collatz revisited

hi all… last months installment was all about pushing the pre vs postdetermined concept as far as it could go and found that it was stretched thin. in sharp contrast to the rosetta diagram idea, relatively ingenious code reveals the postdetermined region can have major divergences. this broke a major conjecture and has left me somewhat thoughtful at best and reeling at worst. candidly, am feeling sometimes like maybe all the powerful ideas that have been exercised have not made any dent whatsoever in the problem. so yeah, a darker mood, and am wondering sometimes if there is anything that can be proven about the problem at all.

didnt have a lot of immediate ideas. but as time goes on without much experimenting (a few weeks), am feeling maybe some ideas coalescing from the emptiness.

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collatz slope correlation revisited

the last installment found a way to construct large “ufos” in the postdetermined region and in crisp clinical terms refuted some longrunning hypotheses, in more informal pov “throwing a wrench in the works” of big overall proof strategies painstakingly built up over years and showing both limitations and strengths of the overall empirical/ datamining approach. however, maybe there is a silver lining; there was a larger hypothesis that maybe escapes largely unscathed, ie in more dramatic terms can yet be rescued amidst some of the substantial wreckage/ smoking ruins (aka “easy come, easy go”™). a recent experiment found that measuring “slope correlation” in the postdetermined region gives high adherence to linearity (ie close to 1) even as iterates get larger. this was discovered with bitwise optimization and never did convert that finding to the stronger/ more rigorous hybrid optimization and it was in the back of my mind to do that.

looked over the hybrid code and had the urge to refactor it. the bit vector initialization was servicable but really funky. also had an idea to extend vectors at a few bit positions at a time, not just at the msbs. also came up with the idea of a corresponding/ symmetric shortening operator.

the basic experiment here was trying to minimize slope correlation ‘sc’ for larger iterates. however the naive code simply found a significantly low ‘sc’ for some small iterates and then didnt get past those smaller iterates, the search got stuck so to speak. while this finding is consistent with the hypothesis my real question was what the trend for ‘sc’ was for higher iterates. so then bit the bullet and did multiparameter optimization for this hybrid code, something that is novel wrt prior code/ experiments also. the multiparameter optimization is based on gaussian normalization recalculated every 100 samples. the optimization is to push up ‘nw’ the iterate bit width and push down ‘sc’ the slope correlation. the code reaches very high iterate sizes ~4.5K and yet cant push down ‘sc’ more than ~0.9684. the multioptimization means that there are smaller iterates with smaller slope correlations, but the algorithm moves past those as pushed to search higher iterates. so this general observation/ trend still seems “robust”.


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collatz ufos

the ufos found in the postdetermined region earlier have been on my mind and they seem to be aptly named because they are mysterious. its a strange emergent pattern that doesnt seem to fit into a lot of other analysis. most of the findings/ “momentum” of analysis is that the 0/1-runs tend to crunch in most situations. the ufos found were not numerous so far and the few found took a lot of processing to discover, and also as mentioned there may be some flickering circumstantial evidence that they could be limited in some way eg maybe to lower iterates, although a lot of other experience with the problem would tend to push against that, ie nearly any pattern seen at small scales seem to be seen at larger ones—actually even more than that, that idea/ general theme is a big part of the underlying motivating ideology of computational investigation techniques.

an idea with the last exercise was hopefully to be able the synthesize ufo type patterns. but some of the findings of that experiment were that after picking a local ufo pattern at random it seems to be hard to create a long prior sequence to it although it also suggested thats not limited to ufos. that code could typically only find pre-iterations in small counts. it was searching for special pre-iterations that are smaller than the final/ target/ pattern iteration bit width, which is maybe not the same as ufos in the postdetermined region, but maybe the same difficulty still holds, it would be nice to better understand those interrelationships. “further TBD”

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collatz comb

this is an idea that occurred to me, building on last prior theme, to look into bit patterns connected to the subsequences of the parity sequence. for a glide there is a predetermined and postdetermined parity sequence. this looks at ‘w’ width bit windows over the iterate sequences, here w=10, for a single long trajectory. for the climb it is clear that the lsbs (in the iterate/ window) tend toward 1 odd. what about adjacent bits? this somewhat ingeniously shows they are indeed also tending toward 1s in 1st graph, ie the familiar 1-lsb runs/ triangles. the visualization is a tree diagram where the branches are 0/1 with 1 the upper and 0 the lower branch, and are easier to draw than one might guess; the code uses a “cumulate coordinate halving” idea. the left side is the climb/ predetermined range and the right side is the decline/ postdetermined range. color coding is by iterate # in the ranges. the 2nd graph is the windows over the msbs instead of the lsbs. close study shows some difference in the “ending” comb density from one side to the other with left side a little denser than right implying some kind of different distribution. the color distribution seems fairly even/ uniform.

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bitcoin 2018 highlights/ overview/ top links

hi all. bitcoin had a wild, rollercoaster year. it seems to have hit some massive threshhold/ tipping/ turning point last year. saw a bitcoin ATM briefly at a mall this year during the huge bubble in the 1st half. the ATMs spread all over the country, and theyre probably down to a fraction of what they were. a sign of the times.

it looks like its starting to level out/ stabilize by the end of the year.

a cohort at work told me that “bitcoin sounds like a science fiction novel at times”. have been telling others that. its really neat to have 1 thing in life that defies the status quo, expectations, groupthink/ conventional wisdom, the Establishment, “consensus reality” etc… do believe that in the 21st century cryptocurrencies will have an extraordinary far-reaching effect on human social systems eg govts, corporations etc… aka all The Powers That Be™.

there is some idea of a “Digital Autonomous Organization” emerging and its more than paradigm shifting, its revolutionary, a worldwide gamechanger.

am hoping it will involve building a more humane system. so-benignly/anodynely-called “late stage capitalism” is a house of horrors, increasingly nightmarish/ dystopian/ even verging on apocalyptic. adam smith would be horrified at the “invisible hand” turned to “iron fist”. and our political system has failed to reign it in, because its fundamentally compromised.

so actually a more humane system is increasingly no longer optional. the future of the human race depends on it.

one might think this is a “mere” emergent/ mindless accident or “unintended consequence”, but decades of study have revealed to me/ others there are hidden architects of our “neoliberal” system, and they seemed to know exactly what they were doing. it was designed to create maximal inequality because an equivalent synonym not well recognized is “power imbalance/ power seizure”.

bitcoin will force them out of the shadows (already happening to some degree) and a day of reckoning is coming. am foreseeing/ predicting some pain, possibly quite serious, but freedom and integrity will win out in the end.

bitcoin is one of the most extraordinary inventions of my lifetime. and have seen a lot by now, have been making some lists on this site. lived thru the dotcom era. bitcoin reminds me of the good old days. silicon valley bumper sticker: “please god just one more bubble!”

bitcoin is a foundation and many very dynamic innovations are being built on top of it, some of it can be seen at the moment but suspect there will be key advances that were not foreseeable by anyone.

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