[HN Gopher] A Scientific American bolt puzzle
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A Scientific American bolt puzzle
Author : zdw
Score : 51 points
Date : 2025-03-03 16:06 UTC (4 days ago)
(HTM) web link (leancrew.com)
(TXT) w3m dump (leancrew.com)
| vessenes wrote:
| Ooh I'm pleased I got this answer right imagining it. But I may
| have imagined it incorrectly -- in my mind I was worried that
| there would be pressure from rotation at the point of contact.
| But as I write it, I realize that the question "pressure in which
| direction?" Shows that's fairly unlikely.
| munchler wrote:
| I grew up on Martin Gardner in the 70's and 80's, so I'm always
| happy to see him referenced. My favorite physics puzzle of his
| is: If you heat a solid iron torus, does the radius of the hole
| in the middle grow or shrink?
| itishappy wrote:
| Love that one, and the closely related hole in a large metal
| plate. Something about that reframing flips my intuition on
| it's head.
| aj7 wrote:
| Grow, of course. I mean, come on.
| jagged-chisel wrote:
| Some intuition says one must consider the outer iron
| expanding into the hole. Some thought allows the realization
| that the only direction for expansion is outward.
| wat10000 wrote:
| Or consider that, assuming the expansion is uniform, it's
| applying a scale transform to the object and otherwise
| leaving the shape exactly the same. All aspects of the
| shape will therefore grow larger.
| zellyn wrote:
| [Edit: removed spoiler]
|
| You can gain a bit of intuition about growing and shrinking
| circles by imagining them to be squares with _very_ rounded
| corners, or equivalently, imagining what happens if you
| lengthen them by inserting straight lengths in four places,
| turning them into squares with very rounded corners.
|
| For example, the old question of: if you have a rope lying on
| the surface of the earth all the way around a great circle, and
| make it 10m longer, how high could it be above the surface?
|
| Even though the square-with-corners thing helps me visualize it
| quite perfectly, I _still_ find it weird that that the answer
| is 1.5m!
| SamBam wrote:
| Anyone who's opened a tight jar lid by putting it under hot
| water should know the answer to this instinctively.
| foodevl wrote:
| Switching the direction that you're twiddling the bolts would
| have to change the direction of any movement. But by symmetry,
| clockwise and counterclockwise twiddling are identical (looking
| down on the head of each bolt, one is always moving clockwise and
| one is always moving counterclockwise). So there must be no
| in/out movement at all.
| ndsipa_pomu wrote:
| This is similar to how I guessed the answer - it's a symmetric
| system, so there's no reason why it would be one direction over
| the other and so logically there would be no movement.
| aj7 wrote:
| No there is not that symmetry, because the helix is handed, and
| the result could depend on the rotation direction with respect
| to that handedness.
| foodevl wrote:
| Relative to the handedness, one bolt is always moving with
| it, one bolt is always moving against it. Switching direction
| doesn't change that. So switching direction can't change
| whether it moves inward or outward.
| rdlw wrote:
| Couldn't you transform twiddling one way into twiddling the
| other way by reflecting through a mirror and turning the
| bolts 180 degrees end-over-end? If you start with the bolts
| moving North, the mirroring makes them go South, and turning
| them around makes them go North again, but now you're
| twiddling the other way. So the bolts would have to go North
| no matter which way you twiddle them, so either twiddling is
| not reversible (which is a repugnant proposition) or they
| must have a speed of 0.
| colanderman wrote:
| Moreover, the problem as posed doesn't specify the direction of
| twiddling, which kind of gives away the answer.
| aj7 wrote:
| Here is my guess. If you twiddle your thumbs in the screw-in
| direction, the heads move together at twice the rate that a head
| would move when screwed into a fixed thread. And in the screw-out
| direction, the heads would move apart at twice the rate of
| dissassembling a bolt from a fixed threaded hole.
| JKCalhoun wrote:
| I know the answer because I've actually done this with real bolts
| (out of boredom -- before I knew Martin Gardner had a puzzle
| about it).
