Major new Carbon NanoTech Alert

Andre Willers

28 Nov 2012

Synopsis:

A macroscopic way of making cheap nano-carbon fibres with amazing and very profitable properties

Discussion :

1.This is already being done on a large scale . See Appendix I

2.The macroprocess is simple and can basically be done in your kitchen . Expect large scale innovation as everybody gets into the act .

3.See the barrier properties and foaming in Appendix II .

This lends itself to hydrogen energy storage , safe NCC Zeppelins , etc

4.Doping the foam can give cheap desalination .

5.NCC has conductive properties . Much cheaper solar energy capture systems using more efficient chlorofil-type mechanisms are possible . This is important , since the basic raw material for NCC is cellulose (basically , plants) . For a closed , renewable cycle we need bubble trees , if need be extra-planetary .

Even now , we can think of designing a self-replicating bubble tree to populate the solar system . All you need is Carbon , Hydrogen , Oxygen , Nitrogen (CHON) and some trace elements .

6. Not to mention foldable screens for TV or PC’s ,

7.Global warming . Better worry about Global cooling . The industrial demand for carbon will lead to large scale CO2 mining . Buying cheap carbon futures (about 10 years) will bring major rewards .

8.The time-span of this technology ?

The forecast (see Appendix I) is about $600 Billion industry by 2020 (8 years from now ) .

I think this is too conservative .

9.Fracking and new gas fields.

If we add this into the mix , we see that the NCC and gas technologies complement each other to an uncanny degree . The gas storage NCC enables at room temperature due to it’s barrier to gas-transfer , makes for an easy adaptation from petroleum gas (petrol) to the new system . And as the gas systems peter out , mining the Earth’s atmosphere (CO2) or the Sun’s atmosphere (Protons , Carbon , etc could be done ) .

10.The biggest prize is Venus . Enough to make any industrialist drool . A readymade chemical reactor on planetary scale . All you have to do is channel the reactions . And now you have the tool (NCC) to exploit it to the max .

11.And the Singularity ?

This speeds it up . Foaming conducting surfaces makes a nice , easy topological transition from flat to multidimensional architectures . See Appendix III and other foam posts .

12. Economic Systems :

This is Real Wealth creation via technological innovation . It is not Zero-sum . It will create an enormous pulse of wealth , much bigger than the invention of the planter in 1700 AD

See Appendix IV what effect Jethro Tull’s little invention had on the world .

We can predict that within the next eight years the demand for metals of any description will drastically decline . Crash is a better word . Steel will be badly effected . NCC is stronger than steel , lighter and does not need high temperatures . Ditto for platinum , copper , aluminium , etc .

This is already happening to some degree , but the rush for the exit has not yet started .

13.The Big Crash

Suitable for number 13 . Enormous amounts of capital had been sunk into technologies to get materials that now can be obtained from the atmosphere or the ocean .

Quelle horreur ! The rich might have to work for a living . As for pensioners , who cares about them ?

14. The Ostrum Principles .

See Appendix V .

How to handle a Common Resource , especially if it as free as the air .

15. Futures .

The whole process will be accelerated by the charming human process of betting on Leveraged Futures , even though they have not the foggiest idea of what is going to happen . Reminds me of a second marriage : “The triumph of hope over experience”

16 An Interesting Aside :

I have not added 3-D printers into the mix . You can make nearly anything with NCC and a 3D printer

Where , oh where , are the artists that make 4D or 5D or nD printers ?

Things are rapidly going to become very interesting .

Have a look at https://www.google.co.za/search?q=ruins+of+detroit&hl=en&tbo=u&tbm=isch&source=univ&sa=X&ei=bn22UNKRIcrIhAf28oCIDA&sqi=2&ved=0CDAQsAQ&biw=1366&bih=643

It was a visceral shock to me to see brand names I grew up with at one with Nineveh .

Keep mobile

Andre

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Appendix I

http://www.newscientist.com/article/mg21528786.100-why-wood-pulp-is-worlds-new-wonder-material.html

Why wood pulp is world's new wonder material

• Updated 11:23 24 August 2012 by Will Ferguson

• Magazine issue 2878. Subscribe and save

• For similar stories, visit the Nanotechnology Topic Guide

THE hottest new material in town is light, strong and conducts electricity. What's more, it's been around a long, long time.

Nanocrystalline cellulose (NCC), which is produced by processing wood pulp, is being hailed as the latest wonder material. Japan-based Pioneer Electronics is applying it to the next generation of flexible electronic displays. IBM is using it to create components for computers. Even the US army is getting in on the act, using it to make lightweight body armour and ballistic glass.

