Instructions for Meditating on Geometric Objects - Circle

I would like to begin giving more detailed instructions on mathematical meditations.  It's easiest to begin with meditations on geometric objects, and with that we begin with the circle.

Draw a circle on paper using a compass. Then look at it for a minute.  Then close your eyes and see a memory image of the circle you were just looking at.  Do this for 1 minute, then let it fade.  Next, mentally visualize a circle drawn in thin white light on a black background.  Do this for 1 minute, then let it fade.  Next, mentally repeat the definition "a circle is a set of points with equal distance from a center" a total of 7 times.  Then sit in silence and feel yourself drawing closer to the pure idea of the circle. 

Understand that this idea is eternal, indestructible, and incorruptible.  You are now coming into contact with a pure mathematical object which subsists within the higher mind.  This is the real circle.  It is a perfect unity, a simultaneous whole and is without parts.  You are becoming more aware of your own eternal nature and your connection to the divine.

Once again, mentally repeat the definition "a circle is a set of points with equal distance from a center" a total of 7 times.  Then visualize a circle for 1 minute, and then draw one on paper using a compass.

When you are drawing the circle on paper, you are operating at the level of body.  When visualizing, you are on the level of soul.  When repeating the definition, you are at the level of intellect.  And when coming into direct union with the real circle you are at the level of The One.

Become aware of a qualitative change of consciousness as you move through the layers.  What do you experience as you move up to the next level?  Why is it important to come back down to the physical level?

Coming back down to the physical level is a powerful meditative movement.  It is a highly theurgical act.  Theurgy is the art of physical action which is in resonance with the downward movement of divine ideas into the physical world.  By engaging in this powerful, albeit simple theurgical ritual, we are resonating with the circular movement of the heavens and the earth, and thus becoming more aware of the emanation of providence into our world from the divine.

Video - Geometric Theurgy 01 - Creation by Numbers

This video will begin the series on Geometric Theurgy by looking at a story of creation by numbers.  We will develop the symbolic meanings of numbers and explain why these meanings go with the numbers.  This is a profound exegesis on the Pythagorean tetraktys.  Learn how you are part of God's unfoldment of self-knowledge.  Once this is understood, you will be well prepared to begin practicing the highest form of theurgy-- creating your own universe.

Video - Ancient Philosophy of Mathematics 07 - The One, Limit, and Unlimited in Geometry

I have added another video to the video series Ancient Philosophy of Mathematics.  This is part seven, titled The One, Limit and Unlimited in Geometry.  We will explore the metaphysics of geometry through The One, Limit and Unlimited.  We will show how geometric constructions correspond to these first principles, with the point symbolizing The One, the circle symbolizing the Limit, and the line symbolizing the Unlimited. We give a basic description of the practice of geometric theurgy, a form of meditation that requires using body movement, thereby grounding the highest metaphysical principles down into the lowest level.  We read from Plato's Philebus and Proclus' Elements of Theology and Commentary on Euclid's Elements.  This video is the foundation for the next series of videos on geometric theurgy.

Video Series - Ancient Philosophy of Mathematics

I have started a series of videos on the Ancient Philosophy of Mathematics on my YouTube channel.  The series currently has 6 videos and I will be adding more in the future.  In this first set of videos, we discuss the Pythagorean and Platonic perspectives on mathematical philosophy.  The focus will be on metaphysics and ontology, symbolism and contemplation, and anagogue, or spiritual ascent.  We will be drawing material from the Introduction to Arithmetic by Nicomachus of Gerasa as well as Proclus' Commentary on Euclid's Elements.

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: