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The 3x+1 Problem [video]

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Re: The 3x+1 Problem [video]

#62

Post by feoren »

gary17the wrote: post #37

This was a great video. But the one titled "Math Has a Fatal Flaw"[1] was even more interesting: the meta-mathematics, thus mathematics of entire mathematics (Gödel). [1] https://www.youtube.com/watch?v=HeQX2HjkcNo

I can't get over the clickbaity, obviously incorrect title to that one. I refuse to watch it for that reason alone. If the flaw is fatal, then every mathematician is wasting their time.

Re: The 3x+1 Problem [video]

#63

Post by lostmsu »

IIAOPSW wrote: post #59
romwell wrote: post #30

My biggest take-away from this was FRACTRAN[1], The Bestest Ever™ programming language designed by the (sadly, late) John Conway. To run a FRACTRAN program, you lookup its catalogue number, and repeatedly evaluate a certain simple function on it (which has the same spirit as the 3x + 1 one in the video). As in 3x+1, all operations are integer operations. FRACTRAN is Turing-complete, of course, so you can rewrite any…

If 3x+1 is a programming language, the Collatz conjecture must be false as otherwise it would always halt. I suspect 3x+1 is not Turing complete.

Or maybe it is, and Collatz conjecture is false.

Re: The 3x+1 Problem [video]

#65

Post by D7x7w9pHnT »

hashmash wrote: post #5

After watching this video, how many of us wrote a program to see if we could just randomly find a case which didn't converge? I wrote one, but of course, the program didn't prove the 3x+1 problem wrong.

lol totally

Did this in Haskell, and since all the lower numbers are known, started searching at 2^361

To end the recursion I just have it print -1 when it reaches 1

    f :: Integer -> Integer
    f n
      | n == 1 = -1
      | even n = f (n `div` 2)
      | odd  n = f (3*n + 1)

    main = print $ map f [2^361..]

Re: The 3x+1 Problem [video]

#66

Post by pronoiac »

pronoiac wrote: post #51

Reading the Wikipedia page for the Collatz conjecture is interesting; the time-space tradeoff item specifically made me consider the benefit of using a couple of terabytes of disk space for it. (I think 2 to the 40th of space, for a factor of 40 speedup.) https://en.wikipedia.org/wiki/Collatz_conjecture#Optimizatio...

Wow, the nerdsniping on this is something. Note, for my math, I failed to consider that entries wouldn't fit in one byte. Figuring out an encoding might help. Laying out a sequence in blocks might also help overcome the speed difference between memory and storage. I'm not even really trying to delve into this, but it's tempting.

Re: The 3x+1 Problem [video]

#68

Post by bob1029 »

imperialdrive wrote: post #18
hashmash wrote: post #5

After watching this video, how many of us wrote a program to see if we could just randomly find a case which didn't converge? I wrote one, but of course, the program didn't prove the 3x+1 problem wrong.

I know so little about programming but this video absolutely left me up late trying to follow along: $count = 1 do { $count++ $i = $count [string]$array = "$i" $range = $i - 1 do { if ($i % 2 -eq 0) {$i = $i / 2} else {$i = (3 \* $i) + 1} $array = "$array" + ",$i" if ($i - $count -gt $range) {$range = $i - $count} if ($i -eq 2) {$i = "Break"} } while ($i -ne "Break") $array = "$array" + ",1" $hits = (($array -split "…

Here's a C# example:

  using System.Numerics;
  using System;

  var myBigStartingNumber = BigInteger.Parse("12893123812148934789012378957891325789012357891238912319824589123589012358915891589158989125");
  Collatz(myBigStartingNumber);
  Console.WriteLine("Collatz returned 1");
        
  static int Collatz(BigInteger x)
  {
      Console.WriteLine(x);
      return x == 1 ? 1 : x % 2 == 0 ? Collatz(x / 2) : Collatz(3 * x + 1);
  }
(stack overflows virtually guaranteed!)

Re: The 3x+1 Problem [video]

#70

Post by pgalvin »

feoren wrote: post #62
gary17the wrote: post #37

This was a great video. But the one titled "Math Has a Fatal Flaw"[1] was even more interesting: the meta-mathematics, thus mathematics of entire mathematics (Gödel). [1] https://www.youtube.com/watch?v=HeQX2HjkcNo

I can't get over the clickbaity, obviously incorrect title to that one. I refuse to watch it for that reason alone. If the flaw is fatal, then every mathematician is wasting their time.

The video is very interesting, I would highly recommend you still watch it.

Derek has has actually made a video before about the YouTube algorithm and has polled the community several times about clickbait-ey titles. He doesn’t like them, but they’re unfortunately necessary.

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