|
| Likewise I also know the answer to which direction the spool
| rolls if you set it on a table and slowly pull on the thread.
| NegativeLatency wrote:
| Having done this IRL before, my mental model is that the other
| screw is just like a nut, except only touching at one point, so
| the behavior is the same as screwing in a bolt normally.
| fsckboy wrote:
| > _so the behavior is the same as screwing in a bolt normally_
|
| ...if you are simultaneously screwing out the other bolt
| normally, because the bolts screw neither in nor out relative
| to one another.
| cleansingfire wrote:
| When you twiddle your thumbs, your thumbnails always point the
| same direction relative to each other. So the bolts relative
| rotation will maintain that. Imagine a stripe on the face towards
| us of the bolts, and twiddling action will not rotate the stripe
| in an absolute or relative sense.
|
| For the two bolts, this is equivalent to rotating both bolts so
| the stripe stays in the same relative position, as if one were
| rotated around the other or they were twisted in the same
| absolute direction. If you are concerned about symmetry violation
| because of the direction of the threads, you can reverse the
| threads on both bolts, with the same result. You can try this
| with a couple of bolts and a couple of rubber bands to keep them
| in the same relative position. The illustration is a hint that
| the motion is equivalent to rotating both in the same absolute
| direction (near side moving up.) Then view that system from the
| head and note the direction each would be moving, away or towards
| you.
|
| If you have to undo a bolt or nut from behind, the bolt head
| moves in a reverse direction from your viewpoint, just as if you
| were to view a glass clock from behind.
| QuadmasterXLII wrote:
| I found it to be much easier in the rotating frame of reference
| where both bolts are spinnimg in place in the same direction
| wilburTheDog wrote:
| It stays stationary because you're effectively tightening one
| bolt and loosening the other. Imagine the point of contact
| between the bolts is a line drawn on a stationary nut instead. Is
| that line moving clockwise or counterclockwise around the bolt?
| One way tightens, the other way loosens. And it's opposite for
| the two bolts.
| fsckboy wrote:
| spoiler alert, directly quoted from article:
|
| > _The heads of the twiddled bolts move neither inward nor
| outward. The situation is comparable to that of a person walking
| up an escalator at the same rate that it is moving down. - Martin
| Gardner_
|
| > _I don't find it an especially helpful analogy. Why is the
| twiddling of bolts like a person walking up an escalator?_
|
| the bolts and the up-the-down escalator are a good comparison
| because if you analyze what happens from one bolt's perspective,
| and then the other bolt's perspective, one is walking up (in) and
| the other down (out).
|
| (as a nit, I don't like when people breezily "reword" what
| somebody says while analyzing it: are "comparable", "analogous",
| and "like" exactly synonymous with one another?)
| dmurray wrote:
| On your nit, I think the author's use of language is good.
|
| If two things are "comparable", they must be "like" each other
| in some way. Otherwise they could be contrasted, but never
| compared. The author's question is equivalent to " _in what
| way_ are these two bolts equivalent to the person and the
| escalator? "
| SamBam wrote:
| I also found it a useful analogy. Or rather, that was the way I
| thought of it.
|
| First I had to think about what would happen if the top bold,
| instead of rotating around a bolt, rotated around a band that
| wrapped straight around the other shaft. It stood to reason
| that the bolt would move backward away from the band, as the
| band moved along the spiral. (Whether it moved outward or
| inward ended up being irrelevant.)
|
| Then I went back to it being two bolts, and visualized the
| movement from the head of each. In one, the other bolt moved
| clockwise, and in the other, the bolt move counter-clockwise.
| So it stood to reason that one bolt would want to move away
| from the other, and the other move towards. So they would stay
| stationary.
| ColinWright wrote:
| I met Martin Garder and spent a morning with him, one on one. I
| have a photo of the two of us together, and on the back his notes
| about our meeting, written in his own hand, given to me by his
| son.
|
| Amazing experience for someone who grew up reading his books.
|
| Lovely man, sharp as a tack right to the end, and sadly missed.
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