There’s an attitude I keep seeing among physics crackpots. It goes a little something like this:
“Once upon a time, physics had rules. You couldn’t just wave your hands and write down math, you had to explain the world with real physical things.”
What those “real physical things” were varies. Some miss the days when we explained things mechanically, particles like little round spheres clacking against each other. Some want to bring back absolutes: an absolute space, an absolute time, an absolute determinism. Some don’t like the proliferation of new particles, and yearn for the days when everything was just electrons, protons, and neutrons.
In each case, there’s a sense that physicists “cheated”. That, faced with something they couldn’t actually explain, they made up new types of things (fields, relativity, quantum mechanics, antimatter…) instead. That way they could pretend to understand the world, while giving up on their real job, explaining it “the right way”.
I get where this attitude comes from. It does make a certain amount of sense…for other fields.
An an economist, you can propose whatever mathematical models you want, but at the end of the day they have to boil down to actions taken by people. An economist who proposed some sort of “dark money” that snuck into the economy without any human intervention would get laughed at. Similarly, as a biologist or a chemist, you ultimately need a description that makes sense in terms of atoms and molecules. Your description doesn’t actually need to be in terms of atoms and molecules, and often it can’t be: you’re concerned with a different level of explanation. But it should be possible in terms of atoms and molecules, and that puts some constraints on what you can propose.
Why shouldn’t physics have similar constraints?
Suppose you had a mandatory bottom level like this. Maybe everything boils down to ball bearings, for example. What happens when you study the ball bearings?
Your ball bearings have to have some properties: their shape, their size, their weight. Where do those properties come from? What explains them? Who studies them?
Any properties your ball bearings have can be studied, or explained, by physics. That’s physics’s job: to study the fundamental properties of matter. Any “bottom level” is just as fit a subject for physics as anything else, and you can’t explain it using itself. You end up needing another level of explanation.
Maybe you’re objecting here that your favorite ball bearings aren’t up for debate: they’re self-evident, demanded by the laws of mathematics or philosophy.
Here for lack of space, I’ll only say that mathematics and philosophy don’t work that way. Mathematics can tell you whether you’ve described the world consistently, whether the conclusions you draw from your assumptions actually follow. Philosophy can see if you’re asking the right questions, if you really know what you think you know. Both have lessons for modern physics, and you can draw valid criticisms from either. But neither one gives you a single clear way the world must be. Not since the days of Descartes and Kant have people been that naive.
Because of this, physics is doing something a bit different from economics and biology. Each field wants to make models, wants to describe its observations. But in physics, ultimately, those models are all we have. We don’t have a “bottom level”, a backstop where everything has to make sense. That doesn’t mean we can just make stuff up, and whenever possible we understand the world in terms of physics we’ve already discovered. But when we can’t, all bets are off.
Great points! I wish everyone understood this about physics ….
This line of thinking is similar to the one Max Tegmark uses when he tries to make the case that, at the end of the day, the physical universe is just a special subset of mathematics (his “Mathematical universe hypothesis”) which is based on a form of radical platonism. There can be no leftover “baggage.” I always kind of liked it.
This raises the obvious questions:
1) Do you think there IS a bottom?
2) How would you ever know for sure that you’d hit such a bottom?
In other words, can physics ultimately avoid running into the same logic traps that in pure math lead to things like Godel’s Incompleteness Theorems or the Halting Problem? The problem with finding a ‘bottom’, with any potential final “theory of everything”, is that it will encounter the same fundamental logic issues that pure math discovered in the 1930s. Whatever properties, symmetries, or other ‘stuff’ you work with in your ‘bottom’ theory- be it abstract ‘information’, quantum states, etc.-, you’ll still going to then raise the obvious question of where THAT stuff comes from (and why).
The good news is that we’re almost certainly nowhere close to such a “theory of everything”, even it it exists. About the closest we’ve come to real physics theories that might suffer from this problem are efforts like “M Theory”, which are really more a collection of conceptual conjectures and pure math work than usable theories of physics. But it means the issue is already on the horizon.
Yeah. I have no idea whether there actually is a bottom. The idea of a physics “turtles all the way down” is vaguely terrifying, and feels on some level like it can’t possibly be the case…but I also can’t imagine how to avoid it.
In practice though, you almost always have an “effective bottom”. There’s a point at which it doesn’t matter whether there’s another layer, because you can’t measure that layer and it doesn’t make calculating anything easier. Most of the time in physics, you’re not looking for the bottom exactly, just “bottom enough”.
I started reading your blog. Great stuff man!
There is potential way out of this “turtles all the way down” issue. I am thinking of the metaphysical framework called ‘Ontic Structural Realism’ developed by James Ladyman and Don Ross in their highly regarded book ‘Every thing Must Go’. According to OST, very very crudely, there simply isn’t a bottom level, instead it’s relations all the way down. For example, when two electrons are in an entangled state it is hard to ascribe individual properties/observables to each separate electron – what is ‘real’ is really the entanglement relation.
Though their book is on metaphysics (a dirty word for many physicists) it does take modern science very seriously, so it’s worth a read (but pretty technical)!
Sounds worth a read!
I suspect the type of reduction Ladyman and Ross have in mind is a bit different than the kind relevant here though. It sounds like they’re looking at ontological reduction, which things are made of which other things. That’s a separate question from (I forget the term for this: theory reduction?), which is what we care about: the question of which explanations/sets of rules are the most fundamental. Those rules can be in terms of objects, or in terms of relations. The only question is whether you’ve got the “final” rules, or whether there’s another “more basic” set of rules they can be derived from.
Help me here. Isn’t all mathematics ultimately based on counting things? Pebbles, strides, apples, whatever? isn’t that the “bottom” of mathematics? What am I missing here?
Even counting isn’t “the bottom”. The most commonly used foundations of mathematics actually derive counting from more basic axioms.
I don’t see where in the linked page is anything supporting the “derivation” of counting. I’m not seeing that.
How something can be part of mathematics and yet so primitive that it must “derive” counting is hard to see also. I may be wrong; that’s for sure. But this seems to an extraordinary claim, requiring extraordinary evidence.
But thanks for your response.
Sorry, I think I was assuming you had heard of that axiom system, and just needed a reminder. It was popularized in the book “Goedel, Escher, Bach”, so a lot of “math fans” have heard of it…but of course that’s far from saying that everyone has, and I shouldn’t have assumed.
This page goes into more detail about how that system is commonly used to derive counting. The idea is you start with very basic notions, that you can have a set of objects and that that set can be empty, and that’s essentially all you need to get a notion of counting.
I have an old, battered copy of Douglas Hofstadter’s book at home. Old because I first embarked on the journey of reading it in the early 70’s; battered because there was more than one occasion where it frustrated me to the point I threw it against the wall.
And picked it up and threw it again.
And then picked it up and read the problematic passages again. And again. I may have to redo all that. It’s been a while, and the book is so broad and deep that I cannot possibly claim to recall everything; but I can say the notion of something so primitive or basic that one can derive counting from it seems extraordinary.
The linked page (thanks!) does not speak of deriving the notion of counting. I do not see how it could since the ZF set theory employs counting to define the natural numbers recursively; how could a method that employs counting claim to derive it thereby? Seems odd to say the least. Frege, Russel, and Hatcher likewise offered proposals for defining natural numbers; but I doubt any of them felt a need to explain what a natural number was; they were already known.
Certainly, these things provide a new, alternate, and useful definitions of natural numbers, but not by being more basic but by getting a different perspective on them. Much like GEB did with many things.
Take care. I hope you have an enjoyable Thanksgiving if you celebrate it. If not, have a good Thursday!