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matt grime

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Everything posted by matt grime

  1. The most obvious thing to say to that explanation is that if the frequencies differ by an irrational proportion then the peaks never overlap. seeing as you hear them when they do, surely you don't hear them in this case either, since they don't occur, so how is that different from what you describe you (don't) hear for perfectly attuned instruments/strings/notes? A similar comment applies when one is an integer multiple of the other. Of course when the over lap perfectly there are *some* (ie all) peaks that meet so why do you no longer hear them then? I think what you're trying to describe is constructive interference, which is a slightly different phenomenon. What do you mean by musical wave?
  2. Erm, cos you say there's a link and you'd be stupid to deny it, but the only evidence you put forward of combined mathematical and musical skills is your own, and you say you can't do maths, but can do music. The evidence doesn't remotely support your conclusion. And saying, wow, look at an oscilloscope doesn't help since that is a mathematical model of a sound wave, not a sound wave. (sound waves are longitudinal for pity's sake, not even transverse.) It's like saying there's a link between mathematics and national debt: look at the graph.
  3. In what form are you used to seeing groups presented? From the question it just asks you what the symmetry group of a 22-gon is, which is either D(11) or D(22) depending on the standards in the course you're using. But how do *you* describe groups? There are many ways of doing it, which do you understand? Bloodhounds description for instance amounts to labelling the corners, and the thing in bracket tells you what to do to each corner, the first is the symmetry sending the corner labelled 1 to that labelled 2, that labelled 2 to 3 and so on reading left to right. This, sorry to say, bloodhound, is about the worst way of writing it since it contains so much redundant information: pick three adjacent corners, once you've said where to map them to the symmetry is fixed otherwise yo'ud have to break the cap. So there are 19 numbers in there that do nothing. The best way, perhaps is in terms of generators and relations.
  4. I don't think you've grasped some of the complexity of the proof that perelman's put forward, and I think you'd need to explain what you think "snipping" means. There are many ways to smooth out singularities, such as crepant resolutions, I don't know which perelman uses, but they are not at all disquieting. Lots of people think that perelman's proof is correct in spirit, though they can't follow the details, and with more complex proofs necessarily being required more frequently that is something w might have to get used to. Look at Wiles's proof of FLT, actually he proved the semi-stable T-S conjecture, and got that wrong to begin with, and with the help of others corrected his proof and gave a lead for proving the general case. That is perhaps what we will find with perelman, that there may be some cases he's not considered fully, but that a group effort will eradicate them. I don't understand what a dumbell has to do with anything.
  5. matt grime


    So what? I'm talking about the argument in the range of the function, since that is where one must take care when making a single valued choice of the square root for complex numbers. And you can easily and unambiguously calculate the square root of a complex number (on the principal branch), since sqrt(re^{it}) = sqrt®e^{it/2} where sqrt of a positive number is positive, the argument of the elements in the range is [0,pi).
  6. matt grime


    You can extend to the complex plane by demanding that the argument lies in the interval [0,pi) without any problems at all, it ceases to be continuous but that is not important.
  7. matt grime


