From which reference frame would it not rotate?
2. Yes, everything "at rest" on earth is in fact rotating at the rate the earth rotates. If you stand on the equator at midday and do not rotate you will be standing on your head at midnight.
This is always true. The origin is just a thing that other things are relative to. It's just as possible to define an origin in the real world as it is on a piece of graph paper.
If you rotate as part of some larger rotating thing then you still rotate. (You also move around.) It's all absolute.
(You can break that down in different ways, i.e. use various choices of generalised coordinates to describe it, so exactly what constitutes "centripetal", "centrifugal", "gravitational", "tidal", etc. forces depends on that. I'm being pretty vague in how I decribe it. Regardless, rotation is absolute, or in other words the equations of physics take a different form in a rotating frame of reference than in a non-rotating one.)
From the point of view of the moon, for the purposes of action due to gravity, anything on Earth is essentially part of the Earth, not an entity that is massive enough to be considered separately. The aggregate centre of mass is what counts. Similar for the Sun looking at the Earth/Moon system: from that PoV Earth+Moon is it a single mass with a centre somewhere between the two major masses that form it.
If the Moon where sufficiently consistent in its shape and density, it could rotate freely in any direction while orbiting the Earth, that fact that it is more dense on one side means that it is more energy efficient for it to spin in step with its orbit such that the dense side keeps facing us. If something massive hit the moon (let's assume this somehow happens without significantly affecting its orbit or causing significant problems for Earth too!) it might push the rotation off for a bit, but it would slowly be pulled back into sync. If something sufficiently massive simply landed on the moon, that would affect the mass distribution and the exact face that points at us would slowly change to reach a new equilibrium.
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.
In terms of this post - I suppose technically Earth does NOT circle the Moon, because we never see its back!
https://www.quantamagazine.org/can-math-help-you-escape-a-hu...
(Of course, the text in the linked article predates Gardner’s work.)
> 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
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 :)
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.
beardyw•1mo ago
beardyw•1mo ago
xlbuttplug2•1mo ago
xnorswap•1mo ago
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•1mo ago
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•1mo ago
xlbuttplug2•1mo ago
adastra22•1mo ago