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Applications for Collatz's Conjecture? - Namir - 09-29-2014 03:55 AM
Joe Horn gave a short talk about the Collatz Conjecture (click here to view the YouTube video). My question to all the math-minded folks out there is, Are there any special or interesting uses for the Collatz sequences? Namir RE: Applications for Collatz's Conjecture? - Joe Horn - 09-29-2014 12:59 PM
(09-29-2014 03:55 AM)Namir Wrote: My question to all the math-minded folks out there is, Are there any special or interesting uses for the Collatz sequences? My personal opinion: Yes: entertainment. Wikipedia's article about the Collatz Conjecture mentions no practical uses for it, but I agree with the following essay from Time Magazine, 18 April 1988: Charles Krauthammer Wrote:It is the pride of political thought that ideas have consequences. Mathematics, to its glory, is ideas without consequences. “A mathematician,” says Paul Erdös, one of its greatest living practitioners and one of the most eccentric, “is a machine for turning coffee into theorems.” Mathematicians do not like to admit that, because when they do, their grant money dries up — it is hard to export theorems — and they are suspected of just playing around, which of course they are. RE: Applications for Collatz's Conjecture? - Thomas Klemm - 09-29-2014 04:49 PM
Charles Krauthammer Wrote:Erdös, an agnostic, likes to speak of God’s having a Book that contains the most elegant, most perfect mathematical proofs. Erdös’ highest compliment, reports Paul Hoffman in the Atlantic, is that a proof is “straight from the Book.” Says Erdös: “You don’t have to believe in God, but you should believe in the Book.” Martin Aigner Günter M. Ziegler Proofs from THE BOOK Cheers Thomas RE: Applications for Collatz's Conjecture? - Namir - 09-29-2014 11:26 PM
I was hoping for an unobvious (and indeed clever) connection between the Collatz sequence and, say, random number generation perhaps based on one or more of the following: 1. The length of the sequence. 2. The maximum value in the sequence. 3. The mean and standard deviation of all or some (like the upper quartile) numbers in the sequence. I am still hoping .... and thinking!!! Namir A mind is a dangerous thing ..................... to waste! |