What is an Integer ?

Andre Willers

8 Apr 2013

“God made the integers, all the rest is the work
of man.” Kronecker

Synopsis:

Defining an Integer is a Hard Problem . Use Riemann’s Zeta
function , Small World Network and Hyperreal numbers to define an Integer .

Discussion :

1.All this should be nauseatingly familiar to anyone who has
done any work in Prime Numbers or RSH cryptanalysis .

2.We start with apples (pears are for the advanced classes)

3.Count them . 1 apple , 2 apples , 3 apples etc to n apples
.

4.Now take that favourite instrument of humans , a humongous
big hammer . Smash Apple1 to smithereens . How many apples do you have now ?
The correct answer is still n apples . The first apple is still there , but
kinda spread out .

5.This spread can be described as a Small World Network . We
can connect and reassemble the apple to any desired degree by using the
algorithm as described in Appendix AAG (Six degrees of separation)

6.What about the lost apple bits ? This why Appendices AAA ,
AAB,AAC,AAD,AAE,AAF is there .

This is just to show that they are immaterial to defining
the integer . The Riemannian orbitals in Appendix AAG of levels 6-7 should do .

7.Finding lost apple bits : They only seem lost . If R
levels of separation was used , the lost bits can quickly (order of 3 quicker)
than random Beth(0) search by using Bayesian systems on the previous levels .

8.Atom Smashers : the same principles apply . All those
millions of plates of futile particle tracks can be re-interpreted . Maybe they
will even find the wily Higgs Boson .

Though he is probably off in the nearest pub getting even
more smashed with the other bosuns .

9.Willers Integer Fractions .

I can’t find any description of this on the Net ,

The alert reader will have noticed that Appendices AAA , AAB
, AAC, AAD means that any integer can be defined this way .

But some bits of the apple will stay lost . See Appendix AAF
. This leads to paradoxes via the usual Cantor's diagonal argument

This leads to expansion of logical systems . See Appendix AAE
.

This leads to the conclusion that all cynics always
suspected : that nobody is all there . Only now we can compute it and use it .

10 .Numbers not all there :

This has a major effect at very small levels . The paradox
simply means that the systems are in superposition . This means we can
manipulate parts of numbers “outside” the number that affects the whole number
.

10.1 Number Spin :

Numbers must then have spin . And we can store energy and
momentum in the spin and release it as we require .

Remember , this is at quantum foam level , but we can
manipulate it at macro-levels .

11. Casimir Amplification .

An example will make it clearer .

Take two ordinary casimir plates . Dot the plates with laser
diodes in sending-receiving fashion . As small as possible, but really small
scales are not necessary . Remember , the EMF will stimulate the “lost” bits of
the numbers , which are still entangled .

This induces a spin on the number . This stores much more
energy than a normal capacitor .

But the eventual energy release can be steered .

11.1 Electricity (charge propulsion) . Like an ordinary
capacitor . Same equations can be used , only much larger energies .

11.2 Selective momentum transfer . A reactionless drive .

A sheet of laser EMF just parallel to one Casimir plate
should do the trick . The spin energy in the integers gets translated into
linear momentum .

Well , it will happen to a lesser degree with high-power
radar installations . I have noticed that really big phase-array radars are very
over-engineered from a mechanical strength viewpoint . This is because they are
actually inefficient space-drives .

The engineers simply strengthened it to work , and the
scientists swept it under carpet . A typically human response .

12.How large ?

I don’t know . See Appendix AAH . At least of the order
squared , with upper boundaries depending on design . I can’t seem to see a
upper boundary . Even black-holes are countered by spinning action .

13. Can numbers have black-holes ?

Yes . We know the answer to this one because it is the brane
we are in .

So , spinning numbers will give 27 quantum levels , each one
generating a mathematical black hole .

The energy storage at max is then information energy = 2^27
of a Avogrado number of electron rest mass energy

This gives

E= 1.34x10^8
x6.022x10^23 x8.19x10^(-14) joules

E = 6.6089 x 10^18 joules per mole

E = 6 g of TNT

Gasoline : 48.1 KJ/mole
See http://www.wou.edu/las/physci/GS361/Energy_From_Fossil_Fuels.htm

The ratio(R) of maximal storage of Spin to Gasoline is then
:

R = 6.6089x10^18 / (48.1x10^3)

R= 1.374 x10^14

This is kinda large , even taking into account
inefficiencies .

