4 ms·

There's even a "hyperorganic" Rubik's Cube algorithm: the stereotypical organic algorithm solves the cube layer by layer, only pulling out the fanciest moves to

There's even a "hyperorganic" Rubik's Cube algorithm: the stereotypical organic algorithm solves the cube layer by layer, only pulling out the fanciest moves to get the last few cubies in place. The hyperorganic algorithm is intensely group theoretic, and starts by allowing any kind of movement, but then cuts it down: from any quarter turns to half turns only, etc. (apparently just at the time no legal moves are left according to the algo, the cube should be solved), and the distinguishing feature is that instead of having clear progress layer-by-layer, it still looks mostly, inscrutably, scrambled until almost the final steps, when it suddenly "crystallises" into a solved cube. Lagniappe: https://www.youtube.com/watch?v=K-yTrFDHpbw https://www.youtube.com/watch?v=K-yTrFDHpbw

Thorrez 2y ago
I don't understand how this comment relates to the article, or how that video relates to the rest of the comment.
- 082349872349872 2y ago
  The "hyperorganic" algo behaves like hyperorganicity in TFA: > Things that are more structurally complex present as statically inscrutable ... Things that are more behaviorally complex present as chaotic even if they’re not. The video relates to TFA independently of the rest of the comment*, specifically Kraftwerk's lyric « Я твой слуга » [and more distantly to Wiener, The Human Use of Human Beings (1950)] * a "lagniappe" is a freebie, a bonus item.
  - djmips 2y ago
    I appreciate your comment and video bonus. The article was free ranging and entertaining and not particularly focused and so when someone asks how your comment and video could relate to the article... Well did they read the whole article?
djmips 2y ago
I'd mused about how we learn solve the cube in a structured approach and that there perhaps could be a better way and in my mind it would be exactly as you described. Have any humans mastered this approach despite it's hyper organic label?
- 082349872349872 2y ago
  Depends upon whether or not we count (table-assisted) mathematicians as humans. The description I remembered comes from 5.6.A (p39) of https://maths-people.anu.edu.au/~burkej/cube/singmaster.pdf https://maths-people.anu.edu.au/~burkej/cube/singmaster.pdf (ca.1980) > [Morwen B. Thistlethwaite's] current algorithm requires at most 52 moves, but ... it may be reducible to 45 with a lot of searching. The method involves working through the following sequence of groups: G_0 = <L, R, F, B, U, D> G_1 = <L, R, F, B, U^2,D^2> G_2 = <L, R, F^2,B^2,U^2,D^2> G_3 = <L^2,R^2,F^2,B^2,U^2,D^2> G_4 = {I} > Once in G_i, one only uses moves in G_i to get into G_i+1 ... The results for stages 3 and 4 require extensive tables comprising about 500 and 172 entries respectively as well as some preliminary reductions. However MBT has told me today that he has reorganized stage 3 and that it no longer requires such extensive tables. S T A G E Max # of moves 1 2 3 4 Total -------------- - - - - ----- Proven 7 13 15 17 52 Anticipated 7 12 14? 17 50? Best possible 7 10? 13? 15? 45? compare https://www.youtube.com/watch?v=9rkp29f7QTU&t=24s https://www.youtube.com/watch?v=9rkp29f7QTU&t=24s EDIT: way more at https://www.jaapsch.net/puzzles/thistle.htm https://www.jaapsch.net/puzzles/thistle.htm see also http://cube20.org http://cube20.org

Thorrez 2y ago

I don't understand how this comment relates to the article, or how that video relates to the rest of the comment.

082349872349872 2y ago
The "hyperorganic" algo behaves like hyperorganicity in TFA: > Things that are more structurally complex present as statically inscrutable ... Things that are more behaviorally complex present as chaotic even if they’re not. The video relates to TFA independently of the rest of the comment*, specifically Kraftwerk's lyric « Я твой слуга » [and more distantly to Wiener, The Human Use of Human Beings (1950)] * a "lagniappe" is a freebie, a bonus item.
- djmips 2y ago
  I appreciate your comment and video bonus. The article was free ranging and entertaining and not particularly focused and so when someone asks how your comment and video could relate to the article... Well did they read the whole article?

djmips 2y ago

I'd mused about how we learn solve the cube in a structured approach and that there perhaps could be a better way and in my mind it would be exactly as you described. Have any humans mastered this approach despite it's hyper organic label?

082349872349872 2y ago
Depends upon whether or not we count (table-assisted) mathematicians as humans. The description I remembered comes from 5.6.A (p39) of https://maths-people.anu.edu.au/~burkej/cube/singmaster.pdf https://maths-people.anu.edu.au/~burkej/cube/singmaster.pdf (ca.1980) > [Morwen B. Thistlethwaite's] current algorithm requires at most 52 moves, but ... it may be reducible to 45 with a lot of searching. The method involves working through the following sequence of groups: G_0 = <L, R, F, B, U, D> G_1 = <L, R, F, B, U^2,D^2> G_2 = <L, R, F^2,B^2,U^2,D^2> G_3 = <L^2,R^2,F^2,B^2,U^2,D^2> G_4 = {I} > Once in G_i, one only uses moves in G_i to get into G_i+1 ... The results for stages 3 and 4 require extensive tables comprising about 500 and 172 entries respectively as well as some preliminary reductions. However MBT has told me today that he has reorganized stage 3 and that it no longer requires such extensive tables. S T A G E Max # of moves 1 2 3 4 Total -------------- - - - - ----- Proven 7 13 15 17 52 Anticipated 7 12 14? 17 50? Best possible 7 10? 13? 15? 45? compare https://www.youtube.com/watch?v=9rkp29f7QTU&t=24s https://www.youtube.com/watch?v=9rkp29f7QTU&t=24s EDIT: way more at https://www.jaapsch.net/puzzles/thistle.htm https://www.jaapsch.net/puzzles/thistle.htm see also http://cube20.org http://cube20.org