The Map of Mathematical Models?
Mindey I.
Mathematical formulas used for science are a world-modeling tool useful in imagining and decision making. However, entering formula is different in each CAS 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, 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?
Number theorists have catalogued 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, or "Non-negative integers" is the ID: 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?
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
Jason Resch
How would we go about creating a referencible repository of mathematical models?
Mathematical formulas used for science are a world-modeling tool useful in imagining and decision making. However, entering formula is different in each CAS 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, 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?
Number theorists have catalogued 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, or "Non-negative integers" is the ID: 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?
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
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Lawrence Crowell
Tomasz Rola
> On Sat, Nov 26, 2022, 1:25 AM Mindey I. <min...@mindey.com> wrote:
>
> > 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
[...]
> mathematical formulae would be an integer encoding of the shortest known
> program for generating that recursively enumerable (computable) set.
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.
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:tomas...@bigfoot.com **
Tomasz Rola
> 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.
And you may also read Borges' "The Library of Babel" in spare
time... I am not sure why but I smell it, somehow.
https://en.wikipedia.org/wiki/The_Library_of_Babel