Before we start, I’d like to thank listener Maurizio Codogno, who published a nice review of the Math Mutation book at goodreads.com. Bizarrely enough, he wrote his review in Italian, but thanks to the magic of Google Translate, that doesn’t stop other listeners from reading it! Remember that if you like the podcast and/or book, I really do appreciate a nice review at iTunes, Amazon, or Goodreads.
Now, on to today’s topic. Recently I’ve been reading a collection of essays, short biographical recollections, and text-based art experiments by the radical 20th-century composer John Cage, titled “A Year From Monday”. You may recall Cage as someone I’ve mentioned in several podcasts, as he composed (if you can call it that) the silent music piece ‘4 minutes 33 seconds”, plus numerous musical pieces generated based on complicated formulas involving random numbers. As usual with Cage, his entries in this book are sprinkled with many instances of weirdness for the sake of weirdness, woven in with a bit of celebrity name-dropping. But worth reading for the bizarre humor and occasional surprising insight.
Cage also used the essays in the book as lyrics for one of his strangest music pieces, “Indeterminacy”. In Indeterminacy, he read each short story at a speed designed to fill a constant interval, while randomly-determined music played in the background. Due to the timing needs of the music, pieces would sometimes be read very quickly, to fit in a lot of words, or very slowly to fill the available time. There also was a random ordering to the stories. As Cage described it, “My intention in putting the stories together in an unplanned way was to suggest that all things – stories, incidental sounds from the environment, and, by extension, beings – are related, and that this complexity is more evident when it is not oversimplified by an idea of relationship in one person’s mind.” I actually bought the 2-CD set a number of years back, but found listening to it a rather frustrating experience, as you can probably guess. As often happens with Cage, the idea of the piece is a lot more fun than the actual end result.
Getting back to the book, one of the aspects that I find most amusing is the conundrum represented in its title, “A Year From Monday”. Apparently Cage was having fun with a group of old friends, and they decided they wanted to get together again. One of them suggested that they would all meet at a favorite spot in Mexico “a year from Monday”, and they all agreed to the proposal, without further clarification. Cage liked the idea, as it appealed to, as he described it, “my interests in ambiguity and my interest in non-measurement”. After leaving, however, Cage started wondering, when exactly did they agree to meet?
As you’ve probably already figured out, the phrase “a year from Monday” is rather ambiguous. How do we define such an interval? The easiest method would be to assume that they just meant the same date next year: if we assume that the discussion occurred on Monday, June 2nd, for example, then they would meet next year on June 2nd. But this will not be a Monday, since the number of days in a year is not divisible by 7— is this is a problem? Normally, when we talk about an interval starting on a day of the week, we expect to meet on that same day again: for example, when scheduling a monthly meeting in a tool like Microsoft Outlook, we usually select options like “the first Monday of every month” or “the second Monday of every month”, so perhaps it would be more reasonable to assume that the plan actually meant to meet on the first Monday of June next year.
There is also the question of how to handle the possible case of a leap year. If the intervening February had an extra day, would they have to meet a day later than originally planned, more like a year from Tuesday? On the other hand, maybe our slavish devotion to human-created calendars is part of the problem. If an objectively-measured solar year was intended, this is about 365.25 days, so it might make more sense to meet 365 days later, but delay the meeting time by 6 hours in order to make the interval precisely one year.
While Cage claimed that he enjoyed the ambiguity, he also had a conflicting tendency to carefully plan and measure musical pieces like an engineer, as shown by the precise time intervals used in Indeterminacy. Thus, eventually he realized that he had to figure out when exactly he was going to Mexico. When he tried to confirm his plans with the other attendees, he soon realized that due to the ambiguous phrasing, most of them had not actually taken the rendezvous seriously. In fact, some had make firm plans which would prevent them from meeting in Mexico anywhere near the proposed date. With that, Cage decided to give up his attempts at planning, realizing that some problems don’t have a clear answer, and simply rely on Fate. As he phrased it, “We don’t have to make plans to be together. (Last July, Merce Cunningham and I ran into Bucky Fuller in the airport outside of Madrid.) Circumstances do it for us.”
And this has been your math mutation for today.