Axiom of Choice

My first website, something like "http://math.wisc.edu/~mariz/", hosted a little set of puzzles called "The Math For Poets" page. It had graphics drawn in pencil and scanned in, and one of those moire-ish blue repeating backgrounds that was popular in 1996. Between the VAX server that hosted it and the general bandwidth of the universe back then, you would be lucky if it only took a minute for a page to load. How sweet and innocent we were then.

One of the exhibits on the Math For Poets site was about the Axiom Of Choice, presenting Bertrand Russel's explication thereof in puzzle form. It went (not really at all) as follows:

You are born on earth and live to a ripe old age but along the way choose the wrong religion and end up in hell (sorry about that). You are assigned to the Lord High Asmodai's Scrum team, and he resources you to the "Sock Sorting" line from the task list. He takes you to a room where there are infinity pairs of socks. He says to you, "We need to designate a new collection of socks, and this collection must contain exactly one sock from each pair in this room." He then gives you a collection of supertask performing daemons and instructs you that all you have to do is tell them which sock to take from each pair and they will create the new set of socks. "Huh, that doesn't seem so bad," you think. You go to the first pair of socks and point to one of the socks, and the daemons instantly grab it and pull it into the new pile. Then you go to the second pair and point to a sock, and instantly the daemons grab it. Then you go to the third pair, then the fourth pair, then the fifth, then you note again that there are infinity pairs of socks, and a sinking realization begins to claw at you. You refer back to the task list and note that the "Sock Sorting" line item has been budgeted at "infinity man-hours". You become desperate. In an effort to halve the development time, you try pointing to socks from two different pairs at once. While the daemons are able to add the socks from two piles to the new pile exactly as fast as they can add one (that is, instantly), you soon realize that infinity man-hours divided by two is still infinity man-hours. Lying on the floor and pointing to socks with your feet and hands at the same time has the same, null, effect. Even the Agile Business Methodology cannot help you. You go to your Stand-Up Meeting every morning, reporting that yesterday you sorted socks, today you will be sorting socks, there are no blocking issues, and your Scrum task has infinity hours remaining. This is how you spend eternity.

I, being a godless heathen, also wind up in hell where I am assigned to your Scrum team. The Lord High Asmodai, or "The Big L.H." as I like to call him, assigns me the "Shoe Sorting" line item from the task list. I note with trepidation that it, too, is budgeted for infinity man-hours. And indeed, my task is virtually the same. I am assigned a set of supertask-performing daemons and am told that I must create a new collection of shoes by selecting a shoe from each one of infinity pairs of shoes. Immediately I am broken and devoid of all hope, for I have seen you at Scrum each morning, reporting that your progress on the Sock Sorting task has gone from infinity hours to infinity hours, suffering the humiliation as Big L.H. publicly berates you for your lack of progress and threatens to stick you with a "Not Achieving" rating for the next review period. I walk into my room filed with infinity pairs of shoes, my supertask daemons in tow. I stare at the infinity pairs of shoes. The daemons hover nearby, awaiting their first instruction. Then, suddenly a thought occurs to me. I turn to the daemons. "Create a new pile of shoes," I say, "by taking the left shoe from each pair." In a flash of supertasking, the daemons create a new pile made up of infinity left shoes, and my once seemingly Sisyphean task is instantly completed. The Scrum burn-down chart drops below the red line for the first time in thirteen billion years. The Lord High tells me he likes my bias for action and my ability to self-manage to project actualization. Then we do lunch.

Next: What the hell was that all about?