We humans have always been fond of invisible things.
Poltergeists, fairies, unicorns, the Yeti, the Lost City of Atlantis.
Just because you can’t see them, it doesn’t mean they aren’t there.
Scientists, no less than any other humans, suffer from this fondness for invisible things.
Phlogiston, miasma, ether, strings.
Just because you can’t see them, scientists have insisted, it doesn’t mean they aren’t there.
Beware these invisible things.
As I explore Wolfram Physics, I’m aware of certain invisible things that we believe in now, but we’re going to have to let go, if Stephen Wolfram is right.
And I’m also aware of the temptation to replace this old set of invisible things with a new set of invisible things.
Here’s why we’d do well to resist.
Behold the Celestial Spheres
When the Ancient Greeks looked up at the sky, they saw the Sun, the Moon and the stars, each moving slowly in circles around the Earth.
Most of the stars moved together, as if they were on the surface of the same sphere, with the Earth at its centre. Five of the stars – Mercury, Venus, Mars, Jupiter and Saturn – moved differently, as if each were on its own sphere, just like the Sun and the Moon.
The crucial thing is that the Ancient Greeks didn’t use the words “as if” when they talked about these celestial spheres.
When the stars move precisely as if they were on the surface of a sphere, those two little words, “as if,” can come to seem superfluous.
The Ancient Greeks pictured a real, honest-to-god sphere carrying the stars around the Earth, and seven other real, honest-to-god spheres carrying each of the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn.
These spheres were made of crystal. Well, obviously. They had to be strong, to carry the Sun, the Moon and the stars, and they had to be transparent, so that you could see the stars on the outermost sphere through the other seven spheres. What’s strong and transparent? Crystal. These were crystalline spheres.
Pull the other one, Plato
Positing things we can’t see – such as crystalline spheres – to explain things we can see – such as the motion of the stars – has a lot going for it.
For one thing, no one can tell you that you’re wrong. If anyone objects: “But I can’t see your spheres,” you can adopt an appropriately patronizing tone: “Well, of course you can’t see them, they’re crystalline! If they weren’t see-through, how on Earth would you be able to see through them to the stars?”
For another thing, you can argue that while you can’t see the thing itself, you can see its effects. You don’t need to be able to see the sphere that carries the stars, since you can see the effect it has, the circular motion of those stars.
And here’s one final tip for the proponents of invisible things: to be completely safe when positing something we can’t see, you should make sure it’s something we can never see.
Are teapots harmless?
You’d think it’d be harmless, positing something we can never see.
It’s like that giant teapot in orbit around Jupiter. It’s invisible, of course, and it has no influence – gravitational, electromagnetic, nuclear or otherwise – on any object passing near it or through it.
I know what you’re thinking.
You don’t believe there’s a giant teapot in orbit around Jupiter.
But it doesn’t do any harm to speculate, right?
Well, it turns out this teapot might not be so harmless.
Things we can never see have no influence on the universe, but they do have an influence on our minds.
All in the mind
Once you get the idea of celestial spheres into your head, you stop seeing the circular motion of the stars for what it is – a circular motion – and start seeing the celestial spheres as reality, and the circular motion of the stars as a mere effect.
So when the Ancient Greeks observed that the motion of the planets wasn’t perfectly circular, instead of abandoning the idea of spheres, they simply added more spheres.
Aristotle, for example, imagined that there must be 47 interconnected spheres. Or maybe 55. It’s so hard to explain the not-quite-circular motion of the planets using spheres that it’s difficult to tell whether there are 47 of them, or 55, or some other number.
Once you have spheres on the brain, it’s hard to think of anything else. Celestial spheres are round, so it’s hard to imagine that the paths of the planets might be anything other than circles, or sums of circles. Celestial spheres are centred on the Earth, so it’s hard to imagine that the planets might be orbiting anything other than the Earth.
Beware invisible things.
For thousands of years, celestial spheres constrained our thinking, making it hard for us to conceive of a universe in which the planets moved in ellipses, not circles, around the Sun, not the Earth,
Smashing the spheres
Despite all the hints that the celestial spheres couldn’t quite capture the motion of the Sun, the Moon and the stars, it took an observation to convince us to banish the spheres from our brains.
Galileo peered through a telescope and discovered four moons orbiting Jupiter.
(He didn’t discover the giant teapot, of course, because that’s invisible, remember?)
You could have argued geometry all day with believers in the celestial spheres, and they’d always have found a way to counter your arguments with their circles.
But the moons of Jupiter? How could these four moons possibly pursue their slow paths around the planet without smashing the crystalline sphere that carried it?
The moment Galileo pointed his telescope towards Jupiter, the celestial spheres were history.
So long, space
Scientists might have let go of celestial spheres, but there are other invisible things they still believe in.
Take uniform, continuous, three-dimensional space.
In What are dimensions in Wolfram’s universe? I argued that three-dimensional space might be a mere approximation to the structure of Wolfram’s graphs at a large scale.
That’s no big deal, right? If it’s approximately correct at a large scale, where’s the harm in holding the concept of uniform, continuous, three-dimensional space in our minds?
Well, once you get the idea of three-dimensional space into your head, you stop seeing the graph for what it is.
For example, because anything can exist at any location in a uniform, continuous, three-dimensional space, it’s possible to imagine an observer of the graph, at some location beyond the graph itself.
But if you’re able to get the idea of three-dimensional space out of your head, you’ll see that for the nonsense it is.
Neither we nor any instrument we might use to observe the universe can be outside the graph, at some disconnected location in three-dimensional space.
Any observer must be inside the graph, part of the graph.
It’s a subtle mindset shift, but as we’ll come to see, it matters.
So long, space-time
Four-dimensional space-time is another invisible thing we’re going to have to let go.
Like three-dimensional space, it’s a useful concept. When Einstein proposed four-dimensional space-time, it helped us understand that even light can be deflected by matter.
And like three-dimensional space, it’s a close approximation to the structure of the graph at a large scale.
Because it’s so useful, and because it’s such a good approximation to the graph, we should continue to hold the concept of four-dimensional space-time in our heads.
But we should hold it lightly.
If it’s not to constrain our thinking – if it’s not to prevent us from conceiving an underlying reality in which space and time are entirely separate phenomena – we should remember that four-dimensional space-time – like the celestial spheres – is an invisible thing.
Ever more invisible things
As we explore Wolfram Physics, and jettison an old set of invisible things, we should be careful about taking on board a new set of invisible things.
At the very lowest level, we will never be able to see the nodes and edges of Wolfram’s graphs.
Any instrument we could conceive to observe the nodes and edges would itself be made of nodes and edges.
We might see the effects of the nodes and edges, but we should keep in mind that it’s the effects that are real, not the nodes and edges we posit to explain them.
And at the very highest level, we will never be able to see any computer that runs the universe.
If, as I explored in Where’s the computer that runs the universe? there is such a computer, then it exists in a whole other universe beyond the one we observe.
It’s fun to speculate about a computer that runs the universe.
But if it’s not to constrain our thinking about reality, we should hold the concept of such a computer lightly.
Beware invisible things.