The Wisdom of Hypatia: Ancient Spiritual Practices for a More Meaningful Life (29 page)

We can imagine Hypatia pausing in her presentation to introduce a simple exer-

cise. She props up a white board with a black equilateral triangle painted onto it (see fig.) and explains the exercise as follows.

Equilateral Triangle

Triangle Contemplation
: Look at the image of the equilateral triangle for a few moments. As you will discover soon, it is only an imperfect sensible image or rep-

resentation of the ideal Equilateral Triangle. Now close your eyes, but keep the

image of the triangle before your mind’s eye.

the macrocosm 145

Triangle Contemplation (continued)
: If it is not too clear, that is OK, because we are not interested in the sensory image; we are interested in the Idea behind it. So

visualize the perfect Equilateral Triangle, with its three sides perfectly straight

and of exactly the same length. Notice this astonishing fact: although the three

sides are exactly the same length, they have no specific length. Your mental im-

age has no size! Nevertheless, if you wish, you can make it smaller or larger, but

still with no specific size. Isn’t that peculiar when you think about it? You can discover facts about the Equilateral Triangle. For example, in your mind rotate the

triangle one-third turn, so that one of the other points is upmost. Since all three

lines are the same length, you know this rotated triangle must coincide with the

original one. And you can see that its three angles must be identical, since they

can be superimposed. Move the top point up a little, and you will see that the

two sides must get longer than the base, but stay the same length as each other.

Move the point down, and the opposite happens. What happens to the lengths

of the sides if you move the top point horizontally to the left or right? Make an-

other equilateral triangle with a side exactly half as long as the original. You can see that you can fit exactly four such smaller triangles in the original one. This

is enough exercise for now; we will draw some conclusions. Notice that your

mental triangle is not in space, because it has no size. Indeed, it has no place.

Where is it? Hovering 2 inches in front of your nose? Between your ears? So this

triangle is not a physical object. Nevertheless it does exist in time, since you can change it. Therefore, you are not directly experiencing the ideal Equilateral Triangle in the world of Forms. Rather, you are experiencing a mutable projection

of it into your own time-bound soul. Nevertheless, this exercise demonstrates

how you can begin to ascend above the level of sensible forms and can begin to

contemplate and investigate the realm of ideal Forms. If you had some trouble

with visualizing the triangles and manipulating them, don’t worry; you will get

better with practice. Of course you can use any geometric forms; there’s nothing

special about equilateral triangles.

Bisected Equilateral Triangle

146 the macrocosm

The Platonic Forms

Platonists look at all “universals” (general terms) and concepts the same way as mathematical ideas. That is, just as there is an ideal form Equilateral Triangle, of which all physical equilateral triangles are more or less accurate copies, so also there is an ideal substance Gold, and chemists and physicists can tell you many of its properties, such as atomic weight, density, hardness, and electrical conductivity; but any actual sample of gold will contain impurities. So also for the ideal form Horse, of which all physical horses are more or less accurate copies. Thus biological species can be understood as ideal Forms (but this notion must be modified in the light of modern biology, as I’ll explain later).

There is much that can be said about this theory, and philosophers (including Plato) have been debating it since Plato’s time. It has a certain commonsense appeal, and that is really all that matters here. For example, if you have never seen a wombat, but I show you a picture of one, there is a good chance you will recognize other wombats. If I show you liquid mercury, you will probably recognize it again. You will have acquaintance and a little knowledge of the forms Wombat and Mercury.

In a sense, just as mathematicians study ideal triangles, but may use physical diagrams of triangles to help them understand ideal triangles, so other scientists study ideal species, substances, processes, etc. by means of specimens, samples, and observations in the field and in the laboratory.

Since ancient philosophy was a way of life, Socrates, Plato, and their successors were especially interested in applying their analysis of ideal forms to ethical ideas. Is there an ideal form of Justice, to which all just acts are only approximations? Are there ideal forms of Courage, Truth, Beauty, Piety, and Wisdom? Is there an ideal form of the Good? These are the sorts of questions addressed in Plato’s dialogs.

If there are such ideal forms, then can a philosopher explore the nature and relation of ethical concepts the same way a mathematician investigates mathematical concepts?

Might one discover ethical universals, independent of historical time and culture, in this way? This has been the goal of Platonists and other idealist philosophers through the ages.

