this post was submitted on 03 Aug 2023
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No Stupid Questions

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What are the most mindblowing things in mathematics? (lemmy.world)
submitted 1 year ago* (last edited 1 year ago) by cll7793@lemmy.world to c/nostupidquestions@lemmy.world
236 comments fedilink hide all child comments
 

What concepts or facts do you know from math that is mind blowing, awesome, or simply fascinating?

Here are some I would like to share:

  • Gödel's incompleteness theorems: There are some problems in math so difficult that it can never be solved no matter how much time you put into it.
  • Halting problem: It is impossible to write a program that can figure out whether or not any input program loops forever or finishes running. (Undecidablity)

The Busy Beaver function

Now this is the mind blowing one. What is the largest non-infinite number you know? Graham's Number? TREE(3)? TREE(TREE(3))? This one will beat it easily.

  • The Busy Beaver function produces the fastest growing number that is theoretically possible. These numbers are so large we don't even know if you can compute the function to get the value even with an infinitely powerful PC.
  • In fact, just the mere act of being able to compute the value would mean solving the hardest problems in mathematics.
  • Σ(1) = 1
  • Σ(4) = 13
  • Σ(6) > 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10 (10s are stacked on each other)
  • Σ(17) > Graham's Number
  • Σ(27) If you can compute this function the Goldbach conjecture is false.
  • Σ(744) If you can compute this function the Riemann hypothesis is false.

Sources:

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[–] billiam0202@lemmy.world 31 points 1 year ago (1 children)

With the caveat that it's not the first shuffle of a new deck. Since card decks come out of the factory in the same order, the probability that the first shuffle will result in an order that has been seen before is a little higher than on a deck that has already been shuffled.

[–] Steeve@lemmy.ca 10 points 1 year ago* (last edited 1 year ago) (1 children)

Since a deck of cards can only be shuffled a finite number of times before they get all fucked up, the probability of deck arrangements is probably a long tail distribution

[–] ialvoi@feddit.de 5 points 1 year ago

The most efficient way is not to shuffle them but to lay them all on a table, shift them around, and stack them again in arbitrary order.