Q: Are shadows 2-dimensional? Are there any real examples of 2-dimensional things in the universe?

Physicist: If you think of a shadow as the lack of light created by an object blocking a light source, then shadows are 3-D.  After all, it’s dark everywhere behind an object, not just on the surface of another object.

Is a shadow the dark volume behind stuff, or the dark surface on other things?

If, on the other hand, you define a shadow to be what we see and intuitively think of (the dark, parroting person on the wall, with whom you can shadow box) and not the volume in between, then shadows are 2-D.

However, that second definition is a little abstract, because there’s no real physical significance.  You could say that the border between countries is a one dimensional line along the ground, but there are no physical laws that have anything to do with national borders, so it doesn’t matter.

Defining exactly where the surface of an object is (what with all of their atoms) is like trying to define exactly where the surface of a ball pit is.

It’s impossible to get something that’s genuinely 2-D in our universe for several reasons, the simplest of which is that atoms themselves are 3-D.  So even the flattest flat thing will still have some 3-D-ness (at least a quarter of a nanometer or more).  That said, there are innumerable examples of things that behave as though they were 2-D.  In situations where one direction is restricted compared to the others you’ll often find that the physics follows suit.

Hurricanes and other very-large-scale weather phenomena roughly obey 2-dimensional physics.

For example, ripples on the surface of water are an example of 2-D waves that behave very differently from ordinary 3-D waves.  Weather systems that are substantially bigger across than they are tall, like hurricanes (e.g., Sandy was about 800 miles across, and only about 5-10 miles high), roughly obey 2-D fluid dynamics.  Normally the energy in a fluid (or gas) starts out with big eddies and moves into smaller and smaller eddies (you can see this if you pour cream into some coffee and then stare at it).  However, very weirdly, in a 2-D fluid you find that the opposite tends to be true: energy starts out in small eddies and moves to larger.

If it weren’t for the flatness of the atmosphere (and some obscure math involving “entropy flow” in 2-D fluids) we wouldn’t get hurricanes!

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9 Responses to Q: Are shadows 2-dimensional? Are there any real examples of 2-dimensional things in the universe?

  1. David Sher says:

    Orbits of planets and moons seem to be 2d. I’m no astrophysicist though.

  2. Amir says:

    I believe this “However, very weirdly, in a 2-D fluid you find that the opposite tends to be true: energy starts out in small eddies and moves to larger” part needs an answer gravy.

  3. The Physicist The Physicist says:

    It really does need some gravy. Unfortunately I can’t remember where I read that particular derivation. It’s in a book or paper or some notes or “other” on “non-equilibrium statistical mechanics” (which is like thermodynamics, but totally off the hook). It was something like; start with the Fokker-Planck and Navier-Stokes equations, and conservation of mass, then re-write all of it in terms of their the Fourier transforms.
    Then, after a day or two, ask for help (because that mess is pretty tricky). You find that in two dimensions the Fourier spectrum tends to “drift down” over time, which means that the size of the “structures” in the fluid get bigger.

  4. The Wonderer says:

    Could you post what the final Forrier transformation looks like?

  5. Buck Field says:

    Again, from a risk management point of view, it is a terrible idea to assert that the existence of hurricanes (physical reality) is dependent on concepts in people’s heads, i.e.: “obscure math involving “entropy flow” in 2-D fluids”.

    This violates a basic foundation of science, that reality exists independent of our perception, and given the profound impact of language on cognition, the “just an expression” justification does not stand in light of persistent, fundamental mysteries.

  6. David Blakey says:

    Wouldn’t rainbows or the the resultant prismatic effects of refraction two-D?

  7. Firepac says:

    If you have a projector and you project an image onto a screen, that image is 2D.

  8. Anthony ratay says:

    I think rainbows and the projector would fall in the same category as the shadow. There is depth to both the rainbow and the projector if you consider the space between the source ( the projector lense) and your eyes or camera iris.

    Are there any examples of anything other than 3 dimensional structures or systems in the universe?

  9. Paul Czerner says:

    A shadow is not a thing, it is the lack of a thing. And in the universe, an object is also the lack of every other object in the same space. That does not make the lack of everything else a 2-dimensional object.

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