To my mind, the interjector is just playing a nitpick game: refocus the question (" I coudn't see it's back") to another ("did you circle the squirrel"), and then acting as though the original question is off topic.
Yes technically he did circle the squirrel from his reference point, what of it? that wasn't the point. The point was he couldn't see the squirrel, and this question is only tangentially related.
One could argue that the moon is orbiting the sun. The fact that it's orbit is a little wobbly because of interferes from the earth is a rounding detail, no?
> An enduring myth about the Moon is that it doesn't rotate. While it's true that the Moon keeps the same face to us, this only happens because the Moon rotates at the same rate as its orbital motion, a special case of tidal locking called synchronous rotation.
My colleagues once spent a good hour trying to explain this fact to me and I still really struggle to accept it. I can see that the moon is rotating on its own axis from the point of view of a space that is external to the system it forms with the earth. But then isn’t everything on earth rotating about its own axis with respect to that external space? It seems arbitrary to isolate the moon from all this other stuff and make a special case of it…
I'm probably butchering this, but in my mind it is something like:
1. From the squirrels frame of reference and local coordinate system, the man has remained "in front" of the squirrel. The squirrel is orienting and rotating in sync with the man and therefore has not observed that the man has "gone round" it.
2. From our perspective (and on reflection from the man), the man has circled the squirrel in the global coordinate system of the scene.
As the reader we assume that our perspective is the authoritative one, but I am sure the squirrel disagrees.
A more modern mind-boggler is the geostationary satellite. You always tilt your head up, it always appears motionless. From either one of your perspectives, you both appear to be still.
I remember reading this book in middle school - got me interested in math by making the problems real an interesting rather than repetitive, boring and having no relation to life.
I remember this being mentioned by Charles Peirce as an argument for pragmatism (the philosophical kind): It's a nonsensical question unless you can phrase it in terms where the answer has some practical consequence.
A group of people decided to seat together and talk about some casual math problems
The one problem I keep remembering is a bet about 1000 men walking by on the street in a row. Random chance is not guaranteed - especially when it's suddenly a parade :)
I remember this from a Martin Gardner “aha!” book (or one in that series) which my parents gave to me somewhere around the age of 10. Those books had a profound effect on me.
(Of course, the text in the linked article predates Gardner’s work.)
That's true. The man did not go around the squirrel. They both were orbiting some point near the center of the tree trunk. Otherwise, one could say that the farther point on the Moon's surface is going around the point that is facing Earth.
I take it that the squirrel didn't circle the man?
Two squirrels running around the same tree, are they circling each other? Or is it that when two bodies are orbiting the same center, then the body with the larger orbit is circling the one with the smaller?
What is the definition of "circling"?
I think the main point of the story is that there 'going around' something is not necessarily precisely defined, and that there can be multiple interpretations of it, some of which depend from which perspective you are defining it. Which is a good way to get a sense of what mathematics is about, really (how can this be defined precisely? Is this definition consistent? What properties do different definitions have?).
> Some years ago, being with a camping party in the mountains, I returned from a solitary ramble to find everyone engaged in a ferocious metaphysical dispute. The corpus of the dispute was a squirrel—a live squirrel supposed to be clinging to one side of a tree-trunk; while over against the tree’s opposite side a human being was imagined to stand. This human witness tries to get sight of the squirrel by moving rapidly round the tree, but no matter how fast he goes, the squirrel moves as fast in the opposite direction, and always keeps the tree between himself and the man, so that never a glimpse of him is caught. The resultant metaphysical problem now is this: Does the man go round the squirrel or not? He goes round the tree, sure enough, and the squirrel is on the tree; but does he go round the squirrel? In the unlimited leisure of the wilderness, discussion had been worn threadbare. Everyone had taken sides, and was obstinate; and the numbers on both sides were even. Each side, when I appeared, therefore appealed to me to make it a majority. Mindful of the scholastic adage that whenever you meet a contradiction you must make a distinction, I immediately sought and found one, as follows: “Which party is right,” I said, “depends on what you practically mean by ’going round’ the squirrel. If you mean passing from the north of him to the east, then to the south, then to the west, and then to the north of him again, obviously the man does go round him, for he occupies these successive positions. But if on the contrary you mean being first in front of him, then on the right of him, then behind him, then on his left, and finally in front again, it is quite as obvious that the man fails to go round him, for by the compensating movements the squirrel makes, he keeps his belly turned towards the man all the time, and his back turned away. Make the distinction, and there is no occasion for any farther dispute. You are both right and both wrong according as you conceive the verb ’to go round’ in one practical fashion or the other.”
Say instead of just walking, the man was laying down a net/barricade around the tree. As soon as the man completes the circumference, the squirrel must admit that it has been gone around.
To my mind, the interjector is just playing a nitpick game: refocus the question (" I coudn't see it's back") to another ("did you circle the squirrel"), and then acting as though the original question is off topic.
Yes technically he did circle the squirrel from his reference point, what of it? that wasn't the point. The point was he couldn't see the squirrel, and this question is only tangentially related.
One could argue that the moon is orbiting the sun. The fact that it's orbit is a little wobbly because of interferes from the earth is a rounding detail, no?
