It is Pi Day today and therefore you risk to be spammed with all sorts of curious facts about pi that you never wanted to know. On planet Genetic Fractals we won’t buck that trend.
Let’s start with a philosophical question: is a secret a secret if no one knows it?
You see, the thing is that ever since I have been on my knightly quest to penetrate the mystery of the three-ish dimensions that we live in, I often come back to the question: and where exactly do these dimensions come from?
For now that is a secret that no one knows. However, I have an intuition that I must share on the basis that a shared intuition is a half-truth and a half-truth shared is a proper secret.
Here is a mind experiment you can do at home. Put a Belgian chocolate on the edge of a porcelain plate you inherited and hate. Spin the plate on your finger but not so fast the chocolate flies away. Easy does it.
Now slowly lower the plate away from the chocolate and leave it flying around in circles. This was a mind experiment remember!?
Now, seen from the side, it appears that the chocolate moves from left to right and back again in a nice oscillating motion. This is the motion of life: a wave, a breathing movement. Mesmerizing, hypnotizing, it makes us meditate on the meaning of it all.
Don’t eat the chocolate yet, there is more. Position yourself right underneath the rotating chocolate and stare in wonder. There is no oscillating movement of life anymore?! There is just a Belgian chocolate in a static orbit, as if on an ugly porcelain plate.
So why should this wonder you? When viewed from the side you had a one-dimensional view of a natural movement that has intrigued people since Archimedes. But when you look from below, seen from a two-dimensional perspective the mystery disappeared as you stared at a static motion.
The complexity (=wonder) depends on your viewpoint. What’s more, it depends on how many dimensions you can view from.
OK, time to bring on the feature character: pi.
If you remember (under duress if necessary), it is a number that is roughly 3.14 and you can use it to calculate the circumference of a circle if you happen to know is diameter. Pi is high school pain. It is a WTF thingy who-cares number. Why does anyone want to celebrate that!?
I have blogged before about the incredible beauty that mathematicians see in equations. Well, a number like pi is even worse. It is simply worshiped. For centuries people have obsessively dedicated entire lives to penetrate the mysteries that are locked in that number.
So, now that pi is on the scene, let me unveil the secret you’ve been waiting for.
Do you you remember how if you multiply the diameter of a circle by pi, you get its circumference? Did it ever occur to you that a diameter is a straight one-dimensional line but that a circle is a two-dimensional shape?
Pi makes one-dimensional things two-dimensional.
Referring to our Belgian chocolate experiment (you may eat it now), when we rotated our viewpoint from one to two dimensions, we gained an invaluable insight in the complexity of life and the universe. Well guess what, such a rotation involves pi (and our Swiss friend Euler, but that is another story).
Whatever: pi has something to do with adding dimensions. Forget that is “three-point-something”. Think about this instead: pi makes dimensions.
How? Why? I don’t know yet. That’s the part of the secret. But it is tugging at my sleeves.
Do you remember the opening lines of the Tao Te Ching?
“The Way that can be told of is not an unvarying way;The names that can be named are not unvarying names.It was from the Nameless that Heaven and Earth sprang;The named is but the mother that rears the ten thousand creatures, each after its kind.”
Now whether you are “into” the Tao or reject it as just another creativity myth, it is very much in agreement with the views of modern physics with the added bonus that it is written in an understandable language.
The Tao refers to duality and its parent, the unnamed and unvarying. For things to exist we need to separate them; the things from the no-things. Then we name them and create our dualistic world. We can only do this if we have space to set them apart. Things and space are implied by each other. First there was the nameless, the un-penetrated mystery, then there was space and then there were things.
Space is a set of dimensions, whether it is one, two, three or more, the existence of spatial dimensions allow reality to be what it is. In modern physics it is mostly assumed that the “birth” of spatial dimensions preceeds pretty much everything else, certainly matter, i.e. “things” came later. Philosophically, it couldn’t be otherwise.
Pi creates dimensions, we noted. So somewhere at the earliest origin, before atoms, electrons, possibly just before time itself, there was a very lonely “thing” called pi. And somehow, that pi with a few friends at the Big Bang party, created the whole thing. Life, the universe and everything.
How? Why? Wouldn’t we want to know the answers to that!
So is pi it?
It looks like it is pretty central to it all. One thing I know for sure, we may be able to calculate pi to a trillion decimals but we haven’t begun to understand its deepest secret.
So folks, ponder and be awed.
Happy Pi Day.