Twitter and URL
Andre Willers
25 Apr 2013
Synopsis :
Why is Twitter so popular ?
Because it reaches 98.85% of the search space .
Discussion :
1.See Appendix AAA
Twitter started with a 140 char limitation . Then added URL’s
. Then shortened the URL’s to 20 bytes . https://support.twitter.com/articles/78124-posting-links-in-a-tweet
This means that a max of 140/20 = 7 . allowing for some other characters , this
means that 6 URL’s can be added .
This is a Small-world Network .
This reaches any search space with 98.85% efficiency .
With an infinite number of characters in the targets of the
URL’s .
2. Twitter is then simply a news network on steroids . With
infinite depth . But with a handy
abstraction effect .
Twitter is smarter .
3.Why does the military like it so much ? .
A new user immediately notices all the US military who want
to be followed . They know that the data self-assembles into credible threats .
They just want more data .
Also , it is just cool .
4.Lies and Twitter :
Roughly 2/3 of anything on Twitter are lies .
Humans having fun and profit .
Humans prefer a mixture of 2/3 lies and 1/3 truth .
A Celebrity mixes these up in a fractal froth .
5. Twitter with URL’s can reach where ordinary URL’s cant .
All this for only a AAA battery and my wife’s virginity ?
You see what I mean .
Regardez cherchez .
Andre
xxxxxxxxxxxxxxxxxx
Appendix AAA
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
xxxxxxxxxxxxxxxxxxxxxxxxxxxx
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 upper boundary of the
reserve needed to survive failures in any element of the Cost-Universe
. Ie , internal fluctuations .
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
Xxxxxxxxxxxxxxxxxxx
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)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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
----------------xxxxxx
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
Xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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
Xxxxxxxxxxxxxxx
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
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
xxxxxxxxxxxxxxxxxxxxxxxxxxxx
No comments:
Post a Comment