A single mole of spin storage is then theoretically
sufficient to put 10^7 grams into orbit . About 10 kg . And it can be scaled up
.

14.Failure to launch :

Will humans do anything ?

Doubtful . You can tell them explicitly . But still they
will ignore it , then moan and complain when the sky falls .

Gaia is going to kill all humans if they do not get
off-planet . They foul their own nest , but Gaia does not really mind .

What did trigger it was the light reflected from orbital
satellites . Even small ones .

15.Somebody much smarter than humans programmed Gaia to
destabilize the planetary weather-ecology on rhythmic stimuli from light
signals from orbital satellites . Especially polar orbitals .

Everybody prays to God . Why are you surprized that He
answers ? Even millions of years before
your prayer .

A not so subtle hint to get the lead out Mac .

Andre .

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Appendix AAA

A delineable entity .

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Appendix AAB

A delineable entity , usually repetitive over time that
allows an infinitesimal matrix

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Appendix AAC

An infinitesimally Fuzzy number is the same as a number .

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Appendix AAD

An infinitesimally Fuzzy integer is the same as a integer .

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Appendix AAE

Equivalent to Beth(1)

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Appendix AAF

The original statement of the paradox, due to
Richard (1905), has a relation to Cantor's diagonal argument on the
uncountability of the set of real numbers

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Appendix AAG

This post was published to Andre's Why at
09:32:36 PM 2013/01/27

**What is an Integer ?**

Six Degrees of Separation Derivation

Andre Willers

27 Jan 2013

Synopsis :

We derive Reliability Percentages for Degrees of Separation
from first principles of Small World Networks . Six Degrees has at most 98.85%
reliability .

Discussion :

See Para 15 below for a real surprise .

1.Small-world Networks :

“A

**small-world network**is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps. Also known as degrees of separation .”
The major principle is that not all
points(nodes) are interconnected . The nodes are clustered , with clusters connected
by long connections

2.Examine an existing Small-world network in
2 dimensions . Sketch it on a piece of paper (2 dimensional) . The connections
are shown as lines .

3.Define a Start node . The sender of the
original message .

4.Then connect the Start Node with every
other node , counting the number connections as Hops . This is computationally
possible (not Hard) because not all nodes are connected .

5.Now , rewrite the Network Map in terms of
Hops , Hops being the radius units from the Start node .

This gives a map of circular bands around the
Start node as origin . The bands include all the nodes outside the Start node ,
with many duplicates .

The duplicates are important . Cluster n-hops
are in them .

This is basically a Riemann-orbital system .
See Appendix H .

6. The Trick !

We minimize the system by squeezing any
wandering test path on the system to return to the Starter Node .

In effect , Riemann’s theorem . We know that
it returns to the origin if the real exponent = -1/2 .

(The only-if part exp=-1/2 is evident , but the theoreticians and
red-pencil brigade have too much fun nit-picking)

7. The upperbound :

We can then calculate the Upperbound and
Reliability percentage :

The actual Zeta = Sigma(x(i) / i^(1/2) , i=1
, 2, 3 ….

Where -1<= x(i) <=+1 at Beth(0) random
for any i .

For the upper boundary , we set x(i) = 1 .

This gives :

Zeta (upper) = 1+(1/2)^0.5 + (1/3)^0.5 +
(1/4)^0.5 + …

The Sum(n) = 1+(1/2)^0.5 + (1/3)^0.5 +
(1/4)^0.5 + …+(1/n)^0.5 , the sum of Zeta(upper) to the n’th term .
This is increasing .

The Diff(n) = (1/n)^0.5 – (1/(n+1))^0.5 is the difference between successive terms
.This is decreasing

The Ratio(n) = Diff(n) / Sum(n) and is
decreasing .

The Percentage Reliability PR(n) =
(1-Ratio(n)) x 100

8.Table of Upperbound Reliability percentages
for minimized Small-world Networks :

N denotes number of degrees (hops) in PR(n)
below

PR(1) = 70.71%

PR(2) = 92.40%

PR(3) = 93.97%

PR(4) = 97.02%

PR(5) = 98.47%

PR(6) = 98.89%

PR(7) = 99.11%

9.What does this mean ?

It means “you pays your money and you takes
your pick “

You get the most bang for your buck at about
n=6 .

Small-world networks are very efficient at
distributing information .

