Tim, I would send you, directly to your house 'Infinitesimal Deformation Theory of Algebraic Structures'
https://studenttheses.uu.nl/bitstream/handle/20.500.12932/6833/NecasNiesserMA2010.pdf?sequence=1&isAllowed=y
due to your 'preference' for algebra, an also,infinitesimals...

https://www.youtube.com/watch?v=ysCNbUOXfbI&ab_channel=MoviesSound

I would say that will affect some possible table products (variations) of the p4 products also.
For example the K4 product (Klein four-group) is affected. The Pacman product with four elements is also affected.
And, in general, any product based on a latin square https://en.wikipedia.org/wiki/Latin_square is affected.
Although the pacman product for p4 is not a latin square, is a "semi-latin square".
And a latin or latin-like kind of product are preffered due to their symmetry.

in his 'Truly Hypercomplex Numbers: Unification of Numbers and Vectors', Redouane makes some comments on
short section 'Epistemological reasons standing behind mathematicians failure to find the hyperspherical
hypercomplex numbers - Main error of the previous attempts' (..and no zero-divs)
His system comply with all the properties of a field, EXCEPT, the distributive property (an important one)
https://arxiv.org/ftp/arxiv/papers/1409/1409.2757.pdf

I dont know, if this p4 aspect in observation has anything to do with the |a||b|=|ab| situation.
Also I dont know the relation of this p4 issue, and the the algorithm of the reciprocal of a Pn number.
Certainly in p6 there is more wood to cut. PLenty of combinatorics (for the combinatorial type of guys).

I am curious if there is other triangular (simplex) type of coordinates (or a spherical-simplex type of coordinates)
that can absorb and produce regular tetrahedron in a native way.

Anyway, I am pretty sure that given (a,b,c,d) is relatively easy to find the
other cancellative triplets, without p2 subcancellation, including for (1,1,0,0). I will inspect the formula
to do all possible cancelaltive partners of (a,b,c,d).

I would say that, is, not actually the product, but, the place where is engendered.

Mmm, I dont if is possible to differentiate if is a "cartesian assumption" or not. The best I can say is that is possible.

Neither Tarski nor Colonel Sanders

On Wednesday, July 26, 2023 at 5:46:43 PM UTC-4, Kentarski Freed Chikeng wrote:
> Tim, I would send you, directly to your house 'Infinitesimal Deformation Theory of Algebraic Structures'
> https://studenttheses.uu.nl/bitstream/handle/20.500.12932/6833/NecasNiesserMA2010.pdf?sequence=1&isAllowed=y
> due to your 'preference' for algebra, an also,infinitesimals...
>
> https://www.youtube.com/watch?v=ysCNbUOXfbI&ab_channel=MoviesSound
>
> I would say that will affect some possible table products (variations) of the p4 products also.
> For example the K4 product (Klein four-group) is affected. The Pacman product with four elements is also affected.
> And, in general, any product based on a latin square https://en.wikipedia..org/wiki/Latin_square is affected.
> Although the pacman product for p4 is not a latin square, is a "semi-latin square".
> And a latin or latin-like kind of product are preffered due to their symmetry.
>
> in his 'Truly Hypercomplex Numbers: Unification of Numbers and Vectors', Redouane makes some comments on
> short section 'Epistemological reasons standing behind mathematicians failure to find the hyperspherical
> hypercomplex numbers - Main error of the previous attempts' (..and no zero-divs)
> His system comply with all the properties of a field, EXCEPT, the distributive property (an important one)
> https://arxiv.org/ftp/arxiv/papers/1409/1409.2757.pdf
>
> I dont know, if this p4 aspect in observation has anything to do with the |a||b|=|ab| situation.
> Also I dont know the relation of this p4 issue, and the the algorithm of the reciprocal of a Pn number.
> Certainly in p6 there is more wood to cut. PLenty of combinatorics (for the combinatorial type of guys).
>
> I am curious if there is other triangular (simplex) type of coordinates (or a spherical-simplex type of coordinates)
> that can absorb and produce regular tetrahedron in a native way.
>
> Anyway, I am pretty sure that given (a,b,c,d) is relatively easy to find the
> other cancellative triplets, without p2 subcancellation, including for (1,1,0,0). I will inspect the formula
> to do all possible cancelaltive partners of (a,b,c,d).

Well, as I see it we have a continuum so you've managed to find the flattened tet, whereas a pure regular one is (1,0,0,0),
and so, if we simply consider the continuum between these two values, so that b in (a,b,c,d) grows from zero to one we'll see the squashing of that regular tet down to the plane in a continuous fashion. It is not a discrete behavior. What is fascinating about this to me is that you've exposed the pancaking behavior of the P4 product without really needing the full map; almost without needing the product at all.

There is possibly a chink in the armor to discuss, in that the geometrical interpretation of the simplex coordinate system as a match to polysign is an ontological chink. Is it observed? Yes. Is it derived? To what degree can we ever claim to be deriving a geometry from an algebra? Certainly it is consistent, and I can argue that it is far more consistent than the Cartesian form. Could it be that the interpretation of (1,1,1,1)=0 is embedded in this analysis? Definitely, it is. It is the cause of the geometry. It is as well the cause of your tet gone planar, though the connection is more mild.

The action of rotation really is what is to blame here, no? We know that P4 is more like circulating its coordinates as we do (MU^n)z. OK. I am starting to feel more like this is familiar, but the coordinate swap really does still make an impression. Especially because we have a purely symmetrical coordinate system. In effect we have a serious property of 4-ary symmetry. It happens to be the first non-prime as well.
Yes, it is connected to the magnitude breakage, to zero divisors, but you've managed to portray it without division and almost without the product. This view purely through the (a,b,c,d),(d,a,b,c),(c,d,a,b),(b,c,d,a) phenomenon exposes another very direct interpretation that is brand new to me. I am amazed. Still, we can state that this is a tetrahedron... is this dimensional analysis then? It may be a tet that is flat as a pancake, but the magnitude of the vertices is holding. Probably there is a name for that, and maybe that label 'deformation' from that paper by Floris Neˇcas-Niessner does matter, but nicely through polysign we have it all in an extremely fundamental and primitive package.

What a shame and a sham that mathematicians never saw the generalization of sign... until now.
Yes we are engaged in a progression, and yet at the same time as we face the accumulation, and I do feel it in that paper, I'd just as soon develop an interpretation from within polysign, which rests on so little that a lighter interpretation is unlikely to follow. Abstract algebra I regard as a compromised subject with ambiguities that are actually contradictory. Yet again, like the Cartesian product, and each does rely upon P2 as its basis, which is no general basis at all in hindsight of polysign, it is possible to attack the purity of the construction, especially in hindsight of polysign. Indeed this is my path to such conclusions.

As I've named it above, there is this slight concession in polysign, of its geometry as implied by its algebraic balance. But you see this is not a contradictory sort of step; it is a consistent step, and really as I focus on it we can call it a jump or a leap to arrive at it. Yet what other geometry is there? If there is another one then that is entirely relevant. We are all steeped in the Cartesian basis by habit and that I might still be suffering some invalid assumption by that habituation is entirely possible; likely, even. Still, the simplex coordinate system is in direct correspondence with polysign algebra and establishes a consistent n-dimensional algebra and geometry.

That zero divisors are inescapable comes from the very algebraic behaviors.... according to abstract algebra... and some day some bright fellow might be able to emplace this from the polysign perspective with a simplicity that cuts to the chase in a matter of a weeks worth of lectures rather than five years worth of lectures... all by generalizing the sign of the real number as we know it in this day. It seems to me that your current discovery is nearing this.

That you've merely shifted the coordinates... still magical to me... I'd like to see directly through it, but then is this a fundamental property of 3D space?

Tet( 1, 0, 0, 0) + Tet( 0, 1, 0, 0 ) = Tet( 1, 1, 0, 0 )
Tet( 0, 1, 0, 0 ) = MU Tet( 1, 0, 0, 0 )
Tet( 0, 1, 0, 0 ) == Tet( 1, 0, 0, 0 ) ?
No. Order matters. Yes, they are the same vertices, and perhaps then we are dealing with a graphical Euclidean bottleneck. We have a directed graph that we are visualizing as an unordered geometrical object. Does this fit?

>
> I would say that, is, not actually the product, but, the place where is engendered.
>
> Mmm, I dont if is possible to differentiate if is a "cartesian assumption" or not. The best I can say is that is possible.
>
> Neither Tarski nor Colonel Sanders

fredag 16 juni 2023 kl. 17:10:37 UTC+2 skrev Timothy Golden:
> ****************************************************
> Fri 16 Jun 2023 10:48:14 AM EDT sci.math
> Challenging the Cartesian product; particularly on things like RxR; or even the abstracted SxS: what good do two copies of the same exact set do? Well: in operator theory it seems this is critical, and without it the sum could barely exist. Group theory and its claims of closure want us to believe that the sum is a function mapping SxS back onto S. As I scrutinize the Cartesian product I find this nearly laughable. Indeed, the fact that the sum works in an n-ary fashion would suggest that we'll need SxSxS in order to consider a+b+c. Why can't they all simply belong to the same set, including the sum? Does simplicity rule mathematics? Is functional analysis king? Can you imagine a function devoid of sums and products within its construction? Isn't this a structural problem?
>
> Along the same lines, we know the utility of the Cartesian product when it comes to geometry. The (x,y) coordinate system has been entrained onto the entire schooled human race for some time now, along with a belief in the fundamental nature of the real number. Thus RxR as representing the plane, and I do believe that it does to the degree that the conventions implied, though not explicitly, are engaged en masse. Yet here I am breaking with the acceptance in order to dig a bit deeper. We know that physically this procedure comes to a halt at RxRxR don't we? We then claim that higher dimension spaces occur in say RxRxRxR, but the physical proof, which got us off the line and into the plane with another line at right angles to the first, is not going to occur. In hindsight should it be said that the line which was drawn indeed had a thickness and a width and that without these attributes the proof would not have been possible? Likewise the plane as represented on a piece of paper back into Euclidean antiquity, clean as that thought may be entrained in our minds; that the compass and the rule and the marker engaged were all three dimensional tools? Then too, that time enters into this mix, and even as a pure fourth and real value according to some... it's all a bit loaded.
>
> As if reality starts from a blank page... and this leads onto the first cosmological principle of isotropy... on average according to some who take great care, and tell me, what would anything average to but monochrome gray? No, I think they've mistaken their piece of paper for physical space, as if it is empty and devoid of matter. Just as physics begins by restricting to a few simple interactions, and preferably reduced to a singular dimension, they've taken the lever arm off the page completely and so they see isotropic space. Yet physical reality is not this at all. This is the only way that I can see such a blunderous mistake getting made that goes accepted not just by cosmologists, but by philosophers and mathematicians as well. Indeed the bounds between these supposed professions must be declared false when a more ultimate truth arrives.
>
> I consider my own ability to point to the big dipper as evidenciary proof against the first cosmological principal. And yet the source of this consideration is a long way around. Still, to declare that spacetime is structured; rather than isotropic; and indeed simply inserting unidirectional time as a fourth ought to deny the tensor its utility. The arbitrary reference frame sensibility of the three dimensional tensor is hereby destroyed and will only get recovered via a lightcone projection, and all of this never attempts to answer the puzzle of those three dimensions does it?
>
> To sit all of theory an empirical pegs is the next great blunder of modern thought; as if this thought actually has not even arrived yet... and indeed this may be our position. That we are engaged in a progression, but one whose accumulation leaves us lost in absorption of that pile rather than putting down the stepping stones for the next mile; really puts us all at odds with academia.
>
> I think that the vector of thought on whether the Cartesian coordinate system is observed or constructed may be a valid concern. Certainly the Cartesian set product claims independence of its components, yet when we arrive in the coordinate system we see an agreement to use perpendiculars, the same scale of units, and to orient two real lines such that their zeros intersect. Even then, all that we've arrived at is a supposedly pure description of geometry. To arrive in the inertial reference frame; a matter of the first derivative. Then too accelerations as force being the third derivative, and what... we stop there? Hmmm... an interesting way to three, isn't it?
>
> For a quick trick, let me introduce a modulo work space; one in which when you leave your paper you come out on the other side of the paper. This is not a trivial thing to engage in, but should our positions and velocities be arbitrary in some moment of creation, then the matter with equivalent momentum and velocity will congeal into larger masses (presuming gravity here), leaving much matter of other momenta and position. Could it be that a red shift would ensue? In effect, the matter which was colliding, having collided largely, essentially congealing, leaves an impression of matter spreading? I'm not sure of this at all, but perhaps it can stimulate somebody else's thought process.
>
> Moving back to fundamentals, we must accept that we do not construct multidimensional spaces actually with our representations that claim such. I can no more take two rulers and cross them and claim to have constructed a plane, though the thought holds up somewhat. It holds up to three rulers so long as they are not all coplanar. Of course all of this thinking has been done granting the fundamental nature of the real value, which is two-signed value, and the investigation of three-signed values and so forth has only just begun. One thing is for certain: nobody ever found emergent spacetime that way. In polysign is is done already in pure math; the true theoretical form.
What is the actual argument being put forward here? You don't buy Cartesian products of sets? Why?

Yep, Tim do not buy too much the cartesian product ;^)

a = b + c
(a,a,a,a) = (b,b,b,b) + (c,c,c,c)
(b,b,0,0) + (0,0,b,b) + (c,0,0,0) + (0,c,c,c) = (a,a,a,a)

By the way, it is possible to design yet another product, like
(-1)(*1) = (√(3/4)).( -1#1 )

Certainly, preserving the same magnitude is important
|(a,b,c,d,)| = k

with an arbitrary p4 number, dividing by reciprocal of it magnitude,
we get an unitary number (1/k)(a,b,c,d), thuis is , its modulus is always 1
|(1/k)(a,b,c,d)| = 1

|(1,1,0,0)| = √(4/3)

The compound of cube and octahedron share vertics with the rhombic dodecahedron
https://en.wikipedia.org/wiki/Compound_of_cube_and_octahedron

BAck to the topic, one approach could possibly study to separate the p4 quads is in pair of pairs like
(a,b,c,d) <--> ((a,c),(b,d))

I guess is strange seeing the transition from (1,0,0,0) to (1,1,0,0).
The itchy issue is that, is it coordinant dependent ? or what other geoemtrical aspect is imbued by this?

