Saturday, January 10, 2015

Vajra as functional weapons .

Vajra as a functional weapon.

Andre Willers
10 Jan 2015
Synopsis :
Vajra seems to have been a zero-point energy light weapon , kickstarted by sonoluminescence and using the Schwinger limit for mining Zeropoint energy .
Discussion :
1.This picture looks awfully like a real piece of destructive hardware . Notice the dings and holes .
Don’t be fooled by the ornamentation . This was standard in European cannon until mass production .
I wonder if it is still functional ?
Maybe a bit of repair , and the sonoluminescence ignition needs replacing .
The arms need loosening and lubrication , as well as some control system .

2.How does it work ?

See Appendix AA for some basic theory .

2.1 Sonoluminescence
The collapsing bubbles at the right frequency causes electric fields that exceed the Schwinger limit . Non-linearity ensues . See AppendixAA .
This is made self-sustaining by the arms that feed back the electric fields into the central ball-assembly .
The bell-assembly seems to be both initiator and controller .
The ball would be filled with some gas . Xenon seems indicated . See below .
This is a bit of a surprise .
Xenon in water gives 1000 times “bright” .
Hence biological sequestering of xenon . For defence and offense.
One would then expect some Indian and Tibetan plants high in Xenon .
See Appendix BB for organic molecule Xenon traps .
This is what CC3 looks like

a, Reaction scheme for the synthesis of CC3 by a one-pot [4 + 6] cycloimination reaction involving four trialdehyde and six diamine molecules, catalysed by ​trifluoroacetic acid (​TFA). b, The largest inclusion sphere inside the cage (…

If its organic , living systems will have it .
And so they do .
Primula as well , which is how xenon gets into the world food chain .
Schwinger in 1992 who hinted the dynamical Casimir effect as a potential photon-emission process.
Radiance (W/nm)
Relative brightness[1]
Very dim
Extremely dim

Solution type
Average max. radiance (W/nm)[1][11]
Xenon in water
Krypton in water
Argon in water
Neon in water
Helium in water
3He in water

2.1.1 Dinosaurs
Dinosaurs had elaborate sound-producing structures .
A dinosaur powered by zeropoint energy is an interesting concept . Is this why they could grow so large ?

2.2 The Feedback system :
The arms . Note the head vomits back into the central ball assembly .
The structure is made of a conductor and acts as an electric field guide .
Note the precisely machined curvature .

2.3 The control system .
This is Missing .
Some precise control would be needed to maintain the feedback process within desired boundaries .
Else it would fizzle out or go “boom”
Seemingly by opening or closing the arms . Note the hinges at the base of the arms .
These would need some loosening and lubrication , as well as the odd lever or four .

2.4 Spacedrive .
Exceeding the Schwinger limit not only delivers a beam of light , there is also a non-linearity of momentum .
A drive .
The machine in the picture above seems to have been part of a drive-mechanism .

So , if you refurbish it , make sure you have a test-pilot handy .
Rather you than me .
Unlimited feedback-type energies give me itchy feet . Notice the monkeys ? Well , be warned . We are not too far away from their position .

3.Estimate of energy release if you can get the contraption to work .
The central ball seems to be about 100cm in radius .
This gives vol=4/3*pi*100^3  cm^3
Vol= 4.1888 * 10^6 cm^3 = 4.1888 m^3
Energy ~ 10^113 Joules/m^3
But we are interested in the energy we can get out , which is dependant on feedback factors .
A characteristic of complex feedback systems is that they follow Power Laws (eg  y=a*x^k) within the same Beth(x) level .
Now , the volume of 4.1888 m^3 represents 2.7 * 10^25 Xenon molecules at STD .
This means that usable energy interconnection Ei = (ln(2.7)*ln(10)*25)^0.5 = (57.176168)^0.5 = 7.56149 .
The square root is because of Random Walk considerations .
See Appendix AA IV A below about Random Walks in multiple dimensions .

