Re: ? understanding the world by math

On Jan 31, 11:18 pm, Mariano Suárez-Alvarez
<mariano.suarezalva...@xxxxxxxxx> wrote:
On Jan 31, 4:57 pm, "Tim BandTech.com" <tttppp...@xxxxxxxxx> wrote:



On Jan 30, 11:17 pm, Mariano Suárez-Alvarez

<mariano.suarezalva...@xxxxxxxxx> wrote:
On Jan 30, 10:27 pm, "Tim BandTech.com" <tttppp...@xxxxxxxxx> wrote:

On Jan 30, 4:09 pm, Cheng Cosine <asec...@xxxxxxxxx> wrote:

Hi:

Math represents a set of powerful tools to help us approach

the true nature of this world. Though linear system theory provides

many very power tools for us to approach the nature, the real world

in many cases is not linear. Then, except conducting linearization

to under a small part of the nature within a small range, whatelse

can we use to understand this world?

The polysign numbers inherently contain spacetime correspondence due
to the behavior of the math beyond sign three. These higher sign
systems are somewhat nonlinear, though I hesitate to use that word
strictly since the higher sign systems do still obey the associative,
commutative, and distributive laws.
[snip]

What does this paragraph possibly mean?!

What does it mean that a sign system is nonlinear? What
difference is there from that to its being only "somewhat"
nonlinear? What on earth is a "spacetime correspondence"?
In what way can an algebraic system "contain" a "spacetime
correspondence"?

The difference (or one of the differences) between math and,
say, poetry is that unless you make explicit the meaning of
the terms you use, you are plainly and simply not saying
anything. Deep sounding mumbo-jumbo only impresses... hmmm...
the editors of Social Text.

-- m

Mariano I am so sorry for you that you cannot understand such a simple
thing.

I honestly cannot tell if I understand or not: as I have stated,
you have, as far as I know, never explained what meaning
the terms I mentioned (and quite a few others I have seen you
use elsewhere) have, and I can confidently say that there is no
standard, well-known meaning attached to a claim such as "The
polysign
numbers inherently contain spacetime correspondence due to the
behavior of the math beyond sign three".

[paragraph on how all humans are limited, and on my refusal
to accept the polysign numbers snipped]
I'll go over the spacetime correspondence here again for you or some
other reader who thinks I am lame. The family of polysign numbers is
large. The family is
P1, P2, P3, P4, P5, ...
Yet of all these systems only three preserve the following behavior:
| z1 z2 | = | z1 || z2 |

I do not recall your listing *what* properties you expect
an absolute value function to have.

I've got to check in right here because you seem to think that I am
defining a new absolute value function. I am not. This is the usual
absolute value. It is the same in P2 as it is on the reals. It is the
same in P3 as it is on the complex numbers. It is the same in P4 as it
is on P3; simply generalize in sign. It is simply the distance
function. The nuances of difference for me come at a different stage
of awareness. That some believe this absolute value to be a higher
form than the types it applies to is a deep mistake. Instead the
polysign construction exposes magnitude as fundamental, sign being a
discrete type whose marriage to this continuous unsigned magnitude
yields the real numbers, the complex numbers, and a myriad of higher
forms... also let's not forget that little rascal P1.

You Mariano insist on applying the old language to a new language and
will claim that any inconsistencies are a failing of the new language.
You see though the consequences of this new language range widely.
There are unmistakeable gains to be had. Upon turning the new language
onto the old one then the inconsistencies become shuffled another way
such that the old language becomes suspect. Because the new language
is a compact form of the old language with additional consequences
that were not present in the old language the mismatch can be
validated from the progressive side looking askance at what has been.
It is a function of human judgement as to which side one will take.
This is no different than the tear between say a string theory and a
classical particle theory. There is room for the pragmatist in the
middle to arbitrate but for me my side is clearly chosen. Your attack
on my statement of the distance function is illogical, for the
geometry is well exposed and the ordinary distance function suffices
directly on the polysign math as is stated at my website. You may
treat this refutation as an answer as well so we can drop the topic
and move on with your other attacks if you see and accept my argument
here. For now I will remain merely at this one point until we fully
address it into congruity. If you insist that I redefine the ordinary
math then so be it. I simply reuse the ordinary system of absolute
value as distance as in Euclidean geometry of the superpositional
space.

We'll eventually come to a dispute over just what is meant by
P1 P2 P3
as a symbolic construction. There is a healthy discussion, but one
that few will undertake because to forsake isotropic space for a
structured spacetime seems beyond hope to that human judgement system,
though Einstein did come part way in his convincing usage of the
Minkowski metric. Here I have answers but first you would properly
have to ask the questions since if I try to preanswer them it's as if
I'm shoving a bunch of information down your throat and it would then
simply become regurgitant. So it goes for the human race. Most simply
gag on my attempts here and so my stream of information simply flows
into databanks. They don't seem to mind holding onto it since it is
just trivia to them.

If the only one you are
interested in is the multiplicative property

(*) | z1 z2 | = | z1 | | z2 |

then you should know that all the Pn *do* have an appropriate
'absolute value function' which is multiplicative.

