Saturday, March 26, 2011

LIBERTIES AND HYDROGEN

I just noticed that liberties on a go board correspond to the placement of hydrogen atoms on simple alkane hydrocarbons, e.g. n-propane includes eight hydrogen atoms and three go stones placed in a straight line will have eight liberties, the same holds true for any straight chain arrangement. Isopropane would correspond with the empty triangle with seven liberties or seven hydrogens––but isopropane does not exist–– if you were to create isopropanol with an opponents stone representing an oxygen atom then the analogy would stand or an isopropyl moiety with the central carbon/stone attached to an R-group. Cyclobutane includes eight hydrogrens and a square four stone unit (not to be confused with a ponnuki) will have eight liberties. Cyclohexane includes twelve hydrogen atoms and the corresponding six stone ring/eye has twelve liberties. I wonder if the convergence does not end there, could the same factors that define the strength and influence of a go shape impact, say, the stability of a molecule?

2 comments:

Beavis said...

Hi Hamilton,

these analogies result from the similarity of the graphs representing a go board and a carbon based molecule. The vertices on a go board got four edges and a carbon atom got four free electrons.
So, how does this topology "define the strength and influence of a go shape impact, say, the stability of a molecule".
There is one thumb rule in go which comes to my mind: It is favorable to have a high freedoms to stone ratio.
This is why three stones in I shape are better than a L shape, or ___ is better than _I_. The problem here with the analogy is, there is no analogy, corresponding molecules in the later cases don't exist.
Or could it work on a more abstract level, surface to volume ratio. How does this influence the stability of a molecule?

Cheers

Gordian

plustax said...

Time for an experiment!

Have two people play a game of go. Establish a winner, and identify the various shapes your winner's pieces took, and assign them to similar carbon chain to see if they match up with stability. That should hold true since long chain alkanes have more stability than branched once, and Beavis just said the higher the stone to freedom ratio the better off you are).