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Hi all, I'm supposed to write a paper about some issue in the social sciences. I wanted to do something with game theory. I was thinking that maybe I should write about how human behaviour should be viewed (more specifically, should human interactions be viewed from a tit-for-tat perspective, or some other perspective?). I was wondering if anyone here knew of any good scholarly articles for or against a tit-for-tat view. There are probably many articles pro tit-for-tat so it would be of even greater help for me to find a scholarly article against it or using a different alternative. [Edit: In restrospect, I should probably narrow my topic by asking whether or not a specific social phenomena should be viewed as a zero sum game or a non zero sum game. Is there any such phenomena that is in current dispute about what type of game it is?] Strangequark

http://vimeo.com/31158841

Someone has pointed out that both the "preferred direction" in the cosmos and the way the expansion of the Universe appears to be accelerating can be explained by the existence of very large gravitational waves (imagine a balloon being inflated but oscillating on a large scale as wel). Nice idea! See this arxiv post.

I've been wondering for a while, what if space were shaped like a fractal? The evidence we have at the moment says that space is shaped like a sphere, so everything's even, but how different would living in a fractal be? I looked at these two videos: http://www.youtube.com/watch?v=AGLPbSMxSUM http://www.youtube.com/watch?v=MKwAS5omW_w And they talk about the space that is "not a knot", and the way light bends to create strange patterns in a space without a certain locus of points. So is there any way to apply this to, say, a point living in the whitespace of the Sierpinski triangle? Is there any way to distort a 2-D infinite space to fit inside only the whitespace of the triangle? Alternatively, is there a function f(x,y) with domain real values of x and y, such that the range is a mapping onto and into the whitespace of the Sierpinski triangle? Or, a simpler question -- picture a 3-D sierpinski triangle, the whitespace of it. It's a bunch of tetrahedrons. Imagine if each tetrahedron was a planet, with sufficient gravity to hold mass onto it, despite lacking mass. The center of each tetrahedron has a heat sorce to sustain life. They're all connected, so it's easy to move between planets, but the direction of gravity gets confusing. Also, planets get smaller as you go farther out. In other words, the blue one: http://en.wikipedia.org/wiki/File:Sierpinski_pyramid.png How would technology evolve on this kind of world, specifically regarding the unique structure? Purely theoretical. I'm just looking for ideas on writing something regarding life on/in a fractal. Dazzle me with imagination!

For ages the mainstream view of dark matter was that it almost certainly existed, but it had not been detected in any way except indirectly as the missing mass in galaxies, even though people had reasonable theories as to what it was (WIMPs). Nice to see some experiments are beginning to claim solid evidence for detection now (even if others are publishing negative results). Strange to think of ourselves in a world that not only has vast swathes of neutrinos passing straight through (almost) undetectably, but now loads of massive particles as well.

Hi, I had a couple of problems with some matrices and I'd appreciate any help if possible: Ax=b in row echelon form, need to find all solns: 1 -2 0 3 1 -2 0 0 1 2 4 5 0 0 0 0 0 0 0 0 0 0 0 0 the 5th column (-2,5,0,0) is the solution set. Forgive my lack of decent syntax. So I was thinking maybe I could start with x5=a, x4=b, x3=5-a-b, or what? I'm suspicious that that I might get too many variables, although I think there are infinitely many solutions. Also if I have a 5 by 3 matrix such that b=a1+a2=a2+a3 i am supposed to see what this tells me about the number of solutions to this Ax=b. I was hoping to write out something like b=x1(a11+a21+...+a51)+x2(a12+...+a52)+x3(a13+a23+...+a53) to try and get an expression with a11+a12+a13+a14+a15=a1, etc. to work with but I really don't know what I'm supposed to be doing.

Could someone with a CAS please evaluate and copy the integration steps (I already know the answer) to the integral from 0 to 1 S(2t+9t^3)sqrt(1+4t^2+9t^4)dt please?

So I just finished high school and im going to college next semester. I want to have a math and philosophy double major. I like number theory, complex analysis, epistemology, and philosophy of religion the most. I have had no philosophy college courses. The math college courses that I have taken are: Calculus 1,2,3, and a proving course (sometimes called "set theory and logic"). What should my track be like? What fun math should I do over the summer? I have been interested in Godel numbering for a long time, but I might take the lame option and just get a head start on linear algebra which will be my first course in the fall. Any advice is much appreciated!

