Dark Matter Update .
Andre Willers
28 Jun 2012
Synopsis :
Dark matter and energy are fictitious , but crumpled branes
seem to be real . This adds significantly to complexity . This reallity might
not be a simulated locale .
Discussion :
Briefly , slingshot-effects are sufficient to explain
supposed gravitational anomalies . They simply exchange energy between rotating
masses and linear kinetic energy . The momentum transfer is called the
slingshot effect . It also means that a significant percentage of the energy in
the system is “in transit” , as it were . We are talking interstellar distances
. It is a dynamical system . The observed effect is either an overmass or an
undermass , depending on the dynamics of the in-transit momentum transferring masses
.
The Crumpling of space-time from brane collisions actually
increases the complexity of possible paths . Luckily , we can compute this from
general theory (See Appendix I) . This is because of one of the few
Hyperdimensional Theorems we know to be true : We can always find a set of
dimensions , so that the distance R from the center of random Beth(0) movements
is R=d*Square root of(n) , where d is a
step and n is the number of steps .
This seems contradictory . But remember , these are deterministic
systems . They only become random because of random constraints . Thus ,
constraints increase randomness by the same order that the constraints are
random .
If the space-time crumpling is beyond our understanding , it is ,by
definition , random . Then we can use
the Crumpled Paper Algorithm . See
Appendix I .
See Appendix III for some Randomness .
Are we in a simulation ?
In Appendix I we derive mu=2.1773242 * 10^ (-4) , meaning
ratio of volume-of-mass to volume in a Planck Universe that is crumpled .
This is another way of saying that the possible number of
crumplings (N) is
N=2^ (1/mu) (from
Binomial distribution .)
The degrees of randomness
in the crumpling .
Also a measure of the degree of complexity .
N = 2^4592.7933 . A large number .
In Appendix II we derive a measure of complexity from observed Planck quantities and found it wanting in the complexity stakes
.
1/dx * 1/dmv
<= 2pi/h ….from Heisenberg
uncertainty principle
<= 9.482514 * 10^33
But , the complexity of the crumpling completely overshadows
the planck complexity .
Thus , if we are in a
simulation , N will have to be drastically lower . In other words few and major
folds in the space-time crumpling . These should be detectable . One thinks of
black-holes . In an artificial locale , the number of black-holes per cubic
parsec should give an indication . A nice little problem for the Dear Reader .
More likely , the number of singularities simply balance the
values of the Planck values . Not cause , but in a dynamic balance .
What use is this argument , one might ask .
Well , you can make a super-battery . Spin a particle in a
capacitor field . Very high energy densities can be achieved . Store energy in
spin .
The Karma of Constraints .
Andre
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Appendix I
Crumpling Paper and Space-Time
Andre Willers
23 Feb 2012
“The moving finger writes , and having writ , crumples it in
random ruins.”
With apologies to Omar Khayyam .
Synopsis:
Crumpled paper gives a good approximation of spacetime as a
membrane with clumpy masses .
“Empty” spaces not occupied by the membrane gives an
impression of dark matter .
We derive an expression to give this ratio using Infinite
Descent and Beth(0) Random Walk .
Discussion :
1.The Crumpled paper :
Consider a paper disk of radius r and thickness d .
It's volume is then Vp=pi * r^2 * d
Draw a line from the center to the edge , in steps of length
d , over the edge , then back to the center Let nu=r/d , a measure of the
thickness of the paper . Note that it is a pure number .
The number of steps in the line is then n0=(2r/d)+1
But the number of steps to the edge of the original paper
disk is n1=r/d=(n0-1)/2
r=d*(n0-1)/2
n0=2*nu+1
Vp=(pi*d^3*(n0-1)^2 )/4
Crumple it up in a way that is as random as flipping a coin
(ie Beth(0) )
The Trick : The line we have drawn up above breaks up into
random vectors by rotating through a third dimension = crumpling into a ball .