So , expected usable energy is scaled down to a bottom threshold of (e^(ln(10)*113))^(1/7.56149) = 10^14.9441 joules

Since  megaton of TNT, =, 4.184×1015 J`
The engine has a max rating of about ½ megaton of TNT .
The release rate is governed by the controls and material durability of supporting structures .
Used as a cannon , it could probably sustain a firing rate of 100 kiloton of TNT indefinitely , as long as it kept moving .
Thrust is unknown , but simple reaction from heating air at say 10^14 joules per meter gives about 10^13 newtons .
One gravity ~ 9.8 newtons for 1 kg .
The machine then could lift about 10^12 kg  , or 1 000 000 000 tons . (1 trillion tons) .
A steel spaceship about 250 m in diameter .
More likely a much smaller warship .

4.Noise .
This contraption was noisy!
The ignition stage would be like an Orion craft taking off . A controlled nuclear explosion .

5.Where to find any .
So , the spaceports would be in very isolated areas .
Surviving ones (if any) , would have been hastily buried .
Look for truncated mountaintops with massive scree slopes  in Takla Makan , Gobi , Northern Indian deserts .

6.What zapped such a formidable machine ?
There are almost certainly buried machines . Once the futility of further flying became evident , the pilots would have mothballed them .
Maybe you lot should look a little harder ?

7.Or build your own .
It seems simple enough .
Most of the heavy lifting has already been done . You even have a rather battered working model .

Let’s do the Matriarch Wars again !

Appendix AA
Why Space goes non-linear .
Andre Willers
14 Jan 2013
Synopsis :
The Schwinger limit
is deduced from gravitational principles .
Discussion :
1.We use brutal , first approximation arguments to get a surprisingly close approximation to theSchwinger limit
of 1.3X 10^18 Volts/Meter .
2.We use Schwarzchild radii to define non-linearity . The space between the Event-horizon of a Black-hole and Schwarzchild radius encompasses
3.Non-linear events . Hawking Radiation can be random , but is definitely non-linear , and can be described by Riemannian random walks between the ergosphere and Schwarzchild globe .
4.If information is encoded in the surface of the black hole in holographic form , then the non-linear events are influenced . You will have to be really smart (Beth (4+) to get any information from that . For us , it will appear random .
5. We the apply this to electric charges . What Electric Field will give the same non-linearity as the gravitational field near a Singularity ?
7.Plugging all these things into the formulaic descriptions , gives
Rq= 259. 68918 x 10-12
Rq~259 picometers
Rq = distance from a charged proton where two charged particles cause non-linearity .
See Appendix IIA for derivation .
See Appendix ZZZ for alternate derivation .
Compare the two :
259 picometers above vs 332 picometers in Appendix ZZZ

6. What does this mean ?
It might even be true .
What do you know !

Welcome to the Avogrado Universe .
Where precise mass-interaction has relevance at low-level if certain limits are exceeded .

In other words , forcibly injecting molecules into an Avogrado stable system will give rise to lots of non-linear effects .
Simple and easy .

6.1 We can manipulate macro-probabilities without being limited to crystals .
See Appendix IIIA
6.2 We are in a simulation . But if Branes are involved , we cannot know even in principle . Any Singularity inside the manifold exports the uncertainty to an infinity (Aleph(0) at least ) . You need to be an Beth(4) or better to understand what is going on .
But can you bootstrap to Beth(4) ? Good luck .

7. Things are weirder than you think .

8. The Spin-doctors of Beth(3) Universes use spin on the holographic surfaces of black-holes , protons and electrons to propagate information biases .

And so it goes and spins .


Appendix IA
Schwinger limit
From Wikipedia, the free encyclopedia


Feynman diagram (box diagram) for photon–photon scattering, one photon scatters from the transient vacuum charge fluctuations of the other
In quantum electrodynamics (QED), the Schwinger limit is a scale above which the electromagnetic field is expected to become nonlinear. The limit was first derived in one of QED's earliest theoretical successes by Fritz Sauter in 1931[1] and discussed further by Werner Heisenberg and his student Hans Euler.[2] The limit, however, is commonly named in the literature[3] for Julian Schwinger, who derived the leading nonlinear corrections to the fields and calculated the production rate of electron–positron pairs in a strong electric field.[4] The limit is typically reported as a maximum electric field before nonlinearity for the vacuum of

