This one time I had this dream —

I don’t want to talk about it.

Okay, I do want to talk about it, but I just don’t know if it’s wise.

Let me try from a different angle. I am a mathematician. I study math. That doesn’t mean that I am a student taking math classes. No. I am a scientist, and I study how mathematics behaves under scrutiny. I study math as if it were a natural physical process to be put under a microscope, as if it were a creature in a cage to be fed specific doses of specific poisons so we could measure the damage to specific tissues and organs at specific times along the poison’s progress.

We’ve trusted math for a long time, assuming two plus two equals four everywhere, all the time, under any circumstances, for the simple reason that it kinda seems to do so and it seems impossible to measure. We measure math with math. It’s like shining a light on a flashlight beam.

Math as we know and use it is based on a set number of unprovable assumptions. Everyone who studies math like I do, all of my fellow members of this fairly large academic cult, know all about this. It makes all of us nervous. Math is difficult. We all like to take shortcuts. We make tools out of all these assumptions and hand these tools to other scientists and knowledgeable people who then tell us all what we know about the world around us. They set us up to be able to build the structures we live in, or drive on, or fly in, and make predictions that allow us to dodge natural disasters if we feel like it, and if we screw up, our structures turn out to be houses of cards and people die. It’s as simple as that.

Every single one of those assumptions could turn out to be the weak link. So we test them everywhere, all the time.

Take your flashlight. Shine it on an imperfect wall. Measure the light that bounces back from the bright circle. You have no idea how much of what you are looking at, in terms of microscopic changes in brightness and darkness, is the light itself and how much is the wall. But here’s the thing. Move the light around the wall. Measure what bounces back. Move it again. Measure. Move it. Measure. Do this a million times. Add all the numbers together. Divide by the number of times you took measurements. If your wall’s surface was random in terms of its microscopic bumpiness, then what you end up with at the end of all of that is a measurement of the light itself. Now you know all about the bright spots and the dark spot from deformations and imperfections in the flashlight’s lens, in the reflector behind the bulb, in the bulb itself.

Or so we assume.

The only way we can check it is by averaging together everything we know about all of our flashlights. Then we find out what we know about light itself. And if we average together everything we know about the phenomenon of light, then all we end up looking at is the math we use to look at the world around us. If we do this everywhere, all the time, then we can make sure that math is consistent enough to bear our weight for everything else. We can know whether we should trust it, and under what circumstances it tries to wriggle in our grasp. When it might try to turn and bite us.

I know, right? It’s unlikely. In an infinite universe, though, the unlikely, if it is possible at all, turns out to be inevitable. That’s just math.

But now math is ubiquitous. Everywhere on earth, and many places in space at various distances, there are instruments taking measurements and computers doing math. Everywhere, all the time. I collect all the data I can, add to it the time and place the measurements were made, the time and place the computations were performed, and average together all of the terms that measure how much of the data is signal and how much is noise. I look at the math that we use to look at our data. I look at the math that we use to look at our math. I measure our assumptions.

This one time I had a dream of a huge glass ball struck by a small hammer. It made a sound like a beautiful bell. The tiny hammer struck again and again and again, and the ringing tones began to overlap to turn into a steady, ugly buzz. The hammer slowed down and sped up so that the buzz changed pitches to settle on a pitch that blended perfectly, beautifully, with the beautiful ringing tone of the glass ball.

Then the glass ball shattered. Then the world shattered. And everybody died.

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