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$10M worth of scientific kit gets written off

I say we tell the worst math jokes we know. Here is one I heard a couple of weeks ago(Game Theory joke). A police officer is called to a scene in which a burgler has just stolen some jeweltry from a home. The officer immediately, upon seeing the burgler, pulls out his gun and threatens to shoot. The burgler darts out and runs off into the alley. The police officer chases after him but comes to a three way fork, each possible path with its own advantages and disadvatanges. In order to decide which alley to run down, the officer pulls out a piece of paper and begins to attempt to solve the game matrix for the problem (Using the Shapley-Snow procedure of course....). Seconds later, the officer's partner runs out and yells, "WHAT THE HECK ARE YOU DOING?!?!?! HE'S GETTING AWAY" The officer looks up with a very confused look and says, "What, I am trying to solve the game, doesn't he have to do that too?" I have another bad one I will post later.

Can one make a constructive proof proving that there exists some statement that cannot be proven constructively, but that only a proof-by-contradiction can establish such a proof? I am assuming it is likely that such a proof would involve some diagonalization method of pairing the qualities in question? Because of course one can make a proof-by-contradiction that is still accepted in that it is still "constructive".

This is a forum devoted to recommendations of various science or math sites that our members may enjoy. I would be interested to see what my fellow teammates recommend, as I have enjoyed such references in the past. Here are a few off the top of my head that I can think of (not in any meaningful order of importance): xkcd.com phdcomics.com various youtube channels galaxyzoo.org wikileaks.org (see mirror sites at present) sciam.com defense.janes.com And some of your favorite sites are?

Thought question for the atheists: is there such a thing as ethics and moral standards? Are they decided by society, or is there a natural law that says what is right and wrong? Or is there no right and wrong?

My chess game is improving and so the 2500 chess engine that my membership gives is becoming less useful. Is there a chess engine for free that can outperform the one of the level of 2500? Which chess engine would you recommend as the best one from the list of free downloads that this site has?

I have created this topic for discussing anything that you can't be bothered to create a topic for, rather than use group notes.

Hi! Does anybody know if Fritz 12 can be used for detailed post-game analysis and if yes, how can I submit the game for it? If Fritz can't do this what program should I download to analyze my finished games in detail?I would like something that is similar to the chess.com engine that tells the quality of each move and maybe gives variations for critical moves and ,of course, has around 3000 ELO. Don't get me wrong...I'm not interested in cheating...or is this cheating?

Section IX -- Earth's Rotation, Magnetic Field and Volcanoes About 2 billion years ago, Earth was composed of only crust and a liquid molten core. It revolved silently around the sun, minding its own business. Then, the fairies came. They spotted Earth and colonized it. They landed at the present day north pole, 7.5 degrees horizontal of Earth's vertical axis, in order to get sunlight, but still remain fairly cool. As the Earh didn't rotate, the ground near the mid-latitudes and equator was very hot. Now, the fairies, having found an ideal place to live, constructed a giant castle, covering most of the inhabitable region. Fairies were to stay inside the castle at all times, as going outside meant a risk of burning or freezing. They were happy and went about blessing particles using their magic, and eventually, Earth gained a magnetic field. Soon after this though, the fairies began overpopulating. The castle was too small and shelters had to be built. They started digging tunnels to live in below the castle. Still, they multiplied and eventually, the Earth's crust below the castle was fulled with burrows. Then, they ran into the problem of the molten core. With quick thinking, they decided to spin the core and therefore, lower the level to allow for more space. As they kept having to spin it faster, the level lowered, and there was more living space. Also, at this time, because of conservation of momentum, the Earth began spinning in the opposite direction. Needless to say, the fairies kept multiplying and continued to spin faster. Eventually though, their tunnels became unstable and couldn't support the weight of their castle. The castle fell through the tunnels, taking many fairies with it, collecting them into a roughly spherical shape, until it came to a stop at Earth's center. The molten core covered them, but as the castle was constructed out of cool material, it was able to stay solid. Thus, the formation of the solid inner core of Earth. Additionally, the fall of the castle and fairies caused some of the liquid core to be displaced, equal to the volume. The liquid then seeped upwards into the crust and filled most of the holes while partially melting some materials. It rose very high and almost overflowed, but luckily it stopped at a certain point. Up to here is now known as Earth's mantle. Now, the majority of speed bumps hit somewhere inside the castle where the fairy survivors are. Some are knocked out each time this happens (and the fairies re-multiply using the new space, as the castle protects them from the heat), and when they leave the castle, more of the outer core is displaced. This is transferred upwards and raises the mantle's level in a few places. Sometimes, there exists enough pressure for the mantle to rise up to Earth's surface. The crust moves upwards like a mountain, but as it is not very elastic, a hole forms in the middle. This is known as a volcano. Occasionally, a fairy manages to escape the volcano without getting burnt. It will then try to relocate its castle's original location. It arrives near the north pole and emits light waves to signal to other fairies that home is here. When one fairy does this, nothing is seen on the larger scale, but when a large population does this, the effects are easily detected. We call this the Aurora Borealis. When an entire cluster of fairies escape, they take a portion of the molten mantle with them. Depending on how their trip went, some of their wings may be singed. If this is the case, they slowly spill out of it, as seen in Hawaiian eruptions. Other times, their wings are fully working, and the go out quickly, spreading and flying in arcs to shake remaining magma off of each other, as seen in a Strombolian eruption. Or if the escape, but their wings have caught fire, smoke is seen Pelean eruption.