where me is the mass of the electronc is the speed of light in vacuum, qe is the elementary charge, and ħ is the reduced Planck constant.
In a vacuum, the classical Maxwell's equations are perfectly linear differential equations. This implies – by the superposition principle – that the sum of any two solutions to Maxwell's equations is yet another solution to Maxwell's equations. For example, two beams of light pointed toward each other should simply add together their electric fields and pass right through each other. Thus Maxwell's equations predict the impossibility of any but trivialelastic photon–photon scattering. In QED, however, non-elastic photon–photon scattering becomes possible when the combined energy is large enough to create virtual electron–positron pairs spontaneously, illustrated by the Feynman diagram in the figure on the right.
A single plane wave is insufficient to cause nonlinear effects, even in QED.[4] The basic reason for this is that a single plane wave of a given energy may always be viewed in a different reference frame, where it has less energy (the same is the case for a single photon). A single wave or photon does not have a center of momentum frame where its energy must be at minimal value. However, two waves or two photons not traveling in the same direction always have a minimum combined energy in their center of momentum frame, and it is this energy and the electric field strengths associated with it, which determine particle-antiparticle creation, and associated scattering phenomena.

Appendix IIA
Derivation of Schwinger limit:
This is a first approximation :
Rq/Rm = Ke/Gm * Q/((Mp/Me)
Where Rq is electrostatic Schwarzchild radius , Rm is gravitational Schwarzchild radius , Ke is electrostatic constant , Gm is gravitational conststant .
Mp/Me is ratio of proton /elctron mass . Q is electron Coulomb
This gives
Rq/Rm = 1.17537474 x 10^( -2)
We plug in Scwarzchild radius calculation for a proton :
Rm = 2GMp /c^2 , where c is speed of light in vacuum .
=2.47456 x 10^-54
This gives
Rq=(29.083 x 10^10-57)^(1/3)
=3.07521 x 10^-19
The third root is because the system needs at least three dimensions . See Appendix IA .

But no system is ever alone .
All the various E-fields sum as Superposition applies (linearity applies)
As a first approximation they have Avogrado's number of molecules per radius= (0.6022x10^27)^(1/3)
Multiplied by Rq above (because the electric fields sum in linear systems) , this gives
Rq = (3.07521 x 10 -19) x (0.84446 x 10^9)
Rq = 2.5968918 x 10^-10 meters
Rq= 259. 68918 x 10-12
Rq~259 picometers

Derivation is more accurate .
Appendix IIIA
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 (10^18 Volt/Meter) . Space itself becomes non-linear . Conservation "Laws" , especially various momenta , become a bit dicey . Literally .

3.How can we improve the likelyhood of these mini-singularities ?
There is a lot of yakkity-yak (see ) , 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 "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 .



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 ?"

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 .
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.
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 .

Appendix I
A way to do it .
Radiometry and metrology of a phase zone plate measured by extreme ultraviolet synchrotron radiation
Enhanced HTML    Acrobat PDF (1065 KB)
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

Appendix II
Look for any of these signs .
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 "Orders of Randomness"
But this already-released technology .
Safety is estimated at 0.98

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 .


Appendix B
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)

Appendix C
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.

Appendix D
A way to concentrate anything , over and over again .
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.
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.

Appendix F
Quartz is used in neutrino detection .
We can make it as big as a postage stamp .
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. 


Appendix G
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]
Appendix H
Infinite Probes 2
Andre Willers
30 April 2008 "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


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

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 .

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 .


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 .

Appendix IV A
Orders of Randomness 2
Andre Willers
15 Aug 2008

See : "Orders of Randomness"

I have been requested to expand a little on orders of Randomness and what it means .
Please note that human endeavours at this date use only randomness of the order of flipping a coin ( Beth(0) )

Aleph is the first letter of the Hebrew Alphabet . It was used by Cantor to denote
Classes of Infinity (ie Aleph(0) for Rational numbers , Aleph(1) for Irrational Numbers , etc

Beth is the second letter of the Hebrew Alfabet . It means "House"

I will first repeat the derivation of Orders of Randomness from : "Orders of Randomness" because it is so important .

