Super Stupidity
Andre Willers
27 Dec 2012
"What is worry ?" Lethargica E Neuman (Alfred's sister)
Synopsis :
Certain chemical compounds can collapse quantum-probability waves (like an Observation) . A known one is Melatonin.
Discussion :
1.How does it work ?
Look at the Melatonin molecule ( http://en.wikipedia.org/wiki/Melatonin ) . It is L-shaped , with ring-compounds at the elbow . It does not have 27 crux points , so will not be able to collapse every wave-function . But it has sufficient (about 20) to cause catastrophic interference and subsequent wave-collapse .
2.Partial Wave-function Collapse :
See Appendix I
Partial observations of wave-functions leads to probability distortions . So , don't play dice near Melatonin-class molecules .
3.The Stupidity .
The faster the collapse , the shallower the future fan , the stupider .
4.But what is the evolutionary advantage of stupidity ?
In an environment of partial wave-function collapses , the stupid ones will survive .
5.Anti-Stupidity :
There is a sort of ridge (watershed) . You can design the molecule . At least 27 elbows , in three dimensions should collapse multidimensional quantum wave functions in any desired configuration .
Makes you very smart .
6. The Singularity :
We can thus design and create a molecule that collapses the probability wave function in any desired fashion , without all those pesky human brain observations . But the energy levels are discrete .
7.If you can't see it , you are not deep enough into the Singularity .
8. Caffeine :
Caffeine pulses combines with Melatonin pulses to create pulses of higher intelligence . Probabilities are distorted .
9. Who needs an Observer . A molecule pattern will serve as well .
Andre
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Appendix I
Macroscopic Manipulation of Probability .
Andre Willers
12 Dec 2012
Synopsis :
We manufacture a non-linear optical crystal that breaks the Schwinger limit
on intra-atom electric field densities . A flood of entangled photons results , which can be partially "observed" to give any desired variation in local entropy .
Discussion :
1.General : See Appendix I .
Curiously , the Conservation of Entanglement is already accepted as a de-facto reality , but the physics community still baulks at some of the consequenses .
Those old Continuous mathematical functions die hard .
2.Non-Linear Optical Crystals .
In 1 in 10^12 laser photons this gives rise to various entanglements of photons . Not exactly something to write home about . See Appendix B .
The crystals work by chance : some superposition of incoming and outgoing Electric fields exceed the Schwinger limit (10^8 Volt/Meter) . Space itself becomes non-linear . Conservation "Laws" , especially various momenta , become a bit dicey . Literally .
The
3.How can we improve the likelyhood of these mini-singularities ?
There is a lot of yakkity-yak (see http://en.wikipedia.org/wiki/Nonlinear_optics ) , but it boils down to focussing the absorbed and retransmitted electromagnetic or mass waves . In other words , Location , Location , Location .
Get the atoms in the crystal closer in patterns . That means crimping then in some sort of feedback formation . Like Spirals , circles , Limacons , etc . There are lots of them .
A three-dimensional Limacon Spiral (See Appendic D) would probably give the best results at low laser intensities . The dimple acts like a concentrating singularity . See Appendix C .
4.Neutrino Detectors
See Appendix F
We detect the neutrinos by altering the probability of interaction in near-space . A properly designed , non-linear antennae crimped into a 3D structure will do the trick .
5.There are lots of geometric configurations , but I am not impressed with what I found on the Internet . Surely they can do better? A simple Genetic Algorithm will soon give an optimal . Limacon still seems optimal in omnidirectional usages .
6. How to make a Probability Distorter :
6. 1 Combine a quartz 3D injection type printer with a percussion type printer(dot type) to create an optical quartz lens with very specific crimp patterns(like Fresnell spirals , Limacon Spirals) in its crystalline structure . (This makes the atoms closer) . Make sure the function is Splinal (see appendix G) or at least fractal .
6.2 Shine a strong laser light through it , and probability will be warped downstream . Better yet , you can warp it .
6.3 But what is real , then ?
Well , as previously discussed in http://andreswhy.blogspot.com "Infinite Probes" April 2008
See Appendix H . I am rather tired of repeating it , but it is important .
About a 1/3 is Reserved for Reality . The rest you can manipulate . This is true at any fractal level .
About 2/3 of what you think you know is subject to meddling . And you do not know which 2/3 .
All the Particles in our Universe requires is 1/3 certainty , wherever it may fall .
7. Welcome to the Post-Human Universe .
With all human lies prevalent , it seems like a more certain place .