Certainly, it is tempting associate the circulation of components, its symmetry, to the regular tetrahedron.
Circulating/permutation seem are like primitive machinery. But strike this sort of "coordinate's dependency"
of an aspect that seem should not.

I would say that it depends on the product, but, more specifically, on a preproduct.
This "pre-product space" does not care on particular products, just on the final set,
this is, in being able to do a cycle, hamiltonian cycle in the case of minus unity.
But, it is the case that this pre-product space generate all the more interesting
and primitive and symmetric type of products.

After sailing here and there in river of theorems associated to the triangle, it is possible to
find at least, other tool, a sister tool

https://en.wikipedia.org/wiki/Sylvester%27s_triangle_problem
http://dynamicmathematicslearning.com/sylvester-general.html (interactive sample)

This is, one of the bros points in the triangle, the circumcenter. This machinery does not make
make use of permutation/circulating of coordinates, just the centroid.

In the case of four p4 number z1,z2,z3,z4, when reduced to having unitary modulus,
evaluate the study cases, for subgroups of two and three numbers.

This tool to getting through tee mud
https://www.youtube.com/watch?v=7jV5B2UIMAk&ab_channel=GlenSchult
https://www.youtube.com/watch?v=taSSpMGJoa4&ab_channel=BASCfilms

On Thursday, July 27, 2023 at 6:42:42 PM UTC-4, Kentarski Freed Chikeng wrote:
> Yep, Tim do not buy too much the cartesian product ;^)
>
>
> a = b + c
> (a,a,a,a) = (b,b,b,b) + (c,c,c,c)
> (b,b,0,0) + (0,0,b,b) + (c,0,0,0) + (0,c,c,c) = (a,a,a,a)
>
> By the way, it is possible to design yet another product, like
> (-1)(*1) = (√(3/4)).( -1#1 )
>
> Certainly, preserving the same magnitude is important
> |(a,b,c,d,)| = k
>
> with an arbitrary p4 number, dividing by reciprocal of it magnitude,
> we get an unitary number (1/k)(a,b,c,d), thuis is , its modulus is always 1
> |(1/k)(a,b,c,d)| = 1
>
> |(1,1,0,0)| = √(4/3)
>
> The compound of cube and octahedron share vertics with the rhombic dodecahedron
> https://en.wikipedia.org/wiki/Compound_of_cube_and_octahedron
>
> BAck to the topic, one approach could possibly study to separate the p4 quads is in pair of pairs like
> (a,b,c,d) <--> ((a,c),(b,d))
>
> I guess is strange seeing the transition from (1,0,0,0) to (1,1,0,0).
> The itchy issue is that, is it coordinant dependent ? or what other geoemtrical aspect is imbued by this?
>
> Certainly, it is tempting associate the circulation of components, its symmetry, to the regular tetrahedron.
> Circulating/permutation seem are like primitive machinery. But strike this sort of "coordinate's dependency"
> of an aspect that seem should not.
>
> I would say that it depends on the product, but, more specifically, on a preproduct.
> This "pre-product space" does not care on particular products, just on the final set,
> this is, in being able to do a cycle, hamiltonian cycle in the case of minus unity.
> But, it is the case that this pre-product space generate all the more interesting
> and primitive and symmetric type of products.
>
> After sailing here and there in river of theorems associated to the triangle, it is possible to
> find at least, other tool, a sister tool
>
> https://en.wikipedia.org/wiki/Sylvester%27s_triangle_problem
> http://dynamicmathematicslearning.com/sylvester-general.html (interactive sample)
>
> This is, one of the bros points in the triangle, the circumcenter. This machinery does not make
> make use of permutation/circulating of coordinates, just the centroid.
>
> In the case of four p4 number z1,z2,z3,z4, when reduced to having unitary modulus,
> evaluate the study cases, for subgroups of two and three numbers.
>
> This tool to getting through tee mud
> https://www.youtube.com/watch?v=7jV5B2UIMAk&ab_channel=GlenSchult
> https://www.youtube.com/watch?v=taSSpMGJoa4&ab_channel=BASCfilms

The case of z=(1,0,1,0) is even more troubling, but it brings us back to the realization that RxC, or P2P3 as embedded in P4:
( 1, 0, 1, 0 ) -> ( 0, 1, 0, 1 ) -> ( 1, 0, 1, 0 ) -> ( 0, 1, 0, 1 ) -> ( 1, 0, 1, 0 )...

If we allow our geometry to carry a bit more than the Euclidean form, then we will still see a tetrahdron here, but it is now doubled over on itself in a most compromised position. In a way, as you substitute (1,1,1,1) for z, you could argue further compactification, but this is the zero dimensional case.

I think what matters is how we interpret these details. One blanket truth is that we are in a nonorthogonal coordinate system. The fact is we started out knowing that (1,1,1,1)=0. We learn from this that any value (a,b,c,d) can actually be reduced by one component by zeroing the form (I like this terminology; like zeroing a meter...) and so arguably the 'three dimensional' nature of P4 is still upheld generally. This reasoning is done by the same rule that develops the real value (P2) where (1,1)=0, or in sign language -1+1=0, or if you prefer -a+a=0. As we use the ordered series representation we know that the sign action is of sliding through the structure and back around to the other side again. In this regard a more clever graphical representation would form a ring, but this is not our common method. It would almost be like inserting a glyph with a count to go back five characters or some such in this text like <ret-5> or some such markup, which would then bulk this text out rather a lot geometrically each time we encounter an ordered series value.

For those who regard the ordered series form (a,b,c,d) as inherently orthogonal: no: here it is not. As to the geometry that is then imposed: in P2 it forms a line. In P3 it forms a plane. In P4 it forms a volumetric space. In Pn n rays exit an origin outward to the n vertices of a simpled centered on that origin. This is the geometry that is coherent to the algebra. Its symmetry is perfect, but that symmetry is broken by sign behavior under product. The # ray of P4 in product has no action; it is neutral. The - ray is the inverse of the * ray, in that one 'rotates' around one way, while the other reverses that effect, though this is the same as jumping by three through the modulo structure. Clearly the active '+' ray is peculiar in P4, in that it jumps two and so never visits the other two. But these are actions under product. It would seem as though all that Kentarski has done here is swap coordinates, and in this regard he has preserved symmetry. The four rays are perfectly symmetrical no matter how you drew them in your reference tetrahedron, so why aren't his four shifted coordinates perfectly symmetrical to the basis? Why do we expect that they should form a tetrahedron and why do we expect that tetrahedron to be regular? I confess I feel that this should be the case, based on my intuition. But the proof is clearly won by Kentarski that this is not the case.

I feel pretty sure that I am being played like a fish. Like here is the bait, and I don't see any hook... but it's in there. Gump; yummy. I'm afraid that I have swallowed already the bait, so please set the hook! Perhaps your line will snap when you do...

I suspect Kentarski knows how to build that regular tetrahedron that we fondle expectantly in our mind, only to witness some pancaked version.

Let's see now: reverse the course by asking can we build a regular tetrahdron from (a,b,c,d), knowing that simply Muing does not guarantee it? Back to the latin square I suppose?
(a,b,c,d) -> (a,c,b,d) -> (a,c,d,b) -> (c,a,d,b) ?
What a strange state of affairs. In the world of perfect symmetry, Mu will not Do. Somehow I think my answer is broken still. Fraid I broke symmetry too much there.

The whole thing is further contaminated: as we set out to actually perform the graphics we freely assign the vertices of the tet to, well, their signs, which I guess it could be said that we simply 'assign the tet'. The arbitrary nature of this assignment, given that asymmetrical action of the signs under product, implies that we are not dealing in an isotropic space. No. Given that this space has actions, and in the past I have called them rotational, though by Kentarski this has to get put into quotes as 'rotational'.... and I am forced to agree here... compelled, really, though I don't mean by a twisted arm as has become the norm by my cuntry... no... we are doing something actually honorable here; not just stuffing dollar bills down our trousers... it may always be true that the best works are done for free... though our naivete is probably about as bad as the fish's was. Still, it is a pleasure to work this way I think. We are right down in the ontological mud, and I think I prefer the boards tied to the feet rather than the fancy new plastics.

Ah. Should I have reduced the coordinates to say (a,b,c,0)? No, Tim, you should have reduced the coordinates to (a,a,0,0)...
(a,a,0,0) -> (a,0,a,0) -> (0,a,a,0) -> (0,0,a,a) ?
Still fishing. Sorry. There are only so many ways to do this though. Seems there will always be an inverse. So
tet(MU) +MU(tet(MU)) != tet(MU)

Hah! Does this mean we are studying z-z here? That could be pretty cool...

I guess four avenues are presented here, follow this idiosyncracy of minus unity, also,
research another path different of the minus unity, or, research some generalization/modification
of the minus unity for all quads (a,b,c,d), or even some other type of unconventional p4 product.

Is it the nature of permutation themselves? are n-roots of unity exclusively related to permutations?

If I ask you Tim, suppose that you had notice this much much earlier in your path, would you have researched
to the extent that you did? (without knowing it)

Is it that cancellation/symmetry describable natively in other coordinate system ? or is it that
a regular-simplex type-of-arrangement is possible without using permutation ?

Is this affecting other family of coordinates that can be related to simplex ? (like trilinear, barycentric
synergetics or anharmonic).

Ok. A solution is possible (for p3) using vector substration, vector negation, vector resizing(scalar multipication),
law of sines and p3 reduction. Basically, given a random unitary p3 number (a,b,c), it is possible to get a good aproximation
of (c,a,b) and (b,c,a), without permuting/circling components. Notice here I am using vector as interchangeable word for
a p3 number. The solution goes on finding a perpendicular vector to (a,b,c), a sort of SubPn-1 (p2 in this case) plane.
The solution is "vectorial", with aid of planar geometry. Obviously, there are easy configurations (specific cases)
where can find its permutation "without permuting". But the important here is for any p3 number.

Now, the solution exist, and is sure that exist many other type of solutions, but, not only a solution is
the important issue, also, what machinery that have been used to solve it. For example, using a dot(or cross) product
may be 'not proper' here. Other issue is that the method of solution needs to be generalizable to p4.
In any case, redundancy of solutions is useful here.

I dont know if some other type of generalizable solution could be got by means of the steiner ellipse
https://en.wikipedia.org/wiki/Steiner_ellipse this is, given three distinct unitary p3 numbers, chose one of them, keep that chosen p3 number (and the centroid), and after, "regularise" the steiner ellipse into a circle, meaning, the other two p3 number "get straighten"
into a equilateral triangle type-of disposition.

related topics https://en.wikipedia.org/wiki/Marden%27s_theorem https://en..wikipedia.org/wiki/Steiner_inellipse

On Tuesday, August 1, 2023 at 5:45:36 PM UTC-4, Kentarski Freed Chikeng wrote:
> I guess four avenues are presented here, follow this idiosyncracy of minus unity, also,
> research another path different of the minus unity, or, research some generalization/modification
> of the minus unity for all quads (a,b,c,d), or even some other type of unconventional p4 product.
>
> Is it the nature of permutation themselves? are n-roots of unity exclusively related to permutations?
>
> If I ask you Tim, suppose that you had notice this much much earlier in your path, would you have researched
> to the extent that you did? (without knowing it)
>
> Is it that cancellation/symmetry describable natively in other coordinate system ? or is it that
> a regular-simplex type-of-arrangement is possible without using permutation ?
>
> Is this affecting other family of coordinates that can be related to simplex ? (like trilinear, barycentric
> synergetics or anharmonic).

I don't view polysign as broken by these behaviors. If anything they are the breakpoint that develops emergent spacetime showing up again. What we see is that:
P1 P2 P3 | P4 P5 P6 ...
we have a natural arithmetic breakpoint. I predict we'll have the same effect in P5, though P5 is prime and possibly is protected from this phenomenon.. To generalize sign is to follow these details out and study their side-effects.

Does another construction exist? I don't think so; no. But in the ontological theory of an exterior versus interior space; one by which we exist in the interior of our physical spacetime; essentially its prisoners; then it is a matter of coming up with this supposed construction from thin air. Polysign simply asks what happens when we generalize sign, and it comes up with these answers. It comes up with nonorthogonal geometry as directly as could be asked for; as directly as the real line delivered it. Polysign delivers general dimensional algebra with nearly no effort. As well it delivers us this breakpoint, and with it the promise of an emergent spacetime basis from pure arithmetic. We are not off in some esoteric branch of 'advanced' mathematics. We are down in the simplest of ground here. We are at the roots, sir. We got the complex number there in P3 by the same rules that develop P2 as the reals. We've got P1 to boot: relieving the time pradox by yielding an accurate geometrical representative. This idea that spacetime is a geometry is satisfied in a new way in polysign because of the zero dimensional aspect of P1. This tells us that spacetime is structured; not isotropic. In other words polysign and its followers reject the first cosmological principal from ground that is abstract; yet does in fact yield this as an observation. That P4 has structure: can we at least make this statement of it? Certainly it is in the sign behavior; the sign product; that this happens. We see the broken symmetry of the signs and their modulo behaviors by:
( s1 x1 ) ( s2 x2 ) = (s1@s2) x1x2

Yet, by your construction here of the mus of (1,1,0,0), and really we can say that of a general z that the mus of z will not generate a regular tet!
It's fabulous! This perfectly symmetrical coordinate system of perfect balance can do this? It still gets me. I can't quite see through it. I do see part way through it, but I do feel like there is a bit more interpretation to do. I get why you linked to that deformation paper. Here though, we are getting the behavior at such a base level. I see how you'd almost declare, 'see, I broke polysign!', yet, no, nothing is really broken. Well, could we declare that you have found flat z in P4? That there are round z in P4? And then a few line z in P4? And of course there is everything in between too.. This sort of interpretation would be consistent with admitting that P4 has structure. In other words there is detail, though the symmetry is perfect.. No, I'm not feeling great about declaring this paragraph as something I'll stand on. Your view through permutations and so forth is apt, but to what degree does it take us away from the fundamental mathematics? It is my hope that polysign can remain free-standing without the need to transfuse the blood of some other animal into them.

