Computer Science

« first day (360 days earlier) ← previous day next day → last day (4059 days later) »

vzn

12:30 AM

@user58512 about what?

user58512

@vzn, hi!

I mean people actually chatting

vzn

pick a topic! btw you mentioned you read about collatz conjecture. what book?

user58512

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

user58512

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?

user58512

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.

user58512

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?

user58512

do you think it's unprovable

vzn

12:36 AM

college?

user58512

yes

vzn

cool found it here

amazon.com/The-Ultimate-Challenge-3x-Problem/dp/0821849409

had heard of lagarias before but didnt know about the book.

user58512

yeah as I said it was boring

vzn

think I gotta get a copy of this. not cheap though. $60

user58512

vzn

12:38 AM

hey its an interesting problem. are you a math major or something

user58512

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:

amazon.com/Unsolved-Problems-Geometry-Mathematical-Expositions/…

anyway thx for the ref. gotta run for awhile. will check in l8r

user58512

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

user58512

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?

user58512

yeah I have been writing some code that does stuff with ordinals

vzn

this is one of my better rated questions on cstheory.se

Q: What is the "nearest" problem to the Collatz conjecture that has been successfully resolved?

I 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

user58512

bye

1 hour later…

vzn

1:45 AM

@user58512 what language?

user58512

anything

I've used most

vzn

"stuff with ordinals" what was that written in

user58512

haskell

pastebin.com/raw.php?i=kgi6RNBP

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.

user58512

huh cool

vzn

1:55 AM

possibly breakthru...

user58512

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?

user58512

nice - what do I need to know about tranducers to follow?

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.

user58512

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.

user58512

(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?

user58512

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.

Jimmy Hoffa

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

Jimmy Hoffa

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…

user58512

9:22 PM

hello

« first day (360 days earlier) ← previous day next day → last day (4059 days later) »

all rooms