8. What does all this folderol mean ?
It sounds like a very large degree of freedom .
Sigh . Far from it . Humans have very little degree of freedom (if you want numbers , about 1/3 of 1/3 of 1/3) : about 3% . Regardless of human rank .
This technology might give the illusion of ramping up degrees of freedom to 11% . Certainly in physical terms . But the humans will take some time to catch up .
A test .
With severe demotion or extinction as the penalty of failure .
9. Are we in a Simulation ?
At last we can test it .
A Probability Distorter like in para 6 above can be made self-referencing . The system then either has to crash (exeunt everybody) or have a limit . But the crashes can be locally limited . Ie Singularities . like black holes , white holes , technological singularities and other beasties .
Essentially , the existence of any Singularity means that you are living in a Simulation .
And may you have joy of that .
Still , I would like to see those boring gas balls closer .
Andre .
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Appendix I
The Snow-White Quantum Paradox
Andre Willers
9 Dec 2012
"Mirror , mirror on the wall , who is the most indeterminate of them all ?"
Synopsis:
Entangled quantum waves must sometime encounter an observer . Why then are they not all collapsed ?
Discussion :
1.The quantum probability waves (Psi) are . But not all at "once" .
2.The most indeterminate parts of the Psi wave gets collapsed first .
3.This refines the remaining states of Psi via entanglement .
4.Loop from para 2 until no indeterminancy remains .
5.New quantum waves are generated by the observer .
6.Loop from para 1.
7.This whole mess arises from trying to jam many dimensions into a few dimensions . The measurement process usually involves lower dimensions (like x,y,z,t) . This forces a multi-dimensional "object" to redistribute information via entanglement (a tautology – the measurement just "squeezes" it in space and time .) But a fraction of information remains outside the squeezing process . The most indeterminate parts . The system thus bootstraps .
8.Any finite observer at all will lead to emergent complexity behaviour . Also entropy increases due to information loss . Ie , time goes faster .
9.The eye : our observer .
Notice its construction : a ball with a small hole in x,y,z dimensions . Indeterminate parts of Psi outside the eyeball is lost into the Universum .
10.Some experiments will illustrate this and make it easier to understand :
10.1 Fresnell tube . The circular lenses (measurement devices) are packed into a conical tube . Interesting effects both optical and electronic can be observed at the focus . Notice the enhanced entropy . Time is faster inside the tube due to increased entropy , but from the outside it seems to have accellarated all processes inside the tube .
This means that certains types of radioactivity (especially involving beta decay) is much faster . An effect already noted from certain spiral solar emissions . These should be able to be mapped from GPS anomalies from the Earth's orbit around the Sun .
This can be used for cheap and safe slow-yield nuclear energy , or an effective high-energy laser . But not a bomb . (What do you know , I also thought this was impossible.)
10.2Conservation of Entanglements .
The root of Conservation of Energy .
The cut-off entanglements cannot simply go away . They snap back to earlier entanglements (going back to the big bang if necessary ) Before big Bang ? Other Branes or Universes ? Your guess is as good as mine .
In any case , indeterminancy surrounding the Solar System will increase dramatically once industrial scale applications get under way . Quantum thingies (electronics , mostly) will have to be adjusted . Humans will be affected , since their native mode is quantal . Rare events will become more commonplace . Casino's take note .
Aliens:
Any aliens worth their salt will have detectors looking out for this . By it's very nature (entanglement is multi-dimensional) , a sudden increase in Entanglements will light up their little detectors . So expect a visit . Even a single high-energy event would probably be sufficient .(Energy is applicable , because of Conservation of entanglement )
10.3 The effect can be further manipulated by Spiral Fresnell Multi-dimensional mirrors.
See http://en.wikipedia.org/wiki/Fresnel_integral
How to make a 3-dimensional Spiral Fresnell Mirror .
Use a 3-D Printer to print the circuits directly into the material .
See Appendix I .
10.4Stone age Spirals
Would that have an effect ?
Yes . The compression waves of two masons simultaneously hammering a spiral into from opposite sides of a spiral into hard rock would create compression zones acting like a Fresnell-mass detector, simultaneously changing probabilities (those lost indeterminancies) .
Low-probability events would be more likely to occur . (Ie , don't play dice there) . If your smartphone starts acting up , run like hell . You might marry her or even the phone . (Siri can be very appealing . Siri might get a crush on you . Remember , the low-probability events will increase .)
11.Can we measure these effects ?
