Which Is The First Element That Can Have An Electron With The Following Set Of Quant: Fill & Download for Free

In light of seeing the same questions repeatedly: For a more detailed, albeit, math-intensive explanation, I recently updated a paper: DESCRIPTIONS HISTORY AND DEFINITIONS OF THE QUANTUM ZENO EFFECT AND ANTI- QUANTUM ZENO EFFECT AS A PROPERTY OF THE EVOLUTION OF THE DESITTER HORIZON IN GENERAL RELATIVITYJanuary 2019 DOI: 10.13140/RG.2.2.22174.59204p.s. thank you Tom Redding for the edit; Thank you Ron Barak for the edit. Thank you Tedd Hopp for the edits.In 1955 Wheeler was trying to understand and make a set of rules regarding Gravity Waves. As he coined the term, Gravitation without mass, which is true and correct.As he was trying to differentiate, or separate, mass and Gravitation, the mass being a result of [math]E=mc^2[/math] energy, it occurred to him that mass must be quantized according to Planck’s constant, just as any other energy is.If energy is quantized, then time, an interdependent quality with energy (there is no such thing as ‘static’ energy, energy is ‘the capacity to do work, which is a process, which is therefore temporal) time must also be quantized.if time is quantized, then length, a dimensionality inseparable from time in General Relativity must also be quantized.This then spills out to every possible thing that occupies space and time, every function, every field, everything. I believe wikipedia has a very long list of Planck Units somewhere, probably under ‘Planck Units.’the derivation Wheeler found (which remains uncontested, the derivation that is) for the Planck interval of time:works out to about 10^-44 seconds, or 10^44 Planck intervals of time per second.notice that Gravitation, the speed of light, and Planck’s quanta are all in there. the 2 pi in the denominator is referred to as the ‘reduced Planck’s constant,’ which I prefer to write out long hand rather than the common h-bar. the 2 pi represents a cycle. By ‘cycle’ I am referring to a sinusoidal wave cycle, thus we see the superintendency between time and energy. If a wave function cannot cycle, there is nothing there. No energy.for the Planck lengthworks out to about 10^-35 meters, or 10^35 Planck lengths in a meter. This is 20 orders of magnitude smaller than a proton diameter.Note that the ‘hard definition’ for the speed of light is c=1Lp/1tpin which case you end up withUltimately, the reason Lp is the shortest slice of space and tp the smallest slice of time is because they are exactly 1 quanta of space and 1 quanta of time. Since the quanta cannot be further divided, neither can Lp or tp.That is, since Planck’s constant, h is the smallest quanta, (regarding G, c, and pi as rock solid) then there is no time or length in normal space-time smaller than h will allow.Just note, the Zero Point Energy, or Zero Point Field falls upon this exact same definition. There can be no pure absolute void (vacuum), only the bottom line of some integer value of h. When you see the term, Quantum Fluctuation, this refers to the ZPE and/or the ZPF jumping to some other value, just like an electron experiences a quantum jump from one orbital to another, but for a different reason. The electron quantum jumps when it absorbs energy or loses energy. The ZPF jump is purely probabilistic.It should be noted that one dissatisfied customer, apparently not familiar with the details of QM, or General Relativity, suggested that energy was independent of time, and referred off to Planck’s original derivation of Planck’s constant, apparently without knowing the derivation or the background.I hate using Wikipedia, but in this case the description is correct:First recognized in 1900 by Max Planck, it was conceived as the proportionality constant between the minimal increment of energy, E, of a hypothetical electrically charged oscillator in a cavity that contained black body radiation, and the frequency, f, of its associated electromagnetic wave. In 1905, the value E, the minimal energy increment of a hypothetical oscillator, was theoretically associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called the photon. In simple terms, Plancks constant is the amount of energy in one cycle of a wave from electromagnetic radiation, regardless of wave length, the amount of energy in a cycle remains "constant" as the name suggests.All of the terms, oscillator, black box radiation, wave function, EM radiation, ‘the amount of energy in one cycle of a wave,’ are time dependent values. In fact, just a wavelength is time dependent, as space and time are inseparable values in General Relativity. The despondent person then goes on to site ‘joules’ as time independent, and that was the reason Planck’s constant is the joule*second.a joule is inthe rationale for the joule*second is to eliminate the s^2 in the denominator, as this refers to an acceleration of mass. He then goes on to argue energy as ‘potential’ vs. action, where ‘potential’ is time independent and action is time dependent.Let’s pretend for an instant that energy is time independent ‘potential.’ A wave function, which describes every known thing and force there is, is obviously time dependent. If you were to stop the Planck Flow of time, freeze time, there would be absolutely no information in that once wave function to reverse engineer a wave function back out of it, start the clock, and reconstruct a wave function.Every aspect of that wave function, field, force has no information in it unless it is in the Planck Flow. THIS WAS THE ORIGIN OF THE INFORMATION PARADOX. Information, which is time dependent, falls onto the Schwarzschild surface (the Black Hole), where time has infinitely dilated (stopped), and that is the end of your information. Although the Black Hole may radiate away, there is no way to reconstruct the information that fell onto its Schwarzschild surface.This led Leonard Susskind to develop or state what he refers to as the -1 law (negative 1 law) of Thermodynamics (zero had already been taken): information cannot be destroyed.The implications of that statement are much further reaching than all of the other laws of physics combined. It is a direct statement, and I think a lot of people miss this, that the Planck Flow cannot stop (time cannot stop, nor infinitely dilate).The relationship between information, time and energy comes from Beckenstein’s paper dating back to the 70’s in Black Hole entropy. Since then, Verlinde has derived the following:The definition for a ‘bit’ of information in Holography is the surface area of the Schwarzschild surface (like the surface of a black hole) /4 Planck lengths squared. This defines a bit asSince c=1Lp/1tp, this is exactly equivalent to sayingc=1Lp/1tp is equivalent to c=1tp/1LpIf you invert the equation it comes out the same. Oddly, people talk about space-time being ‘pixelated.’ However, this definition renders a trigonal pyramidIn any case, any regular shape is impossible on a Planck scale. For instance, the heights, hypotenuse, and so on are not integer values of Lp, so the shape cannot exist. A circle has a pi x diameter of the circumference, also not an integer value of Lp, so a circle is not possible. This goes on to every possible shape.On a Planck scale, the domain becomes shapeless, and Wheeler, while defining these things, described space-time as having a ‘foamy’ characteristic. I wrote at length on the space-time foam in another post, I don’t remember which.I’ll wait for all the arguments that will come as a result of that.Thank you Ron Barak for the edit.I’ve been working on this issue since the last posting of it. There is no evidence in any field of QM for time or space being infinitely divisible. Although some mathematical approaches ‘approve’ of infinitely divisible space-time, all of the mathematical estuary hypotheses of QM; quantum field theory, string theory, m-theory, and so on, are improvable.However, I found an obvious but overlooked phenomenon noted by Saul Hernandez, the Bohr quantization of the electron orbital. This is a phenomenon that is as rock solid as any axiom. When an electron jumps up or down between orbitals, actually, there is no ‘in between,’ the electron is in one orbital, then it is in the next, with no time interval (instantaneously) marking a transition from one position and vector and the next. This is absolute.If space-time were indeed continuous (infinitely divisible), the electron would have to pass through an infinite number of states between its current position and vector (orbital) and the next. The first approach is to think of a Riemann sum, where an infinite number of infinitesimals equals some value (slice an apple into infinitely thin slices, then add those infinite number of infinitesimal slices together and you get your apple back). However, this approach does not work for zero. If you try and divide zero you get zero. If you add an infinite number of zeros together you get zero.Most importantly, this would require an infinite amount of information to describe, and therefore, by convention, an electron jump would then be a black hole. Since this is obviously not the case, spacetime is simply quantized, which is why and how Bohr quantized the electron orbital. In this, there is no mystery to the jump. Metaphorically, spacetime is then a ladder, the electron either takes a step up or down the ladder. There is nothing between the steps.The quantized Bohr electron is the only rock solid evidence that exists, and absolutely requires space-time to be quantized at some value greater than zero (not infinitely divisible, not continuous). Wheeler’s derivation is therefore correct and rock solid, with the only compelling evidence that exists being the Bohr quantization of the electron orbital.The next obvious question is that this appears to be similar to quantum entanglement. Is quantum entanglement a similar quantization of space-time dependent phenomenon? The problem in answering that question is that quantum entanglement is being taken to strange places. For instance, QE is an approach to looking at the QED vacuum, and therefore quantum gravity. That is, gravitation being an emergent phenomenon from entangled vacuum regions, based on Wheeler’s ‘Quantum Foam.’The following is not standard stuff.We think of a tiny region of space-time, and fractalize it down or up in size. We then consider any frac to either have or have not a virtual particle in it. If a given frac does have a virtual particle, then another frac must contain the virtual anti-particle, and the two fracs are entangled regions of space-time.This has led me into a rabit hole of fracking everything in the form:With G’ being the state:and t’ as a Schwarzschild transformation:note the (+/-) is always the emergent result of a square root, you can’t just discard the negative result. This then pours out to:the Nicolini’s approach:with the Schwarzscild metricandthenMeaning that the fractal approach even works in Holographic Theory (hypothesis). This makes perfect sense, because any force on a black hole surface can only be limited to the surface, as a black hole has no actual interior. The only respect to an interior can be regarded as an infinite amount of information (length infinitely dilating without bound) as the Anti-deSitter approach requires. That is, rather than an infinite amount of information, a single bit of information having infinite value. As the number of bits on a Schwarzschild surface is given by N=area/4Lp^2.This, of course is off the top of my head, not ‘standard stuff.’However, I need point out that the entire artifact of expansion is the result of the lack of Conformal Correction to the ‘locally quantized meter stick.’ That is, in another post [actually a paper at ARTIFICIAL ALTERATION OF THE GEOMETRY OF SPACE-TIME VIA THE QUANTUM ZENO EFFECT]There I describe the Conformal approach to DeSitter space, and the fact that we are on the DeSitter Horizon, which makes no sense unless you read the paper. I have a slightly less difficult to read post at Bill Bray's answer to How can an electron be in a superposition state but change when being observed?There I describe the DeSitter Horizon, which is Holographic Theory, via the Statistical Mechanics of a Markov Dyadic process, where space-time splits off from g(m) to g(mn) every Planck interval of time. As such, we exist on the surface of the DeSitter Horizon, and every event out to 1 Planck length is at some distance below the DeSitter Horizon.Then we haveIn a global pattern that is fracked like this:The lizards in the center are larger than the lizards where we exist on the surface. That is our locally quantized meter stick. It takes a lot of those tiny lizards on the surface of the Holographic (DeSitter) Horizon to equal 1 lizard near the center. As a result, any velocity we measure would seem to increase as we look deeper into the center (which means further into the past).The problem with the statement that the expansion is accelerating is that it is correct, but for the wrong reason. The astronemers did not correct for the abberation of our locally quantized meter stick, regardless of the fact that the direct measurement of the frequency of light indicates it is longer (dilated, redshift). The primary culprit here is that Lorentz equation is upside down, length dilates with velocity, this also is at length in another post. [Bill Bray's answer to In space and space travel in science fiction, we see the ships always run their engines. Why would they need to constantly fire their engines?]So, (there’s good English for you) there is no possible way, since the locally quantized meter stick in my hand has a different value than that 13 billion years ago that G is constant. This is why I take t’ and correct it. In the above post the t’ factor and all of the associated principles of General Relativity are derived and quantized. SR and GR are quantized because, no matter how much I kick and scream, I have a locally quantized meter stick. Since my meter stick is quantized, I cannot take a non-integer value of Lp or tp measurement of a SR or GR phenomenon. Since I can only take a qauntized measurement of an observed phenomenon under SR and/or GR, SR and GR are quantized.The astronomers who made the initial claim that the expansion was accelerating took redshift data from some 13 billion light-years away, but used brightness of supernova at an entirely different patch of space much closer. So of course, the values, if you look at lizard world (DeSitter Space, the Holographic Horizon) you directly measure a length dilated photon (actually, the photon is not dilated as a result of ‘receding,’ we are egressing from that fixed point). However, they do not know to apply the Conformal Correction, which is right there in the direct redshift data, and also correct for the distribution of the photon population as the photon population (under statistical group theory) passes through some 1E40 or more fracks in space-time.As a result, and we can measure this as fine as a fraction of the diameter of a proton, the dissipiation of the population does not dissipate according to the 19th century 1/4piD^2, you have to figure in the Statistical Mechanics of the Dyadic Markov chains it has to pass through, using a modified form of Shannon Entropy (Information Theory, where n = 2)The dissipation has a very slightly different value of D^(2+ln2). If you apply that correction, and the Conformational Correction