I’ve recently seen a couple of interesting posts pondering to what degree mathematics models actual real world objects.

For an upcoming episode of the Rationally Speaking podcast, Massimo Pigliucci and Julia Galef interviewed Max Tegmark, who seems to believe that all of reality is ultimately mathematical. Note that Tegmark doesn’t mean that it is precisely described by mathematics, but that it *is* mathematics. Massimo is skeptical, while noting that mathematics is so useful it’s hard to imagine it doesn’t in some way relate to real world objects.

Jason Rosenhouse, who I’m very happy to see blogging again after a break, highlights an interview with Edward Frenkel, who seems to believe that while mathematical objects exist, they are outside of the physical world and consciousness. While noting that this belief is common among mathematicians, Jason expresses skepticism, but like Massimo, he also seems to believe that mathematics relates to something in the world.

This seems to be a timeless question. Personally, I think mathematical concepts do model real world patterns, at least to some degree of approximation. A mathematical model is either right or wrong. That rightness or wrongness ultimately resolves to how well it relates to real world problems.

Of course, you could say that since mathematics doesn’t exactly match real world patterns, that it’s just a useful tool invented by humans. But you could say that about *anything*. A tree exists, except that our conception of a tree is just a mental model we use to describe a complex evolving pattern of elementary particles. Our model of a tree never matches the reality exactly. Therefore, we could say that the tree concept is just a tool for humans.

From a certain point of view, that view is true. But I’m not sure how useful that truth is, except perhaps to caution us about the limitations of our understanding of reality.

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Thanks Eric. The simulation hypothesis is interesting, but I’m a bit skeptical that we could ever devise a conclusive test for it. Any anomalies we might find could be due to graininess or some other flaw in the simulation, or it could simply be how reality works. I’m not sure how we could tell the difference. As beings inside the simulation, we would have no reference to the outside “real” world to compare to the conditions inside the simulation.

The interesting question is what our responsibilities would be if we ourselves ever build simulations with simulated beings in them. If those simulated beings think they’re real, and we then cut off the simulation, will we have just committed genocide?

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I’m not pushing it – the thing is that a computer as we have come to understand them is a device that uses limited states to express anything and everything that is inside of it – data related, that is. New computers will attempt to harness quantum physics that allows for potentials – thus limited states will occur as needed, and otherwise the resources will remain non-physical. Usually when people discuss the universe as a simulation, they ar thinking in terms of a home computer on a grander scale — not so.

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Actually mathematics derives from observation or from consciousness. Either our brains designed it because it helps us cope or it is inherently our reality.

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I agree. I think mathematics models the real world, but not necessarily from empirical observation. I’ve seen studies implying that we may be born with a simple understanding of quantities, and I suspect that this fundamental understanding, this evolved instinct, confuses us about whether or not mathematics pertains to the real world.

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If you look about, there are a few descriptions somewhere by Max Planck and by Richard Feynman that indicate that mathematics is a language of the heart.

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Great post! I absolutely love the tree analogy. I personally always though if mathematics as a tool, but now now I’m not so sure. Love this kinda stuff! 🙂

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Thanks! On loving this stuff, I very much agree.

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While I’m not necessarily convinced by Tegmark, it is thought-provoking. Why should “things” get ontologically privileged above relations? Does it make more sense to claim that there’s a “thing” at bottom rather than a “relation”?

In case I haven’t said this, I really like how you are posting bulletins of interesting things, with some comments. There’s tons of interesting stuff out there, and collecting it is a valuable service. Thank you!

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I agree that it is thought provoking. I can see where he’s coming from. Reality might be structure all the way down.

I’m grateful for the feedback, particularly from a successful blogger! I generally try to only link to things when I have something to say about it, not having the time or energy to be a news source. It’s heartening to hear that you find it useful.

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