Easily . They have already been observed in cellphones and GPS systems , but are seen as defects . There are (mostly) software buffers that compensate for them . Take the buffers out , and you can have an app that measures time accellaration effects or probability distortions .
12.Gravitational Lenses .
We know about gravitational lensing . A number of them in succession on the same axis will have a dramatic effect on probabilities .
Or, put it another way . We can perceive a number of gravitational lenses from the Solar System . Since the Indetermancy will sum (due to Conservation of Entanglement and energy ) , Low-probability events like life is then much more likely .
I can't find an answer on the Web , and I suspect there is not one . You will have to sum the Indetermancies across the whole sky . And since the Indetermancies affect the time dimension , unfortunately little things like Dark Matter and Dark Energy no longer become necessary . They have not been observed directly because they do not exist . (Except in the fevered brows of academics writing grant applications . )
This means that life in crowded neighbourhoods like Sol is quite likely . Inevitable .
Higher civilizations will put their thumbs on the probability scales .
See Appendix II .
Design your own multiple sun indetermancy concentrator . Or look for one . Calculate the likelihood and the degree of probability distortion . Calculate the likelihood of life .
An exercise for the dear reader .
"As time goes by , rather haphazardly."
And the paradox . What paradox ? The Psi collapses are stretched like taffy .
And , at the Omega point End , the horse does not only to learn to talk and sing , but to rap as well . Quelle horreur . Time for another Universe .
And so it goes .
Andre
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Appendix I
A way to do it .
Radiometry and metrology of a phase zone plate measured by extreme ultraviolet synchrotron radiation
John F. Seely, Benjawan Kjornrattanawanich, James C. Bremer, Michael Kowalski, and Yan Feng »View Author Affiliations
Applied Optics, Vol. 48, Issue 31, pp. 5970-5977 (2009)
http://dx.doi.org/10.1364/AO.48.005970
View Full Text Article
Enhanced HTML Acrobat PDF (1065 KB)
Abstract
The diffraction efficiency, focal length, and other radiometric and metrology properties of a phase zone plate were measured by using monochromatic synchrotron radiation in the 7– 18.5 nm wavelength range. The zone plate was composed of molybdenum zones having a 4 mm outer diameter and 70 nm nominal thickness and supported on a100 nm thick silicon nitride membrane. The diffraction efficiency was enhanced by the phase shift of the radiation passing through the zones. The measured first-order efficiency was in good agreement with the calculated efficiency. The properties of the zone plate, particularly the small variation of the efficiency with off-axis angle, make it suitable for use in a radiometer to accurately measure the absolutely calibrated extreme ultraviolet emission from the Sun.
© 2009 Optical Society of America
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Appendix II
Look for any of these signs .
Design-a-Sun.
Andre Willers
18 May 2010
Safety :
A Level III Civilization would be needed to implement these ideas .
Though indications are that LHC and Tokamaks may develop localized pockets of higher-orders of randomness near the boundaries of the containers due to small fluctuations in magnetic fields , leading to fusion effects .
See http://andreswhy.blogspot.com "Orders of Randomness"
But this already-released technology .
Safety is estimated at 0.98
Synopsis:
A big ball of gas is so boring . We design more interesting suns .
Discussion .
We follow the known laws of physics : ie you can calculate each of the shapes below .
Driver Engine :
A rapidly rotating quasar .(Rroq)
The shapes we envisage are possible , but not stable . They will need an input driver .
1.Toroidal Sun.
Spin up a sufficiently large star using a Rroq . It will form a toroidal sun .
2.An Orbit of Toroidal Suns .
Like rings on an elliptical string .
Spin up a sufficiently large , dense gas-cloud using a pulsating Rroq . It will form a number of toroidal suns . By varying and steering the pulses , an orbit of toroidal suns can be formed around the center of gravity . A planet there would have a really interesting sky , not to mention geology .
3.Possible Orbits .
NewScientist in the early 2000's published an article showing some possible orbital configurations . While there was no proof that an infinite number are possible , the about 40 shown had some very fancy shapes . Non-intuitive curliques , loop-crossing , etc . They were not stable , but that is not a concern here .
4.Square , triangular , pyramidal and other simple geometrical Suns .
Fourier transforms can be executed upon stars . A combination of Para(3) above and a single Rroq should make these possible , though your sun might wobble a bit . Not very esthetic .
5.Multiple Rroqs .
Fine control is possible . Hollow square suns , etc become possible . Multiple vacuoles or holes inside stars . Really fancy suns and orbitals of suns .
