hi all, have been holding out on you a bit while writing up other stuff on the blog. finally wrote up (coded) an idea that was nagging at my neurons for quite awhile. enjoyed building the genetic algorithm code to attack collatz from over a year ago, and was thinking of new approaches. since then, have a new bag of tricks such as 8 different hardness algorithms and it was always in the back of my mind to maybe return to a GA approach (now over a year old… time flies!).
wrote up a very complex/ ambitious GA approach within the last few weeks, and was running it for days at a time. it has many features and want to tout/ brag about them at some point, but that would take some more writeup.
was pondering however on why the GA was not really finding much improvement in solutions, and then zoomed into this particular issue that is very much worth sharing/ writing up/ detailing.
hi all. wired reported last dec that Craig Wright is Satoshi Nakamoto,[a6] and then followed shortly after saying he “might be a hoaxer”[a13] and motherboard concurred[a10]. there is now a lot of press coverage.[a] a new wave of press coverage just burst forth mainly following on the heels of BBCnews.[a3] however as that article mentions he seems to have convinced other elite bitcoin participants including Andresen and Matonis. he was promptly hit with a tax raid/ confiscation on his properties leading to the natural question of whether he would have been better off without “coming out the closet”.[a9] Nakamoto is thought to be worth about $400M in bitcoins, pseudonymous or not (assuming the keys arent lost!). wright is highly educated, referred to as “australian professor”; [a2] points out he has 2 phds and 8 masters degrees. he says he doesnt care if people believe him or not (but then what is his motivation in disclosure?). the pseudonymous Nakamoto has now been nominated for a Nobel Prize (economics).[a12]
bitcoin technology/ ideology is continuing to advance with some bordering-on-feverish advocacy [b] and more sober/ restrained but still favorable/ optimistic povs.[c] its apparently outperforming currencies based on stability and/or gains [b13]. a new australian political party claims it will improve democracy,[b14] another a “fairer world”,[b10] another wonders if it could replace SWIFT,[c6] even the new yorker looking at it,[c11] and a new coursera course.[c12] a very thorough free article/ analysis showed up in london review of books.[c9] early signs are it seems to evoke a large possible role, maybe bordering on radical/ revolutionary, in remittances[c15] and currency exchange[c16] which are a very big deal in international finance.
scale and misuse/ spam [d9][d10] aspects is an increasingly gaping, bordering on critical problem [d][d13][d15][d17] as exactly as forewarned by Andresen.[d14][d18][d8] bitcoin was not necessarily built to scale early on, although so far its still working. [d4] says its growing 25% faster than early internet growth! there are issues with forked code.[d6][d7] serious academic researchers (Cornell etc) have gotten into the analysis with proposed solutions.[d12][d16]
hi all. this continues/ advances the idea of analysis of bertrands postulate via a CS/ automated thm proving approach.
was looking for some existing code around the internet just to see what has been done. years ago, built multiplication circuits in SAT in both C (early 1990s) and Perl (2000s). alas, neither code is still available. (can really tell that you are all on the edge of your seat for that, lol)
there are some interesting papers on fast modulus calculation using highly tuned hardware such as FPGAs. this turned up in a google search pointing to DTIC, Defense Technical Information Center (US military!) and without a citable link on the site, in contrast to many other papers there.[a2][a3][a4]
➡💡❗⭐😮😀😎❤ hi all, more signs that physics is in a golden age esp in the area of quantum computing and quantum mechanics. EU just announced a $1B initiative to fund quantum computing. this combines with two other existing/ similar projects to analyze the brain and advance graphene technology/ understanding.[a]
the Manifesto[a1] is a sign that we are in dramatic times. you will not much hear scientists ever use the word Manifesto in their entire lifetimes. (marx was a rare exception.) another word that you will rarely hear scientists use is “revolution” but they are calling quantum computing the 2nd quantum revolution. as the chinese say, may you live in interesting times.
the announcement is utterly buried in a bureacratic document[a3] under the section “What is the financial impact of the Cloud Initiative? Where will the money come from and how will it be invested?” but Nature blared it anyway.[a2] apparently those bureacrats are a little gun shy after criticism of the $1B brain initiative as too ambitious or infeasible etc.
these are other big 2015 Q1 developments/ highlights. as usual its hard to keep up with lightning fast advances in this field. even the canadian prime minister is talking about QM these days.[b1][b2] DWave seems to be further confounding its critics with real, measurable performance.[b9][b4] somewhat similar to the EU announcement, chinas Alibaba announced a major QM research initative.[b8] they are intending to start out with encryption applications and hundreds of engineers, working toward QM computing technology.
hi all. was thinking really hard this week and then came up with some cool ideas about prime theorem proving and more advanced stuff. it all led back to an idea thats now over 2yrs old on this blog, “SAT induction”.[a]
there is a “hall of mirrors” type aspect of working on undecidable problems. there are many equivalent ways to formulate the same undecidable problem. its like a sort of core that crosscuts many fields, some unexpected. (lately there is some excitement that it shows up in theoretical physics etc).
however, think that there is a way out of the “going in circles” and SAT induction seems to be it.
consider what a proof of infinite primes would look like using SAT instances. the immediate idea is to use Bertrands postulate, also proved by Erdos in a surprising elementary proof. in SAT one might encode instances of the problem in the form “if there is a prime with n bits, then there is a prime with n+1 bits”. (alternative idea, very similar: “there exists a prime with n bits”.)
then one could lay out these finite instances of the infinite problem, say Fn for each n. this would lead to an array of SAT instances. (over 2 decades ago, built SAT circuits that factor numbers in binary. these circuits are similar.)
now, encode the SAT instances as graphs. and look for graph similarities between Gn and Gn+1. and then one is attempting to build graph Gn in terms of graph Gn-1. this is where the machine learning problem comes in. but for some problems, such as Bertrands postulate encoded, presumably there is not an extremely difficult solution that could be found by machine learning. one finds a systematic relation between Gn and Gn+1 and then one has to show that this also leads to the property that if Fn is satisfiable then so is Fn+1 (based on the graph relation). this reminds me of the concept of “satisfiable/ unsatisfiable core” that is being explored in SAT research, suspect it would be relevant.[c]
this is an almost radically new form of automated theorem proving that is not explored almost anywhere in the literature. and, it doesnt entirely sound like implausible/ inconceivable science fiction. there are decades of results in automated theorem proving and massive effort in the area, many different software algorithms/ packages developed and research programs (see eg wrt this problem [b]). but none come anywhere close to this.