hi all, have gotten a sizeable spike in hits over the last week on collatz related blog posts! it seems to be traceable to an old reddit page on collatz from jun 2015 by
level1807 talking about using a new feature in Mathematica to graph the collatz conjecture. profiled that finding/ graph myself here in this blog around that time. not sure how people are finding that page again, but googling around, it looks like this graph is now immortalized in a mathematical coloring book which was announced in a recent March 28th numberphile video getting just a few thousand short of ~200K hits at the time of writing this (maybe a few ten thousand in a few days!), and profiled the same day by a popular mechanics blogger weiner under the title of the Sea Monster. so, essentially viral, but putting the bar a little lower for mathematics! and as for the “elephant in the room” much to my amusement/ chagrin the video never once uses the word fractal (bipolar moods again attesting to a longterm love-hate relationship, not to mention the other (mal?)lingering facet of mania-depression!).
and this coincides very nicely with my announcement of the following. have been making some big hints lately and think finally have a Big Picture/ Big Idea from the most recent experiments. (yeah, no hesitation in the open Big Reveal on a mere blog after years of a similar routine…)
what is looking very plausible at this point is a formula in the form of a matrix difference equation/ matrix recurrence relation. the devil is of course in the details, but heres a rough sketch. prior experiments have some “indicator metrics” that are based mainly on binary density of iterates, and other “surface-like” aspects such as 0/1 run lengths etc… and its now shown that these are strong enough to predict future iterate sizes (10 for now) with some significant degree of accuracy.
hi all. have blogged before here (admittedly, enthusiastically, even ebulliently) on the “digital physics” concept, an enamoring idea (for some!). recently within last few weeks and last year there seems to be substantial new interest and developments even in “semimainstream” physics, and now even the mainstream media is in a semi-lather over close topics. (skeptics will ofc argue the word “semimainstream” sounds something like “semipregnant”!) its hard to keep up! there are many different angles of povs, events, personalities, etc… this post attempts to collect and summarize some of this and bang it all into a semicoherent story (as much as such a thing is possible). some old but evocative buzz/ magic words thrown around about internet expansion into multiple industries come to mind: consolodation/ convergence…
to start, these ideas are now going under the headline of the “holographic universe/ principle”[a2] or “simulated universe/ hypothesis”[a1] concepts. they are interconnected in major and/ or subtle ways.
mentioned Aaronsons recent blog[i3] on subj citing Hossenfelder [i1][i2] in a recent near-throwaway comment in the SE physics chat room “hbar”[a5] to a new accomplished user BenNiehoff (phd KU Leuven working on string theory with 9 papers on arxiv!). hes met a lot of famous physicists at conferences personally eg Susskind, Zee, Green, Schwarz, and Witten and other famous theorists. am trying to recruit him for a guest session in our elite and popular series, but thats another story!
laid out some of the basic concepts/ “pros” of the simulation hypothesis ideas incl/ eg longtime endorsement/ driven pursuit by nobel prize alumnus ‘t Hooft, which thought were not generally very controversial, but the room denizens/ regulars reacted quite adversely-bordering-on-negatively, with some really stinging retorts! guess those big fat shiny nobel prizes and the proverbial “trip to stockholm” just aint what they used to be! Ben expressed his disinclination and looks like they all smelled blood in the water & went in for the kill! 😮 😦
Ah, as usual you have no actual argument to make, I should’ve known. —ACuriousMind [a6]
vzn; do you have any mainstream views? —John Rennie [a7]
hi all, two recent high profile events caught my eye, #1 the meltdown of Milo Yiannopoulos and #2 pewdiepie losing a lucrative contract with Disney for his controversial youtube content. these seem to me to be strongly reflecting current cyber zeitgeist in various ways. so, a release of another/ the latest huge batch/ selection of items/ headlines.
in case #1 its “live by the sword, die by the sword”.[a] yiannopoulos reminds me of british commentator piers morgan who made a big splash years ago with his biting/ acerbic analysis of america, but seemed to burn out from his high profile/ near-trollery. did not track milo much at all but his downfall splattered very heavily across sites regularly browsed. it seems like a case of “troll culture”. theres also connections to the video game area. and of course, intense connections to current politics/ Trumpism which is still impacting cyberspace with roiling waves.[i]
this tightens the screws some )( on the prior findings and show they generalize nicely. prior analysis seems very solid but there is always the shadow of question of bias in the generation algorithms which start from small seed sizes and build larger ones out of smaller ones. an entirely different strategy for generating sample seeds is used here based on a genetic algorithm. the idea is to start with a fixed bit width and alter the bits in it just like “genes”. fitness is based on glide length (or equivalently ‘h2’ for a constant seed width). it starts with 20 random parents of given length. there is 1 mutation operator and 2 crossover operators. 1 crossover operator selects adjacent/ contiguous bits from parents at a random cutoff/ crossover point (left to right) and the other just selects bits randomly from parents not wrt adjacent/ contiguous position.
fit24 is again used for the linear regression fit. these runs are for 50, 80, 100 bit sizes and ~200 points generated for each. 50K iterations.
because of declining # of points for higher widths, this is circumstantial evidence that as widths increase long glides (relative to width, ie ‘h2’) are (1) increasingly hard to find and/ or (2) rare. these two aspects interrelate but are not nec exactly equivalent. hardness of finding seeds with certain qualities ie computational expense does not nec mean theyre rare. an example might be RSA algorithm. finding twin primes is somewhat computationally expensive (although still in P) but theyre not so rare. technically/ theoretically rareness and computational expense are related through probabilistic search aka “randomized algorithms”.
hi all, what a blur its been since the last cybersec post here. US obama admin announced sanctions against russia in response to intelligence agency consensus that Russia hacked US election as part of state govt efforts, and intended to get Trump elected. wild info! the repercussions continue to fall out, it looks like congress will be all over this issue for months to come at least, and maybe years.
the trump admin hostility toward the intelligence agency apparatus is remarkable/ extraordinary/ unprecedented. when the mainstream media starts to talk about the “deep state” you know that its a new world we’re living in.
the actual evidence that russian govt was involved in the hacking does not seem all that strong to me, it appears to be more assertion by widespread consensus, which is questionable to say the least.
this stuff hit the Full Trifecta over Obama,[d] Trump,[c] Putin[e] / Russia.[b]
theres a lot of continuing headlines on fake news, and it looks like maybe the concept is not going to go away with the election and is a new concept in the collective consciousness.[f] apparently a permanent gamechanger.
apparently as stated earlier, the age of cybersecurity/ infowarfare is on us in full force. dizzying times we live in at times so to speak.