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Showing results for tags 'Mathematics'.
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If you're even casually into chess, this is a delightful video to behold:- 1 reply
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Our numbering system uses Base 10 because we have 10 fingers; yet, because of that, we end up with numbers such as "Pi," which is irrational (infinite and non-repeating) - irrational literally means, "unable to be put into a ratio." I haven't checked this, but the possibility dawned on me that there is a more universe-based numbering system that conforms with physics instead of our own human bodies. I cannot possibly be the first person to think of this, but has it ever been discovered? Maybe something like "Pi" would end up being a nice, round number in this "Universal Base" numbering system, like 10. I'm sure we'll always have irrational numbers, but maybe things could be a little "neater" than with our self-centered, Base 10 system. Who knows? Maybe this theoretical "Universal Base" is itself an irrational number, if it even exists.
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This is incredible - watch the video in the article. Mar 8, 2018 - "Rubik's Robot Solves Puzzle in 0.38 Seconds" on bbc.com Here's the video without the article, but the article is worth reading, and can be read in two minutes.
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This video of "The Game of the Century" is easily understandable even to the casual chess player - as long as you have a modicum of understanding (knowing what "castling" is, for example), you'll be able to understand what Bobby Fisher was able to accomplish - there are two moves of such brilliance that I don't see how even a modern computer could have devised them: 1) Fisher's Na4, which came out of nowhere, and is called "one of the greatest moves in chess history." 2) Fisher's insane, legendary, Queen sacrifice, Be6, which resulted in a "Windmill," where the opponent is reduced to spectator status, moving their king back-and-forth to avoid checkmates, and watching their pieces get captured, one-at-a-time. And, it's interesting to see Fisher walking Donald Byrne's King down the bottom row at the end to force a checkmate. Of particular note: Byrne was the consummate sportsman in letting Fisher finish this game, instead of resigning - he recognized the greatness of Fisher's play, and thought Fisher deserved to play it out for the world to see. This is an astonishing video that I promise you'll understand, and you'll be just as awestruck as I am. Well-worth your time to watch!
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"Jean Bourgain, Problem-Conquering Mathematician, Is Dead at 64" by Kenneth Chang on nytimes.com
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TREE(1) = 1 TREE(2) = 3 How big is TREE(3)? Bigger than anything you can conceive of:
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It's funny how one thing leads to another. Because of Jim's post, I'm watching "Rain Man" for the second time in my life. (By the way, this film is a whole lot deeper than I thought it was.) All because I was thinking about Daniel Tammet, and there's one thing I don't understand: In his Wikipedia entry, it says that Tammet: --- In his mind, Tammet says, each positive integer up to 10,000 has its own unique shape, colour, texture and feel. He has described his visual image of 289 as particularly ugly, 333 as particularly attractive, and pi, though not an integer, as beautiful. The number 6 apparently has no distinct image yet what he describes as an almost small nothingness, opposite to the number 9 which he calls large, towering, and quite intimidating. He also describes the number 117 as "a handsome number. It's tall, it's a lanky number, a little bit wobbly".[9][32] In his memoir, he describes experiencing a synaesthetic and emotional response for numbers and words.[9] --- What I don't understand ... is it the actual, mathematical quantity that Tagget finds ugly/beautiful, or is it the look of the Arabic Numerals that he finds visually repulsive/attracitve? My guess is that it's the Arabic Numeral representations - I can see the numbers "117" and "333" as being "beautiful," and the number "289" as being "ugly," but only in their Arabic notation; not as a string of bits. I distinctly remember Tagget telling David Letterman that he looked like a "117" - Letterman is tall and lean, and this would be intuitive. I'm pretty sure 117 is a prime number, and mathematically speaking, I can't imagine what's so beautiful about that as opposed to, say, 113 (which I'm guessing is also prime) - it must be the Arabic representations, right? Does what I'm saying make sense? More than anything else, Tammet comes across to me as a genuinely nice person - I've seen him on numerous occasions, and have paid close attention to what he does, says, and how he acts - he is just an all-around good human being, and that's what impresses me about him the most.
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Why is the Mandelbrot Set any more significant or inexplicable than Pi? And have there been any attempts to relate them? This seems like a pretty obvious correlation to me; just don't ask me to explain why.
