On the "unreasonable effectiveness of mathematics" I approach this - as you know - ala *Hartry Field*:
https://as.nyu.edu/content/nyu-as/as/faculty/hartry-field.html https://en.wikipedia.org/wiki/Hartry_Field *Field holds that the existence of sets <https://en.wikipedia.org/wiki/Set_(mathematics)> may be denied, in opposition to Quine–Putnam indispensability argument <https://en.wikipedia.org/wiki/Quine%E2%80%93Putnam_indispensability_argument> of Quine <https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine> and Putnam <https://en.wikipedia.org/wiki/Hilary_Putnam>.* I have my own version: https://codicalist.wordpress.com/2018/08/26/mathematical-pulp-fictionalism/ On the simplicity of equations, if is hard to see how this equation is pretty: https://www.symmetrymagazine.org/sites/default/files/images/standard/sml.png (The equation for the Standard Model - can you count how many symbols/glyphs are there?) On the *connectional vs. equational paradigm* in physics: I think the connectional could profoundly change what is both practically and philosophically viewed as a model of physics, and that the equational is left behind in a past era of platonism. @philipthrift On Saturday, February 8, 2020 at 6:37:16 PM UTC-6, Russell Standish wrote: > > On Sat, Feb 08, 2020 at 06:44:16AM -0800, Philip Thrift wrote: > > > > Connectional physics > > > > Some have written on how the connectional (neural network) approach will > not > > rival the traditional equational ( https://inews.co.uk/news/science/ > > this-is-the-equation-stephen-hawking-wanted-on-his-tombstone-323699 ) > approach, > > but then why should nature necessarily be expressed in simple language. > > Both equations and connectionist models rely on finding and expoiting > patterns in nature. Why these patterns exist is really Wigner's hoary > old question of the "unreasonable effectiveness of mathematics". To > which, I would answer because of the Solomonoff-Levin theorem, > sometimes called the Occams Razor theorem. > > The equation approach is remarkably effective for some situations (eg > celestial mechanics), and before we had decent computers, we focussed on > domains where these models were effective. Now we find that some > models (think weather models, for example), where the computational > cost of the equation approach exceeds the computational cost of > throwing a neural network at it, allowing considerable speedup of > computing the model using a connectionist shortcut. I think it is > interesting from a having another tool in the toolbox, but probably > not interesting philosophically. > > > > -- > > ---------------------------------------------------------------------------- > > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders hpc...@hpcoders.com.au > <javascript:> > http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > -- 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/243bcdbc-f6e4-45ef-84db-99865a9e6666%40googlegroups.com.
