❗ 💡 😀 😎 ⭐ last month was quite a tour de force against collatz, the culmination of many months or even years of hard work and creative ideas, and many different approaches all combined (pyramid-like) to lead to very solid results verging on a “candidate solution”. another theme that was pursued earlier here are “adversarial algorithms” which has been used with great success eg by Google/ Deepmind against Go. the basic theme is “two algorithms competing against each other” so to speak. along these lines there is one final idea to try against the prior Collatz “solution”.
starting these blogs out, sometimes dont really know where they will lead ahead of time, but its a new month and a new pov. so the (“inherently a priori“) title is typically either “whats happening at the moment” or “some general/ larger theme intended to be pursued,” in this case the former. (now pondering that, am intending to revisualize the last collatz experimental angle in particular but on other hand, nearly entire theme of this overall research prj/ program in general could be said to be “revisualization”!)
at 1st was thinking maybe not all the major extra effort for polished/ pretty visualization was worth it at the moment, but couldnt resist, just wanted to see it, and was curious/ wondering about a few additional statistics. there was some real payoff by saving all the intermediate data and coming up with a major refactoring of the visualization code, ie decoupling visualizing and generation phases, and did a fairly massive rewrite without having to rerun the very expensive generation code. all easier imagined/ said than done! took quite awhile/ substantial effort.
the title is semi ironic, because it seems there is never a vacation with a hard problem. only a hiatus? did go on a trip last wk and had a great time, didnt think about math much at all! which is a good thing! work/ life balance and all that! although for some, math is life! would go into more juicy detail for all my loyal readers (like last years epic saga) but alas, havent heard from any of you in ages so not sure you really exist 😳 😥
just picture me in tattered/ dusty/ dirty clothes on the side of a busy cyberhighway, weathered/ sunburned/ wrinkled/ unshaven skin, sitting in the blazing hot sun with a cardboard sign scrawled with marker, million-mile staring-into-distance plaintively…
will write for comments! 😐 😳 🙄
in contrast to sometimes having no idea about future directions with these posts, the last blog gave some excellent themes/ ideas for research directions and this new post. to put it in the vernacular, am finally really on a roll! aka/ reminds me of “hot hand!” and yet also lately feeling really strong flow in more ways than 1! 😮 😀
💡 ❗ ⭐ this code has a lot of moving parts and took quite awhile but is also a culmination of many previous ideas. it has the same distribution generation mechanism as last run (slightly modified/ adjusted), but its a 1st cut on evaluating the significance/ accuracy of the MDE/RR model as a predictor of trajectory length. the better the accuracy of its modelling, the more “plausible” a (“analytic”!) model it is and viable for exploiting for further derivations.