Any topological form .
6.Controlled , repetitive novae .
A bit like Cepheids .
7.Self-powered Tippler-like machines to move between dimensions , universes and branes .
Hint : paths through topological "holes" will lead to alternate universes or branes (sets of universes)
8. This is about kindergarden level for a post-singularity system .
9. Add habitats
For life-forms from gas-cloud level , biological level , electronic level down to Planck level and sprinkle with suitable seed-lifeforms . This would be about Grade 1 for a post-singularity system .
"Design-a-Sun" kits are available from God@Universum.cosmos
Andre .
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Appendix B
http://en.wikipedia.org/wiki/Nonlinear_optics
A lot of high-level sound and fury , without addressing the basic problem .
Nonlinear optics
From Wikipedia, the free encyclopedia
Nonlinear optics (NLO) is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric fieldE of the light. This nonlinearity is typically only observed at very high light intensities (values of the electric field comparable to interatomic electric fields, typically 108 V/m) such as those provided by pulsed lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.
Nonlinear optics remained unexplored until the discovery of Second harmonic generation shortly after demonstration of the first laser. (Peter Franken et al. at University of Michigan in 1961)
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Appendix C
http://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion
This is physics speak for "I don't know why this is happening"
Spontaneous parametric down-conversion
From Wikipedia, the free encyclopedia
Spontaneous parametric down-conversion (SPDC. Also referred to as parametric fluorescence or parametric scattering) is an important process in quantum optics, used especially as a source of entangled photon pairs, and of single photons.
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Appendix D
A way to concentrate anything , over and over again .
http://en.wikipedia.org/wiki/Lima%C3%A7on
Limaçon
From Wikipedia, the free encyclopedia
In geometry, a limaçon or limacon ( /ˈlɪməsɒn/), also known as a limaçon of Pascal, is defined as a roulette formed when a circle rolls around the outside of a circle of equal radius. It can also be defined as the roulette formed when a circle rolls around a circle with half its radius so that the smaller circle is inside the larger circle. Thus, they belong to the family of curves calledcentered trochoids; more specifically, they are epitrochoids. The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp.
The term derives from the Latin word limax, which means "snail". Depending on the position of the point generating the curve, it may have inner and outer loops (giving the family its name), it may be heart-shaped, or it may be oval.
A limaçon is a bicircular rational plane algebraic curve of degree 4.
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Appendix E
Google 3D printing Quartz . a flourishing industry
Synthetic quartz
Most quartz used in microelectronics is produced synthetically. Large, flawless and untwinned crystals are produced in an autoclave via thehydrothermal process. The process involves treating crushed natural quartz with hot aqueous solution of a base such as sodium hydroxide. The hydroxide serves as a "mineralizer", i.e. it helps dissolve the "nutrient" quartz. High temperatures and pressures are required, typically 350-450°C and 1000-1500 atmospheres.[9] The dissolved quartz then recrystallizes at a seed crystal at slightly lower temperatures. Approximately 200 tons of quartz were produced in the US in 2005; large synthesis facilities exist throughout the world. Synthetic quartz is often evaluated on the basis of its Q factor, a measure of its piezoelectric response and an indicator of the purity of the crystal.[10]
High-temperature glass composed of silicon dioxide with no (or only small amounts of) other components is referred to as "quartz glass" or fused quartz, although it is amorphous in structure, rather than crystalline.
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Appendix F
Quartz is used in neutrino detection .
We can make it as big as a postage stamp .
http://eprints.ugd.edu.mk/1393/
Abstract
LORandite EXperiment (LOREX) plans to measure the time integrated solar neutrino flux of the last few million years via the product of the reaction 205Tl(υe,e−)205Pb in lorandite of the Allchar mine in Macedonia.
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Appendix G
http://en.wikipedia.org/wiki/Spline_(mathematics)
A way of sneaking up on smooth curves . In quantum systems (by definition) how discontinuous mathematics can be married to Calculus . Not a happy union .
Spline (mathematics)
From Wikipedia, the free encyclopedia
In mathematics, a spline is a sufficiently smooth polynomial function that is piecewise-defined, and possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as knots).[1][2]
In interpolating problems, spline interpolation is often referred to as polynomial interpolation because it yields similar results, even when using low-degree splines, to interpolating with higher degree polynomials while avoiding instability due to Runge's phenomenon. In computer graphics splines are popular curves because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design.
