World
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Proposed Solution to Conway Notation Quiz
February 2, 2008
Josh Purinton’s Conway Notation Quiz consists of a diagram and a question: 
How would you notate move 23 in the attached diagram?
Josh originally sent this quiz to various WGOSA members in an email, a few months ago. I promptly missed it.
I should say a word about the appellation Conway notation. This appellation was used in some of the Math Forum messages in which the notation (WGOSA notation, the official notation of WGOSA Classic) was developed. John Conway helped with this development and did not seem to object to the appellation, but he never really gave explicit approval either, which is why the appellation is not proudly trumpeted on the website now.
I should mention that Josh Purinton has perfected an alternative notation which is in many ways superior. He calls this notation left hand path notation, or LHP for short. I once proposed that LHP be considered a second official club notation, and I still think that might be a good idea. LHP is described with mathematical precision and seems the perfect notation for computer/human interaction.
A position similar to Josh’s quiz arose in a game in the 2005 championship, which I directed. I believe I fumbled that one also. It seems to me now, referring back to our current description of Conway notation, that the canonical solution is 16(23)21![6], but if I were playing the move in a tournament, I would write simply 16(23)21[1,4,5]. (Please note that 16(23)21[2,4,5] is a legal, but completely different move.) Another correct designation is 16(23)21[2,6], but 16(23)21[6], my original answer to Josh’s email, is definitely wrong.
But please note the word "seems" in the previous paragraph. The exclamation mark was originally added to the notation system to resolve subtle notational perplexities. There is nothing subtle about the difference between the moves 16(23)21[1,4,5] and 16(23)21[2,4,5]. An argument perhaps could be plausibly advanced on this basis that my "canonical" 16(23)21![6] is therefore improper. I can only answer that as a tournament director, if an interpretation needed to be made, I currently would interpret 16(23)21![6] as synonymous with 16(23)21[2,6] and 16(23)21[6] as synonymous with 16(23)21[1,6]. But these days I much prefer clarity to canonicity.
One last specification that I currently consider correct is 16(23)21[4,5], again exploiting (and possibly misusing) the "clockwise bias" that was invented to prevent ambiguities related to handedness. This specification is nearly as concise as 16(23)21![6], and the absence of the exclamation could be considered an aesthetic advantage. I have often wondered if the criteria of canonicity should include a bias against exclamations.