For the primary options I thought of, there’s a key second within the course of the place a choice have to be made about who acts first (with apologies for the crudeness of the illustration – I am not an artist!)
At this second, every “you” has simply
touched field 2, along with your arm nonetheless totally inside field 1.
Doable resolution 1
If at this second, we suppose that you simply act after your clone inside field 1 (and so forth as much as infinity)
the result’s the reply already given – your clone removes field 3 and locations it inside field 1, you take away field 2 and place it in your field, after which your clone in field -1 removes field 1 and locations it of their field the place you now not have easy accessibility to it, after which your total field will get eliminated and positioned in field -2 so you haven’t any remaining entry to the odd quantity bins.
For the reversal of this,
a large hand seems and locations field 1 again inside your field, after which you are taking field 2 and put it again inside field 1 (changing into the “big hand” in your smaller clone)
Doable resolution 2
An alternate is that you simply act earlier than your clone in field 1. On this case:
Field 1, which nonetheless has your arm inside it, is pulled out, so you might be additionally pulled out of your field and positioned subsequent to a sequence of more and more bigger clones of you. After this, you pull field 2 out of field 1, with the smaller you continue to having their arm inside it, and place it subsequent to you.
On the finish, on this case
Not one of the bins are inside one another, they’re all laid in a line beside one another on no matter infinite floor the “largest” infinite field had been on. Equally no person continues to be inside a field.
To reverse this,
you seize field 2 (which your smaller clone by now already has their arm inside), and place it into field 1. Earlier than you have fairly completed, the following bigger “you” grabs the field you’ve got your arm inside and locations it again in your unique field.
Doable resolution 3
For everybody performing “concurrently”,
The system will get jammed up with the bins as proven. You may’t take away field 2 from field 1 as a result of your smaller clone continues to be holding onto it, and your bigger clone is concurrently attempting to take away a field you might be nonetheless interacting with.
Nonetheless, there was a key perception that I missed…
Last(?) resolution
Utilizing the perception from Pranay’s second reply with an animation
though the animation in that reply is not totally appropriate, we are able to modify the diagram in order that it does not get “jammed up”, for instance as follows:
On this diagram, everybody pulls their field via the aspect of the next-smaller field, which has a big sufficient opening in your arm and the next-smaller field to suit via unobstructed.
The second you progress field 2 by even an infinitesimally small quantity, the amplified results of the infinitely bigger clones beginning to pull the bins aside many ranges up shall be enough to completely take away field 1 out of your field and thus field 2 from field 1, and many others. [… or maybe not – see the later observation]
Be aware that if we in three-d house, and the bins begin equally to the primary diagram, or do not but have a gap within the wall, we are able to first rotate field 1 by 180° and reduce a big sufficient gap in its wall earlier than continuing to try to take away field 2.
“Reversibility” of this
Creates a special sort of paradox – the simultaneous elimination of all of the totally different bins from one another has left every field infinitely removed from its next-larger field. In principle if you happen to had been to very exactly reverse the actions, stopping on the precise appropriate place with infinite precision, you’d find yourself again within the scenario you began…
… and but on the identical time, no motion you do can, by itself, trigger the next-larger field to re-appear via the wall of your field such that your field will get inserted into it, and definitely not with the infinite precision required of stopping on the precise second that traces up all of the bins all the way down to nano-scale, femto-scale and past with the identical relative positions.
Later observations (which possibly name the above into query)
Think about the scenario a small fraction after field 1 begins to maneuver in direction of the sting of your field. On this illustration, I moved it 20 pixels, then (manually, and imperfectly!) mounted up the remainder of the picture to create:
As I’ve 40% scaling between every field, field 2 strikes 8 pixels to the suitable inside field 1 (excepting copy-paste and positioning errors), however as a result of field 1 itself moved 20 pixels to the left, the general impact is that the field 2 you might be holding onto strikes 12 pixels to your left.
To “pull” field 2 out of field 1, you should thus, considerably unintuitively, push it away from you.
Skipping ahead to the purpose the place your physique elements are totally faraway from field 1,
getting so far concerned “pushing” your field even additional away from you, however the quantity your field is being concurrently pushed away from the next-larger field signifies that it nonetheless ends in field 1 additional exiting your field and field 2 additional exiting field 1, and many others.
In case you push field 2 to the very fringe of your field, field 1 totally exits your field, and field 2 totally exits field 1 and many others., however certainly now pulling field 2 again in direction of you’d certainly be synchronised along with your clone 2 steps up pulling your field in direction of them, and thus beginning to re-insert field 1 (simply exterior your field at that second) again into your field.
In order that then results in additional questions like
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How onerous would you get squashed between field 1 and the wall of your field if you happen to as a substitute tried to drag field 2 in direction of you (and all of your bigger/smaller clones acted in the identical method with proportionally bigger/smaller actions and forces)
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What further actions at the moment are attainable with all physique elements totally faraway from field 1, and the way can these assist?
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What sequence of actions will mean you can totally take away field 2 from field 1, and hold (or return) field 2 inside your field, while all of your clones are concurrently making the very same actions scaled up/down?
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If the odd-numbered bins do certainly grow to be inaccessible throughout this sequence, which motion turns into inconceivable to reverse and why?
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How can we reconcile the near-infinite actions attributable to the clones many steps bigger than you within the chain with the seemingly easy and actions created by the belief that the scenario retains symmetry?