To ramp up production, the US opened its first NCC factory in Madison, Wisconsin, on 26 July, marking the rise of what the US National Science Foundation predicts will become a $600 billion industry by 2020.

So why all the fuss? Well, not only is NCC transparent but it is made from a tightly packed array of needle-like crystals which have a strength-to-weight ratio that is eight times better than stainless steel. Even better, it's incredibly cheap.

"It is the natural, renewable version of a carbon nanotube at a fraction of the price," says Jeff Youngblood of Purdue University's NanoForestry Institute in West Lafayette, Indiana.

The $1.7 million factory, which is owned by the US Forest Service, will produce two types of NCC: crystals and fibrils.

Production of NCC starts with "purified" wood, which has had compounds such as lignin and hemicellulose removed. It is then milled into a pulp and hydrolysed in acid to remove impurities before being separated and concentrated as crystals into a thick paste that can be applied to surfaces as a laminate or processed into strands, forming nanofibrils. These are hard, dense and tough, and can be forced into different shapes and sizes. When freeze-dried, the material is lightweight, absorbent and good at insulating.

"The beauty of this material is that it is so abundant we don't have to make it," says Youngblood. "We don't even have to use entire trees; nanocellulose is only 200 nanometres long. If we wanted we could use twigs and branches or even sawdust. We are turning waste into gold."

The US facility is the second pilot production plant for cellulose-based nanomaterials in the world. The much larger CelluForce facility opened in Montreal, Canada, in November 2011 and is now producing a tonne of NCC a day.

Theodore Wegner, assistant director of the US factory, says it will be producing NCC on a large scale. It will be sold at just several dollars a kilogram within a couple of years. He says it has taken this long to unlock the potential of NCC because the technology to explore its properties, such as electron scanning microscopes, only emerged in the last decade or so.

NCC will replace metal and plastic car parts and could make nonorganic plastics obsolete in the not-too-distant future, says Phil Jones, director of new ventures and disruptive technologies at the French mineral processing company IMERYS. "Anyone who makes a car or a plastic bag will want to get in on this," he says.

In addition, the human body can deal with cellulose safely, says Jones, so NCC is less dangerous to process than inorganic composites. "The worst thing that could happen is a paper cut," he says.

When this article was first posted, Jeff Youngblood was incorrectly quoted as saying that nanocellulose is 2 nanometres long. It also incorrectly stated that NCC material has eight times the tensile strength of stainless steel – this has now been corrected.

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Appendix II

Some excerpts from Wikipedia

http://en.wikipedia.org/wiki/Nanocellulose

Nanocellulose

From Wikipedia, the free encyclopedia

Nanocellulose

Nanocellulose, or microfibrillated cellulose (MFC), is a material composed of nanosized cellulose fibrils with a high aspect ratio (length to width ratio). Typical lateral dimensions are 5–20 nanometers and longitudinal dimension is in a wide range from 10s of nanometers to several microns. It is pseudo-plastic and exhibits the property of certain gels or fluids that are thick (viscous) under normal conditions, but flow (become thin, less viscous) over time when shaken, agitated, or otherwise stressed. This property is known as thixotropy. When the shearing forces are removed the gel regains much of its original state. The fibrils are isolated from any cellulose containing source including wood-based fibers (pulp fibers) through high-pressure, high temperature and high velocity impact homogenization (see manufacture below).

Nanocellulose can also be obtained from native fibers by an acid hydrolysis, giving rise to highly crystalline and rigid nanoparticles (generally referred to as nanowhiskers) which are shorter (100s to 1000 nanometers) than the nanofibrils obtained through the homogenization route. The resulting material is known as nanocrystalline cellulose (NCC).[1]

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Mechanical properties

It has long been known that crystalline cellulose has interesting mechanical properties for use in material applications. The tensile strength of crystalline cellulose has been shown to be on the order of 500MPa, which is similar to aluminum's. Its stiffness has been shown to be in the order of 140–220 GPa, which is in the same size order as for instance Kevlar and is better than, for example, glass fibers, both fibers used commercially to reinforce plastics. Films made from nanocellulose have been shown to have high strength (over 200 MPa), high stiffness (around 20 GPa) and high strain (12%). Its strength/weight ratio is 8 times that of stainless steel.[7]

