MATHEMATIC/NUMBER-THEORY INSIGHTS from TOE project, Discuss TOE implications for maths/geom.

Hi all,



IAMoraes-

I wouldn't call "thinking" a talent. It seems more in the realm of "auto-function", like breathing. Very fortunately, we have a written history to look upon, and to use as "starting points of thought", where we can apply logic, and other sources, to come to new conclusions.


You are showing an "instinct", if this is without any prior "thought":

We have a fairly long tradition of assigning "imaginary numbers" to these "not-dots", like "-1" , "sq rt -1" ( i ), and "zero". From there, measuring the "wiggle" of energy in space and time (including the complex plane) has progressed to the state we have today.


http://mathworld.wolfram.com/RiemannHypothesis.html

In this link, http://primes.utm.edu/notes/rh.html , we get a little more of the details:

Yet another way, that I call a "harmonic zeta function", which enters the field of irrationals , that is bound (limits) by "1 and 2"; also defining "one" as that interval, rather than between "0 and 1". It is "quasi-logarithmic", yet perhaps better stated as a "spiraling exponential". It is "emergent" from the assumption that "something" (1) exists, prior to the "question", or experiment. My personal opinion is that, to "emerge from zero" requires too much complexity, and even a bit of "magic", or the need to suppress "questioning" itself, and instead, be content with a "belief". (ala the Copenhagen Interpretation) This is also consistent with the "fibonacci" like build up, with the assumption of "one" as a dualistic starting point.


I want to leave those "indeterministic" values behind, and live in a World that transcends the separation, and unites through "shades of resonance".


If there is a pattern in the "zeros", that is accessed through an "alternating zeta function", which requires "imaginary concepts" like "-1", and its square, and that pattern also lines up with "1/2" in the "Real part", what does it say about the relationship between 1 and 1/2 (or between 2:1/2)? Did the "zero" exist between 1 and 2 ?


We hear, in MV Berry's words, that " ..a mysterious hidden structure in the density of the primes in the rising number sequence which he defined using a quantity that he called the Riemann zeta function. There are fluctuations in the density that are encoded in a series of frequencies, or magic numbers, called the Riemann Zeros. Bizarrely, these frequencies appear to match the energy levels of the periodic orbits of the quantum equivalent of a chaotic system."

Caustics, catastrophes, and quantum chaos
Nexus news, Feb 97


"Bizarre" is a word that loses its meaning the more the phenomenon occurs. Will it still seem bizarre, when we see that the same "not-dots", when represented in the way that I have mentioned, in the quantum equivalent of an ordered system, the frequencies "appear to match the energy levels of the eigenstates of the periodic table & isotopes, as well as the Standard Model particles" themselves?


In simple terms, an ordered representation captures the symmetry of the "equilibrium states", while a disordered representation captures the symmetry of the "perturbations" to said "ground states".


The only "fine tuning" (renormalization/scaling) that this method uses, is "fractal/autopoietic", and stems from a relativistic relationship between "frequency", and the constant " c ", as f = c^2, c^3, c^4..
The "fundamental form" is "doppler shifted" until (@~c^2), the "helix" begins to create new "closed space", and we find the seeds of inertia, and topological charge.


See Is the electron a photon with toroidal topology? for part of this story.


The exponentially increasing interval must be "re-gaged" in order to keep subsequent measurements relative to our "universal" starting point. However, the "new metric" is a fractal boundary: it is the same simple ratios that we started out with, that allow "sub-steps" to be taken between our original intervals.



regards,

T.Roc


This post has been edited by TRoc on Sep 5 2007, 09:57 PM

BTW,


You may be interested in this, as it applies to fundamental experiments, like the double slit:

link to DSE thread.


You might want to read back several pages from there.



ciao,

T.Roc

Technology.

I am sorry, I can't comment intelligently because I don't understand much mathematics. However, there are many many places where the fact that 1 has *four* halves screams at me. I don't even really read the material sometimes, I just scan them and there it is.

That is not a mistypo , I said 1=1/2+1/2+1/2+1/2.