Remember , this is a very general derivation
.

10 .What if just one node is left out ?

I suspect that the above will still hold .

It is a topological suspicion (the worst
kind) . Even one little puncture causes a major shift in topological
classifications .

In the class of “a little bit pregnant”

This has major consequences in the real world
.

Plan on that there is always somebody on the
“need-to-know” list being left out . This might be you .

11. What if many nodes are left out ?

Surprisingly , the system will default to 70%
efficiency . Civil Service level . But remember that this is only the
upperbound .

But is this then the Lowerbound for PR(2) and
better ? I Think so , but some deeper
analysis is called for .

No wonder civilization manages to struggle
along .

Notice how close it is to 67% of Appendix H
Infinite Probes .

12.The Family Paradox :

“My spouse does not understand me .”

Of course they don’t . You are at PR(1) = 70%
reliability as long as you communicate directly (eg language) . Just about
bottommed out .

Add some more nodes . Usually this is
children , grandparents , friends , hobbies , interests .

But different levels like emails , notes ,
flowers , presents , etc will work .

Even saving the Dodo .

Join the Dodo Liberation Army .

13. This is equally applicable to your work
environment .

14. A surprising application .

How to turn your personal network into a
Small-world network .

(Then you can use the system as described
above )

14.1 Get long-range contacts . Pen-friends .
Internet friends (but be careful) .

Even one will change the topology of your
network .

You don’t have to frantically network .

14.2 Virtual Topologies :

An imaginary friend .

These are available .

Notice the interesting addition of Internet
at the bottom of Maslow’s hierarchy of needs .

A Facebook account for an imaginary friend
with strict access control will bounce parental communication with a child from
70% to 90% .

15.Marital Problems :

Or even between couples who have
communication problems . A virtual friend on Facebook where only the two
partners have access will increase communication by a whopping 20% !

What a surprise !

Not exactly what I was expecting .

15. Upgrading to higher dimensional networks
.

Project the many hops onto a
two-dimensional space as above . Then
crumple them . See Appendix C .

This collapses into the same Riemannian space
as discussed above

16. Virtual Topologies :

Viva La Dodo Liberation Army !

Andre

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Appendix
H

__Infinite Probes 2__
Andre Willers

30 April 2008

From discussing this with various recipients , there
seems to be a need for a simpler explanation . I thought I had explained it in
the simplest fashion possible . The subject matter is inherently complex .

But , here goes .

__How much must you save ?__
If you save too little , a random fluctuation can wipe
you out .

If you save too much , you lose opportunity costs . If
you are in competition , this loss can be enough to lose the competition (ie
you die)

Intuitively , you can realize there is an optimum
level of saving .

Methods exist of calculating this optimum in very
specific instances (ie portfolios of shares ,eg Kelly criteria , or tactics in
war eg MiniMax ) .

__The General Case__
We need to hold a Reserve in case Something goes wrong
. But we do not know what thing goes wrong .

Infinite Probes tries to answer the general case .
What is really , really surprising is that a answer is possible .

The Infinite bit comes from using the mathematical
expansion of the Definition of Eulers Constant e = ( 1 + 1/2! + 1/ 3! + … 1/n!
+ …)

Where n!= n*(n-1)*(n-2)*(n-3)*…*(1)

This approaches a constant , widely used in
mathematics and physics .

(e = 2.718…) .

All we need is a system that can be subdivided
indefinitely (to infinity) .

First , we divide by 1

Then 2

Then 3

Then 4

And so forth till infinity .

What is important is not that we do know what these
divisions are , only that they are possible . We also do not know which one
element goes wrong .

The other critical insight is that it is the relation
between elements that is important . (Permutations) (The failure of an element
in total isolation cannot affect the whole system by definition .)

We can count the number of relationships where there
is failure of one element .

It is n! , where n is number of divisions where only
one failure .

Multiple failures are handled by summing :

Our Reserve(R ) is divided by n to infinity and summed
.

TotReserve= R*( 1 + 1/2! + 1/ 3! + … 1/n! + …)

TotReserve= R * e

To find the boundaries of our Reserve , we set
TotReserve = Cost

Then

R = 1/e * Cost

R ~ 0.37 * Cost

__What does this mean?__
This method measures the

**needed to survive failures in any element of the Cost-Universe . Ie , internal fluctuations .**__upper boundary of the reserve__
This is the surprising bit . Any society that keeps at
least 37% reserves , can only be destroyed by something outside it’s envelope .
It is internally stable , no matter what .

