Jul. 19th, 2017

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When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.

~Walt Whitman



I first encountered this poem in high school English, and I come across it again every few years. I can't explain entirely the rage it summons in me.

But maybe this is the point I wish to make. A friend mentioned the Randall-Sundrum model of the universe and I went to that wikipedia page to try to learn what that was. Pretty soon I was desperately linkhopping- I have a basic education in relativity and differential geometry, but pretty basic, and even the vocabulary I did learn at some point, it's been a decade since and I needed to refresh my memory.

So I clicked on anti-de-Sitter space and from there to Lorentzian manifold and from there to Riemannian manifold, and I want to point out something about these four articles.

The article on Randall-Sumdrum model begins "In physics" The article on Anti-de-Sitter Space begins "In mathematics and physics." The articles on Lorentzian Manifold and Riemannian Manifold begin "In differential geometry." There's that tricksy slippage between physics and mathematics Whitman is writing about. Are the learn'd astronomer's "proofs, the figures," his "charts and diagrams" a meaningful and interesting representation of the actual stars, or are they just lifeless mathematical models that lack the "mystical" potency of observing the stars with the naked untrained eye? Aside from answering this question, though, the distinction is, I think, actually important to doing physics. Because if you theorize that spacetime takes a certain shape that can be modeled by a particular manifold, and then your measurements in an experiment don't match the manifold, you have to consider two different possibilities: One, that spacetime doesn't match your theorized model, and two, that your measurements were inaccurate. But if you're a mathematician working with a manifold and it doesn't match your expectations, only your math is wrong.

So this distinction Whitman writes on matters. There are the mathematical models of the stars, and there are the actual stars themselves, and if you forget this you end up confusing the manifold with the spacetime. A physicist needs both to do their work.

Nonetheless, I feel a great rage when I read Whitman's poem, a rage at the idea that the untrained eye bestows a more exciting and therefore truer reality than the subtle delver into the measureable mysteries of the cosmos can attain through experimentation and analysis. This may be dogmatic scientism on my part, but if so, let it be!

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