# I never solved Rubik’s cube even once the right way. Most I could get is two sides. But as I kid I knew how to take it apart so… :)

I never solved Rubik’s cube even once the right way

. Most I could get is two sides. But as I kid I knew how to take it apart so…

I tried sodoku about 10 years ago. I kind of liked it up to a point but after that it was too hard, but I tried it Crossword puzzles I could never do well. Takes a lot of patience and all I can think is, “It’s just a game, stop trying” and I’d stop. But pickup sticks I could do. Jenga too. Same kind of thing.

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Oh this is interesting: A ‘pick-up sticks’ template for a Neural network to try to identify unknown cunieforms. While not what I was looking for, an amazing idea. Wonder if it’s stil

l in use? “Makido Algorithm” shows up here and there. Looks like this MIGHT be the source from 1996

It’s 23 yr old AI but I like it. I’ll have to see if it’s changed names.

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“As a consequence, every simple dual braid in every spherical type Artin group is a Mikado
braid, the reduction to the irreducible case being immediate.”

the reduction to the irreducible case being immediate.

ie – pick-up sticks is hard

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I dunno what this is but these folks seem pretty proud of their

work. Now I gotta learn a thing I think?

“We show that the simple elements of the dual Garside structure of an Artin group of type D n are Mikado braids, giving a positive answer to a conjecture of Digne and the second author. To this end, we use an embedding of the Artin group of type D n in a suitable quotient of an Artin group of type B n noted by Allcock, of which we give a simple algebraic proof here. This allows one to give a characterization of the Mikado braids of type D n in terms of those of type B n and also to describe them topologically. Using this topological representation and Athanasiadis and Reiner’s model for noncrossing partitions of type D n whic

h can be used to represent the simple elements, we deduce the above‐mentioned conjecture.”

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What it’s showing by not touching is that you CAN always remove a pickup stick – at SOME point in the game. But each graph you make will be irreducable – that is – you need a new map every time.

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pickup sticks goes to the roots of braid theory and knot theory.
https://ncatlab.org/nlab/show/Reidemeister+move
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The geometric descriptions is complicated but basically it’s saying the COORDINATES are all scrambled up (the sticks are laying all on top of each other in crazy ways) – BUT that ULTIMATELY – you CAN separate them all by mapping the “found coordinates” (unique to EACH GAME) with the coordinates of a nice bunch of sticks not touching in standard Euclidean space.

BASICALLY, if you can play pickup sticks, you know APPLIED braid theory.

At least you know the “Artin group”, 100%.
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Where braids fit in.
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BUT i like pictures and animations. I typed x-1y in Google and I got this.

This is for EACH move in pickup sticks. (a single braid).

It means: YES you can remove that stick…. and that stick is not going to move ANY other sticks.

But…. you have to apply this OVER… and over and over again. and there doesn’t SEEM to be ANY WAY to figure out the right order to do this in (which one you can remove when) that applies to every pickup sticks game.

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They found some deep connections but now can’t figure out how to connect it to infinities – BECAUSE it’s not infinite and can’t be. So, I wonder what’s next?
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Math folks got odd ways of doing things sometimes but it works. It’s just amazing that it takes ALL OF THIS to describe pickup sticks.
Totally diff paper (2018) but wow: Basically, there’s NO STRAIN on a pile of pickup sticks and it’s flexible. So Flexible, it can’t hold itself together.

BUT if you introduce a physical strain (say, gravity), suddenly, it’s rigid and supports itself – but ONLY in a particular way that’s unique.

This can be useful to make VERY SPECIFIC load bearing properties that ONLY work under a very particular condition that can be just as easily removed.

Think of it like this: IF YOU COULD CONTROL GRAVITY…

… and turn it off…

What’s holding the pickup sticks together?

NOTHING.

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This is important in biology, particular cell structures.
https://www.nature.com/articles/nphys3628…
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