Empires like the Ancient Egyptians , Romans , Chinese
are possible , as long as there is no climactic fluctuation , new inventions ,
diseases ,etc . Rare events . Hence the technological stasis of old
civilizations . The two are synonymous .

This is true at any scale (except quantal , by
definition.) .

Individuals too . Humans can be seen as empires of noospheres
.

The upper boundary does not take any double-counting
into account . It is true for any system whatsoever .

A truly remarkable precise result from such general
axioms .

__The Lower Boundaries .__
This is where it gets interesting .

Remember , we are just counting the number of ways in
which permutations of one element can fail . We then sum them to get the effect
of the failures of other elements

The easiest is the business that just starts and is
not selling anything . It fails on n elements on every term . It’s floor
capital must then be

R=Cost/(1+e)

R=0.27*Cost

This is the initial reserve to get off the ground .

This is true in any ecosystem . This is why it is so
difficult to start a new business , or why a new species cannot succeed . Or
why waves of pandemics are scarcer .

For the epidemically minded , this 10% difference is
responsible for the demise of the Black Death ( smallpox outcompeted bubonic
plaque variants for the CR5 access site.Ironically , the reason why we have
only a limited HIV plague is the high competition for this site , probably some
flu vectors . As one would expect , the incidence of HIV then becomes inversely
proportional to connectivity (ie flights) .

A cessation of airplane flights will then lead to a
flare-up of diseases like these .

Not exactly what anybody has in mind . )

When we find that we really need the spread of
infectious vectors to stay healthy , then we know we have really screwed
ourselves .

**.**

__These are the two main boundaries__
The literature is full of other limits the series can
approach . Keep a clear head on what the physical significance is .

__Fat__
I cannot leave the subject without the thing closest
to human hearts : appearance .

Fat and fitness .

Sadly , the present fad for leanness is just that .
The period of superfluous food is coming to an end .

Rich individuals can afford to be lean because the
reserves are in the monetary wealth Women have to bear children individually ,
so they cannot store the needed reserves externally . Hence their fat storage
is close to the theoretical optimum even in Western societies (33%) . In other
societies the percentage is about 37-40% .

Human males have been bred (Mk III humans) for muscle
and little fat (8% in a superbly fit male) . He does not have reserves to
withstand even garrison duty (even little diseases will lay him low .) Note the
frequent references to diseases laying whole armies low .

Note what is left out : the camp-followers . They
survived The women and babyfat children . Every army seeded the invaded area
with women and children .

The bred soldier has to eat a high-carb food
frequently : not meat or fat , his body cannot store it . This is the
definition of a wheat-eating legionary .

__Ho ! Ho! Ho!__

__The Atkinson diet .__
No wonder it does not make sense in evolutionary terms
.

Mesomorphic humans have been bred not to transform
expensive proteins and fats into bodymass .

The soldier-class were kept on a carbohydrate leash ,
which could only be supplied by farming .

__The Smell of Horses .__
Horses exude pheromones that promote body-leanness in
humans . This has an obvious advantage to horses . Horses are breeding jockeys
.

The time-span is enough : at least 8 000 years . (400
generations)

Because pregnant women cannot ride horses , there was
a selection pressure to breed horses who have a pheromone that block female
dominance pheromones , especially since females have to weigh more because of
fat-reserve considerations .

Outside a farming environment , horses will sculpt
their riders as much as the riders are sculpting them .

Small Mongolian ponies , small Mongolians .

This is why alpha-males like horses and
horse-dominated societies were able to conquer and keep matriarchies .

Note the effect of the pheromones on women riders .
Androgeny .

On males it becomes extreme blockage of oestrogen . It
seems like a surge of male hormones , but it is just an imbalance . (If too
much male hormones , the men just kill their horses )

This is why the auto-mobile had such a big
sociological effect . No horses , so the men became more effeminate .

Want to be Lean and Mean ?

Sniff Horse sweat pheromone .

Perfumiers take note .

__Dogs__
The other leg of the human-horse-dog triumvirate .

Dogs accept female pack-leaders and have evolutionary
reasons for blocking horse inhibitions of human female pheromones .

While the males are away , the females look after and
rely on the dogs .