I am doing something lately and got to thinking that because while a galaxy has a black hole as a nucleus the system may will add to 1, but if a galactic nucleus is a double black hole, then the whole system would add up to more than 1. But I already said that the "spin" of a black hole is 2 and I am unwilling to contradict myself because I Can't Not Be Right

The "Reimann hypothesis", whatever that is (I have never seen it written in BASIC thus it is incomprehensible to me) can only be right if, ultimately, it takes the form of the "certainty" principle, which would be roughly
"Any product n divided by one of its divisors gives a leftover of zero"

If there is no universe except for a system whose value would add up to 2 (because I am reducing ad absurdum by considering a minimal universe of total value 2, and nothing else) then there is NO "any product" in a system whose whole value is 2. There is only 2. Thus the process of finding a result is a whole 1 and the rest of the system is the other 1 for a sum total of 2. Thus, what this "half" that the Riemann hippopotamus keeps bumping into is supposed to be is a limitation of a mathematical process, limitation that has an entire value of 1. The "field of irrationals" or "imaginary" numbers these equations deals with only has a value of 1/2 and 0 has a value of 1/2 too. If it weren't I would be contradicting myself twice: 1-I have stated that there is something between adjacent alephs, and there is no chance I will back from that because I am a *** --the statement is literally worth a million dollars which I will never get but neither will anyone else. (loooong story... and I won't tell it.); and 2-I have stated before that the radius of a 1d circle is half the area of the 1d circle, and I am not willing to go against that either.

This is all very much an abstraction, of course, and I will keep from mentioning it ever again because I look like an idiot stating extremely specific conditions of truthlyhoodness for an equation that I do not understand nor care to in a thread I can contribute way too little to.

I will definitely take a close look at the links and papers that you suggested, but don't expect much from me from this point on... I am way out of my depth. Sorry

But thanks for the links, T.

How important was the planck lenght to begin the actual Special project....

0 1 2 3 4 5 6 7 8 9 10
0 1 1 2 3 5 8 13 21 34 55
0 1 2 3 5 8 13 21 34 55 89
0 1 2 3 5 8 13 21 34 55 89
0 1 2 3 4 7 11 18 29 47 76
0 1 2 3 4 5 9 14 23 37 60
0 1 2 3 4 5 6 11 17 28 45
0 1 2 3 4 5 6 7 13 20 33
0 1 2 3 4 5 6 7 8 15 23
0 1 2 3 4 5 6 7 8 9 17
0 1 2 3 4 5 6 7 8 9 10

hppnq


was that a question, or an answer?? (or a statement)


J-

Some would say the answer is 42, but I suspect it is rather to be 44. So it makes me wonder why E8 has only 8 or so rings of 30 vertices...

What is 42, what do you suspect is 44, and what does it have to do with E8 and/or its rings?

re: 42
http://en.wikipedia.org/wiki/Answer_to_Lif..._and_Everything

re: 44
I'm currently pondering the intersection of concentric circles and keep seeing 11, 22, 44 ''ripples'' appear. I was thinking it could be a strange interference pattern andor some emergent property of intersecting circles. Anyhow, it looks cool. Since then, I figured out it's simply the nature of concentric circles. Voila!

re: e8
E8 has very interesting properties. (http://en.wikipedia.org/wiki/E8_polytope)
I was counting the rings of the dots and the spacing of those rings and was left wondering why it structured so.

PJ Parent


This post has been edited by PJParent001 on Jan 18 2008, 01:27 PM

Interesting pattern.

Modified Fib series it would seem, excepting the counting numbers at the begiining and end. Are you referencing the curve formed?

And why the rejiggerring of the first terms? To show the correlation in rank distribution manner?

Feel free to expand, as your intent is unclear to me.

