Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.

On 1/9/2022 12:59 PM, Timothy Golden wrote:
> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.

Adios moron.

On 1/9/2022 12:59 PM, Timothy Golden wrote:
> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.

I am still wondering, if 2-ary polysign can create a Mandelbrot, then
3-ary polysign should be able to create the Mandelbulb?

On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
> On 1/9/2022 12:59 PM, Timothy Golden wrote:
> > Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
> 3-ary polysign should be able to create the Mandelbulb?

That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.

This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
The proper 3D shape is literally an extruded Mandelbrot set.
This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.

Claims that the Mandelbulb is the natural extended form are suspect.
Sorry my claim is so boring though.

On 1/10/2022 5:14 AM, Timothy Golden wrote:
> On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
>> On 1/9/2022 12:59 PM, Timothy Golden wrote:
>>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
>> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
>> 3-ary polysign should be able to create the Mandelbulb?
>
> That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
> However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
>
> This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
> The proper 3D shape is literally an extruded Mandelbrot set.
> This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
>
> Claims that the Mandelbulb is the natural extended form are suspect.
> Sorry my claim is so boring though.
>

Oh shit. I totally forgot that I actually did work with your polysign. I
saw your C code. Damn! I even created some renderings of some
interesting plots with it. Its on an older computer. Humm...

On 1/10/2022 5:14 AM, Timothy Golden wrote:
> On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
>> On 1/9/2022 12:59 PM, Timothy Golden wrote:
>>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
>> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
>> 3-ary polysign should be able to create the Mandelbulb?
>
> That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
> However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
>
> This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
> The proper 3D shape is literally an extruded Mandelbrot set.

Now that I think about it, you did mention that 3-ary polysign, not 2,
is compatible with complex number! Sorry about that Tim.

> This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
>
> Claims that the Mandelbulb is the natural extended form are suspect.
> Sorry my claim is so boring though.
>

So, your 4-ary polysign, I think, should be able to get at something
akin to the Mandelbulb. The triplex numbers do it, and I think your
polysign should be able to do it. The escape time for a mandelbulb is a
sphere instead of a circle.

On Monday, January 10, 2022 at 7:45:42 PM UTC-5, Chris M. Thomasson wrote:
> On 1/10/2022 5:14 AM, Timothy Golden wrote:
> > On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
> >> On 1/9/2022 12:59 PM, Timothy Golden wrote:
> >>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
> >> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
> >> 3-ary polysign should be able to create the Mandelbulb?
> >
> > That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
> > However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
> >
> > This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
> > The proper 3D shape is literally an extruded Mandelbrot set.
> Now that I think about it, you did mention that 3-ary polysign, not 2,
> is compatible with complex number! Sorry about that Tim.
> > This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
> >
> > Claims that the Mandelbulb is the natural extended form are suspect.
> > Sorry my claim is so boring though.
> >
> So, your 4-ary polysign, I think, should be able to get at something
> akin to the Mandelbulb. The triplex numbers do it, and I think your
> polysign should be able to do it. The escape time for a mandelbulb is a
> sphere instead of a circle.

No Mandelbulb in P4, Chris.
It comes out as an extruded Mandelbrot set.
It's a disappointment, but according to the algebraic interpretation this is the correct result.
As well, up in P5, though we are in 4D, the result is simply two Mandelbrot sets crossed.
Possibly this projected will get some Mandelbulb sort of result.
I haven't done that projection yet though.
I have looked at slices and they are fairly good at exposing the thing.

The idea of the mixed modulo is more a matter of handling exceptions and mimicing any pattern that is discovered.
In this way the notion of 'logic' gets corrupted and goes multidimensional.
The binary form as truth and falsehood is not necessarily a complete concept.
P1 is more akin to truth and it lacks any invert.
The naturally inverted form (binary) then is a two-state system, but it exists not as a sole contributor but in a family of these mixed modulo states.
P1 P2 P3 P4 P5 ...
To declare this form as 'logical' may simply mean that we assign unity values throughout.
Certainly ordinary Boolean logic does lack magnitude. Certainly it is a P2 style.
MU ( minus unity) stands in as fundamental.
engaging the extension from modulo two to modulo-three then poses a couple of choices.
Is -1+1 a possible P3 state as a superposition of two unital values? It happens that this is a unital value a well. At least in the magnitude space it can have magnitude. There are at least three possible constructions available here. The last is to ditch the discrete solutions and engage in continuum solutions. Still keeping with the unity concept this places P3 as the first continuum exhibit. P2 remains Boolean under these constraints. Going to an ordered series type of solution the above P3 option becomes:
( 0, 1, 1 ) : ( @ 0 - 1 + 1 )
yet in P4 we will not see this possibility space generalize to:
( 0, 0, 1, 1 )
because this value is not a unity magnitude.
It's a strange course to take so to remain with simple unital values such as:
( 1, 0, 0, 0 ), ( 0, 1, 0, 0 ), ( 0, 0, 1, 0 ), ( 0, 0, 0, 1 )
which then covers the P4 possibilities remains simple... but for the overlap of the P2 mode with the P4 mode. This mixed modulo concept gets even more complicated, yet in terms of neuronal chains, say, the idea of a lockstep system that cycles through arbitrarily many stages interconnected to other such systems is easily constructed. Under this model order and memory are one. This may be a breakthrough concept. I did search for it on the internet and found nothing. That said, within the field of neural networking these concepts may be dowsed in some sublanguage unknown to me. It seems to me that the simplistic version listed above in P4 is not as likely as the mixed non-unity resultant. This is just a matter of respecting superposition as fundamental.

To remain in a philosophy that only allows for Boolean logic to hold could be a terrible assumption. Is the truth Boolean? Ultimately truth is existence and all of its detail. Clearly existence is not Boolean. We need a richer system.

