All numbers lead to one

#1

Post by zeratul » Tue, Oct 04, 2011, 5:24 PM UTC

Re: All numbers lead to one

#2

Post by drewda » Tue, Oct 04, 2011, 6:47 PM UTC

FYI, Jason Davies has been doing great work with Mike Bostock on the d3 visualization library, which is used in this example: http://mbostock.github.com/d3/

Re: All numbers lead to one

#3

Post by ciaranbradley » Tue, Oct 04, 2011, 6:56 PM UTC

Cheers for this, I didn't know the mathematical basis for it, but our eldest child brought this "puzzle" home for year 7 homework a while ago. We spent the weekend experimenting with loads of bits of paper on the floor coming to the conclusion that once you land on a base 2 number, you have a path directly back to 1.

He learned binary in a weekend and we had a fun few days hacking math :)

Re: All numbers lead to one

#4

Post by Jach » Tue, Oct 04, 2011, 7:16 PM UTC

ciaranbradley wrote: post #3

Cheers for this, I didn't know the mathematical basis for it, but our eldest child brought this "puzzle" home for year 7 homework a while ago. We spent the weekend experimenting with loads of bits of paper on the floor coming to the conclusion that once you land on a base 2 number, you have a path directly back to 1. He learned binary in a weekend and we had a fun few days hacking math :)

Don't you mean on an even number? Or just a power of 2? Or are you talking about a base 10 number that's composed of all 1's and 0's? (All natural numbers are base 2 numbers...)

Also related: http://xkcd.com/710/

Re: All numbers lead to one

#5

Post by mdda » Tue, Oct 04, 2011, 7:24 PM UTC

This is a simple visualization of http://en.wikipedia.org/wiki/Collatz_conjecture - and from the Wikipedia article :

Paul Erdős said, allegedly, about the Collatz conjecture: "Mathematics is not yet ripe for such problems." and also offered $500 for its solution.

Which is a very strong indication that this will be a tough nut to crack... Even if many people are given it as year 7 homework.

Re: All numbers lead to one

#6

Post by Swizec » Tue, Oct 04, 2011, 7:33 PM UTC

If you do this for long enough eventually all your friends will stop calling to see if you want to hang out ( http://xkcd.com/710/ )

I've read somewhere that no other mathematical problem in history has wasted so much time of such brilliant minds. I wonder if it's true ...

Re: All numbers lead to one

#7

Post by 0x12 » Tue, Oct 04, 2011, 7:48 PM UTC

Someone claimed to have solved this:

http://preprint.math.uni-hamburg.de/public/papers/hbam/hbam2...

Then withdrew it, and is currently busy trying to fix the problem.

Re: All numbers lead to one

#8

Post by ciaranbradley » Tue, Oct 04, 2011, 7:51 PM UTC

Jach wrote: post #4

ciaranbradley wrote: post #3

Cheers for this, I didn't know the mathematical basis for it, but our eldest child brought this "puzzle" home for year 7 homework a while ago. We spent the weekend experimenting with loads of bits of paper on the floor coming to the conclusion that once you land on a base 2 number, you have a path directly back to 1. He learned binary in a weekend and we had a fun few days hacking math :)

Don't you mean on an even number? Or just a power of 2? Or are you talking about a base 10 number that's composed of all 1's and 0's? (All natural numbers are base 2 numbers...) Also related: http://xkcd.com/710/

Sorry, I mean a power of 2 :)

Re: All numbers lead to one

#9

Post by Someone » Tue, Oct 04, 2011, 9:45 PM UTC

Swizec wrote: post #6

If you do this for long enough eventually all your friends will stop calling to see if you want to hang out ( http://xkcd.com/710/ ) I've read somewhere that no other mathematical problem in history has wasted so much time of such brilliant minds. I wonder if it's true ...

For any mathematics problem, we can never know whether studying it is wasted time.

For example, look at number theory. For centuries, it was without utility. Then, suddenly, it got practical applications, making all the time spent on it wasted time :-)

Similarly, the Collatz problem may seem useless enough, but what if, in a few millenia, someone applies it to physics or to sociology?

Re: All numbers lead to one

#10

Post by TheEzEzz » Tue, Oct 04, 2011, 10:08 PM UTC

The Collatz Conjecture nearly killed me. Literally.

For three months I was consumed with the conjecture. I slept, ate, and breathed it. I was sure I was on to a successful line of attack, using some sort of inverse tree approach mixed with a density argument. One day, while working on the conjecture as usual, I heard cars honking but couldn't see what the fuss was. I turned around and realized I had just ran a red light at a busy intersection going 40 MPH.

I haven't thought about the problem since.