Start Quote:
First , simple Randomness .
Flip of a coin .
Heads or Tails . 0 or 1
Flip an unbiased coin an infinite number of times ,write it down below each other and do it again .
All possible 0 and 1's

An example : Beth(0)
Flips(1) 0,1,1,1,1,… etc
Flips(2) 0,1,1,1,0,… etc
Flips(infinity) 0,0,0,0,0,0,…etc

This describes all possible states in a delineated binary universe .
"delineated binary" means a two sided coin which cannot land on it's side .

Now draw a diagonal line from the top left of Flips(1) to Flips(infinity) .
At every intersection of this diagonal line with a horizontal line , change the value .
The Diagonal Line of (0,1)'s is then not in the collection of all possible random
Horizontal coin-Flips(x) .

This means the Diagonal Line is of a stronger order of randomness .
This is also the standard proof of an Irrational Number .

This is the standard proof of aleph numbers .
Irrational numbers ,etc
Since any number can be written in binary (0,1) , we can infer that the order of randomness is the same as aleph numbers .

This means we can use number theory in Randomness systems .
Very important .

Google Cantor (or Kantor)

Define coin-flip Randomness as Beth(0) , analogous to Aleph(0)
Then we have at least Beth(1) , randomness an order stronger than flipping a coin .
Then we can theorize Beth(Omega) <->Aleph(Omega) .

End Quote

Cardinal Numbers .

The cardinal number is the index x of Aleph(x) .
Cantor proved that
Aleph(n+1) = 2 ^ Aleph( n )

Where n is the cardinal number of the infinity .

Tying them together :
He also proved that
P(A) = 2^ n
Where A is any set , P(A) is the PowerSet of A and n is the cardinal number of set A
Thus , Cardinal Number of P(A) =(n+1)

The PowerSet of A = the Set of all subsets of A .
This sounds fancy , but it is simply all the different ways you can combine the elements of set A . All the ways you can chop up A .
You can see it easily in a finite binomial expansion (1+1)^n = P(A) = 2^n

See : "Infinite Probes"
There we also chop and dice , using infinite series .

Can you see how it all ties together ?

Why 2 ?

This derives from the Delineation Axiom . Remember , we can only talk about something if it is distinct and identifiable from something else . This gives a minimum of 2 states : part or non-part .

That is why the Zeta-function below is described on a 2-dimensional plane , or pesky problems like Primes always boil down to 2 dimensions of some sort .

This is why the irrational numbers play such an important part in physics .
Z=a+ib describes a 2-dimensional plane useful for delineated systems without feedback systems

Its in the axiom of Delineation , dummy .

But we know that Russell proved that A+~A
The difference can be described as the Beth sequences . Since they are derivatives of summation-sequences(see below) , they define arrows usually seen as the time-arrows .

These need not to be described a-la-dunne's serial time , as different Beth levels address the problem adequately without multiplying hypotheses .



Self-referencing systems and Beth sequences .

A Proper Self-referencing system is of one cardinal Beth number higher than the system it derives from .
Self-referencing systems (feedback systems) can always be described as sequences of Beth systems . Ie as Beth(x) <-> Beth(y) . The formal proof is a bit long for inclusion here .

The easiest way to see it is in Bayesian systems . If Beth(x) systems are included , Bayesian systems become orders of magnitude more effective .

Life , civilization and markets are such . See below .

Conservation Laws :
By definition , these can always be written in a form of
SomeExpression = 0

Random (Beth(0) Walk in Euclidean 2-dimensions

This is a powerful unifying principle derived from the Delineation Axiom .

In Random Walk the Distance from the Center is = d * (n)^0.5 . This is a property of Euclidean systems .
(Where d = step , n=number of random beth(0) steps)

Immediately we can say that the only hope of the Walker returning to the center after an infinity of Beth(0) steps is if d ~ 1/(n)^0.5 . This is the Riemann Hypothesis .

Now , see a Universum of 2-dimensional descriptors z=a+ib

Sum all of them . Add together all the possible things that can be thus described .

