Message #4123

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D cuboid
Date: Tue, 04 Sep 2018 19:12:27 -0700

Hello Marc,

FYI, I discussed your mini puzzle to Don Hatch last night and he was understandably skeptical. He did however think that the general class of 4D cuboids should be easy for him to implement, so I expect he will knock that out soon. It’s again unfortunate that our code bases had accidentally diverged, and we talked about resolving that but it could be quite a while before results show up in MC4D at least. Anyway, I forwarded your video from this morning to him. He watched it and replied simply "Ah ok, I believe it."

Your use of nested macros is an extremely clever and useful trick.

-Melinda

On 9/4/2018 12:40 PM, Marc Ringuette ringuette@solarmirror.com [4D_Cubing] wrote:
> Here’s the result of yesterday’s efforts (and a few hours this morning
> making the video and writing the summary), as sent to the mailing list.
> You probably shouldn’t watch the whole video - it’s pretty obscure.
> Skim the message below, and sample a minute of the video, that’s my
> suggestion.
>
>    https://youtu.be/e0aUuN0L1Dc
>
>
> M.
>
>
> On 9/4/2018 12:00 PM, Marc Ringuette wrote:
>> Hi gang!
>>
>> I had a lively day yesterday exploring the nature of the 2x2x2x1 mini
>> puzzle, also known as the twisty stacky 2^3.   Thanks to Luna
>> particularly for a bunch of help with it!   Thanks also to Andy,
>> Dylan, and Joel.
>>
>>
>> "Cuboid, not so much."   After studying it for a couple of days, our
>> consensus is that this mini puzzle should probably NOT be called a
>> "2x2x2x1 cuboid".  That would be more misleading than helpful.  The 4D
>> version of it has the dimensions of the 2x2x2x1 cuboid, but the
>> stacking moves and/or the Gyro move, that provide access to the full
>> 12 orientation states of the 4D pieces, do not seem to correspond to
>> 4D rotations that would apply naturally to generalized cuboid
>> puzzles.  In fact, I’ve stopped calling the Gyro for the puzzle "the
>> FR rotation" or even a rotation at all. It moves and reorients pieces,
>> and it holds the F-B and R-L axes fixed, but unless we discover that
>> the Gyro has a natural geometric interpretation as a 4D rotation, I’ll
>> quit calling it a rotation altogether.
>>
>> As Luna says about the mini puzzle, "I think it’s just a subset of the
>> 2^4. A puzzle that’s obvious with our physical puzzle, but ultimately
>> random. It’s still interesting though."
>>
>>
>> I’ve made a reasonably nice emulation of the mini puzzle inside the
>> MC4D 2^4 hypercube puzzle using a big pile of macros. Hopefully
>> that’ll help us clarify further what the mini-puzzle is in relation to
>> the full puzzle and to other subsets of it.  Here’s a 10 minute
>> side-by-side video.
>>
>>   32   Side by side demo for 2x2x2x1 mini puzzle    10m14s
>> https://youtu.be/e0aUuN0L1Dc
>>
>> I’ve attached my MC4D macros file to this mail.   Anybody with MC4D
>> can play with the virtual mini-puzzle.   I’ve scrambled and solved the
>> puzzle using the macro buttons, and it’s not too horrible to use.
>> The handles for the macros are my usual ones, with the mnemonic "IFUR
>> FUR" (find the IFUR sticker, and click its F U R subfaces).   Just go
>> into macro creation mode using those handles, then click freely on the
>> buttons.   Sliding the "Eye W Scale" knob to the right will make the
>> I-O axis skinnier as in my video.
>>
>> All later macro buttons can be composed from sequences of the first 7
>> (the twists and the Gyro).  Non-obvious algorithms used:
>>    Gyro(phys) = M S R2 F2 R2 y’ z2    (from Luna)
>>    Gyro(virt macro using 2^4 moves) = RFro UF2 IF2 UF2   (from Luna)
>>    M U M’ (virt macro using prev macros) = x Gyro L2 F2 L x’ Gyro B2
>> L2 x   (from Marc)
>>    Monoflip RUF by x2 =  y’ S R S’ R U2 R’ U’ R U’ R’ U2 S R’ S y R U
>> R’ U R U2 R’ U2  (from Marc, applies to both real & virt 2x2x2x1)
>>
>>
>> Probably we’ll end up considering the 2x2x2x1 mini puzzle to be a fun
>> oddity:  a somewhat arbitrarily defined subset puzzle that’s quick and
>> easy to try if you already have Melinda’s 2x2x2x2.
>>
>>
>> Cheers
>> Marc
>>
>
>
> ————————————
> Posted by: Marc Ringuette <ringuette@solarmirror.com>
> ————————————
>
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> ————————————
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