to the DeSitter Horizon vs the DeSitter Depth (my little lizard vs the bigger lizards in the middle), then the values match.Oddly, the astronomers use z because it is unitless, which makes placement of z arbitrary (numerator or denominator). Regardless, the brightness not matching the Conformal change means nothing, except that you failed to apply the correction factor you just directly measured.Failing to understand or apply the correction, they chose to arbitrarily place z in the denominator, becuase if placed in the numerator, that states the expansion is slowing, which is what is expected. So they got a Nobel for failing to do the math, not the first time.They also failed to recognize the equations as being upside down. I have an entire text, it is almost 2000 pages of math equations in physics that are upside down or incorrect. And I correct them. Booly for me. For example, after you are done reading Maric’s derivation she did for her husband, you can look at pi and ‘e’. Pi cannot be irrational unless the circle is of infinite diameter, the lower limit of ‘squaring the circle’ algorithm must stop at the Planck length. Since our cosmos is not an infinite domain, nor is it infinitely stable (referred to as a False Vacua, meaning not infinitely stable, and will not exist for infinity) pi is rationjal and finite. The same principle is applied to ‘e’, Where e is derived by:The choice o angles is finite, limited by the Mitrofanov angle: [IGOR G. MITROFANOV Space Research Institute, Profsojuznaya str. 84/32, 117810 Moscow, COSMIC GAMMA-RAY BURST SOURCES: THE PHENOMENON WITH THE SMALLEST ANGULAR SIZE IN THE OBSERVABLE UNIVERSE. THE ASTROPHYSICAL JOURNAL, 424:546-549, 1994 April 1 (i) 1994. The American Astronomical Society. April 1, 1994...424:546-549]In a sphere.Lorentz is upside down, GR is quantized, SR is quantized, pi and e are rational, dogs and cats lying together….It’s a chaotic collapse into randomness. I also wrote a paper on Information Entropy in Science. I think it is at, https://www.researchgate.net/publication/327288640_INFORMATION_ENTROPY_AS_A_CHAOTIC_FRACTAL_COLLAPSE_OF_SCIENTIFIC_KNOWLEDGEI should add here that the Planck length squared is the surface area of the smallest theoretical black hole, about 10^-70 m^s, the Planck time is the theoretical amount of time such a black hole would take to evaporate away via Hawking radiation, and the Planck mass is the minimal amount of mass possible to make a black hole, e.g., a black hole with exactly 1 bit of information entropy.So, the terms Lp, tp, and mp describe as a trio the smallest possible black hole, any smaller would be less than 1 bit of entropy. This then yields the definition for what is 1 bit of information entropy. It is the mass-energy of about a flea egg (actually quite large) confined within a surface area of 10^-70 m^s that would radiate back into normal space-time in about 10^-44 seconds.Then there is the ‘probing problem.’ If we want to build a particle accelerator to probe at higher energies, meaning smaller sizes in terms of wavelength, astaking note that the lambda in the denominator, as it grows smaller, E grows larger. What happens is that taking any mass and accelerating it closer and closer to the speed of light, confines that mass-energy into a smaller and smaller package, until a black hole of 1 Planck mass is formed, e.g., 1 bit of information entropy, when the mass-energy is confined into a diameter of 1 Planck length.Applying more energy does not resolve the issue, but simply makes a black hole in multiples of 1 Planck mass, in multiples of 1 Planck length, in multiples of 1 bit of information entropy. Thus, we see that mass and gravitation (which describes the geometry of space-time) bottoms out at the point where we increase the mass of our accelerated particle to 1 Planck mass, by definition must be 1 Planck length, and a micro-black hole forms; then goes up in multiples of the Planck mass in multiples of the Planck length in diameter.There is therefore no possible means to probe a limit below the Planck length. As a result, gravitation, which describes the geometry of space-time has a limit at the Planck length.An odd side effect is that the Planck mass is the maximum mass that can describe a conventional wave function for any single particle. That is, if you tried the double slit experiment on a mass larger than the Planck mass, since no wave function can describe it, it will not produce an interference pattern. We then have the upper limit for a wave function.As a result, above that upper limit in wavelength, you have to split off into another separate wave function, a second ‘particle.’ This is where we start to talk about entanglement, as the second wave function is the product of the first. approaches to quantum gravity take this to mean that if there is greater distance between the wave functions, they are ‘less entangled.’ That is, the underlying geometry of space-time is such that as we describe entanglement as an ‘instantaneous event,’ since there is no such thing as ‘simultaneous events’ in real space-time, we use the hard definition c=1Lp/1tp, and therefore Lp=tp/c; leaving the more or less entangled feature with only multiples of the Planck length.The rest of the approach is still in the making. Quantum ‘Loop’ Gravity is this entanglement feature, ‘looping’ regions of space-time, rather they have information in them or not; given that if a region does not have information in it, it is ‘vacuum state,’ and will give rise to virtual particle-antiparticle production (Quantum Foam). As it turns out, a vacuum region (very tiny) is less likely to produce a virtual anti-particle a billion light-years away then it is to give rise to a virtual antiparticle 1 Planck length away. The Quantum Gravity approach then, is to consider the QED vacuum as divided into Planck regions which may give rise to particle-antiparticle entangled pairs, more likely in close proximity than farther apart. It is information and probability.As information, then, and particularly information entropy, the Wheeler derivations have led to the definition for exactly what information is, the minimal amount of yes/no that describes the least amount of entropy possible in normal space-time.As a result, any smaller amount of information is impossible, and as such, continuous space-time (infinitely divisible, requiring infinite information to describe an infinitesimal) is an impossibility.This is also not standard stuff.Which brings us to ‘compactified dimensions,’ dimensions compactified within the 4 observable dimensions. String Theory, m-theory, and so on have as of yet no approach to such dimensionality as per information. At this time, since there has been no approach to describe such information at values smaller than the Planck intervals and mass, it looks bad for ‘compactified dimensions.’I would expect Susskind, t’ Hooft, or Buosso to be the first to at least partially resolve these. But being no fan of string or m-theory, it goes like this:The information needed to describe a ‘vibrating string’ of 1 Planck length is not possible, as it requires slicing such a wave function into slices not possible in normal space-time. compactifying dimensions within the wave function does not resolve the issue, as such a thing can only have 1 of 2 possible states, +1 or -1.In Quantum Temporal Dynamics (Temporal Mechanics 101) I describe this system as having an underlying architecture of:as oscillating in any 1 or more dimensions between +1 and -1, then go on to describe all of the particle zoo, fermions, bosons, particle interactions, mass, fields, and gravitation from this scaffold. And as it turns out, the Planck length, time, and mass are the exact derivatives of this approach. But that’s a 1200 page text. Also not ‘standard stuff,’ but purely hypothetical.1.Furuta, Aya (2012), "One Thing Is Certain: Heisenberg's Uncertainty Principle Is Not Dead", Scientific American.2.Ozawa, Masanao (2003), "Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement", Physical Review A, 67 (4): 42105, arXiv:quant-ph/0207121 Freely accessible, Bibcode:2003PhRvA..67d2105O, doi:10.1103/PhysRevA.67.0421053.Loudon, Rodney, The Quantum Theory of Light (Oxford University Press, 2000), ISBN 0-19-850177-34.D. F. Walls and G.J. Milburn, Quantum Optics, Springer Berlin 19945.C W Gardiner and Peter Zoller, "Quantum Noise", 3rd ed, Springer Berlin 20046.D. Walls, Squeezed states of light, Nature 306, 141 (1983)7.R. E. Slusher et al., Observation of squeezed states generated by four wave mixing in an optical cavity, Phys. Rev. Lett. 55 (22), 2409 (1985)8.Breitenbach, G.; Schiller, S.; Mlynek, J. (29 May 1997). "Measurement of the quantum states of squeezed light" (PDF). Nature. 