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What does it all mean?

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.

  1. Jon Carter
    June 13, 2012 at 3:03 pm

    I really like this blog, Alex. Got me thinking, hopefully not too randomly.

    I like to think I’m not afraid of maths but I certainly share the view you present in here. Taking your Digital analogy and stretching it a bit, in many ways trying to understand nature (the very large and the very small) from where we are is like reverse engineering the Intel processor operation, starting with this Facebook app. There are so many theories that I could come up with as to how it works but we need to understand each layer properly before we can peel another layer off the onion and find out how the next level down of smaller things work.

    I’m a fan of the elegance principle for science and I think reading between the lines, so are you. If something looks a bit too complex or clunky there’s normally something not quite right with the model you are using. I think that in general complexity emerges from the interactions of relatively simple things – and layers of things working with building blocks from the next layer down.

    I certainly agree that an algorithmic rather than equational approach to modelling physics would certainly help many people ‘get it’ more easily. Just had a similar discussion this morning about modelling notations that IT people use. You can’t really talk to business (or normal!) people using UML notation – in my poor analogy like the maths of the software engineering.

    Introducing elements just because it makes the maths works – in the absence of a more logical/algorithmic backing – seems like a massive fudge. This can be valid as a hypothesis but demonstrating it purely based on mathematical proof seems a bit shaky.

    e.g. I was reminded of the Backprop Neural Network training algorithm. This algorithm works just fine but I remember a lecture on the proof (lots of maths!) that it would terminate. Great, so we know that the algorithm won’t get into an infinite loop. Wouldn’t demonstrating that more algorithmically have been a lot clearer to the class? Of course, there are times when proof is a requirement but then we’re into that whole tricky area of maths/science of provable and non-provable conjectures, aren’t we?

    Thinking more about your blog reminded me of the strong AI / behaviourist AI debate that we covered way back when. There’s an argument that if our model (however many additional dimensions we need to throw in!) works and enables us to make predictions about particular scenarios, then that’s great. However, the more fudges we have to add, the more likely our next scenario will break the model. But that’s the scientific process, provided we remain open to the fact that any scenario can break our model and we will need to refine it (hopefully not by adding fudges!) to make it work. And so we iterate towards a model that does actually accurately represent the way things really work.

    Coming back to the specifics of what you’re looking at, the massive problem with sub-atomic particle physics, quantum theory etc. is that it can be really hard to test things. How long is it since Higgs suggested his boson and we still haven’t been able to see if it’s real or not – to test the hypothesis! However, although maths helps and is a very powerful tool, it is man-made and I think we need some empirical evidence of things rather than relying on the fact that the maths says it is. I’m reminded of a recent episode of The Big Bang Theory where Sheldon asks Stephen Hawking to read his paper only to have Stephen point out an arithmetical error on page 2….

    As you say, this is where Digital Physics can help, surely. We can build models of the universe and test things out. It seems that in the world of the very small, there are far fewer things to worry about than e.g. when trying to model Meterology! We might not understand yet what all the interactions are but we can test some things out and these models can then help us a lot when we go looking for empirical evidence. And again, if the models accurately make predictions – let’s take advantage of that until we break them. Even if this means doing without extra dimensions and so. Regardless of what the currently received maths says – to heinously paraphrase Holmes, if the model works, however unlikely, it might well be the answer.

    • June 13, 2012 at 11:30 pm

      Hi Jon! Great to hear from you!

      Basically, yes. Agreed. We’re on the same page and I’m delighted that you’re enjoying the blog. And I’m definitely a fan of the elegance principle.

      Throughout the processes of research and blogging, I’ve tried hard to be fully honest with myself about what I’m seeing and doing. I’m not a physicist. When I read the science papers, I’m constantly thinking uphill. However, the more time I spend exploring this field, the more I become convinced that this kind of modeling has something to add.

      It’s extremely easy to create ornate mathematical structures to describe nature that are completely self-consistent, but just wrong. Take tachyons, for example. The moment we take one of these structures and use it to explore the realm beyond experimental testability, we have a problem. Our mathematical castles are only as robust as the cognitive clouds we place them on. Thus, when testability is lacking, something else must take its place, even if, at the end of the day, it’s a pale substitute. This is where computability and implementability come in.

