Random Cubing Discussion

You know, I think it would be pretty interesting to hook a cuber up to an MRI machine or something to see what happens physiologically and psychologically. I feel like in the middle of a longer session faster cubers could enter some meditative state or similar like the way chess grandmasters sometimes can.
 
which commutator(s) take the most number of moves to solve using slice place commutators?
setups to [M', U2]

I thought the max was 9 moves but I found a case (DF FL LD) that takes 11 moves

so is 11 the max?
 
You know, I think it would be pretty interesting to hook a cuber up to an MRI machine or something to see what happens physiologically and psychologically. I feel like in the middle of a longer session faster cubers could enter some meditative state or similar like the way chess grandmasters sometimes can.

To add onto this I'd want to look at their visual processing system as there could be interesting circuits in there that specifically code for things like CLL recognition. Can also look at sensorimotor cortex
 
How many moves on average would it take to use <R,r,U,M> to solve the EOLine (aka EO + DF + DB) given FB solved?
 
That's maybe a little unclear, since only the events that you have competed in matter. For example, Nicolas Naing only did megaminx and got WR, so he didn't have a nemesis.
Not super relevant but it's cool that now nicolas naing has a nemesis. Highest event rank to have a nemesis?
 
You know, I think it would be pretty interesting to hook a cuber up to an MRI machine or something to see what happens physiologically and psychologically. I feel like in the middle of a longer session faster cubers could enter some meditative state or similar like the way chess grandmasters sometimes can.
I think they probably do. The Johannesburg 2014 competition took place in a science centre, which had a machine with EEG headsets which measure your brain activity. Just for fun, Mats and Feliks put the headsets on while they were cubing. They were basically in a pure zen state while cubing.
 
Does doing 2 random state scrambles back to back give you a random state?

Doing a uniform random-state scramble followed by anything (as long as this "anything" is independent of the first scramble) will preserve the uniform distribution, so yeah.

Edit: Not true for bandaged puzzles like squan, since the second scramble might not be compatible with the first.
 
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Doing a uniform random-state scramble followed by anything (as long as this "anything" is independent of the first scramble) will preserve the uniform distribution, so yeah.

Edit: Not true for bandaged puzzles like squan, since the second scramble might not be compatible with the first.

Is it also not true for puzzles with equivalent pieces? Since not all permutations are in the scrambler
 
Can you converge on a random state scramble by:
Hand scrambling a bit
Throwing cube up in air and catching
Some sufficiently large n number of times?

My impression is that, even if your hand scramble is always the same, your scramble is essentially some permutation P interspersed between random rotations. Which should be random (hm, unless P is something weird like a 3cycle, halfturn, identity, etc, but i hope people aren't hand scrambling like that)
 
Can you converge on a random state scramble by:
Hand scrambling a bit
Throwing cube up in air and catching
Some sufficiently large n number of times?

My impression is that, even if your hand scramble is always the same, your scramble is essentially some permutation P interspersed between random rotations. Which should be random (hm, unless P is something weird like a 3cycle, halfturn, identity, etc, but i hope people aren't hand scrambling like that)

That's essentially like doing a longer and longer random move scramble, which approaches an even distribution of states with more moves but never reaches it
 
Is it also not true for puzzles with equivalent pieces? Since not all permutations are in the scrambler

This is a bit tricky to answer. The key observation to make is that, even on puzzles with equivalent pieces, every possible move is a permutation of all the possible states—in other words, that every move can be undone. After applying a random-state scramble, the probability of being in any state is equal (= 1 / (# of states)).

Applying any fixed move after a random-state scramble only shuffles these probabilities around, which effectively does nothing at all since they were equal to begin with. Likewise, applying any fixed move sequence also effectively does nothing. Consequently, applying a move sequence chosen at random from any set will also do nothing.

On the other hand, if you apply random moves before the random-state scramble, then on puzzles with equivalent pieces, this is not necessarily the same as just doing one random-state scramble. The above argument doesn't work because you don't start in the stationary distribution, and you can't just "take the inverse" to force the above argument, because puzzles with equivalent pieces (usually**) don't have a group structure.

** I think there was some puzzle that was isomorphic to one of the sporadic simple groups despite having equivalent centres. Can't remember what it's called, though. (Edit: it's the trapentrix, which isn't one of the sporadic simple groups.)
 
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