Mental Nuts-- Can You Crack 'em?

[classicman]

Originally Posted by infinite monkey

No, it's geometry.

If the hunter circles the tree and the squirrel is ON the tree, then the hunter circles the squirrel.

[footfootfoot]

Originally Posted by classicman

If the hunter circles the tree and the squirrel is STATIONARY ON the tree, then the hunter circles the squirrel.

The earth does not orbit mercury

Maybe this experiment will help: you will need someone to play the squirrel and you will need a piece of rope.

Premise: If you go around someone or something with a piece of rope (with one end of the rope affixed to the someone or something, the other end in your hand) then when you have made a complete circle they will have one turn of rope wrapped around them. Do you agree?

If you do not encircle them then there will be no rope wrapped around them. Do you agree?

Now, try going around your pretend squirrel with one end of the rope in your hand and the other affixed to the squirrel. If the squirrel is stationary you will encircle the squirrel with the rope.
Now try the same thing only this time, the squirrel always turns in the same direction as you. For added realism you can do this outside around a tree. See how many times you managed to encircle the squirrel with the rope.

Have someone record a video of it and put it up on youtube.

[BigV]

Originally Posted by footfootfoot

The earth does not orbit mercury

Maybe this experiment will help: you will need someone to play the squirrel and you will need a piece of rope.

Premise: If you go around someone or something with a piece of rope (with one end of the rope affixed to the someone or something, the other end in your hand) then when you have made a complete circle they will have one turn of rope wrapped around them. Do you agree?

If you do not encircle them then there will be no rope wrapped around them. Do you agree?

Now, try going around your pretend squirrel with one end of the rope in your hand and the other affixed to the squirrel. If the squirrel is stationary you will encircle the squirrel with the rope.
Now try the same thing only this time, the squirrel always turns in the same direction as you. For added realism you can do this outside around a tree. See how many times you managed to encircle the squirrel with the rope.

Have someone record a video of it and put it up on youtube.

But no one, except you, perhaps, define how to make a circle this way, where both ends are moving.

I, and some others, I daresay, define a circle (in this vernacular, vulgar example) as a closed path lying in a plane, with a center and a stationary radius. The area swept by the radius is "inside" the circle, the path traced by the other end of the radius not at the center "is" the circle and everything else beyond the distance of the radius is "outside" the circle.

Stuff inside the circle has been circled.

In your illustration, there are an infinite number of ways to get a turn of rope around the squirrel. And, yes, I can clearly see the situation you describe, and the squirrel won't be encircled. I see that. In your illustration NOTHING will have been encircled, not even the tree. Are you saying that by "attaching one end of the rope to the squirrel" that the tree escapes too?

[jimhelm]

Originally Posted by footfootfoot

The earth does not orbit mercury

Maybe this experiment will help: you will need someone to play the squirrel and you will need a piece of rope.

Premise: If you go around someone or something with a piece of rope (with one end of the rope affixed to the someone or something, the other end in your hand) then when you have made a complete circle they will have one turn of rope wrapped around them. Do you agree?

If you do not encircle them then there will be no rope wrapped around them. Do you agree?

Now, try going around your pretend squirrel with one end of the rope in your hand and the other affixed to the squirrel. If the squirrel is stationary you will encircle the squirrel with the rope.
Now try the same thing only this time, the squirrel always turns in the same direction as you. For added realism you can do this outside around a tree. See how many times you managed to encircle the squirrel with the rope.

Have someone record a video of it and put it up on youtube.

this is a bit of a straw man. you would need to anchor the other end of the rope to the tree in order to be analogous to the problem at hand.

[Clodfobble]

Originally Posted by footfootfoot

Yes. The hunter does not go around the squirrel. They both go around the tree but the squirrel always keeps the tree between himself and the hunter. For the hunter to go around the squirrel it would need to stay in one place on the tree.

Well you know what else? Heisenberg says both are orbiting the tree, and you can't say for certain where either one is in their orbital path at a given time. But you do know that the hunter is in a higher orbital than the squirrel, and the higher orbital plane does encircle the lower orbital plane. The more time that passes, the higher the statistical probability that the hunter has orbited the squirrel. Nyeah.

[footfootfoot]

Originally Posted by Clodfobble

Well you know what else? Heisenberg says both are orbiting the tree, and you can't say for certain where either one is in their orbital path at a given time. But you do know that the hunter is in a higher orbital than the squirrel, and the higher orbital plane does encircle the lower orbital plane. The more time that passes, the higher the statistical probability that the hunter has orbited the squirrel. Nyeah.

NO, you have to re-read the question. There is no treadmill involved. They are moving at the same rate around the same axis. The squirrel will never be encircled by the hunter. The spot where the squirrel had been will be encircled, but not the squirrel itself.

Consider a bicycle wheel for example. The hole in the rim for the valve stem is opposite the seam of the rim. The wheel revolves around the axle. The valve stem and seam each go around the axle every revolution. They do not go around each other. They do go around the position the other previously occupied however. Compare this to a ratchet wrench. The socket is the axis, the handle goes around the axis, but the handle does not go around itself.
The squirrel always keeps the tree between himself and the hunter. The tree is the axis, the squirrel is the seam on the rim and the hunter is the valve stem.

No, the hunter does not walk around his gun. His gun is not stationary, it moves with him. He may walk around the location his gun used to be, but that is not the same as walking around his gun. Unless he has one of those special mag-lev guns that just hangs in mid air while you circumambulate around it. Otherwise, if it is a normal gun then he will be taking it with him when he walks around the tree.

[footfootfoot]

And another thing, you all avoided
How I need a drink, alcoholic in nature, after the tough chapters involving quantum mechanics!

[HungLikeJesus]

Cipher - I like that. Isn't that what Jethro Bodine used to say?

[footfootfoot]

Yes, but did he affix them? Another cromulent word that is under-used these days.

and can you affix nothing to something?

[HungLikeJesus]

The answer to #33 is yes.

The force on the pulley will be the same with two equal weights (W+W) or with a weight (W) on one side and the second side anchored to the floor.

[infinite monkey]

Yes. And it's really non-debateable.

[jimhelm]

Originally Posted by footfootfoot

The earth does not orbit mercury

but it does circle it

[footfootfoot]

Originally Posted by jimhelm

but it does circle it

How about the moon, does the earth circle that?

[HungLikeJesus]

(She moves in circles, and those circles move.)

[footfootfoot]

They were practical in those days. In those days it was nothing to be ashamed of to borrow a sheep. Folks helped each other out, you know, it takes a viking to raze a village.