Wikipedia:Reference desk/Archives/Mathematics/2009 November 14

= November 14 =

maths
what is maths —Preceding unsigned comment added by 124.43.90.158 (talk) 08:29, 14 November 2009 (UTC)

2=2= —Preceding unsigned comment added by 124.43.90.158 (talk) 08:30, 14 November 2009 (UTC)


 * See the article mathematics and in particular, Mathematics (this particular section of the article illustrates that mathematicians do not care about basics like 2 = 2). For particular "tastes" as to what mathematics is, see the high quality articles vector space, group (mathematics), ring (mathematics) and set theory (set theory being the most important of all). The reason people think mathematicians care about 2 = 2 (and such trivial equations, formulas, or basic arithmetic), is because they think that mathematics has not advanced in the time of the Greeks (whereas, they know that science has advanced since that time and discoveries are made everyday). These people are terribly incorrect and obviously do not understand the significance of time. Please consider that mathematicians are intelligent (nothing to do with "human calculators") people who research abstract concepts - that is, the purpose of mathematics is not only for daily life. Abstraction subsumes objects which do not have any direct connection with our universe, as well as objects embedded within higher-dimensional analogues of our universe. Have you ever considered the idea of how higher dimensional spheres wrap around lower dimensional spheres? This is an example of mathematics (see homotopy groups of spheres). -- PS T  09:24, 14 November 2009 (UTC)

Mathematics is the application of logical thinking in the study of games which have non-contradictory rules. The word game is used in the most general sense. 122.107.207.98 (talk) 00:35, 15 November 2009 (UTC)

Maybe the article titled abstract structure is also relevant here. Michael Hardy (talk) 16:52, 15 November 2009 (UTC)

Math is what two apple trees and two bicycles have in common. The former is a plant, it produces apples. The latter is manufactured part by part by people, and produces nothing. The former is quite stationary. The latter moves easily, and can be ridden. Seemingly, there is nothing that two apple trees and two bicycles have in common. Yet, if you sell someone the two apple trees at $10 each or if you sell someone the two bicycles at $10 each, you will have the same amount of money, $20, in each case. Why should this be the same, if two apple trees and two bicycles have nothing in common? If each apple tree can fill four baskets with apples, and each bicycle can transport 4 pizzas, then the two apple trees can fill the same number of baskets (8) with apples as the the bicycles can transport pizzas (8). Why should this number be the same, what does an apple tree have to do with transporting pizza? The answer is that what is the same is mathematics -- mathematics is what remains when you remove the concrete, and focus on some abstraction, in this case the number "two" that there are of each. 92.230.70.229 (talk) 22:00, 16 November 2009 (UTC)

tessalation
tesselation —Preceding unsigned comment added by 124.43.90.158 (talk) 08:35, 14 November 2009 (UTC)
 * There will be no responses to this "word" due to its lack of clarity as a "question". Unless you illustrate that this question was asked with good faith, it may also be considered vandalizm (and consequently, be removed). -- PS T  09:12, 14 November 2009 (UTC)


