The Monkey and the Stick

I was reading the introduction to _The Canterbury Puzzles_ by Ernest Dudeney.

In that introduction, he mentions an old saw: a young boy is holding one end of a
stick, and he walks around in a full circle. Sitting on the other end of the
stick is a monkey. As the boy walks, the monkey always turns to face the boy.

Does the boy go around the monkey, or not?

Dudeney was emphatic that, yes, the boy did go around the monkey, and those who
try to say otherwise have to come up with contrived definitions of what it means
to "go around" something.

It's certainly true that they boy did walk around in a circle, and the monkey was
within that circle, and he passed the monkey by the east, north, west, and south.

But there was one way in which one could think of him as not having gone around
the monkey - in his walk, he never had the chance to sneak up on the monkey from
behind. So if one defines a co-ordinate system centered on the monkey, with one
axis pointing in the direction the monkey is facing, then the boy didn't circle
around the monkey from _that_ point of view.

John Savard

Quadibloc wrote:
I was reading the introduction to _The Canterbury Puzzles_ by Ernest Dudeney.

In that introduction, he mentions an old saw: a young boy is holding one end of a
stick, and he walks around in a full circle. Sitting on the other end of the
stick is a monkey. As the boy walks, the monkey always turns to face the boy.

Does the boy go around the monkey, or not?

Dudeney was emphatic that, yes, the boy did go around the monkey, and those who
try to say otherwise have to come up with contrived definitions of what it means
to "go around" something.

It's certainly true that they boy did walk around in a circle, and the monkey was
within that circle, and he passed the monkey by the east, north, west, and south.

But there was one way in which one could think of him as not having gone around
the monkey - in his walk, he never had the chance to sneak up on the monkey from
behind. So if one defines a co-ordinate system centered on the monkey, with one
axis pointing in the direction the monkey is facing, then the boy didn't circle
around the monkey from _that_ point of view.

John Savard


But doesn't your last case count as a contrived definition?

On Sunday, 15 May 2016 14:26:11 UTC+2, Quadibloc wrote:
I was reading the introduction to _The Canterbury Puzzles_ by Ernest Dudeney.

In that introduction, he mentions an old saw: a young boy is holding one end of a
stick, and he walks around in a full circle. Sitting on the other end of the
stick is a monkey. As the boy walks, the monkey always turns to face the boy.

Does the boy go around the monkey, or not?

Dudeney was emphatic that, yes, the boy did go around the monkey, and those who
try to say otherwise have to come up with contrived definitions of what it means
to "go around" something.

It's certainly true that they boy did walk around in a circle, and the monkey was
within that circle, and he passed the monkey by the east, north, west, and south.

But there was one way in which one could think of him as not having gone around
the monkey - in his walk, he never had the chance to sneak up on the monkey from
behind. So if one defines a co-ordinate system centered on the monkey, with one
axis pointing in the direction the monkey is facing, then the boy didn't circle
around the monkey from _that_ point of view.

John Savard

The only obvious variation allowed [within the explicit parameters expressed] is that the monkey is not at the center of the boy's circle.

Any part of the length of the stick is allowed to be the center of the boy's circle.

They both rotate about that center but the boy does not pass around the monkey.

In article ,
Quadibloc wrote:
I was reading the introduction to _The Canterbury Puzzles_ by Ernest Dudeney.

In that introduction, he mentions an old saw: a young boy is holding one end of a
stick, and he walks around in a full circle. Sitting on the other end of the
stick is a monkey. As the boy walks, the monkey always turns to face the boy.

Does the boy go around the monkey, or not?

Dudeney was emphatic that, yes, the boy did go around the monkey, and those who
try to say otherwise have to come up with contrived definitions of what it means
to "go around" something.

It's certainly true that they boy did walk around in a circle, and the monkey was
within that circle, and he passed the monkey by the east, north, west, and south.

But there was one way in which one could think of him as not having gone around
the monkey - in his walk, he never had the chance to sneak up on the monkey from
behind. So if one defines a co-ordinate system centered on the monkey, with one
axis pointing in the direction the monkey is facing, then the boy didn't circle
around the monkey from _that_ point of view.

So the Moon goes round the Earth, but the Earth does not go around the Moon?

This breaks the symmetry of physical laws; in that your frame of reference
does not matter.

-- mrr

On Monday, May 16, 2016 at 7:33:24 AM UTC-6, Morten Reistad wrote:

So the Moon goes round the Earth, but the Earth does not go around the Moon?

This breaks the symmetry of physical laws; in that your frame of reference
does not matter.

The Earth and Moon both go around their common center of gravity; and they both
go around the Sun.

Accelerated frames of reference aren't symmetrical in that sense, as
acceleration can be detected. It can even be distinguished from gravity, if one
is engaged in detection over an area or volume instead of a point.

John Savard