387 (6632): 471–475. Bibcode:1997Natur.387..471B. doi:10.1038/387471a0.9.G. Breitenbach, S. Schiller, and J. Mlynek, "Measurement of the quantum states of squeezed light", Nature, 387, 471 (1997)10.Entanglement evaluation with Fisher information - http://arxiv.org/pdf/quant-ph/06...A.I. Lvovsky, "Squeezed light," [1401.4118] Squeezed light11.L.-A. Wu, M. Xiao, and H. J. Kimble, "Squeezed states of light from an optical parametric oscillator," J. Opt. Soc. Am. B 4, 1465 (1987).12.Heidmann, A.; Horowicz, R.; Reynaud, S.; Giacobino, E.; Fabre, C.; Camy, G. (1987). "Observation of Quantum Noise Reduction on Twin Laser Beams". Physical Review Letters. 59: 2555. Bibcode:1987PhRvL..59.2555H. doi:10.1103/physrevlett.59.2555.A.Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, "On-Chip Optical Squeezing," Physical Review Applied 3, 044005 (2015). [1309.6371] On-Chip Optical Squeezing13.Ou, Z. Y.; Pereira, S. F.; Kimble, H. J.; Peng, K. C. (1992). "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables". Phys. Rev. Lett. 68: 3663. Bibcode:1992PhRvL..68.3663O. doi:10.1103/physrevlett.68.3663. PMID 10045765.14.Villar, A. S.; Cruz, L. S.; Cassemiro, K. N.; Martinelli, M.; Nussenzveig, P. (2005). "Generation of Bright Two-Color Continuous Variable Entanglement". Phys. Rev. Lett. 95: 243603. arXiv:quant-ph/0506139 Freely accessible. Bibcode:2005PhRvL..95x3603V. doi:10.1103/physrevlett.95.243603. PMID 16384378.15.Grote, H.; Danzmann, K.; Dooley, K. L.; Schnabel, R.; Slutsky, J.; Vahlbruch, H. (2013). "First Long-Term Application of Squeezed States of Light in a Gravitational-Wave Observatory". Phys. Rev. Lett. 110: 181101. arXiv:1302.2188 Freely accessible. Bibcode:2013PhRvL.110r1101G. doi:10.1103/physrevlett.110.181101.

I'll try to explain about what quantitative research is, based on which you can try to guess what are the characteristics of a quant researcher and what kind of work he/she does.via Introduction to Quant Research as presented in SAGE - the natural home for authors, editors and societies. SAGE is a leading international publisher of journals, books, and electronic media for academic, educational, and professional markets : Unexpected ExceptionQuantitative research is essentially explaining phenomenon by collecting numerical data that are analyzed using mathematically based methods.Let’s go through this definition step by step. The first element is explainingphenomena. This is a key element of all research, be it quantitative or qualitative.When we set out to do some research, we are always looking to explain something. In education, this could be questions like ‘why do teachers leave teaching?’, ‘what factors influence pupil achievement?’, and so on.The specificity of quantitative research lies in the next part of the definition.In quantitative research, we collect numerical data. This is closely connectedto the final part of the definition: analysis using mathematically based methods. In order to be able to use mathematically based methods, our data have to be in numerical form. This is not the case for qualitative research. Qualitative data are not necessarily or usually numerical, and therefore cannot be analyzed by using statistics.Therefore, as quantitative research is essentially about collecting numericaldata to explain a particular phenomenon, particular questions seem immediately suited to being answered using quantitative methods. Like the questions which arise at quant firms - "are there any trends that the market is following?", "how does news effect stock prices", and so on.The last part of the definition refers to the use of mathematically basedmethods, in particular statistics, to analyze the data. This is what peopleusually think about when they think of quantitative research, and is often seen as the most important part of quantitative studies. This is a bit of amisconception, as, while using the right data analysis tools obviously mattersa great deal, using the right research design and data collection instrumentsis actually more crucial.I work at WorldQuant currently and I'll explain how the above stuff fits into my work life. People working at other firms may have a different experience. But the the essence is the same.Explaining phenomenon:Quant firms try to understand the market. The better the understanding is, the more money they make out of the markets. This is just another way of saying - how long I keep my job (or how well I'm paid) is directly proportional to how accurately I can predict the market movements.There is no way anyone can understand completely how the markets work. If they say they do, they would be lying. So, I study the factors effecting the market, one by one, all the while hoping that the markets don't change so much that it renders my current understanding of the markets invalid. This has happened before.Example - Crash of 1987 which changed the shape of Implied Volatility curve foreverSo, I adapt to the changes in the markets as fast as I can, make as much money as possible with my current understanding (before the markets themselves adapt), and move on.Data Collection:I'm not allowed to talk about it in public (confidentiality issues). Oops!Suffice it to say that we have a data team which tries to collect as much data about the markets as possible.Mathematics Involved:At WorldQuant I have freedom to use whatever mathematical tools I have in my pocket, to predict the future market movements. How do I do this?1. A hypothesis: Based on previous trends or some kind of logical reasoning that I have developed about the markets, I come up with a hypothesis. Again, I can't give you any kind of ideas here (confidentiality issues). But let's say my prediction is that "In case of the occurrence of an event X, an event Y could be triggered in the stock markets.". This would be my hypothesis.2. Testing: Now this is where your coding/mathematical skills come into the picture. How you would model the event X or the event Y entirely depends on you. And then you perform statistical hypothesis testing. Based on historical data you either accept the hypothesis (in which case traders use your model to predict the markets and make money) or reject the hypothesis. Accepting a hypothesis is always provisional, as new data may emerge that reject it later on.3. While (not_bored_of_the_job || not_earned_enough_money){Repeat 1, 2;}This is my job as of now (I started the job 4-5 months back) and I've tried to explain it as well as I can.