 * Point-set topologist: The burden of proof does not lie with the person making the post; it lies with those assuming a lack of good faith. See WP:AGF. Also, the original post does not constitute vandalism. See WP:VAN, and its subsections WP:VAN and WP:VAN. Finally, I recommend you read WP:BITE. Dr Dec  (Talk)   23:31, 14 November 2009 (UTC)
 * There are two reasons behind my assertion that the OP's question was not asked with good faith. Firstly, the OP posted a question above ("what is maths?") in which he apparently sought to ridicule mathematics (he asked a question and answered his own question with "2=2="). It is quite clear that this was the case (nevertheless I still answered the question in a civil manner). Secondly, according to the guidelines at the top, the OP should in general give some importance to being specific in his/her question. The response given below by Bo Jacoby is the best response but I feel that my judgement of the nature of the question was correct. Although I try 95% of the time to assume good faith, this particular instance quite clearly resembles the OP either in pursuit of wasting our times, or trying to ridicule mathematics. I do not see the point in continuing this thread since I remember clearly the reasons for the most recent dispute between us (you appear to have forgotten them). Consequently, I recommend that you do not reply to this post (you may reply, but I shall not respond). Although I agree that my post was on the borderline of the policies above, I should repeat that, in my opinion, my judgement was perfectly correct - we should not give importance to people who do not wish to cooperate. As you will notice, my answer to the above question ("what is maths?") (by the same OP) was perfectly appropriate - the only reason I responded differently in this instance was because it was clearly not asked with good faith. Please interpret policies appropriately or do not mention them - WP:AGF asks to assume good faith when unsure. However, I was sure in this particular instance. -- PS T  03:28, 15 November 2009 (UTC)
 * The reference to WP:AGF was perfectly correct. You say that the OP needs to prove his good faith. I say that you need to prove his bad faith. This last post of yours examplifies a worrying trend I have noticed: you seem to be acting as the RD's unelected spokesperson. This is not the first time you have made comments like "There will be no responses to this..." Please stop and let us speak for ourselves. (I'm not sure why you're mentioning any disputes; which are unrelated to this topic of dicussion. For your reference I do recall the reasons for our most recent dispute; and I also recall the community's reaction to your complaints.)  Dr Dec  (Talk)   22:36, 16 November 2009 (UTC)
 * Although I promised not to reply to your post, the recent circumstances forbid it. It is a serious matter, perhaps more serious than that of which you are accusing me, to use multiple accounts to challenge a user. An IP posted this comment on my talk page, which I subsequently removed, in which he claimed that "I should stop being so possessive of the math reference desk". Above you claim that "you seem to be acting as the RD's unelected spokesperson"; precisely the same accusation. I usually tend not to concern myself with childish comments, and this case is no different since I have always seen you as a valuable editor of the RD for your constructive contributions. However, it greatly saddens me that, if further evidence permits, I might be obliged to file a WP:SOCK case against you; a rather serious accusation. Concisely, although you are welcome to discuss with me any issues about my behaviour using your own account, any further retaliations with sock puppets will be considered a serious breach of Wikipedia conduct. -- PS T  04:30, 17 November 2009 (UTC)
 * If you go to this webpage you will be able to enter the user's IP address and get a geographical location. You will see that the user you mention has an IP address registered some where close to the Yorkshire Dales. I suggest that instead of making public accusations you go and speak to a checkuser, they will check my IP address and find that it is registered to a Greater Manchester address. Try Sockpuppet investigations for more information. I hope that, upon receiving the result that the IP and myself are different people in different parts of the country, you will be as public in your apology as you have been in your accusations. It seems that instead of sock puppetry the truth is that I'm not the only one that thinks you've been acting as the RD's spokesperson. Dr Dec  (Talk)   12:06, 17 November 2009 (UTC)
 * Dr. Dec: I was wrong to accuse you of sockpuppetry without sufficient evidence, and sincerely apologize. Although I still do not completely concur with you with regards to the nature of the OP's posts ), I should not have accused you of sockpuppetry. Once again, I shall apologize. -- PS T  04:54, 18 November 2009 (UTC)
 * I thank you for, and fully accept, your apology. Dr Dec  (Talk)   22:36, 18 November 2009 (UTC)