This can be done as follows :
From z=a+ib Raise both sides to the e
e^(z) = e^(a) . e^i(b)
Raise both sides to the ln(j) power where j is real integers.
j^(z) = j^(a) . e^(b/ln(j))

Now , sum them :
Zeta=Sum of j^(z) for j=1 to infinity

Now we extract all possible statements that embody some Conservation Law . Beth(1)

This means that Zeta is zero for the set of extracted statements if and only if (b/ln(j)) is of the order of Beth(0) and a=(-1/2)

Tensors .
The above is a definition of a tensor for a discontinous function .

Riemann's Zeta function.
This can describe any delineated system .
If Zeta = 0 , conservation laws apply .

Zeta = Sigma(1/j )^z for j=1,2,3,…,infinity and z=a+ib , where z is complex and i =(-1)^0.5
The z bit is in two dimensions as discussed above .

This function has a deep underlying meaning for infinite systems .
If you unpack the Right-Hand side on a x-yi plane you get a graph that looks like a random walk .

If every point is visited that a random walk would visit over infinity (ie all) , without clumping , then Zeta can only be non-trivially zero if a=(-1/2) .

Why (x – yi) plane ? See "Why 2 " above . The system is fractal . Two dimensions are necessary in any delineated system .

Remember , randomwalk distance from origin = step*sqrt(number of steps) .
So if the steps = 1/ ( sqrt(number of steps) ) , then the Origin might be reached if and only if a= -1/2
This is easily proven .

If a= - 1/2 , then b can be any real function . This would include Beth(0) and Beth(1) , but not higher orders of beth .

If a= -1/2 and b is an unreal number , then a cannot be equal to -1/2 anymore . Conservation cannot hold at any level .

Conservation Laws can only hold for Beth(0) and Beth(1) systems .

This is forced by the two dimensions of delineation .

Mathematically , this means that Beth(2+) systems of feedbacks can only be described in terms of attractors or/and fractal systems (ie not in isolation)

Physically , conservation of energy and momentum need not hold for Beth(2+) systems .

This has an interesting corollary in decryption (unpacking) . A Beth(2) mind unpacking Beth(0) or Beth(1) encryption is functionally equivalent to Non-Conservation of Energy
Appendix ZZZ
Molecules that collapse Quantum Waves


Andre Willers
31 Dec 2012
Synopsis :
We find other molecules that collapse (observe) quantum probability waves to some degree .

Discussion :
1.We know Melatonin does it . So , we look for melatonin-like molecules .
2.We find Valdoxane and Serotonin
3.Melatonin-Class wave-function collapsars .
These are characterised by two ring-shaped chemical structures , with antennae at the 10 o'clock and 2 o'clock positions .
4.Non-linear systems:
This gives an Electric field value of 1.3 x 10^18 V/m for non-linearity .
How close does two charges have to be to get these values ?
Plugging the values into classical equations gives 
r= 3.325 x 10^(-14)
=332.5 picometers (pm) .
5.Atomic Distances
The picometre's length is of an order such that its application is almost entirely confined to particle physicsquantum physics, and chemistryAtomsare between 62 and 520 pm in diameter, and the carbon-carbon bond has a length of 154 pm. Smaller units still may be used to describe smaller particles (some of which are the components of atoms themselves), such as hadrons and the upper limits of possible size for fermion point particles.
6. Now can you see what is happening ?
Incoming wave functions squeeze particular atoms so close that the Schwinger-limit is exceeded . The system goes non-linear . Entangled wave packets are emitted , in the process collapsing the wave-function .Entanglement is conserved , especially angular momentum . Remember ,everything rotates .
This is both Observation and generation of new entanglements . 
7. Hence the Antennae-like structure of the molecules at angles . They whip around very close to the ring-structures to trigger very specific , metered responses . Which , presumably , can be picked up by similar systems .
8.These would not be supra-luminal . You need at least 27+1 nexi for that . 
These molecules are about 22 nexi . Sufficient , but nothing to write home about .
9.Dopamine :
Similar to melatonin-class , except there is only one ring . A precursor, from an evolutionary viewpoint .

