Is reality continuous or discrete?

Reality is whatever it is… only our models of it can be considered continuous or discrete (or true, or false, or useful).

I say this like it’s obvious, but it’s a potentially controversial opinion. 🙂

People have a strong tendency to confuse the map with the territory. So a very successful theory becomes synonymous with reality itself.

But things get murky when we investigate all the details of the theory. If we are being extra cautious about what we consider “real”, then we can always wait for experimental confirmation before believing in the existence of some thing or process proposed by a theory.

The most recent example of such an experimental confirmation is the finding of the Higgs boson. The Higgs boson was predicted by a prominent model of mass, and something very much like it was observed in our experiments. So we say it’s real.

Models in many branches of physics are so numerically accurate that there is little to be lost in treating them as synonymous with reality.

But discreteness is not really something an experimentalist can find in the same way as they might find a Higg’s boson.

Continuity is a convenient and extremely helpful assumption in mathematics — many of the tools of calculus rely on it. So to the extent that reality is accurately described by calculus, we can say (if we like) that reality is continuous.

But in practice all our measurements are discrete, because measuring devices have a least count — the smallest unit of measurement that the device can resolve accurately.

So if you are really committed to the idea that the universe is discrete, you can (if you like) insist that the continuity-based tools used in calculus are just convenient approximations of some deeper discrete reality. The onus is on you then, to show that equivalent discrete mathematics can give results of the same accuracy (or ideally, greater accuracy).

Roughly speaking, this is the direction that digital physics goes. The digital physicists have not yet replaced all the continuity-based mathematical tools with discrete versions, however. So for the time being, the real line will remain “real”. 🙂

But because of the practical limits on measurement that I mentioned before, it strikes me that no experiment will even be able to settle the debate.

At this stage someone might point to cosmological models that predict measurable phenomena that would be consistent with a discrete universe. It’s true that such models are possible, and may even be testable. But a sufficiently imaginative physicist or philosopher on the other side of the debate should be able to come up with an argument (either purely conceptual or mathematical) that can restore faith in the continuous-universe idea.

So… in my opinion ontological debates like this are pretty inconclusive. But that shouldn’t dissuade you from reading deeply about them! Sometimes inconclusive activities are fun. 🙂

Check out these articles in the Stanford Encyclopedia of Philosophy:

 

For what it’s worth, I like the idea that the universe “is” continuous, mostly because I dislike the idea that the universe “is” a simulation (for reasons that are too complex to get into here). This dislike is largely aesthetic. 🙂

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This originally appeared as an answer on Quora.

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The discreteness versus continuity debate resonates with Alan Watts’s distinction between “prickles” and “goo”. Someone made an animation to accompany Watts’s discussion of this, which you can watch on YouTube.