[Guest]

I was walking in the city last week when I came across an old fashioned organ grinder. He had a monkey on top of the organ who would dance as the old man rotated the drum. The monkey stared at me as I stopped to look. I then slowly began to walk around the organ, all the time the monkey kept turning and staring at me. When I got back to the point I had started from it was clear that I had walked around the organ, but had I walked around the monkey?

[Guest]

This is a variation on a classic puzzle...

Of course you walked around the monkey! The usual argument that you didn't goes something like, "from the monkey's perspective, you were always in front of him, so you never went around him/her."

Unfortunately, there are a couple of simple counterarguments:

1) From an inertial reference frame (the monkey's isn't one), you clearly went around the monkey.

2) The monkey and organ occupy the same point on the ground, so any statement like "I clearly walked around the organ" automatically precludes the possibility that you didn't also walk around the organ.

3) If you draw the path that you followed, it makes a closed curve that is homeomorphic to a circle, and which therefore has an inside and an outside. The monkey is on the inside, so you walked around him/her.

[Guest]

does a Geosynchronous satellite travel around the world? It always has the same view... thus never "sees" what's "around" the other side. I would think that orbit and going around don't necessarily mean the same.

Since the organ grinder did not turn, the traveler saw all angles of the organ and it's grinder. But no so for the monkey.

Edited November 27, 2009 by mabus

[Guest]

You walked around the organ as it was stationary, but the monkey I don't think so as it was turning as you were. Kind of like a wheel on a bike, the outside of the wheel (ie. yourself in this case) turns, as does the centre of the wheel (ie. the monkey).

otherwise it would be more like a disc on a spindle, the disc moves around a stationary point.

But I'd say no you didn't walk around the monkey, only around the monkey's position relative to yours'.

[Guest]

It only depends on the definition of "walking around" that you use.

[Guest]

I'm on g0atb0y37's side. Of course one goes around the monkey in going around the organ grinder. For one thing he circles the monkey's center of gravity just as surely as he does the organ grinder's. It is the same with the moon, that keeps the same hemisphere turned toward the sun. Can you imagine saying that as the Earth revolves around the sun once each year that the Moon (ours) does not also (give or take a few days, depending on its position relative to our planet)?

[Guest]

Seems more a problem of semantics than logic or math.

[pdqkemp]

At first I was 100% with g0atb0y37 and thought that it was irrelevant that just because the monkey rotated doesn't mean that you didn't go around him. The best argument against that was mabus' point about a Geosynchronous satellite. From the perspective of the satalite you might say, "no, the satalite never actually goes around the Earth."

However, what if the satalite was traveling the opposite direction from the Earth's rotation? From the satalite's perspective, it would revolve around the Earth twice per day. But from any point "A" to that same point "A" it clearly only makes 1 revolution per day.

I'm with "Yes". The man did go around the monkey. The perspecitive of either party is irrelevant.

Tuckleton made a good point in that it's really a question of symantics. To take my point to an extreme, let's roll a quarter across a table. I could say that the edge of that quarter went around and around Washington's head. Did it? Is it any different logic just because the edge of the quarter is connected directly to Washington's head? I think it's not any different. I think the edge DOES go around his head, but I think you could argue the symantics of "around".

[Guest]

Seems more a problem of semantics than logic or math.

It's not really semantics, substitute "encircle" for "go around". I did encircle the organ, but did I encircle the monkey?

[Guest]

I dunno. It seems to me that if you provided a rigorous definition of what you mean by 'go around', or encircle, the question would answer itself.

But, in keeping with the spirit of the question:

It all depends on which frames of reference are allowed under the definition of encircle. In this case I'm with g0atb0y37. I mean sure, from the monkey's perspective it's true you didn't, but from the monkey's perspective it's also true that almost everything else in the universe DID.

[Guest]

I still say he did not go around the monkey. Further more, if the monkey turn in the opposite direction at the same speed, then the man would have went around the monkey twice.

On the other hand, what if the monkey spun around while the man just stood there? What then? The man would not have went around him at all... arrg.. I am arguing with myself now. Make it stop. Make it stop!