Difference between revisions of "Finiteness assumption in explorable media"

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Explorable and interactive media seem to bake in an assumption of finiteness, which makes it challenging to interact with the infinite and arbitrary objects that appear in mathematics.
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'''Video games work with finite and discrete objects'''. Explorable and interactive media (especially [[explorable explanation]]s) seem to bake in an assumption of finiteness, which makes it challenging to interact with the infinite and arbitrary objects that appear in mathematics. An extremely common move in a math proof is to say "Let x be an arbitrary element of X" where X is some class of objects of interest, typically infinite. There is no obvious way to allow "moves" like this in a game.
  
 
Examples:
 
Examples:
  
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* the explorables in https://explorabl.es/math/
 
* [https://www.youtube.com/playlist?list=PL5dr1EHvfwpNYbS_yqCZg30lEnpiEF6O2 The Witness] builds up complex puzzles starting from simple ones. But each puzzle is finite (finite board size, finite state space)
 
* [https://www.youtube.com/playlist?list=PL5dr1EHvfwpNYbS_yqCZg30lEnpiEF6O2 The Witness] builds up complex puzzles starting from simple ones. But each puzzle is finite (finite board size, finite state space)
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The kind of explorable medium that I'm interested in would somehow encode the proof-writing/proof-generating process so the user can do real math. But how do you prove things about e.g. an arbitrary compact metric space? How would you "explore" something that requires a proof by contradiction (which would require representing impossible situations)?
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The tricky thing about math is that you regularly have to deal with infinity, i.e. you need to figure out how to draw objects (such as sequences) which are not finitely representable. You could retreat to finite objects in fields like [[Probability and statistics as fields with an exploratory medium|combinatorics]] i think, but it feels more satisfying to come up with a general solution that would work in any field.
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==See also==
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* [[Video games comparison to math]]
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* [[Probability and statistics as fields with an exploratory medium]]
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* [[Representing impossibilities]]
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==What links here==
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{{Special:WhatLinksHere/{{FULLPAGENAME}} | hideredirects=1}}
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[[Category:Learning]]

Latest revision as of 00:46, 17 July 2021

Video games work with finite and discrete objects. Explorable and interactive media (especially explorable explanations) seem to bake in an assumption of finiteness, which makes it challenging to interact with the infinite and arbitrary objects that appear in mathematics. An extremely common move in a math proof is to say "Let x be an arbitrary element of X" where X is some class of objects of interest, typically infinite. There is no obvious way to allow "moves" like this in a game.

Examples:

The kind of explorable medium that I'm interested in would somehow encode the proof-writing/proof-generating process so the user can do real math. But how do you prove things about e.g. an arbitrary compact metric space? How would you "explore" something that requires a proof by contradiction (which would require representing impossible situations)?

The tricky thing about math is that you regularly have to deal with infinity, i.e. you need to figure out how to draw objects (such as sequences) which are not finitely representable. You could retreat to finite objects in fields like combinatorics i think, but it feels more satisfying to come up with a general solution that would work in any field.

See also

What links here