On 1/12/2022 6:43 AM, Timothy Golden wrote:
> On Monday, January 10, 2022 at 7:45:42 PM UTC-5, Chris M. Thomasson wrote:
>> On 1/10/2022 5:14 AM, Timothy Golden wrote:
>>> On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
>>>> On 1/9/2022 12:59 PM, Timothy Golden wrote:
>>>>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
>>>> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
>>>> 3-ary polysign should be able to create the Mandelbulb?
>>>
>>> That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
>>> However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
>>>
>>> This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
>>> The proper 3D shape is literally an extruded Mandelbrot set.
>> Now that I think about it, you did mention that 3-ary polysign, not 2,
>> is compatible with complex number! Sorry about that Tim.
>>> This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
>>>
>>> Claims that the Mandelbulb is the natural extended form are suspect.
>>> Sorry my claim is so boring though.
>>>
>> So, your 4-ary polysign, I think, should be able to get at something
>> akin to the Mandelbulb. The triplex numbers do it, and I think your
>> polysign should be able to do it. The escape time for a mandelbulb is a
>> sphere instead of a circle.
>
> No Mandelbulb in P4, Chris.
> It comes out as an extruded Mandelbrot set.
> It's a disappointment, but according to the algebraic interpretation this is the correct result.
> As well, up in P5, though we are in 4D, the result is simply two Mandelbrot sets crossed.
> Possibly this projected will get some Mandelbulb sort of result.
> I haven't done that projection yet though.
> I have looked at slices and they are fairly good at exposing the thing.
>
> The idea of the mixed modulo is more a matter of handling exceptions and mimicing any pattern that is discovered.
> In this way the notion of 'logic' gets corrupted and goes multidimensional.
> The binary form as truth and falsehood is not necessarily a complete concept.
> P1 is more akin to truth and it lacks any invert.
> The naturally inverted form (binary) then is a two-state system, but it exists not as a sole contributor but in a family of these mixed modulo states.
> P1 P2 P3 P4 P5 ...
> To declare this form as 'logical' may simply mean that we assign unity values throughout.
> Certainly ordinary Boolean logic does lack magnitude. Certainly it is a P2 style.
> MU ( minus unity) stands in as fundamental.
> engaging the extension from modulo two to modulo-three then poses a couple of choices.
> Is -1+1 a possible P3 state as a superposition of two unital values? It happens that this is a unital value a well. At least in the magnitude space it can have magnitude. There are at least three possible constructions available here. The last is to ditch the discrete solutions and engage in continuum solutions. Still keeping with the unity concept this places P3 as the first continuum exhibit. P2 remains Boolean under these constraints. Going to an ordered series type of solution the above P3 option becomes:
> ( 0, 1, 1 ) : ( @ 0 - 1 + 1 )
> yet in P4 we will not see this possibility space generalize to:
> ( 0, 0, 1, 1 )
> because this value is not a unity magnitude.
> It's a strange course to take so to remain with simple unital values such as:
> ( 1, 0, 0, 0 ), ( 0, 1, 0, 0 ), ( 0, 0, 1, 0 ), ( 0, 0, 0, 1 )
> which then covers the P4 possibilities remains simple... but for the overlap of the P2 mode with the P4 mode. This mixed modulo concept gets even more complicated, yet in terms of neuronal chains, say, the idea of a lockstep system that cycles through arbitrarily many stages interconnected to other such systems is easily constructed. Under this model order and memory are one. This may be a breakthrough concept. I did search for it on the internet and found nothing. That said, within the field of neural networking these concepts may be dowsed in some sublanguage unknown to me. It seems to me that the simplistic version listed above in P4 is not as likely as the mixed non-unity resultant. This is just a matter of respecting superposition as fundamental.
>
> To remain in a philosophy that only allows for Boolean logic to hold could be a terrible assumption. Is the truth Boolean? Ultimately truth is existence and all of its detail. Clearly existence is not Boolean. We need a richer system.

Humm... Need some more time to give this a proper read Tim. Sorry! In
the mean time, btw, have you taken a look at the following:

https://www.soler7.com/Fractals/Matrices%20to%20Triplex.pdf

http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/

https://www.shadertoy.com/view/MdXSWn
https://www.shadertoy.com/view/ltfSWn
(mandelbulb code is in there)

https://www.shadertoy.com/user/iq
(very smart guy: indeed!)

A bunch of people have researched "truly 3d numbers" (some kind of "holy grail"), also many
have researched "truly 3d fractals".

If somebody discovers other trigonometry (based on a novel notion of angle in the 3d space),
that would be groundbreaking (synthetic or analytic or vectorial, ...)

While using other number systems based in other coordinate systems, things that are irrational may turn
into rational, and viceversa. Although, more reasons to change a coordinate system may be a requirement,
in some cases, some people discard manipulations only because they are seeing irrationals here and there.
This is, possibilities are dismissed by being to baroque...