I am trying to follow you below here, which carries on from above. You know, other systems don't even have this ability to slide through the coordinate file. It is a luxury of polysign that we simply can coordinate through mu all of the coordinates. It's so interesting that there is a confluence of geometry and algebra... and something else? Please do carry on. I'm trying to follow you. At some level the simplex coordinate system has correspondence, but it is exact correspondence, isn't it? I think so. Still, this does not exclude some other geometry, if it could be found.

>
>
> Ok. A solution is possible (for p3) using vector substration, vector negation, vector resizing(scalar multipication),
> law of sines and p3 reduction. Basically, given a random unitary p3 number (a,b,c), it is possible to get a good aproximation
> of (c,a,b) and (b,c,a), without permuting/circling components. Notice here I am using vector as interchangeable word for
> a p3 number. The solution goes on finding a perpendicular vector to (a,b,c), a sort of SubPn-1 (p2 in this case) plane.
> The solution is "vectorial", with aid of planar geometry. Obviously, there are easy configurations (specific cases)
> where can find its permutation "without permuting". But the important here is for any p3 number.
>
> Now, the solution exist, and is sure that exist many other type of solutions, but, not only a solution is
> the important issue, also, what machinery that have been used to solve it.. For example, using a dot(or cross) product
> may be 'not proper' here. Other issue is that the method of solution needs to be generalizable to p4.
> In any case, redundancy of solutions is useful here.
>
> I dont know if some other type of generalizable solution could be got by means of the steiner ellipse
> https://en.wikipedia.org/wiki/Steiner_ellipse this is, given three distinct unitary p3 numbers, chose one of them, keep that chosen p3 number (and the centroid), and after, "regularise" the steiner ellipse into a circle, meaning, the other two p3 number "get straighten"
> into a equilateral triangle type-of disposition.
>
> related topics https://en.wikipedia.org/wiki/Marden%27s_theorem https://en.wikipedia.org/wiki/Steiner_inellipse

mmm, the deformation of algebraic structure article was an offtopic joke. I know that you dont like too much algebraic strucutres, and I thought that infinitesimal deformation of such mathematical objects would have been like the icing of cake, so to speak.

No, actually it has the advantage side. Otherwise every p4 point would have infinite cancellations. The permutation topic kind of reduce the sign rotations to just one family, multiplication-wise.

On Wednesday, August 2, 2023 at 3:02:28 PM UTC-4, Kentarski Freed Chikeng wrote:
> mmm, the deformation of algebraic structure article was an offtopic joke. I know that you dont like too much algebraic strucutres, and I thought that infinitesimal deformation of such mathematical objects would have been like the icing of cake, so to speak.
>
> No, actually it has the advantage side. Otherwise every p4 point would have infinite cancellations. The permutation topic kind of reduce the sign rotations to just one family, multiplication-wise.
Yes, I think I get what you mean. All organized in mu, basically. This idea that minus one is more fundamental than plus one is obscured by the history of the real number... and the lack of general thought when it came to sign. How lucky we don't have to alter the notation too badly to get going. But then there at P3 we see the identity sign change form, so it is short lived.

I'm still baffled: each sign component proceeds to the next position in the structure; the geometry of the rays could even be swapped about in their perfect symmetry within the graphical rendering; well, just once of course at the onset of the graphical rendering, and out comes a flat tet in nmuz form. Let's see now: MU^n z = (n mu) z, though the n has changed form here. Best of all it is z-z that is flat... what a riot... Hmmm...

what if z = -1+2*3? z-z = - 1 + 2 * 3 + 1 * 2 # 3 = - 1 + 3 * 5 # 3 = + 2 * 4 # 2.
z = -1+2*4 : z-z= -1 + 3 * 6 # 4 = + 2 * 5 # 3
Not flat, right? Of course it's probably not a regular tet, either. It will likely have some deformation. It's really MU-MU that got you there; not z-z. You probably see more going on here than I do. The miff really is felt when we consider that the rays are perfectly symmetrical and balanced with each other. But for the product there isn't really anything distinguishing them from each other. We have (1,1,1,1)=0, or -1+1*1#1=0, or (a,a,a,a)=0, if you like, and even (z,z,z,z)=0. Is this latter interesting to you? It really does conjure up 16 components. If we go to the form (z1,z2,z3,z4) have we achieved a matrix? Are we going to be doing linear algebra with it? The idea of getting coordinate reference frames in an arbitrary basis has not actually been done yet. For my rotating projections in the code I go back to Cartesian, then do the rotation. Of course ultimately we've got to project down to (x,y) Cartesian coordinates. It does sort of remind me of your division algorithm. Beyond me. Maybe going back to square just doesn't interest me as much as getting triangular P1P2P3|P4P5...

I do feel there is plenty that could be done. We're not getting very far. If we don't see your result in P5 then couldn't we admit that this is a prime defect rather than the product defect? It would be like having two breakpoints there rather than the one that I am basically a zombie to. I do hope you take offence the the term 'defect', but if you think about it like defecting from Hitler's army then maybe it comes more true. Without a defect we will not have emergent spacetime, or another type of interpretation would be required.

Thinking of the multiples of MU and the circulation of signs geometrically.... and it is very difficult to visualize P4. Even as we go through the signs we see their broken symmetry in terms of product; the - and * being complementary and the + doing its own skip and the neutral #. In P5 we have none of that. I guess I could whip together some code that would measure the angle amongst random z in Pn through say P20. That would get us a map. A random z is likely to be out of round somewhat and so the angles amongst MU^nz will show through... somehow... well relative to the unit tet, which is cleanly built from z= (1,0,0,0).

El jueves, 3 de agosto de 2023 a las 12:38:11 UTC-4, Timothy Golden escribió:
> On Wednesday, August 2, 2023 at 3:02:28 PM UTC-4, Kentarski Freed Chikeng wrote:
> > mmm, the deformation of algebraic structure article was an offtopic joke. I know that you dont like too much algebraic strucutres, and I thought that infinitesimal deformation of such mathematical objects would have been like the icing of cake, so to speak.
> >
> > No, actually it has the advantage side. Otherwise every p4 point would have infinite cancellations. The permutation topic kind of reduce the sign rotations to just one family, multiplication-wise.
> Yes, I think I get what you mean. All organized in mu, basically. This idea that minus one is more fundamental than plus one is obscured by the history of the real number... and the lack of general thought when it came to sign. How lucky we don't have to alter the notation too badly to get going. But then there at P3 we see the identity sign change form, so it is short lived.
>
> I'm still baffled: each sign component proceeds to the next position in the structure; the geometry of the rays could even be swapped about in their perfect symmetry within the graphical rendering; well, just once of course at the onset of the graphical rendering, and out comes a flat tet in nmuz form. Let's see now: MU^n z = (n mu) z, though the n has changed form here. Best of all it is z-z that is flat... what a riot... Hmmm...
>
> what if z = -1+2*3? z-z = - 1 + 2 * 3 + 1 * 2 # 3 = - 1 + 3 * 5 # 3 = + 2 * 4 # 2.
> z = -1+2*4 : z-z= -1 + 3 * 6 # 4 = + 2 * 5 # 3
> Not flat, right? Of course it's probably not a regular tet, either. It will likely have some deformation. It's really MU-MU that got you there; not z-z. You probably see more going on here than I do. The miff really is felt when we consider that the rays are perfectly symmetrical and balanced with each other. But for the product there isn't really anything distinguishing them from each other. We have (1,1,1,1)=0, or -1+1*1#1=0, or (a,a,a,a)=0, if you like, and even (z,z,z,z)=0. Is this latter interesting to you? It really does conjure up 16 components. If we go to the form (z1,z2,z3,z4) have we achieved a matrix? Are we going to be doing linear algebra with it? The idea of getting coordinate reference frames in an arbitrary basis has not actually been done yet. For my rotating projections in the code I go back to Cartesian, then do the rotation. Of course ultimately we've got to project down to (x,y) Cartesian coordinates. It does sort of remind me of your division algorithm. Beyond me. Maybe going back to square just doesn't interest me as much as getting triangular P1P2P3|P4P5...
>
> I do feel there is plenty that could be done. We're not getting very far. If we don't see your result in P5 then couldn't we admit that this is a prime defect rather than the product defect? It would be like having two breakpoints there rather than the one that I am basically a zombie to. I do hope you take offence the the term 'defect', but if you think about it like defecting from Hitler's army then maybe it comes more true. Without a defect we will not have emergent spacetime, or another type of interpretation would be required.
>
> Thinking of the multiples of MU and the circulation of signs geometrically... and it is very difficult to visualize P4. Even as we go through the signs we see their broken symmetry in terms of product; the - and * being complementary and the + doing its own skip and the neutral #. In P5 we have none of that. I guess I could whip together some code that would measure the angle amongst random z in Pn through say P20. That would get us a map. A random z is likely to be out of round somewhat and so the angles amongst MU^nz will show through... somehow... well relative to the unit tet, which is cleanly built from z= (1,0,0,0).

Some features are pertaining only to n-dimensions, where n+1 being only an even number, other when n+1 is a compound number

There a lot of developable paths. From the quadrays wiki, shows that
you can circle (2,1,1,0) and you obtain vertices in a square arrangement also,
they belong to the cuboctahedron. Notice that (1,1,0,0) + (1,0,1,0) = (2,1,1,0)
The cub-octahedron can be considered a sort of middle term between the octahedron
and the cube. If instead of starting with the vertices (1,0,0,0) of a regular tet,
you may use also the vertices of a regular dodecahedron (in other way a compound of
tetrahedrons and, a sort of cube on steroids). The regular tetrahedron include the
vertices of a regular tet, but each vertice cancellate with other three points also(two tets per vertex)
The icosidodecahedron by the convex hull can be considered a compound of five octahedra
https://en.wikipedia.org/wiki/Compound_of_five_octahedra (full cartesian pack in 3d)
in a similar vein as the cuboctahedron can be considered a compound of three squares.

Also the cuboctahedron, taking (2,1,1,0), you can fix the 'one' of the second (or the third)
component, a circling the rest of the component, and you get a regular triangle.
fixing the one of the second component (2,1,1,0) , (0,1,2,1) , (1,1,0,2)
or fixing the one of the third component (2,1,1,0) , (0,2,1,1) , (1,0,1,2)

Well, the thing with (z,z,z,z), that I interpret as circling or "muing" any p4 number is that you contemplating
at the same time all the whole range of possibilities from (1,1,0,0) to (1,0,0,0) and in between.
For the moment, an unfinished business is given a arbitrary p4 number z, get all the posible families
of points that cancellate in a regular tet disposition, but also, in all the possible square disposition
regarding the point being considered.

It says "The regular tetrahedron include the vertices of a regular tet, but each...", it shoud say " "The regular dodecahedron includes the vertices of a regular tet, but each..."

On Thursday, August 3, 2023 at 4:34:47 PM UTC-4, Kentarski Freed Chikeng wrote:
> For the moment, an unfinished business is given a arbitrary p4 number z, get all the posible families
> of points that cancellate in a regular tet disposition, but also, in all the possible square disposition
> regarding the point being considered.

I would thing that the RxC method will expose them as on that circle. Well, then again, maybe not.
I really just wanted to run another concept by you while the internet is still working, and of course, have you on the other end of it with it working too.

I fits better the larger scheme of this thread. Typically we build up from the simplest things to develop more complicated things. The natural numbers for instance we consider start with unity and work their way upward, but in the case of dimension possibly it is a time to ponder the reversal of this. From existence, and by this I mean physical existence, we must arrive in the accepted three dimensions or some alternative that mimics them. To claim that we came from below is the obvious form:
P1 P2 P3
but to claim that we got from up high and came down and stopped there is another option:
... P6 P5 P4 | P3 P2 P1
and this would be more of a residue theory, and it would suggest that the material from which we started in high dimension could be considerably simpler than the residue which is left behind, here in my current position now, for instance.

I am a terrible house keeper no matter how clean I keep my math. The other oddity that this theory accommodates is a return to orthogonality without sign, as you know in high Pn the vertex angles approach 90 degrees. If I didn't scrooge the math already at P1000 we have 89.943 degrees.
Up here in high sign we have lots of room and everything could have its place without much worry of bumping into anything else. Indeed we would like I think to see it extremely organized from the get-go; something like MU^n which I guess could be called mun, especially since MU^n and (mu)(n) are the same thing, carefully interpreted, of course, and then we maybe would actually want a defect to occur; a sort of little snap rather than a big bang, and the dimensional collapse begins. The sum is naught so far, and that is good. We would like to get something from nothing, and the next best thing is to get something from nearly nothing. It is an exotic way to get it, but in its profound complexity suggests that in the tradeoff the utter simplicity of the initial condition could be thus. Then perhaps atomic theory could lay to the other side of P4; in P4+. It is extremely abstract, but in terms of continuum space versus discrete dimension and the loading that we land in coming from down low to engage the infinite; and not necessarily the actually infinite here; Such a model might have an N figure and we would no doubt wind up zoning down onto it just as there are claims of the number of atoms in the universe; but no doubt that N figure would be very large. To claim that there would be dramatic consequences between 10^82 and 10^81, for instance, is not likely. It is almost like calculus will generally work out very good at n=10000. Well, now that is solvable, isn't it?