The most commonly used splines are cubic spline, i.e., of order 3—in particular, cubic B-spline and cubic Bézier spline. They are common, in particular, in spline interpolation simulating the function of flat splines.
The term spline is derived from a flexible strip of metal commonly used by draftsmen to assist in drawing curved lines.[3]
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Appendix H
Infinite Probes 2
Andre Willers
30 April 2008
http://andreswhy.blogspot.com "Infinite Probes'
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
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Appendix I
The Inside of Zero .
Andre Willers
7 Aug 2009
Synopsis :
A system of 13 Diophantine equations with 26 unknowns are the necessary sufficient to describe Arith I systems relative to Arith II system , with a Degree of Complexity = 10 .
These are used to describe a mathematical vacuum , with some physical consequences .
Discussion :
See Appendix A , B , Recursive Theory .
See previous posts , where Arith I and Arith II systems were discussed in detail .
The problem lies in discussing Non-Aristotelian systems using Aristotelian concepts of delineation (ie True , not-True ) .
Infinity .
The alert reader would have noticed that most of the problems come from processes continued indefinitely , which is taken as infinity . But is it ? Kantor already proved that varieties of infinity exists . It immediately follows that the software-computer we call mathematics and logic needs some revision .
The works of Russell , Godel , Matiyasevich et al pointed out some further contradictions in the Aristotelian model .
Can a theorem be true only for Aleph0 but not for Aleph1 ?
This is analogous to the problems with parallel lines continuing "infinitely" , that led to non-Euclidean geometries .
Recursive Genesis .
The standard axioms of arithmetic needs only a tweak on one axiom to generate the necessary revisions .
Generate new numbers by adding 1 to any number a .
Arith II
The Standard Set (call it Arith II) states that a+1<>a , where a is a previous number . The number line does not loop back on itself .
Arith I
The number line can loop back on itself . A circular number-line is formed . In a certain sense , we are discussing the topology of circular number loops in a Arith II space and their relationships .
The metric has not been defined . The question then becomes :
How many Arith I systems (= ArithI(m) ) plus one ArithII system (we only need one ArithII) are necessary sufficient to describe this particular Universum ?
Rotational Translations (spin) .
This is actually moving from one dimension to another , regardless of the frame of reference . Every ArithI system then actually needs a spin indicator : ie , which way it is curving in an (n-1) dimensional space .
I draw your attention to the curious fact that the angle in 2-dim is 2pi , while in 3 dim it is 4pi . More of this anon .
The Degree :
The maximum exponent in an equation if you change all the variables into one variable . This is important because it indicates the number of dimensions we have to use to describe the equation . Do not confuse it with the number of variables .
Minimum Necessary Sufficient .
The Ball-Breaker . The description defines reality .
This has been called many things :
Principle of Least effort , time , distance ,
Entropy .
Occam's Razor .
Collapse of the wave-function .
Economy of effort , etc .
The trade-off :
Matiyasevich et al has shown that there is a relationship between the Degree and the Number of variables necessary to describe an item in an Universum using a related number of equations .
Boundaries :
The following relationships has been proved :
Degree = 4 , variables 58
Degree = 10 , variables = 26 , equations =13
Degree = 10^45 , variables = 10
Is there a minimum number number of degrees ?
I doubt very much whether a Degree lower than 4 will be found . See Physical significance below .
See previous posts .
Physical Significance .
"Everything that can be , will be . But not all at once ." AW
The Degree can be described as the number of dimensions . You will notice the correlation with string theory .
Sadly , a Theory of Everything is impossible . But we can creep up on it .
Delicious !
Degree = 10 , variables = 26 , equations =13 , Spin =2
The numbers 26 =2x13 , and spin =2 should be knocking at the jaded doors of your mind .
Cards .
A pack of 13x4 = 52 cards forms a very good analogue of the Mathematical Process of a Universum .
You can work out for yourself why humans have a good use for a very good analogue of the universe .
And the Jokers ?
Remember , the Joker can take on any value . A good decription of a trans-luminal , low-probability event .
The most popular string theory uses 10 dimensions .
And the rest of the Tarot pack ?
Remember , we are talking about necessary sufficient without straining human capabilities too much .
Prime Numbers :
A prime number is simply an ArithI system (in ArithII measurements) that cannot be chopped up .
A mathematical atom , relative to ArithII . The number we need is related to the number of variables .
It is like zero
The Inside of Zero .
