5 ms·

Round and Round

59 points by beardyw 10mo ago

elsjaako 10mo ago
By the same logic that the man goes around the squirrel, I go all around the world every day.
beardyw 10mo ago
It took me longer than it should to get this!
- beardyw 10mo ago
  On reflection, does the squirrel consider itself to have been "gone round"? I don't think so.
  - xlbuttplug2 10mo ago
    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.
    - xnorswap 10mo ago
      Now let us suppose the squirrel is at the same distance as the man. Has the man have gone around the squirrel and the squirrel around the man? If it's only radii less than the other, where is the limit? To get it I think I have to re-frame it like this: If you hold out an object toward the centre, you clearly go around it when completing an orbit. If you keep extending that to the origin but then go beyond, so your arm is longer than the radius, then you still go around it, until your arm reaches twice the radius.
      - xlbuttplug2 10mo ago
        The article says the man was trying to see the squirrel's back implying a larger radius. But yeah if your circuit completely fits inside the other person's circuit, then you've been gone around, no matter how slow or fast you both are.
- moconnor 10mo ago
  To get what?
  - xlbuttplug2 10mo ago
    That the man technically went around the squirrel without ever having caught up to it.
    - adastra22 10mo ago
      It is still not clear to me. The periodicity of their orbit around the tree is the same. I think this is an instance of us meaning different things by “go around”
n0n0n4t0r 10mo ago
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?
- OscarCunningham 10mo ago
  But is a geostationary satellite going around the Earth?
  - shhsshs 10mo ago
    No, because it never sees its back!
- leeoniya 10mo ago
  > 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/ https://science.nasa.gov/resource/the-moons-rotation/
  - unhba 10mo ago
    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…
    - Hendrikto 10mo ago
      Pick the sun as reference: the moon rotates. Pick the earth as reference: the moon rotates. Stand on the moon and pick any star as reference: the moon rotates. From which reference frame would it not rotate?
deleted 10mo ago
[deleted]
Tistron 10mo ago
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"?
- rcxdude 10mo ago
  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?).
weinzierl 10mo ago
Similarly, a rolling wheel (without slipping and on flat ground) does a pure rotation around the touch point and not its center.
sudosays 10mo ago
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.
- NedF 10mo ago
  [dead]
- widforss 10mo ago
  Does Earth orbit Mercury?
  - shhsshs 10mo ago
    By the astronomical definition of the word "orbit", no. Earth does circle Mercury though (and Mercury circles Earth). In terms of this post - I suppose technically Earth does NOT circle the Moon, because we never see its back!
    - widforss 10mo ago
      Now I had to imagine Mercury's motion in Earth's reference system, and that was painful.
Slava_Propanei 10mo ago
[dead]
NAR8789 10mo ago
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-hungry-bear-20210629/ https://www.quantamagazine.org/can-math-help-you-escape-a-hu...
koenh1 10mo ago
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.
- cubefox 10mo ago
  William James, not Charles Peirce.
zkmon 10mo ago
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.
alexfoo 10mo ago
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.)
silvandeboer 10mo ago
Due to the Earth's rotation, the man could be circling the squirrel even when standing still.
cubefox 10mo ago
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
NooneAtAll3 10mo ago
"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 :)
OrderlyTiamat 10mo ago
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.
Zorbanator 10mo ago
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.
naaqq 10mo ago
Round the squirrel only if the squirrel is still on the tree.
edgineer 10mo ago
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.
imzadi 10mo ago
I thought this was going to be about prepositions, which was taught to me as "Anything a squirrel can do to a log."
zem 10mo ago
"mathematics can be fun" was one of my favourite books when I was a kid. I remember spending a lot of time on this particular puzzle, wrapping my head around the various rotational motions of something both rotating around its axis and orbiting something else. there was also the related puzzle of how many rotations a coin makes when rolling around another identical coin.

Round and Round

59 points by beardyw 10mo ago

elsjaako 10mo ago

By the same logic that the man goes around the squirrel, I go all around the world every day.

beardyw 10mo ago

It took me longer than it should to get this!

beardyw 10mo ago
On reflection, does the squirrel consider itself to have been "gone round"? I don't think so.
- xlbuttplug2 10mo ago
  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.
  - xnorswap 10mo ago
    Now let us suppose the squirrel is at the same distance as the man. Has the man have gone around the squirrel and the squirrel around the man? If it's only radii less than the other, where is the limit? To get it I think I have to re-frame it like this: If you hold out an object toward the centre, you clearly go around it when completing an orbit. If you keep extending that to the origin but then go beyond, so your arm is longer than the radius, then you still go around it, until your arm reaches twice the radius.
    - xlbuttplug2 10mo ago
      The article says the man was trying to see the squirrel's back implying a larger radius. But yeah if your circuit completely fits inside the other person's circuit, then you've been gone around, no matter how slow or fast you both are.
moconnor 10mo ago
To get what?
- xlbuttplug2 10mo ago
  That the man technically went around the squirrel without ever having caught up to it.
  - adastra22 10mo ago
    It is still not clear to me. The periodicity of their orbit around the tree is the same. I think this is an instance of us meaning different things by “go around”

n0n0n4t0r 10mo ago

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?

OscarCunningham 10mo ago
But is a geostationary satellite going around the Earth?
- shhsshs 10mo ago
  No, because it never sees its back!
leeoniya 10mo ago
> 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/ https://science.nasa.gov/resource/the-moons-rotation/
- unhba 10mo ago
  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…
  - Hendrikto 10mo ago
    Pick the sun as reference: the moon rotates. Pick the earth as reference: the moon rotates. Stand on the moon and pick any star as reference: the moon rotates. From which reference frame would it not rotate?

deleted 10mo ago

[deleted]

Tistron 10mo ago

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"?

rcxdude 10mo ago
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?).

weinzierl 10mo ago

Similarly, a rolling wheel (without slipping and on flat ground) does a pure rotation around the touch point and not its center.

sudosays 10mo ago

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.

NedF 10mo ago
[dead]
widforss 10mo ago
Does Earth orbit Mercury?
- shhsshs 10mo ago
  By the astronomical definition of the word "orbit", no. Earth does circle Mercury though (and Mercury circles Earth). In terms of this post - I suppose technically Earth does NOT circle the Moon, because we never see its back!
  - widforss 10mo ago
    Now I had to imagine Mercury's motion in Earth's reference system, and that was painful.

Slava_Propanei 10mo ago

[dead]

NAR8789 10mo ago

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-hungry-bear-20210629/ https://www.quantamagazine.org/can-math-help-you-escape-a-hu...

koenh1 10mo ago

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.

cubefox 10mo ago
William James, not Charles Peirce.

zkmon 10mo ago

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.

alexfoo 10mo ago

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.)

silvandeboer 10mo ago

Due to the Earth's rotation, the man could be circling the squirrel even when standing still.

cubefox 10mo ago

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

NooneAtAll3 10mo ago

"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 :)

OrderlyTiamat 10mo ago

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.

Zorbanator 10mo ago

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.

naaqq 10mo ago

Round the squirrel only if the squirrel is still on the tree.

edgineer 10mo ago

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.

imzadi 10mo ago

I thought this was going to be about prepositions, which was taught to me as "Anything a squirrel can do to a log."

zem 10mo ago

"mathematics can be fun" was one of my favourite books when I was a kid. I remember spending a lot of time on this particular puzzle, wrapping my head around the various rotational motions of something both rotating around its axis and orbiting something else. there was also the related puzzle of how many rotations a coin makes when rolling around another identical coin.