We thus have a continuous line of random steps of known
number of steps .
In 3 dimensions , the mean square distance from the center
then is known
R = d * (n0)^0.5 ….
See true for all dimensions as long as all are of Beth(0) order of randomness.
Volume of crumpled ball Vb=4/3*pi*R^3
The Ratio Vb/Vp = mu then gives the ratio of crumpled ball
space to volume of paper mass .
Mu={4/3*pi*d^3 *n0^(3/2)} / (pi*d^3*(n0-1)^2 )/4
Notice the d^3 term and pi cancels out . This has profound
physical implications .
This simplifies to
Mu=4*4/3*(n0^3/2/(n0-1)^2)
Expressed as thickness of paper , nu , which is a pure number
independent of metric chosen .
mu=4*4/3(2*nu+1)^3/2 / (2*nu)^2
mu=4/3*(2nu+1)^3/2 /
nu^2
This gives a quartic equation in nu , which can be solved
exactly algebraically .
(mu)^2*(nu)*4 – 2^7/3^2 *(nu)^3 – 2^6/3^2 (nu)^2 –
2^5/3^2 * (nu)^1 - 2^4/3^2 =0
Test it on A4 paper:
A4 paper has thickness d~0,1 mm and r~150 mm
nu=150/0,1
nu=1500
mu=4/3*(3001^3/2)/(1500^2)
mu=0.097421589
mu= 1- 0.90257841
This means that the crumpled A4 paper ball encloses about 90%
empty space .
This agrees with experimental results . See NewScientist.
Note that the force applied does not matter . As long as the
paper is untorn , mu will be the same .
How many times can it be folded ?
Solving the above (see below) gives mu=1 for about nu=14.7 to
14.8 .
This means there are no empty spaces left to fold into .
This can get complicated , so I will keep it simple .
Take a piece of paper and fold it . You then have a new piece
of paper .The test-circle of same r will have double the thickness .
Ie , nu will double .
Between 7 and 8 folds , nu will hit the ceiling of mu=1 ,
regardless of the starting value of nu .
This is the maximum number of paper folds , as confirmed from
other sources .
Physical interpretations :
Take an m-dimensional space . Randomness of order Beth(0)
applies equally to all . The underlying equalizer . Collapse it to three
dimensions and let the third one approach single Planck lengths .
Then we can use the above paper approximation . Notice how d
cancels out except for an addition of 1 in final ratio .
What does it mean ?
See the physical universe as a brane (ie sheet of paper) in a
multiverse . Crumpling it means it has mass and singularities . Both are
aspects of the same thing .
An estimate of the number of singularities can be made from
edges and points in crumpled paper .
Can we crumple the paper to a ball that is just paper ?
That is a particle .
The answer is “Yes” .
Such crumpling means that mu=1 (no empty space in any dimension
)
This gives an quartic equation in nu that solves to four
values , other dimensions than three denoted by i=(-1)^0.5
See http://www.1728.org/quartic.htm
for a calculator
nu1= 14.722181 (this makes the physical particle universe
possible . Mass .
Nu2= - 0.004167 + i*0.49558
(Rotation :Spin :charge and magnetism)
nu3 = - 0.004167 -
i*0.49558 (Rotation :Spin :charge and
magnetism) notice the minus sign .
Nu4= - 0.49164542 (quantum effects as the particles dither.
Inertia?)
What does a negative nu mean ?
nu=r/d . A negative nu means one of r or d must be negative .
1.If r is negative , it can be interpreted as curled up
dimensions , inside the “outside” dimensions as defined by i . See http:andreswhy.blogspot.com “ The inside
of zero” Aug 2009
2.If d is negative , it can be interpreted as quantum effects
. A particle does not “occupy” all the space . Likes hopscotch .
3.But notice the the two are interrelated .The notorious
observer effect . Where we place the minus sign between r or d .
There should be relationships between nu2 , nu3 and nu4 .
