginally. Meanwhile, modern physics, and mathematics, and certainly engineering all will yield the vector form as substantial, and what is a vector but a ray, and why should your ray be built upon the line, which is composed of two such rays? Why should a 2D space require four such rays? If it could be done in three would you care to celebrate? If you could have your three by the same rules that you have your two could you be any happier? And then of course to follow with four, and five, and so forth, and definitely let's not overlook their little sibling, the one.

What we find when we generalize sign is a direct route to what others have discovered the long way around, regarding higher algebraically behaved results. The three-signed numbers are the complex numbers in a new suit, and yet this new suit is merely the modulo-three form of the old modulo-two suit. In effect the real number loses its significance, and is rendered a part of history. It is sequestered as P2 and as no more fundamental than any of its siblings. Since when does symmetry stop at a binary image? Polysign sort of says, "take your yin-yan and shove it." It says, "Your two-party system is a farce, sir!" It asks, "Why can't you get to three?", and humanity dully looks on, mumbles a dismissive groan, and returns to quibbling over accumulated stupidity.