For example, take pi.
Pi cannot be found in nature – nothing can weigh pi grams, or be pi meters long, or last for pi seconds. To see this, imagine that I told you that my lucky penny weighed pi grams, and that you owned a scale that went to infinity digits that could weigh my penny and allow you to disprove it. You wouldn’t have to turn on the scale to know that I was lying. Because the universe cannot create something that weighs pi grams. There are of course objects that weigh 3 grams, and that weight 3.1 grams, and that weigh 3.14 grams, and that weigh 3.141 grams – and so on and so forth. But at a certain point, as one progresses down the infinity of numbers after that decimal point, one “runs out of bottom.” Once you get down past adding one more atom, one more neutron, one more quark, one more Higgs boson (the carrier of mass, we think), one more string (do those things even have mass?) you are simply done. You have run out of bottom, because you have no more smallest conceivable unit of mass to add to my 3.14159…etc. gram object – in this case, I have claimed, a penny. And so – long before you’ve reached infinity (math joke, sorry) – you’ve hit the wall. That penny of mine is not going to weigh pi, and furthermore, nothing else ever is.
You can play the same game with length and width and height, or energy, or time, or any other physical quantity. And this is all assuming a classical world; forget that Heisenberg, where structure is probabilistic, means that you definitely couldn’t claim such a thing! It doesn’t matter what aspect of the physical universe you choose: in each case, you will find that pi cannot exist in the world.
And yet: pi “exists.”
I mean, we are talking about it right now, and understand it perfectly. Right? We have, at least in principle, since at least elementary school when we learned to imagine taking spaghetti noodle circles and spaghetti noodle diameters and comparing their ratios, been able to think about pi easily for years. Which is to say, we can imagine pi. It’s just not “out there.” It’s “in here.”
Now we think we know where there is. But where in the world is here? This points us squarely to the problem I have been hinting at with the last two posts – on statistics and zebras. Non-empirical objects, often called rational objects, those famous unobservables and undetectables that make modern metaphysics so vexing: they don’t have spatial location. They don’t have mass. They don’t have duration. And so we can’t map them on a Cartesian axis or map of the universe, which means we don’t know where in the world they are.
Which leaves us with this vexing question. Since we know it must be somewhere, where is pi?