(The reason why Mongols ride from yurt to yurt: they
are too scared of the dogs.)

With dogs around , the male testosterone activity is
ameliorated . This is a well known effect , especially if horses are around .

Hence the female love of lap-dogs . They are actually
quite ferocious , and exude large amounts of pheromones that soothes the savage
male breast .

Your attention is drawn to the Pekinese lapdog , which
has had a disproportionately large effect on human history .

If this sounds convoluted , it is because this is
exactly how this type of bio-system operates : by inhibitions of inhibitions of
inhibitions ,etc .

Andre

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Appendix IV A

**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

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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

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Appendix B

For Blast

Blast
from the Past

Andre
Willers

13
Jan 2012

Synopsis:

High
intensities of gamma- and X-ray radiation on Earth from the center of our
galaxy can be expected during 2013 AD , due to an infalling gas cloud into the
central Milky Way black hole .

Discussion
:

The
discovery was made by Stefan Gillesson of the Max Planck Institute for
Extraterrestrial Physics

in
Garching , Germany .

References
:

- “Nature” , DOI 10.1038/nature10652
- “New Scientist” 17 Dec 2011 p16 “Cloud suicide could
transform black hole”

A
gas cloud of an estimated three earth masses is expected to impact the
supermassive , rotating black hole at the center of our galaxy (“Sagittarius
A*”) in 2013 AD . Note that radiation from this event can be expected shortly
afterward in local time .

A
large part of this mass will be converted to electro-magnetic energy .

Now
, three earth masses is not a lot of energy in the galactic scheme of things ,
but the way it is distributed does .

Briefly
, the energy release is characterized by very short wavelenghts (gamma or
x-ray) and lobe-shaped distributions of the pulse-wavefronts in the galactic
ecliptic .

There
is a combination of relativistic and quantum effects in the last few cm's
before the event horizon .

1.There
is a slingshot effect , because the gas cloud must be lumpy , even if only at
atomic scale . The gas cloud vanishes in a few Planck -time units , emitting
very short-wave radiation due to differential tidal friction .

2.But
the black hole is large and rotating , which forms time-bands of slower time ,
which gives enough time for feedback . Depending on the size and rotation speed
of the black hole , this will lead to 2n lobes of wavefronts on the rotation
equator , where n=1,2,3,...

3.Hawking
Burps .

This
process in para 2 above “foams” the event horizon , leading to a drastically
increased Hawking radiation . (The “foam” would be something like Sierpinsky
chaotic triangles)

The
density and time-band concentrations of energy separates particle-anti-particle
pairs to give Hawking radiation .

This
burp of energy sweeps matter from the neighborhood of the black hole and
reduces the mass of the black hole , preventing black holes from swallowing
everything . Elegant .

4.Turning
a Hawking Burp into a White Hole .

There
is a narrow window where the Burp becomes self-sustaining . A large black hole
then evaporates in an awesome release of energy . Even the tiniest random
fluctuation (eg matter-antimatter) will get magnified and perpetuated .

Not
the place to take your mother for a picnic .

5.Foaming
Space-time .

Well
, space-time is already foamed , but only to a simple level . (Quantum foam)

Call
it Foam(0)

We
can churn this to higher orders of foam (Foam(1) , Foam(2) , Foam(3)
,...,Foam(b) )

where
b can be derived from Kantor's Aleph classes combined with chaos theory .

Taken
to the logical extreme , this leaves only Foam ordered into Branes .

The
smile on the Cheshire cat just after he brushed his teeth .

So
what does this mean to us ?

A
full frontal impact from a lobe will give a definitive answer to Fermi's
Paradox : “Where are they ?” Why , extinct .

More
likely is an immersion in the higher radiation levels alongside the lobes for a
long time .

Can
be survived , given enough warning .

Apply
to the Max Planck Institute for Extraterrestrial Physics for more .

Friday
the thirteenth can be quite a gas .

Andre

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Appendix
C

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

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

Xxxxxxxxxxxxxxxxxxxxxxxxxxxx

Appendix AAH

How spin energy and rest energy relates (sort of) . A lot of yakkity–yak
.

But a non-linear relationship E~ (Spin) ^2 seems to exist . This suggests a
quadratic maximum . As expected from a capacitor-type system . Energy storage
over a certain max will lead to a discharge . But the energy storage will be
very much larger than ordinary capacitors.

I am too stupid to calculate it .

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