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What Science Is

In my last post, I promised to start convincing you that believing in discrete space was the same thing as believing in science. For some of you out there, that’ll be a pretty tall order. I have no idea whether I’m going to pull it off, but that, in part, is what blog is all about. If you disagree with what I have to say, please comment. We invite all critiques, because without crits, our ideas don’t grow.

Having said this, probably the best place to start is to say what I think science is, and what it means to believe in it. The mighty Wikipedia suggests to us that science is, perhaps unsurprisingly, a system of acquiring knowledge based on scientific method.

It goes on to suggest that science advances based on the iteration of approximately four steps:

1. Use your experience: Consider the problem and try to make sense of it. Look for previous explanations. If this is a new problem to you, then move to step 2.
2. Form a conjecture: When nothing else is yet known, try to state an explanation, to someone else, or to your notebook.
3. Deduce a prediction from that explanation: If you assume 2 is true, what consequences follow?
4. Test: Look for the opposite of each consequence in order to disprove 2. It is a logical error to seek 3 directly as proof of 2?

The philosophy of science is a deep and thorny topic, and there are no doubt many people who’d debate the outline above, but for our purposes, it’ll do as a starting point. What’s important about this process, I’d suggest, is that it’s a recipe for building a model.

What I mean by this is that an explanation describes a phenomenon in terms of causes and effects, and ties them together using mechanisms that are simpler to understand than the thing we originally sought to explain. Once again, Wikipedia can help us. It describes an explanation as:

a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequences of those facts. This description may establish rules or laws, and may clarify the existing ones in relation to any objects, or phenomena examined.

To put it simply, an explanation is a statement of why something happens, in terms of other types of experience that we already know how to model and predict. (Note that this means that the act of explaining anything is fundamentally reductionist, and that every explanation is, in essence, a kind of program.)

What’s different about the models that science comes up compared to, say, religious models or paranoid fantasies, is that scientific models are judged entirely on the basis to which they fit experience. Science doesn’t care how much we like a particular explanation, or how useful it’s been to us in the past. It either fits the data or it doesn’t. Science also insists that the models it uses have predictive power. Explanations like ‘God did it’, or ‘the universe is mysterious’ can tidily match any kind of data we want to look at, but they won’t tell us what’s likely to happen next.

I would argue, then, that to believe in science is to believe that a sequence of reductionist statements are going to be all that we need to explain the entire universe we live in down to its smallest components. And that those statements will never need to invoke some underlying mechanism that lacks any predictive power. (We’ll never need to reach some level where we throw up our hands and say ‘God did it!’) However, before I explore the implications of this idea, it’s first worth mentioning another important feature of scientific thinking.

A deeply held goal of scientific explanations is that they be elegant. Many people are familiar with the idea of Ockham’s Razor: that when considering two explanations, we should prefer the one that is simpler. However, they’re generally less familiar with the work of Leibniz, who had some deep and interesting things to say on the value of simplicity. Here’s how the great mathematician Herman Weyl described Leibniz’s position:

The concept of a law becomes vacuous if arbitrarily complicated laws are permitted, for then there is always a law. In other words, given any set of experimental data, there is always a complicated ad hoc law. That is valueless; simplicity is an intrinsic part of the concept of a law of nature.

This statement relates back to the idea that our explanations must be predictive. In essence, what we’re saying here is that if we have to keep extending our explanation every time we see something new, it’s not very scientific. The most scientific explanations, then, are the ones that grant the most predictive power from the least number of model components.

What this means is that coming up with a scientific model is a bit like zipping up a file on a computer. When we zip up a file, we look at the contents and work out whether there’s a way to store everything in it that requires the usage of less bits of information. Just as zipping up a file is data compression, modeling nature is, in effect, experience compression. We want to work out what will happen in an experiment in a way that’s more efficient than just watching it happen each time.

While this principle of elegance is important, it’s one that science holds to less tightly than the others we’ve mentioned. That’s because it’s possible to come up with a lot of very elegant looking theories that don’t actually fit the data. Sometimes you have to throw elegance out in order to get the answer right.

Perhaps the most extreme example of this comes in the case of a TOE, or Theory of Everything, of the sort that contemporary physicists are looking for right now. A TOE describes all the phenomena that the universe can come up with. Theoretically, if we had one, we could run a simulation using that theory, along with a big bucket of random numbers, and simulate a universe that looked very much like our own. However, it’s important to note that such a theory can only be as elegant as nature actually is. There can be no compression in such a model because in order to do its job, it needs to match everything. This is a different kind of elegance to the elegance of, say, Newton’s Laws. Newton’s Laws give us a very accurate sketch of how objects behave for a small computational cost. However, at root, they’re inaccurate. With a TOE, this isn’t allowed. What constitutes elegance, then, changes with how much of the universe we expect our explanation to capture.

This idea of what elegance means is going to be important to us later on, and now that we’ve covered what believing in science actually entails, we’re in a great place to explore what it implies. So far, though, I’ve still said nothing about discrete space, let alone convince you that it’s vital to the future of physics. Sadly, though, I’m out of time for today. Next time, I’ll start explaining where digital physics fits in. Either that or I’ll start posting some results. So far, my blog posts have been a little heavy on philosophy and light on action. That’s got to change.

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Categories: Uncategorized
  1. March 4, 2010 at 11:17 am

    “There can be no compression in [a TOE] because in order to do its job, it needs to match everything.”

    I’m not sure this is necessarily true, is it? We can ‘compress’ the infinitude of natural numbers with a simple series descriptor, can’t we? We can get any number we want to by running this descriptor through a computer until we have the one we’re after.

    Similarly, I’m not sure why Newton’s laws are “at root” inaccurate? Are the inaccuracies you mention down to the inability to have perfect starting data? If so, why would this mean that the Newtonian models are inaccurate, rather than that our ability to operate those models are hampered? Just because you can only feed ‘contaminated data’ into a perfect machine, it doesn’t necessarily make the machine imperfect…

  2. March 4, 2010 at 1:50 pm

    Incidentally, I found this online book fascinating and very clear on the subject:

    http://www.mtnmath.com/book/rev.html

  3. Keir Finlow-Bates
    June 1, 2012 at 4:42 pm

    Let’s shoot for a TOAE instead then…

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