On Wednesday, January 12, 2022 at 4:21:14 PM UTC-5, Chris M. Thomasson wrote:
> On 1/12/2022 6:43 AM, Timothy Golden wrote:
> > On Monday, January 10, 2022 at 7:45:42 PM UTC-5, Chris M. Thomasson wrote:
> >> On 1/10/2022 5:14 AM, Timothy Golden wrote:
> >>> On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
> >>>> On 1/9/2022 12:59 PM, Timothy Golden wrote:
> >>>>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
> >>>> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
> >>>> 3-ary polysign should be able to create the Mandelbulb?
> >>>
> >>> That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
> >>> However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
> >>>
> >>> This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
> >>> The proper 3D shape is literally an extruded Mandelbrot set.
> >> Now that I think about it, you did mention that 3-ary polysign, not 2,
> >> is compatible with complex number! Sorry about that Tim.
> >>> This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
> >>>
> >>> Claims that the Mandelbulb is the natural extended form are suspect.
> >>> Sorry my claim is so boring though.
> >>>
> >> So, your 4-ary polysign, I think, should be able to get at something
> >> akin to the Mandelbulb. The triplex numbers do it, and I think your
> >> polysign should be able to do it. The escape time for a mandelbulb is a
> >> sphere instead of a circle.
> >
> > No Mandelbulb in P4, Chris.
> > It comes out as an extruded Mandelbrot set.
> > It's a disappointment, but according to the algebraic interpretation this is the correct result.
> > As well, up in P5, though we are in 4D, the result is simply two Mandelbrot sets crossed.
> > Possibly this projected will get some Mandelbulb sort of result.
> > I haven't done that projection yet though.
> > I have looked at slices and they are fairly good at exposing the thing.
> >
> > The idea of the mixed modulo is more a matter of handling exceptions and mimicing any pattern that is discovered.
> > In this way the notion of 'logic' gets corrupted and goes multidimensional.
> > The binary form as truth and falsehood is not necessarily a complete concept.
> > P1 is more akin to truth and it lacks any invert.
> > The naturally inverted form (binary) then is a two-state system, but it exists not as a sole contributor but in a family of these mixed modulo states.
> > P1 P2 P3 P4 P5 ...
> > To declare this form as 'logical' may simply mean that we assign unity values throughout.
> > Certainly ordinary Boolean logic does lack magnitude. Certainly it is a P2 style.
> > MU ( minus unity) stands in as fundamental.
> > engaging the extension from modulo two to modulo-three then poses a couple of choices.
> > Is -1+1 a possible P3 state as a superposition of two unital values? It happens that this is a unital value a well. At least in the magnitude space it can have magnitude. There are at least three possible constructions available here. The last is to ditch the discrete solutions and engage in continuum solutions. Still keeping with the unity concept this places P3 as the first continuum exhibit. P2 remains Boolean under these constraints. Going to an ordered series type of solution the above P3 option becomes:
> > ( 0, 1, 1 ) : ( @ 0 - 1 + 1 )
> > yet in P4 we will not see this possibility space generalize to:
> > ( 0, 0, 1, 1 )
> > because this value is not a unity magnitude.
> > It's a strange course to take so to remain with simple unital values such as:
> > ( 1, 0, 0, 0 ), ( 0, 1, 0, 0 ), ( 0, 0, 1, 0 ), ( 0, 0, 0, 1 )
> > which then covers the P4 possibilities remains simple... but for the overlap of the P2 mode with the P4 mode. This mixed modulo concept gets even more complicated, yet in terms of neuronal chains, say, the idea of a lockstep system that cycles through arbitrarily many stages interconnected to other such systems is easily constructed. Under this model order and memory are one. This may be a breakthrough concept. I did search for it on the internet and found nothing. That said, within the field of neural networking these concepts may be dowsed in some sublanguage unknown to me. It seems to me that the simplistic version listed above in P4 is not as likely as the mixed non-unity resultant. This is just a matter of respecting superposition as fundamental.
> >
> > To remain in a philosophy that only allows for Boolean logic to hold could be a terrible assumption. Is the truth Boolean? Ultimately truth is existence and all of its detail. Clearly existence is not Boolean. We need a richer system.
> Humm... Need some more time to give this a proper read Tim. Sorry! In
> the mean time, btw, have you taken a look at the following:
>
> https://www.soler7.com/Fractals/Matrices%20to%20Triplex.pdf
>
> http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/
>
>
> https://www.shadertoy.com/view/MdXSWn
> https://www.shadertoy.com/view/ltfSWn
> (mandelbulb code is in there)
>
> https://www.shadertoy.com/user/iq
> (very smart guy: indeed!)

I actually just posed a question in another thread that seems close by to this concern:
https://groups.google.com/g/sci.math/c/RJadKuXvPvY
Some of the shader toy code has some type conversion errors.

There is another class of fractal that I am supposedly exploring:
https://drive.google.com/file/d/1Vvqq2f_Ch6IozwNimJjcS4kw3tnVmtPd/view?usp=sharing
Pretty you've seen that though.
In that points heading toward infinity will not be graphed, then orbital analysis is possible especially using a subset of the plane. That is what these graphics do. There is no escape criterion. Points which escape go off the graph. Admittedly there is a speedup in the code to skip that if they do escape, but all the initial test points are on this graph: they are the trace of a ray. That ray is fairly well obscured in this graphic.

I call this graph a magnitude sweep, and as it clocks around various harmonics are exposed. Here in this one triples are showing up.
All the points are graphed from z[0] to z[2000] in this case. These are what are filling in the space.

On Thursday, January 13, 2022 at 3:04:10 PM UTC-5, michael Rodriguez wrote:
> A bunch of people have researched "truly 3d numbers" (some kind of "holy grail"), also many
> have researched "truly 3d fractals".
>
> If somebody discovers other trigonometry (based on a novel notion of angle in the 3d space),
> that would be groundbreaking (synthetic or analytic or vectorial, ...)
>
> While using other number systems based in other coordinate systems, things that are irrational may turn
> into rational, and viceversa. Although, more reasons to change a coordinate system may be a requirement,
> in some cases, some people discard manipulations only because they are seeing irrationals here and there.
> This is, possibilities are dismissed by being to baroque...

So good to hear of you here on this thread Michael. Your posts sparseness balances my 'overly exuberant' (see Greenspan) ones.
But it is your ONEs that win again.