> An enduring myth about the Moon is that it doesn't rotate. While it's true that the Moon keeps the same face to us, this only happens because the Moon rotates at the same rate as its orbital motion, a special case of tidal locking called synchronous rotation.
https://science.nasa.gov/resource/the-moons-rotation/
My colleagues once spent a good hour trying to explain this fact to me and I still really struggle to accept it. I can see that the moon is rotating on its own axis from the point of view of a space that is external to the system it forms with the earth. But then isn’t everything on earth rotating about its own axis with respect to that external space? It seems arbitrary to isolate the moon from all this other stuff and make a special case of it…
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But is a geostationary satellite going around the Earth?
This tickled my brain in a nice way.
I'm probably butchering this, but in my mind it is something like:
1. From the squirrels frame of reference and local coordinate system, the man has remained "in front" of the squirrel. The squirrel is orienting and rotating in sync with the man and therefore has not observed that the man has "gone round" it.
2. From our perspective (and on reflection from the man), the man has circled the squirrel in the global coordinate system of the scene.
As the reader we assume that our perspective is the authoritative one, but I am sure the squirrel disagrees.
Does Earth orbit Mercury?
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A more modern mind-boggler is the geostationary satellite. You always tilt your head up, it always appears motionless. From either one of your perspectives, you both appear to be still.
I remember reading this book in middle school - got me interested in math by making the problems real an interesting rather than repetitive, boring and having no relation to life.
I thought this was going to be about prepositions, which was taught to me as "Anything a squirrel can do to a log."
By the same logic that the man goes around the squirrel, I go all around the world every day.
I remember this being mentioned by Charles Peirce as an argument for pragmatism (the philosophical kind): It's a nonsensical question unless you can phrase it in terms where the answer has some practical consequence.
Round the squirrel only if the squirrel is still on the tree.
"Mathematics can be fun" is an awesome book
A group of people decided to seat together and talk about some casual math problems
The one problem I keep remembering is a bet about 1000 men walking by on the street in a row. Random chance is not guaranteed - especially when it's suddenly a parade :)
Due to the Earth's rotation, the man could be circling the squirrel even when standing still.
I remember this from a Martin Gardner “aha!” book (or one in that series) which my parents gave to me somewhere around the age of 10. Those books had a profound effect on me.
(Of course, the text in the linked article predates Gardner’s work.)
That's true. The man did not go around the squirrel. They both were orbiting some point near the center of the tree trunk. Otherwise, one could say that the farther point on the Moon's surface is going around the point that is facing Earth.
I take it that the squirrel didn't circle the man? Two squirrels running around the same tree, are they circling each other? Or is it that when two bodies are orbiting the same center, then the body with the larger orbit is circling the one with the smaller? What is the definition of "circling"?
I think the main point of the story is that there 'going around' something is not necessarily precisely defined, and that there can be multiple interpretations of it, some of which depend from which perspective you are defining it. Which is a good way to get a sense of what mathematics is about, really (how can this be defined precisely? Is this definition consistent? What properties do different definitions have?).
From the title I thought this was going to be a variation on the bear and swimmer puzzle.
https://www.quantamagazine.org/can-math-help-you-escape-a-hu...
Similarly, a rolling wheel (without slipping and on flat ground) does a pure rotation around the touch point and not its center.
The original:
> Some years ago, being with a camping party in the mountains, I returned from a solitary ramble to find everyone engaged in a ferocious metaphysical dispute. The corpus of the dispute was a squirrel—a live squirrel supposed to be clinging to one side of a tree-trunk; while over against the tree’s opposite side a human being was imagined to stand. This human witness tries to get sight of the squirrel by moving rapidly round the tree, but no matter how fast he goes, the squirrel moves as fast in the opposite direction, and always keeps the tree between himself and the man, so that never a glimpse of him is caught. The resultant metaphysical problem now is this: Does the man go round the squirrel or not? He goes round the tree, sure enough, and the squirrel is on the tree; but does he go round the squirrel? In the unlimited leisure of the wilderness, discussion had been worn threadbare. Everyone had taken sides, and was obstinate; and the numbers on both sides were even. Each side, when I appeared, therefore appealed to me to make it a majority. Mindful of the scholastic adage that whenever you meet a contradiction you must make a distinction, I immediately sought and found one, as follows: “Which party is right,” I said, “depends on what you practically mean by ’going round’ the squirrel. If you mean passing from the north of him to the east, then to the south, then to the west, and then to the north of him again, obviously the man does go round him, for he occupies these successive positions. But if on the contrary you mean being first in front of him, then on the right of him, then behind him, then on his left, and finally in front again, it is quite as obvious that the man fails to go round him, for by the compensating movements the squirrel makes, he keeps his belly turned towards the man all the time, and his back turned away. Make the distinction, and there is no occasion for any farther dispute. You are both right and both wrong according as you conceive the verb ’to go round’ in one practical fashion or the other.”
— William James, Pragmatism, 1907
It took me longer than it should to get this!
On reflection, does the squirrel consider itself to have been "gone round"? I don't think so.
Say instead of just walking, the man was laying down a net/barricade around the tree. As soon as the man completes the circumference, the squirrel must admit that it has been gone around.
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To get what?
That the man technically went around the squirrel without ever having caught up to it.
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