collatz undaunted

💡 this following code/ signal came up somewhat indirectly, incidentally, almost by accident. had an experiment to generate long ‘cgnw2’ glides with nearly ½ entropy to force them into the undifferentiated region; as explored last month the ½ density constraint is not sufficient for that, leading to long 1-lsb runs nearly ½ the iterate width. the ~½ entropy constraint works fairly well but then found small initial 1-lsb runs even in those. so wrote some code to cut off the leading 1-lsb runs of the glide, and analyze remaining glide carefully.

was looking for any kind of signals at all, lots out of the “bag of tricks,” also looking at 3-power sequence, and again it seemed to come up undifferentiated mush with lots of sophisticated analysis. there is a lot of signal found in prior 3-power sequence analysis but in general, a lot of it was related to Terras density glides. the hybrid approach tends to produce more “in the wild” glides. there is still some hidden order, maybe significant, in Terras glides that various experiments have isolated. but some, much, most, or nearly all this seems to melt away on “in the wild” glides.

notably, this hasnt been pointed out, but the (local) density metrics associated with the 3-power sequence naturally tighten even for random iterates. so its important to try to separate this “typical” tightening from “atypical” tightening, and thats not a trivial exercise.

but then started working on some “baseline” comparison ie control data, and then chasing down some stuff, lost my focus on the glides entirely. the simple way to generate this is via random ½ density iterates and then look at the drains. then started looking at features over these drains. some of this work has already been done, but it seems that some key signals have been missed. this straightfwd/ finetuned/ yet conceptually near basic code is on ½ density drains only.

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collatz outline

last month wrote out a remarkable outline. did anyone catch that? it seems potentially gamechanging and have been rolling it around in my brain, impatient to work on it, with a kind of background excitement + methodical intent bubbling/ mounting, a tricky combination to balance, maybe like walking a tightrope, and building the risky urge to rush. was very busy last week with a family visitor on a rare trip + other key family member mixed in too and couldnt get to it quickly. after thinking it over carefully the basic idea is a mix of 2 patterns that have already been explored: nearest neighbor plus the hybrid search algorithm. the NN algorithm handles creating/ matching a finite set of classes, and the hybrid search algorithm tries to find samples that “break” the classification, or improve it; those two sometimes go hand in hand.

the sample relationships are mapped out in a DAG like structure over the classes. the concept of breaking the classification (via optimization parameters) is still yet fuzzy and indistinct but some ideas have been laid out. my immediate idea was that classes with a high out-degree are more “ambiguous” and therefore less desirable. on further thought a key criteria is looking for loops in the DAG, which relate to indistinct feature classes creating an illusion of possible nonterminating sequences, although am not sure exactly/ fully yet how loops relates to class ambiguity (with outdegree a rough measure, or maybe others), it seems likely there is some relationship but its not immediately obvious.

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collatz standing on shoulders of giants (not!)

RJL has a nice new blog that cites collatz/ Taos recent work on it. wrote a comment on it and it led to a negligible # of hits. lol!

this is some recent hybrid code that has some minor improvements and didnt want to lose the changes. the basic idea was to start with limited 1-runs and see how much the trajectory size could be optimized. it has to throw away candidates that exceed the 1-run limit. the limit is determined by average statistics with ½ density iterates. the graph code is a little improved by numbering multiple graphs etc. it was found the prior “init” routines were not working as expected and/ or had low probability of creating sub-threshhold runs so they were adjusted.

(uh oh!) wordpress has a new editor. always run into funky quirks in the past, some of them nearly showstoppers eg incorrectly handling escaping of code blocks thereby screwing them up/ aka corrupting them every time saved. but maybe this one will be slightly better. you cannot imagine how many times have edited posts, saved them, then had to scroll back to the point where was previously editing. omg, who the @#%& asked for that? what an unbelievably tedious “feature” that shouldnt have gotten past UAT even one nanosecond and yet was default functionality for years, lol! (argh already found a code-set shortcut doesnt work, sigh) oh and it only took me about 30m to figure out how to insert the excerpt indicator… thanks guys! and it took yet more “fiddling” to find the rearranged controls for image embedding. welcome to 2020 the age of ubiquitous smartphones and endless fiddling, lol! Nero would be happy! also the idea of going back to old blogs to edit them, esp long ones, and trusting wordpress to “do the right thing” is a bit terrifying right now. welcome to modern software which is that weird mix of both extremely powerful and extremely fragile at the same time… its probably not unlike the ancient art of metal sword forging and the old word/ concept is called brittleness o_O