Well I didnt have a question about syllogisms per se, but I was wondering if anyone here had any knowledge of syllogism based proofs for any particular philosophy of mathematics. During my summer reading I have grown tired of semi-popular math "philosophy" books written by physicists and sociologists/cognitive scientists that are little more than a history of mathematical philosophical thought, with very little actual proof based content as opposed to a liberal use of quotations giving mere assertions of a paticular philosophy of math outlook. So does anyone know of any books or links that give real attempts at proofs for platonism/intuitionism, etc.?

Awe-inspiring stuff!

http://www.newscientist.com/article/dn20084-neutron-star-seen-forming-exotic-new-state-of-matter.html "The dense core of a nearby collapsed star is undergoing a rapid chill, providing the first direct evidence that such stars can produce a superfluid of neutrons – a state of matter that cannot be created in laboratories on Earth. Neutron stars are the remnants of exploded stars. Their cores are so dense that atomic nuclei dissolve, and protons and electrons combine to form a soup dominated by neutrons. If conditions are right, these neutrons ought to be able to pair up to form a superfluid – a substance with quantum properties that mean it flows with zero friction. Superfluids formed in laboratories can do bizarre things such as creep up the walls of a cup, or remain still even while their container is made to spin. It has long been assumed that neutrons in the cores of neutron stars become superfluid, but without any direct evidence that they do so. That changed in 2010, when astrophysicists Craig Heinke and Wynn Ho examined measurements taken by NASA's orbiting Chandra X-ray Observatory of the 330-year-old neutron star at the heart of the dusty supernova remnant Cassiopeia A."

Well, the school year is near ending, so the time has come to give presentations of a chosen topic related to discrete math. I chose Langton's Ant, but that's another story. One person chose to present 20 Questions, so we later went into the computer lab to play the game. I decide to fool the machine by choosing Halite, knowing it will say salt, given my answers to the questions. So I click classic 20Q, and the first question, of course, is Animal, Vegitable, or Mineral? Mineral. I go on, and question 9 is: Is it killed for its fur? Another friend also chose halite later, and for question 10, does it live in water? The following writing is an accurate description of my thoughts (It was written by hand, so there are some ideas that escaped me before I could get them down, and this may be subject to edits later): Section XIII -- Halite Hunters The sense of taste is one which many take for granted. It is divided into 5 subsenses, bitter, sweet, sour, spicy, and salty (and the elusive umame, but that is outside the purposes of this writing). These have all been very useful to our survival in the eons of evolution. Poisonous plants and animals have triggered our bitter sense, enabling us to eject the food before it is consumed. Sweet food implies high caloric content, and triggers dopamine, which helped when food was scarce, but is now ruining our species. Sour foods are generally acidic. Spicy foods are useful antibiotics. But there is no obvious reason for our sense of salty. For that, we must observe the salcricetus. When humans physically or mentally exert themselves, chemical reactions are needed. These raise our body temperature. If no counter measures are taken, overheating could ensue at dangerous temperature levels. For that reason, we sweat. Sweat is composed mostly of water, which can evaporate and cool our skin. But it contains not only water, but some minerals as well. The most abundant is salt. Some people are more prone to sweating than others. But there is an animal that uses its sweat as a lethal weapon, the salcricetus. The salcricetus appears to be a small furry herbivore, vulnerable to various predators. It is actually a cunning scavenger. Rather than the fly that dresses like a bee, this species provokes predators into attacking it. The fur is covered and saturated in salt crystals, resulting from over-sweating. If a predator bites it, the attacker will consume a dangerous quantity of salt from the salcricetus's coat, which will render it immobile if not dead. The salt crystals are quite heavy, so the salcricetus is unable to move quickly, but it can easily catch and consume struggling dehydrated animals, be it snake, eagle, or lion. This was before animals developed their salty sense. During the agricultural revolution, humans discovered that salt crystals are consumable in small amounts. Since then, the salcricetus has been widely hunted for its skin, as salt became highly valued, almost to the degree of gold. The abundance of salt in modern day is mostly due to the hunting of salcricetuses, though undocumented. Why is the plight of these creatures so hidden? The initial discovery of the salcricetus domestication was by Sal, hence salt was named after him. He is also the subject of the fable, “The Goose That Laid The Golden Egg”. After people found out about the salt, Sal slowly traded small amounts out. But being both a scientist and merchant, he wanted a way to extract even more salt from the salcricetuses. One by one, he performed surgical operations, including cutting the salcricetuses open. Alas, he found no way to acquire more salt. As time went on, he became more desperate, and eventually, in a fit of rage, slaughtered all of the salcricetuses. This left him without a source of salt, and the townspeople, thinking he was hoarding salt, raided his house. Sal was killed in the process. Because of greed from both sides, there were many deaths, and this story was passed by word of mouth, later becoming a popular fable. After some time passed came the period of Renaissance, when a small group of people speculated on the origin of “The Goose That Laid The Golden Egg” and soon after, discovered it revolves around the salcricetuss. Since then, they have formed what are known as the Halite Hunters, to secretly hunt these animals for their fur. They have also discovered a way to remove the salt production gene from the salcricetus (also causing it to become an herbivore) and produced the long-haired rabbit, a common pet. History had to be rewritten multiple times for the safety of the Halite Hunters, as if they are discovered, many people and organizations would profit in kidnapping or "disappearing" members of their organization. Therefore, no further information will be given regarding them.