10. Three-ring .
This should be possible in a free-evolutionary environment . I don't know of any , but they are doubtlessly there .
11. More than Three-ring :
These would have to be designed . The pockets of probability that make them possible are too precisely defined to easily evolve without higher Beth(x) input . Think probability ~ 1/Aleph(0) 

12.An interesting Aside :
Cold Fusion and all that jazz .
The Dear Reader would have noticed that biologicals are necessary to get atoms close enough to violate the . To get at least beta-decay . 
Breathing on it would be enough , but spitting would help .
The Contaminant is the Experiment . (With apologies to Marshall MCluhan)

14.Can we design a purely artificial quantum-collapsar molecule ?
Yes .
See Appendix I and II .
The problem is that all these molecules also have biological functions , some in the higher Beth regions .
Creating a completely artificial quantum-collapsar molecule will bypass many of these problems .
On the other hand , it might kill you all .
Or worse, put you into a superposition state .
15. For the Paranoid Conspiracy Theorists :
Prions are a defense system , soaking up deleterious quantum-signals from wherever . Some prions are part of the immune system , soaking up random information packets from normal metabolic processes . But a collimated beam targeting defensive prions is something else .
A nice weapon .

The technique initially incubates a small amount of abnormal prion with an excess of normal protein, so that some conversion takes place. The growing chain of misfolded protein is then blasted with ultrasound, breaking it down into smaller chains and so rapidly increasing the amount of abnormal protein available to cause conversions.[1][2] By repeating the cycle, the mass of normal protein is rapidly changed into misfolded prion (termed PrPSc).

16. But , we can turn it around .
Instead of misfolded protein , we start with properly folded proteins . Then do the amplification . PFCA .
It works both ways . If we design the folded protein exactly to collapse certain wave functions , we can target and eliminate to low levels the transmission vectors of certain diseases .
Cheap and simple .
17. The applications for alzheimers , etc are obvious .Just shift the balance . If you know what you are doing , you can even do it electromagnetically . But , humans are too enamoured with needles and threads .

18 . Really great astronomical detectors .
A few blobs of Protein Folding Cyclic Amplification (PFCA) will give you Gravity Wave detectors , as well as some pretty good EM detectors .

19.Energy Detectors and Energy sources .
Well , an energy detector is an energy source . It depends on the scale .
We can certainly use Genetic algorithms and PFCA to automate an optimization system to get some amps out of the ambient energy wash . This is not zero-point energy , more like the energy that clusters around zero-points . Good for low-energy applications like cell-phones , etc .
For something with more oomph , you will need a feedback system . Carbon biologicals simply have not the carrying capacity . Try silicon prions .
See Appendix I

20.Well , now you know how to cure a lot of diseases easily , get some low-level energy cheaply everywhere and maybe how to get high-density energy sources .
The rest is up to you .
21. What ! Nothing to steal ?
Try working for a living .

Would you flip a Beth(x->infinity) coin with God ?


Appendix I
The Beauty of the Genetic Code .
Andre Willers
22 Feb 2010

The present TerraIII genetic code is elegantly optimized to give the most robustness possible per unit of information .

Discussion :
You have to be familiar with the concepts in:
1. "NewTools:Reserves" and Beth(n) orders of Randomness .
2.NewScientist of 23 Jan 2010 p34 "Another kind of evolution"

Brief recap of Reserves argument :
We take any identifiable entity , slice and dice it with an order of randomness like that of a coin (ie Beth(0) ) . We then calculate a minimum reserve (which is equivalent to the least errors of all possible Beth(0) paths per benefit . )
This works out at 1/3 on the average over Aleph(0) infinities .

The Beauty of the Genetic Code :
Four Base pairs (A,U,C,G) in triplet codons give a possible 4*4*4 = 64 codons .
But together , they code only for 20 amino acids , plus a Stop and a Semi-Start .

