unread,
What does Linear Mathematics measure?
What does Linear Mathematics measure? |__|__| 1i *2i = 2i^2. ? ////////////| |__|__|__/ 1i *1i *3i =
12:25 AM
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Socratis T.n.p.'s profile photo
Socratis T.n.p.
,
Lucrezio S
5
How do you think that 0.4 *0.4 *4 = 0.64 and that's it?
> Greetings Tnp 5i *20i *30i =3000i^3 =3m^3 => for 1m^3 =1000i^3. 1i=1dm > >0.5 *2 *2 =
May 25
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On Friday, May 26, 2023 at 5:54:44 AM UTC-4, Archimedes Plutonium wrote:
> unread,
> What does Linear Mathematics measure?
> What does Linear Mathematics measure? |__|__| 1i *2i = 2i^2. ? ////////////| |__|__|__/ 1i *1i *3i =
> 12:25 AM
> 
> Socratis T.n.p.'s profile photo
> Socratis T.n.p.
> ,
> Lucrezio S
> 5
> How do you think that 0.4 *0.4 *4 = 0.64 and that's it?
> > Greetings Tnp 5i *20i *30i =3000i^3 =3m^3 => for 1m^3 =1000i^3. 1i=1dm > >0.5 *2 *2 =
> May 25
> 

I think you are challenging the Cartesian product here.
I've done it the other way around.
This is a good slant on it possibly when the challenge formalized better.
The blend as physical versus arithmetic may be relevant.
All numbers in practical use will achieve some dimension.
Whether it is cats or dogs, or sheep, say...
Then what of spots or stripes, or solids, say...
Now this Cartesian product which can yield striped cats and spotted sheep carries the Cartesian product flavor of independence of the two sources. Yet what we do geometrically is to copy the first and claim a Cartesian product geometry; typically RxR to yield the plane. So entrained are we on this format that to challenge it could seem foolhardy.
But clearly the sensibility is lacking. By what right can we take two copies of the same thing and claim to have constructed something far superior?
In truth the Cartesian product RxR does represent the plane with an ordered pair (a,b) but there is more to it than a pure Cartesian product.
There is a loose agreement that these supposedly independent copies meet at zero and lay perpendicular to each other, and even follow a right hand rule if you want to get very strict. Are these qualities of the Cartesian product? Did I need or can I even state those things on animals versus patterns? Quickly the answer is no. Whether two copies of the real line can in fact construct the plane is ultimately what I see is the depth of the investigation. Then onward from there do three construct a volume, and four engage us in some space that is beyond our access? No: somehow all of our work was carried out in a three dimensional space, and in time as well, and as to why this is the case nobody has any idea other than to empirically draw down such dimensions in their analysis. That theory then rests its head on the empirical is the least acceptable feature of a subject that does impinge on mathematics. That boundary is artificial.

Polysign numbers do beget dimension from the same law that builds the reals and their one dimensional geometry. As the real line (P2) behaves with -a+a=0 so a three-signed system P3 behaves -a+a*a=0, and so on and so forth on into Pn. That P3 are the complex numbers in a new suit is no flaw. That P4 are their 3D counterpart... just what you were looking for? Hah! I suppose this medium is just as badly censored as all others, and there is an exclusive club which we are not allowed into. Anyway, as to constructing a space: Polysign does indeed place formal requirements on the geometry of the space. Simply consider it back in P2... and this is a great common defense of polysign since the revered real value is P2... without the balance of the rays via -a+a=0 there could be no real line. Likewise in P3 three rays equally opposed require the plane with rays at 120 degrees apart. Some want to fit P4 onto the plane as well, but this would require some additional constraints like +a#a=0 take place, and instead we see only -a+a*a#a=0, and so the rays emanating from the center of a tetrahedron out to its vertices are the coordinate system.

The arithmetic product exists and is obvious once you toy with them. It is from this ground of polysign that I have come to challenge much of existing mathematics, and that challenge does include the Cartesian product. Two independent real lines would be truly independent. They would have no means of control over each other or restrictions upon them. As to what is a representative of a space versus a construction of a space... could this subtle distinction apply? Certainly polysign do have explicit geometry built into their core. The progressive form:
P1 P2 P3 | P4 P5 P6 ...
does not even require a Cartesian product because each is unique from the other! In this regard we can call this a pure product, just as in the case of the animals versus the patterns on their fur. Yet now then what was the need of that Cartesian product claim? We're into type safety here as I see it, and whether an ordered pair is even necessary under such circumstances when the types are embossed into the values... what a shame I didn't get to that little bar.