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Subject: Re: Extending complex number to spaces with 3, 4 or any number of dimensions
From: Timothy Golden <timbandtech@gmail.com>
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On Thursday, March 3, 2022 at 1:59:22 PM UTC-5, tita...@gmail.com wrote:
> Le mardi 1 mars 2022 =C3=A0 16:24:47 UTC+1, timba...@gmail.com a =C3=A9cr=
it :=20
> > On Monday, February 28, 2022 at 6:13:52 PM UTC-5, tita...@gmail.com wro=
te:=20
> > > Le samedi 26 f=C3=A9vrier 2022 =C3=A0 13:47:13 UTC+1, timba...@gmail.=
com a =C3=A9crit :=20
> > > > On Friday, February 25, 2022 at 5:17:47 PM UTC-5, tita...@gmail.com=
 wrote:=20
> > > > > Le vendredi 25 f=C3=A9vrier 2022 =C3=A0 16:04:55 UTC+1, timba...@=
gmail.com a =C3=A9crit :=20
> > > > > > On Thursday, February 24, 2022 at 4:34:54 PM UTC-5, tita...@gma=
il.com wrote:=20
> > > > > > > Le jeudi 24 f=C3=A9vrier 2022 =C3=A0 19:46:34 UTC+1, timba...=
@gmail.com a =C3=A9crit :=20
> > > > > > > In fact, I=E2=80=99m working on physics, more precisely in re=
lativity and Electromagnetic. While computing the trajectory of Oumuamua, I=
 wanted to use complex number for numerical root searching with Newton=E2=
=80=99s method. Then, I tumbled on multidimensional complex number.=20
> > > > > > >=20
> > > > > > > My 3D complex number is a vector whose angles are that of a r=
eference of orientation, like Euler=E2=80=99s reference, and these angles a=
re the arguments of the complex number. When we multiply one complex number=
 with another complex number, this is equivalent to rotate the first vector=
 with the angles of the second, that is, the arguments of the second comple=
x number.=20
> > > > > > >=20
> > > > > > > As I=E2=80=99m not a mathematician, I do not know the meaning=
 of =E2=80=9CSignet non d=C3=A9fini=E2=80=9D, nor that of =E2=80=9Cpolysign=
 in P4=E2=80=9D=20
> > > > > > That was from you own work....=20
> > > > > > https://www.proz.com/kudoz/french-to-english/other/250526-signe=
t-non-d%C3%A9fini.html=20
> > > > > > Hah! Must have been a typo that your interface printed up to me=
..=20
> > > > > >=20
> > > > > > I get that you are coherent. Sparring here on usenet is a thing=
 and you are holding up just fine.=20
> > > > > > Few here can even give each other that much credit.=20
> > > > > >=20
> > > > > > So if I told you that there can be a four-signed number system =
would it be any wonder that:=20
> > > > > > - 1 + 1 * 1 # 1 =3D 0 ,=20
> > > > > > especially given that the two-signed real numbers obey:=20
> > > > > > - 1 + 1 =3D 0=20
> > > > > > and the three-signed numbers obey:=20
> > > > > > - 1 + 1 * 1 =3D 0 ?=20
> > > > > >=20
> > > > > > The product is trivial. They are rotational in nature. They nat=
urally generate simplex geometry without any need of the cross product; the=
 Cartesian product, so to speak. They are n-ary, and goodness: P1 hasn't ev=
en gotten under the lens yet.=20
> > > > > >=20
> > > > > > The fact that you are into emag is great. I'm trying to work it=
 into polysign. Rather hoping it will come out of polysign.=20
> > > > > I see. =E2=80=9CSignet non d=C3=A9fini=E2=80=9D is a failed cross=
 reference in my document.docx=20
> > > > >=20
> > > > > I see what polysign is about. Complex number can be seen as a P2,=
 3D complex P3 etc.=20
> > > > >=20
> > > > > PK=20
> > > > No. P2 are the real numbers. They are two-signed numbers. Instances=
:=20
> > > > -1.23 , + 0.01 , - 2.3 + 0.01=3D -2.29=20
> > > > P3 are the complex numbers, but they are in a new format:=20
> > > > -1.23 + 2.3 * 0.1=3D -1.13 + 2.2=20
> > > > but you see there is no further reduction in this P3 value. P3 are =
two dimensional just as P2 were one dimensional, yet there is no orthogonal=
ity in use here. To truly generalize sign exposes the balance that P3 have =
achieved:=20
> > > > - 1 + 1 * 1 =3D 0=20
> > > > no different than back in P2:=20
> > > > - 1 + 1 =3D 0 .=20
> > > > The P3 signs are in a plane and are equally spaced 120 degrees apar=
t. They form a simplex, and of course P4 are the 3D version forming rays fr=
om the center of a tetrahedron out to its vertices. Do not draw the frame o=
f the tet. Just the rays are needed. They are perfectly balanced:=20
> > > > - 1 + 1 * 1 # 1 =3D 0 .=20
> > > > These are the 3D version that polysign yields with no further rule =
system than was already in use in P2. It's just that in four-signed math th=
e sign mechanics are modulo four:=20
> > > > - - =3D +=20
> > > > - - - =3D *=20
> > > > - - - - =3D #=20
> > > > - - - - - =3D -=20
> > > > so you see we reuse the signs but their meaning is eccentric to the=
