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The 3x+1 Problem [video]

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Re: The 3x+1 Problem [video]

#31
On the wikipedia page for the Collatz conjecture, there is a statement of the Collatz conjecture "in reverse" by growing a graph where R(n) = {2n, (n-1)/3} for n ≡ 4 mod 6, and R(n) = 2n for n ≡ 0,1,2,3,5 mod 6.

I wonder how many attempted proofs attempt to solve through this bottom up approach rather than top-down.

Re: The 3x+1 Problem [video]

#32
post #25

It sometimes amazes me how utterly random problems like this end up being their own fields in mathematics. This ended up being a pretty fascinating problem, but coming up with an arbitrary equation like this and then checking to see if it satisfies yet another arbitrary requirement doesn't seem very difficult to do. Am I completely missing something here?

> doesn't seem very difficult to do.

What makes you think this? You just had area experts tell you otherwise. Do you think that mathematicians are lying to you?

Re: The 3x+1 Problem [video]

#33
post #25

It sometimes amazes me how utterly random problems like this end up being their own fields in mathematics. This ended up being a pretty fascinating problem, but coming up with an arbitrary equation like this and then checking to see if it satisfies yet another arbitrary requirement doesn't seem very difficult to do. Am I completely missing something here?

The conjectures where the condition is very simple (Collatz, Goldbach, Fermat) but the proof is very elusive are not as common as you think.

Re: The 3x+1 Problem [video]

#34
post #25

It sometimes amazes me how utterly random problems like this end up being their own fields in mathematics. This ended up being a pretty fascinating problem, but coming up with an arbitrary equation like this and then checking to see if it satisfies yet another arbitrary requirement doesn't seem very difficult to do. Am I completely missing something here?

> doesn't seem very difficult to do. What makes you think this? You just had area experts tell you otherwise. Do you think that mathematicians are lying to you?

Mathematicians don't really claim that creating Collatz-like conjectures is difficult... they claim that proving Collatz is hard.

Re: The 3x+1 Problem [video]

#35

Earlier quoted context omitted.

> doesn't seem very difficult to do. What makes you think this? You just had area experts tell you otherwise. Do you think that mathematicians are lying to you?

Mathematicians don't really claim that creating Collatz-like conjectures is difficult... they claim that proving Collatz is hard.

I read "checking to see if it satisfies" as "proving", but I could be wrong.

Re: The 3x+1 Problem [video]

#36

I watched this the other day. I was left wondering one big question. Why does this need to be solved? Would that even change anything?

From reading other comments here, we need it because it inspires some people to become (better) programmers. :-)

Re: The 3x+1 Problem [video]

#40

I watched this the other day. I was left wondering one big question. Why does this need to be solved? Would that even change anything?

I think the answer is we _want_ to solve it.

Now the important question is why human beings want to solve this, and what exactly do human beings want.

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