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Wittgenstein's Question

Elizabeth Anscombe reports the following anecdote about Wittgenstein:

He once greeted me with the question: 'Why do people say that it was natural to think that the sun went round the earth rather than that the earth turned on its axis?' I replied: 'I suppose, because it looked as if the sun went round the earth.' 'Well,' he asked, 'what would it have looked like if it had looked as if the earth turned on its axis?'

Of course, the answer to Wittgenstein's second question is that it would look the same.

But Anscombe's answer to Wittgenstein's first question isn't quite right. It's not so much that it looks like the Sun orbits the Earth, but that it feels like it.

Imagine yourself on a playground roundabout. As you spin around, you feel the air rushing past you and the centrifugal force flinging you outwards. Intuitively, we think that if the Earth was rotating on its axis then we would also be able to feel it, and since we don't feel anything, we conclude that the Sun must be orbiting the Earth.

But our human scale physical intuition is mistaken when it comes to the rotation of the Earth. We don’t feel the air rushing past us because the atmosphere is rotating along with the planet. And we don't feel the centrifugal force because it is extremely weak (only 1% of what you would feel on a playground roundabout) and gets completely swamped by gravity.