    of course it makes sense, picking the principal branch of the square root function
  8. There are several threads there to develop. Though first it might be better if each person said what aspects of mathematics and music were linked. The original idea that the physical dexterity required to play a complicated instrument doesn't mean the player could have written Bach's preludes and fugues, so how that implies they'd be able to understand the proof of Fermat's last theorem is a mystery. And please understand I am deliberately emphasizing the purely mechanical without meaning to imply that the organist isn't "musically talented", I'm sure she is, but I know of some people capable of playing with great flair but only the things they've mechanically learnt. So is it the ability to mechanically play a piece of music, to mechanically write a proof, to understand the flow of a piece of music and know where its progressions will lead, though that is a cultural phenomenon based upon our choice of scale, to see a proof before it's explained to you, to appreciate the music on some higher scale, to understand what a mathematician means when she describes a proof as beautiful or elegant? All or some of these facets. What level of mathematics do you mean, what level of musical ability? From reading this forum it seems like few people here are beyond high-school mathematics, which isn't mathematics as those of us who do research understand it, even degree mathematics bears no relevance to research, but then maybe that isn't the level of mathematics the comes into people's minds when the think of this alleged link. One thing that is required in both areas is an ability to follow rules. And here is a similarity: there are those people to whom you can explain the rules as often as you wish, and they may even be able to recite the rules, but they can never learn to use them. They will just stare at the page blankly. So perhaps we can say that there are correlations between those able to not only understand the rules (though understand is a philosophically interesting word) but to implement them (Wittgenstein might have said that unless you can implement them you haven't understood them).
  9. The evidence for the link is anecdotal at best, if not apocryphal. One of my lecturers, when I was an undergrad, was a concert standard violinist. On the other hand, another was completely tone deaf. Do you mean this on the basic academic level, for then the link ios probably the same as for any other pair of subjects: if a student gets straight As in one class, they probably get them in most classes. If you mean that extra spark of talent of creativity, then perhaps there might be a link. I'd like to expand on an idea of Tim Gowers (Fields Medal) that the link, if it even exists, perhaps can be explained by the need to find beauty in abstract forms that defy verbal description sometimes, and to do either to a high level requires a commitment to something intangible, and a certain mindset common to both. However an aptitide at one certainly doesn't imply an aptitude at another. A musician tried to get me to explain the simplest proof known to man, that root 2 is irrational, and they just didn't understand why it worked, why, even after we'd got to the stage "suppose not, and let root 2 equal a/b" (which took some effort to reach in itself) I'd want to square both sides. But, that is just more anecdotal evidence that I'd dismiss.
  10. matt grime


    your orginal post contains a vague philosophical question, and this is a mathematics forum. it might be better to explain what you mean by "exist", as there are platonists and intuitionists and wittgenstinian people to mention but a few who all interpret that question differently. In fact your original statement was: "I would just like to state that the concept of Infinity does not actually exist" which is either badly written or just plain wrong since the *concept* certainly does exist, whether or not you think that *concept* encapsulates something tangible is different, and might show you either to be a platonist or a formalist. However, being either, or neither, of those two does not affect how you actually do mathematics. Although seeing as the concept of infinity doesn't exist to you, you must find it very hard to do any analysis, geometry, topology...
  11. then why do you keep sending me unsolicited emails with you pet theories in them if you do not wish me to comment upon them. the last three are dated the 23,24,25 of august, after you wrote this message. this a mathematics forum, you do not understand the first thing about mathematics, and I will keep saying so if i ever notice you posting on any forum that i read.
  12. matt grime


    with no infinity, everything must be finite, in particular the set of natural numbers is finite, hence there must be a largest one. what is it mr troll?
  13. For other forum users: Doron is a notorious poster on many forums. In physicsforums.com he has posted under the psuedonyms Lama, Organic, www, and many more (each mambership was blocked from posting in the mainstream forums), and all threads he started there were moved to Theory Development, including threads he hijacked. He adopts the terminology of mathematical discourse, and then refuses to use the objects according to their definitions, and generally refuses for a long time to acknowledge this or offer his definitions. In some cases he adamantly insists he is using the terms correctly (his abuse of "tautology" springs to mind when he kept posting a wikipedia definition as if that were his usage, when eventually he admitted he didn't mean it in that sense). He will generally not answer questions directly and will only post more garbage in response. If you wish to keep this forum to mainstream ideas then you probably ought to lock these threads
  14. There is no contention there at all. Arithmetic operations can and are easily defined on infinitely long decimal representations.
  15. try finding the n'th power of a matrix for n large, then, if possible diagonalize, repeat the operation and see why. also seeing as people prefer applied reasons, you can find the direction and magnitude of max min strain, resistance etc in tensors from the diagonaliztions and the eigenvectors/values
  16. 0.99.. is equal to 1, that is provable from the definition of what the real numbers are. i'd be interested to see if any of the people who are so sure they are not equal can actually define the real numbers.
  17. If you have a set of n linearly independent vectors in R^n they span.
  18. Let us clear some things up. Two sets have te same cardinality iff there is a bijection between them. There is a bijection between N and the set of primes in N, and further there is a bijection between N and any infinite subset of N. There is also a bijection with Q. Sets that biject with N are called countable, The set of Reals is not countable, nor is the power set of N.
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