For almost all practical purposes, space is homogeneous and isotropic.Philip Warren AndersonBasic Notions of Condensed Matter Physics ( 1984 )Look, I am going to make a hypothesis :: Frank Wilczek is playing a massive joke on all of us, to see if we've gone collectively crazy. He is one of the great physicists of the last century.Saying the words perpetual motion machine was meant, I think, as a marketing gimmick - that worked, through the noise of Twitter and Wired.The man is a genius. He wears awesome T shirts full of math and physics wisdom and humor.. He also says funny things while also saying quite profound things. And he totally looks like what you would expect from Paul Giamatti's uncle. I made that up. As far as, I know, he is not Paul Giamatti's uncle. However, that does not mean that his papers will not lead to something incredibly awesome. Here is why.Why does spontaneous time symmetry breaking not imply a perptual motion machine?A perpetual motion machine of the first kind in common lore is a device that accomplishes more work than is put into it. A perpetual motion machine of the second kind extracts work from a thermal bath, like Maxwell's demon. Wilczek is referring to the first kind. The limiting case of the second kind was resolved in a paper on the thermodynamics of computation by Charles H. Bennett - IBM Research, where Bennett calculated the entropic cost of the erasure of memory.An analogous phenomena is persistent currents in normal metals, where non-superconducting electrons can flow through resistive metals without dissipation when their wave functions have the appropriate boundary conditions.The Jack Harris Lab at Yale did a beautiful experiment demonstrating the phenomena of persistent currents in aluminum, measuring them on silicon cantilevers through their angular mechanical signatures instead of through their magnetic signatures via SQUIDS.Persistent Currents in Normal Metal RingsDid Jack create a time crystal?Maybe. There is a sense in which something is moving in the experiments and Jack measures that movement, persistently. But, perhaps a more correct statement would be to say that he observed a momentum crystal.Did Jack observe perpetual motion?Well, yes, sort of, but you could not power anything with it, though, because the persistence is in the ground state.None of the above involves perpetual motion, in the sense of a perpetual motion machine, of the first kind, because you cannot extract any work from the systems - they are already in their lowest energy state.Another way to think about conservation of energy and time crystals is to note, analogously, you cannot extract infinite momentum from a space crystal, even though conservation of momentum in a space crystal is not strictly conserved and only conserved under modular arithmetic - that is, mod the inverse of the lattice spacing.That is the summary.----Here is a proposal to investigate the physics in the paper.Does an atom exist with an electronic ground state with non-zero angular momentum that is not rotationally symmetric?We know that atoms exist that have ground states - lowest energy states - that have non-zero angular momentum, in analogy with persistent currents in normal metals.The main difference between Jack's experiment and Wilczek's proposal is that Jack did not break rotational symmetry. As far as we know, persistent currents in normal metals actually depend on not breaking that symmetry, by extending the wavefunction of the free electron in the metal symmetrically around the ring.Think of a circle. Now, rotate the circle a bit. Looks the same. Now, put a dot on the circle. Rotate the circle a bit. Looks different. That dot can be used to track the motion precisely. But, of course, not too precisely, because their exists an uncertainty relation between measuring space and momentum.You could imagine using a different material for the ring that had interactions between the electrons appropriate and strong enough - or even tunable by a magnetic field - to produce a soliton ( the dot), or some rotational symmetry breaking, like a p wave, in the ground state. Then, you could measure the soliton or whatever moving around the ring, persistently or not. That would also be a time crystal, in the sense Wilczek defined it, just the solid state version rather than the cold atom version.The uneven distribution around the ring would create a wobble behavior, like an imbalanced spinning plate, that would certainly show up in the resonance coupling to the cantilever. The problem with localizing anything into a soliton is that you might lose the global boundary conditions necessary for the persistent current. That is the real issue here, mathematically.In the normal metal ring, the electron wave function wraps around the ring and the current is enforced by the requirement that the wavefunction be continuous where the electron meets itself on the other side. The question is whether or not you can have some stable kink as you wrap around the ring while maintaining the persistent boundary conditions.I do not know of any principle that says by creating a soliton, which itself depends on special boundary conditions, you also need to lose the boundary conditions that allow for persistent currents. If it exists, it's probably a theorem in topology, either way.We already know and observe momentum crystals, which yield perpetual or persistent motion, all the time in quantum coherent phenomena like superconductors, superfluids and coherent electron persistent motion in normal metals.If you think of a spatial crystal lattice being a system collapsing around a single spatial vector that defines the lattice, then these persistent flow quantum coherent phenomena all are momentum crystals where the system of particle collapses around a single momentum vector that defines the flow.All the electron pairs that compose a superconductor, for example, flow together with the same momentum. That crystallization in momentum space gives the superconductor the rigidity to flow without dissipation, just as a solid like copper exhibits a certain rigidity.That is, of course, relevant because the quantum mechanical model used by Wilczek is basically the same model used to describe superconductivity, macroscopically.Also interesting to note that the other mathematical models studied in the papers show striking resemble to PT symmetric quantum mechanical models of Carl Bender, if one were to complexity them by adding a complex real space variable in addition to the higher derivatives of momentum.Physics Video Archive COLLOQ_BENDERI think that is an extremely promising way to look at these models, since they are the discrete ( reflection ) symmetry versions of the proposals that want to break continuous time and spatial symmetry separately, but maintain some remaining combined symmetry.In the PT symmetric models, an extremely precise mathematical relationships is developed between systems that have balance gain and loss and systems that do not, related to the PT symmetry itself being broken or unbroken. Such systems have been realized in many experiments, quantum and classical, and have subtle and critical boundary condition relationships.Finally, PT symmetric models are deeply related to the more general CPT symmetry, which is essential for Lorentz invariance. The proposal by Wilczek is strikingly reminiscent at a schematic level of CPT Violation Experiments.By the way, I have a time crystal for you that exhibits perpetual motion and periodicity in time. Light. Photons have a well defined frequency and never rest.Speaking of light, note that though Wilczek was inspired by the Lorentz symmetry between time and space to look for time crystals, none of his models are relativistic.They cannot be, in the manner he is investigating time crystals, because all the models are non-relativistic with non-linear dispersion relations.