On Saturday, August 5, 2023 at 12:32:44 PM UTC-4, Timothy Golden wrote:
> On Thursday, August 3, 2023 at 4:34:47 PM UTC-4, Kentarski Freed Chikeng wrote:
> > For the moment, an unfinished business is given a arbitrary p4 number z, get all the posible families
> > of points that cancellate in a regular tet disposition, but also, in all the possible square disposition
> > regarding the point being considered.
> I would thing that the RxC method will expose them as on that circle. Well, then again, maybe not.
> I really just wanted to run another concept by you while the internet is still working, and of course, have you on the other end of it with it working too.
>
> I fits better the larger scheme of this thread. Typically we build up from the simplest things to develop more complicated things. The natural numbers for instance we consider start with unity and work their way upward, but in the case of dimension possibly it is a time to ponder the reversal of this. From existence, and by this I mean physical existence, we must arrive in the accepted three dimensions or some alternative that mimics them. To claim that we came from below is the obvious form:
> P1 P2 P3
> but to claim that we got from up high and came down and stopped there is another option:
> ... P6 P5 P4 | P3 P2 P1
> and this would be more of a residue theory, and it would suggest that the material from which we started in high dimension could be considerably simpler than the residue which is left behind, here in my current position now, for instance.
>
> I am a terrible house keeper no matter how clean I keep my math. The other oddity that this theory accommodates is a return to orthogonality without sign, as you know in high Pn the vertex angles approach 90 degrees. If I didn't scrooge the math already at P1000 we have 89.943 degrees.
> Up here in high sign we have lots of room and everything could have its place without much worry of bumping into anything else. Indeed we would like I think to see it extremely organized from the get-go; something like MU^n which I guess could be called mun, especially since MU^n and (mu)(n) are the same thing, carefully interpreted, of course, and then we maybe would actually want a defect to occur; a sort of little snap rather than a big bang, and the dimensional collapse begins. The sum is naught so far, and that is good. We would like to get something from nothing, and the next best thing is to get something from nearly nothing. It is an exotic way to get it, but in its profound complexity suggests that in the tradeoff the utter simplicity of the initial condition could be thus. Then perhaps atomic theory could lay to the other side of P4; in P4+. It is extremely abstract, but in terms of continuum space versus discrete dimension and the loading that we land in coming from down low to engage the infinite; and not necessarily the actually infinite here; Such a model might have an N figure and we would no doubt wind up zoning down onto it just as there are claims of the number of atoms in the universe; but no doubt that N figure would be very large. To claim that there would be dramatic consequences between 10^82 and 10^81, for instance, is not likely. It is almost like calculus will generally work out very good at n=10000. Well, now that is solvable, isn't it?

I didn't mean to get too carried away here. The evolution of such a system is not stated at all yet, but we do know of a phenomenon in polysign of dimensional collapse. The idea that we start from up high and work our way down... down to what? Here we stop at three; not zero. We reach the breakpoint the other way around. Now, this thinking has its equivalent in the natural numbers, but the thought process is a matter of inverting them. This does intersect set theory as well, and as I mention these diverse ideas clung together in a couple of sentences then they need to be pulled away from each other, and of course the natural number will bottom out at one, or even at none if you can accommodate the one as well. There lays a discrete discovery versus a continuous discovery. Hmmm. Arguably the system that lands at none, at least within this thinking, is continuous in nature. The system that lands in one is of another category. This actually does fit the categories of infinity that I had been working on.

So probably somebody already developed this thinking, as we know that set theory sometimes discusses the universe. The thing is their universe is already a sequestered construction of a simple set. Well, I should not stuff too many words into their mouths. I apologize. The universe here, as the source of set theory, is the physical universe. Not only the source of set theory, but the source of a natural value theory, and a continuous value theory.. By coming down from up high... it carries a direct sense of truth about it in that as you focus on one golf ball, say, sitting at the top of your keyboard between the f6 and f7 keys; now nudged over to the f7 and f8 keys, the inpression that this golf ball does in fact exist in a universe, and while you may count golf balls locally on your desk top and acquire a nice easy natural value, the true superset of the universe is not practically countable, though crude estimates might be made, and the definition of a golf ball will come into focus. Now, in the oneness of that singular golf ball at the top of your keyboard, we have acquired the sensibility of the natural number, but its physicality is in its nondivisible nature. Rather than hacking into the golf ball and unwinding that obnoxious rubber band that is sitting under that profoundly strong outer skin, just simply take it in your hand away from the keyboard, and we'll see that there are no golf balls left on your keyboard. But did the golf ball disappear? No: this is not a physical reality: things don't just disappear like that. And so you see that the makings of set theory and the universe are still present here. As we study golf balls on the keyboard (put back first golf ball f7f8, add second golf ball f9f10) its pretty clear that this set of golf balls is a subset of the universe. This achieves a definitional conception of a set as a subset, which is more truthful to physical reality than is the set which magically appears and has say three objects in it, and then another set appears with just two of those objects, as if physics did not matter one iota.

The cause of truth within this mindset is physical reality; the universe. Even within an attempt to isolate one being out of the universe, and here I'll use myself: Tim Golden; there I did it, right? Well, there are other Tim Goldens in the universe. One writes for the NYT. Another is a linux programmer our of Dover NH. Now that one might have stolen my identity, but that is the sort of thing that the deep state has need for. For the most part he's kept a low profile and I keep a low profile, and as to which we are discussing: this is a matter of definition. This idea of definition itself as encompassing the universe of possibilities really exposes the linguistic barrier as well as the local limitations. As we come to the need for new words that nobody else will speak then we arrive in a system like polysign numbers, which only a small handfull of people seem to understand. As they have led me around the branches of mathematics to arrive at this fairly fresh but relevant position.

Anytime a teacher is going to attempt the natural numbers with physical correspondence there is going to be a boundary established. This boundary would be one view of set theory. It is very unlikely that the prof will be discussing sheep in the universe, because it will be a large quantity that is unknown. Could you imagine a system which keeps repeating within its definitional stage 'the quantity of which is large and unknown'? Perhaps it follows that definitions require a unital form, yet the very utility of the definition is typically because there are many of them and so the need for the qualification. I guess it really isn't necessary even to dwell here and try to come up with a conviction of thought. That the option exists is enough, and possibly that is where I should have gone: can the natural numbers be defined from high to low? We certainly bump into plenty of people fixated on infinity when we develop them the other way around. Why shouldn't there be as many fixated on unity when we invert? Now there is a sensible solution!

I do not what to say or how to proceed.But it is always nice
when things under the radar come to the surface. It s like
when security is all around, uncertanty knocks your door, so
to speak.

For the moment you may code an study, similar to the spherical
product study, where a point travels through a loxodrome of the
sphere, but, this time, is to study the three permutation's tetrahedron
in each point, for visual purposes. For that effect, also is possible
to calculate the six edges of the tetrahedron, calculating the magnitude
of z @ ~permut(z) for each edge, but it is not necessary.

On the other side, the guys that where developing more exclusively regarding
the context of triangular coordinates, that were much more connected
with coordinates, probably missed, although, they were aware that
that some permutations induced flat, but, by some breadth of the serendipity,
they were not situated in the context of , what you call, sign.

I do not what to say. Expecting some though of the deep comes to surface.

On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed Chikeng wrote:
> I do not what to say or how to proceed.But it is always nice
> when things under the radar come to the surface. It s like
> when security is all around, uncertanty knocks your door, so
> to speak.
>
> For the moment you may code an study, similar to the spherical
> product study, where a point travels through a loxodrome of the
> sphere, but, this time, is to study the three permutation's tetrahedron
> in each point, for visual purposes. For that effect, also is possible
> to calculate the six edges of the tetrahedron, calculating the magnitude
> of z @ ~permut(z) for each edge, but it is not necessary.
>
> On the other side, the guys that where developing more exclusively regarding
> the context of triangular coordinates, that were much more connected
> with coordinates, probably missed, although, they were aware that
> that some permutations induced flat, but, by some breadth of the serendipity,
> they were not situated in the context of , what you call, sign.
>
> I do not what to say. Expecting some though of the deep comes to surface.
Unless specilized academics not necessarily the mathematicians themselves realize the absurd & abnormal fictionality of the negative & immaginary as well, they would be certainly damn astray

Physicists generally don't realize the danger upon their theoretical sensible science that is purely sourced from the false refuted mathematics about a real belived number & much more fictions about mathematical existing objects like the non-existing angles for instance

So to say, no theoretical sciences would go true with many false inhireted beliefs among mathematicians where so unfortunately Physicists try to comply with

In fact, the basic principle which mathematics itself based on is a real number, which is infact purely physical as being a "distance ", where also three orthogonal distances forms the dimentionl space that every existing object must necessarily belong to

In shorter words, mathematics must not be left freely for mathematicians, since they are allowing illegally every insane academic 🧌 Trolls to establish whatever their imaganative desires into many contradictory frames, where they talk about physics much more than physicians do

Which is why physics is becoming a mere victims of many delusional mathematicians

It is the suitable times to realize how many fictional beliefs had been well-refuted in sci.math that usually mathematicians inhereted & so unfortunately aren't aware of nor do they want to confess openly & globally for keeping their meaningless business & the illegall control on physical theoretical sciences by means of usefulness & practicality

The evil 😈 is there & so obvious in human established mathematical knowledge for sure

🔊 Bassam Karzeddin 🔊

On Friday, August 11, 2023 at 10:58:32 PM UTC-4, bassam karzeddin wrote:
> On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed Chikeng wrote:
> > I do not what to say or how to proceed.But it is always nice
> > when things under the radar come to the surface. It s like
> > when security is all around, uncertanty knocks your door, so
> > to speak.
> >
> > For the moment you may code an study, similar to the spherical
> > product study, where a point travels through a loxodrome of the
> > sphere, but, this time, is to study the three permutation's tetrahedron
> > in each point, for visual purposes. For that effect, also is possible
> > to calculate the six edges of the tetrahedron, calculating the magnitude
> > of z @ ~permut(z) for each edge, but it is not necessary.
> >
> > On the other side, the guys that where developing more exclusively regarding
> > the context of triangular coordinates, that were much more connected
> > with coordinates, probably missed, although, they were aware that
> > that some permutations induced flat, but, by some breadth of the serendipity,
> > they were not situated in the context of , what you call, sign.
> >
> > I do not what to say. Expecting some though of the deep comes to surface.
> Unless specilized academics not necessarily the mathematicians themselves realize the absurd & abnormal fictionality of the negative & immaginary as well, they would be certainly damn astray
>
> Physicists generally don't realize the danger upon their theoretical sensible science that is purely sourced from the false refuted mathematics about a real belived number & much more fictions about mathematical existing objects like the non-existing angles for instance
>
> So to say, no theoretical sciences would go true with many false inhireted beliefs among mathematicians where so unfortunately Physicists try to comply with
>
> In fact, the basic principle which mathematics itself based on is a real number, which is infact purely physical as being a "distance ", where also three orthogonal distances forms the dimentionl space that every existing object must necessarily belong to
>
> In shorter words, mathematics must not be left freely for mathematicians, since they are allowing illegally every insane academic 🧌 Trolls to establish whatever their imaganative desires into many contradictory frames, where they talk about physics much more than physicians do
>
> Which is why physics is becoming a mere victims of many delusional mathematicians
>
> It is the suitable times to realize how many fictional beliefs had been well-refuted in sci.math that usually mathematicians inhereted & so unfortunately aren't aware of nor do they want to confess openly & globally for keeping their meaningless business & the illegall control on physical theoretical sciences by means of usefulness & practicality
>
> The evil 😈 is there & so obvious in human established mathematical knowledge for sure
>
> 🔊 Bassam Karzeddin 🔊

Thanks Kentarski, and King Bassam.

The term 'reductionsim' comes to mind as we consider developing number from the top down. Nicely enough, we can land in discrete terms and in continuous terms as we do so. If we find the need to assign an arbitrary unity to arrive with a unit then we have a continuous system. If we find that a unital object exists then we have a discrete form. Polysign numbers is a marriage of the two: sx, where s is discrete sign, and x is continuous magnitude. The idea that these would develop from the largess and that we must subset that universe in order to do our discovery is acceptable I think from a philosophical perspective. We would admit our place as a locality within a very large system that we wonder about. This is a physical method of arriving at mathematics. We dismantle reality to arrive in mathematics; reality encompassing the observable universe. What would be most lovely is to wind up with derived atoms and electrons and photons from this theoretical perspective. It is one thing to find an emergent spacetime basis, and it is another to find space-time-matter. From the bottom up the former does appear. Possibly from the top down the latter can be had.

In effect, this top down theory, in its confession of cosmological existence, denies the separation of the branches of philosophy, mathematics, and physics. These are provably false divisions, and so the entire mindset of modern academia can be put aside. 'as a fraud' I almost wrote here on the tail of that sentence, but I'm trying to be less inflammatory these days. Sometimes it feels like these may be our last days as current events develop. So it is a good time to get such thoughts out rather than hoard them. Please do use it freely, and claim it for your own if you must, but here possibly a record does exist that can provide some accountability. Still, ideas do not really have owners once they are unleashed. They stand freely on their own, if they are strong enough.

