
All numbers lead to one - zeratul
http://www.jasondavies.com/collatz-graph/
======
TheEzEzz
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.

~~~
paxcoder
I can't believe that. Unless you write a blog post with the "trip" detailed.
Pretty please ;-)

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drewda
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/>

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Swizec
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 ...

~~~
Someone
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?

~~~
granite_scones
Your analogy is off. With number theory, even if no one had an external use
for it, progress was (is) made, new theorems were proved, so time was not
wasted in that regard. The problem with the Collatz conjecture is whether the
effort spent on it is actually generating any insights into the problem.

~~~
Someone
But there is 'progress'. Looking at the Wikipedia page:

"The proof of the conjecture can indirectly be done by proving the following:

\- no infinite divergent trajectory occurs

\- no cycle occurs

thus all numbers have a trajectory down to 1.

In 1977, R. Steiner, and in 2000 and 2002, J. Simons and B. de Weger (based on
Steiner's work), proved the nonexistence of certain types of cycles."

I am placing 'progress' in quotes because one cannot measure progress in
maths. Before one has a proof, we cannot know whether existing approaches are
true dead ends or whether they just need that one extra insight.

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mdda
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.

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ciaranbradley
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 :)

~~~
Jach
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/>

~~~
ciaranbradley
Sorry, I mean a power of 2 :)

~~~
Natsu
It's very interesting to watch in binary, actually.

You first check if the LSB is 1. If not, you right shift it until it is. Once
the LSB is 1, you add it to itself shifted left by one bit, then increment.

Watching the bits go by and shrink over time reminds me of cellular automata
in a way.

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0x12
Someone claimed to have solved this:

[http://preprint.math.uni-
hamburg.de/public/papers/hbam/hbam2...](http://preprint.math.uni-
hamburg.de/public/papers/hbam/hbam2011-09.pdf)

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