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Thales' Theorem (named after Thales of Miletus, and theorized about 2,500-years ago) is a remarkably simple, yet brilliant, piece of work: 1. You have a circle 2. You draw a line, making a diameter. 3. Form a triangle anywhere inside the circle, using that line (AC) as one of the sides. 4. No matter where you put point B, the angle ABC will be 90 degrees. It's easily understood when visualized - go to the "Thales' Theorem" link. It's really quite beautiful, if math can be beautiful. Thales' is also, alas, the first person ever to make an attempt at "cornering the market" on something (olive-oil presses - really!) I feel badly that this is what inspired this thread. In ten years, people will be playing Tiddly Winks with Bitcoins, and I don't want anyone here to lose their shirts - take it from someone who lost 2/3 of his net worth in a stock market crash. (I made a good percentage before the crash, so it isn't all *that* bad, but I came out behind, and one thing I learned is that you don't know when something has collapsed, until after it has collapsed: Take. Your. Profits.)
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Such sad news: Maryam Mirzakhani has passed away. "Maryam Mirzakhani, Mathematician, Dies at 40" by Daniela Breitman on earthsky.org
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I watched "The Man Who Knew Infinity" yesterday, and liked it very much (without loving it). I knew of Srinivasa Ramanujan, because he kept popping up on these listicles of 'Uneducated Minds That Changed the World' - I knew him as 'some uneducated genius from India with an IQ through the ceiling, and a gift for math that was nearly savant-like,' but that's all I knew of him. For the education alone, I have to give this film personal points. Two films that came to mind - very quickly - when I first started watching this were (surprisingly *not* "Good Will Hunting," even though Ramanujan is mentioned in that film, and not "A Beautiful Mind") ... anyway, they were "The English Patient" and "Shine." Why these two films, instead of the others, popped into my head, I have no idea, but they did. "The English Patient," as David Foster Wallace once emphasized, is "a slick, commercial product," and that's how I felt about "The Man Who Knew Infinity." "Shine" was released in the same year as "The English Patient" (1996), and both of these films were - remarkably and tragically - nominated for an Academy Award for Best Picture (incredibly, "The English Patient" actually won). I thought this film was *much* better than "Shine," maybe because I'm a better pianist than I am a mathematician, and I thought "Shine" was just impossibly stupid; this at least taught me something (I had no idea, for example, of Ramanujan's role in Combinatorics, a field I was very interested in during graduate school). While the overall execution of "The Man Who Knew Infinity" resulted in a film clearly for the masses, I enjoyed it, and I learned from it (and at the end of the day, aren't those the two chief ends of literature: to instruct and delight?) Linking this post back to the discussion we were having above about a universal base, I can't help remembering the line in the movie that went something like, 'every single positive integer is Ramanujan's personal friend.' It's interesting that "positive integers" are only "positive integers" because we use a human-based, Base-10 numbering system; in the universe-based, Base-X system I was proposing, these wouldn't even be integers. I suppose you picked up on that when you mentioned the film? Ramanujan (and really, *every* mathematician) unearthing these "universal truths" is really doing nothing more than "unearthing universal truths based on an entirely man-made product," as Base 10 is a completely arbitrary construct. Anyway, "recommendation" (if it was a recommendation) much appreciated, and I'm glad I saw the film, even if it did cost me a whopping $5.99 on Amazon Prime. (For those who haven't seen it, Dev Patel was also the star of "Slumdog Millionaire," which I suppose makes him the most famous Indian movie star in America right now.)
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Many of you might not know who Terrence Tao is, but suffice it to say he's *smart as hell*. A mathematician and Fields Medal winner, Tao's primary love (forgive the pun) is prime numbers. And yet, he makes a pretty blatant boo-boo in this clip on The Colbert Report - see if you can spot it: Here's a question for mathemeticians: 13 is number that can be paired with a sexy prime on either side of it (19 and 7) - is this a special genre of sexy prime? Does it have a name? Actually, now that I think about it, you have 5, 11, 17, 23, and 29, making five consecutive numbers that are sexy primes: Has this been proven to be the greatest number of consecutive sexy primes, or does it remain unproven? Or, does nobody give a shit? ETA: Actually, I know for a fact that {5, 11, 17, 23, 29} is the largest possible sequence of sexy primes. It would be impossible to come up with a sequence of 6, and there aren't any other sequences of 5. I can explain it more easily than I can prove it: Any other number ending in 5 is not prime (obviously, since it would be divisible by 5). Therefore, the sequence must start with a number ending in 1. So, the numbers would be X1, X7, X3, X9, and ... you're back to a number ending in 5 again at the 5th number in the sequence, so this is the *only* occurrence of 5 consecutive sexy primes there is. How's that! Did I just win a Fields Medal? What this does, is make 17 a unique number, in that it has *2* sexy primes on either side of it - out of every number in the universe, this is the only number with this property. That's a big deal. I think.
