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MathAddict

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  1. A rather good reason(to not get windows 8) I found on the net:
  2. [quote name='Selenaut' timestamp='1354075500' post='5004827'] Jeez, I'm an idiot. Why not just have two squares with each holding one of the poles in its center, and laying one on the bottom of the other (ignoring the obvious deformation)? So like, the edges of the squares would be the equator, and moving east and west would rotate the tiles on the square... Though to be perfectly honest, at this point I'm beginning to wonder if it's possible to map this with circles. [/quote] You can try that but it won't be a very accurate simulation of a planet. It all depends on how accurate you want to be. If you are making a game it's fine, but it's not good for making a simulation. To see an example of the possible inaccuracies, take a look at this picture(taken from wikipedia): [img]http://upload.wikimedia.org/wikipedia/commons/thumb/9/97/Triangles_%28spherical_geometry%29.jpg/350px-Triangles_%28spherical_geometry%29.jpg[/img] If you were to try to represent that triangle on a flat surface, you will see that the angles of the triangle will be different than the ones shown(more specifically, the angles will sum up to 180 degrees, they should not).
  3. Look up non-euclidean surfaces and non-euclidean geometry. [url="http://en.wikipedia.org/wiki/Non-Euclidean_geometry"]http://en.wikipedia....lidean_geometry[/url] (Or:[CODE]http://www.youtube.com/watch?v=zHh9q_nKrbc[/CODE]) The maths is different in non-euclidean geometry. For example, go look at the earth's atlas. When you said that wrapping around from the south pole gets you to the north pole, that's wrong. The wraparound will keep you in the north pole except it will displace you 180 degrees to either side. For example if I am going up along the 20 degree longitude ill wraparound to the 180+20 = 200 degree longitude, then ill keep going forward and reach the south pole then wrap around back to 20 degree longitude. Another thing is that the distance between the two ends keeps on changing depending on the latitude. If you are at the equator, and if you go east along the equator and come back to the same point you will travel 2*Pi*earth's radius distance. As you go up this distance(to keep going east until you reach the same point) keeps decreasing and at the poles, its 0. So when you said you want to go east from the poles, you will keep standing at the same point because the pole's 'radius' is 0. (Because non-euclidean east is not the same as euclidean east) What you actually meant to say was "I go to the north pole, turn 90 degrees to one side, then start walking" in which case, you will just switch longitudes. So if you went to the pole along 20 degree longitude and turned 90 degrees and started walking, you would end up moving down along (20+90+180) = 290 degrees longitude. Moving along that longitude you eventually find the south pole as expected. If you don't understand anything I am saying, get a globe of earth and an atlas of earth(which is essential a 2D representation of the earth - what you want to achieve) and move your finger around the globe and plot the path your finger takes on the atlas. Try to do the things you talked about(moving east from the pole etc.) and see how it plots on the atlas.
  4. If you like maths, [url="http://projecteuler.net/"]http://projecteuler.net/[/url] could teach you how to make more efficient code. It also has very fun problems.
  5. A game in which the boss of the previous level is the 'common enemy' of the current level. Imagine: You fight so hard to defeat the last boss, but once you defeat him, it becomes easy to defeat him again and again. The game shouldn't give the player more power over the levels i.e. nothing like after you defeat the boss, you get a gun which insta-gibs the boss. The player should have equal resources throughout the game, only thing that changes is his own skill. Amorhpous+ does this nicely.
  6. [quote name='swiftcoder' timestamp='1353445568' post='5002757'] [quote name='MathAddict' timestamp='1353443140' post='5002745'] AFAIK quantum mechanics has random elements in it[/quote] Too far, too fast. How do we know that quantum events are random? Because we can observe no discernible patterns. Is that sufficient to prove randomness? No, because we can't see the entire sequence (and even if we could, we might not be able to figure out the derivation - imagine looking at a random slice of 100 digits of pi...) [/quote] I refrained from using quantum mechanics because I don't know much about the subject. What I meant to say was - if physics depends on randomness, determinism is not possible. The quantum mechanics thing was just a real life example. EDIT: [media]http://www.youtube.com/watch?v=dmX1W5umC1c[/media] According to that, there is a way to check whether 'this sort of classical underlying explanation of quantum mechanics can exist even in principle' and it turns out there isn't.
