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vzn
12:30 AM
@user58512 about what?
 
@vzn, hi!
I mean people actually chatting
 
vzn
pick a topic! btw you mentioned you read about collatz conjecture. what book?
 
I think it was called "the ultimate challenge" but it didn't tell me anything useful about the problem
 
vzn
what was the book about
 
recently I saw a paper by John Conway saying he thinks the problem is unsettleable meaning you can't prove it, you can't prove you can't prove it, and you can't prove you can' prove you can'tprove it, etc.etc.etc.
it was entirely about collatz conjecture, but it wasn't very interesting - no one gets any good results
 
vzn
12:32 AM
yes conway has an important related proof that a near variant of the problem is undecidable.
the book was entirely about the collatz conjecture?
 
yeah, I know about that but I really really think Collatz is provable
yes
I sort of think Conway just says that to make people want to prove him wrong - I doubt he really believes it..
 
vzn
conway has good reason to believe it. there is no reason for him to mislead.
where did you get the book
conway worked a lot with cellular automata. a cool mathematician.
ahead of his time.
there is actually a ton of research on collatz.
many interesting results.
 
it was just in my library, it wasn't very interesting though - I don't recommend it
really? I thought there literally zero results known about it
 
vzn
like a school library?
 
do you think it's unprovable
 
vzn
12:36 AM
college?
 
yes
 
vzn
cool found it here
had heard of lagarias before but didnt know about the book.
 
yeah as I said it was boring
 
vzn
think I gotta get a copy of this. not cheap though. $60
 
:(
 
vzn
12:38 AM
hey its an interesting problem. are you a math major or something
 
I'm telling you not to waste your money
yeah
I used to not care about it, but recently realized it is very interesting
 
vzn
why do you now think it is very interesting? and wouldnt the book be interesting if the problem is interesting?
fyi 1st read about it in this book:
anyway thx for the ref. gotta run for awhile. will check in l8r
 
well ok there is a chapter that is just an old paper by Conway explaining FRACTRAN... that chapter is great but you can just read that paper on its own
i'm telling you not to! :p
aw, bye then
I was looking at the goodstein sequence and how you prove it terminates with ordinals, I bet Collatz will be solved that way
 
vzn
how can you be a math major and not find lagarias book fascinating? maybe you are in the wrong field. but you changed your mind. so maybe you are in the right field :p
 
the other horse I'd bet on is trancendence theory
 
vzn
12:43 AM
I have some cool/remarkable code for this problem & mentioned it on my latest blog entry but nobody said anything =( ... do you like to play with code at all?
 
yeah I have been writing some code that does stuff with ordinals
 
vzn
this is one of my better rated questions on cstheory.se
5
Q: What is the "nearest" problem to the Collatz conjecture that has been successfully resolved?

vznI am interested in the "nearest" (and "most complex") problem to the Collatz conjecture that has been successfully solved (which Erdos famously said "mathematics is not yet ripe for such problems"). It has been proven that a class of "Collatz-like" problems is undecidable. However, problems that ...

what language are you using?
the answer to that question is cool
l8r
 
bye
 
 
1 hour later…
vzn
1:45 AM
@user58512 what language?
 
anything
I've used most
 
vzn
"stuff with ordinals" what was that written in
 
haskell
I also asked a question on the site about them math.stackexchange.com/questions/317797/…
 
vzn
@user58512 have an attack on collatz based on fsm transducers. got very interesting results recently.
 
huh cool
 
vzn
1:55 AM
possibly breakthru...
 
I have actually never seen transducers
finite state machines yes
what did you find?
 
vzn
ok well this takes a little while to describe. need to write it up on a blog.
basically, a hidden order that has probably not been discovered previously afaik.
it looks like its pretty solid to lead to an inductive proof.
found the "order" but havent taken the further step of crunching it into an inductive proof.
did you read the whole lagarias book?
 
nice - what do I need to know about tranducers to follow?
no
I don't think it's worth reading
 
vzn
transducers are actually very simple.
why not worth reading? do you find it interesting or not? cant follow you on that
the transducer approach to 3n+1 is fairly straightfwd but have never seen it written up in a paper or book. am thinking of asking on one of the stackexchanges about that.
 
it's just not got any results in it, just random things vaguely related and probabilistic "collatz is almost surely true" type stuff
 
vzn
1:59 AM
the transducer approach is mentioned in the wikipedia article but it doesnt have a citation.
 
(except the paper by conway which you can read without opening that book)
 
vzn
hmm ok.
on hard problems, whatever is known is a "result."
the problem has been open 3/4 century or so.
what did you like about conways paper?
 
everything.....
I mean the FRACTRAN one, not the "unsettleable" one
there was some reallycool bits in the unsettleable one, but mostly it was uncompelling
amusical sequence
which is another collatz like problem which seems even harder.. :D
ok really got to sleep, see you later
 
vzn
ok l8r (where are you?)
re probabilistic arguments yeah not fond of those either.
although they're regarded very highly in some key areas of TCS....
ps think this transducer idea might generalize to arbitrary problems... part of the idea in developing it...
feels like tip of very big iceberg to me.
collatz was just a simple "toy" problem to use as a proof-of-principle for the deeper principle.
 
2:24 AM
@vzn I get what that paper is saying and all the details and such, it's just.. there's no revelations in it, you know? Maybe it's just me, but it felt more like a glossary for the new computing frontier than any form of guide.
it talked about things we already know are important for parallelism, and talked about why (which we already know)
the hardware stuff I can't speak to though, I dont' know the first thing about actual hardware design. Perhaps some of that was relevant
their idea of "manycore" for instance, I guess in 2006 maybe not everyone knew that, but I feel like a lot did..
it's definitely rather obvious right now that the future is going to be hundreds, to thousands of cores where every operation possible is atomized
 
vzn
3:24 AM
@jimmy yeah ok what was once revolutionary becomes drab & conventional wisdom...
"obvious in retrospect"
2020 hindsight
 
3:52 AM
@vzn I just mean, I figure at the time it was pretty well known as well considering there's been a lot of work in the parellism space since even before then
 
 
17 hours later…
9:22 PM
hello
 

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