A Scientific American bolt puzzle

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?

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.

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.

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.<p>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.<p>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.

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.<p>Amazing experience for someone who grew up reading his books.<p>Lovely man, sharp as a tack right to the end, and sadly missed.

spoiler alert, directly quoted from article:<p>&gt;<i>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><p>&gt;<i>I don’t find it an especially helpful analogy. Why is the twiddling of bolts like a person walking up an escalator?</i><p>the bolts and the up-the-down escalator are a good comparison because if you analyze what happens from one bolt&#x27;s perspective, and then the other bolt&#x27;s perspective, one is walking up (in) and the other down (out).<p>(as a nit, I don&#x27;t like when people breezily &quot;reword&quot; what somebody says while analyzing it: are &quot;comparable&quot;, &quot;analogous&quot;, and &quot;like&quot; exactly synonymous with one another?)

I know the answer because I&#x27;ve actually done this with real bolts (out of boredom — before I knew Martin Gardner had a puzzle about it).<p>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.

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.

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.

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.

I found it to be much easier in the rotating frame of reference where both bolts are spinnimg in place in the same direction

But I&#x27;ve played around with bolts a lot as a kid with Meccano etc so the answer is second nature.