Reciprocal System Research Society

Dave, have you been able to come up with a reason for these coincidences? They appear to be geometric relationships. Square roots are indicative of a phase relationship between two different geometries.

For example, in a recent conversation with Doug, he reminded me of the old solution to the Pythagorean "square number" problem, where the hypotenuse of a right triangle of side = 1 was the sqrt(2), which was an irrational number and incompatible with the Pythagorean take on numbers.

The solution was that it was actually a square of side = 2, 2², and the hypotenuse was just one side of the inscribed square of 4 diagonals, the length being the inverse measure of 2^1/2. So it could be represented with whole numbers, that number being the relationships of 2. The only time it became irrational was when the inverse measure was viewed in the perspective of the original measure, not from its own perspective.

With the use of square roots in the constants, it looks like something similar going on where the "inscribed" geometry is that of time, related to the circumscribed geometry of space.

Have you investigated these constants using complex numbers, since i is a rotational operator? The imaginary component might give a clearer picture of where the constants originate.

bperet wrote:

Dave, have you been able to come up with a reason for these coincidences? They appear to be geometric relationships. Square roots are indicative of a phase relationship between two different geometries.

I haven't yet, but I was flipping through Tetrascroll by R. Buckminster Fuller, and found this...

from http://lampsacus.com/documents/Buckmins ... scroll.pdf

"Goldy goes on to discover that multiplying

numbers by themselves can be identified not only

with the rate at which the number of similar squares

multiply within a modularly subdivided square but

also with the rate at which the number of triangles

multiply within a modularly subdivided triangle,

accomplished by a symmetrical and modularly

uniform three-way grid, subdividing any triangularly

bound area. A triangle whose edge module is two

has a two-times-two-equals-four- triangles area. A

triangle with edge module three contains nine

similar triangles. Edge four contains sixteen similar

triangles, edge five contains twenty-five similar

triangles, and so on. Whereas this phenomenon of

“second powering” of numbers has always hereto-

fore been identified (even by all scientists) only with

“squares,” Goldy saw that a square consists of two

triangles and that identifying the product of a given

number multiplied by itself only with “squaring”

requires twice as much area as does “triangling” and

is therefore inefficient. Since she has been assured

by physicists that Nature always employs the most

economical (or least effort) solutions to its prob-

lems, Goldy decides to adopt “triangling” as her

method of accounting area experiences and discov-

eries.

Goldy then discovers that a second multiplying of a

number by itself (i.e., 2 X 2 X 2 = 8) as a method of

volumetric accounting can be identified with the rate

of omni-symmetrical expansive growth of tetrahedra,

whereas scholars, including scientists, have always

identified this third powering of a number exclu-

sively with the rate at which cubes multiply them-

selves when symmetrically amassed in an arithmeti-

cal progression of the overall cubes’ symmetrically

and modularly divided edges.

Goldy finds that each cube has six square faces

which, being structurally unstable, collapse but

which can be subdivided into two triangles each by

the six diagonals that bisect each of the cube’s

square faces. The six diagonals are produced by

omni-interconnecting four of the cube’s eight

corners-two of the opposite top corners with each

other, and the latter with each of the two diagonally

opposite bottom corners as well as interconnecting

the latter two bottom corners with each other.

Not only do the six omni-interconnected diagonals

of the six faces of the cube structurally stabilize the

cube with minimum effort by omni-triangulation,

but those diagonals are seen by Goldy also to be the

six edges AB, A C, AD, BC, BD, CD of the tetrahe-

dron, which Goldy has already found to be not only

the minimum structural system of Universe but also

to be one quantum unit of the quanta mathematics

of the physicists."

Regarding my post above about 210, check out this 3D Pascal Triangle (Fig 13), and look at the center number...
http://buckydome.com/math/Article2.htm

If the levels are viewed as possible permutations of displacement ratios (the side ratios always total 8, ie, 7:1 6:2 5:3 etc) we have an interesting way to view to possibilities of displacement ratios. Larson says S/T is always 1 to 1, but one component reverses.

I'm intrigued by spin being integer multiples of (sqrt3)/2. This has the look of a tetrahedral relationship.

Also, check out this fascinating plot of primes...

http://buckydome.com/math/ulam/triangle.htm

While trying to figure out why the decimal result of 1/89 results in the Fibonacci numbers, I came up with a new way to find the reciprocal of a number.

If you want 1/7, take 10-7=3, and take the infinite sum of the following series...

3^0 /10^1 .100000000

3^1 /10^2 .030000000

3^2 /10^3 .009000000

3^3 /10^4 .002700000

3^4 /10^5 .000810000

3^5 /10^6 .000243000

3^6 /10^7 .000072900

3^7 /10^8 .000021870

(repeating)

=.142857... repeating

When you do this in Excel, it's amazing to see how the increasing powers of (10-n) "line up" to keep the repeating decimal going!!!!!

I think this SUMMING as opposed to Division may have something to do with the Zeta function...
http://www.timetoeternity.com/time_spac ... e_time.htm

By the way, while 1/89 appears to give the Fibonacci numbers, it is really giving the squares of 11, as becomes visible when you give the numbers a little room to express themselves...

