On Sat, Nov 26, 2022 at 08:27:54AM -0500, Jason Resch wrote: > On Sat, Nov 26, 2022, 1:25 AM Mindey I. <min...@mindey.com> wrote: > > > *How would we go about creating a referencible repository of mathematical > > models?* > > Great idea!
Indeed. Please do not read my remarks below as downplaying. The idea is fine, but there is stack of problems to actually doing it. Some are because the science of computation/calculus is hard. Some are because difficulty when group of N humans tries to work together grows like, at best, a(t)*N*N. The a-factor is small first, but can quickly increase, depending on time t and size of group N. In non deterministic way. > > Mathematical formulas used for science are a world-modeling tool useful in > > imagining and decision making. However, entering formula is different in > > each CAS <https://en.wikipedia.org/wiki/Computer_algebra_system> software [...] > The closest thing I can think of to an objective coordinate system of > mathematical formulae would be an integer encoding of the shortest known > program for generating that recursively enumerable (computable) set. If you are thinking about goedelization, please bear in mind those numbers grow frantically big, for even the shortest sentences... Also, (big) numbers are cumbersome to parse for a human. They are cumbersome to paste in an email - "the formula 9447...(put 600 digits here) is better than formula 4809...(put 601 digits here)". 600 decimal digits is less than 2000 bits, which, if one uses it with Baudot code, will give a sentence about 400-characters long. Some systematic way would be required, sure. But so would be some systematic way to translate the integer into human readable program formula. This opens a can of worms. To assign symbolic names to formulas - say, "bubble sort 3" for shorter implementation than "bubble sort 2" would require a committee of a kind. A committee of a kind means a centralisation of a kind and from this follows an organisation of a kind... With groups of interest... of a kind... One way to do it in decentralised way, would be to have namespaces. There would be a formula named "20221127/Resch/Jason/sort/bubble/3". It would still require some kind of central point, where you would have to register, supposedly today, to receive unique id for your personal namespace - "20221127/Resch/Jason". Inside this namespace, to each his or her own (with perhaps the requirement, that at least first level of names is standardised, hence ".../Resch/Jason/computer-science/sorting/bubble/3"). And let users sort them out, the best of them. Which is another can of worms... because so few users have much clue about anything, or will think calling "Ohm's/law" as "Pinky/pony/electric" to be good way of solving a problem with calling formulas. And guess what, they would have about few millions of supporters. Oh, and speaking of algorithms and programs, those are usually written in some language. Even as simplified as so called pseudocode. There is many of them and each has their group of vocal supporters. This discussion group is relatively unknown to wider masses, but just wait until "codahs" learn about dispute, they will come in hundreds to prove their point. BTW I am huge supporter of LISP-based pseudocode. It is easy to parse, I mean, it is possible to write parser on something as small as programmable calculator (with few kilobytes of program memory), it will be possible to parse it a thousand years from now, and there is mathematical foundation to this pseudocode, called lambda calculus. But I am good with any other form as long as there could be translation to and from LISP. And I promise not to tell anybody about this discussion group :-) . > Note that there is no way to prove a given known shortest program is indeed > the shortest possible program, so the online database that tracks these > must be flexible enough to adapt to new discoveries and update references > to the formula coordinates when a shorter one is discovered. AFAICT even comparing supposedly "same" programs (implemented by two people etc) is very tricky. Proving that supposedly same programs actually perform in the same manner, or at least give same answer for same arguments? Haha. Very funny. -- Regards, Tomasz Rola -- ** A C programmer asked whether computer had Buddha's nature. ** ** As the answer, master did "rm -rif" on the programmer's home ** ** directory. And then the C programmer became enlightened... ** ** ** ** Tomasz Rola mailto:tomasz_r...@bigfoot.com ** -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/Y4LdBA5Tf6tHGTFP%40tau1.ceti.pl.
