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Background
Background
Pythagoras (c. 570 BC - c. 495 BC) was an Ionian Greek philosopher born in Samos. Samos is a Greek island just off the coast of Turkey. At the time, there were many Greek colonies all over the mediterranean. (They’re in blue in the map below - there were Greek colonies in Denia and around Valencia).
During Pythagoras’ life, the Kingdom of Lydia and all the coastal towns were taken over by Cyrus the Great of Persia. Pythagoras is most famous for coming up with Pythagoras’ theorem about the relationship between the lengths of the sides of right-angled triangles.
The Mediterranean c. 6th century BC: Phoenician settlements in red, Greek areas in blue, and other territories as marked.
By Javierfv1212 (talk) - Own work (Original text: self-made), Public Domain, https://commons.wikimedia.org/w/index.php?curid=18186718An outline of Pythagoras’ ideas
An outline of Pythagoras’ ideas
For the Pythagoreans, the world was understandable because it was filled with forms. To Pythagoras and his followers these forms were known as máthēma (μάθημα) , meaning that which is learnt - the word from which we get the word mathematics. (Those belonging to Pythagoras’ school were known as mathēmatikoi (μαθηματικοί) or learners).
For the Pythagoreans, ta mathemata (the things we learn) are all those things that help us to make sense of the world. Ideas like numbers, time, space, shapes. Without such ideas, we would have no way of describing anything.
For Pythagoras there were four kinds of mathemata:
Arithmetic - numbers
Geometry - shape
Astronomy - time
Music - sound
These Mathemata were mystical, sacred things. They didn’t exist as physical objects: Consider the definition of a line - a length without a width. If something doesn’t have a width, then it doesn’t really exist. So (a Pythagorean would say) it must exist in a mystical realm.
Pythagoras and his followers believed that it was our soul which was able to connect with these mystical objects. Our soul, they thought, was trapped in our body, and after death would migrate to a new body - i.e. that we would reincarnate as a new being.
…the so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything. And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analogues of what is and comes into being—such and such a property of number being justice , and such and such soul or mind , another opportunity , and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers, and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion (or harmony) or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nine that are visible, they make the "antichthon" the tenth…
-Aristotle, the Metaphysics (985-986)Discussion
Discussion
Look at this photograph of a baby. Can the baby see a rattle? Explain your answer.
–well the baby’s eyes work, so yes the baby can see the rattle.
–but does it see a rattle?
–well it doesn’t know what a rattle is, so it doesn’t know that it is a rattle, perhaps it just sees a shape.
–But the baby doesn’t know what a shape is either, or a colour, or a texture. So it can’t know that it sees those things either!
The baby can see the rattle in the sense that it’s eyes function, but it can’t see a rattle insofar as it cannot understand or comprehend the object as a rattle.
The word ‘rattle’ can refer to this particular rattle, or it can refer to a type or category of thing. The baby can see the particular thing, but it doesn’t understand what kind of thing it is.
How do you think this relates to Pythagoras' mathemata?
How do you think the mathemata relate to our memory? Why can we not remember anything from the time before we can talk?
Tasks
Tasks
What does ta mathemata mean?
Why are the mathemata important?
What were the four types of mathemata according to Pythagoras?
Why were they mystical for the Pythagoreans?
What do you think of Pythagoras’ account of the Mathemata?
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