 * PST, multiple users have asked you multiple times to quit harassing queriers and acting as a wannabe arbiter on this refdesk (count me in, if I didn't as yet). The idea that Dr Dec is the same person as a random IP just because they, too, complain about this behaviour of yours is a ridiculous accusation, except that it's not actually funny at all. You should worry about your conduct, not that of others. — Emil J. 12:42, 17 November 2009 (UTC)
 * EmilJ: As with every other user at the RD/M, 90% (if not more) of my edits have been accepted as extremely constructive by both the users here, and the OP's who ask them (a quick glance at the current version of the page will show you this, as well as of any past revision of the page in the last 8 months). Of the possibly controversial edits I have made, only Dr. Dec (in the last 8 months) has actually commented on them, and does not always gain full support (please do provide evidence if you know of other users accusing me in the recent past, and I will correct myself). In the first few weeks of helping at the RD/M, I do remember questioning OP's frequently. However, I have learnt quickly from this, accepted my faults, and moved on (in that I have been far more careful, valid and infrequent in doing so). If these instances subsume the mutliple requests to change my behaviour, then please do remember that once someone has made a fault, accepted it and moved on, it is only hurtful (and not very productive) to bring it up later on (to clarify, I am referring to my first few weeks at the RD/M). The comment I made above to the OP was indeed controversial (and impolite), but I feel that the reasons behind the comment were appropriate (thus, in the future, I will word such comments differently if at all I make them). I have always considered you to be one of the experts of logic who are vital to the RD/M. However, your comment could have been phrased in a civil manner which may have not only convinced me of your point, but also have made me more welcome here (and currently, I should add that if I am seen in the manner you suggest, it makes me feel upset about editing here). -- PS T  04:54, 18 November 2009 (UTC)
 * Just to dispel any impression that there might be a consensus forming about PST's posts being controversial - I for one certainly did not notice any problematic trend in his behavior (though there were, admittedly, a few debatable posts recently, as happens to anyone).
 * By the way, this is RD/Ma or RD/Math, not RD/M. -- Meni Rosenfeld (talk) 07:56, 18 November 2009 (UTC)
 * Thanks, Meni. I appreciate your comment. -- PS T  08:49, 18 November 2009 (UTC)

See the article Tesselation. Bo Jacoby (talk) 09:49, 14 November 2009 (UTC).
 * When written in capitals as 'TESSELATION' every letter has a symmetry and most can be tesselated when represented using unit squares. You can't fill the gap in 'A' though. Perhaps I'm wittering. No signal in tends to lead to noise out. Dmcq (talk) 12:28, 14 November 2009 (UTC)
 * How do you tesselate with 'S'? Seems the void in the curve will be impossible to fill. Taemyr (talk) 11:37, 17 November 2009 (UTC)
 * Surely the intended representation is

*** * ***  * ***
 * which tesselates quite nicely. -- Meni Rosenfeld (talk)

Symmetric difference
How to prove A∊P(M)∧B∊P(M)⇒(A∆B)∊P(M), where A, B, and M are sets? --84.61.179.99 (talk) 15:12, 14 November 2009 (UTC)


 * A∪B∊P(M), and A∆B⊆A∪B...
 * Damnit, I've said too much. I was supposed to like, ask what you have done with this problem before starting to give you some, like, vague direction, without full-out giving you all the answers, as I've done above.
 * I'm a failure. :( --COVIZAPIBETEFOKY (talk) 16:03, 14 November 2009 (UTC)


 * Is there anything to prove? What's your definition of A∆B? (I wonder if there is a definition of A∆B for which that implication is not obvious). --pma (talk) 20:36, 14 November 2009 (UTC)
 * The first steps into logic... ;) -- PS T  13:23, 17 November 2009 (UTC)

Fractal complexity
Whence comes the complex, feature rich properties of 2 and 3 dimensional fractals? A good example might be the screenshots on this page, but let's restrict ourselves to the 2d Mandelbrot set, governed by the rule $$z_{n+1} = z_n^2 + c$$.

Is the properties of the complex numbers that cause the complex structure, or the rule itself? A multiplication and an addition doesn't seem to be a particularily powerful transformation, but I've not seen what the Mandelbrot set looks like under a small amount of iterations, so while it starts off simple, a modification is added each time, and the visual representation of the set becomes increasingly complex.

It just seems so arbitrary. There is obviously reflectional symettry about the x-axis, but that's really the only thing. Could we perhaps see an example of a function such as $$f(x)=x^2$$ graphed over increasing iterations if treated like a mapping? —Preceding unsigned comment added by 94.171.225.236 (talk) 19:55, 14 November 2009 (UTC)
 * You might like the article chaos theory. 69.228.171.150 (talk) 00:57, 15 November 2009 (UTC)