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

Hi TRoc,

Are you sure?... degrees are such an arbitrary unit to relate to such a "pure" number in the Universe. Why would "God" choose 360 degrees in a circle over some other number? The "ratio" might have some deeper purpose and that would be important.

For interest here is a "goldmine" of "fine structure constant" derivations ... you never know one may be a "natural".
Fine Structure Constant Collection
I kinda like I. Gorelik's solution because it ties into what we were discussing elsewhere.

Cheers

GE,


You asked "Are you sure?... degrees are such an arbitrary unit to relate to such a "pure" number in the Universe."

My answer: I'm only as sure as the accuracy of the equation above. (not very)

All I'm saying is that it CAN be approximated by using phi. I am questioning the concept that nature uses quantities that are EXACTLY represented by our numeric symbols. Man's 1 = God's 1 ?? This leads to the question: Are approximations good enough? My answer: most likely.

We all know Pi's value. It is in practical use now, and for a thousand years (or so) prior. We still don't have the EXACT answer; but it WORKS in approximating a circle when you know the radius.

We could use 355/113 to APPROXIMATE Pi, but that would be a waste of time, because we already have 3.14_.. which works! (why do the extra calculation?)

The same can be said for the above discussion, we really don't need to divide 137 point anything by 1 to get the fine structure constant, because our predecessors have defined it for us, and with an accuracy that is already bordering anal.

Let us move FORWARD in our knowledge (not in loops). I showed you an approximation for energy in electron volts. It works EASIER (with less computations) than the system shown to me by "the book." I came up with it by trial and error, not by, for example, the sq.root of 1.96468_..e-3. That type of procedure makes "the system" MORE complex; something I believe we should stay away from. (given the current state of UNDERSTANDING)

If energy transitions take place in INTEGERS, then we are allowed to "round off". One electron volt is going to do something predictable; and it won't significantly change "the system" if 1.0935_.. electron volts are used instead.

Just some ramblings on 360: It is the best number to use because it is divisible by the most integer quantities, AND cover the IMPORTANT angles of 90/270 (x axis), 0/180 (y axis), and the "45's" (to allow sine curve-like tapering off of interactions).

If we divide a circle (or a forward moving 2 phase virtual spiral) by 12 equal parts, and analyze the "colors" of the parts (frequencies), is it COINCIDENCE that there is a "separation" at 138.4165_.. degrees that divides yellow and green? Fine structure does not apply here, it can only be used to define values between cyan and yellow. This is completely analogous to there being NO harmonic between B and C in sound. This means that, from 0 degrees, values less than 138.4 (ie. 137.0360..) can be viewed as dualistic. From 180 degrees, in the same direction, you can make another separation. What you end up with is "red" and "yellow" frequencies as being a duality, and "violet" and "cyan" being another. At low frequencies, you see the same lines of separation represented by the void between E & F, and B & C. In electromagnetism, the 90 degree EMF demonstrates the same principal. Now our wave mechanic has the right tool in his box.

The virtual spiral is CONTINUOUS, and the coupled dualistic phases are QUANTUM (discreet). This is where we need to go in order to join SR/GR and QM. Gravity is not a "coupled" wave, but still is seen to "propagate" at © because of the relationship between mass and inertia. If you could subtract that relationship, gravity would be seen as "instantaneous".


T.Roc

Oh right! I didnt see it that way thanks Troc

GE & all,


I apologize for any confusion I have caused, which, if you were following the last 2 paragraphs, surely must have happened. I left out a KEY part of the idea.

You divide the circle into 12 equal parts, and this gives the Quantum.

However, Time is Continuous; in order to make a complete turn (cycle, octave, etc.), you must ADD a step because the "zero degree" line is also zero time. That is reflective of nothing, and we are looking for symmetry.

If we (the 12 yogis) are going to share a pie that is cut into 12 pieces, and we remove them 1 by 1 (take a mental picture of the pie with 1 piece missing), when we are at the last piece, we have ANTI-symmetry. (reverse direction) If the "act of removing" the pieces is called a "step", then we will have to take 13 steps to return symmetry. Consider the mental picture of the 1st piece missing, and its' opposite, all EXCEPT the 1st piece missing.

