"The Pythagoreans, who saw number as a guide to reality, noticed that music could be described in mathematical terms, since the intervals between notes correspond to the ratios between strings. "
Did Pythagoreans see numbers? Or did they see ratios?/1
Did Pythagoreans see numbers? Or did they see ratios?/1
https://twitter.com/firstthingsmag/status/1435680587235344386
"But this is to misunderstand the Greek preoccupation with number and harmony."
Were the Greeks preoccupied with number? /2
Were the Greeks preoccupied with number? /2
"This thought shows up in the cosmology of Plato, who was a Pythagorean at heart. The sign over his Academy bearing the motto “Let no one ignorant of geometry enter” is apocryphal but apt."
Was geometry of the Ancient Greeks algebra? /3
Was geometry of the Ancient Greeks algebra? /3
Pythagorean theorem
The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
"Numbers don’t enter the picture, and the proof is done geometrically."
/4
The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
"Numbers don’t enter the picture, and the proof is done geometrically."
/4
"A modern text that formulates the Pythagorean Theorem by saying “a right triangle with sides a, b, and hypotenuse c satisfies a2 + b2 = c2”
The theorem would no longer describe visualizable relationships among geometric figures. /5
The theorem would no longer describe visualizable relationships among geometric figures. /5
"Ancient mathematicians devised an elegant way around this by appealing to the notion of ratio. For us, the proportion stating that “the ratio of 2 to 5 is the same as the ratio of 4 to 10” can be expressed as the equation “2/5 = 4/10.” /6
The book is very thick and is a guide for non-experts to understand a different way of thinking, to trace the origins of modern scientific thought. /7
thenewatlantis.com/publications/m…
thenewatlantis.com/publications/m…
It is extremely hard if at all possible for the best academics from top schools to advance scientific knowledge and arrive at some semblance of truth. We start with facts and beliefs. In this case that Ancient Greeks were into numbers. Then build from there. /8
We should question facts, beliefs, assumptions. In case of medicine, when we build on shaky foundations that rest of myth, fact, and belief, we arrive nowhere. /9
Bach. The Well-Tempered Clavier. / 10
Star Wars. A New Hope. /11
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