This follows trivially from the fact that the Pn, when
m >= 2, are isomorphic as rings to direct products of
copies of R and C. The actual formulas, though, are rather
messy (but they can be obtained in principle with simple
linear algebra)

I am suspect that these can be clearly instantiated in your system. My
own analysis of P4 as an RxC space exposes that the error in the
product is symmetrical to the resultant, suggesting that an infinite
series will be necessary to cleanly compute the correct resultant.
While the analysis on this webpage is partly graphical the linear
compensations that might make your claim clean in two iterations have
been tried:
http://bandtechnology.com/PolySigned/Deformation/P4T3Comparison.html
So perhaps you'll be able to state the problem to some precision
level. Until you've done this I think maybe you better keep this
argument in check a bit. You say it is possible, but who has actually
done it? The polysign space is new. Could it be that it can challenge
the ways that you preach? I do think it is possible, especially given
the reaching attempts of Grassman and the bunk that has become
acceptable in the name of progress. People have been reaching for this
new ground for some time. I should be more respectful, but when the
reachers have become accepted and the reached unaccepted then the
shaky footing of the reaching tower leaves one wondering what they are
doing hanging around in its midst.

- Tim


For example, if x = a0 e0 + a1 e1 + a2 e2 + a3 e3 is an
element of P4 (with the e0, ..., e3 the 'signs' and
the a0, ..., a3 the coefficients, which as usual are real
numbers), you can define

|x| = sqrt( ((a0 - a2)^2 + (a1 - a3)^2) (a0 - a1 + a2 - a3)^2 )

Then if y is another element of P4 a computation will show that

|x y| = |x| |y|

This can be done by hand.

Things get scarier as n grows. For example, when n = 5 and
x = a0 e0 + a1 e1 + ... + a4 e4, you obtain a multiplicative
function putting

|x| = Sqrt[
(((-4*a[0] + a[1] - Sqrt[5]*a[1] + a[2] + Sqrt[5]*a[2] + a
[3] +
Sqrt[5]*a[3] + a[4] - Sqrt[5]*a[4])^2 +
(10*(-((1 + Sqrt[5])*a[1]) - 2*a[2] + 2*a[3] + a[4] +
Sqrt[5]*a[4])^2)/(5 + Sqrt[5]))*
((Sqrt[5 + Sqrt[5]]*(-a[2] + a[3]) + Sqrt[5 - Sqrt[5]]*
(a[1] - a[4]))^2/8 +
(a[0] - ((3 + Sqrt[5])*a[1] - 2*(a[2] + a[3]) +
(3 + Sqrt[5])*a[4])/(2*(1 + Sqrt[5])))^2))/16
]

Cute, isn't it? The ugliness comes from the fact that
pentagons are complicated beasts! Mathematica did not manage
to check multiplicativity in the 10 minutes I gave it, but the
formula does work. If you are so inclined, you can check (*)
on randomly generated elements.

When n = 6, the corresponding formula is much nicer:
if x = a0 e0 + ... + a5 e5, setting

|x| = Sqrt[
((a[0] - a[1] + a[2] - a[3] + a[4] - a[5])^2*
(3*(a[1] + a[2] - a[4] - a[5])^2 +
(2*a[0] + a[1] - a[2] - 2*a[3] - a[4] + a[5])^2)*
(3*(a[1] - a[2] + a[4] - a[5])^2 +
(-2*a[0] + a[1] + a[2] - 2*a[3] + a[4] + a[5])^2))/16
]

does the trick---and Mathematica can check the multiplicative
property (*) in a minute or so.

&c.

This is the usual familiar conservation of magnitude of the reals and
the complex numbers. While the higher sign systems are well behaved
arithmetically they break this rule. Distances are no longer conserved
in P4+.

The well behaved members of the family are
P1 P2 P3
which form a sufficient representation of spacetime including
unidirectional time.

See, you are here trying to explain what you meant by "The polysign
numbers inherently contain spacetime correspondence due to the
behavior of the math beyond sign three", yet you have not given
any explanation whatsoever of what a "representation of spacetime"
is, what the difference between such a representation that includes
unidirectional time (whatever that may be) and one which does not
include it is, and what it means for something (the polysign numbers,
in this case) to be a "sufficient" representation.

A great professor I had used to refer to the Principle of
Preservation of the Difficulty: your "explanation" is a great
example of that principle in action.

[Paragraph concluding that someone named Mario is a loser snipped]

-- m

.

Relevant Pages

  • Re: ? understanding the world by math
    ... In what way can an algebraic system "contain" a "spacetime ... to accept the polysign numbers snipped] ... defining a new absolute value function. ... will claim that any inconsistencies are a failing of the new language. ...
    (sci.math)
  • Re: Imaginary Space
    ... existing physics. ... a family called polysign numbers. ... Under a polysign spacetime interpretation the structure ... Shouldn't the math which represents time be inherently ...
    (sci.physics)
  • Re: ? understanding the world by math
    ... to the behavior of the math beyond sign three. ... In what way can an algebraic system "contain" a "spacetime ... to accept the polysign numbers snipped] ... any explanation whatsoever of what a "representation of spacetime" ...
    (sci.math)
  • Re: ? understanding the world by math
    ... the new language does carry slight inconsistencies with the old ... The math can be taught to a capable high school student I ... look at the structures in these graphics. ... I plead with you to consider seriously the polysign numbers. ...
    (sci.math)
  • Re: ? understanding the world by math
    ... systems are somewhat nonlinear, though I hesitate to use that word ... In what way can an algebraic system "contain" a "spacetime ... Well I suppose all math is simple isn't it? ... someone who claims to understand the polysign system to refuse their ...
    (sci.math)