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! > 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 > systems (like Maple, Mathematica, SageMath, Sympy, Maxima, R, GeoGebra, > etc.) is different, meaning that every time want to use a function or > equation in context of another CAS system, we have to manually enter or > rewrite the same formula in other syntactic rules, which is > attention+time-consuming. It's like having one address, and looking it up > on each different geographical maps application manually. It has to be > automated. Geographers, in the development of Wikipedia, had solved this > via a straightforward script, called GeoHack script > <https://geohack.toolforge.org/geohack.php?pagename=North_Pole¶ms=90_N_0_E_region:XN>, > tha gives a list of links to open geographic coordinates in a set of > different map providers. Can we have something like coordinates for > mathematical formulae? > 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. 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. Number theorists have catalogued > <https://oeis.org/wiki/Welcome#Welcome_to_The_On-Line_Encyclopedia_of_Integer_Sequences.C2.AE_.28OEIS.C2.AE.29_Wiki> > the > integer sequences by building "The On-Line Encyclopedia of Integer > Sequences" - oeis.org, so today, we can say "Positive Integers" is the > ID: A000027 <https://oeis.org/A000027>, or "Non-negative integers" is the > ID: A005843 <https://oeis.org/A005843>, and so on. > > However, in the rest of mathematics, physics, chemistry and lifesciences > this isn't the case. While we have repositories of genomes with each gene > ID, there seem to be no IDs for the important relationships like "Taylor's > expansion", "Ohm's Law", "Bayes theorem", "Combined gas law", "Pythagora's > theorem", "Relativistic rocket equation" or pretty much any other important > relationship, there's no ID or a coordinates for that formula. > > Do you know any systematic index or map of mathematical models online? > I am not aware of this, but I can see great utility in systematizing a library of useful functions/equations/formulae. Note one limitation of defining functions in terms of computability is that there will by mathematical objects not representable, such as continua, real numbers, infinities, infinite sets, etc. The best that could be done in that case might be a program that defines Pi as one that continues computing more and more digits of Pi. This also brings to mind the question of different algorithms that compute the same thing. For example, quick sort vs bubble sort are two well known sorting algorithms,. At a high level each does the same mathematical operation of sorting, but both are very different in terms of how they work and have very different runtime efficiencies. Does each algorithm get it's own coordinate/database entry? I think there's a strong case for that. Otherwise we might have only the shortest (but wildly inefficient) formula for computing Pi, rather than a slightly longer but exponentially faster formula, which is the one everyone will use and want. Jason What such map should be? Link to any ideas and projects about creating such > an map. > > Here is my thoughts on creating such a map: > https://wefindx.com/method/178001/ (should I repost it here?) > > What would be your thoughts? > > -- > Mindey > > -- > 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/69af170e-6913-439d-aaa6-5cd096f4fbaen%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/69af170e-6913-439d-aaa6-5cd096f4fbaen%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CA%2BBCJUgKuL8D0kS1qFpWVPJDe%2BeV9NB0-R_Xb6_gMHcNpJhSwg%40mail.gmail.com.