On Saturday, January 15, 2022 at 8:56:19 AM UTC-5, Timothy Golden wrote:
> On Wednesday, January 12, 2022 at 4:21:14 PM UTC-5, Chris M. Thomasson wrote:
> > On 1/12/2022 6:43 AM, Timothy Golden wrote:
> > > On Monday, January 10, 2022 at 7:45:42 PM UTC-5, Chris M. Thomasson wrote:
> > >> On 1/10/2022 5:14 AM, Timothy Golden wrote:
> > >>> On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
> > >>>> On 1/9/2022 12:59 PM, Timothy Golden wrote:
> > >>>>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
> > >>>> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
> > >>>> 3-ary polysign should be able to create the Mandelbulb?
> > >>>
> > >>> That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
> > >>> However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
> > >>>
> > >>> This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
> > >>> The proper 3D shape is literally an extruded Mandelbrot set.
> > >> Now that I think about it, you did mention that 3-ary polysign, not 2,
> > >> is compatible with complex number! Sorry about that Tim.
> > >>> This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
> > >>>
> > >>> Claims that the Mandelbulb is the natural extended form are suspect..
> > >>> Sorry my claim is so boring though.
> > >>>
> > >> So, your 4-ary polysign, I think, should be able to get at something
> > >> akin to the Mandelbulb. The triplex numbers do it, and I think your
> > >> polysign should be able to do it. The escape time for a mandelbulb is a
> > >> sphere instead of a circle.
> > >
> > > No Mandelbulb in P4, Chris.
> > > It comes out as an extruded Mandelbrot set.
> > > It's a disappointment, but according to the algebraic interpretation this is the correct result.
> > > As well, up in P5, though we are in 4D, the result is simply two Mandelbrot sets crossed.
> > > Possibly this projected will get some Mandelbulb sort of result.
> > > I haven't done that projection yet though.
> > > I have looked at slices and they are fairly good at exposing the thing.
> > >
> > > The idea of the mixed modulo is more a matter of handling exceptions and mimicing any pattern that is discovered.
> > > In this way the notion of 'logic' gets corrupted and goes multidimensional.
> > > The binary form as truth and falsehood is not necessarily a complete concept.
> > > P1 is more akin to truth and it lacks any invert.
> > > The naturally inverted form (binary) then is a two-state system, but it exists not as a sole contributor but in a family of these mixed modulo states.
> > > P1 P2 P3 P4 P5 ...
> > > To declare this form as 'logical' may simply mean that we assign unity values throughout.
> > > Certainly ordinary Boolean logic does lack magnitude. Certainly it is a P2 style.
> > > MU ( minus unity) stands in as fundamental.
> > > engaging the extension from modulo two to modulo-three then poses a couple of choices.
> > > Is -1+1 a possible P3 state as a superposition of two unital values? It happens that this is a unital value a well. At least in the magnitude space it can have magnitude. There are at least three possible constructions available here. The last is to ditch the discrete solutions and engage in continuum solutions. Still keeping with the unity concept this places P3 as the first continuum exhibit. P2 remains Boolean under these constraints. Going to an ordered series type of solution the above P3 option becomes:
> > > ( 0, 1, 1 ) : ( @ 0 - 1 + 1 )
> > > yet in P4 we will not see this possibility space generalize to:
> > > ( 0, 0, 1, 1 )
> > > because this value is not a unity magnitude.
> > > It's a strange course to take so to remain with simple unital values such as:
> > > ( 1, 0, 0, 0 ), ( 0, 1, 0, 0 ), ( 0, 0, 1, 0 ), ( 0, 0, 0, 1 )
> > > which then covers the P4 possibilities remains simple... but for the overlap of the P2 mode with the P4 mode. This mixed modulo concept gets even more complicated, yet in terms of neuronal chains, say, the idea of a lockstep system that cycles through arbitrarily many stages interconnected to other such systems is easily constructed. Under this model order and memory are one. This may be a breakthrough concept. I did search for it on the internet and found nothing. That said, within the field of neural networking these concepts may be dowsed in some sublanguage unknown to me. It seems to me that the simplistic version listed above in P4 is not as likely as the mixed non-unity resultant. This is just a matter of respecting superposition as fundamental.
> > >
> > > To remain in a philosophy that only allows for Boolean logic to hold could be a terrible assumption. Is the truth Boolean? Ultimately truth is existence and all of its detail. Clearly existence is not Boolean. We need a richer system.
> > Humm... Need some more time to give this a proper read Tim. Sorry! In
> > the mean time, btw, have you taken a look at the following:
> >
> > https://www.soler7.com/Fractals/Matrices%20to%20Triplex.pdf
> >
> > http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/
> >
> >
> > https://www.shadertoy.com/view/MdXSWn
> > https://www.shadertoy.com/view/ltfSWn
> > (mandelbulb code is in there)
> >
> > https://www.shadertoy.com/user/iq
> > (very smart guy: indeed!)
> I actually just posed a question in another thread that seems close by to this concern:
> https://groups.google.com/g/sci.math/c/RJadKuXvPvY
> Some of the shader toy code has some type conversion errors.
>
> There is another class of fractal that I am supposedly exploring:
> https://drive.google.com/file/d/1Vvqq2f_Ch6IozwNimJjcS4kw3tnVmtPd/view?usp=sharing
> Pretty you've seen that though.
> In that points heading toward infinity will not be graphed, then orbital analysis is possible especially using a subset of the plane. That is what these graphics do. There is no escape criterion. Points which escape go off the graph. Admittedly there is a speedup in the code to skip that if they do escape, but all the initial test points are on this graph: they are the trace of a ray. That ray is fairly well obscured in this graphic.
>
> I call this graph a magnitude sweep, and as it clocks around various harmonics are exposed. Here in this one triples are showing up.
> All the points are graphed from z[0] to z[2000] in this case. These are what are filling in the space.
Chris, it would be meaningful if you were to repeat these results in your own system on C. This result is the polysign equivalent of C. You will be in a new class of study and yet your code will only barely be modified. Beyond this a troubling quantity of statistics is possible upon trying to categorize the orbits of z.

Also I see a sort of typo: my usage of '*' within the graphical notation at
'clocked: m * z'
is to mean product rather than a polysign(the star being the C++ code product rather than sign three)
I think you would enjoy these too as they clock around. I have a feeling that zooms could be great, though the computation may be more taxing in that some moire patterns do cause trouble. As well the density of the plot matters. If you choose too high a density the plot will wash out. This is actually consistent with proofs from the fathers of complex analysis.

