Finiteness assumption in explorable media - Revision history

Issa at 00:46, 17 July 2021

2021-07-17T00:46:55Z

Issa at 20:46, 30 March 2021

2021-03-30T20:46:09Z

Issa at 22:01, 2 March 2021

2021-03-02T22:01:04Z

Issa: /* See also */

2021-03-02T21:58:28Z

‎See also

Issa: /* See also */

2021-02-27T19:20:44Z

‎See also

Issa at 18:56, 27 February 2021

2021-02-27T18:56:14Z

Issa at 18:55, 27 February 2021

2021-02-27T18:55:53Z

Issa at 00:18, 22 April 2020

2020-04-22T00:18:29Z

Issa at 02:16, 20 April 2020

2020-04-20T02:16:11Z

Issa: Created page with "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 mat..."

2020-04-20T02:11:32Z

Created page with "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 mat..."

New page

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.

Examples:

*
* [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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 * [[Probability and statistics as fields with an exploratory medium]]
 * [[Representing impossibilities]]
 [[Category:Learning]]

← Older revision		Revision as of 20:46, 30 March 2021
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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.	+	'''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:

← Older revision		Revision as of 22:01, 2 March 2021
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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)?		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 [[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.

	==See also==		==See also==

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 * [[Video games comparison to math]]
 * [[Probability and statistics as fields with an exploratory medium]]
 [[Category:Learning]]

← Older revision		Revision as of 19:20, 27 February 2021
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	* [[Video games comparison to math]]		* [[Video games comparison to math]]
		+	* [[Probability and statistics as fields with an exploratory medium]]

	[[Category:Learning]]		[[Category:Learning]]

← Older revision		Revision as of 18:56, 27 February 2021
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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)?		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)?
		+
		+	==See also==
		+
		+	* [[Video games comparison to math]]
		+
		+	[[Category:Learning]]

← Older revision		Revision as of 18:55, 27 February 2021
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−	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.	+	'''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.

	Examples:		Examples:

← Older revision		Revision as of 00:18, 22 April 2020
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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.	+	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.

	Examples:		Examples:

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 Examples:
+* 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)