summer fun/break/vac & the may collatz breakthru

stock-photo-9964394-technology-breakthroughhi all. hows your summer goin? have had a busy few wks doing fun summer stuff & my favorite nonwork activities like concerts, movies, bicycling, rollerblading, reading, playing the harmonica etcetera. hey computer science theory is way cool but ya gotta be well rounded right? it would be fun to do it all the time, but Id have to be a machine or robot myself to pull off that stunt.

and then of course theres projects that blur the line between work and play, like my decades-long quest to hack the stock market with statistics, AI, datamining, etcetera.

have noticed in my life that sometimes when one doesnt always think about problems directly, sometimes one gets ideas in the meantime, in the “space between”. this has been backed up by recent psychological research that says daydreaming actually serves an important mental function!

life has to have punctuation marks just as it has sentences and words, right? this is also called “the lateral approach” or “lateral thinking”. in zen buddhism there is a lot of study of—even fascination with—space, or emptiness, or the void, etcetera, and its significance in our lives. the classic analogy is that of the bowl, which derives its utility exactly by encompassing/enclosing space effectively.

for many summer is like a “space between” hard work, as we all take vacations, slack off a little, enjoy all life has to offer.

for those of us who work on very hard problems, its somewhat easy to become obsessed. nice summer weather and vacations give us a chance to realize that even the greatest theoretical breakthrough of centuries is a fundamentally different sphere than our daily, human lives, ie “work life balance”, “quality of life”. as the saying goes, its not an either-or proposition. I saw someones philosophy of life expressed delightfully briefly as “more play, less work”. words to live by.

* * *

about 2mo ago back at near the end of may, I think I finally had a breakthrough on a problem Ive worked on and off for about two decades now, the collatz conjecture. I put up a page on some of my Collatz code a few months ago, advertised it a bit in comments in other blogs, and it gets hits, but have gotten zilch response as far as comments/feedback. ouch! this is a very famous conjecture in number theory and computer science, but sometimes it seems paradoxically the more famous a conjecture, the fewer people who are directly interested in/engaged with it.

number theory was one of my 1st theoretical loves, I can honestly say I learned about number theory before I learned about Turing machines, although not that far apart. have been collecting a few of the links on the recent twin primes breakthru by zhang (congratulations!), have my own minor bkg take/angle on that & am intending to write them up in a brief blog.

I was fascinated as an early teenager or possibly preteen about FLT, fermats last theorem. I wrote up a facetious todo list as a freshman in college and one item was “prove FLT”. amazingly it was proven only a few years later as I graduated as a senior. the sense of excitement in the community was really heady and enthralling. NYT article on the subject of Wiles historic breakthru. was it on the front page? I do believe so.

so years ago I submitted an econophysics paper to arXiv, and it got rejected by David Mermin as I recall as not “on topic” for any physics sections. ouch! that has always hurt. and so Ive been toying with the idea of writing up in LaTeX and submitting a new Collatz paper to arXiv. but, it can be a bit of a hassle if you arent “affiliated with a university” which yrs ago was determined by the “.edu” on your email addr. however, from some comments on stackexchange, my understanding is that maybe the CS sections are not quite as strict as the physics sections.

but, it will take me quite awhile to write up a LaTeX paper. LaTeX typesetting is beautiful but takes quite an effort to generate. its almost like/analogous to installing a compiler and creating/developing a tested/debugged program in it. am thinking maybe an HTML paper would be better, but I dont know of any examples of those on arXiv. has anyone else seen one?

actually though I have to do some work to convert this amazing Collatz pattern that I discovered into a proof. finding the pattern is probably more than half the battle there. but the conversion of the pattern to a proof is quite nontrivial. I was thinking it would be fun to “outsource” the proof after the pattern is found, and maybe someone else could build the proof.

on the other hand though, I would probably not get [much?] credit for the proof in that case, even though imho the detection of the pattern is quite significant and took many years of trial and error to find [but the final form/description is quite brief]. math can be like that. “asymmetric” in various ways such as effort vs size of proofs, etcetera. [one of the deep/surprising/mysterious aspects that has always totally fascinated me since the beginning.]

but to even get anyone with enough expertise to look at the pattern seriously looks like it would be quite unlikely for me, even with all the networking I do regularly in cyberspace:

  • comment on other blogs eg Tao’s collatz page
  • comments/chats references on stackexchange
  • polymath other proposed project page

so did attempt for several months and various ways to get anyone knowledgeable to show up here with a comment on Collatz, but so far, zilch. ouch!

so I am seriously toying with this new idea of just simply *posting the preliminary pattern/result* to my blog! the odds of anyone recognizing its extraordinary significance without further effort on my part [ie a paper describing it in more detail, and possibly nothing less than the complete proof] are probably nearly infinitesimal. in other words I can post the partial results and intermediate progress with almost no fear whatsoever that anyone can/would “scoop” or “steal” it from me [what does that mean, anyway? and why does it or would it bother me anyway?]. nobody reacts much to this blog so far in comments, so I can use this to my advantage.

in fact am thinking of posting regular updates on my progress on getting anyone to pay any attention at all to these results. this could be an interesting experiment, what does it take to get anyone else to engage with a breakthrough new mathematical result in cyberspace, with only cyberspatial efforts/actions [eg posting to blog, publicizing elsewhere, etc]? in a way, an end goal of mathematics is to *communicate* ideas. it would be an experiment in mathematical memes with cyberspace as the propagation medium.

my hope would be that I could communicate this cool new breakthrough [that is really my ultimate objective], without going through all the trouble to write an entire paper but am not holding my breath on that one! in fact based on all my experience with cyberspace, I think there is a solid possibility that even after I published a paper with a correct proof of this important number theory problem, and that the proof would likely have substantial, possibly even revolutionary implications outside of merely this proof, that nobody would pay much attention for quite a bit of time…

how long will it take? how much effort will be required? what twists and turns will ensue on this road to somewhere-or-other? hope you join me on this journey into terra incognita! if/when you reply, then it will actually exist! otherwise, its just a floating message in a bottle in the ocean of cyberspace! for a cyberspace meme to propagate, if it generates comments, “therefore it is”!

a. collatz

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