[edit]Barrier properties

In semi-crystalline polymers, the crystalline regions are considered to be gas impermeable. Due to relatively high crystallinity,[17] in combination with the ability of the nanofibers to form a dense network held together by strong inter-fibrillar bonds (high cohesive energy density), it has been suggested that nanocellulose might act as a barrier material.[16][19][20] Although the number of reported oxygen permeability values are limited, reports attribute high oxygen barrier properties to nanocellulose films. One study reported an oxygen permeability of 0.0006 (cm³ µm)/(m² day kPa) for a ca. 5 µm thin nanocellulose film at 23 °C and 0% RH.[19] In a related study, a more than 700-fold decrease in oxygen permeability of a polylactide (PLA) film when a nanocellulose layer was added to the PLA surface was reported.[16]

The influence of nanocellulose film density and porosity on film oxygen permeability has recently been explored.[21] Some authors have reported significant porosity in nanocellulose films,[22][23][24] which seems to be in contradiction with high oxygen barrier properties, whereas Aulin et al.[19] measured a nanocellulose film density close to density of crystalline cellulose (cellulose Iß crystal structure, 1.63 g/cm³)[25] indicating a very dense film with a porosity close to zero.

Changing the surface functionality of the cellulose nanoparticle can also affect the permeability of nanocellulose films. Films constituted of negatively charged cellulose nanowhiskers could effectively reduce permeation of negatively charged ions, while leaving neutral ions virtually unaffected. Positively charged ions were found to accumulate in the membrane.[26]

[edit]Foams

Nanocellulose can also be used to make aerogels/foams, either homogeneously or in composite formulations

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Appendix III

If you are zero , you are a Zen hero .

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

Jump to: navigation, search

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.

Contents

[hide]

• 1 Examples

• 2 Matiyasevich's theorem

o 2.1 Proof technique

• 3 Application to Hilbert's Tenth problem

o 3.1 Logical structure

o 3.2 Refinements

• 4 Further applications

• 5 Footnotes

• 6 References

• 7 External links

[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

1. ^ The two definitions are equivalent. This can be proved using Lagrange's four-square theorem.

2. ^ 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

3. ^ 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

• Matiyasevich theorem on Scholarpedia.

Retrieved from "http://en.wikipedia.org/wiki/Diophantine_set"

Categories: Diophantine equations | Hilbert's problems

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Appendix IV

Written in Dec 2005 .

The crucial effects of one invention that was applied .

Jethro Tull – Super Hero

In 1701 an Englishman called Jethro Tull invented the seed drill . By quickly and reliably planting seeds at the optimal spacing and depth , this invention enabled about a fourfold increase in yield within one season .

This invention created the largest pulse of wealth in history . Bigger than the invention of fire . Bigger than the invention of agriculture . Bigger than the invention of the internal combustion engine or transistor .

It kick-started the Industrial Revolution .

The reasons:

Most wealth was agricultural.

The increase in wealth was within one season . Malthusian population growth would take about 2 to 3 generations to catch up . Imagine getting a 400% raise in your salary in one year without inflation . This was the effect . This pulse of wealth propagated onwards , giving leisure and incentive to inventors . (ref Baby Boomer Pulse)

The result was a pulse of wealth stimulating other individuals to make similar inventions . The Age of Reason was born . The problem was the massive increase in population made possible by the efficient mechanized systems .

The large number of surplus males and the means to support large armies led to the First Large War (Napoleontic) . This gave the Age of Reason a knock (Nationalism), but you could still state unpopular beliefs without being killed for it . The Second Large War (WWI) destroyed the Age of Reason and ushered in the ideologies (Communism , Marxism , Fascism , Capitalism ). If you stated an unpopular belief , you stood a good chance of being heavily penalized for it . The demise of ideologies collapsed the system back to Religious Fundamentalism , where you can be killed for stating an unpopular belief . The Age of Reason is finally dead . This is the state at circa 2006 AD .

The Age of Reason only lasted a century , but gave rise to our present wealth .

When evaluating ideas like that of Huebner ( see “Waiting for the lights to go out” in Sunday Times of Oct 16 2005 ) , it is important to remember that changes come in pulses . Things might seem to be going to hell in a hand-basket (cf horse-poop in New York circa 1890’s) , but discontinuities generate pulses of change and wealth . You might as well try to explain a transistor using Newtonian mechanics . In other words , analyzing pulses of change as simple statistics of numbers of people over time is garbage .

Is Reason a Good Thing ?

The human race is trembling on the brink of extinction because of the inability of reason to resolve the problem of population and competition .

Example: China

Twice China has limited expansion:

1 Destruction of exploration fleets in 15 th century : the result was Western domination 200 years later (not very long) .

2 One child families in the 20 th century . The Result was a pulse of wealth (as more resources was devoted to education of the lone children) , but their main competitor India is exceeding their population .

