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 21/2. 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.
Constant coincidences
Constant coincidences
Every dogma has its day...
Constant coincidences
bperet wrote:
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
I haven't yet, but I was flipping through Tetrascroll by R. Buckminster Fuller, and found this...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.
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
Constant coincidences
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
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
Constant coincidences
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... .
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... .
Constant coincidences
And why is this remarkable ?
...because PI is the half of the natural counterspace unit (turn) ?
...because PI is the half of the natural counterspace unit (turn) ?
Constant coincidences
Horace wrote:
Looking at Dave's concepts and references, I see three connected factors:
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.And why is this remarkable ?
...because PI is the half of the natural counterspace unit (turn) ?
Looking at Dave's concepts and references, I see three connected factors:
- They are spatial measurements of counterspatial events.
- They are scale variant, requiring a series expansion to define ("hall of mirrors" measure).
- The numerical coincidences are shadows on the wall of Plato's cave... projections.
Every dogma has its day...
Constant coincidences
davelook wrote:
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
Amazingly, this can be generalized in the following way...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
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
Constant coincidences
davelook wrote:
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:
Very interesting article on the Zeta function, and synchronistically, very much like the post I just made!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
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:
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?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.
Every dogma has its day...
Constant coincidences
bperet wrote:
Let me get these exams out of the way, and I am all in!
A mouth-watering proposition, particularly the last part!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?
Let me get these exams out of the way, and I am all in!