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      CommentAuthorAngus
    • CommentTimeMar 14th 2020
     
    Relational operators are important too. There's "sorta like", "somewhat bigger" and "less, I think". And there's the imperative operator as well : "make it so".
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    In fuzzy statistics, all probabilities reduce to (roughly) 50 percent, because something either happens, or it doesn't.
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    This turned up in my "suggestions" feed: Another brilliant and long-legged professor plays with primes:

    https://www.youtube.com/watch?v=LvFvtjn3wgg
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    Lurking out there after the LSD.... is, like, what? 2CB? DMT? The dreaded Scopolamine?
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    Why did they prove this amazing theorem in 200 different ways? Quadratic Reciprocity MASTERCLASS with Mathologer
    https://www.youtube.com/watch?v=X63MWZIN3gM

    Settle in for some jolly decent fun!
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      CommentAuthoralsetalokin
    • CommentTimeApr 2nd 2020 edited
     
    I on the other hand am fascinated by repeating decimal numbers with long repeats. Just now I encountered one with a 42-digit repeat:

    5110/215215 = 0.023743698162302813465604163278581883233046023743698....
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      CommentAuthorDuracell
    • CommentTimeApr 2nd 2020
     
    A grim number to be reaping ...
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    It's one of a family of irrational numbers called "Aw Fuck". More are being discovered every day.
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    Did I say "irrational" ? I meant "unthinkable".
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    Posted By: alsetalokinI on the other hand am fascinated by repeating decimal numbers with long repeats. Just now I encountered one with a 42-digit repeat:

    5110/215215 = 0.023743698162302813465604163278581883233046023743698....


    But both numerator and denominator of 5110/215215 are divisible by 35, so this is a sloppy representation. Better would be 146/6149 = (2x73) / (11x13x43) in prime factors.
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    Posted By: Andrew PalfreymanSettle in for some jolly decent fun!
    For instance, you can state the proof that log103 is irrational from memory, for use in casual conversation!
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    You could change your last name to Ramanujan and save an entire letter.
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    Much as it would be beneficial to your cause, it does not take a genius to see that your representation was sloppy.
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    My representation was taken from the raw data. I'll be sure to forward your criticisms to the Graves Registration Division.
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    Then next time don't be so sloppy. (k a) / (k b) impresses nobody.

    It is indeed an impressive repeat however. Is there any theory backing it up? I recall a similar go-around on the 'trap some years back.
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    My theory is that I'm too stupid to be a theoretician so I tend to leave the theorizing to others. With something this deep though, I don't even know how to confirm that it isn't some software rounding error or a cosmic ray flipping a bit in the hardware. But it sure seems that there are a lot of these deep repeating decimals encountered when one looks at ratios of integers. (even if the numerator and denominator have common factors)

    I suppose there exists some kind of proof that pi, for instance, does not repeat even after a bazillion digits deep into the decimal expansion. But what about shifted or reversed reading frames, or skip-n sequences?
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    Posted By: Andrew Palfreyman(k a) / (k b) impresses nobody.


    Doctor standing over patient on gurney, clipboard in hand:
    "I have good news and bad news. The bad news is that by factoring out the least common denominator and feeding the death versus survival data through a fast Fourier transform and plotting it on a semilog-log graph using multicolored lines... sir? SIR? SIR?
    Nurse, I have good news, another vent just got freed up!"
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    Posted By: alsetalokinI suppose there exists some kind of proof that pi, for instance, does not repeat even after a bazillion digits deep into the decimal expansion.
    Oh FFS.
    That is precisely the content of my previous post which you chose to ignore.

    Well, almost. I am assuming that a repeat is always due to a rational number, so that any irrational number contains no "sustained" repeats (as per your example). Obviously there are always repeats of any length in an infinite sequence of digits, but they are sporadic and governed by statistics and nothing deeper.
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      CommentAuthoralsetalokin
    • CommentTimeApr 2nd 2020 edited
     
    I'm not concerned with what you are calling sporadic repeats, only sustained repeats with no intervening gaps as in the 42-digit repeating example. The point about reading frames etc. was just an analogy to RNA/DNA biocodecs.
    Since such repeats extend to finer and finer detail beyond any conceivable mapping between the value and the real physical world I think they are particularly salient illustrations of the fact that mathematics either describes reality incompletely, or with an unnecessary and indeed surfeit level of detal.

    Or both, if I am recalling my ancient math homework sets properly.
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      CommentAuthorAngus
    • CommentTimeApr 2nd 2020
     
    Posted By: AngusThe discussion we had about cyclic primes ( "moletrap numbers" ) was aroundhere. It was rather fun.