Is it more correct to say that a dog wags its tail, or that the tail wags the dog?

Common thinking is that the larger mass influences or moves the smaller one. But if Newton is right, then it is also true that the tail is wagging the dog, because for each and every action, there is an equal and opposite reaction.

In conclusion, a dilemma arises: should we indeed think of dogs as wagging their tails, as we have it in ordinary parlance? I leave you with a quote:

"The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it." - Bertrand Russell

  • 1
    "Does this universal gravitational constant make me look fat?"
    – user4894
    May 11 at 2:20
  • There was a similar ancient question about a flag fluttering in winds. Some say it's flag which is moving, while others say it's wind which is moving... May 11 at 2:46
  • Let $p$ be that the dog wags. Let $q$ be the dog has a tail. Let $r$ be that the tail has a dog. $p$ implies $r$ but also $q$ implies $r$. Interesting...Let $F$ be that the dog has a field's medal. None of these imply $F$. May 11 at 2:50
  • The wailing originates in the nervous system of the dog, so definitely even in free fall the dog is wailing its tail, not the other way around.
    – armand
    May 11 at 11:07

When a dog wags its tail, the tail exerts a counterforce on the dog which is small compared to the weight of the dog. In this instance it is common to say that the dog wags its tail, meaning that the tail does most of the wagging and the dog's body does very little.

If the dog's body weighed the same as the dog's tail, then when the dog flexes its muscles to wag the tail, the counterforce is great enough that both the dog and its tail are wagging in opposition to one another.

  • 1
    There's also the fact that the dog is in contact with the ground so the force of static friction prevents the momentum change of the tail during a single wag from causing a completely equal and opposite momentum change to the dog alone--due to the friction that momentum ends up getting dissipated into the ground under the dog's feet (see this answer on the physics stack exchange). If the dog was floating in a space capsule you might be able to see the tail wagging the dog, at least a tiny bit!
    – Hypnosifl
    May 11 at 2:59
  • @Hypnosifl, why not post this as an answer? May 11 at 4:50

Common thinking is that the larger mass influences or moves the smaller one.

Common thinking sure. But not Newton. The sun is hugely, gigantically bigger than Earth so it can be treated as purely orbiting the sun. But Jupiter is big enough that the combined centre of mass with the sun, is a solar radius beyond the suns surface. It is often convenient to talk as though the sun is stationary, but the equations are always about both masses.

Reference frames, and conceptual groupings, are about their usefulness. We use the phrase 'That's the tail wagging the dog' exactly to highlight a small actor exerting unexpected influence.

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