On Sunday, August 13, 2023 at 12:31:47 AM UTC+3, Timothy Golden wrote:
> On Friday, August 11, 2023 at 10:58:32 PM UTC-4, bassam karzeddin wrote:
> > On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed Chikeng wrote:
> > > I do not what to say or how to proceed.But it is always nice
> > > when things under the radar come to the surface. It s like
> > > when security is all around, uncertanty knocks your door, so
> > > to speak.
> > >
> > > For the moment you may code an study, similar to the spherical
> > > product study, where a point travels through a loxodrome of the
> > > sphere, but, this time, is to study the three permutation's tetrahedron
> > > in each point, for visual purposes. For that effect, also is possible
> > > to calculate the six edges of the tetrahedron, calculating the magnitude
> > > of z @ ~permut(z) for each edge, but it is not necessary.
> > >
> > > On the other side, the guys that where developing more exclusively regarding
> > > the context of triangular coordinates, that were much more connected
> > > with coordinates, probably missed, although, they were aware that
> > > that some permutations induced flat, but, by some breadth of the serendipity,
> > > they were not situated in the context of , what you call, sign.
> > >
> > > I do not what to say. Expecting some though of the deep comes to surface.
> > Unless specilized academics not necessarily the mathematicians themselves realize the absurd & abnormal fictionality of the negative & immaginary as well, they would be certainly damn astray
> >
> > Physicists generally don't realize the danger upon their theoretical sensible science that is purely sourced from the false refuted mathematics about a real belived number & much more fictions about mathematical existing objects like the non-existing angles for instance
> >
> > So to say, no theoretical sciences would go true with many false inhireted beliefs among mathematicians where so unfortunately Physicists try to comply with
> >
> > In fact, the basic principle which mathematics itself based on is a real number, which is infact purely physical as being a "distance ", where also three orthogonal distances forms the dimentionl space that every existing object must necessarily belong to
> >
> > In shorter words, mathematics must not be left freely for mathematicians, since they are allowing illegally every insane academic 🧌 Trolls to establish whatever their imaganative desires into many contradictory frames, where they talk about physics much more than physicians do
> >
> > Which is why physics is becoming a mere victims of many delusional mathematicians
> >
> > It is the suitable times to realize how many fictional beliefs had been well-refuted in sci.math that usually mathematicians inhereted & so unfortunately aren't aware of nor do they want to confess openly & globally for keeping their meaningless business & the illegall control on physical theoretical sciences by means of usefulness & practicality
> >
> > The evil 😈 is there & so obvious in human established mathematical knowledge for sure
> >
> > 🔊 Bassam Karzeddin 🔊
> Thanks Kentarski, and King Bassam.
>
> The term 'reductionsim' comes to mind as we consider developing number from the top down. Nicely enough, we can land in discrete terms and in continuous terms as we do so. If we find the need to assign an arbitrary unity to arrive with a unit then we have a continuous system. If we find that a unital object exists then we have a discrete form. Polysign numbers is a marriage of the two: sx, where s is discrete sign, and x is continuous magnitude.. The idea that these would develop from the largess and that we must subset that universe in order to do our discovery is acceptable I think from a philosophical perspective. We would admit our place as a locality within a very large system that we wonder about. This is a physical method of arriving at mathematics. We dismantle reality to arrive in mathematics; reality encompassing the observable universe. What would be most lovely is to wind up with derived atoms and electrons and photons from this theoretical perspective. It is one thing to find an emergent spacetime basis, and it is another to find space-time-matter. From the bottom up the former does appear. Possibly from the top down the latter can be had.
>
> In effect, this top down theory, in its confession of cosmological existence, denies the separation of the branches of philosophy, mathematics, and physics. These are provably false divisions, and so the entire mindset of modern academia can be put aside. 'as a fraud' I almost wrote here on the tail of that sentence, but I'm trying to be less inflammatory these days. Sometimes it feels like these may be our last days as current events develop. So it is a good time to get such thoughts out rather than hoard them. Please do use it freely, and claim it for your own if you must, but here possibly a record does exist that can provide some accountability. Still, ideas do not really have owners once they are unleashed. They stand freely on their own, if they are strong enough.

I see the mere space itself as "nothingness " where there maybe no meaning to ask why does the space exist endlessly without a boundary? Almost the same for the time!

The puzzling matter how any from of energy comes suddenly into existence withen space?

As per pure mathematics, space does have some mathematical properties that Phythagorus theorem uncovered about three orthogonal distances intersecting at a location that framed the space with positions & locations, where every existing object is formed by distances,such that an arbitrary unity exiting distance can be a true measure of any other existing object
But so unfortunately, nither the smallest distance nor the longest distance ever exists in complete analogy with number properties, as If the whole matter of existence is something illusionary in human minds only

But I think the secrets are their lying behind the many solvable Diaphontine Equations that we hardly know a little about them 🤔

It seems too puzzling when theoretical physics try to explain itself like mathematics!

BKK

On 8/12/2023 5:23 PM, bassam karzeddin wrote:
> On Sunday, August 13, 2023 at 12:31:47 AM UTC+3, Timothy Golden wrote:
>> On Friday, August 11, 2023 at 10:58:32 PM UTC-4, bassam karzeddin wrote:
>>> On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed Chikeng wrote:
>>>> I do not what to say or how to proceed.But it is always nice
>>>> when things under the radar come to the surface. It s like
>>>> when security is all around, uncertanty knocks your door, so
>>>> to speak.
>>>>
>>>> For the moment you may code an study, similar to the spherical
>>>> product study, where a point travels through a loxodrome of the
>>>> sphere, but, this time, is to study the three permutation's tetrahedron
>>>> in each point, for visual purposes. For that effect, also is possible
>>>> to calculate the six edges of the tetrahedron, calculating the magnitude
>>>> of z @ ~permut(z) for each edge, but it is not necessary.
>>>>
>>>> On the other side, the guys that where developing more exclusively regarding
>>>> the context of triangular coordinates, that were much more connected
>>>> with coordinates, probably missed, although, they were aware that
>>>> that some permutations induced flat, but, by some breadth of the serendipity,
>>>> they were not situated in the context of , what you call, sign.
>>>>
>>>> I do not what to say. Expecting some though of the deep comes to surface.
>>> Unless specilized academics not necessarily the mathematicians themselves realize the absurd & abnormal fictionality of the negative & immaginary as well, they would be certainly damn astray
>>>
>>> Physicists generally don't realize the danger upon their theoretical sensible science that is purely sourced from the false refuted mathematics about a real belived number & much more fictions about mathematical existing objects like the non-existing angles for instance
>>>
>>> So to say, no theoretical sciences would go true with many false inhireted beliefs among mathematicians where so unfortunately Physicists try to comply with
>>>
>>> In fact, the basic principle which mathematics itself based on is a real number, which is infact purely physical as being a "distance ", where also three orthogonal distances forms the dimentionl space that every existing object must necessarily belong to
>>>
>>> In shorter words, mathematics must not be left freely for mathematicians, since they are allowing illegally every insane academic 🧌 Trolls to establish whatever their imaganative desires into many contradictory frames, where they talk about physics much more than physicians do
>>>
>>> Which is why physics is becoming a mere victims of many delusional mathematicians
>>>
>>> It is the suitable times to realize how many fictional beliefs had been well-refuted in sci.math that usually mathematicians inhereted & so unfortunately aren't aware of nor do they want to confess openly & globally for keeping their meaningless business & the illegall control on physical theoretical sciences by means of usefulness & practicality
>>>
>>> The evil 😈 is there & so obvious in human established mathematical knowledge for sure
>>>
>>> 🔊 Bassam Karzeddin 🔊
>> Thanks Kentarski, and King Bassam.
>>
>> The term 'reductionsim' comes to mind as we consider developing number from the top down. Nicely enough, we can land in discrete terms and in continuous terms as we do so. If we find the need to assign an arbitrary unity to arrive with a unit then we have a continuous system. If we find that a unital object exists then we have a discrete form. Polysign numbers is a marriage of the two: sx, where s is discrete sign, and x is continuous magnitude. The idea that these would develop from the largess and that we must subset that universe in order to do our discovery is acceptable I think from a philosophical perspective. We would admit our place as a locality within a very large system that we wonder about. This is a physical method of arriving at mathematics. We dismantle reality to arrive in mathematics; reality encompassing the observable universe. What would be most lovely is to wind up with derived atoms and electrons and photons from this theoretical perspective. It is one thing to find an emergent spacetime basis, and it is another to find space-time-matter. From the bottom up the former does appear. Possibly from the top down the latter can be had.
>>
>> In effect, this top down theory, in its confession of cosmological existence, denies the separation of the branches of philosophy, mathematics, and physics. These are provably false divisions, and so the entire mindset of modern academia can be put aside. 'as a fraud' I almost wrote here on the tail of that sentence, but I'm trying to be less inflammatory these days. Sometimes it feels like these may be our last days as current events develop. So it is a good time to get such thoughts out rather than hoard them. Please do use it freely, and claim it for your own if you must, but here possibly a record does exist that can provide some accountability. Still, ideas do not really have owners once they are unleashed. They stand freely on their own, if they are strong enough.
>
> I see the mere space itself as "nothingness " where there maybe no meaning to ask why does the space exist endlessly without a boundary? Almost the same for the time!
>
> The puzzling matter how any from of energy comes suddenly into existence withen space?
>
> As per pure mathematics, space does have some mathematical properties that Phythagorus theorem uncovered about three orthogonal distances intersecting at a location that framed the space with positions & locations, where every existing object is formed by distances,such that an arbitrary unity exiting distance can be a true measure of any other existing object
> But so unfortunately, nither the smallest distance nor the longest distance ever exists in complete analogy with number properties, as If the whole matter of existence is something illusionary in human minds only
>
> But I think the secrets are their lying behind the many solvable Diaphontine Equations that we hardly know a little about them 🤔
>
> It seems too puzzling when theoretical physics try to explain itself like mathematics!
Math can be fun:
https://youtu.be/hnRZepld6dg
Math for the graphics _and_ the music. Fun!
:^D

On 8/12/2023 6:24 PM, Chris M. Thomasson wrote:
> On 8/12/2023 5:23 PM, bassam karzeddin wrote:
>> On Sunday, August 13, 2023 at 12:31:47 AM UTC+3, Timothy Golden wrote:
>>> On Friday, August 11, 2023 at 10:58:32 PM UTC-4, bassam karzeddin wrote:
>>>> On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed
>>>> Chikeng wrote:
>>>>> I do not what to say or how to proceed.But it is always nice
>>>>> when things under the radar come to the surface. It s like
>>>>> when security is all around, uncertanty knocks your door, so
>>>>> to speak.
>>>>>
>>>>> For the moment you may code an study, similar to the spherical
>>>>> product study, where a point travels through a loxodrome of the
>>>>> sphere, but, this time, is to study the three permutation's
>>>>> tetrahedron
>>>>> in each point, for visual purposes. For that effect, also is possible
>>>>> to calculate the six edges of the tetrahedron, calculating the
>>>>> magnitude
>>>>> of z @ ~permut(z) for each edge, but it is not necessary.
>>>>>
>>>>> On the other side, the guys that where developing more exclusively
>>>>> regarding
>>>>> the context of triangular coordinates, that were much more connected
>>>>> with coordinates, probably missed, although, they were aware that
>>>>> that some permutations induced flat, but, by some breadth of the
>>>>> serendipity,
>>>>> they were not situated in the context of , what you call, sign.
>>>>>
>>>>> I do not what to say. Expecting some though of the deep comes to
>>>>> surface.
>>>> Unless specilized academics not necessarily the mathematicians
>>>> themselves realize the absurd & abnormal fictionality of the
>>>> negative & immaginary as well, they would be certainly damn astray
>>>>
>>>> Physicists generally don't realize the danger upon their theoretical
>>>> sensible science that is purely sourced from the false refuted
>>>> mathematics about a real belived number & much more fictions about
>>>> mathematical existing objects like the non-existing angles for instance
>>>>
>>>> So to say, no theoretical sciences would go true with many false
>>>> inhireted beliefs among mathematicians where so unfortunately
>>>> Physicists try to comply with
>>>>
>>>> In fact, the basic principle which mathematics itself based on is a
>>>> real number, which is infact purely physical as being a "distance ",
>>>> where also three orthogonal distances forms the dimentionl space
>>>> that every existing object must necessarily belong to
>>>>
>>>> In shorter words, mathematics must not be left freely for
>>>> mathematicians, since they are allowing illegally every insane
>>>> academic 🧌 Trolls to establish whatever their imaganative desires
>>>> into many contradictory frames, where they talk about physics much
>>>> more than physicians do
>>>>
>>>> Which is why physics is becoming a mere victims of many delusional
>>>> mathematicians
>>>>
>>>> It is the suitable times to realize how many fictional beliefs had
>>>> been well-refuted in sci.math that usually mathematicians inhereted
>>>> & so unfortunately aren't aware of nor do they want to confess
>>>> openly & globally for keeping their meaningless business & the
>>>> illegall control on physical theoretical sciences by means of
>>>> usefulness & practicality
>>>>
>>>> The evil 😈 is there & so obvious in human established mathematical
>>>> knowledge for sure
>>>>
>>>> 🔊 Bassam Karzeddin 🔊
>>> Thanks Kentarski, and King Bassam.
>>>
>>> The term 'reductionsim' comes to mind as we consider developing
>>> number from the top down. Nicely enough, we can land in discrete
>>> terms and in continuous terms as we do so. If we find the need to
>>> assign an arbitrary unity to arrive with a unit then we have a
>>> continuous system. If we find that a unital object exists then we
>>> have a discrete form. Polysign numbers is a marriage of the two: sx,
>>> where s is discrete sign, and x is continuous magnitude. The idea
>>> that these would develop from the largess and that we must subset
>>> that universe in order to do our discovery is acceptable I think from
>>> a philosophical perspective. We would admit our place as a locality
>>> within a very large system that we wonder about. This is a physical
>>> method of arriving at mathematics. We dismantle reality to arrive in
>>> mathematics; reality encompassing the observable universe. What would
>>> be most lovely is to wind up with derived atoms and electrons and
>>> photons from this theoretical perspective. It is one thing to find an
>>> emergent spacetime basis, and it is another to find
>>> space-time-matter. From the bottom up the former does appear.
>>> Possibly from the top down the latter can be had.
>>>
>>> In effect, this top down theory, in its confession of cosmological
>>> existence, denies the separation of the branches of philosophy,
>>> mathematics, and physics. These are provably false divisions, and so
>>> the entire mindset of modern academia can be put aside. 'as a fraud'
>>> I almost wrote here on the tail of that sentence, but I'm trying to
>>> be less inflammatory these days. Sometimes it feels like these may be
>>> our last days as current events develop. So it is a good time to get
>>> such thoughts out rather than hoard them. Please do use it freely,
>>> and claim it for your own if you must, but here possibly a record
>>> does exist that can provide some accountability. Still, ideas do not
>>> really have owners once they are unleashed. They stand freely on
>>> their own, if they are strong enough.
>>
>> I see the mere space itself as "nothingness " where there maybe no
>> meaning to ask why does the space exist endlessly without a boundary?
>> Almost the same for the time!
>>
>> The puzzling matter how any from of energy comes suddenly into
>> existence withen space?
>>
>> As per pure mathematics, space does have some mathematical properties
>> that Phythagorus theorem uncovered about three orthogonal distances
>> intersecting at a location that framed the space with positions &
>> locations, where every existing object is formed by distances,such
>> that an arbitrary unity exiting distance can be a true measure of any
>> other existing object
>> But so unfortunately, nither the smallest distance nor the longest
>> distance ever exists in complete analogy with number properties, as If
>> the whole matter of existence is something illusionary in human minds
>> only
>>
>> But I think the secrets are their lying behind the many solvable
>> Diaphontine Equations that we hardly know a little about them 🤔
>>
>> It seems too puzzling when theoretical physics try to explain itself
>> like mathematics!
>
> Math can be fun:
>
> https://youtu.be/hnRZepld6dg
>
> Math for the graphics _and_ the music. Fun!
>
> :^D
>

