:arrow: :star: :star: :star: :!: :o :D :cool: hi all. Terence Tao, who is regarded as one of the greatest living mathematicians although of course not by himself (he does not even have a picture on his “about” page), has proved the Erdos Discrepancy Problem, fresh off a profile by the NYT.[a2] Tao has the distinction as being one of the very few mathematicians who has won the $3M breakthrough award, and also has said virtually nothing about it publicly (except at the awards ceremony). he’s too busy blogging about math ofc!
the EDP is a very interesting problem that relates in some sense to patterns in random walks. functions related to primes turn out to be basically very similar to “pseudo random walks”. this has been known for decades and there is a relation to the Riemann conjecture documented by Good/ Churchhouse in 1968.[g2]
the connection of hard math/ CS problems, and automated theorem proving, with analyzing random walks is a thread Ive been pursing myself over the last few years in my Collatz conjecture research. this gives me a nice moment/ opportunity/ milestone to write it all up.
its also another huge feather in the cap of the polymath project which was peripherally involved in the solution and a big triumph for cyber-collaborative mathematics.[b] a now-near-legendary almost-offhand musing in a blog comment led Tao in the right direction. “the devil is in the details…” :twisted:
Kalai is already casting around for the next “Big Kahuna”. any ideas? [b14] ;) :D
:idea: :idea: :idea: :!: :!: :!: :star: :star: :star: :o hi all, am coding/ working late on a weeknite which is uncommon for me these days but was fueled by some flashes of inspiration. was dinking around with some engaging/ fresh ideas and then came up and ran into this apparent ***BREAKTHRU*** so am not waiting to share it! (carpe diem!)
this code generates a random hard trajectory with glide length over 100, and then computes the 2nd (integer/ sequence) “derivative” (difference), and its running sum, which is always often less than or equal to zero!
following are two graphs of the 2nd derivative in red and the running sum in green, for the loge of iterates and the simple floor(log2(x)) function (ie binary width of the iterate), and it gets the same result on each. the loge results are very small decimal values, am betting right now that the floating point precision is not a factor in this finding and the resilience with the base-2 length supports that.
it seems likely this nanosecond that this property is extremely significant towards a proof and some kind of sequence/ series analog of the concept, “provably concave downward”!
hi all this is not a spectacular finding but it is the latest, seems interesting, and my last collatz post is starting to runneth over.
earlier there was some examination of the comparison of msb’s of 3n where n is the number of 3x+1 operations and the trajectory iterate and showed a remarkable correspondence, basically a correlation between them expressed/ tracked by a “plateau metric”. this analysis builds on that and wonders about how the plateau metric oscillates. the plateau metric moves “left or right” depending on the boundary between matching and unmatching msbs. but notice it never moved more than about ~10 increments at a time.
:o :!: :?: hi all. 1st heard this story in the online stackexchange physics chatroom in the morning, someone posted the foxnews link. then only a few hours later, it clearly went viral, partly after obama’s response in a twitter msg inviting Ahmed Mohamed to the white house.
so its now exploded all over cyberspace and bounced around. we have conspiracy theorists along with Richard Dawkins questioning Mohameds intent, and others questioning what he actually built. Mohamed has held a press conference with his parents and accepted the offer to visit the white house. he also says hes not returning to his old school. microsoft sent him a hacker package. hillary clinton, sarah palin, and mark zuckerberg have commented on it also. the topic showed up in the republican pre-debate.
hi all. Part II. within the last few months theres been a huge blaring in the media over AI vs humans due to a variety of factors. one of the chief factors seems to be Elon Musk jumping into the issue with his announcement of “committing $10M on new projects to control AI”. he does not seem to have a lot of history in this area but the media pays intense attention to this intense individual (who is supposedly the model for iron man’s Tony Stark). but a lot of his very high profile cohorts are blaring the issue also: Hawking, Gates, Kurzweil, Deutsch, and others. the warnings are quite dire, even verging on shrill, but somehow, find it hard to take all this entirely seriously myself. for example Gates and Musk seem to be far more of a threat to global wealth inequality. and, all due respect, but did Hawking even write anything on computer science in his life?[a]
another element of the discussion is that google is now realized to be working on cutting edge AI through all their acquisitions, and they announced the creation of an ethics board.[c] others are discussing the issue in a more reasoned way without so much “sky-could-be-falling” type urgency/ alarm.[b] it appears this issue is becoming subject to expert and scientific polarization much like global warming in some ways. there are many parallels, eg each issue is not expected to impact humanity much immediately but more so, possibly catastrophically, in decades, there is intense debate about the actual seriousness, etc.
also part of the zeitgeist, many numerous brain simulations in universities and industry are difficult to track and getting extremely advanced in some cases at least in the hardware capability (and the software/ intelligence gap is still the continuing challenge).[d]