Reason (ie logic) has two major drawbacks :

1 The Universum (Venn) is unbounded . This has been proven rigorously in 1906 (Principia Mathematica by Whitehead and Russell) . This means that no theory of everything is possible . ( If you think you have a TOE , you can always define items outside the delineated boundary which , by definition , do not fit inside TOE.)

2 Chaos Theory shows that that even inside a deterministic system , time-sequence predictions are only possible with varying degrees of error (cf weather) . The number of near equipotential branches grow exponentially after a finite number of time units .

This means that the End Does Not Justify The Means .

At best , a prediction must have some sort of probability margins .

This argument is only valid if no time-travel is possible .

Is there hope?

Our present locale (the sidereal Universe) can be expressed as Locale I , defined by the principle that conservation laws are possible There are rules !. Seeing Locale I as delineated , means pockets of being (particles) , space , time and curvaceous space-time. But it is unstable iro non-conservation systems (defined as Locale II). Locale I is maintained artificially by Locale II .

Locale I is maintained primarily as a nursery (try bringing up kids where there are no rules!) , but also as a holiday (going primitive) and trading/warfare locale . This is because interactions can be enforced in Locale I (ie the rules:conservation of something) , whereas in Locale II you cannot force an interaction .

The above reasons work better if there is a lot of variety .Also , the usual reasons of humanity , looking after the planet , etc , etc do not apply except as insofar they illustrate a lesson . In other words , nobody is innocent except the children , and they get the lessons they need .

What does this mean ?

There will be a variety increase soon .

This can be

1. Massive depopulation (plague , eco)

2. Aliens in space

3. Aliens in time

4. Both (most likely : there is only one singularity per universe : the first contacts from the local viewpoint will be on most similar interfaces.)

Merry Christmas

The Alien.

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Appendix V

How to avoid a Tragedy of the Commons .

Professional and Ostrum .

Andre Willers

25 Nov 2012

Synopsis:

We analyse demands on the Professional’s attention using Ostrum Metarules .

Discussion :

The eight actual metarules are in Appendix I .A below . Humans do not have the capability of grasping or seeing them all at once , so we will have to do them item-by-item .

Can humans actually “grow”” to encompass all the 27 Rules necessary and Sufficient to describe the Universes ? . Not difficult at all . They then create new Universes , but make them more interesting by pinching boundaries .

1.The Common Resource is all the Information Demanding systems wanting a portion of the Professional’s attention .

2.Tragedy of the Commons variant .

Exploitation of the free information to the max , with attempts to inhibit certain channels . Doomed to failure . The resource is effectively infinite , because (A + ~A < Universum) . No constraint is possible in the long term .

Short term constraints are possible .

3.Network Theory :

“Small worlds” networks are the general human networks of pushing information . This simply means that most information is sent and handled by “close” nexi , but there are long-range neurons that carry information to other nexi (or mirror networks) .

4.First Pass on Overstimulation of Information :

Simply pass it on to onto the subsidiary networks , except for Amygdala Interrupts . (See Appendix II)

5. Second pass :

Correlations have been made at very low levels . Rethinks .

6. Third and n’th passes :

You get the drift . The system refines itself through feedback processes .

7.Predictive rewards :

This is where we get to the nitty-gritty of Ostrum Systems .

Any farming system , agricultural or not, foregoes present reward for future benefits . You have to get Oabout eight things right to make a living .

Thoe domain of dopamine-systems . Once you enter it , you cannot leave it .

8. Humans farm the noosphere the same as they farm the land . But that same pesky 8’th term disturbs things . The relationship to higher Beth(x) beings . The disturbance is built-in and unavoidable.

9. Osrtum managed to get 7/8 system rules independent of the observer . A significant accomplishment .

What does this mean ? Small scale systems can be predicted and manipulated .

10. This means you !

A Small thing , but my own .

Andre

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Appendix I

The only Game in town .

The Ostrum Game

Andre Willers

30 Oct 2011

“One Game shall bind them all .” , ( with apologies to Tolkien)

“This time , we know for sure the grass is greener somewhere”

“A Revolution , any Revolution.”

Synopsis :

A Game for Grown-ups .

The Eight Ostrum Design Principles are Meta-rules that generate self-consistent sets of rules that encompasses competition , co-operation , catastrophe , hierarchies and other systems undreamt of , all between discrete , interacting , self-organising systems .

Your avatar can go from SecondLife to Simworld , to War Worlds , to any desired locale .

Reality becomes a subset .