---- FUTURE RADIO EDIT :: Almost everything below that is not referenced is pure speculation. Read for enjoyment, not for physical accuracy. All lot above this line is speculative. I am going to continue to edit and learn about this area, because it is a fascinating area of physics. I might do that in a blog, and get more detailed with the mathematics. The answer is redundant in some places and certainly incorrect or poorly written in others, but I wanted to get it up so you could enjoy and learn from pieces of it; and hopefully, explore some of the questions yourself with more powerful tools and analogies.You should also check out Carver Mead's book Collective Electrodynamics: Quantum Foundations of Electromagnetism: Carver A. Mead: 9780262133784: Amazon.com: Books because it takes as its logical foundation the following coherent quantum phenomena.1911 Superconductivity1933 Persistent Current in Superconducting Ring1954 Maser1960 Atomic Laser1961 Quantized Flux in Superconducting Ring1962 Semiconductor Laser1980 Integer Quantum Hall Effect1981 Fractional Quantum Hall Effect1995 Bose-Einstein Condensate2009 Persistent Currents in Normal Metal Rings----Four dimensional crystallography is a different path to investigate the idea ::Ordinary crystallography deals with regular, discrete, static arrangements in space. Of course, dynamic considerations— and thus the additional dimension of time—must be introduced when one studies the origin of crystals (since they are emergent structures) and their physical properties such as conductivity and compressibility. The space and time of the dynamics in which the crystal is embedded are assumed to be those of ordinary continuous mechanics. In this paper, we take as the starting point a spacetime crystal, that is, the spacetime structure underlying a discrete and regular dynamics. A dynamics of this kind can be viewed as a “crystalline computer.” After considering transformations that leave this structure invariant, we turn to the possible states of this crystal, that is, the discrete spacetime histories that can take place in it and how they transform under different crystal transformations. This introduction to spacetime crystallography provides the rationale for making certain definitions and addressing specific issues; presents the novel features of this approach to crystallography by analogy and by contrast with conventional crystallography; and raises issues that have no counterpart there.Tommaso ToffoliA pedestrian’s introduction to spacetime crystallography ( 2004 )Lets use the same analogy that Wilczek used to come up with the idea of time crystals by looking at spatial crystals.Here's the key analogical observation to make ::Solids spontaneously break the continuous symmetry of space down to periodic discrete symmetry, yet we cannot extract infinite momentum from them, even though momentum is not strictly conserved in the solid.Noether's theorem tells us that in mechanical and quantum mechanical systems describable by a Lagrangian, any symmetry transformation that leaves the Lagrangian invariant leads to a conservation law.Continuous time translation symmetry yields conservation of energy.Continuous space translation symmetry yield conservation of momentum.Continuous rotation translation symmetry yields conservation of energy.Sometimes, however, that symmetry is broken naturally, as in a solid state crystal.As Wilczek says, "When a physical solution of a set of equations displays less symmetry than the equations themselves, we say the symmetry is spontaneously broken by that solution."Similarly, a time crystal does not imply that we can extract infinite energy from the system even if the system spontaneously breaks the continuous symmetry of time down to periodic discrete symmetry.As Wilczek says, " ... one interesting case, that will concern us here, is of the lowest energy solutions of a time-independent,conservative, classical dynamical system. If such a solution exhibits motion, we will have broken time translation symmetry spontaneously ... Speaking broadly, what we’re looking for seems perilously close to perpetual motion."[ emphasis mine ]A crystal lattice formed by atoms in a solid is a great example of spontaneous symmetry breaking. The fundamental equations describing the dynamics of the nuclei and electrons of the atoms have continuous time, space and rotational symmetry. However, at low enough average energy ( related to temperature ), elemental atoms may form solutions to these equations that do not exhibit that full symmetry. Specifically, a solid state lattice exhibits discrete rather than continuous translation symmetry such that conversation of momentum is no longer strictly conserved, but rather only conserved modulo a specific value related to the inverse of the lattice spacing. For example ...At 2,835 degrees Kelvin, Copper atoms transition from a gas state to a liquid state. At 1,357.77 K, copper atoms will solidify naturally into a face centered cubic lattice crystal structure of the cubic crystal system.The type of lattice a particular atom will solidify into is determined by its electronic structure; however, the group theory of crystallography mandates that only, starting with the 14 Bravais lattice and keeping one point of the lattice fixed, one obtains the 32 Point groups. If the latter are combined with translations, one obtains the 230 Space groups (ascertained in 1891).Image :: The Bauhinia blakeana flower on the Hong Kong flag has C5 symmetry; the star on each petal has D5 symmetry. A beautiful book on symmetry is The Symmetries of Things by the great mathematician John Horton Conway.What happens in a solid is that [ a ] the symmetry breaking results in a "rigidity" of the system in space and [ b ] the dynamics particles flowing through that solid - electrons or phonons, for example - only conserve momenta under modular arithmetic. What do I mean by that?The easiest way to see what is happening to conservation of momentum in a crystal that break spontaneously breaks spatial symmetry is to look at a Bloch wave, which simply describes the wave function of a particle such as an electron in any periodic potential, like that found in a solid state crystal.First, lets temporarily remove the lattice atoms completely and just analyze free space. Say you took an electron in free space and applied an electric field. The electron would accelerate and gain momentum and energy. Note that you are not creating a perpetual motion machine. The electric field comes from somewhere and you had to do work to create it.If you remove the electric field at some point, the electron will continue to move with the same momentum and energy for eternity, precisely because free space is homogeneous and isotropic. That means, if you shift free space a little in time or space, or rotate free space slightly, nothing changes about free space. It's like if you moved an infinite line a little to the left or right. It looks exactly the same. Well, a particle moving along a line is exactly the same as a line moving along a particle. Momentum conservation reduces to tautology if you think about it correctly. If something is symmetric, it does not change. If something is conserved, it does not change.By Noether's Theorem, free space being homogenous and isotropic means all physical systems conserve momentum, energy and angular momentum. Just because the particle moves forever - perpetually - after you've removed the electric field does not make it a perpetual motion machine, either. It's actually just Newton's first law of motion, dressed up in a little more sophistication.Now, lets put the face centered cubic arrangement of atoms of copper, or whatever, and assume they fill all of the universe. A giant block of solid copper. Now, apply an electric field. Remember