Various rotations between macro- and micro dimensions .
This means the contraption is not symmetrical But we already know that ,
Physical constants :
Things like charge , mass , etc should be derivable from
these basics . Hint:use lots of crumpled paper .
There is hope . The fact that it is quartic equation , which
is always solvable , means that the Universe can be understood . Complicated
and perverse , but as long as you stick to Beth(0) randomness , it can be
understood . For higher orders of randomness , good luck .
Dark Matter :
I nearly forgot . Using Planck units , we can define the
ratio of thickness of the brane as
nu=c*PlanckTime/(1*Planck Time)
nu=c = 3*10^8
This gives a
Mu=4/3*(2c+1)^3/2 /
c^2
Simplifying (c is very large) . This gives the approximation
mu=4/3* 2^1.5 / c^0.5
mu=2.1773242 * 10^ (-4)
mu = 1-0.999783357
This means that 99.9783357 % of the universe can be
interpreted as being “Dark Matter”.
Ie with attractive and repulsive qualities . Basically empty
space .
May you have joy of that .
An interesting aside :Creative artists .
How many pieces of paper does an artist need to crumple up
and throw away before he finds something acceptable ?
Something acceptable would translate to mu=1 . Thus , we can
say 7-8 truly random foldings should
give a result .
The same holds for cryptanalysis or any attempt to find an
unknown .
Algorithm :
Try 8 times , crumple , then put it aside and try again later
.
There is a quantum connection , strange as it might seem .
And what about a nice little Crumpling App for smartphones ?
But the randomness should be from truly random tables , not
pseudo-random generators .
Randomly yours.
Andre
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Appendix II
Slingshots , Dark Matter and Dark Energy.
Andre
Willers
17 Apr 2011
Synopsis :
Dark matter
and Dark energy are misinterpretations of slingshot effects where the
probe-mass is not infinitesimal .
In other
words , they are observational artifacts .
Discussion .
Reproduced
in Appendix A for ease of reference .
Field Theory
assumes that Probe Masses can be infinitesimal . Yet , if we combine finite
probe masses with SlingShot theory , a better fit to explain astrophysical anomalies
is obtained . Also meson interactions .
Why
Slingshot ?
1. Because
we do not have a theory of three interacting masses . But we can do it for two
masses . But everything rotates and orbits . So , we can describe all moving
delineated masses as interactions of two masses slingshotting .
2. It is a
valid mechanism for converting angular momentum into linear momentum .
See Penrose
Process (http://en.wikipedia.org/wiki/Penrose_process )
And
vice-versa .
The alert
reader will notice reactionless drives and high-energy storage devices lurking
in these seeming innocuous statements .
An Example :
A simple
slingshot , though the principles hold for more complex cases .
V2={(1-m/M)v1+2U1}
/ {1+m/M}
We choose
not to let m be small relative to M .
But we are
also too lazy , ignorant and old to count every particle in a universe .
So we cheat
and say : let x = m/M , then integrate v2 for 0 <= x =<1 .="" nbsp="" o:p="">
This means
that the probe mass m takes on finite values from zero to our major mass M .
This then includes subatomic and atomic and any other particles .
This gives values
Integral (v2)
dx (from x= 0 to 1) =
2*ln(2)*(v1+u1) ………(1)
Integral
{(v2)^2} dx (from x= 0 to 1) =
2*(v1+u1)^2 – 4*ln(2)*v1*u1 + 1 ……(2)
Equation (1)
tells you how to make an inertialess drive .
The
Spindizzy strikes again !
Equation (2)
is an Energy equation and is responsible for all those horrible contortions of
Mond (especially the last term of +1) .
It also
tells you how to make stable , high , density energy storage devices .
Remember ,
magnetism is spin . If there is spin , there are Slingshots .
Galaxies
seeming to orbit too close and fast/slow are simply exchanging slingshot masses
(cf mesons)
Bits and
pieces of the universe keep on flying around , creating space-time as they go.