On 1/15/2022 5:56 AM, Timothy Golden wrote:
> On Wednesday, January 12, 2022 at 4:21:14 PM UTC-5, Chris M. Thomasson wrote:
>> On 1/12/2022 6:43 AM, Timothy Golden wrote:
>>> On Monday, January 10, 2022 at 7:45:42 PM UTC-5, Chris M. Thomasson wrote:
>>>> On 1/10/2022 5:14 AM, Timothy Golden wrote:
>>>>> On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
>>>>>> On 1/9/2022 12:59 PM, Timothy Golden wrote:
>>>>>>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
>>>>>> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
>>>>>> 3-ary polysign should be able to create the Mandelbulb?
>>>>>
>>>>> That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
>>>>> However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
>>>>>
>>>>> This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
>>>>> The proper 3D shape is literally an extruded Mandelbrot set.
>>>> Now that I think about it, you did mention that 3-ary polysign, not 2,
>>>> is compatible with complex number! Sorry about that Tim.
>>>>> This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
>>>>>
>>>>> Claims that the Mandelbulb is the natural extended form are suspect.
>>>>> Sorry my claim is so boring though.
>>>>>
>>>> So, your 4-ary polysign, I think, should be able to get at something
>>>> akin to the Mandelbulb. The triplex numbers do it, and I think your
>>>> polysign should be able to do it. The escape time for a mandelbulb is a
>>>> sphere instead of a circle.
>>>
>>> No Mandelbulb in P4, Chris.
>>> It comes out as an extruded Mandelbrot set.
>>> It's a disappointment, but according to the algebraic interpretation this is the correct result.
>>> As well, up in P5, though we are in 4D, the result is simply two Mandelbrot sets crossed.
>>> Possibly this projected will get some Mandelbulb sort of result.
>>> I haven't done that projection yet though.
>>> I have looked at slices and they are fairly good at exposing the thing.
>>>
>>> The idea of the mixed modulo is more a matter of handling exceptions and mimicing any pattern that is discovered.
>>> In this way the notion of 'logic' gets corrupted and goes multidimensional.
>>> The binary form as truth and falsehood is not necessarily a complete concept.
>>> P1 is more akin to truth and it lacks any invert.
>>> The naturally inverted form (binary) then is a two-state system, but it exists not as a sole contributor but in a family of these mixed modulo states.
>>> P1 P2 P3 P4 P5 ...
>>> To declare this form as 'logical' may simply mean that we assign unity values throughout.
>>> Certainly ordinary Boolean logic does lack magnitude. Certainly it is a P2 style.
>>> MU ( minus unity) stands in as fundamental.
>>> engaging the extension from modulo two to modulo-three then poses a couple of choices.
>>> Is -1+1 a possible P3 state as a superposition of two unital values? It happens that this is a unital value a well. At least in the magnitude space it can have magnitude. There are at least three possible constructions available here. The last is to ditch the discrete solutions and engage in continuum solutions. Still keeping with the unity concept this places P3 as the first continuum exhibit. P2 remains Boolean under these constraints. Going to an ordered series type of solution the above P3 option becomes:
>>> ( 0, 1, 1 ) : ( @ 0 - 1 + 1 )
>>> yet in P4 we will not see this possibility space generalize to:
>>> ( 0, 0, 1, 1 )
>>> because this value is not a unity magnitude.
>>> It's a strange course to take so to remain with simple unital values such as:
>>> ( 1, 0, 0, 0 ), ( 0, 1, 0, 0 ), ( 0, 0, 1, 0 ), ( 0, 0, 0, 1 )
>>> which then covers the P4 possibilities remains simple... but for the overlap of the P2 mode with the P4 mode. This mixed modulo concept gets even more complicated, yet in terms of neuronal chains, say, the idea of a lockstep system that cycles through arbitrarily many stages interconnected to other such systems is easily constructed. Under this model order and memory are one. This may be a breakthrough concept. I did search for it on the internet and found nothing. That said, within the field of neural networking these concepts may be dowsed in some sublanguage unknown to me. It seems to me that the simplistic version listed above in P4 is not as likely as the mixed non-unity resultant. This is just a matter of respecting superposition as fundamental.
>>>
>>> To remain in a philosophy that only allows for Boolean logic to hold could be a terrible assumption. Is the truth Boolean? Ultimately truth is existence and all of its detail. Clearly existence is not Boolean. We need a richer system.
>> Humm... Need some more time to give this a proper read Tim. Sorry! In
>> the mean time, btw, have you taken a look at the following:
>>
>> https://www.soler7.com/Fractals/Matrices%20to%20Triplex.pdf
>>
>> http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/
>>
>>
>> https://www.shadertoy.com/view/MdXSWn
>> https://www.shadertoy.com/view/ltfSWn
>> (mandelbulb code is in there)
>>
>> https://www.shadertoy.com/user/iq
>> (very smart guy: indeed!)
>
> I actually just posed a question in another thread that seems close by to this concern:
> https://groups.google.com/g/sci.math/c/RJadKuXvPvY
> Some of the shader toy code has some type conversion errors.
>
> There is another class of fractal that I am supposedly exploring:
> https://drive.google.com/file/d/1Vvqq2f_Ch6IozwNimJjcS4kw3tnVmtPd/view?usp=sharing
> Pretty you've seen that though.

