553 | Pythagoreans think mathematical principles are the principles of all of nature [Aristotle on Pythagoras] |
554 | Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Aristotle on Pythagoras] |
638 | Pythagoreans define timeliness, justice and marriage in terms of numbers [Aristotle on Pythagoras] |
644 | For Pythagoreans the entire universe is made of numbers [Aristotle on Pythagoras] |
1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
17858 | Pythagoreans say the whole universe is made of numbers [Aristotle] |
1517 | The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature' [Sext.Empiricus] |
3645 | To understand the universe mathematics is essential [Galileo] |
19356 | Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz] |
19592 | The basic relations of nature are musical [Novalis] |