Anyone care to comment on John Conway's Game of Life Theory or about Emergence? Is there a good book out there? http://en.wikipedia.org/wiki/John_Horton_Conway http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life http://en.wikipedia.org/wiki/Emergence

The ever mind-boggling Arxiv blog described a surprising new theoretical result. It's something to do with Cauchy horizons (which are something I have very little knowledge of, except that they are entirely different to event horizons).

Conservation laws in a discrete universe

See New Scientist article

I am trying to understand Godel numbering, and any help would be much appreciated. For fun, I was just trying to make some Godel numbers for functions (is this even allowable?) to try to investigate properties of these functions with arithmetical proofs on the Godel numbers. So I had a few questions: 1. I can use induction on Godel numbered statements, right? 2. Is it fine to number functions? 3. If it is fine, how do I represent operations arithmetically. For example, how could I arithmetize something like g(f(x))?

http://www.newscientist.com/article/mg20627622.700-matter-the-next-generation.html Unfortunately the website asked me to subscribe to read the whole article so I don't have too much on this...if you find more about this please let me know. "TWO teams working at the Tevatron particle smasher in Batavia, Illinois, have found hints of a new generation of fundamental particles - to add to the three generations we already know about. What's so special about these new particles? If they really do exist, they might explain a long-standing puzzle - how the universe avoided self-destruction in its earliest moments after the big bang. First a rundown on what we know already. Each of the three known generations of matter contains two types of fundamental particle - quarks and leptons. First generation leptons include the familiar electron and neutrino (see images, right). The first generation of matter can explain everything we encounter in everyday life. Atomic nuclei are composed of protons and neutrons, which are in turn composed solely of "up" and "down" quarks. The second and third generations were introduced to explain the dozens of varieties ..."

http://www.newscientist.com/article/mg20927994.100-vacuum-has-friction-after-all.html "A BALL spinning in a vacuum should never slow down, since no outside forces are acting on it. At least that's what Newton would have said. But what if the vacuum itself creates a type of friction that puts the brakes on spinning objects? The effect, which might soon be detectable, could act on interstellar dust grains. In quantum mechanics, the uncertainty principle says we can never be sure that an apparent vacuum is truly empty. Instead, space is fizzing with photons that are constantly popping into and out of existence before they can be measured directly. Even though they appear only fleetingly, these "virtual" photons exert the same electromagnetic forces on the objects they encounter as normal photons do. Now, Alejandro Manjavacas and F. Javier García de Abajo of the Institute of Optics at the Spanish National Research Council in Madrid say these forces should slow down spinning objects. Just as a head-on collision packs a bigger punch than a tap between two cars one behind the other, a virtual photon hitting an object in the direction opposite to its spin collides with greater force than if it hits in the same direction. So over time, a spinning object will gradually slow down, even if equal numbers of virtual photons bombard it from all sides. The rotational energy it loses is then emitted as real, detectable photons (Physical Review A, DOI: 10.1103/PhysRevA.82.063827)."

http://www.newscientist.com/article/dn20080-zapping-the-brain-sparks-bright-ideas.html "Transcranial direct current stimulation (tDCS) is a safe and non-invasive method of temporarily altering the activity of neurons by passing weak currents through electrodes on the scalp. It can enhance mathematical skills, memory, attention and language learning."