This gives
20/64 = 31.22% for 20 amino acids
21/64 = 32.81% for 20 amino acids + Stop
21.3333…/64 = 33.3333… for 20 amino acids + Stop + Semi-Start
22/64 = 34.375 %

Stop = (UGG) , (UGA) , (UAG) ,
Start = (AUG) , but this also codes for methionine . Hence the decimal notation . The system cannot come closer to 1/3 because of quantal considerations . Try it and see .
This also is the portal for the Epigenetic System ( note use of methiolization) .

Beautiful !!

Consider the ways of Gaia .

Linear and Sideways evolution .
Linear : 
The standard , gene and chromosome based inheritance
Equivalent to Beth(1+x) in our notation .
1>= x >=0

Sideways :
Genetic material exchanged without going through all that genotype-phenotype procedures .
Equivalent to Beth(1-x) in our notation .
1>= x >=0

Note that the system could not possibly get as close to the optimum reserve without this stage .

The Breeder , genetic engineer .
Equivalent to Beth(2+x) in our notation . Humans or proto-humans .
Infinity>= x >=0

This gives a full spectrum of Beth capabilities .
(Negative Beth is outside the scope of this discussion)

You will notice that the system becomes chaotically unstable as x->0 from any direction . At that point , the system will exhibit symptoms of great stress and bifurcation . Once over the hump , it steadies either in an evolutionary manner (in
Probability = 1 - ( Beth(n+1)/Beth(n) ) ^0.5 . Admittedly a rough estimate .)

Or in a devolutionary manner , evolutionary manner here described as degrees of complexity .

Stable Gene Engineering :
1.Keep the same Triple-Base Codon Cell-Machinery .
The easiest . Existing cells can be used . Increase the number of bases to 5 .
Then we can optimally reliable make 1/3*5^3 = 40 amino acids + stop + semistart .
Different kinds of Stop and Start would be advisable .
So , maybe 18 new amino acids + 2 different types of Stop + SemiStarts

This would not even be hard .
Well within present technological capability .
(Wanna make an animal with a Kevlar skin ? Well , you can using this method .)

The system would even be self-assembling under the right condition . The main thing is the optimal stability .

This is already evolving as we speak . There a fifth base occasionally involved . So there is a fruitful interaction point .

2.Make 4-Base Codon Cell-Machinery .
A real remake . Not within human capability at the moment .

3.General :
nAminoAcids + nStops + nStarts = 1/3 * ( (nDNA-bases) ^ (nBasesPerCodon) )
where the prefix n denotes "number of"

A further stability would be introduced if nStarts ~ 1/3 * nStops in a fractal fashion .
This because life-forms evolve in a pedal-to-the-metal fashion . The problems are the brakes .

There is a relationship between the Beth level and the nBasesPerCodon . The minimum number sufficient for Beth(2+) is nBasesPerCodon=3 .
Else there is insufficient complexity .

Now go out there and evolve !

Andre .
Appendix II The Beauty of the Genetic Code 2
Andre Willers
16 Mar 2010

Hi ,

See ""Rewriting life in four-letter words" , NewScientist 20 Feb 2010 p14.
I just read it (16 Mar 2010) , as I get New Scientist in a haphazard fashion via the library . 

See para 2 of original post below
"2.Make 4-Base Codon Cell-Machinery .
A real remake . Not within human capability at the moment ."

I was wrong .
It  has already been done by  Jason Chin and colleagues at the University of Cambridge . They successfully redesigned some ribosomes and transfer RNA(tRNA) to manufacture a novel amino acid (a novo-calmodulin protein) , expressed via E.Coli .

Important note:
This worked so easily because it worked parallel to the three-Base expression without noticeable inerference .
This hints that the meta-controls (see Phene-system posts) already has provisions for 4-Base cell-machinery .

1.See "Pandora bacteria acts as one organism" , NewScientist 27 Feb 2010 , p11.
Electron-conducting protein nanowires link oxygen-poor sub-mud sulfur eating bacteria on the seafloor in an interactive network suggestive of a neural net .

The manufacture of such a protein nanowire would almost certainly require 4-Base Codon cell machinery . Hence the the existence of parallel meta-controls . 

Room-temperature organic superconductors seem to be a distinct possibility .

