Re: ? understanding the world by math

Timothy Golden wrote :

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.

well , i do agree with mariano actually.

you are defining a NEW absolute value , in the sense that your absolute value is - i assume* - just the distance to the origin.

( * correct me if im wrong about that assumption )

its kind of weird that you consider an algebra where
a * b = b * a = ab but abs(a)*abs(b) =/= abs(ab).

your ' distance observation ' is correct , although i doubt that only occurs for polysigned as you claim ...



This is the usual
absolute value.

no.

its not even the usual numbers that you consider :p

and picking distance from origin as absolute value seems arbitrary , even unlogical as explained above.

even your zero-divisors do not neccessarily have absolute value of 0 ??

thats far from usual.


dont get me wrong , i have nothing against your ' distance ' or even ' magnitude ' but i wouldnt call it absolute values ( abs ).


this does not mean that i am not open to several distinct interpretations of absolute value though.

in fact , personally , for P4 i use 2 absolute values.

and , in fact , one of those matches mariano's given below.



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.

in a way it is neccesary to at least try to apply the old language to a 'new language' , for e.g. explaining the concepts.


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.

chill dude :)



We'll eventually come to a dispute over just what is
meant by
P1 P2 P3
as a symbolic construction.


thats not fair , in fact there is no such dispute , mariano understands P1 P2 P3 perfectly well.

( i wont mention higher to be neutral )


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.

pardon my french , but mentioning einstein doesnt make you smarter or prove you are correct.


mariano wrote :



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.

YES !

i had this dispute with timothy golden too.

you are completely correct mariano.



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)

there are 2 types of 3D numbers.

do you know that mariano ?

if you consider them to be :

1 ) P4 or R x C

2 ) R x R x R

then 2) is Beresford.

if you consider all 3d numbers isomorphic to R x C

you are wrong.


i want this clarified , because we might or might not agree on this.

and it would be silly to have a dispute based upon bad notation and misunderstandings while actually agreeing.




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/P4T3
Comparison.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

i asked above about an important opinion of mariano that might resolve this dispute and/or confusion.




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.

this is - as mentioned above - one of the absolute values i use myself for P4.

Mariano chooses to have the property

abs ( zero-div ) = 0.

which is reasonable.

and i used myself.


but there are others too that satisfy :

|x y| = |x| |y|

one could even generalize to complex-valued abs and alike.



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
]

i used that abs too.

so same comment as above.



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.

why doesnt mathematica find it in 10 minutes ??

and how did you find your abs for P4 and P5 ??

by computer ?

simple algoritm ?

fast algoritm ?



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.

i cant confirm this , i havent computed abs(P6) myself , though it looks good at first sight.

these absolute values are intresting.

there are still open questions not ?

like , whats the pattern for absolute values of P n with n as parameter ?

how about the topology of those hypersurfaces ?

let P(n) denote the abs for dimension n.

how do the hypersurfaces of e.g. P(n) = 1 look like ?

topology ?



&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]

super mario is a loser.

super sonic rules :)


-- m


regards

tommy1729
.

Relevant Pages

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