  7. I think one can ask the following questions: 1 - Can an external observer determine the state of the universe at any given time t given the initial state of the universe(at t=0) and the laws of physics? Let's assume that the external observer cannot 'affect' the universe, he can only observe and conclude. It all depends on, I think, the laws of physics. If we assume all the laws of classical mechanics are true, then the answer will be yes because none of the laws in classical mechanics have a random element. With the advent of quantum mechanics I am not sure if we can come to the same conclusion, because AFAIK quantum mechanics has random elements in it. One way of looking at it is: A function, say f(x) takes the current state of the universe x and returns the state of the universe at the next 'moment of time' If the function is one to one then the external observer can determine the future state of the universe. If the function is one to many then the external observer will not be able to determine the future state of the universe. An example of a one to one function is f(x) = x+1, here every value of x will have only one corresponding value of f(x)(0->1 , 1->2 etc) A one to many function would be something like f(x) = sqrt(x), here if x is say 9, f(x) can either be -3 or +3 therefore there is no way of determining what is the exact value of f(x) and therefore the external observer won't be able to determine the future state of the universe given a function like f(x). 2 - Can an internal observer determine the state of the universe at any given time t given the initial state of the universe and the laws of physics? By internal observer I mean people like you, me or any random scientist. Can we predict the future given enough knowledge and computational ability? If the laws of physics have random elements then ofcourse we can't using the same explanation as above. But if the laws of physics are non-random? What happens if I predict my own future then try to falsify it on purpose. For example, I, knowing myself and all the laws of physics, predict that tomorrow morning I will pick up my cup of tea with my right hand. But tomorrow morning I will pick it up with my left hand instead, just to prove myself wrong. Ofcourse when I first predicted this, I would take that into consideration and conclude that because my future self would like to prove my past self wrong, so he will pick it up with the left hand instead. But then my future self, knowing I had predicted that he would pick it up with the left hand, would now pick it up with his right. And the loop goes on and on... Imagine the following scenario: There is a Robot that is programmed to predict his the future. The robot knows the initial state of the universe and all the laws of physics. What is the robot is going to do is simulate an 'alternate reality' using the initial state and the laws of physics. In his alternate reality, he will have the simulate himself too(because he is a part of the universe). His simulation of himself will also try to simulate the alternate reality. His simulation of himself then will have a simulation of itself(which is the simulation of the simulation of the robot). And the simulation of the simulation of the robot will again have a simulation of himself. So using this sort of brute force algorithm of simulating the future, the robot will run into an infinite loop and he will not be able to predict the future. This was only an example of how an algorithm for future-prediction can be made and does not prove that an internal observer cannot predict the future with a non-random ruleset for their might be another algorithm that can accurately predict the future. But until that algorithm is found, we cannot say that an internal observer can determine the future state of the universe. All my thoughts on the subject in a nutshell.
  8. [quote name='Hodgman' timestamp='1350528464' post='4991317'] how many other games have their own [url="http://www.gomtv.net/"]b[/url][url="http://www.gomtv.net/league/index.gom"]roadcaster[/url], and [url="http://wiki.teamliquid.net/starcraft2/BoxeR"]people[/url] earning over a quarter of a million $USD/annum from playing it? [/quote] Look up Dota 2.
  9. [quote name='JohnnyCode' timestamp='1347896230' post='4980908'] this was a programing exercise on Carl University, faculty of Informatics and math: the program gets on input the position of a horse. The chess desk is empty, with only the horse.Program should plan the path of the horse so that the horse visits every position on the desk exactly once. (is it allways possible?) [/quote] [url="http://en.wikipedia.org/wiki/Knight"]http://en.wikipedia....ight's_tour[/url] One use of 'always winning' AIs is putting them up against another AI and seeing the consequence. It's always fun to see computer vs computer chess matches. Another thing is to possibly see how the AI reacts to different situations. For example, one can make an AI that learns via trial and error(tries pressing every possible key on the keyboard, tries moving the mouse around, clicking the mouse randomly, and seeing what happens, then storing results in a database that can be later referred to) and then make the AI play a simple game such as pacman and see what happens. (The AI should know ofcourse that dying is bad and getting a higher score is good) Also the reply to the original topic, look up the Petersburg Paradox([url="http://en.wikipedia.org/wiki/St._Petersburg_paradox"]http://en.wikipedia....ersburg_paradox[/url]). It shouldn't be too hard to make a program that simulates a million games and see the average outcome. I did that and found fluctuating values, at one try it would get an average outcome of say 18, and in the second try I would get an absurd value like 124. I did up to 1 billion iterations and the average was something around 25. Edit: And yay! My first post! Edit 2: Ack! For some reason I can't get the first link to work(It redirects to Knight). Just google Knight's Tour and click the wikipedia page.