again that we had to create the electric field, so we are putting work into the system. For those in the know, I am about to describe Bloch oscillations, which clearly demonstrate the modular arithmetic of momenta in solid state crystals.As you apply an electric field on the electron in the copper lattice, the momentum of the electron increases. However, the crystal lattice structure puts an upper limit on the momenta that is the inverse of the lattice spacing. Lets say in appropriate units that upper limit is 12.After applying the extremely weak electric field for 1 hour, the momentum of the electron is now 1; and so on. Now imagine the clock you are using to measure time. When you reach 12, you start back again at zero. That's modular arithmetic. And that's what happens to momentum in a solid. Actually, a better way to think of the clock is starting at minus 6 at the bottom, zero at the top and plus six approaching the bottom clockwise. The momentum of a particle in a solid literally goes from plus six to minus six instantly due to the symmetry breaking of the lattice. That is because momentum is only conserved mod 12. So, plus and minus six are equivalent.However, there is absolutely no way to exploit that momentum jump to extract infinite momentum outside the solid because from the perspective of the lattice plus and minus 6 are smoothly connected in momentum space, which takes the shape of a 3-torus for a cubic lattice.( By the way, a circle is a 1-torus and a torus is a 2-torus. )That is, you cannot simply apply an electron field to silicon and copper and extract infinite momentum in a perpetual motion machine. Intel and Samsung would have a field day with that, if you could, and your Apple iPhone would power your city. What you can do is interpret the seemingly large momentum shift as an interference scattering effect of the electron wave function off the periodic lattice, recalling that on the atomic scale, electron dynamics behave according the quantum mechanical wave equations. And, of course, the lattice nuclei are much much heavier than the electrons, so the electrons hitting the lattice is like a ball bouncing off a wall.Modular arithmetic is extremely useful and powerful in number theory. For me, it's fascinating to see it arise in quantum mechanics as a result of discrete symmetry in Bloch waves.Now, lets play some games here.Ironically, the relativistic notion of mixing time and space through Lorentz transformation was used as a motivation for the work. However, the theory of special relativity requires a linear relationship between energy and momentum. That allows linear transformations between energy and momentum to occur and allows energy and momentum to be combined into a single, highly compact energy-momentum four vector.At low energy, you can expand out any relativistic equation with the speed of light in the denominator of any terms and extract non-relativistic physics by ignoring those terms, since their effect will be very small. What you end up with is a relationships between energy and momentum that is parabolic rather than linear, if no interactions between particles or other objects in the theory add any further complexity.The papers take as a starting point a relationship between energy and momentum - a dispersion relation - that is both non-linear, as noted, and exhibits a cusp singularity. The dispersion relation looks a swallow's tail, like the shape of the swallowtail butterfly in the images above at the beginning of the answer. The curve shows a crossing where the body of the butterfly rests.They have a parabolic term and a quartic term.Guess what the dispersion relation of Bloch waves are?The cosine function. The cosine function is non-linear and periodic.Guess what the first two terms Taylor series expansion of a cosine function yields up to an overall constant?A parabolic with a negative coefficient and a quartic term with a positive coefficient. The same form as in Wiczek's papers.Guess how you get from electric field to magnetic fields in electromagnetism?Lorentz transformations. The basis of the spacetime physics that inspired Wilczek to write his papers. And note that the primary example used in his papers is a particle oscillating around a circular lattice in a weak magnetic field.I am playing with the idea that Wilczek "discovered" the "time version" of Bloch oscillations. And, just as Bloch waves in a solid ( aka a "space crystal" ) do not violate conservation of momentum in a manner that enables a perpetual motion machine, Wilczek waves in a "time crystal" do not violate conservation of energy in a manner that enables a perpetual motion machine.I do not even think it's appropriate to call them the time version, in the experiment being proposed in cold atoms. The appropriate name for the experiment being proposed would be magnetic Bloch oscillations.A space-time crystal actually implies that the lattice atoms disappear for a well-defined time step; just as in a space crystal, matter disappears for a well defined spatial step called the lattice spacing in a well defined crystallographic arrangement. Have we found a system that breaks continuous time translation symmetry such that matter blinks in and out of existence periodically?I do not think we have. That would be a true time crystal, in my mind.That system would require a quantum field that oscillates in time between a ground state with a mass gap and a ground state that is gapless.Such a system would also not allow you to build a perpetual motion machine, even though it violates conservation of matter and energy.That is, you could not extract energy by coherently scattering from a time crystal just as you cannot extract momentum by coherent scattering off a space crystal. Furthermore, given the analogy with Bloch oscillations, which is nearly mathematically equivalent to the example used by Wilczek, a system that exhibits periodic motion in the ground state is not actually that surprising.Actually, it turns out that what Wilczek is saying is even less surprising when you think about superconductivity in the right way. Superconductors are essentially crystals in momentum space. Just as atoms condense to a specific spatial lattice vector in solids that are "rigid," electron pairs condense to a specific momentum lattice vector in superconductors, yielding persistent currents that are, in their own way, "rigid."That observation is, in fact, how London developed his London equations of superconductors. A superconducting condensate exhibits a persistent current because the condensate collapses to a momentum vector, which implies motion. That motion may be angular, around a ring and periodic with a magnetic field.So, not only is Wilczek simply describing the magnetic version of Bloch oscillations in his papers; he is also simply describing the persistent currents of superconductors. The requirement he posits to break a cylindrical spatial symmetry of a persistent current condensate in order to then break time symmetry by making the motion in the ground state more salient does not actually make any difference.In non relativistic quantum mechanics, we have real space and momentum space, which are simply related by Fourier transforms. The reason you cannot isolate the location of a superconductor condensate is because the Fourier transform of a single momentum vector is completely and evenly spread out in real space. Conversely, in a solid state lattice, the momentum distribution is relatively spread out.If you want to create a time crystal in the sense Wilczek is after, you have to be in the relativistic regime. However, to be in the relativistic regime, you need a linear dispersion relation. But, the only way that you can