Section X -- Socks and Precipitation Every once in a while, an event occurs where water magically falls from the sky. Although this sounds very far-fetched, it is actually very common. Scientists were able to determine where the water comes from in the sky. They noticed the white, fluffy, thingies in the sky contained water vapor and decided to call them clouds. Now the fact that water can just be up there and not fall until some other time is extremely mind-blowing, but eventually the scientists hypothesized the method to which the water can move up. This is known as the Evaporation Theory. It says that water molecules hit each other and knock each other into the air. Now everyone who has been in the plastic ball pit knows that that just doesn't work. The only way for them to disappear is if someone steals them. But who would dare to steal water molecules if they're already so common? It is the same monster responsible for the disappearance of socks from washing machines worldwide. It is known only as, The Invisible Sock Monster *dramatic chord*.Just like demons, the ISM is too small to observe, but only its actions may be seen. It is easily noticed on a week-to-week basis when socks somehow magically disappear. The exact reason to which it steals socks and water is unknown, but it appears that groups of them work together to mix socks and water to create the fluffy things in the sky they call heaven. Of course, everyone wants their own piece of heaven, so other groups will try to take the socks and make their own clouds. Socks are, after all, a scare resource; take too many and humans will get suspicious. As it is the socks that hold water suspended in the sky like a parachute, stealing them causes the water to fall. Because bigger clouds are more difficult to manage, it is easier to steal socks from bigger clouds, so it is more likely for water to fall when there are more clouds. Apparently, this is know to many as rain. Now any time someone tries to steal they run the risk of being caught. If one tribe catches another in the act of stealing, a great battle ensues. Socks are whisked every-which-way, sweeping water with them. The water clumps into a ball and freezes as the ISM's touch it, but melts as well when the socks hit it. During this time, it also collects more and more water. Eventually, it is too heavy even for socks to hold up, and it falls down. This is called hail. Alternatively, during the battle, some sock pieces are left forgotten. They gather water in a pretty hexagonal shape and freeze as they fall provided it is cold enough below. This makes it gain a fractal pattern, and it is called snow. Of course, no two sock strands are exactly alike, meaning no two snowflakes are exactly alike.As the precipitation precipitates, people may try to eat or drink pieces of it. Why then, don't they eat sock pieces as well and choke? ISM's are nearly everywhere, and are very thorough in making sure every sock piece is collected. Halfway down from a raindrop's fall, the ISM's take notice and grab the sock piece inside, leaving the rest of the water to fall to the ground. Of course, this water doesn't stay grounded for long, as the greed of the ISM's lead them back to take the water molecules back into the air and continue the cycle of precipitation. And alas, the socks lost to the ISM's in washing machines are very unlikely to be recovered. Even airplanes flying through the clouds are too slow to reclaim the lost socks from the devious ISM's. Soon, all socks will disappear off the face of the Earth, and clouds will cover the atmosphere and rain will be eternal. Crops will die and populations will starve. There is but one way to prevent this and that is to use aerosols and take out the ozone layer in select parts of the world covered by the evil clouds. The incoming UV radiation will destroy the sock molecules and end the lives of the clouds. Of course, once the cloud disappears, there is a risk that those previously living under the cloud get skin cancers and die out, but some risks are necessary to take in order to further the survival of the human race. The effects of the increasing amount of socks in our atmosphere can already be felt in the spinny things over water and land. An increasing amount of socks mean the ISMs can over-populate, and the increasing volcanoes mean there are more fairies in the atmosphere as well. The ISM's sometimes view the fairies as hostile and attack them. Fairies can't really fight back, so as they're shot down out of the sky, they release electrical energy from within. It trails downwards until it hits the ground. If there are a significant amount of zapped fairies, then light is emitted as they fall, and they make a loud cracking sound as they hit the ground. If they fall on a person, they may be electrocuted, and even falling onto the ground may cause power surges. This is far from the worst that could happen though. Eventually, the fairies realize they are being attacked. They try to get away, but due to the hidden magnetism, they are forced to stay in clusters. Thus, they start to spin in a circle, and catch the ISM's and socks with them. The clouds spin and fall. When they reach the ground, they are spinning really, really, fast. If this happens over water, there is a chance of an enormously high amount of ISM's and clouds, and a hurricane is a possibility. If ISM's overpopulate, hurricanes will get bigger and bigger, and eventually consume the Earth. A hurricane the size of the Great Red Spot of Jupiter will also destroy all humanity. Between eternal rain, hyper power surges, and super hurricanes, the ISM's and fairies are forces to be reckoned with, and pose nearly as big a threat to humans as the aliens do. No specific doomsday event is set here, as the effects are gradually changing, depending on how many socks are in the washing machines at a given time. There is but one way to stop this from happening and that is to hand-wash all socks and use a clothesline to dry them. This will be mandatory anyway soon, as the power surges will devastate all washing machines functioning on electricity. The ISM's will be too intimidated to steal socks from the open, and the eternal rain is temporarily delayed.

