Room for heather and vzn

1:22 AM

@heather hi heather theres no rush on writing here, the room stays open 2wks without activity. learning involves tactical & strategic elements. theres an old quote by sun tzu on that. glad you are maintaining your interest. if you describe the symptoms of your code glitch, can give you hints. is anyone else in your school interested in coding? do encourage you to hook up with them. teachers/ other students etc... there are probably local clubs. what state did you say you were in again?

glad you liked the videos, just found em a few wks ago, delighted that there are few on collatz on youtube, am thinking there are probably other good ones out there, it would be fun to try to collect more... have long mused on an apparent connection between collatz problem & fractals & its great to see it fleshed out more. maybe the history of fractals needs to be rewritten a bit to include it... it looks like it was not realized to be fractal-like until relatively recently...

heather

@vzn, I'm in Iowa. I think it would be cool for me to make a video about the Collatz conjecture - that would be fun. Yeah, a lot of my friends are nerds like me and interested in coding. There is robotics club but I'm not able to take part due to transportation constraints. I do have an engineering/robotics class second semester that I'm looking forward too. Yeah, the fractals connection is really interesting.

vzn

@heather are your friends who are interested in coding m/f? feel free to invite em onto SE, the more the merrier :)

heather

@vzn, I already invited one or two, I don't know if they've joined. What do you mean by m/f?

vzn

male or female

heather

@vzn, a mix, honestly

@vzn, oh, I had one other interesting thing I wanted to ask you about:

So, I was messing with the Collatz Conjecture quite a bit, and I found an interesting thing that probably already has been found out but excited me.

vzn

1:32 AM

re m/f in CS, as you are presumably aware of, theres been a long gender disparity/ imbalance, have blogged on that, personally have not met many girls interested in CS/ math...

heather

Yeah, that makes sense.

vzn

@heather sure "ask me anything" :)

heather

=)

It all started when I was doing some number, 3 I think, on my paper in the middle of class and once it got to 16 I remember thinking how easy it was to get to 1. And then I thought further and realized, hey, it's because they are all even, and so you divide by two. And then I multiplied by two the other way and realized, hey, this is the sequence of powers of 2, with 1 being $2^0$! So all powers of 2 are automatically clear.

So then I was thinking further and I was like, ah, darn, how do you prove the inbetween numbers. And that's what I've been thinking about for a couple of days.

So then I was trying to look into other approaches. And I haven't been able to find many, I guess because people don't really publish failed proofs. So I was wondering if you had any pointers to help me get unstuck.

vzn

@heather exactly, all powers of 2 are "converging" and there are other sets of converging numbers, but nobody has found a pattern for all of them "yet"

heather

@vzn, what are the other sets?

vzn

1:36 AM

@heather there are some papers that prove formally "nearly all numbers chosen at random are converging" based on more definite criteria.

dont feel bad about being "stuck" because many top mathematicians in history have all been "stuck" (wrt it) also.

heather

@vzn, no, I know, I just somehow got it in my mind that I could figure this out. =)

vzn

the problem is ~¾century old, have worked on it myself off/on about ~¼century... o_O

heather

And I've been trying to think of new approaches.

Hey, out of curiosity, what do you do (as a job, I mean)?

vzn

IT/ java developer/ "software engr" finance business

heather

Cool!

vzn

1:39 AM

if you want to play around more "hardcore" you could try running some of my code (ruby)... its easy to run...

heather

@vzn, I saw your page. Is there a way to online compile ruby? I also wrote that python program and expanded it, and also a wolfram mathematica program.

vzn

@heather ruby is easy to install, yes think there may be a site that runs ruby online, trying to remember where that was, thought it worked for python code maybe...

heather

@vzn, oh, wait, was it maybe repl.it?

Yup, repl.it can do ruby. So that's good. I'll start running some of your programs!

vzn

@heather could have been it, rats should have bookmarked it, found some code & pressed a button & it seemed to run, cant remember...

@heather :) there is one piece of code in particular that creates large trajectories using different algorithms, demonstrates a lot of ideas

heather

@vzn, ok, I'll be sure to run them all. Do you think reading this paper and its sequel would be helpful?

vzn

1:43 AM

@heather lol have written dozens and dozens of pieces of code that will take you awhile :P

lagarias is a top author on this topic, glad you found him, yes thats one of best places to start is anything written by him

heather

@vzn, when I'm super excited about a topic, I spend hours on it. so I'll be glad to run all your programs. About Lagarias, he wrote a book but I could not find it for free online, sadly, so I probably will not be able to gain access to it.

But I will read his papers and whatever others I can find. =)

vzn

@heather lol just start by running one & dont get carried away to begin with, but thx for the great enthusiasm :P

there is another author that is coming to mind, douglas hofstadter, his books were some of the 1st read myself wrt CS etc as preteen possibly, they might engage you; many comp scientists have credited him as big influence.... CS can have an "alice in wonderland" flavor that he captured delightfully well...

heather

just found this super streamlined function for collatz: $F(x) = \frac{3x + 1}{2^{m(3x+1)}}$ where m(x) is the number of factors of 2 contained in 3x+1. I had an idea surrounding this but I can't remember it now, I'll think about it. I'll have to look up Hofstadter, he sounds interesting.

Got to go, see you tomorrow

vzn

seeya

have refd this problem myself in the blog as an interesting way of understanding collatz. take a look maybe, possibly/ apparently originated by hofstadter

MU puzzle

The MU puzzle is a puzzle stated by Douglas Hofstadter and found in Gödel, Escher, Bach. As stated, it is an example of a Post canonical system and can be reformulated as a string rewriting system. == The puzzle == Has the dog Buddha-nature? MU! Suppose there are the symbols M, I, and U which can be combined to produce strings of symbols. The MU puzzle asks one to start with the "axiomatic" string MI and transform it into the string MU using in each step one of the following transformation rules: == Solution == The puzzle's solution is no. It is impossible to change the string MI into...

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♦ Room for heather and vzn