| 553 | Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle] |
| Full Idea: The Pythagoreans thought that the principles of mathematical entities were the principles of all entities. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 985b |
| 644 | For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle] |
| Full Idea: For Pythagoreans the entire universe is constructed of numbers. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 1080b |
| 638 | Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle] |
| Full Idea: The Pythagoreans offered definitions of a limited range of things on the basis of numbers; examples are timeliness, justice and marriage. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 1078b |
| 554 | Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle] |
| Full Idea: Pythagoreans said that entities existed by imitation of the numbers, whereas Plato said that it was by participation. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Aristotle - Metaphysics 987b |
| 375 | When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato] |
| Full Idea: When our predecessors discovered musical scales, they also discovered similar features in bodily movement, which should also be measured numerically, and called 'tempos' and 'measures'. | |
| From: report of Pythagoras (reports [c.530 BCE]) by Plato - Philebus 17d |
| 1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
| Full Idea: Everything which is known has number, because otherwise it is impossible for anything to be the object of thought or knowledge. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B04), quoted by John Stobaeus - Anthology 1.21.7b |
| 1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
| Full Idea: It would have been impossible for the dissimilar and incompatible sources to have been made into an orderly universe unless harmony had been present in some form or other. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B06), quoted by John Stobaeus - Anthology 1.21.7d |
| 473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
| Full Idea: The nature of number and harmony admits of no falsehood; for this is unrelated to them. Falsehood and envy belong to the nature of the Unlimited and the Unintelligent and the Irrational. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B11), quoted by (who?) - where? |
| 17858 | Pythagoreans say the whole universe is made of numbers [Aristotle] |
| Full Idea: For Pythagoreans the entire universe is constructed from numbers. | |
| From: Aristotle (Metaphysics [c.324 BCE], 1080b16) | |
| A reaction: The original view seems to have been more extreme than the mere idea that mathematics is the guide to nature, or the language of God. Stones are made of numbers. Aristotle was unimpressed. |
| 1517 | The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature' [Sext.Empiricus] |
| Full Idea: The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature', because nature is a harmony of three concords (4th,5th and octave), and these ratios (4:3, 3:2, and 2:1) are found in the tektraktys. | |
| From: Sextus Empiricus (Against the Professors (six books) [c.180], 7.95) |
| 3645 | To understand the universe mathematics is essential [Galileo] |
| Full Idea: The great book of the universe cannot be understood unless one can understand the language in which it is written - the language of mathematics. | |
| From: Galileo Galilei (Il Saggiatore ('The Assayer') [1623], VI.232) | |
| A reaction: Nice, though one might say that humans created the language of maths to help them discuss the patterns they perceived in nature. Maybe what is special is order, and all order can be described mathematically. |
| 24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |
| Full Idea: I have discovered that all the sciences which have as their aim the search for order and measure are related to mathematics. | |
| From: René Descartes (Rules for the Direction of the Mind [1628], 04) | |
| A reaction: Note that he sound a more cautious note than Galileo's famous remark. It leaves room for biology to still be a science, even when it fails to be mathematical. |
| 19356 | Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz] |
| Full Idea: In music, the soul counts the beats of the vibrating object which makes the sound, and when these beats regularly coincide at short intervals, it finds them pleasing. Thus it counts without knowing it. | |
| From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [L]) | |
| A reaction: Only a mathematician would see music this way! He is defending his account of the unconscious mind. The proposal that we unconsciously count sounds highly implausible. He needs to recognise the patterns that ground mathematics. |
| 19592 | The basic relations of nature are musical [Novalis] |
| Full Idea: Musical relations seem to me to be actually the basic relations of nature. | |
| From: Novalis (Last Fragments [1800], 10) | |
| A reaction: Novalis shows no signs of being a pythagorean, and then suddenly comes out with this. I suppose if you love music, this thought should float into your mind at regular intervals, because the power of music is so strong. Does he mean ratios? |