This first video in the series will outline the distinction between Pythagorean and Platonic approaches to mathematical philosophy. The Pythagorean approach focused on symbolism and instituted the "quadrivium", the 4-fold breakdown of all mathematics into arithmetic, harmonics, geometry, and astronomy. The Platonic approach focused on the ontological status of mathematical objects, and grounding mathematics into a metaphysical hierarchy.
In this second video, we will outline the very basics of Proclus' philosophy of mathematics. Proclus lived in the 5th century AD in Athens and wrote commentaries on Plato, but also on Euclid's Elements. His commentary on Euclid is the only systematic philosophy of mathematics from antiquity, which is notable for classifying mathematics within a Platonic metaphysical hierarchy of being. We will demonstrate Proclus' classification of mathematical objects onto the level of Understanding, which is below Intellect and above Opinion.
In part 3, will give the Pythagorean definition the Quadrivium following Nicomachus of Gerasa in his text Introduction to Arithmetic. We begin with the division into multitide and magnitude, which is what we think of today as the discrete and continuous, or integers and real numbers. Then multitude is split into arithmetic and harmonics, while magnitude is split into geometry and astronomy, thus establishing the Quadrivium as essentially a 4=2x2 system.
In this fourth video in the series, we will explain why arithmetic must go at the beginning of any study of the Quadrivium. Again looking at the text of Nicomachus of Gerasa, the Introduction to Arithmetic, we will read his dialectic explaining how arithmetic naturally comes first. If geometry were eliminated, we would have to eliminate arithmetic as well, for how could we define a triangle without the number 3?
In part five, we will explain the meanings of numbers as qualitative ideas, viewing numbers as symbols for archetypal ideas of an unfoldment process from the Monad (1) to the Decad (10). Internalizing these meanings open us up to perceptions that lead to abilities like prophecy and divination. We give keywords for each number, so that meditating on them unlocks the ineffable reality of numbers as Platonic ideas.
In part six, we will show how to construct meditation cards for doing the meditations on number symbolism using the meanings of numbers given in part five. We explain the meditation process and give guidelines for how to achieve the best results, as well as indications of more advanced programming techniques that will come later.
I would appreciate any feedback you may have, please post your comments to the individual videos on the respective YouTube pages, or if you want to comment on the whole series, you can do that here.
Books mentioned in this post:
No comments:
Post a Comment