It depends
on their entanglements . The present universe looks more like an amoeba , with
tentacles shooting out . The extent of space and time depends on where you
look.
Vacuoles ?
Mini-universes
created by tendrils of slingshot masses enclosing . Interesting spin effects as
different tendrils have different velocities .
These should
be able to be created in the laboratory .
Complexity :
Invert the
Heisenberg Principle to define the Complexity of a Beth(0) Universe .
dx*dmv >=
h/2pi ….Heisenberg uncertainty
principle
Let 1/dx be
all the possible values of x (ie the complexity of space)
Let 1/dmv be
all the possible values of momentum . (ie complexity of time)
1/dx * 1/dmv
<= 2pi/h ….from Heisenberg
uncertainty principle
<= 9.482514 * 10^33
This is the
measure of Complexity of the Beth(0) Universe we find ourselves in .
This almost certainly means that we are in a
simulation .
The
Complexity of Beth(0) is too small .
But is it
sufficient for open-ended complexity of Beth(>0) ?
I can intuit
that there is a threshold .
Bah .
I can also
intuit that we are probably on a chaotic boundary threshold .
Go one way ,
and you recycle (Karma concept)
Go another
way , advance .
And it was
designed this way .
Storming
Heaven .
Shooting
tendrils of space-time into the multiverse will decrease the Heisenberg
constant , thereby increasing the complexity past the threshold of recycling .
The Poor
Civilization's Singularity .
The mass of
the soul .
This can now
be calculated from first principles from the complexity of momentum .
It is about
4! gm = 24 gm relative to the
surrounding universe simulation .
And may you
have joy of that .
May God have
Mercy .
Andre
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Appendix A
The Problem with Fields .
Andre
Willers
21 Dec 2008
A sad tale of Hidden Assumptions and Fictitious Forces
.
Our story
begins with Isaac Newton about 400 years ago . He proved that radially
symmetric bodies (like balls) can be treated as a point-mass from a
gravitational viewpoint as long as f=G*m(1)*m(2)/ (R^2) holds . This is his famous Law of Gravitation
.
Fast forward
to the Twentieth Century . Space probes were measured to have accelerations not
predicted by expected theory . (See New Scientist 20 Sept 2008 p38
"Fly-by Fright." )
Fright
indeed . Physical laws were under threat .
It was first
noticed with the Pioneer probes and stimulated the MOND (Google it)
modification to Newton's Law .
But the
effect was small and controversial .
But then
even a bigger shock came . Probes doing slingshots around the Earth (like
Gallileo in 1992 , Near Shoemaker in 1998 ) showed such large divergences from
expected velocities after the slingshot that the matter could not be swept
under the carpet anymore . (The favourite human response.)
Is our understanding of physics wrong ?
No .
What is going on ?
They treated
planets as point sources in their programs .
(Remember ,
these are the guys that mixed up newtons and poundals on the Mars probe) .
The Earth-Moon illustration .
The system
orbits around a common center of gravity which lies inside the Earth .
Even school
atlases' state this .
You can
treat the Earth as a gravity point-source , but then you must include the Moon
as well (and other bodies , but their effect is very small) .
The velocity
change during the slingshot maneuver is dependant on the Earth's rotation
around the common center of gravity . The Earth-Moon rotational plane coincides
roughly with the Earths equator . Hence the observational datum that the
velocity change is proportional the difference in the angles incoming and
outgoing with reference to the equatorial plane .
What is happening ?
Are
conservation laws being violated ?
No .
Internal Slingshot .
It is simply
a slingshot maneuver around a virtual mass .
The
Earth-Moon rotating system is not radially symmetric . It is lumpy . The velocity change is dependant on a large
number of factors , but can be calculated .
The energy
comes from the weak coupling between angular momentum and linear momentum .