create a time crystal in the way Wilczek wants to is by being in a highly non-linear, non-relativistic regime.What would be interesting is if someone could describe and experimentally realize a state that naturally interpolated back and forth between a solid ground state, collapsed on a spatial vector, and a superconducting ground state, collapsed on a momentum vector, in a closed, non-relativistic quantum mechanical system that was both naturally conservative and time independent.You could then watch the momentum and space vectors of the state collapses and expand, periodically in time.It actually turns out that someone has done that, in a sense,Greiner - Mott Insulator to Superfluid transitionbut that transition was still driven rather than occurring naturally in a conservative, time independent system.Perpetual motion machines are out. Time crystals have not been created. What specifically is going on in the time crystal papers that is interesting?The basic mathematical problem that arises in Wilczek's papers is that the energy is multivalued in the momentum. That, actually, is a fascinating area of physics. There is, I should mention, an entire book on multivalued quantum fields ::Multivalued Fields: In Condensed Matter, Electromagnetism, and Gravitation: Hagen Kleinert: 9789812791719: Amazon.com: Booksbut, I have not yet read it. I've been meaning to for a while. Any book with a Riemann surface on the cover with detailed mathematical descriptions of superconductors and gravity in the interior should be read by people like me.So, I will, now, within the decade.In fact, the quantum mechanical equation to be solved is the non-linear, non-relativistic Schrödinger equation that is used in Ginzburg–Landau theory to describe the Cooper pair condensate in superconductors in a single wavefunction. The non-linearity of the theory results from the emergent physics of superconductivity and leads to topological objects like flux vortices, as discovered by Alexei Alexeyevich Abrikosov. The theory includes a momentum term that is parabolic and a momentum term that is quartic when related to energy. The mathematical qualities of the coefficients of these terms matter greatly.The non-linear theory is emergent because it evolves via a process of renormalization from a completely linear quantum mechanical theory of electrons interacting with each other via repulsive Coloumb forces and with phonons - excitations of the underlying solid state lattice. At low enough temperatures, the interactions between the electrons and the phonons effectively switch the interactions between the electrons to be attractive rather than repulsive. The electrons pair up to form bound states that are bosons, the electromagnetic field mediating the interaction between electrons attains a mass gap and the boson condense into a collective state describable by the theory mentioned above.Topologically, Wilczek's swallowtail curve looks like the curve on the cover of the book Elliptic Tales: Avner Ash, Robert Gross: Amazon.com: Kindle Store. It's very similar to the curves found in Jack Huizenga's answer ::Given two low-degree polynomials defined on the integers, how can one find the integers which are in the range of both polynomials?In that answer, Jack gives a procedure for analyzing the intersection of two curves :: complexify, projectify ( to infinity and beyond), and normalize ( that is, smooth over the singularities).You might immediately object to apply anything like that procedure to analyzing a Hamiltonian system. If you are a physicist you know that the Hamiltonian of a quantum system must be Hermitian - that is, both real and probability conserving.However, as Carl Bender shows us in [quant-ph/9809072] PT-Symmetric Quantum Mechanics, we can relax that mathematical condition and replace it with a physical condition of PT symmetry and find some interesting results. The PT symmetry physical condition relaxes the constraint that the Hamiltonian is real; for example,[math] H = p^2 + i x^3 [/math]is PT symmetric, but obviously not Hermitian since it is complex. That is a hugely powerful constraint to relax and opens up an entire new world of mathematics to explore. You can actually see the mathematics that Bender is revealing to us in any power of the momentum. That is, he already solved Wilczek's problem, by the process - complexify, projectify, normalize. That work started with something known as the Yang Lee edge singularity.I do not know what that is, yet.Why do I care?Wilczek's class on topological quantum physics at MIT was by far my favorite course while I was in graduate school at Harvard. I wrote a paper on trying to extend Alexei Kitaev's K-theory classification in [0901.2686] Periodic table for topological insulators and superconductors to strongly interacting topological condensed matter systems using the success of the Seiberg–Witten invariants that survive strong coupling in supersymmetric QCD as a guide, which can be embedded in string theory [hep-th/9611190] Introduction to Seiberg-Witten Theory and its Stringy Origin.What Seiberg Witten theory describes is the electromagnetic dual of a superconductor. In fact, it describes a condensation of magnetic monopoles that allow electric flux tubes to form as a simplified model of QCD, as opposed to the condensation of electron ( pairs ) that allow magnetic flux tubes to form in a real superconductor. The face they used complex curve theory to solve their equations always fascinated me. Why?I wanted to somehow use the idea of a coobordism to track how the structure of the theory evolved under the tuning of the interaction strength; and, to show that certain invariant quantities survived that the tuning of the interaction strength in the topological electronic systems. The topological invariants would tell you if two different topological phases were connected through a strongly interacting regime, which would otherwise be hidden you by traditional analytic calculations involving an expansion in a small parameter. Seiberg-Witten theory is one of the few strongly interacting theories that is completely soluble, due to the strong supersymmetry in the theory.My paper completely failed to do that. He still gave me an "A" in the class, though everything I said was complete nonsense. I think he is returning the favor to the rest of us now. Kitaev later wrote a paper accomplishing what I had hoped to accomplish in [0904.2197] The effects of interactions on the topological classification of free fermion systems. Actually, that paper only identified a problem in the previous classification with small interactions.But, the problem of understanding topological phases still remains largely a mystery, though recent progress was made by Xiao-Gang Wen, now at the Perimeter Institute, in his paper [1106.4772] Symmetry protected topological orders and the group cohomology of their symmetry group. That's important because, from everything we know about M / string theory and topological quantum field theory ( which by the way has no dynamics and a Hamiltonian of zero ) understanding black holes and quantum gravity requires a deep understanding of topological phases.Wilczek's analysis showing up in the news gave me a different idea, one related to my M theory ideas here ::What do theoretical physicists think of Mark Morales' answer about M-theory?Whatever the case, I cannot wait to see someone create a Calabi Yau manifold in their laboratory hologram.Postscript :: If you followed my link above, you'll see that I proposed a general shift in mathematical approach to M theory. Along those lines, I found a good introduction to Elliptic Curves and Cryptography from Josh Alman ::Good introduction to elliptic curves?