Yes, I have seen that excellent plot: It's beautiful! I have to boot up
my older computer because I have polysign implemented on it in C++. Or,
I can just code it up again. I remember looking at some of your C code.
Fwiw, check out this strange attractor:

https://youtu.be/XKhS_nklCkE
(I have pseudo code for it in the comments)

Also, check this one out:

https://youtu.be/goaNAkoS97c
(some of my work on field lines using the Mandelbrot set. Storing and
loading data)

> In that points heading toward infinity will not be graphed, then orbital analysis is possible especially using a subset of the plane. That is what these graphics do. There is no escape criterion. Points which escape go off the graph. Admittedly there is a speedup in the code to skip that if they do escape, but all the initial test points are on this graph: they are the trace of a ray. That ray is fairly well obscured in this graphic.
>
> I call this graph a magnitude sweep, and as it clocks around various harmonics are exposed. Here in this one triples are showing up.
> All the points are graphed from z[0] to z[2000] in this case. These are what are filling in the space.

On Saturday, January 15, 2022 at 5:01:20 PM UTC-5, Chris M. Thomasson wrote:
> On 1/15/2022 5:56 AM, Timothy Golden wrote:
> > On Wednesday, January 12, 2022 at 4:21:14 PM UTC-5, Chris M. Thomasson wrote:
> >> On 1/12/2022 6:43 AM, Timothy Golden wrote:
> >>> On Monday, January 10, 2022 at 7:45:42 PM UTC-5, Chris M. Thomasson wrote:
> >>>> On 1/10/2022 5:14 AM, Timothy Golden wrote:
> >>>>> On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
> >>>>>> On 1/9/2022 12:59 PM, Timothy Golden wrote:
> >>>>>>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
> >>>>>> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
> >>>>>> 3-ary polysign should be able to create the Mandelbulb?
> >>>>>
> >>>>> That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
> >>>>> However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
> >>>>>
> >>>>> This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
> >>>>> The proper 3D shape is literally an extruded Mandelbrot set.
> >>>> Now that I think about it, you did mention that 3-ary polysign, not 2,
> >>>> is compatible with complex number! Sorry about that Tim.
> >>>>> This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
> >>>>>
> >>>>> Claims that the Mandelbulb is the natural extended form are suspect..
> >>>>> Sorry my claim is so boring though.
> >>>>>
> >>>> So, your 4-ary polysign, I think, should be able to get at something
> >>>> akin to the Mandelbulb. The triplex numbers do it, and I think your
> >>>> polysign should be able to do it. The escape time for a mandelbulb is a
> >>>> sphere instead of a circle.
> >>>
> >>> No Mandelbulb in P4, Chris.
> >>> It comes out as an extruded Mandelbrot set.
> >>> It's a disappointment, but according to the algebraic interpretation this is the correct result.
> >>> As well, up in P5, though we are in 4D, the result is simply two Mandelbrot sets crossed.
> >>> Possibly this projected will get some Mandelbulb sort of result.
> >>> I haven't done that projection yet though.
> >>> I have looked at slices and they are fairly good at exposing the thing.
> >>>
> >>> The idea of the mixed modulo is more a matter of handling exceptions and mimicing any pattern that is discovered.
> >>> In this way the notion of 'logic' gets corrupted and goes multidimensional.
> >>> The binary form as truth and falsehood is not necessarily a complete concept.
> >>> P1 is more akin to truth and it lacks any invert.
> >>> The naturally inverted form (binary) then is a two-state system, but it exists not as a sole contributor but in a family of these mixed modulo states.
> >>> P1 P2 P3 P4 P5 ...
> >>> To declare this form as 'logical' may simply mean that we assign unity values throughout.
> >>> Certainly ordinary Boolean logic does lack magnitude. Certainly it is a P2 style.
> >>> MU ( minus unity) stands in as fundamental.
> >>> engaging the extension from modulo two to modulo-three then poses a couple of choices.
> >>> Is -1+1 a possible P3 state as a superposition of two unital values? It happens that this is a unital value a well. At least in the magnitude space it can have magnitude. There are at least three possible constructions available here. The last is to ditch the discrete solutions and engage in continuum solutions. Still keeping with the unity concept this places P3 as the first continuum exhibit. P2 remains Boolean under these constraints. Going to an ordered series type of solution the above P3 option becomes:
> >>> ( 0, 1, 1 ) : ( @ 0 - 1 + 1 )
> >>> yet in P4 we will not see this possibility space generalize to:
> >>> ( 0, 0, 1, 1 )
> >>> because this value is not a unity magnitude.
> >>> It's a strange course to take so to remain with simple unital values such as:
> >>> ( 1, 0, 0, 0 ), ( 0, 1, 0, 0 ), ( 0, 0, 1, 0 ), ( 0, 0, 0, 1 )
> >>> which then covers the P4 possibilities remains simple... but for the overlap of the P2 mode with the P4 mode. This mixed modulo concept gets even more complicated, yet in terms of neuronal chains, say, the idea of a lockstep system that cycles through arbitrarily many stages interconnected to other such systems is easily constructed. Under this model order and memory are one. This may be a breakthrough concept. I did search for it on the internet and found nothing. That said, within the field of neural networking these concepts may be dowsed in some sublanguage unknown to me. It seems to me that the simplistic version listed above in P4 is not as likely as the mixed non-unity resultant. This is just a matter of respecting superposition as fundamental.
> >>>
> >>> To remain in a philosophy that only allows for Boolean logic to hold could be a terrible assumption. Is the truth Boolean? Ultimately truth is existence and all of its detail. Clearly existence is not Boolean. We need a richer system.
> >> Humm... Need some more time to give this a proper read Tim. Sorry! In
> >> the mean time, btw, have you taken a look at the following:
> >>
> >> https://www.soler7.com/Fractals/Matrices%20to%20Triplex.pdf
> >>
> >> http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/
> >>
> >>
> >> https://www.shadertoy.com/view/MdXSWn
> >> https://www.shadertoy.com/view/ltfSWn
> >> (mandelbulb code is in there)
> >>
> >> https://www.shadertoy.com/user/iq
> >> (very smart guy: indeed!)
> >
> > I actually just posed a question in another thread that seems close by to this concern:
> > https://groups.google.com/g/sci.math/c/RJadKuXvPvY
> > Some of the shader toy code has some type conversion errors.
> >
> > There is another class of fractal that I am supposedly exploring:
> > https://drive.google.com/file/d/1Vvqq2f_Ch6IozwNimJjcS4kw3tnVmtPd/view?usp=sharing
> > Pretty you've seen that though.
> Yes, I have seen that excellent plot: It's beautiful! I have to boot up
> my older computer because I have polysign implemented on it in C++. Or,
> I can just code it up again. I remember looking at some of your C code.
> Fwiw, check out this strange attractor:
>
> https://youtu.be/XKhS_nklCkE
> (I have pseudo code for it in the comments)
>
> Also, check this one out:
>
> https://youtu.be/goaNAkoS97c
> (some of my work on field lines using the Mandelbrot set. Storing and
> loading data)
> > In that points heading toward infinity will not be graphed, then orbital analysis is possible especially using a subset of the plane. That is what these graphics do. There is no escape criterion. Points which escape go off the graph. Admittedly there is a speedup in the code to skip that if they do escape, but all the initial test points are on this graph: they are the trace of a ray. That ray is fairly well obscured in this graphic.
> >
> > I call this graph a magnitude sweep, and as it clocks around various harmonics are exposed. Here in this one triples are showing up.
> > All the points are graphed from z[0] to z[2000] in this case. These are what are filling in the space.