Well actually sort of engineering problems. I was thinking about the fact that in a billion years, life on Earth will become impossible due to the increase in the solar constant (the orbit will grow but not enough). Then I suddenly thought, why not move the Earth? We have plenty of time, but do we have enough energy? The two sources of energy I considered were sunlight incident on the Earth, and fusion of hydrogen from the oceans. Is either one or both of these adequate to provide an amount of energy similar to the Earth's kinetic energy? What fraction of the ocean is equivalent to a year of sunlight? [You may ignore efficiency factors, which should affect answers by much less than an order of magnitude. All numbers needed should be found from general Internet sources].

There has been a change in the way everyone can now view all their current vote chess games. Staff here at chess.com have been working hard on this and after listening to everyones suggestions they have created this page which can be found by placing your cursor over "my home" and selecting "my vote chess". You can also access it by clicking : http://www.chess.com/votechess/myhome.html

Following on from the thread concerning Godel's first incompleteness theorem, looking at the proof made me think about how the technique used to create a self-referential statement could be used to implement the classical "Cretan liar's paradox". [Incidentally, I suspect Paul misunderstood this 4th century work when he misrepresented it in Titus 1:12 ""One of themselves, even a prophet of their own, said, the Cretans are always liars, evil beasts, slow bellies." ] Ironically, I would guess that Godel probably did this first and then later used an adaptation of the idea to prove the first incompleteness theorem. Using some of the machinery of the incompleteness proof, it is easy to create a statement F(n) that says: "statement n is false" where n is the unique natural number for another statement. We can add a free variable to this statement to give a statement F(x, y) s.t. if y is substituted for x, it says "statement y is false". If the Godel number of F(x,y) is p, the statement F(p, p) is a self-referential statement saying "this statement is false". So is the statement F(p,p) true or false? It is easy to see that if it is true then it is false, but if it is false then it is true, so if it has either value the theory is inconsistent. This would be bad news as this would mean number theory and the whole of mathematics would be inconsistent. The solution is that the statement simply has no truth value - it is indeterminate. There is certainly no proof within the theory that it is true and no proof that it is false (otherwise the system would be inconsistent). Strangely, it can be proved that since the statement is indeterminate, we can formally extend the system to another (relatively consistent) system where this statement is chosen to be either true or false as an axiom (like with the axiom of choice or the continuum hypothesis), but I believe the statement could not be interpreted in the same way in this artificial system. To me this example puts the law of the excluded middle on very shaky ground, as it means that in any system powerful enough to deal with number theory, there are statements that are indeterminate within the theory, but also have no valid truth value that makes sense (which seems more awkward than statements which are true but unprovable). The solution to this discomfort may lie in constructivism, where self-reference may be avoided, in the same way as in axiomatic set theory, sets may never be members of themselves, or members of sets that are members of the original set, or so on. Maybe even more safe is constructive set theory. Constructivism may avoid awkward self-reference (or then again, it may not).