Discussion :

1.An incredible amount of money can be made .While money still has some meaning .

Without too much work . See Para 8 in Appendix A

Each Game Company is a base nested institution .

They bind easily together , releasing a lot of energy and money .

Explosive Feedback Synergism .

A run-up to the Singularity .

2.Feedback between Games and Reality :

The Meta-rules make no differentiation between Game-characters and Real-characters .

Indeed , many Real-characters have been spun into Game-characters , and vice-versa .

Think Sherlock Holmes , MacGyver , Gauss , young Werther etc

See “mirror-neuron networks” , any soap opera , etc .

Real-life problems get treated the same way as Game problems . The more diverse and sophisticated the Game interactions become , the more effect on any real or Game system .

Eventually , they become undistinguishable as technology progresses .

3.The Grass is provably greener somewhere .

Long known as a wishful thinking fallacy , until Ostrum published the Design Principles in 1990 .

This was the trigger event of under-the-surface knowledge about Ostrum Rules building up .

Suddenly , it became possible .

A Phase-change in the noosphere occurred .

It meant that a Disaster of the Commons or an Empire was not inevitable . Grandchildren could survive .

WE CAN MAKE THE GRASS GREENER , EVEN IF WE HAVE TO PAINT IT ONE BLADE AT A TIME .

Enormous tensions began surfacing . These effects are still playing out now .

A really , really major Hysterical Focus started forming , and is still intensifying .

Now , are you surprised that 1990 was the year of huge revolutions , when the USSR collapsed ?

The Ostrum Game beat the Ring of Power .

And you have not seen anything yet .

The pace of Revolutions is intensifying .

A good thing , if Homo wishes to escape extinction .

4.Automating Ostrum Rules :

They might be Meta-rules , but they are still rules .

We can certainly write programs that can serve to guide past most of the pitfalls and suggest alternatives .

5.Multicellular Bodies as Commons :

We can certainly analyze bodies in terms of Commons . The Dear Reader will find many interesting things if he does that .

Note the emphasis on communication .

Talk to your body . Aloud . And listen in the silences in between .

Create a virtual body and note the interactions .

Use the Ostrum Design principles .

6.Singularity :

It is immediately obvious that humans are then not limited to Real biochemical definitions of personality . The emphasis on communication means that personalities are distributed across Real and Game spaces . The Game space personality segments are only limited by internal non-contradictory rules . That can be done via Ostrum Design principles .

Not exactly instantaneous , but I can intuit that the time can be calculated . It would be less than real time .

The putative developing system would have ethical constraints on abandoning Real-part personalities under Ostrum Rules .

Told you it would be kindler , gentler .

7.Phase Change :

The system has already undergone an irrevocable phase change in 1990 .

You can fast-forward the rest .

8.Did Ostrum know what she was unleashing ?

The Revolutionary aspects , nearly certainly .

In her quiet way , she is one of the greatest Revolutionaries in Homo Sapiens history . Worthy of being called a Matriarch .

The Singularity aspect is more uncertain . She certainly knew that she unleashed major fairness , but the phase-change in the Noosphere I do not know .

Still , a tour-de-force .

How do feel like being a pet of your avatar ?

Andre .

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Appendix A

See http://en.wikipedia.org/wiki/Elinor_Ostrom

To quote from Wiki : (comments in brackets are my own ).

“ Ostrom identifies eight "design principles" of stable local common pool resource management:[10]

1. Clearly defined boundaries (effective exclusion of external un-entitled parties;

2. Rules regarding the appropriation and provision of common resources that are adapted to local conditions; (Equal sharing of debts and rewards)

3. Collective-choice arrangements that allow most resource appropriators to participate in the decision-making process; (Consensus decisions-no leveraged hierarchies)

4. Effective monitoring by monitors who are part of or accountable to the appropriators; (Policing)

5. A scale of graduated sanctions for resource appropriators who violate community rules; (Opportunity to learn from mistakes )

6. Mechanisms of conflict resolution that are cheap and of easy access; (Fair and Fast Justice . See how Inquisitorial Justice systems like Chinese , French or Sharia does it.)

7. Self-determination of the community recognized by higher-level authorities; (Autonomy within clearly defined levels . Something like a Federation.)

8. In the case of larger common-pool resources,organization in the form of multiple layers of nested enterprises, with small local CPRs at the base level. (Clear and quick relations with others. A potential sticky point with states.)

Governing the Commons: The Evolution of Institutions for Collective Action Ostrom, Elinor, Cambridge University Press, 1990 “

The most important book in the Twentieth Century .

Try to read it .

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