From a
really basic viewpoint , this can be easiest seen as the difference between a
straight line touching a circle and the continuation of the circle . (Newton's
laws measure forces by disturbances from a straight line .)
Another way
of looking at it :
The
gravitational attractions on an outside probe of masses rotating around each
other and about a common center of gravity do not cancel out . A small
vector-residue is left .
This is a
dynamical effect . Movements only need apply .
This can be calculated ,
But will
vary in every instance .
(A
software-computer (General Theory) is not possible .) This is because there are
three bodies involved :
Earth , Moon
and Probe .
The
Three-body Problem has no general solution . This is well known in
mathematics Now are you happy ?
Calculating
this gravitational difference gives rise to a disturbing effect : the
mathematical terms for the field probe does not vanish .
In hindsight
, a necessary effect because of the general insolubility of the Three-Body
problem . But not obvious beforehand .
This is
simply restating there is no general solution of the Three-body Problem .
Two bodies
plus a probe makes a three-body problem . Every case will be different . Use
Chaos theory .
This will be
true for any body in the solar System (ie Pioneer probes) , as well as any
rotating set of bodies in this Universe .
The Field Assumption .
Beloved of
theoretical physicists , mainly because they are too lazy to do it properly .
The
Classical definition is a probe mass , charge or whatever examined near the
identifiable object . The forces the probe experience are defined as the Field
. The Probe is then ignored .
This has the
hidden assumption that the effect of the probe can be cancelled out .
(Ie that it
is really a Two-body Problem).
In most
radially symmetric objects like balls or charges this can be done .
But , alas ,
it breaks down if the objects are lumpy . Then the pesky mathematical terms
denoting the probe just won't go away .
Without the
hidden assumptions about symmetry , error margins have to be specified .
We cannot
use our software computer (ie theory) to cancel out the interference of our
test-probe .
This is
analogous to Heisenberg's Uncertainty Principle , but not similar .
You have to
understand levels of Randomness
Error-margins
at Beth(x+1) level for Beth(x) levels
can be made arbitrarily small (although maybe not zero) .
General Relativity
and Tensors .
This effect
can be clearly seen if you use Ricci's Tensors to denote gravitational fields.
This is the really general granddaddy of fields .
Tensor
theory very clearly requires that tensors are only defined in continuous and
differentiable spaces . (Rather amusing , since this takes place before any
metric is assigned . Sub-Space !) Hence
the problems with quantum gravity . A quantal system is by definition discontinuous . Trying to describe it by
continuous methods is futile .
Or
Bio-fields . Things are just too idiosyncratic for meaningful abstractions
using fields .
Fictitious Forces .
The major
culprit is centripetal force (also known as centrifugal force ) . This is a
fictitional force to balance the theory's bookkeeping .
From the
above you can see that a large composite body like a galaxy composed of many
objects rotating around each other and all around a center will have a nett
attraction either larger or smaller than by gravity alone .
If larger , objects that we observe to fall
around it in orbit will have a higher speed than required by the fictitious
centripetal force of purely gravitational attraction .
Dark matter
, anyone ?
If smaller , things fly apart .
Negative
Dark matter , anyone ?
If you look
at the maths , being exactly the same will smack
of design (The probability of this is very small for Beth(0) randomness ) .
Stellar
engineering on Beth(2) or Beth(3) scale .
Does this
sound familiar ?
Dark Matter .
Phlogiston ,
ahoy! Your buddy Dark Matter is coming .
You can then
dance the Ptolemaic Gavotte .
Can Fields be salvaged ?
Maybe .
But then
horrible contortions are necessary .
Dimensions
writhe in semi-being . As a last resort , a marriage counselor might have to be
called in .
But why
bother ? There are better ways .
If you have
to , assign error margins to every field-point and interact the error-margins .
This will automatically result in spiky discontinuities . Gauss would have
loved them , but unless you are as expert as he was, try the simpler route .
Once again ,
why bother ? Use Beth(x) systems .