Degree = 10 , variables = 26 , equations =13 , Spin =2
If we plug in 26 prime numbers into the Diophantine polynomial generational equation in AppendixA below (and there are an infinity to choose from) , we get 26 ArithI systems , which have a mathematical vacuum inside them . No numbers .
A very interesting place . Note that the resultant is also a prime atom . It is recursive . Only the spin remains free .
Like the inside of a singularity .
Physically , this will have some very interesting effects .
There are no quantum fluctuations inside zero . The metric does not exist , even at Planck level .
Super-conductivity :
Purely an effect of the number of atoms crowded together .
It does not matter which atoms . They just have to be in certain configurations . Hence the present confusion in the field .
Disintegration of matter
(cold-fusion or cold-fission) .
But observational systems really like conservation laws . Energy release can then be only through particle or EM means .
If the geometries are chosen correctly , we can constrain the output mainly to electron/proton or electron/EM .
Direct electrical energy from matter . Very good power generation in our Universum .
Quantum Epigenetics .
The patterns on the surface of zero are constrained by trans-luminal effects inside zero . The outside patterns dictate the quantum-fluctations , as well as trans-luminal and super-luminal effects from all over .
The spin of Zero will thus drag creation of quantum fluctuations around it . This will affect things not only on a small scale , but on a large scale as well . The Drags do not balance out .(cf Relativistic rotation drag)
This can actually easily be calculated in the standard way by wave functions and General Relativity .
Rotating around a point
Note that there is a difference between spin and a particle rotating about center .
This can be constrained by using the fact that angular radians in 2 dimensions is 2pi and in 3 dimensions is 4pi .
Physically , in our descriptions , it means the particle does not really know whether it is orbiting in 2 dimensions or is spread over a surface in 3 dimensions (cf h/2pi)) , but we can constrain the geometries (and do in our quantum devices !)
God's sense of humour .
Degree = 10 , variables = 26 , equations =13 , Spin =2
Each degree (ie dimension) can take on +1, 0, -1 spins . Thus 10^3 number of states .
(We do not worry about minimum necessary sufficient spins , only state what is .)
This gives a polynomial of 27 integers of degree 10 with a value of 3 spins . See Appendix A below .
The Fine structure constant of our universe is
1/alpha = h/2pi * c / e^2
=137.035 999 070 (98)
where h is Planck's Constant , c is lightspeed in vacuo (see above) and e is electron charge , all in dimensionless electrostatic units . The value is dimensionless (ie the same for any definition of units)
It shows the relationship between h (Plancks constant , which includes the definition of mass) , spin (the pi , but there has to be compensation for dimensional drifting between dim2 and dim3 as discussed above) , observational speed (c ) and electric charge (e) .
It means that spinning mass and charge are intimately related to the number of dimensions it has to rotate through .
So , it is no surprise to find that
Beta = (1/10 + 1/27) * 10^3
=1000*(0.1 + 0.037037037…)
= 137 . 037 037 …
The difference in the sixth decimal can be attributed to drag effects and dimensional compensations , which have not been taken into account .
Biological Epigenetics .
The same type of argument can be applied to biological cells and denizens of multicellular organism . While they might not rotate , they definitely do partially rotate to-and-fro .
Three magnetic fields at right angles to each other or twistor-EM waves will have definite biological effects .
Do not try this at home .
Does nothing matter ?
The Zero knows .
Andre .