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collatz histogram discrepancy

based on 3mo 90d span, summer ⅔ over, it always goes in a blink. its like a colorful butterfly, bright, energetic, shortlived. have been telling people its like the Lost Summer this year. but as the infections continue to stretch out (two bigger states TX, FL esp feeling the pain), its almost turning into the Lost Year. the word unrelenting comes to mind as well as this old evocative analogy surveyed by RJL, 2009. but, as the japanese say, fortune and misfortune are like a rope twisted, or, the reverse side has a reverse side, so is that a con or a pro? coincidentally “unrelenting” is the kind of spirit/ discipline reqd to solve problems with world-class difficulty…

this is a quick take on the histogram discrepancy idea and already have new ideas, but its worth recording. my initial idea was to try to find expected values/ curves for histogram discrepancy of ½ density iterates. however, that is not a straightfwd undertaking, its maybe even a little daunting. theres not really a straight line, theres some curve, and curve fitting while very commonplace is still timeconsuming, and the other trickiness is that the curve would vary over iterate sizes. construct146 from last month show this a clear/ nonnoisy/ but shifting/ nonlinear/ nontrivial trend.

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collatz trials+tribulations

😎 ⭐ ❗ 😮 hi all. some rare, living on the edge, near-liveblogging this time around. am delighted to report, now typing this on a brand new chromebook, my 1st ever after eyeing them for years, just bought about 90m ago, my mask just taken off is probably still a little warm! this is a sort of modern miracle of technology. the netbook lives! scifi realized in my lifetime. it only took about 2 decades. or maybe ~1½. the latter is roughly how long google has been working on the software/ hardware; google apps predates chromebooks by maybe ½ decade? however the phrase probably originated in the mid to early 1990s from legendary Suns Gage hence now a sprawling 2½+ decade undertaking/ saga; dating it to the origins of the internet puts it at over ½ century of work!

so “standing on the shoulders of giants” in the 20th century, google is an amazing, astonishing company at times. and yes, think minimalist building an entire computer almost from software backwards, ie the browser, is an engineering genius masterpiece, and quite radically upside down in many ways vs prior history of PCs + Windows even Unix yet utterly inspired, brilliant. a complete rethink, a work of art,™ a thing of beauty.™ the extraordinary mounting share of chromebooks over the years and its now strong inroads into entire market segments eg schools attests to this. why buy one? its a little bit of a long story. so to speak. it will take me a little bit to unroll it all. feeling more than a little amped up/ excited right now! there are several headspinning elements going on all at once… (the box has the words in search of incredible on it outside/ inside…)

  • the model is an asus cx22NA. the list price of this machine is already remarkable at $200. it was only an extraordinary $140 at microcenter discounted $60, ie knockout 30% discount, what might be called dirt cheap. this is currently $50 less than best buy which has now been open only 1mo since shutdown. anyway my local best buy was sold out of the machines at the higher price! very strangely, asus does not currently list this model on their own web site! the wonders of modern supply chains/ merchandising systems never cease to amaze/ baffle me.
  • hooked up a microsoft USB wireless mouse/ receiver without any trouble. ran so fast without any setup screen/ msg, am not even sure the machine downloaded a driver…? plugged it in after the machine setup sequence but wondering if it might have worked even at beginning? for someone who used to sweat bullets trying to install linux on windows machines even in the mid 1990s with (early) device drivers one of the biggest grating achilles heels of linux, feel this is another extraordinary feat of modern technology/ cyber age…
  • ⭐ ⭐ ⭐ 💡 ❗ 😮 😎 grand finale magic trick viola— it has linux nearly built in! just bring up “chrome app switcher” and type terminal. it downloads quickly, for me within minutes. it seems to use about ~1.3GB (acc to “storage management/ linux beta” section on the settings screen). this apparently uses amazing new linux/ VM technology called crostini/termina running debian (stretch). it was announced ~summer 2019. although it showed up in new versions as early as late 2018 or even earlier in the summer of 2018 but was maybe not very supported/ widespread. my idea was to buy the cheapest chromebook and see if linux worked on it either recipe for disaster, or success! honestly this is nearly more than 80% of my motivation on this impulse buy and am kicking myself a bit for not trying this cool feature sooner! but yes, its cutting edge stuff conspicuously marked BETA. so “at my age” still living a bit on the wild side.

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