======================================

By way of comparison, a few Fib Scales beginning with index # -2 (n= - 2) and ending with index # 12 (n = 12)

Fibonacci (F_n)
-1, 1 :: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

Lucas (L_n)
3, -1 :: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322

Golden (G_n)
-1, 3 :: 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555

-------------------------------------------------------------------------
And two I've been working with, the naming convention being mine since they currently have no name:
-------------------------------------------------------------------------

Ionian (I_n)
7, 1 :: 8, 9, 17, 26, 43, 69, 112, 181, 293, 474, 767, 1241

Negative Ionian (0_n)
17, -9 :: 8, -1, 7, -6, 13, -19, 32, -51, 83, -134, 217, -351

======================================
A Few IOnian (I:0) Scale Identites

|I_n| - |O_n| = 10*F_n
(for n not = to 1)

|I_n| + |O_n| = 8* L_n
(for n not = to 1)

|I_n| * |O_n| = 10*(F_(n-3))^2 + F_(n+3))^2

======================================

You can create some pretty interesting geometrical constructions with these if you imagine cycling "across" the scales rather than simply back and forth down one progression "string." Will eventually post a couple...

Also important to note is the palindromic nature of the Golden Scale.

ex. 131, 212, 343, 555, 898

Best,
Raphie

This post has been edited by Raphie Frank on Jan 28 2008, 06:38 PM

Hej RealityCheck et all,

Generalized recursive operations

This has a fascinating intutive appeal, especially the appearance of even negative integers-just like trivial 0 of Riemann zeta function.

What are the few next values on other axis (- 3, ..., - 5, ... ) and how accurate they seem to be? Meaning is e.g. -1,85..(fixed point of recursive pentation) really close to asymptotic value or it can be - 1,9..

I am asking because of this sum:

=1/1,85035452902718^8-1/(2*1,85035452902718)^7+1/(3*1,85035452902718)^6-1/(4*1,85035452902718)^5+1/(5*1,85035452902718)^4=0,007297583=1/137,0316766

which makes sense to me as long as we include only (operations up to) pentation in its approximation.

So long as pentation is faster than tetration, it means that processes (phase transitions) described by tetration need pentation to run processes inside them, - and so on. Infinitely nested phase transitions and not only phase transitions- nested time scales in general.

Ivars Fabriciuss

Our learned and intuitive notion that mathematics are creatively limited are based on fact that the part of MATH that deals with OPERATIONS (motions) was essentially left undeveloped since infinity and divergence was forbidden and engineering took over "exact" sciences. In principle, You are able to "differentiate" operation to get a new one by a set of rules that is not more complicated than normal math, just contra intuitive). You just need a space of operations, space of structures (which we know are set infinity apart) and some correspondence set between them by (infinite) set of observer functions. As there are 3 of them , there will always be scales at which they are not in balance, so uniqueness and certain unpredictability at certain scales will be present still.

In this sence, 1/2 is a balance point between Operations and structures ( numbers) while Observer functions are in no way in perfect balance- in fact, thay have infinite number of balances on both sides of this balance. They are like ropes that hold this 1/2 balance in place, rooted in both predominantly motion ( infinitesimal, SQ, imaginary) and predominantly structure ( above quantum, number, negative) spaces.

This post has been edited by Ivars on Feb 5 2008, 11:55 AM

no but now that you mention it, it would seem you might know

FOR COMPARISON & CROSS-CORRELATION
(for any who may be interested...)

Mersenne Prime Exponents (0 - 22)
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941
via Wikipedia: http://en.wikipedia.org/wiki/Mersenne_prime

FIB SERIES (0 - 22)
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711

LUCAS SERIES (0 - 22)
2, 1, 3 ,4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603

GOLDEN SCALE (0 - 22)
2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 898, 1453, 2351, 3804, 6155, 9959, 16114, 26073, 42187, 68260, 110447

Best,
Raphie

P.S. This is kind of "neat." Sum seven terms beginning from M_16:

S (M_16, M_22) = 2203 + 2281 + 3217 + 4253 + 4423 + 9689 + 9941 = 36007
= 100 "Logical Circles" + 7

Also note the large "gap" between M_19 and M_20 relative to the terms preceding and postceding...

This post has been edited by Raphie Frank on Feb 9 2008, 07:08 AM