1/89=0.011235955056179775280898876404494

1/989=0.0010111223458038422649140546006067

1/9989=1.0011012113324657122835118630494e-4

1/99989=1.0001100121013311464261068717559e-5

1/999989=1.0000110001210013310146411610528e-6

getting there...

from http://en.wikipedia.org/wiki/Riemann_zeta_function

During several physics-related calculations, one must evaluate the sum of the positive integers; paradoxically, on physical grounds one expects a finite answer. When this situation arises, there is typically a rigorous approach involving much in-depth analysis, as well as a "short-cut" solution relying on the Riemann zeta-function. The argument goes as follows: we wish to evaluate the sum 1 + 2 + 3 + 4 + · · ·, but we can re-write it as a sum of reciprocals:

(see link above, text is gargled.)

Yea!, it IS related to Pi, just found this...(!)

from http://www.geocities.com/hjsmithh/Numbers/Zeta.html

The Riemann Zeta function:

Zeta(x) = 1 + 2^−x + 3^−x + ... = Sum{k=1, infinity}[k^−x], x > 1.

Zeta is defined for all values of x except x = 1 where it is infinite.

For example, Zeta(2) = 1 + 1/4 + 1/9 + 1/16 + ... = Pi^2/6 = 1.64493,40668,48226,43647... .

And why is this remarkable ?

...because PI is the half of the natural counterspace unit (turn) ?

Horace wrote:

And why is this remarkable ?

...because PI is the half of the natural counterspace unit (turn) ?

The turn in counterspace is unbounded; it has infinite angle so it would just be an integer count. Now, when you have to project that turn into observable space, there is no way to represent the concept of an unbounded/infinite angle, since you have to use the laws of the observable environment which say that a "rotational motion" is BOUNDED (like linear motion is bounded in counterspace as a vibration). So a Turn of 'n' angle becomes a rotation of n/2(2*PI) in space.

Looking at Dave's concepts and references, I see three connected factors:

1. They are spatial measurements of counterspatial events.
2. They are scale variant, requiring a series expansion to define ("hall of mirrors" measure).
3. The numerical coincidences are shadows on the wall of Plato's cave... projections.

One can learn a lot from shadows, but I think it would be far more interesting to find what is casting those shadows, then extract the "coincidences" from that projection. That would be pretty awesome.[/]

davelook wrote:

While trying to figure out why the decimal result of 1/89 results in the Fibonacci numbers, I came up with a new way to find the reciprocal of a number.

If you want 1/7, take 10-7=3, and take the infinite sum of the following series...

3^0 /10^1 .100000000

3^1 /10^2 .030000000

3^2 /10^3 .009000000

3^3 /10^4 .002700000

3^4 /10^5 .000810000

3^5 /10^6 .000243000

3^6 /10^7 .000072900

3^7 /10^8 .000021870

(repeating)

=.142857... repeating

When you do this in Excel, it's amazing to see how the increasing powers of (10-n) "line up" to keep the repeating decimal going!!!!!

I think this SUMMING as opposed to Division may have something to do with the Zeta function...
http://www.timetoeternity.com/time_spac ... e_time.htm

Amazingly, this can be generalized in the following way...

18-5=13, so sum the following infinite series...

5^0 / 18^1

5^1 / 18^2

5^2 / 18^3

5^3 / 18^4

... = 1/13

for lower numbers, ie 11+2=13, 11 is 2 LOWER than 13, so sum the following series and it still works...

-2^0 / 11^1

-2^1 / 11^2

-2^2 / 11^3

-2^3 / 11^4

-2^4 / 11^5

... = 1/13

davelook wrote:

I think this SUMMING as opposed to Division may have something to do with the Zeta function...
http://www.timetoeternity.com/time_spac ... e_time.htm

Very interesting article on the Zeta function, and synchronistically, very much like the post I just made!

They are talking about the projection of a complex relation (here a 1-dimensional function), with the Riemann zeros occurring where the function is COMPLETELY imaginary--the real component being zero. Thus, it disappears from observation. They are implying that these disappearances occur at the prime numbers, or quantum energy level "gaps", which makes sense because we observe SPACE, and when there is no space to observe, we'll get a gap (discrete break).

Zeta(n) = 1 + 1/2ⁿ + 1/3ⁿ + 1/4ⁿ + ...

If that doesn't look like a Time Region function (s=1, t varying), I don't know what does! The denominator with the increasing series is scale variant, with a fixed dimensionality. Riemann put in complex numbers for 'n' -- equivalent space + temporal rotation.

Quote:

And now whoever cracks it will find not only glory in posterity, but a tidy reward in this life: a $1 million prize announced this April by the Clay Mathematics Institute in Cambridge, Massachusetts.

Hey Gopi, want to help me work out the math of this as a TR function, based on the RS, and I'll split the million dollar prize with you and move to India, where the money would actually be worth something! Man, can you imagine what winning that prize would do for the acceptance of the RS theory? Not to mention what it would do to your standing at IIT Kanpur--can you just imagine Snape's face?

bperet wrote:

Hey Gopi, want to help me work out the math of this as a TR function, based on the RS, and I'll split the million dollar prize with you and move to India, where the money would actually be worth something! Man, can you imagine what winning that prize would do for the acceptance of the RS theory? Not to mention what it would do to your standing at IIT Kanpur--can you just imagine Snape's face?

A mouth-watering proposition, particularly the last part!

Let me get these exams out of the way, and I am all in!

Yes, go for it guys!