1. How can one prove that a Godel sentence can or cannot be found in principle by us? Despite reading TENM, Shadows, Beyond the Doubting of a Shadow,some of the FOM archives, and talking to a few people, my knowledge is running dry. I would be most pleased if someone here could outline a positive or negative proof of such a premise. 2. We are on the verge of having 200 members! What would you like the future of this group to be? What features would you like to increase or decrease?

I hope my deduction is correct.If anybody wants to learn more about trigonometric functions go here: http://en.wikipedia.org/wiki/Trigonometric_functions

Hi! Does anybody know where can I download an opening database for Chessbase Light 2009?

A rather wild offshoot of the Pogonina versus chess.com post-game discussion made me think of the topic of the role of gender in religion. An interesting issue is the tremendously sexist attitude of the main religious texts but, leaving that for another discussion, I have a simple metaphysical question. I will introduce my question with some context. Anyone who doesn't believe in biology can skip the next bit and read the question (in bold type below). On Earth we define male and female by the roles they play. Females have haploid eggs, males provide haploid sperm/pollen or whatever, and the result is a hybrid diploid entity, which develops into a new organism, (I'll ignore where this development takes place, as it varies such a lot). In some organisms the distinction is functionally rather flimsy - eg fish laying eggs and adding sperm in water, where the main functional difference is merely that the eggs are the more substantial object, with some food stored. The key persistent distinction seems to be that the male provides nothing but half the genes, the rest comes from the female. Interestingly, the origin of this bifurcation is believed to be a sort of symbiosis between a virus like organism and a bacterium. Most people do not realise how fundamental such interspecies interactions have been to higher organisms, with the very mitochondria that power our cells being still in a real sense separate organisms. These organisms have been in symbiosis with us and our ancestors for aeons, getting more and more dependent and integrated. Also some of our DNA originates from viruses and bacteria from interactions in the past, and of course our guts contain kilograms (yes, kilograms) of bacteria without which we would be very sickly indeed. Back to the subject in question. Question: How do you define the gender of a spiritual creature (such as a deity). "Define" is a key word in the above question.I need something definite (like the definitions for physical organisms). I will disclose that my personal beliefs are simply that in an age where males ruled and women were chattels, the men who told people what to believe found it natural to assume their deity was male, and never even considered what it meant. This could be hilarious if people have to resort to attributes of personality, but what else is there?

Let us attempt to test the existence of a god as a scientific hypothesis (independently of historical falsifiability). 1) Examine the attributes of the desired god. 2) Look for any possible inconsistency paradoxes in their natures. 3) For such reductio proofs that require physical premises, prove logically that there can be no other way to reconcile consistency without disagreeing with the premise. 4) If the god in question is to remain consistent certain physical implications by the premise must be true. A common example would be the nature of time as relating to an immutable being. 5) If it has been rigorously empirically proved that time, space, or another such physical consequence does not agree with the conclusion from the nature of that god, it is very unlikely that such a god exists. If such a physical testable hypothesis based on the nature of a god it is very likely that that god exists (assuming no logical inconsistencies in such a god's nature). Note: 3 is a very hard step and the most crucial step, all else is easy except possible disagreement over rigorous in 5 (a possible theistic argument here cannot be ad hoc, however).