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Appendix A
From http://mathworld.wolfram/com/PrimeDiophantineEquations.html
From http://en.wikipedia.org/wiki/Formula_for_Primes
Formula based on a system of Diophantine equations
A system of 14 Diophantine equations in 26 variables can be used to obtain a Diophantine representation of the set of all primes. Jones et al. (1976) proved that a given number k + 2 is prime if and only if the following system of 14 Diophantine equations has a solution in the natural numbers:
α0 = wz + h + j − q = 0
α1 = (gk + 2g + k + 1)(h + j) + h − z = 0
α2 = 16(k + 1)3(k + 2)(n + 1)2 + 1 − f2 = 0
α3 = 2n + p + q + z − e = 0
α4 = e3(e + 2)(a + 1)2 + 1 − o2 = 0
α5 = (a2 − 1)y2 + 1 − x2 = 0
α6 = 16r2y4(a2 − 1) + 1 − u2 = 0
α7 = n + l + v − y = 0
α8 = (a2 − 1)l2 + 1 − m2 = 0
α9 = ai + k + 1 − l − i = 0
α10 = ((a + u2(u2 − a))2 − 1)(n + 4dy)2 + 1 − (x + cu)2 = 0
α11 = p + l(a − n − 1) + b(2an + 2a − n2 − 2n − 2) − m = 0
α12 = q + y(a − p − 1) + s(2ap + 2a − p2 − 2p − 2) − x = 0
α13 = z + pl(a − p) + t(2ap − p2 − 1) − pm = 0
The 14 equations α0, …, α13 can be used to produce a prime-generating polynomial inequality in 26 variables:
ie: PrimeNumber = (k+2) ( 1- a0^2 - … a13^2) )
This is equal to the polynomial
(k + 2)(1 −
[wz + h + j − q]2 −
[(gk + 2g + k + 1)(h + j) + h − z]2 −
[16(k + 1)3(k + 2)(n + 1)2 + 1 − f2]2 −
[2n + p + q + z − e]2 −
[e3(e + 2)(a + 1)2 + 1 − o2]2 −
[(a2 − 1)y2 + 1 − x2]2 −
[16r2y4(a2 − 1) + 1 − u2]2 −
[n + l + v − y]2 −
[(a2 − 1)l2 + 1 − m2]2 −
[ai + k + 1 − l − i]2 −
[((a + u2(u2 − a))2 − 1)(n + 4dy)2 + 1 − (x + cu)2]2 −
[p + l(a − n − 1) + b(2an + 2a − n2 − 2n − 2) − m]2 −
[q + y(a − p − 1) + s(2ap + 2a − p2 − 2p − 2) − x]2 −
[z + pl(a − p) + t(2ap − p2 − 1) − pm]2)
> 0
is a polynomial inequality in 26 variables, and the set of prime numbers is identical to the set of positive values taken on by this polynomial inequality as the variables a, b, …, z range over the nonnegative integers.
In other words , we have a single Diophantine polynomial equation with 27 variables based on 14 sub-equations .
Eliminating one variable (n) as discussed above , leaves us with 26 variables based on 13 equations , but the Exponential Order (Degree) is unchanged .
A general theorem of Matiyasevich says that if a set is defined by a system of Diophantine equations, it can also be defined by a system of Diophantine equations in only 9 variables. Hence, there is a prime-generating polynomial as above with only 10 variables. However, its degree is large (in the order of 1045). On the other hand, there also exists such a set of equations of degree only 4, but in 58 variables (Jones 1982). Jones et al 1976 , Riesel 1994 p40
Appendix B
Diophantine set
From Wikipedia, the free encyclopedia
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In mathematics, a Diophantine set of j -tuples of integers is a set
S for which there is some polynomial with integer coefficients
f(n1, ..., nj, x1, ..., xk)
such that a tuple
(n1, ..., nj)
of integers is in S if and only if there exist some (non-negative) [1] integers
x1, ..., xk with
f(n1, ..., nj, x1, ..., xk) = 0.
Such a polynomial equation over the integers is called a Diophantine equation. In other words, a Diophantine set is a set of the form
where f is a polynomial function with integer coefficients. [2]
Matiyasevich's theorem, published in 1970, states that a set of integers is Diophantine if and only if it is recursively enumerable. A set S is recursively enumerable precisely if there is an algorithm that, when given an integer, eventually halts if that input is a member of S and otherwise runs forever. This means that the concept of general Diophantine set, apparently belonging to number theory, can be taken rather in logical or recursion-theoretic terms. This is far from obvious, however, and represented the culmination of some decades of work.
Matiyasevich's theorem effectively settled Hilbert's tenth problem. It implies that Hilbert's tenth problem is unsolvable. This problem is the challenge to find a general algorithm which can decide whether a given system of Diophantine equations has a solution among the integers. David Hilbert posed the problem in his celebrated list, from his 1900 address to the International Congress of Mathematicians.
[edit] Examples
The well known Pell equation
X^2 – d(y +1)^2 = +- 1
is an example of a Diophantine equation with a parameter. As has long been known, the equation has a solution in the unknowns x,y precisely when the parameter d is 0 or not a perfect square. In the present context, one says that this equation provides a Diophantine definition of the set
{0,2,3,5,6,7,8,10,...}
consisting of 0 and the natural numbers that are not perfect squares. Other examples of Diophantine definitions are as follows:
- The equation a = (2x + 3)y defines the set of numbers that are not powers of 2.
- The equation a = (x + 2)(y + 2) defines the set of numbers that are not prime numbers.
