Infinite Possibilities

It is thought that Plato learned geometry from the Pythagoreans, members of a secret society in Greece. The Pythagoreans traced their origin back to Pythagoras, a mystic, who is said to have learned geometry in Egypt.


During this time in Egypt, science, religion, and magic were not separate subjects at all; they were one subject, and those who taught this subject believed that an invisible order indwelled and formed the visible world. Pythagoras’ school, therefore, taught geometry and mysticism.

Pythagoras is respected still today, thousands of years later, for the Pythagorean theorem. But do we respect him as a mystic? Why did the study of geometry drop its mystical significance? Are we just smarter now … are all of us smarter than Pythagoras because we don’t believe in the mystical stuff?

Let’s see what Rudolf Steiner* has to say:

If we study human evolution impartially, we cannot fail to be impressed by the exceptional progress made in recent times by the sciences concerned with the outer world… [T]housands of years ago the sun rose in the morning and passed across the heavens just as it does today… The course of the sun was the same then, for external observation, as it was in the days of Galileo, Newton, Kepler, Copernicus, and so on. Can we suppose that the modern knowledge of which we are so justly proud has been gained by merely contemplating the external world?
If the external world could itself, just as it is, give us this knowledge, there would be no need to look further: all the knowledge we have about the sense-perceptible world would have been acquired centuries ago. How is it that we know so much more and have a different view of the position of the sun and so on?
It is because human understanding, human cognition concerning the external world, has developed and changed in the course of hundreds or thousands of years. Yes, these faculties were by no means the same in ancient Greece as they have come to be with us since the 16th century.
… [Human beings] have learned to see the outer world differently because something was added to those faculties which apply to the external sense-world … a study of human evolution will show that something evolves within man; the faculties for gaining exact knowledge of nature were at first asleep within him, and have awakened by stages in the course of time. Now they are fully awake, and it is these faculties which have made possible the great progress of physical science.
Is it then inevitable that these inner faculties should remain as they are now, equipped only to reflect the outer world?

Excerpt from Metamorphosis of the Soul, Paths of Experience, Lecture 1, 14/10/1909 by Rudolf Steiner.

Steiner shows that over the course of time, humanity lost its connection to the spiritual world even as it gained its capacity to contemplate the world of the senses. It is now possible once again to find a living relationship with the spiritual world, but we must seek it ourselves; it is no longer provided to us as a gift. But to whom do we turn to seek it? Well, we can turn to those who, like Pythagoras in his time, are the scientists and philosophers of our day.

Right now, in 2018, we can major at Yale University in a field called  Mathematics and Philosophy; we can take a course at Oxford by the same name, and many other universities offer a course called Philosophy in Mathematics.

We can find many books on the subject of science and philosophy such as the 2017 book by H. Chris Ransford, God and the Mathematics of Infinity: What Irreducible Mathematics Says About Godhood or the 2006 book by George Greenstein and Arthur Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (Physics and Astronomy).

So, apparently, science actively connects with philosophy. Let’s take a quick look at the prologue of the Greenstein/Zajonc book: “… the challenges to our understanding posed by quantum theory extend all the way to our conceptions of the nature of physical reality and of the proper function of science itself. The research we describe has made abundantly clear that the conventional view is entirely inadequate … modern research on the foundations of quantum mechanics has generated an extensive philosophical literature…”

What do they mean by the nature of physical reality? The proper function of science? Is our understanding of science itself evolving? Does Steiner’s revelation of a world beyond our physical reality need to be taken seriously? If you’re interested in knowing more, you can read Steiner.


“Intuitionism in the Philosophy of Mathematics”

“Holism and Reductionism in the Entwined History of Light and Mind”

Plato and Pythagoreanism