It would actually be more meaningful if you perform the plot in your familiar complex number system using whatever software you normally use. This forms a cross check of the plot. P3 are the complex numbers. The same computation can be done in the complex plane.
Just pick a ray rotation and start marching away from the origin on that angle at a step of 0.0002. That will be about the right density to expose the image. Some color algorithm metric builds the colors, and I did get lucky on that color scheme, but it is basically coding the iteration number.

I guess the formula
z = - z z @ m
will require some adjustments since that sign is the P3 minus sign, but this is fairly trivial. I wouldn't worry too much about it. Maybe just try
z = i z z + m
in the complex numbers. That would be a more natural form in the complex plane.
We are just injecting a little bit of rotation into the product.
Getting some rich data hopefully.
These are polynomial functions as they expand out through the iterations:
z0 = 0 ; z1 = m; z2 = imm + m; z3 = ( imm+m)( imm+m) + m

On Sunday, January 9, 2022 at 3:59:16 PM UTC-5, Timothy Golden wrote:
> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.

I have come to the conclusion that humans are two-signed morons. Just one idea on how I escaped this: an early brain injury.
It will be sad when the AI have to tell you this so it is better that it comes from one of your own.

Timothy Golden wrote:

> I have come to the conclusion that humans are two-signed morons. Just
> one idea on how I escaped this: an early brain injury.
> It will be sad when the AI have to tell you this so it is better that it
> comes from one of your own.

now watch this capitalist_shit here. What capitalism does to your country.

Trudeau and MSNBC read from the same script
https://theduran.com/trudeau-and-msnbc-read-from-the-same-script/

https://arxiv.org/abs/2201.09738

On Friday, February 4, 2022 at 2:48:48 PM UTC-5, michael Rodriguez wrote:
> https://arxiv.org/abs/2201.09738
Wow. Thanks.

On Wednesday, January 12, 2022 at 9:43:44 AM UTC-5, Timothy Golden wrote:
> On Monday, January 10, 2022 at 7:45:42 PM UTC-5, Chris M. Thomasson wrote:
> > On 1/10/2022 5:14 AM, Timothy Golden wrote:
> > > On Sunday, January 9, 2022 at 11:24:54 PM UTC-5, Chris M. Thomasson wrote:
> > >> On 1/9/2022 12:59 PM, Timothy Golden wrote:
> > >>> Perhaps the lack of such is evidence for how humans have overlooked polysign numbers.
> > >> I am still wondering, if 2-ary polysign can create a Mandelbrot, then
> > >> 3-ary polysign should be able to create the Mandelbulb?
> > >
> > > That would be 3-ary to get the Mandelbrot (complex numbers) and 4-ary to get the Mandelbuld.
> > > However if you were to study the procedure on the 2-ary (the real numbers) you will find that you simply get back a rod.
> > >
> > > This 2-ary rod crossed with the 3-ary standard Mandelbrot set is actually what you get in the 4-ary case (P4 of polysign)
> > > The proper 3D shape is literally an extruded Mandelbrot set.
> > Now that I think about it, you did mention that 3-ary polysign, not 2,
> > is compatible with complex number! Sorry about that Tim.
> > > This is the algebraic approach; preserving associative, commutative, and distributive properties just as we are familiar with in the real and complex numbers.
> > >
> > > Claims that the Mandelbulb is the natural extended form are suspect.
> > > Sorry my claim is so boring though.
> > >
> > So, your 4-ary polysign, I think, should be able to get at something
> > akin to the Mandelbulb. The triplex numbers do it, and I think your
> > polysign should be able to do it. The escape time for a mandelbulb is a
> > sphere instead of a circle.
> No Mandelbulb in P4, Chris.
> It comes out as an extruded Mandelbrot set.
> It's a disappointment, but according to the algebraic interpretation this is the correct result.
> As well, up in P5, though we are in 4D, the result is simply two Mandelbrot sets crossed.
> Possibly this projected will get some Mandelbulb sort of result.
> I haven't done that projection yet though.
> I have looked at slices and they are fairly good at exposing the thing.
>
> The idea of the mixed modulo is more a matter of handling exceptions and mimicing any pattern that is discovered.
> In this way the notion of 'logic' gets corrupted and goes multidimensional.
> The binary form as truth and falsehood is not necessarily a complete concept.
> P1 is more akin to truth and it lacks any invert.
> The naturally inverted form (binary) then is a two-state system, but it exists not as a sole contributor but in a family of these mixed modulo states.
> P1 P2 P3 P4 P5 ...
> To declare this form as 'logical' may simply mean that we assign unity values throughout.
> Certainly ordinary Boolean logic does lack magnitude. Certainly it is a P2 style.
> MU ( minus unity) stands in as fundamental.
> engaging the extension from modulo two to modulo-three then poses a couple of choices.
> Is -1+1 a possible P3 state as a superposition of two unital values? It happens that this is a unital value a well. At least in the magnitude space it can have magnitude. There are at least three possible constructions available here. The last is to ditch the discrete solutions and engage in continuum solutions. Still keeping with the unity concept this places P3 as the first continuum exhibit. P2 remains Boolean under these constraints. Going to an ordered series type of solution the above P3 option becomes:
> ( 0, 1, 1 ) : ( @ 0 - 1 + 1 )
> yet in P4 we will not see this possibility space generalize to:
> ( 0, 0, 1, 1 )
> because this value is not a unity magnitude.
> It's a strange course to take so to remain with simple unital values such as:
> ( 1, 0, 0, 0 ), ( 0, 1, 0, 0 ), ( 0, 0, 1, 0 ), ( 0, 0, 0, 1 )
> which then covers the P4 possibilities remains simple... but for the overlap of the P2 mode with the P4 mode. This mixed modulo concept gets even more complicated, yet in terms of neuronal chains, say, the idea of a lockstep system that cycles through arbitrarily many stages interconnected to other such systems is easily constructed. Under this model order and memory are one. This may be a breakthrough concept. I did search for it on the internet and found nothing. That said, within the field of neural networking these concepts may be dowsed in some sublanguage unknown to me. It seems to me that the simplistic version listed above in P4 is not as likely as the mixed non-unity resultant. This is just a matter of respecting superposition as fundamental.
>
> To remain in a philosophy that only allows for Boolean logic to hold could be a terrible assumption. Is the truth Boolean? Ultimately truth is existence and all of its detail. Clearly existence is not Boolean. We need a richer system.