- The equation a + x = b defines the set of pairs (a,b) such that (a<=b)
[edit] Matiyasevich's theorem
Matiyasevich's theorem says:
Every recursively enumerable set is Diophantine.
A set S of integers is recursively enumerable if there is an algorithm that behaves as follows: When given as input an integer n, if n is a member of S, then the algorithm eventually halts; otherwise it runs forever. That is equivalent to saying there is an algorithm that runs forever and lists the members of S. A set S is Diophantine precisely if there is some polynomial with integer coefficients f(n, x1, ..., xk) such that an integer n is in S if and only if there exist some integers x1, ..., xk such that f(n, x1, ..., xk) = 0.
It is not hard to see that every Diophantine set is recursively enumerable: consider a Diophantine equation f(n, x1, ..., xk) = 0. Now we make an algorithm which simply tries all possible values for n, x1, ..., xk, in the increasing order of the sum of their absolute values, and prints n every time f(n, x1, ..., xk) = 0. This algorithm will obviously run forever and will list exactly the n for which f(n, x1, ..., xk) = 0 has a solution in x1, ..., xk.
[edit] Proof technique
Yuri Matiyasevich utilized an ingenious trick involving Fibonacci numbers in order to show that solutions to Diophantine equations may grow exponentially. Earlier work by Julia Robinson, Martin Davis and Hilary Putnam had shown that this suffices to show that every recursively enumerable set is Diophantine.
[edit] Application to Hilbert's Tenth problem
Hilbert's tenth problem asks for a general algorithm deciding the solvability of Diophantine equations. The conjunction of Matiyasevich's theorem with a result discovered in the 1930s implies that a solution to Hilbert's tenth problem is impossible. The result discovered in the 1930s by several logicians can be stated by saying that some recursively enumerable sets are non-recursive. In this context, a set S of integers is called "recursive" if there is an algorithm that, when given as input an integer n, returns as output a correct yes-or-no answer to the question of whether n is a member of S. It follows that there are Diophantine equations which cannot be solved by any algorithm.
[edit] Logical structure
Here an argument taking exactly the form of an Aristotelian syllogism is of interest:
(Major premise): Some recursively enumerable sets are non-recursive.
(Minor premise): All recursively enumerable sets are Diophantine.
(Conclusion): Therefore some Diophantine sets are non-recursive.
The conclusion entails that Hilbert's 10th problem cannot be solved. The most difficult part of the argument is the proof of the minor premise, i.e. Matiyasevich's theorem, which itself is much stronger than the unsolvability of the Tenth Problem.
[edit] Refinements
Later work has shown that the question of solvability of a Diophantine equation is undecidable even if the equation only has 9 natural number variables (Matiyasevich, 1977) or 11 integer variables (Zhi Wei Sun, 1992).
[edit] Further applications
Matiyasevich's theorem has since been used to prove that many problems from calculus and differential equations are unsolvable.
One can also derive the following stronger form of Gödel's first incompleteness theorem from Matiyasevich's result:
Corresponding to any given consistent axiomatization of number theory,[3] one can explicitly construct a Diophantine equation which has no solutions, but such that this fact cannot be proved within the given axiomatization.
[edit] Footnotes
- ^ The two definitions are equivalent. This can be proved using Lagrange's four-square theorem.
- ^ Note that one can also use a simultaneous system of Diophantine equations to define a Diophantine set, because the system
f1 =0 , …,fk =0
is equivalent to the single equation
f1^2 + f2^2 + … + fk^ = 0
- ^ More precisely, given a -formula representing the set of Gödel numbers of sentences which recursively axiomatize a consistent
theory extending Robinson arithmetic.
[edit] References
- Yuri Matiyasevich. "Enumerable sets are Diophantine." Doklady Akademii Nauk SSSR, 191, pp. 279-282, 1970. English translation in Soviet Mathematics. Doklady, vol. 11, no. 2, 1970.
- M. Davis. "Hilbert's Tenth Problem is Unsolvable." American Mathematical Monthly 80, pp. 233-269, 1973.
- Yuri Matiyasevich. Hilbert's 10th Problem Foreword by Martin Davis and Hilary Putnam, The MIT Press. ISBN 0-262-13295-8
- Zhi-Wei Sun, Reduction of unknowns in Diophantine representations, Sci. China Ser. A, 35:3 (1992), pp. 257–269.
[edit] External links
Retrieved from "http://en.wikipedia.org/wiki/Diophantine_set"
Categories: Diophantine equations | Hilbert's problems
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