And if you
are feeling adventurous , try numbers that only exist at different Beth(x>1)
levels .
Guaranteed
to lose weight .
Andre .
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Appendix III
Orders of
Randomness 2
Andre
Willers
15 Aug 2008
I have been
requested to expand a little on orders of Randomness and what it means .
Please note
that human endeavours at this date use only randomness of the order of flipping
a coin ( Beth(0) )
Aleph is the
first letter of the Hebrew Alphabet . It was used by Cantor to denote
Classes of
Infinity (ie Aleph(0) for Rational numbers , Aleph(1) for Irrational Numbers ,
etc
Beth is the
second letter of the Hebrew Alfabet . It means “House”
I will first
repeat the derivation of Orders of Randomness from http://andreswhy.blogspot.com : “Orders
of Randomness” because it is so important .
----------------xxxxxx
Start Quote:
First , simple Randomness .
Flip of a
coin .
Heads or
Tails . 0 or 1
Flip an
unbiased coin an infinite number of times ,write it down below each other and
do it again .
All possible
0 and 1’s
An example :
Beth(0)
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Flips(1)
0,1,1,1,1,… etc
Flips(2)
0,1,1,1,0,… etc
.
Flips(infinity)
0,0,0,0,0,0,…etc
Xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
This
describes all possible states in a delineated binary universe .
“delineated
binary” means a two sided coin which cannot land on it’s side .
Now draw a
diagonal line from the top left of Flips(1) to Flips(infinity) .
At every
intersection of this diagonal line with a horizontal line , change the value .
The Diagonal
Line of (0,1)’s is then not in the collection of all possible random
Horizontal
coin-Flips(x) .
This means
the Diagonal Line is of a stronger order of randomness .
This is also
the standard proof of an Irrational Number .
This is the standard proof of aleph numbers .
Irrational numbers ,etc
Since any
number can be written in binary (0,1) , we can infer that the order of
randomness is the same as aleph numbers .
This means
we can use number theory in Randomness systems .
Very
important .
Google
Cantor (or Kantor)
Define coin-flip Randomness as Beth(0) , analogous to Aleph(0)
Then we have
at least Beth(1) , randomness an order stronger than flipping a coin .
Then we can
theorize Beth(Omega) <->Aleph(Omega) .
End Quote
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Cardinal Numbers .
The cardinal
number is the index x of Aleph(x) .
Cantor
proved that
Aleph(n+1) =
2 ^ Aleph( n )
Where n is
the cardinal number of the infinity .
Tying them
together :
He also
proved that
P(A) = 2^ n
Where A is
any set , P(A) is the PowerSet of A
and n is the cardinal number of set A
Thus ,
Cardinal Number of P(A) =(n+1)
The PowerSet
of A = the Set of all subsets of A .
This sounds
fancy , but it is simply all the different ways you can combine the elements of
set A . All the ways you can chop up A .
You can see
it easily in a finite binomial expansion (1+1)^n = P(A) = 2^n
There we
also chop and dice , using infinite series .
Can you see
how it all ties together ?
Why 2 ?
This derives
from the Delineation Axiom . Remember , we can only talk about something if it
is distinct and identifiable from something else . This gives a minimum of 2
states : part or non-part .
That is why
the Zeta-function below is described on a 2-dimensional plane , or pesky
problems like Primes always boil down to 2 dimensions of some sort .
This is why
the irrational numbers play such an important part in physics .
Z=a+ib
describes a 2-dimensional plane useful for delineated systems without feedback
systems
Its in the
axiom of Delineation , dummy .
But we know
that Russell proved that A+~A
The
difference can be described as the Beth sequences . Since they are derivatives
of summation-sequences(see below) , they define
arrows usually seen as the time-arrows .
These need
not to be described a-la-dunne’s serial time , as different Beth levels address
the problem adequately without multiplying hypotheses .
Self-referencing systems and Beth sequences .