So, in my previous post, I failed to mention that 138.41615_.. was a "time", or step derivative. At the 5th step, we have removed 5 pieces, and are at "the line" between the 5th and 6th piece. In my color analogy, this is the line between green and yellow. You can not subtract values from green to get yellow, and you cannot add values to yellow to get green. (this is current theory)

1/13 is a "step", 1/137 is a "piece".

I cannot resist mentioning the "esoteric" properties of the numbers 1-3-7

1 = the beginning; the tonic
3 = the dimensions; the function of the triad
7 = the fundamentals; the basic approach
(13) = the "secret", or hidden approach to circular symmetry

I hope that my idea is more clear to you now.


T.Roc

All,


So, now we have two sets of numbers, each produced by an "internal code". Our standard "n+1", and the "golden set" of N=N(-1)+N(-2). (the "-" symbol representing position in the set from N)

Let me introduce another that might meet the requirements. The idea is to produce ALL possible whole integers, have fast "build up", include resonance (probably THE most important single "phenomenon" in Science), not include zero (as a quantity; we can still use exponentials), allow rational numbers, have symmetry, use circular, or spiral geometries (the sine wave/vibration), and if you could produce some constants, that would be a bonus.

The set {1,2,4,8,16,32..} certainly meets the resonance criteria, produces very large numbers quickly (ie. 3x10e8), has no zero, could produce the spiral form BUT, it lacks true symmetry (all Yin, and no Yang), leaves out the irrationals, and (AFAIK) produces no Constants.

We have the Good, The Bad, and the Ugly. Well, ok, we have the Slow (but complete), the Beautiful (but sporadic), and the Fast Harmonic (but selfish).
It's starting to sound like a family reunion! It's almost as if these sets could produce personalities too. Hmm..

Is there a way to combine these 3 sets? Some set that will satisfy our need to reproduce the reality that we see? A set that would cover such profound and independent concepts such as Harmony, Resonance, Vibration Waves, The Quantum, Electromagnetism, The Speed of Light, Gravity, Attraction/Repulsion, Direction Relative to the Observer, The Spectrum of Visible Light, Thought, Sound, Intuition, Smell, Taste, Conservation, Frequency/Wavelength, Spin, Consciousness Levels, Multiple Wave Relations, Symmetry, Duality, Energy, Etheric "particles", Heat, and the things that can be produced with the above ideas, in case I left them out.

That is quite a tall order, but I believe that is what we are Seeking. An "Omni-band Harmonic Matrix of Resonant Potentials", or something to that affect.



TRoc

Hi RC,thanks.


TRok, ZAPPER,Good Elf ,esin, ZEPHIR, and all.


GREVITATION AND TEMRETURE (HEAT CAPICITY) DIRECT RELATION MAY BE.
Gravitation permits to capture heat within nucleolus, not allowed radiating or conducting, not very with thermoplastic flow as convection of heat (out coming plates cool down but
Drop mass regain heat within magma.)(Earth never going to cool down. captured heat at equilibrium states.)
Each point of material from surface of globe to centre gravitation force and heat capacity both increases.
Gravitational pressure of vicinity mass of any globe of existence (IMPOSE SHRINK EFFECT-EXITED STATE OF MATTER) towards center of body posses and capture allow holding thermal energy (CURRECTION BY EXPANSION-EQUILIBRIUM OF EXITEMENT).
Same atom heat capacity increase refers towards centre. (Increase from surface to centre)

In matter positive raise temperature (above Kelvin) from surface to centre. (Planets)

In anti matter negative raise temperature (below Kelvin) from surface to centre. (Comets)

Why gravitation permits to capture heat within nucleolus, not allowed radiating or conducting, not very with thermoplastic flow as convection of heat.
Sintering process we are aware of.
Answer is when gravitation increases pair nucleons within nucleolus (p-g and n-g)lying d closer, which is exited states, correction done by increase heat capacity, absorb and permitted to posses, so nucleons lying apart again.
This is stable states of existence

Giving example of compression of spring by gravitation, decompress by temperature.
Each globe of universe subject to combine gravitation/temperature effect. (May be some option here)

Combine effect is pulling the mass is attraction from surface up to any intermediate vicinity of globe.