HD res:

https://youtu.be/Gm0NWMdcbmU

On Saturday, August 12, 2023 at 8:23:28 PM UTC-4, bassam karzeddin wrote:
> On Sunday, August 13, 2023 at 12:31:47 AM UTC+3, Timothy Golden wrote:
> > On Friday, August 11, 2023 at 10:58:32 PM UTC-4, bassam karzeddin wrote:
> > > On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed Chikeng wrote:
> > > > I do not what to say or how to proceed.But it is always nice
> > > > when things under the radar come to the surface. It s like
> > > > when security is all around, uncertanty knocks your door, so
> > > > to speak.
> > > >
> > > > For the moment you may code an study, similar to the spherical
> > > > product study, where a point travels through a loxodrome of the
> > > > sphere, but, this time, is to study the three permutation's tetrahedron
> > > > in each point, for visual purposes. For that effect, also is possible
> > > > to calculate the six edges of the tetrahedron, calculating the magnitude
> > > > of z @ ~permut(z) for each edge, but it is not necessary.
> > > >
> > > > On the other side, the guys that where developing more exclusively regarding
> > > > the context of triangular coordinates, that were much more connected
> > > > with coordinates, probably missed, although, they were aware that
> > > > that some permutations induced flat, but, by some breadth of the serendipity,
> > > > they were not situated in the context of , what you call, sign.
> > > >
> > > > I do not what to say. Expecting some though of the deep comes to surface.
> > > Unless specilized academics not necessarily the mathematicians themselves realize the absurd & abnormal fictionality of the negative & immaginary as well, they would be certainly damn astray
> > >
> > > Physicists generally don't realize the danger upon their theoretical sensible science that is purely sourced from the false refuted mathematics about a real belived number & much more fictions about mathematical existing objects like the non-existing angles for instance
> > >
> > > So to say, no theoretical sciences would go true with many false inhireted beliefs among mathematicians where so unfortunately Physicists try to comply with
> > >
> > > In fact, the basic principle which mathematics itself based on is a real number, which is infact purely physical as being a "distance ", where also three orthogonal distances forms the dimentionl space that every existing object must necessarily belong to
> > >
> > > In shorter words, mathematics must not be left freely for mathematicians, since they are allowing illegally every insane academic 🧌 Trolls to establish whatever their imaganative desires into many contradictory frames, where they talk about physics much more than physicians do
> > >
> > > Which is why physics is becoming a mere victims of many delusional mathematicians
> > >
> > > It is the suitable times to realize how many fictional beliefs had been well-refuted in sci.math that usually mathematicians inhereted & so unfortunately aren't aware of nor do they want to confess openly & globally for keeping their meaningless business & the illegall control on physical theoretical sciences by means of usefulness & practicality
> > >
> > > The evil 😈 is there & so obvious in human established mathematical knowledge for sure
> > >
> > > 🔊 Bassam Karzeddin 🔊
> > Thanks Kentarski, and King Bassam.
> >
> > The term 'reductionsim' comes to mind as we consider developing number from the top down. Nicely enough, we can land in discrete terms and in continuous terms as we do so. If we find the need to assign an arbitrary unity to arrive with a unit then we have a continuous system. If we find that a unital object exists then we have a discrete form. Polysign numbers is a marriage of the two: sx, where s is discrete sign, and x is continuous magnitude. The idea that these would develop from the largess and that we must subset that universe in order to do our discovery is acceptable I think from a philosophical perspective. We would admit our place as a locality within a very large system that we wonder about. This is a physical method of arriving at mathematics. We dismantle reality to arrive in mathematics; reality encompassing the observable universe. What would be most lovely is to wind up with derived atoms and electrons and photons from this theoretical perspective. It is one thing to find an emergent spacetime basis, and it is another to find space-time-matter. From the bottom up the former does appear. Possibly from the top down the latter can be had.
> >
> > In effect, this top down theory, in its confession of cosmological existence, denies the separation of the branches of philosophy, mathematics, and physics. These are provably false divisions, and so the entire mindset of modern academia can be put aside. 'as a fraud' I almost wrote here on the tail of that sentence, but I'm trying to be less inflammatory these days. Sometimes it feels like these may be our last days as current events develop.. So it is a good time to get such thoughts out rather than hoard them. Please do use it freely, and claim it for your own if you must, but here possibly a record does exist that can provide some accountability. Still, ideas do not really have owners once they are unleashed. They stand freely on their own, if they are strong enough.
> I see the mere space itself as "nothingness " where there maybe no meaning to ask why does the space exist endlessly without a boundary? Almost the same for the time!
>
> The puzzling matter how any from of energy comes suddenly into existence withen space?

It's good feedback Bassam. I do think that your mindset is how they wind up insisting that space is isotropic, and stay mum on spacetime as isotropic. Is it valid to falsify your position by explaining that spacetime is not empty? Every early physics problem starts out with a couple of objects and works out their interactions, preferably even in one dimension for simplicity. Before you jotted down those objects onto the paper the space was empty; a blank sheet of paper. Meanwhile that planar sheet of paper is sitting on a desk, let's say, which is in a room, which is on the surface of a sphere at around 293K, and remarkably stable, presuming you aren't in Ukraine at the moment, and presuming that war doesn't grow much worse.
This is to say that empty space is not empty, and furthermore that supposedly 2D representation you are working on is still in 3D space, which is how your tools come to its surface and your vision allows its interpretation. In cosmology much the same happens: as they attempt to prove that the universe is isotropic they are forced to gray out the matter! Careful renditions will explain that on average the universe is isotropic, and I doubt if you'll find much that isn't under that condition. This falsification is very direct. Isn't the alternative to admit that the universe is structured? That we can point say to the big dipper on a clear night is evidence that the universe is not isotropic, for an isotropic universe would appear gray, and that is what they did when they averaged out the structure. I think it might be different if we claimed that the universe is balanced, or somehow retain the qualities of physical spacetime as we witness them from our locality, but really I'm not sure that the universe is balanced; the large scale structure is established as well, and you'll even see that the careful ones who attempt to uphold the first cosmological principle even have a figure, which I suppose wipes out those tendrilly web structures that apparently emerge at large scale. It is utterly ridiculous to carry on like that.

I see that set theory from the start under this new way feels good. Given the overwhelming qualities of the universe we would like to work with a portion that we can make sense of, or that makes sense on its own, preferably. This would be known as a high quality subset. Yet here from the get-go we see that the word 'set' is unnecessary. Already we are in a subset. In effect set and subset are the same thing. This is as it works from the top down. From the bottom up we'll see other forms, and I don't believe that I'll be falsifying those so readily as the first principle, but we can remark on the quality of them as realistic. When for instance the Greeks derived the atom, that was a pretty serious claim of a subset system. And of course that gnawing awareness of continuous versus discrete is there. As well all of our modern knowledge of molecular qualities and subatomic constituents too, which you could argue falsify it if you like. Whatever: the atom is a high quality set theory, and the Greeks got it from the top down, or at least they never proved it physically by isolating an atom. An atom of apple was more their thinking, as I recall.

Counting apples on a tree is obviously a subset concept. It is really two subset contexts: one is the selection of the type of fruit, and the other is the volume of space from which you are going to work. Giving up either of these we are going to encounter difficulty. The idea that the natural number has no hope of resolution without these somewhat complexifies its physical correspondence. In some regards we could admit that every natural number that has physical significance must carry around such 'units' and that for instance to forgo them we will have no trouble adding the number of apples on that tree to the number of sheep in a field and will feel none the stupider. Such a denial: is this what forms pure mathematics? This way of looking at things has such power. The divorce of mathematics from physical reality was not such a great move. It has provided some of the best minds the means to escape the problems that we need them working on. The naming conventions are terrible. To claim that natural and discrete are equivalent in meaning is horrible; that real and continuous are synonymous is grotesque. No: real and natural are perfectly wonderful things, as are discrete and continuous. And then there is the term 'ring'. Ohhh, what have they done?

On Saturday, August 12, 2023 at 5:31:47 PM UTC-4, Timothy Golden wrote:
> On Friday, August 11, 2023 at 10:58:32 PM UTC-4, bassam karzeddin wrote:
> > On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed Chikeng wrote:
> > > I do not what to say or how to proceed.But it is always nice
> > > when things under the radar come to the surface. It s like
> > > when security is all around, uncertanty knocks your door, so
> > > to speak.
> > >
> > > For the moment you may code an study, similar to the spherical
> > > product study, where a point travels through a loxodrome of the
> > > sphere, but, this time, is to study the three permutation's tetrahedron
> > > in each point, for visual purposes. For that effect, also is possible
> > > to calculate the six edges of the tetrahedron, calculating the magnitude
> > > of z @ ~permut(z) for each edge, but it is not necessary.
> > >
> > > On the other side, the guys that where developing more exclusively regarding
> > > the context of triangular coordinates, that were much more connected
> > > with coordinates, probably missed, although, they were aware that
> > > that some permutations induced flat, but, by some breadth of the serendipity,
> > > they were not situated in the context of , what you call, sign.
> > >
> > > I do not what to say. Expecting some though of the deep comes to surface.
> > Unless specilized academics not necessarily the mathematicians themselves realize the absurd & abnormal fictionality of the negative & immaginary as well, they would be certainly damn astray
> >
> > Physicists generally don't realize the danger upon their theoretical sensible science that is purely sourced from the false refuted mathematics about a real belived number & much more fictions about mathematical existing objects like the non-existing angles for instance
> >
> > So to say, no theoretical sciences would go true with many false inhireted beliefs among mathematicians where so unfortunately Physicists try to comply with
> >
> > In fact, the basic principle which mathematics itself based on is a real number, which is infact purely physical as being a "distance ", where also three orthogonal distances forms the dimentionl space that every existing object must necessarily belong to
> >
> > In shorter words, mathematics must not be left freely for mathematicians, since they are allowing illegally every insane academic 🧌 Trolls to establish whatever their imaganative desires into many contradictory frames, where they talk about physics much more than physicians do
> >
> > Which is why physics is becoming a mere victims of many delusional mathematicians
> >
> > It is the suitable times to realize how many fictional beliefs had been well-refuted in sci.math that usually mathematicians inhereted & so unfortunately aren't aware of nor do they want to confess openly & globally for keeping their meaningless business & the illegall control on physical theoretical sciences by means of usefulness & practicality
> >
> > The evil 😈 is there & so obvious in human established mathematical knowledge for sure
> >
> > 🔊 Bassam Karzeddin 🔊
> Thanks Kentarski, and King Bassam.
>
> The term 'reductionsim' comes to mind as we consider developing number from the top down. Nicely enough, we can land in discrete terms and in continuous terms as we do so. If we find the need to assign an arbitrary unity to arrive with a unit then we have a continuous system. If we find that a unital object exists then we have a discrete form. Polysign numbers is a marriage of the two: sx, where s is discrete sign, and x is continuous magnitude.. The idea that these would develop from the largess and that we must subset that universe in order to do our discovery is acceptable I think from a philosophical perspective. We would admit our place as a locality within a very large system that we wonder about. This is a physical method of arriving at mathematics. We dismantle reality to arrive in mathematics; reality encompassing the observable universe. What would be most lovely is to wind up with derived atoms and electrons and photons from this theoretical perspective. It is one thing to find an emergent spacetime basis, and it is another to find space-time-matter. From the bottom up the former does appear. Possibly from the top down the latter can be had.
>
> In effect, this top down theory, in its confession of cosmological existence, denies the separation of the branches of philosophy, mathematics, and physics. These are provably false divisions, and so the entire mindset of modern academia can be put aside. 'as a fraud' I almost wrote here on the tail of that sentence, but I'm trying to be less inflammatory these days. Sometimes it feels like these may be our last days as current events develop. So it is a good time to get such thoughts out rather than hoard them. Please do use it freely, and claim it for your own if you must, but here possibly a record does exist that can provide some accountability. Still, ideas do not really have owners once they are unleashed. They stand freely on their own, if they are strong enough.