Does anyone here know or have a referance for a constructive proof that sqrt2 is irrational?

The last discussion this topic, Razor and the Multiverse, yielded: a) laughter and/or useless comments, b) insufficient discusssion, and c) whether or not we should take Occams's Razor so seriously. This forum then, is designed to discuss proof for or against cosmological darwinism plus the issue of testability. Now, Lee Smolin is largely responsable for putting forward such a notion. Let us examine his statements and arguments (as found on http://www.universaldarwinism.com/documents/Scientific%20Alternatives%20to%20the%20Anthropic%20Principle.pdf): 1. Testability: As opposed to anthropic answers which may be deemed unsatisfactory (not here to debate about this point too strongly), according to Lee Smolin this theory has advantages in this respect alone: "It is important to emphasize that the process of natural selection is very different from a random sprinkling of universes on the parameter space P. This would produce only auniform distribution random(p). To achieve a distribution peaked around the local maxima of a fitness function requires the two conditions specified. The change in each generation must be small so that the distribution can ‘climb the hills” in F(p) rather than jumparound randomly, and so it can stay in the small volumes of P where F(p) is large, and not diffuse away. This requires many steps to reach local maxima from random starts, which implies that long chains of descendents are needed....The hypothesis that the parameters p change, on average by small random amounts, should be ultimately grounded in fundamental physics. We note that this is compatible with string theory, in the sense that there are a great many string vacua, which likely populate the space of low energy parameters well. It is plausible that when a region of the universe is squeezed to Planck densities and heated to Planck temperatures, phase transitions may occur leading to a transition from one string vacua to another. But there have so far been no detailed studies of these processes which would check the hypothesis that the change in each generation is small. One study of a bouncing cosmology, in quantum gravity, also lends support to the hypothesis that the parameters change in each bounce[48]." As for proof: Lee Smolin explains in this article how black hole birth as predicted by his outlined theory supports known evidence for current data concerning low energy physics: "The study of conditions 1) to 4) leads to the conclusion that the number of black holes produced in galaxies will be decreased by any of the following changes in the low energy parameters: • A reversal of the sign of m = mneutron − mproton . • A small increase in m (compared to mneutron will destabilize helium and carbon. • An increase in melectron of order melectron itself, will destabilize helium and carbon. • An increase in mneutrino of order melectron itself, will destabilize helium and carbon. • A small increase in will destabilize all nuclei. • A small decrease in strong , the strong coupling constant, will destabilize all nuclei. • An increase or decrease in GFermi of order unity will decrease the energy output of supernovas. One sign will lead to a universe dominated by helium. Thus, the hypothesis of cosmological natural selection explains the values of all the parameters that determine low energy physics and chemistry: the masses of the proton, neutron, electron and neutrino and the strengths of the strong, weak and electromagnetic interactions. However, explanation is different from prediction. These cannot be considered independent predictions of the theory, because the existence of carbon and oxygen, plus long lived stars, are also conditions of our own existence. Hence, selection effects prevent us from claiming these as unique predictions of the theory of cosmological natural selection." Criticisms answered: "Several arguments were made that S is in fact contradicted by present observation [49, 50, 51]. These were found to depend either on confusions about the hypothesis itself or on too simple assumptions about star formation." Lee Smolin then goes on to put forth other objections which he answers which build the case of falsifiability along the way. Another link: http://en.wikipedia.org/wiki/Cosmological_natural_selection#Fecund_universes describing two other criticisms to Smolin's ideas: " In a critical review of The Life of the Cosmos, the astrophysicist Joe Silk suggested that our universe falls short by about four orders of magnitude of being maximal for the production of black holes.[5] In his book Questions of Truth, the particle physicist John Polkinghorne has another difficulty with Smolin's thesis, in that one cannot impose the consistent multiversal time which would be required to make the evolutionary dynamics work, since otherwise short-lived universes with few descendants would dominate long-lived universes with many [sic]" I do hoever think that with such criticisms, being properly met or not, we can validly say that cosmological darwinism is a scientific theory and testable.