Combine effect is neither attraction nor repulsion to mass is nature within intermediate vicinity of globe.

Combine effect is below intermediate vicinity of globe up to centre of globe Combine effect is mass subject to up thrust. (Negative gravitation) or repulsive gravitation force observe.
GREVITATION AND TEMRETURE NEED TO COMBINE STUDY.NEVER THEY SEPARATE EXIST.
I think.

Hello, Everyone.

I just posted over in the TOE forum, where I've asked a few basic questions. Turns out that the concept of the scalar potential (‘SCALAR’ OMNI-DIRECTIONAL POTENTIAL) is easily identified in the number system by simply considering something that, according to Hestenes, Clifford was the first to recognize the importance of, but originated with Grassmann: Two interpretations of number are possible, the "quantitative" and the "operational." The quantitative interpretation answers "how much" or "how many," but with the operational interpretation, number describes a relation between quantities.

This has a profound impact on things when we define a scalar number this way. For example, we can take the mysterious number 1 (which is what we are starting the TOE off with, when you think about it), and by operationally defining it, we can do away with zero, and form, from the natural numbers, the rational numbers. So, 1/1, a rational number, formed from the first and most important natural number, becomes the perfectly symmetrical scalar of the integer number system, though an operational interpretation.

Here's how: n/n = n+1/n+1 = n + ...n/n+...n, which is scaling in its truest and finest form. But by spontaneously breaking the symmetry to m/n, or n/m, our operationally defined scalar becomes the signed integer system, without zero! That is,

...n/m, n/n, m/n = ...-1, 0, 1...!

Thus, in one simple step, by changing our view of what a number is, we've generalized the natural number system (counting numbers) to include "direction," or a polarity.

The next step was also shown by Clifford. By expanding the dimensions of the signed integers, operationally interpreted, we can generate the reals, the complexes, the quaternions, and the octonions, which generalizes numbers to include "direction" and three dimensions + the scalar. Taking the dimensions to higher numbers only causes a repetition of the original pattern (Bott's periodicity), which should tell us something about the meaning of higher dimenisons.

To see how this works, just look at the first four rows of the Pascal triangle.

More later...

Excal

Rock Instead of n+1 in a decimal or some other finite base why not an infinite base?

This is as close as I can get to your thought. Would God need to use a finite base in math? I think not.

Excal,

Thank you for the differentiation. I had failed to define the opposing (dualistic) concepts of operational and quantitative. My posts in the TOE project took much longer because of that. The key difference between what I seek, and what you have posted, is that I would like to traverse the line between positive and negative without generating the problematic Zero. {-1,0,1..} This is done with the first set mentioned, using Phi/phi as the operator. {-1.618,-.618,.618,1.618..}

Nick,

No, I do not believe God (or the beginning cause) would use the finite base. Indeed, I do not believe there would be "math" at all; that would be our after the fact interpretation of the duality (quantitative vs. operational). If you have followed my TOE posts, you will see my view on a concept that is "one" being interpreted as dualistic (two) only after some "movement" has taken place (position, reflection, observation, etc.).


ALL,


I believe that Wave Theory is the answer that we seek, and that our current Wave Theory is focused entirely on one half of the duality. Namely the operational side, or more relevantly, the form of the wave. From Taylor and Euler, to Schroedinger and Einstein, our focus has been on the form of a vibrating string (including curvature of "space-time"). It is not surprising that many great minds of today are looking for "strings" in space, and still viewing empty space as being endowed with the potential for "curvature". In Socratic form, I ask "what of the flute?" The manifestation that we call "sound" is not created by the deforming of the instrument, yet the flute and violin can be "coupled" in coherent vibration, from simple to complex.