It seems to me, at the moment, that the universal approach is cause to trouble over division, as high quality sets are somewhat divided out of it. If only we had the high quality sets correct than all will come clean. Still, conceptually would this division problem lead to copies of set, and would it lead in particular to three copies of the same set? As a universal means of locating your object? This is suspect. Such a strange state of affairs, and yet we can carry on this analsis. I'm not going to even claim that this is a strong analysis, but it is a simple analsis:

In polysign we have developed a series of number systems which are general dimensional:
P1, P2, P3, | P4, P5, P6, ...
These systems are characterized via the generalization of discrete sign with continuous magnitude sx, where s is sign and x is magnitude(obviously devoid of sign). We observe that the two-signed numbers are the real numbers and that -1+1=0, which is a statement of balance amongst the signs. Clearly the three-signed number system obeys -1+1*1=0, and but for creating sign symbols, which thus far are mnemonic and we can extend to P4 with #, which takes four strokes to draw, and witness that -1+1*1#1=0, but that breakpoint that was enlisted is somewhat already engaged; without ever even seeing the product definition. Already these balance statements develop the geometry of these systems as the rays emanating from the center of their n-verticed simplex out to its vertices. The simplex frame can be demolished; it is just these rays that we are after. They carry exact correspondence to this balance principle.

Now, historically speaking, as we go through the product definition and its rotary qualities:
(s1 x1)(s2 x2) = (s1@s2)x1x2
where this '@' implies the modulo sum of the signs, which by the way in P2 is consistent with the real numbers whose modulo two behavior is familiar to everyone. So, in P3 we develop the plane, and I would argue that in P4 we develop the volume, but here lays a common mistake of beginners who will (coherently) put the signs in the plane in order to visualize their rotary qualities. So these challengers to coherency choose to put four signs as if they were the rays of the complex plane and say, see; these are balanced too, and your product works out clean as you sum the angles in Pn; meaning that you can plot P5 in the plane and get your sign mechanics as rotations, and so on. Certainly this is true about the sign mechanics, but it offends the law of balance. For instance, going back to P4 if this planar geometry were correct we would as well have +1#1=0, and -1*1=0 as planar effects. These are not a part of polysign. Still, though, they can state cleanly that in Pn the sum over the signs of a constant magnitude will balance to naught, so they have met the first balance, and they've done it all in P3. It's like they are coming up through the spectrum and found a convenient stop along the way. And there lays the breakpoint. And so too, coming down from on up high we are going to hit the same breakpoint, and low and behold we will be stopped in a 3D space, and by this usage of '3D' I do mean it in the traditional real valued sense, and we are in P4, and no tricks are played. Well, one trick really has to be discussed, and that is whether we are off by one or not, and such breakpoints might be argued either way, but suffice it to say, some people's minds do hit this breakpoint, whereas somehow mine crossed it more readily.

Anyway, and I'm sorry to be so long-winded, but the point of all that was merely to get through the product to discuss the division problem, but along the way I've found a double-back to an earlier detail in this thread where the thought of the (z,z,z,z) format, and the idea that it relates to the product could somehow relate it to division. To be clear, though the rudimentary product was laid out up above, the general product z1z2 in P4 has sixteen terms. And of course the structure (z1,z2,z3,z4) has sixteen as well. The rotary qualities of product simply rotate around in this series structure. Thence a sigma could be applied at the end which resolves us back to z3=z1z2, and it all seems trivial, and yet I am bumping now into the problem that I've just invoked division as fundamental from a top down thought process. I am sorry to a beginner for mixing up these two disparate concepts, but we do have a natural wall at P4, and as we come down the ladder of polysign systems if we halt there then we have emergent support for space. Down lower at P1 we see time, and what then of P2 and P3? These last two standing, you see, encompass much of existing mathematics. They are the outliers; not the others, in this strange reacquaintance with reality. Electromagnetics are under the hood in this model; just where Maxwell would like them.

On Wednesday, August 16, 2023 at 10:02:46 AM UTC-4, Timothy Golden wrote:
> On Saturday, August 12, 2023 at 5:31:47 PM UTC-4, Timothy Golden wrote:
> > On Friday, August 11, 2023 at 10:58:32 PM UTC-4, bassam karzeddin wrote:
> > > On Friday, August 11, 2023 at 11:24:58 PM UTC+3, Kentarski Freed Chikeng wrote:
> > > > I do not what to say or how to proceed.But it is always nice
> > > > when things under the radar come to the surface. It s like
> > > > when security is all around, uncertanty knocks your door, so
> > > > to speak.

> As to how this works: taking the set theory from the top is a divisional concept. That we land in a natural value which encompasses two divisions of this universe; this is a starkly different mindset than building a universe from the natural value of old. As if the continuum could be built atop such a discrete concept, onward go the mathematicians of old; Pythagoreans all; for their claims of divorce and diversion away from reality. That our very culture has suffered thus may be at the hands who obfuscated philosophy to the rank of humor. Physical theory is lost to a sea of experimental adventures where the fury of ocean is tamed just so to get just thus a result that fits a curve that fits a curve, all the while claiming theory.
>
> Possibly I am discussing a tank two microverse. It's not strong. That's for sure.
Possibly I am discussing a rank two microverse. It's not strong. That's for sure.

This divisional problem becomes as well a subtractive problem. Even if we are bolstered by admitting some large universal N, and this of course is a terribly simple universe, to arrive down at a singular element via a destructive process; as if it could be separated from the universe; is not an actual physical process. It is a conceptual one. We are able to operate on the physical world as animals, and without these abilities we would find even less to work with. In the back yard is an apple tree, and a quick count yields 61 apples. Picking time comes and those apples are transported into a box via human labor, and the count goes to 67 apples, and cheerily so. A child from their unusual vantage spots one last shiny apple from near the trunk looking straight up through the tree, bringing the total to 68, and with a pole with a basket on the end it is picked. The concern over this number is not so critical as the natural numbers would have it. Chopping down the apple tree to verify the figure, for instance, is not going to happen. A log is made of the figure in the journal of the homestead for future reference, with a lightness in attitude that makes it easily done. As this homesteader puzzles over the figure and harkens back to Peano, the idea that any one of these apples is the successor to another seems a filthy lie. He pulls out one apple with a soft side and a hole in it, eating from the good side, but does not decrement the count in the journal. In the end that will keep the count higher rather than lower through the winter.

The idea that a container lays in the basis of the natural number is somewhat a software awareness, or at least there lays one vector of thought on it, with correspondence to the physical universe. As to whether any human could ever explain 'natural values' without such a means is perhaps what Peano was after. By the way, the man with the apple tree never really was terribly worried about all of the apples in the universe, either. He built boxes to hold roughly 50 apples, and knew he'd need two of them this year. That's about as far as he got on the container theory side of things as well. Sure, they had taught him to count into as many digits as he liked at school. Counting his beans out one by one was not his thing though.

There is a sort of accuracy in Peano whereby the numbers come from thin air, and there is another sort of accuracy as attempted from the universal mindset, and there is yet another very practical version which needs neither. All of these are in the terms of a discrete quality which goes assumed beneath the fray of the mind that beholds the puzzle. Thence we move on to another practical value; that of the continuous value; where we find that a figure like 6.1 is really the reuse of the discrete value with a secondary unital figure tied on, taking the discrete form of that little dot. This is about as far as we've come with the concept of number. Well: you say: what about sign? Why, yes, I say, how about it? It turns out that this stage of numerical development has unfolded in the last twenty years, let's say, which accommodates emergent spacetime, though the physics is unknown; the basis is purely arithmetical. As to whether more accoutrements to the number are deserved has to be left an open question. As to whether continuous values deserve to be confused with their discrete forbears is problematic. This leads to the professors of the real value positing its exquisite detail and exactness, and this lie further divorces mathematics from physics. Certainly any who were teetering on the edge have been driven one way or the other. Yet to admit that we do not actually have clean representation; that we are merely engaged in a fairly early stage of the progression of number is actually already proven from the vantage of polysign numbers. It is by following them that I can make such a statement.

I had meant to arrive in a subtractive argument here which would incur damage onto the universal sourcing of sets and other phenomenon. Instead I've wound up denying the problem even exists. On the puzzle of a universe in N: one option that we haven't gone over is a factorable form:
P1, P2, P6, P24, P120, ...
whereby each space carries the modulo qualities that it holds dear in modulo m and less for Pm!
where that reads 'Pee sub (em factorial)'. That is a strange option, and maybe a dumb choice, for it leaves P3; arguably a component in P6; out of the progression. Well, in the factored form it will show up then, won't it? All of them will. Thinking largely, what this would do is guarantee that N is not actually just any large value, but fits quite a distinct and well spread set of possibilities, with a nice added balance in the balancing act. Whereas before I was caught saying that in a high N universe you probably wouldn't know the difference, and that an N+31 might be about like an N, engaging in factorials demolishes this argument. It suggests you could arrive at N. And furthermore, that its particulate behaviors would be quite well behaved.

Is mathematics just a shell game; put in place simply to fluster humanity? Where is the progress thanks to pure mathematics? Where is the emergent spacetime basis? Why, it's right under your nose here. Just generalize sign. The rest falls out for free. Your number, sir, is highly suspect.
Duplicity, sir, is the problem. You won't have it any other way, will you. Well, complicity is her name, then, isn't it?

FAFA
WAAOOA

On Friday, August 11, 2023 at 4:24:58 PM UTC-4, Kentarski Freed Chikeng wrote:
> I do not what to say or how to proceed.But it is always nice
> when things under the radar come to the surface. It s like
> when security is all around, uncertanty knocks your door, so
> to speak.
>
> For the moment you may code an study, similar to the spherical
> product study, where a point travels through a loxodrome of the
> sphere, but, this time, is to study the three permutation's tetrahedron
> in each point, for visual purposes. For that effect, also is possible
> to calculate the six edges of the tetrahedron, calculating the magnitude
> of z @ ~permut(z) for each edge, but it is not necessary.
>
> On the other side, the guys that where developing more exclusively regarding
> the context of triangular coordinates, that were much more connected
> with coordinates, probably missed, although, they were aware that
> that some permutations induced flat, but, by some breadth of the serendipity,
> they were not situated in the context of , what you call, sign.
>
> I do not what to say. Expecting some though of the deep comes to surface.

So I did finally code this, and it took very little time. It turns out there is no protection by primes or anything like that:
TryRandomSimplex()
-------------------

2: Ref:3.14159 Rand:3.14159
3: Ref:2.0944 Rand:2.0944
4: Ref:1.91063 Rand:2.28118
5: Ref:1.82348 Rand:1.27732
6: Ref:1.77215 Rand:2.18293
7: Ref:1.73824 Rand:1.84671
8: Ref:1.71414 Rand:2.18835
9: Ref:1.69612 Rand:2.10752
10: Ref:1.68214 Rand:1.57497
11: Ref:1.67096 Rand:1.56298
12: Ref:1.66183 Rand:1.76183
13: Ref:1.65423 Rand:1.98727
14: Ref:1.6478 Rand:1.68437
15: Ref:1.64229 Rand:1.32575
16: Ref:1.63751 Rand:2.1687
17: Ref:1.63334 Rand:1.56938
18: Ref:1.62965 Rand:1.91124
19: Ref:1.62638 Rand:1.56668

int TryRandomSimplex()
{ cout << "\n\n TryRandomSimplex()\n -------------------\n";
for( int i = 2; i < 50; i++ )
{
Poly zr(i); zr.Random();
Poly z1(i); z1[0] = 1;
Poly mu(i); mu[1] = 1;

cout << "\n" << i << ": Ref:" << z1.Angle( z1 * mu )
<< " Rand:" << zr.Angle( zr * mu );
}
return 0;
}

There is nothing fixed about the random angles; the criterion is whether they match the unitary form, and beyond P3 there is no match. So this behavior follows the breakpoint:
P1 P2 P3 | P4 P5 P6 ...
By Ref we are simply looking at the angle between (1,0,0,0,...) and (0,1,0,0,...), which is the regular simplex angle, whereas Rand is a random value (not printed for simplicity) and its mu shifted value. These polysign values in C are nu first values, nu being neutral unity, and mu being minus unity.

I don't honestly feel edified by the experiment. It is not surprising, though I don't quite see it either. I had a shred of hope that the primes would not abide the pattern. It is so easily shown in P4, and yet by the symmetry of the coordinate system I feel that we are indeed expressing pure simplices. They are not, however, regular simplices. Clearly their mu'd vertices will sum to naught. Egad! Is this to say that these are reasonable bases for the geometry to hold in? Are these coordinate transforms?

I have generally said that were there other options for the geometry to hold in that they would be of interest. Clearly the option to pick a z and take its mu'd forms is going to fit. They are naturally skewed forms... Please, Kentarkski, pick up...

Am I confusing ( mu ^ n )( z ), where z is random; versus z ^ n , where z is mu? Certainly. This is the topic at hand. Still surprised that you could find life in what seems to be lifeless. Such symmetry, and symmetry breaking, happening all at once. I've gotten nowhere with this, but to expose that the breakpoint holds.

I suppose there is a sort of question that calling these forms bases poses as to the applicability of the product in those forms, where very surprising results would occur. In linear algebra no such product exists. My filter is for physics, but I have no sense here. Actually, maybe one small lead: back in the early days there was some hope of yielding general dimensional spheres as z=nu-dz, since such a value in P3 in its powers z^m trace out a circle, perhaps the correct selection in P4 would trace out the surface of a sphere, and so on upward for P5 and so forth, but I never found any stable result.
Ahh... should I have tried mu-dz? That would at least get the first n points right. Really, I have learned a respect for mu, that is not nu. All you binary twats: step aside, please.