A Proper
Self-referencing system is of one cardinal Beth number higher than the system
it derives from .
Self-referencing
systems (feedback systems) can always be described as sequences of Beth systems
. Ie as Beth(x) <-> Beth(y) . The
formal proof is a bit long for inclusion here .
The easiest
way to see it is in Bayesian systems . If Beth(x) systems are included ,
Bayesian systems become orders of magnitude more effective .
Life ,
civilization and markets are such . See below .
Conservation Laws :
By
definition , these can always be written in a form of
SomeExpression
= 0
Random
(Beth(0) Walk in Euclidean 2-dimensions
This is a
powerful unifying principle derived from the Delineation Axiom .
In Random
Walk the Distance from the Center is = d * (n)^0.5 . This is a property of
Euclidean systems .
(Where d =
step , n=number of random beth(0) steps)
Immediately
we can say that the only hope of the
Walker returning to the center after an infinity of Beth(0) steps is if d ~
1/(n)^0.5 . This is the Riemann Hypothesis .
Now , see a
Universum of 2-dimensional descriptors
z=a+ib
Sum all of
them . Add together all the possible things that can be thus described .
This can be
done as follows :
From z=a+ib
Raise both sides to the e
e^(z) =
e^(a) . e^i(b)
Raise both
sides to the ln(j) power where j is real
integers.
j^(z) =
j^(a) . e^(b/ln(j))
Now , sum
them :
Zeta=Sum of
j^(z) for j=1 to infinity
Now we
extract all possible statements that embody some Conservation Law . Beth(1)
This means
that Zeta is zero for the set of extracted statements if and only if (b/ln(j))
is of the order of Beth(0) and a=(-1/2)
Tensors .
The above is
a definition of a tensor for a discontinous function .
Riemann’s Zeta function.
This can
describe any delineated system .
If Zeta = 0
, conservation laws apply .
Zeta =
Sigma(1/j )^z for j=1,2,3,…,infinity and z=a+ib , where z is complex and i
=(-1)^0.5
The z bit is
in two dimensions as discussed above .
This
function has a deep underlying meaning for infinite systems .
If you
unpack the Right-Hand side on a x-yi plane you get a graph that looks like a
random walk .
If every
point is visited that a random walk would visit over infinity (ie all) ,
without clumping , then Zeta can only be non-trivially zero if a=(-1/2) .
Why (x – yi)
plane ? See “Why 2 “ above . The system is fractal . Two dimensions are
necessary in any delineated system .
Remember ,
randomwalk distance from origin = step*sqrt(number of steps) .
So if the
steps = 1/ ( sqrt(number of steps) ) , then the Origin might be reached if and
only if a= -1/2
This is
easily proven .
If a= - 1/2
, then b can be any real function . This would include Beth(0) and Beth(1) , but not higher orders of beth .
If a= -1/2
and b is an unreal number , then a cannot be equal to -1/2 anymore . Conservation cannot hold at
any level .
Consequences:
Conservation
Laws can only hold for Beth(0) and Beth(1) systems .
This is
forced by the two dimensions of delineation .
Mathematically
, this means that Beth(2+) systems of feedbacks can only be described in terms
of attractors or/and fractal systems (ie not in isolation)
Physically ,
conservation of energy and momentum need not hold for Beth(2+) systems .
This has an
interesting corollary in decryption (unpacking) . A Beth(2) mind unpacking
Beth(0) or Beth(1) encryption is functionally equivalent to Non-Conservation of
Energy .
Some other consequences :
If a<
-½ , then Riemannian Orbitals are
described . Beth(any)
Also
described as nuclei , atoms .
If a>
-½ , then a diffuse cloud is described .
Beth(any)
Also
described as magnetic effects .
What does
this mean?
Present
technology uses Beth(x) technology in a rather haphazard way .(Quantum physics)
.
A better
understanding will bring about a sudden
change in capability .
Andre
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