In the last few posts, I’ve talked a fair bit about relativity and have struggled to make my thinking on the subject clear enough to read. What that process has revealed to me is that some topics in science are just hard to talk about. In part, that’s because they’re counter-intuitive, but there’s a lot more to it than that. A lot of what’s going on is, I’d propose, social, and deeply concerning about how we engage with science.
Open any number of pop-science books that attempt to give you a grand overview of the universe and somewhere near the start there are usually the same two chapters. One of these is on relativity and the other is on quantum mechanics. These chapters are the author’s attempt to explain the ‘wacky’ things that happen in physics. In most cases, the author ends by saying something like, “this might sound incredible, but it’s what we see in experiments, so suck it up”.
And this is usually where real scientific dialog with the public stops. Subsequent chapters in these books are usually short on specifics and relatively thick on prose like “Geoff and I were sitting eating a sandwich, feeling sad, and suddenly it occurred to me that if we ran the same simulation backwards, it would give us the eigenvectors we were looking for, only with the parameters inverted! We raced back to the lab without even finishing our lunch!”
Different books make the break in different places but the effect is usually the same. The physicist in question gives up on trying for an intuitive explanation of what they were doing and resorts to personal drama to try to retain reader interest.
Underpinning this switch is the belief that the only way to really understand the ideas being discussed is to do the math. Without the math, you just can’t get there. At some level, the math is the understanding. I take issue with this notion pretty strongly. Not only is it dead wrong. It’s counter-productive. In fact, it’s an angry badger driving a double-decker bus into the side of the temple of science.
Let’s go over some of the problems that this ‘math equals understanding’ approach creates.
First, it causes the public to disengage. People feel that if they aren’t good at math, they’ll never get it. Yet life goes on, so science can’t possibly be relevant to them. And, at the end of the day, this creates funding problems.
Second, and far worse, is that the people who do the math and get the answer right feel like they have understood it, even though deep down, it still doesn’t make any sense. They sweep that feeling under the rug and press on but become increasingly defensive when pressed on topics that make them feel uncertain. This just makes the gulf between scientists and everyone else all the wider.
On top of this, attempts to communicate the math, rather than the meaning, to the public end up creating a folk-notion of how physics ‘has to be’. This creates a whole stew of junk reasoning when people try to extend that folk-notion. For instance, in relativity, people are told that you can’t go faster than light because if you did, you’d be travelling backward in time in someone else’s reference frame. This is incredibly, insanely wrong. And it’s just one step from there to “if I go faster than light I go backwards in time”.
Perhaps most horribly of all, this process creates physicists who can’t uncouple the tools they’re used to using from the problems they’re trying to solve. This creates massive blind-spots in the reasoning of some of our brightest and finest researchers, because these people are never tested to see whether they have understood the principles in the absence of the math.
Here’s an example from relativity: “spacetime exhibits Lorentz-invariance”. This might sound fine, until you think about the fact that we can only ever examine spacetime by passing things through it. We have no idea what properties spacetime exhibits, because we can never directly test it. All we can know about is the things we can observe. Saying that test on moving objects yield a pattern of Lorentz invariance is fine, but often, that’s not what’s said.
Here’s another relativity example from my own life. I sat down in a cafe a few years ago with a grad-student in particle physics to talk over some things I wanted to understand. We got on to the subject of using a compact dimension for spacetime interval in the way I outlined in the last post. He pulled a face.
“I don’t think you can do that with just one dimension,” he said. “I think you need three.”
We debated the point for some time, even breaking out some equations on a napkin. In the end, he still wasn’t convinced, though he couldn’t say why, or point out a hole in my reasoning. All this despite the fact that his math skills were far in advance of my own.
Why did he make the assertion that he did, even though fifteen minutes of basic logic crunching could have demonstrated otherwise? Because the way relativity is taught makes use of the idea of Lorentz boosts. People use six dimensions to model what’s going on because it makes the math easier. They never just use one dimension for s. This fellow, extremely bright and talented though he was, was wedded to his tools.
So where do we go from here? What do we do? If science has a problem, how do we solve it?
I’d propose that all math can ever do is supply a relation between things. “If this is true, then that is true”. Math gives you a way to explore what the implications of an idea are, without ever saying anything about the idea itself, other than whether it’s self-consistent. In essence, math in physics tries to describe how things behave solely in terms of constraints, and without ever trying to provide an implementation. In other words, it deliberately avoids saying what something means, and says only what it does. This is because meaning, I’d propose, is a property that comes with a choice of specific model.
This is why physics tends to become fuzzy and unsatisfying when it diverges from physical experience. We can describe relativity or quantum mechanics easily using math by defining the constraints on the behavior we see. However, we are used to having a specific model to back our reasoning up–the one provided by intuitive experience of the world. When that model goes away, we lose touch with the implications of our own logic.
Does this mean that we are forced to rely on math for insight at that point, as is commonly proposed? No. In fact, I’d suggest that the reverse is true. This is the point at which we should trust math less than ever. This is because self-consistency is only as good as the conjectures you apply it to. I think it was Bertrand Russell who said that from a false premise you can prove anything. The only way to determine whether our physical premises are correct is to have more than one way at arriving at confidence in their validity. That’s why physical intuition is a vital tool for preventing self-consistent nonsense from creeping into theory.
Hence, instead of just leaning on our analytical crutch, we should strive harder than ever to find metaphors for physical systems that do work, and which bring phenomena such as relativity within easy mental reach.
And this, to my mind, is exactly where digital physics can help. Digital physics asserts that we should only consider a physical theory reasonable if we can construct a viable implementation for it. If a system is self-consistent, but non-implementable, then we shouldn’t expect it to match nature, as nature clearly is implemented, by virtue of the fact that we are witnessing it. By requiring concrete implementations, we force ourselves to create metaphors with which to test our understanding.
In other words, if the math leaves us asking the question, ‘what does it all mean?’, then we haven’t done enough digital physics yet.
Does this mean that any one of the implementations we pick is correct? No. In fact, the more workable implementations, the better. Digital models are not theories.
Does it mean that digital physics represent a substitute for mathematical reasoning? No, of course not. Math lies at the heart of physics. It just can’t exist in a vacuum of understanding.
Digital physics, then, is a different tool, through which the set of theoretical models of nature can be tested and understood. It’s a way of ruling out theories that don’t add up even if the math works out. It is, I would propose, the best antidote to Geoff and his half-eaten sandwich that physics has going for it.