 signature of the system. This is as it should be. This notation is complet=
ely consistent with the real value and ordinary nomenclature around it:=20
> > > > - - =3D +=20
> > > > - - - =3D -=20
> > > > so the modulo two nature of the real value sign is exactly consiste=
nt with P2.=20
> > > >=20
> > > > The real numbers are two-signed numbers. They are balanced by these=
 signs. This balance yields their geometry. This same is true of P3, P4, an=
d strangely enough of P1 as well. Oddly, in Pn the angle will tend toward n=
inety degrees for high signature.=20
> > > Thanks.=20
> > Presuming you accept these details there is quite a lot more that unfol=
ds. P1 you see is consistent with time as a unidirectional feature. The odd=
ity is that P1 is zero dimensional as well. Time actually does obey this se=
eming conundrum, and in hindsight it is real valued time that is to blame f=
or so much of the stupidity. As we observe the three dimensions of space vi=
a experimental practice we do in fact observe time as zero dimensional: we =
observe no freedom to move an object in time. It is this method which allow=
s us to claim the three dimensions of space. Even this language though of d=
imension is built on the back of the real value as if it was fundamental. I=
n polysign the real value is P2 and it is no more fundamental than P3 or P4=
.. These are n-ary siblings.=20
> >=20
> > As you may know there is a quest for emergent spacetime under way withi=
n at least one branch of physics. Polysign numbers are yielding an emergent=
 spacetime without even doing any physics. How? So far you have seen how th=
ey are general dimensional. So where is the breakpoint? Have a look at the =
behavior:=20
> > | z1 z2 | =3D | z1 | | z2 |=20
> > In polysign it only holds through P3. In effect we have a natural break=
point :=20
> > P1 P2 P3 | P4 P5 P6 ...=20
> > and now whether you look at the bottom three as spacetime, or throw spa=
ce in as P4 even; there are two emergent spacetime candidates there. The on=
e which included P4 is a 6D system:=20
> > P1 : 0D=20
> > P1 P2 : 1D=20
> > P1 P2 P3 : 3D=20
> > P1 P2 P3 P4 : 6D=20
> > though again the usage of 'dimension' is faulty from the context of pol=
ysign. Well, I shouldn't quite push it that far: P2 are the first graphical=
ly renderable system with distinct features. Still, the inclusion of unidir=
ectional time as natural within polysign is quite a high merit; something u=
ntouchable by two-signed morons (TSMs).=20
> >=20
> > Polysign has led me on a journey that goes into abstract algebra and ba=
ck onto operator theory and out the other side to the construction of the r=
eal value whereupon I have found fault with the rational value; the irratio=
nal value merely being a teaser to get beyond the dubious nature of the rat=
ional value. It sort of ends in the quagmire of the engineer versus the mat=
hematician upon the value=20
> > 2.01=20
> > for instance, whereby the engineer sees this value as gray and the math=
ematician sees a perfect value. The continuum and its analysis is quite rel=
evant here. Epsilon/delta shows the way for the mathematician by chasing di=
gits but for them the notion that close enough is good enough was forgotten=
.. Their immunity provides quite a gap. Sadly the consequences of their igno=
rance travel through the subject and much of it comes out rotten even as th=
e beast carries onward in accumulation. Oh, what an accumulation. So we mus=
t carry on and try not to become carrion.=20
> >=20
> > As capitalist backed Nazis are prepared to burn communists alive in the=
 streets fears awaken. As to who is at the reigns: did you get your grant? =
Will they burn socialists too? These are questions slowly coming to the min=
ds of mathematicians in a free world that is exposed as a series of lies. F=
reedom is something that we take as individuals; it is not something grante=
d from on up high. That humans are great followers is well exposed in music=
; in sports; in politics; in the media. That humans are programmable beings=
.... this is what we have to deal with now.
> I see that you have a huge project which is mathematical as well as philo=
sophical. But I think that the 0 dimensional nature of time is an interesti=
ng idea, which will be useful in relativity.=20
>=20
> PK

Thank you. There is much to discuss. Electromagnetics has been claimed to c=
ome out cleanly in 6D systems right? The progression
0D 1D 3D 6D 10D 15D 21D
encompasses rather a lot of theories.=20

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