My Theory will focus on the other side of the duality, the relationship of the vibration after its formation. My "set" will reflect this, and produce consistent numeric answers to the combination of 3 or more vibrations. If you think deeply, you will see that we have only studied 1 at a time, or the relationship between 2 vibrations (that are often couched in duality such as cold/hot, +/-) I will not change any of these understandings, only go to a more fundamental level that will better explain the known, and allow us to enter a new era of understanding the complex.

I will post this set in about a week from now.


from Cusco,
TRoc

Try to have look to the Aether wave theory. The spacetime changes are forming the massive environment for the subsequent dimension convolution / vibration level according the geometrodynamic theory.

An up and coming junction-

JUNCTION
#1.
We should NOT eliminate the possibility that the total "bulk" did not change/evolve to become our universe. It could still be there. We could be an embedded/sprouted universe in this "bulk" that we perceive/observe to have operating instructions/rules/laws/structures/particles which could be different then the in the "bulk".
#2.
The words that we use will influence the development of our logic. I hate the word "sphere" because it automatically includes 3d.
We should eliminate the possibility that our universe could have have gone through a 2d stage or even that "a 2d spot" can be oriented/folded/rotated/spin which would make us perceive 3d/etc.
I know that I could have used a diferent word. (string/branes/membranes/wave)
jal

All,


Some introductory thoughts:

From 0 to 1
How can something arise from nothing? I believe it to be impossible.

From 1 to 2
How is this primary resonance (& duality) performed? (a "double" value) Keep in mind that whatever function you do must be repeatable, and continue to produce harmonic values. It cannot be "plus one", as I have shown above. It cannot be "multiplied by itself", or we would never get off the ground.

Restating some requisites: Produce the digits 1-9, so our system of math is the same. Produce irrational numbers (nature doesn't seem to mind "rounding"). Use resonance and harmonics as primary functions. (also produces large numbers in the fastest way) As simple as possible (dualistic, symmetrical, rotational). Not allow, by any function, to arrive at "nothing" (zero). Perhaps most importantly, be reflective of the world we see, hear, and feel (other senses too, but these have the most empirical data accumulated; ie. "light, sound, and temperature"), even as far as outlining consciousness and communication of thought. If your brow is not "crunched up" right now, you need to re-read! There is no way to fully understand what I have just said without building the "Omni-band Harmonic Matrix of Resonant Potentials" for yourself (on MS Excel, for example) and PRINTING it (& then pasting the pages together). It is too big to appreciate on your monitor, and I will not attempt to do it for you. It will be available "at fine bookstores near you" in the next few weeks, at a price that should be less than your "wage" investment of the 1 hour or so needed to make your own copy.

(here: to 5 decimal points for brevity; for the complete story: allow for 15 per column, 13 columns, and start with 1.0267093)


{1.02670, 1.08776, 1.15244, 1.22097, 1.29357, 1.37049, 1.45198, 1.53832, 1.62979, 1.72671, 1.82938, 1.93816, 2.05341}

The "operator" is the 12th square root of 2. (1.059463094355929526456182529494)

Subsequent "rows" in the "matrix" are harmonics of this row; down from this row, all values are x2 ; up from this row, all values are /2 .

The CENTER of the matrix is vertically between column 7 and 8, and horizontally between row 14 and 15. (with the above "set" being row 1)

© 2004 Thomas Roccetta

enjoy!

TRoc

To your questions:


Do not start this on your line (row) 1 in Excel. Start at around line 50 (or 100 if you want a larger matrix).

I do not know if the up/down direction is infinite; I have a hunch that the numbers will "merge", or "reconnect" at some magnitude, as they do from right to left.

You will need to go at least 35 row down from line 14, and 35 rows up from line 15 in order to "see the light" (in color!).

The most important constant produced is the speed of light. Rotational-symmetric movement products from the CENTER produce ©. (IE. up 1 and right 1 x down 1 and left 1; or up 35 and right 5 x down 35 and left 5)


TRoc

I hope a newbie contribution is OK here..

My thought is that a 'proper' universe would have collapsed back into itself very rapidly. The result being that we have the 'wrong' constants which (fortunately) don't work properly. We may be looking for elegance in what is essentially a foul-up. A very nice foul-up so I'm not complaining.
-c2

I'm trying to learn how to post a picture.