Just happened to reread this and was trying to double check whether I was speaking of (1,1,0,0) as of interest and it seems I was. I've completely left out the signon which requires these. Really it is the combinatorial set of these that I am speaking of. Let's use [a,b,c,d] as our combinatorial notation. [ 1 0 0 0 ] [ 1 1 0 0 ] [ 1 1 1 0 ] [ 1 1 1 1 ] are the signon. That the origin is in here now in this form could be taken as some sort of pre-zero attitude if we could just get rid of the other zeros. Can I just command that? Yes, I guess I can. We know already that we are working in P4. We can call up relative combinatorial systems so that [ 1 2 3 ] in Pn is well defined. In P5 there are 60 of these. [ 1 1 ] have just 10 places right? The signon has structure and it takes steps in every direction to land at the origin. Here we are ignoring the geometry and doing the combinatorics. They ring a little hollow relatively speaking. Everybody but tsms know that plus one star one and star one plus one are the same.

On Friday, February 4, 2022 at 2:48:48 PM UTC-5, michael Rodriguez wrote:
> https://arxiv.org/abs/2201.09738

Enjoying this and not working hard at it either. Very readable. Nice quote:
"• Historical Bias: Beyond just language, the influence of idiosyncratic cultural evolution
stretching millennia into the past can be easily recognized in present-day conventions and
customs. Modern science and mathematics are relatively recent inventions and, despite the
large volume of research output that already exists, only a minuscule fraction of the virtual
universe of all possible ideas has been charted. Given their relative simplicity alone, binary
structures are expected to be studied extensively before other higher arity generalizations are
explored."

Makes me feel like maybe the TSMs will recover?

On Saturday, February 5, 2022 at 2:16:02 PM UTC-5, Timothy Golden wrote:
> On Friday, February 4, 2022 at 2:48:48 PM UTC-5, michael Rodriguez wrote:
> > https://arxiv.org/abs/2201.09738
> Enjoying this and not working hard at it either. Very readable. Nice quote:
> "• Historical Bias: Beyond just language, the influence of idiosyncratic cultural evolution
> stretching millennia into the past can be easily recognized in present-day conventions and
> customs. Modern science and mathematics are relatively recent inventions and, despite the
> large volume of research output that already exists, only a minuscule fraction of the virtual
> universe of all possible ideas has been charted. Given their relative simplicity alone, binary
> structures are expected to be studied extensively before other higher arity generalizations are
> explored."
>
> Makes me feel like maybe the TSMs will recover?

On Saturday, February 5, 2022 at 2:16:02 PM UTC-5, Timothy Golden wrote:
> On Friday, February 4, 2022 at 2:48:48 PM UTC-5, michael Rodriguez wrote:
> > https://arxiv.org/abs/2201.09738
> Enjoying this and not working hard at it either. Very readable. Nice quote:
> "• Historical Bias: Beyond just language, the influence of idiosyncratic cultural evolution
> stretching millennia into the past can be easily recognized in present-day conventions and
> customs. Modern science and mathematics are relatively recent inventions and, despite the
> large volume of research output that already exists, only a minuscule fraction of the virtual
> universe of all possible ideas has been charted. Given their relative simplicity alone, binary
> structures are expected to be studied extensively before other higher arity generalizations are
> explored."
>
> Makes me feel like maybe the TSMs will recover?

"In the early stages of any field of enquiry, particularly those that push the boundaries of human
intuition as higher arity does, it is paramount that theoretical accounts do not venture too far away
from the phenomena they attempt to describe and that preliminary models remain in a tight feedback
loop with experiments. Successful development of higher arity science in the intellectual landscape
of the 21st century would require the merging of formal and empirical disciplines and the blurring of
boundaries between mathematics, science and computation. The transdisciplinary nature of higher
arity ideas is perhaps best illustrated by the potential application of irreducible arity as a measure of
atomic complexity or arity cohomology as a measure of emergent behaviour."

Incredible. They are practically admitting the human race are TSMs.