      Your point about AI is well taken, and I think it’s relevant here. It often strikes me how what I’m building is an extension of an AI research approach into a non-AI field. I think the process of thinking and exploring complex, unpredictable algorithmic systems is relatively rare outside of AI, even in mainstream computer science. Both digital physics and AI seem to me to come under the heading of experimental computer science, a field that I don’t thing is fully recognized yet, despite rapid growth over the last ten years. The same field of study encompasses a host of agent-based, and network-based, models in biology.

      Work on machine learning has had a wonderful impact on cognitive science, IMO, even though no-one is expecting the brain to turn out to be a Unix box. Framing an old problem in a different guise can be incredibly useful.

  2. June 18, 2012 at 2:09 pm

    Wow, this post says it all for me. In my own blog, I am trying to express my views of reality, based on my intuitive interpretations of present day physics and cosmolgy. I do this in a journalistic style from the standpoint of an educated layman generalist. I then sugar-coat it with cosmic satire to engage a general audience and maybe create more public interest in this stuff. But for a serious discussion and interpretations of reality based on today’s science from one of the world’s most brilliant minds–whom I think would agree with your viewpoint–read either of David Deutsch’s two fine books: “The Beginning of Infinity” and “The Fabric of Reality”

    • June 19, 2012 at 9:56 pm

      H Mark!
      Thank you for the recommendations and also your enthusiasm for this post! I’m familiar with David Deutsch’s work, though I haven’t yet read his books. He seems an interesting thinker. I suspect I will differ with him over the significance of QM and the many-worlds interpretation, but that’s all part of the fun.

  3. June 19, 2012 at 11:14 pm

    Maybe you will differ on the many-words interpretation, but I think you are on the same page as far as what you were suggesting in this post. He sees science as very much depending on explanations of what is going on–not just mathematical calculations.

    • June 20, 2012 at 12:11 am

      Which is marvelous. I’ve heard him speak and he was very impressive. Now that you’ve prompted me, I’m going to give his book a try. After all, one shouldn’t let a few trillion hypothetical universes stand in the way of a good read. 🙂

  4. Jon Carter
    June 20, 2012 at 12:03 pm

    I was going to ask your view on the multiple-universes thing. Going back to the “maths says it would work, so…” thing – and rather, looking at Digital Physics, what does the Digital perspective tell us (if anything) about the multi-universe situation?

    Stretching your approach to use my software analogy again, multi-universes suggests that at each decision point, the object representing me is cloned and that clone is sent to one of the new universes. An object cannot straddle more than one universe, and future decision points would take each clone into vastly different contexts, so there would need to be copies not references!

    The thing that concerns me is what counts as a decision point? Do I create one each time I tap a key, so there’s a universe where I never mistype and have to back up? Any kind of rule about what counts as a decision point seems to be something really nasty – making decisions about the scale or scope of the decision point could get rather subjective and therefore not very predictable. I don’t think that a decision point requires interactions with other ‘objects’ – again, too complex. So that leaves us with everything. Every potential decision. That’s a lot of decision points and therefore a lot of universes. I don’t think trillions does it!

    And of course, at what scale does this apply. Surely, if it applies for me, it applies to every person on this planet and all the others and right down to every fundamental particle in the universe. Possible, but seems increasingly messy – and to me a bit less likely.

    That we [at least appear to] interact with other objects (people, atoms in my laptop, etc.) suggests that either each of us lives in their own virtual reality or that these multiple universes overlap so that one of your multi-verses is also one of mine. I’d like to see the algorithm for that – because that can’t be purely random. The decisions I make have to have some sense of relevance for the decisions that you’ve made for us to exist in the same multiverse.

    I’m going to stop now on this (!) but it strikes me that although theoretically possible, trying to construct the digital environment to model this accurately might suggest that it’s not as straight forward as all that.

    Disclaimer: I’m writing all this based on very little reading about the multiple universes theories, so I may be talking rubbish!

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