John Conway and mental exercise rituals


John Horton Conway (1937–2020) came up with an algorithm in 1973 for mentally calculating what day of the week a date falls on. His method, which he called the “Doomsday rule” starts from the observation that every year, the dates 4/4. 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, and 11/7 fall on the same day of the week [1], what Conway called the “doomsday” of that year. That’s Monday this year.

Once you know the doomsday for a year you can bootstrap your way to finding the day of the week for any date that year. Finding the doomsday is a little complicated.

Conway had his computer set up so that it would quiz him with random dates every time he logged in.

Mental exercises

Recently I’ve been thinking about mental exercise rituals, similar to Conway having his computer quiz him on dates. Some people play video games or solve Rubik’s cubes or recite poetry.

Curiously, what some people do for a mental warm-up others do for a mental cool-down, such as mentally reviewing something they’ve memorized as a way to fall asleep.

What are some mental exercise rituals that you’ve done or heard of other people doing? Please leave examples in the comments.

More on Conway

The drawing at the top of the page is a sketch of Conway by Simon Frazer. The strange thing coming out of Conway’s head in the sketch is Alexander’s horned sphere, a famous example from topology. Despite appearances, the boundary of Alexander’s horned sphere is topologically equivalent to a sphere.

Conway was a free-range mathematician, working in a wide variety of areas, ranging from the classification of finite simple groups to his popular Game of Life. Of the 26 sporadic groups, three are named after Conway.

Here are some more posts where I’ve written about John Conway or cited something he wrote.

[1] Because this list of dates is symmetric in month and day, the rule works on both sides of the Atlantic.



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