But That’s Certainly Irrational

There can be an infinite number of polygons, but only five regular solids.  Four of the solids were associated with earth, fire, air and water.  The cube for example represented earth.  These four elements, they thought, make up terrestrial matter.  So the fifth solid they mystically associated with the Cosmos.  Perhaps it was the substance of the heavens.  This fifth solid was called the dodecahedron.  Its faces are pentagons, twelve of them.  Knowledge of the dodecahedron was considered too dangerous for the public.  Ordinary people were to be kept ignorant of the dodecahedron.  In love with whole numbers, the Pythagoreans believed that all things could be derived from them.  Certainly all other numbers.
So a crisis in doctrine occurred when they discovered that the square root of two was irrational.  That is:  the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were.  “Irrational” originally meant only that.  That you can’t express a number as a ratio.  But for the Pythagoreans it came to mean something else, something threatening, a hint that their world view might not make sense, the other meaning of “irrational”.
—    Carl Sagan
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On This Day In:
2023	A Dash Of Yellow
	In The Grand Scheme Of Things…
2022	Suggestions (The Order Of Precedence Is Optional)…
2021	But That’s Certainly Irrational
	Just Goin’ To My Room (In My Room)
2020	The Butterflies Are In Trouble
2019	The Deep Center
2018	Oh, Heaven (Too)
2017	Now Pausing Makes Sense
2016	Just Spicy
	Only One Part
2015	Positive Acts Of Creation
2014	One Thing Is Clear
2013	Corrections
	See Greatness
2012	Gemutlichkeit
2011	Back On The Asphalt

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