2.Many old-age and degenerative diseases seems reminiscent of 4-Base Codon cell machinery activating over time .

But what do I know .

It is your poblem now .
I hope your molecular shamans are better than your climatologist shamans .


Appendix BB
Separation of rare gases and chiral molecules by selective binding in porous organic cages
·         Linjiang Chen,
·         Paul S. Reiss,
·         Samantha Y. Chong,
·         Daniel Holden,
·         Kim E. Jelfs,
·         Tom Hasell,
·         Marc A. Little,
·         Adam Kewley,
·         Michael E. Briggs,
·         Andrew Stephenson,
·         K. Mark Thomas,
·         Jayne A. Armstrong,
·         Jon Bell,
·         Jose Busto,
·         Raymond Noel,
·         Jian Liu,
·         Denis M. Strachan,
·         Praveen K. Thallapally
·         Andrew I. Cooper
·         Affiliations
·         Contributions
·         Corresponding author
Nature Materials





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16 June 2014 
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The separation of molecules with similar size and shape is an important technological challenge. For example, rare gases can pose either an economic opportunity or an environmental hazard and there is a need to separate these spherical molecules selectively at low concentrations in air. Likewise, chiral molecules are important building blocks for pharmaceuticals, but chiral enantiomers, by definition, have identical size and shape, and their separation can be challenging. Here we show that a porous organic cage molecule has unprecedented performance in the solid state for the separation of rare gases, such as ​krypton and ​xenon. The selectivity arises from a precise size match between the rare gas and the organic cage cavity, as predicted by molecular simulations. Breakthrough experiments demonstrate real practical potential for the separation of ​krypton, ​xenon and ​radon from air at concentrations of only a few parts per million. We also demonstrate selective binding of chiral organic molecules such as ​1-phenylethanol, suggesting applications in enantioselective separation.

Filtering gases out of the air has been commonplace for quite some time, but not all gases are easily sorted. Noble gases, for instance, don’t readily react with other elements, so they pose somewhat of challenge. The lower the concentration, the more difficult and inefficient the process becomes. Some new research, however, may improve efficiency and even help save lives.
Researchers at the University of Liverpool, in conjunction with the Pacific Northwest National Laboratory, have developed a new material with atomic selectivity. The technique uses an organic cage molecule, called CC3, to trap gas atoms of just the right size. Atoms which are not the correct dimensions are not collected, thereby operating with exceptional selectivity.
According to the University of Liverpool, “By a process of adsorption – where molecules or atoms stick onto the surface – the right gas molecules are held in place, while others such as water or nitrogen are released.” This concept of collecting matter through molecular cages is not new and not limited to atoms (see concept for nitrobenzene in image), but the development for noble gases does introduce some promising applications. CC3 has been found efficient at collecting xenon, krypton and radon.
Researchers used computer simulation to study the molecular cage structure of CC3 and found that it undergoes a natural expansion and contraction which oscillates around the size of xenon, krypton and radon. As the cage expands, the gas atom enters, and as it contracts, it becomes effectively trapped, having a higher likelihood of entering than exiting. (More on this mechanism here)
While xenon and krypton have a variety of research and industrial uses (like dark matter detection, for xenon), these elements are typically expensive due to their rarity and noble nature. Radon, on the other hand, is a common killer, accounting for 21,000 deaths per year according to a 2010 Surveillance, Epidemiology, and End Results (SEER) analysis.
The Environmental Protection Agency (EPA) action limit on radon is 4 pCi/L, a level at which you have the same likelihood of dying from radon as you would in a car crash. It’s higher if you smoke. Although there are radon mitigation systems readily available which use a pressure differential to keep radon out, a method of filtration and/or precise detection could greatly enhance general well-being.
The CC3 material does show promise for being an effective means for separating these gases, especially as it operates at or near room temperature whereas current separation methods rely on expensive, cryogenic operations. That said, don’t be looking for a CC3 radon filter on the supermarket shelf just yet. Hopefully, though, this sort of work will result in some trickle down improvements to daily life.
If you can get access and are interested, the scientific article, published in Nature Materials, is here.


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