The log

Everyone knows Raphael’s painting The School of Athens. It is a fresco in the Vatican, illustrating philosophy, by showing one great big happy cocktail party with all the ancient philosophers.

I had a background in classic science fiction, and one of the many Robert Heinlein quotes from my schooldays was that education was just a log with a teacher at one end and a student on the other. There has likely never been so significant a log as the one occupied by the two central figures in the image. Plato on the left, and his student Aristotle on the right. Aristotle in turn was the teacher of Alexander the Great, so obviously there was something going on.

Plato and Aristotle had opposing views on a crucial point in viewing the cosmos. Plato reckoned that there was more to the universe than what we could see. There had to be a divine realm occupied by the higher truths. The concepts of Beauty and Justice, for example. Everyone knew what they were – or thought they did – but you couldn’t actually go out and find them in the world. Just examples of them, rather than the things themselves.

Aristotle, on the other hand, said that there was only one world, and that was the one we could perceive. If it couldn’t be seen or touched or measured in some way, it had no being. From Aristotle’s way of thinking, we get the scientific method of observing the world, conducting experiments, measuring the results and coming to conclusions about how the universe operates.

I like his way of thinking, but still, I tend to be a Platonist in my own views. I think that there is more to the universe than what we can see and measure. There has to be.

Where does pi live, for example? Pi is the irrational number ratio of a circle’s circumference over its diameter, usually approximated to 3.14159. It can be calculated to a precision of trillions of digits, it has no non-trivial repeating sequences after the decimal point, it is as random in its distribution of digits as it is possible to be, and yet the same value applies everywhere. From one side of the universe to the other, circles all have the same value of pi. This is not something we can ever measure directly, as per Aristotle, because where could we possibly find a circle large enough to run a tape measure over and get a result down to trillions of digits of precision?

To my mind, there has to be some realm of forms – as Plato put it – where all the eternal, unchanging, constants of the universe reside. How atomic particles work. How light travels in a vacuum. The laws of mathematics. The fact that the interior angles of a triangle total pi radians (which, of course, is 180°). Logarithms. All that stuff.

There’s no middle ground. Either the physical universe is all the reality there is, or true reality resides elsewhere, and what we can see and feel is just an example or reflection of the real thing.

So, dear reader, where do you stand on the question of reality?


philosophy , , , ,


  1. I’d like to believe “reality resides elsewhere, and what we can see and feel is just an example or reflection of the real thing”. Open to being convinced 🙂


    1. This is just Plato’s Forms, restated. The underlying rules of the cosmos are eternal, infinite, and unchanging. A triangle will always have half the number of degrees in a circle. Hydrogen will fuse into Helium etc.


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