On Tuesday, September 19, 2023 at 12:39:58 PM UTC-4, sci.math wrote:
> On Friday, August 11, 2023 at 4:24:58 PM UTC-4, Kentarski Freed Chikeng wrote:
> > I do not what to say or how to proceed.But it is always nice
> > when things under the radar come to the surface. It s like
> > when security is all around, uncertanty knocks your door, so
> > to speak.
> >
> > For the moment you may code an study, similar to the spherical
> > product study, where a point travels through a loxodrome of the
> > sphere, but, this time, is to study the three permutation's tetrahedron
> > in each point, for visual purposes. For that effect, also is possible
> > to calculate the six edges of the tetrahedron, calculating the magnitude
> > of z @ ~permut(z) for each edge, but it is not necessary.
> >
> > On the other side, the guys that where developing more exclusively regarding
> > the context of triangular coordinates, that were much more connected
> > with coordinates, probably missed, although, they were aware that
> > that some permutations induced flat, but, by some breadth of the serendipity,
> > they were not situated in the context of , what you call, sign.
> >
> > I do not what to say. Expecting some though of the deep comes to surface.
> So I did finally code this, and it took very little time. It turns out there is no protection by primes or anything like that:
> TryRandomSimplex()
> -------------------
>
> 2: Ref:3.14159 Rand:3.14159
> 3: Ref:2.0944 Rand:2.0944
> 4: Ref:1.91063 Rand:2.28118
> 5: Ref:1.82348 Rand:1.27732
> 6: Ref:1.77215 Rand:2.18293
> 7: Ref:1.73824 Rand:1.84671
> 8: Ref:1.71414 Rand:2.18835
> 9: Ref:1.69612 Rand:2.10752
> 10: Ref:1.68214 Rand:1.57497
> 11: Ref:1.67096 Rand:1.56298
> 12: Ref:1.66183 Rand:1.76183
> 13: Ref:1.65423 Rand:1.98727
> 14: Ref:1.6478 Rand:1.68437
> 15: Ref:1.64229 Rand:1.32575
> 16: Ref:1.63751 Rand:2.1687
> 17: Ref:1.63334 Rand:1.56938
> 18: Ref:1.62965 Rand:1.91124
> 19: Ref:1.62638 Rand:1.56668
>
> int TryRandomSimplex()
> {
> cout << "\n\n TryRandomSimplex()\n -------------------\n";
> for( int i = 2; i < 50; i++ )
> {
> Poly zr(i); zr.Random();
> Poly z1(i); z1[0] = 1;
> Poly mu(i); mu[1] = 1;
>
> cout << "\n" << i << ": Ref:" << z1.Angle( z1 * mu )
> << " Rand:" << zr.Angle( zr * mu );
> }
> return 0;
> }
>
> There is nothing fixed about the random angles; the criterion is whether they match the unitary form, and beyond P3 there is no match. So this behavior follows the breakpoint:
> P1 P2 P3 | P4 P5 P6 ...
> By Ref we are simply looking at the angle between (1,0,0,0,...) and (0,1,0,0,...), which is the regular simplex angle, whereas Rand is a random value (not printed for simplicity) and its mu shifted value. These polysign values in C are nu first values, nu being neutral unity, and mu being minus unity.
>
> I don't honestly feel edified by the experiment. It is not surprising, though I don't quite see it either. I had a shred of hope that the primes would not abide the pattern. It is so easily shown in P4, and yet by the symmetry of the coordinate system I feel that we are indeed expressing pure simplices. They are not, however, regular simplices. Clearly their mu'd vertices will sum to naught. Egad! Is this to say that these are reasonable bases for the geometry to hold in? Are these coordinate transforms?
>
> I have generally said that were there other options for the geometry to hold in that they would be of interest. Clearly the option to pick a z and take its mu'd forms is going to fit. They are naturally skewed forms... Please, Kentarkski, pick up...
>
> Am I confusing ( mu ^ n )( z ), where z is random; versus z ^ n , where z is mu? Certainly. This is the topic at hand. Still surprised that you could find life in what seems to be lifeless. Such symmetry, and symmetry breaking, happening all at once. I've gotten nowhere with this, but to expose that the breakpoint holds.
>
> I suppose there is a sort of question that calling these forms bases poses as to the applicability of the product in those forms, where very surprising results would occur. In linear algebra no such product exists. My filter is for physics, but I have no sense here. Actually, maybe one small lead: back in the early days there was some hope of yielding general dimensional spheres as z=nu-dz, since such a value in P3 in its powers z^m trace out a circle, perhaps the correct selection in P4 would trace out the surface of a sphere, and so on upward for P5 and so forth, but I never found any stable result.
> Ahh... should I have tried mu-dz? That would at least get the first n points right. Really, I have learned a respect for mu, that is not nu. All you binary twats: step aside, please.

I guess I should try to simplify the puzzle of whether these are potential bases; in the sense of linear algebra, which is a bit confusing. Part of the confusion is the fact that we even have a product in polysign, and the handiness of the product to portray the basis as MU^n. This is minus unity to the nth power; in P4 this is:
(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)
There is an annoyance of mu-first or nu-first in this coordinate form, and guess what? In the process there is even another mu positioned the other side of nu; possibly taking a name of imu, and it is always there, though in P2 it is equal to mu, in the higher forms it can do the work of mu. We are in this strange world where specifying a single z=mu, or z=imu, actually specifies the other coordinates in P4, for instance. That these have remained unital is helpful and easy, and what Kentarski has done is to consider any z, muz, mumuz, mumumuz, for instance in P4, for any z. To use ordinary polysign math these are simply @z, -z, +z, *z. Yet they refuse to match up with the power series of the simple unital form, which originally produced a regular simplex. Now we have irregular simplices. Yet by irregular even, we have to be careful. They do in fact sum to naught, which is the fundamental requirement of the polysign basis, which got us to the original simplex geometrical solution. Perfect balance in perfect symmetry. In low n they will hold up, but in P4 and beyond they will not. This is a sort of symmetry breaking even while symmetry is in the basis.

Anyway, I've said many times, that if there were another geometry satisfying sum over s of sx equals zero, that it would be of interest, and here they are... sort of. That they are built upon the very basis that built them is ad nauseum true. That they almost appear to be coordinate transforms, just in the utterance of any z: somewhat true, for the ease by which the brethren [e] of the real linear algebra form is not needed in polysign where the powers of mu can do this job. And yet, upon choosing z=(1,0,1,0) all will be cast to P2; to R, in effect. Of course this assumes that the product is the transformation. That is an extremely simple system. So it has some merit there, at least. What seems apparent easily in P4 is more tricky in P5, but the same results will be had when the symmetries are laid correctly.

Here, way up in P16, the critical points are readily found simply by studying the iterated product, which hones onto these compositions https://drive..google.com/file/d/1UF1pum8eLOR09jTIpt3GdMZlgxYiH5zR/view?usp=drive_link
as RxC^7, and you can even make out the neutral unity of the R, being the larger splotch of points with its mu opposite.
Why google are such pigs that they won't let you have the gif I have no idea. I am sorry that I am playing with evil here now.

On Thursday, September 21, 2023 at 8:32:31 AM UTC-7, Timothy Golden wrote:
> On Tuesday, September 19, 2023 at 12:39:58 PM UTC-4, sci.math wrote:
> > On Friday, August 11, 2023 at 4:24:58 PM UTC-4, Kentarski Freed Chikeng wrote:
> > > I do not what to say or how to proceed.But it is always nice
> > > when things under the radar come to the surface. It s like
> > > when security is all around, uncertanty knocks your door, so
> > > to speak.
> > >
> > > For the moment you may code an study, similar to the spherical
> > > product study, where a point travels through a loxodrome of the
> > > sphere, but, this time, is to study the three permutation's tetrahedron
> > > in each point, for visual purposes. For that effect, also is possible
> > > to calculate the six edges of the tetrahedron, calculating the magnitude
> > > of z @ ~permut(z) for each edge, but it is not necessary.
> > >
> > > On the other side, the guys that where developing more exclusively regarding
> > > the context of triangular coordinates, that were much more connected
> > > with coordinates, probably missed, although, they were aware that
> > > that some permutations induced flat, but, by some breadth of the serendipity,
> > > they were not situated in the context of , what you call, sign.
> > >
> > > I do not what to say. Expecting some though of the deep comes to surface.
> > So I did finally code this, and it took very little time. It turns out there is no protection by primes or anything like that:
> > TryRandomSimplex()
> > -------------------
> >
> > 2: Ref:3.14159 Rand:3.14159
> > 3: Ref:2.0944 Rand:2.0944
> > 4: Ref:1.91063 Rand:2.28118
> > 5: Ref:1.82348 Rand:1.27732
> > 6: Ref:1.77215 Rand:2.18293
> > 7: Ref:1.73824 Rand:1.84671
> > 8: Ref:1.71414 Rand:2.18835
> > 9: Ref:1.69612 Rand:2.10752
> > 10: Ref:1.68214 Rand:1.57497
> > 11: Ref:1.67096 Rand:1.56298
> > 12: Ref:1.66183 Rand:1.76183
> > 13: Ref:1.65423 Rand:1.98727
> > 14: Ref:1.6478 Rand:1.68437
> > 15: Ref:1.64229 Rand:1.32575
> > 16: Ref:1.63751 Rand:2.1687
> > 17: Ref:1.63334 Rand:1.56938
> > 18: Ref:1.62965 Rand:1.91124
> > 19: Ref:1.62638 Rand:1.56668
> >
> > int TryRandomSimplex()
> > {
> > cout << "\n\n TryRandomSimplex()\n -------------------\n";
> > for( int i = 2; i < 50; i++ )
> > {
> > Poly zr(i); zr.Random();
> > Poly z1(i); z1[0] = 1;
> > Poly mu(i); mu[1] = 1;
> >
> > cout << "\n" << i << ": Ref:" << z1.Angle( z1 * mu )
> > << " Rand:" << zr.Angle( zr * mu );
> > }
> > return 0;
> > }
> >
> > There is nothing fixed about the random angles; the criterion is whether they match the unitary form, and beyond P3 there is no match. So this behavior follows the breakpoint:
> > P1 P2 P3 | P4 P5 P6 ...
> > By Ref we are simply looking at the angle between (1,0,0,0,...) and (0,1,0,0,...), which is the regular simplex angle, whereas Rand is a random value (not printed for simplicity) and its mu shifted value. These polysign values in C are nu first values, nu being neutral unity, and mu being minus unity.
> >
> > I don't honestly feel edified by the experiment. It is not surprising, though I don't quite see it either. I had a shred of hope that the primes would not abide the pattern. It is so easily shown in P4, and yet by the symmetry of the coordinate system I feel that we are indeed expressing pure simplices. They are not, however, regular simplices. Clearly their mu'd vertices will sum to naught. Egad! Is this to say that these are reasonable bases for the geometry to hold in? Are these coordinate transforms?
> >
> > I have generally said that were there other options for the geometry to hold in that they would be of interest. Clearly the option to pick a z and take its mu'd forms is going to fit. They are naturally skewed forms... Please, Kentarkski, pick up...
> >
> > Am I confusing ( mu ^ n )( z ), where z is random; versus z ^ n , where z is mu? Certainly. This is the topic at hand. Still surprised that you could find life in what seems to be lifeless. Such symmetry, and symmetry breaking, happening all at once. I've gotten nowhere with this, but to expose that the breakpoint holds.
> >
> > I suppose there is a sort of question that calling these forms bases poses as to the applicability of the product in those forms, where very surprising results would occur. In linear algebra no such product exists. My filter is for physics, but I have no sense here. Actually, maybe one small lead: back in the early days there was some hope of yielding general dimensional spheres as z=nu-dz, since such a value in P3 in its powers z^m trace out a circle, perhaps the correct selection in P4 would trace out the surface of a sphere, and so on upward for P5 and so forth, but I never found any stable result.
> > Ahh... should I have tried mu-dz? That would at least get the first n points right. Really, I have learned a respect for mu, that is not nu. All you binary twats: step aside, please.
> I guess I should try to simplify the puzzle of whether these are potential bases; in the sense of linear algebra, which is a bit confusing. Part of the confusion is the fact that we even have a product in polysign, and the handiness of the product to portray the basis as MU^n. This is minus unity to the nth power; in P4 this is:
> (1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)
> There is an annoyance of mu-first or nu-first in this coordinate form, and guess what? In the process there is even another mu positioned the other side of nu; possibly taking a name of imu, and it is always there, though in P2 it is equal to mu, in the higher forms it can do the work of mu. We are in this strange world where specifying a single z=mu, or z=imu, actually specifies the other coordinates in P4, for instance. That these have remained unital is helpful and easy, and what Kentarski has done is to consider any z, muz, mumuz, mumumuz, for instance in P4, for any z. To use ordinary polysign math these are simply @z, -z, +z, *z. Yet they refuse to match up with the power series of the simple unital form, which originally produced a regular simplex. Now we have irregular simplices. Yet by irregular even, we have to be careful. They do in fact sum to naught, which is the fundamental requirement of the polysign basis, which got us to the original simplex geometrical solution. Perfect balance in perfect symmetry. In low n they will hold up, but in P4 and beyond they will not. This is a sort of symmetry breaking even while symmetry is in the basis.
>
> Anyway, I've said many times, that if there were another geometry satisfying sum over s of sx equals zero, that it would be of interest, and here they are... sort of. That they are built upon the very basis that built them is ad nauseum true. That they almost appear to be coordinate transforms, just in the utterance of any z: somewhat true, for the ease by which the brethren [e] of the real linear algebra form is not needed in polysign where the powers of mu can do this job. And yet, upon choosing z=(1,0,1,0) all will be cast to P2; to R, in effect. Of course this assumes that the product is the transformation. That is an extremely simple system. So it has some merit there, at least. What seems apparent easily in P4 is more tricky in P5, but the same results will be had when the symmetries are laid correctly.
>
> Here, way up in P16, the critical points are readily found simply by studying the iterated product, which hones onto these compositions https://drive.google.com/file/d/1UF1pum8eLOR09jTIpt3GdMZlgxYiH5zR/view?usp=drive_link
> as RxC^7, and you can even make out the neutral unity of the R, being the larger splotch of points with its mu opposite.
> Why google are such pigs that they won't let you have the gif I have no idea. I am sorry that I am playing with evil here now.

If it results "closed forms" they can be "infinite series" with regards to "closed forms".

I.e. if you can divide out powers and result an addition formula, many or most useful
"actions" in mathematics are along such lines.