Before proceeding it will be worthwhile to take a brief excursion through etymology, which will help you to understand the Neoplatonic understanding of these “forms” or

“ideas.” The Greek word
idea
, from which get our word, is related to a verb meaning “to see.” Thus
idea
originally meant the visual appearance of something, especially its
shape
or
form
, that by which it might be recognized. Already before Plato, the meaning of
idea
had been extended to include any property or characteristic of something, even a symptom. It the macrocosm 147

was further extended to refer to the class, kind, or species of things, and to the power that gives anything its potential, its potency. All of these meanings are implicit in the word
idea
(and its Latin translation,
forma
) when used by Plato and his successors.204

Often, as is customary, I will capitalize Idea and Form when I mean them in the Pla-

tonic sense, or somewhat redundantly I will write “ideal form” to emphasize that I do not mean “form” in the ordinary sense. Nevertheless, as you have seen, the ordinary meaning is part of the Platonic meaning. I will also capitalize the names of particular ideal forms, such as Equilateral Triangle, Horse, Gold, and Justice.

Being and Becoming

Hypatia continues her explanation of the Forms. “An important difference be-

tween the Ideal realm and the material (or sensible) world, according to Platonism,

is that the Ideas are eternal and unchanging, while things in the physical world are always changing, and nothing lasts forever. The Equilateral Triangle is a good example.

First, the mathematical object is unchanging, whereas any particular physical triangle that we make will come into being at some point in time (when we make it) and eventually decay (for it is made out of matter). In the meantime, it will be changing, perhaps slowly and imperceptibly, perhaps more rapidly. Second, and more importantly, the

ideal Equilateral Triangle is eternal, not so much in the sense that it will last forever, but in the sense that it is out of time altogether; that is, the concept of time does not apply to it, since it is not a thing in the physical world, where time exists. It is, we say,
atemporal
, that is, timeless.

“The ideal realm is called the realm of Being (where things either are or are not) in contrast to the material world, which is called the realm of Becoming (where everything is in the process of becoming something that it was not). Therefore the individual Ideas may be called Beings.

“Since the Ideas exist independently of us, we can think of them existing in some

place separate from individual human minds. Plotinus says they are
there
or
beyond
, not
here
, but where is
there
? Where can we find the ideal Equilateral Triangle? In a sense this universe of independently existing Ideas constitutes a ‘Cosmic Mind’. Mind here is taken to be equivalent to its contents: its ideas and the relations among them.

There is no thinking Mind separate from the Ideas it thinks, but we cannot assume that the Cosmic Mind is conscious in the sense that our minds are conscious.

148 the macrocosm

“Essential to Platonic philosophy is the primacy of the ideal forms. For example, the ideal Equilateral Triangle is the
real
equilateral triangle; individual physical equilateral triangles are imperfect images or reflections of that ideal reality. Therefore, general-izing, the Ideas are considered the ultimate causes of physical things and processes, which are their effects. Furthermore, to explain something, we Platonists look to the Form in which it participates (that is, of which it is an image). If you want to understand why a particular triangle has the (approximate) properties it does, then study the mathematical Triangle that it approximates. If you want to understand why a horse is eating hay, then study the ideal Horse. To understand a just act, study Justice.”

This is still very much the perspective of science, at least in its more mathematical forms.

Scientists have discovered various mathematical laws that describe how objects behave. If they want to explain why something happens in the physical world, they appeal to these laws by way of explanation. For example, Newton’s laws explain why a cannon ball travels in an (approximately) parabolic arc. Although our knowledge and understanding of the laws of physics change as science progresses, the laws themselves (even if we do not understand them perfectly) are eternal. These unchanging laws describe the Form of the processes of change in the material world. Contemporary science is very Platonic, indeed, Pythagorean.

“Since the Ideas are causes,” Hypatia continues, “we cannot think of them as purely

passive; there is an active aspect to them too. Plotinus describes the Ideas as
Thoughts
, which means both timeless acts of thinking and the things thought about.”

Aedesia, who is one of Hypatia’s Pagan students and wears the simple white wool-

en robe of a philosopher, raises her hand and asks, “What are ‘timeless act of thinking’?” 205

“They are eternal connections and relations among the Ideas (the Thoughts), such

as the timeless relations between the Equilateral Triangle and the Lines that make up its sides. The Cosmic Mind, as the totality of Thoughts, in both senses, is both the object of thought and the subject doing the (timeless) thinking, so at this level, subject and object are two sides of the same reality. Nevertheless it is important to keep in mind that this is not thinking in the everyday sense of that word, but eternal relationships among ideal forms.

the macrocosm 149

“If you think of the Ideas not as static Forms, but also as causes and as acts of