There are a few pieces of popular music that break out of the strait-jacket of 4/4 time, or its somewhat less popular cousin 3/4 time. Dave Brubeck’s “Take Five” comes to mind of course, the jazz classic that alternates between 5/4 and 4/4 time signatures.

I recently realized that the 1981 hit Golden Brown by The Stranglers has an intro in 13/4 time. I can’t think of anything else in pop music with a 13/4 time signature.

In particular, the song’s instrumental intro is formed from sequences of four measures that have 3,3,3,4 beats, respectively, for a total of thirteen beats.

Very strange, yet it all works. When you’re just listening to the intro it feels oddly exotic, but completely right. I suspect that there might be some perceptual number theory working under the surface: Three groups of three-beat measures, and then every fourth measure having four beats. Perhaps the logic of this is so compelling that it trumps our cultural expectations.

And I love the fact that when you say the words “Golden Brown” out loud, the rhythm you hear is exactly the same as when you say “13/4”.

It is wonderful when artists do something that according to conventional rules should not work — and then it does.

Three mountains

I was talking yesterday with somebody I know who is very spiritual. She asked how I was doing, and I told her that my life right now is focused on a big grant proposal (due in about a week), followed by a major talk/presentation (a few weeks after that), followed by a publication deadline (about a month after the talk). They are all on the same general topic, so it feels like one continuous journey. A very challenging journey.

As I was describing this to her, I automatically switched over to language appropriate to talking with someone who thinks about spiritual things. After describing the specifics, I said “so I have three mountains to climb, one after the other”, which I guess made it sound like a spiritual journey.

And as I said the words, I realized that it is a spiritual journey. Working continuously toward something you believe in, over a sustained period of time, requires a level of mental awareness and physical preparedness that cannot be achieved by intellectual effort alone. On some level you really do need to transform yourself into a proper vessel for the change you want to make.

As we got off the phone, she said to me, in a wonderfully warm and supportive way, “Good luck climbing your three mountains.”

Bookshelves in science fiction

Every once in a while, in a futuristic science fiction movie or TV show, I notice that the office of the captain or the head scientist or some other important personage has a fancy bookshelf with real books.

I understand why this is there. It serves as a visual short-hand to audiences, conveying high social status based on learning and erudition. Yet in most such shows the Sci Fi world portrayed has moved beyond books, generally to some sort of system of touch surfaces or floating holographic projection screens.

I understand the concept — the owner of these books expresses his/her high status through the display of an archaic and undoubtedly highly expensive technology of old, much as the CEO of a large corporation in Tokyo might decorate his office with a rare Samurai sword.

Yet in real life we do not decorate our offices with archaic information technology. Except in very rare cases there are no ancient Athenian scrolls or Egyptian papyri on display in high-status offices.

Information technology does not seem to age as gracefully as weaponry, when it comes to using symbols to express high social status. So I wonder — hundreds of years in the future, will there really be rows of old books displayed in offices as signifiers of power and intellectual importance? Or would such a thing merely come across to visitors as quaint, and more than a little odd?

Local translational control

I neuroscientist friend explained to me yesterday that in recent years scientists have come to understand the principle of “Local translational control” — namely that all the proteins and other substances needed for proper functioning at the cellular level are generated locally, wherever they are needed. Cells are highly versatile factories, capable of switching from one specialized manufacturing mode to an entirely different one, depending on circumstance. All the recipes needed are right there in the 3,000,000,000 base pairs of every copy of DNA, ready to be triggered. He told me that many people find this concept difficult to understand.

Yet it occurred to me that this is exactly how things work in our daily lives, something we take for granted. The human brain is a powerhouse of protean capability, yet most of the time almost all of those capabilities remain dormant. It is only when triggered by our environment that our vast array of capabilities come into play. When we encounter a pencil sharpener, our brain can guide us to sharpen pencils. When we encounter another person, we become a conversationist. When we pick up a hammer or a screwdriver, we become a carpenter.

It is this tremendous redundancy — the localization of vast potential power into the brains and bodies of every one of millions of individuals, that allows society to function in a way that we take for granted. The “ordinary” is built from an enormous wealth of distributed potential capability.

That same principle of enormous wealth of redundant capability, available everywhere and drawn upon whenever and wherever needed, is exactly what is going on in our bodies at the cellular level.

The wisdom of Groucho

A friend and I were discussing the phenomenon whereby people are often more attracted to people who are not as attracted back. I told my friend about the great line by Groucho Marx: “I wouldn’t want to belong to any club that would have me as a member” (invoked so memorably by Woody Allen in Annie Hall).

My friend pointed out that this actually makes sense. If some club (euphemistically speaking) is aggressively courting you, then (1) you still don’t know what it’s really like being a member of the club, and (2) you realize the club doesn’t really know who you are either. So much premature enthusiasm can come off as a little nuts.

Which made me realize that feeling wary of strangers who seem to be very into us, rather than being a dysfunctional response, is actually sensible. We all know that sexual attraction has a large instinctive component. On some level, our genetic code is really using us to propagate itself, and our conscious selves are mostly along for the ride (and to be sure, it can be a very exciting ride).

Which means that if somebody is aggressively pursuing you before you think they have any real sense of who you are, then there is a good chance it’s just the instinct talking. And that does not bode well for the long term prospects of a relationship.

Ah, the wisdom of Groucho! And of my friend. 🙂

Unbreakable codes, the old-fashioned way

On the puzzle page of the New York Times, in addition to the daily crossword, are a 4×4 and a 6×6 KenKen puzzle. The 4×4 is simple enough that to make it interesting I do it in my head, and then write down the answers in order (the top row left to right, then the second row, etc).

It has occurred to me that this would make a diabolical secret code to use in a spy novel. Spy number one picks up the daily paper, scans the puzzle page, and then encrypts that day’s sensitive message with some substitution code that uses the sequence 1,3,2,4 or 3,2,4,1 as its encryption key, or whatever permutation of 1,2,3,4 forms the top row of that day’s KenKen.

Spy number two just needs to look at the daily paper, find the same key, and decode the message. Since the code would change every day, nobody else would be able to figure out the coding scheme just by looking at the daily messages that passed between the two intrepid spies.

There’s nothing new about the basic idea. To form a secure code, you and I just need to settle on any key that is known to both you and me, but not to anybody else. There are well-known mathematical techniques to create secure codes, such as PGP encryption, but they generally require access to a computer. There is something charming, in an old-fashioned way, about being able to create a secure message without computation.

So I started pondering, given that you and I both get the daily paper, how we might use the paper as a source for encrypting and decrypting messages, without anybody else being able to figure out our code. We could, for example, agree to use the first line of the second article in the Sports pages.

Yet in this age of search engines, just about any rule that simple could be cracked by a dedicated computer hacker with access to the daily newspaper. Could we charmingly old-fashioned spies, with our copy of the Times rolled up under the arm of our gray-tweed suit, figure out a clever way to use the daily paper as a shared key, without our code being cracked by those young whippersnappers with their infernal computing machines?

Global irony

In yesterday’s New York Times, an article entitled “A new era of gunboat diplomacy” discussed how various nations of the earth (notably the U.S. and China) have been angling for control of seas that contain oil deposits, in many cases beefing up their naval capacity. Several paragraphs into the article I came across the following little tidbit:

“Several powers, including Russia, Canada and the United States, are eagerly circling the Arctic, where melting polar ice is opening up new shipping routes and the tantalizing possibility of vast oil and gas deposits beneath.”

So there you have it: Global warming causes melting of the Earth’s ice caps, thereby creating new opportunities to extract and burn more oil, and therefore to accelerate global warming.

Isn’t that special?

Cultural reverse peristalsis

There is an alarming tendency for pop cultural references to double back on themselves, reversing cause and effect. This is understandable. Pop culture is, by nature, a vulturous beast, consuming gobfuls of source material in its insatiably cavernous maw, as it digests anything and everything in its massive gelatinous path to a soft syrupy pulp.

Which sometimes results in an odd sort of reverse peristalsis. The very food upon which pop culture feeds becomes regurgitated and turned upside down. When this happens, people can become confused.

Case in point: In the era when “Star Trek, the Next Generation” was on the air, that intrepid Starship captain Jean-Luc Picard was the man of the moment. I remember students, upon first encountering the films of Jean-Luc Goddard, being amused that this french filmmaker had the same first name as the captain of the U.S.S. Enterprise.

Of course they had it all backwards. J.J. Abrams and his associates had named Jean-Luc Picard in homage to the great nouvelle vague director, a point that was missed entirely by these students.

Similarly, people who were raised on “Pinky and the Brain” cartoons might be taken aback the first time they see a performance by Orson Welles. “Gee,” they might think, “this guy sounds a lot like that little cartoon mouse.” Same goes for anybody who watched “Ren and Stimpy” as a child, upon first encountering a Peter Lorre movie. Or anybody who sees a film with Lionel Barrymore only after having watched “Underdog”.

People introduced to Bach after hearing the intro to Lady Gaga’s “Bad Romance” might wonder whether this guy ripped off her style. Young people with a bad sense of chronology might wonder whether Dylan Thomas was named for Bob Dylan, or whether Richard Burton, the geographer, explorer, translator, writer, soldier, orientalist, cartographer, ethnologist, spy, linguist, poet, fencer and diplomat, was named for Richard Burton, the actor.

And of course, anyone under a certain age, upon visiting a Scottish castle for the first time, will probably be astonished at how faithfully somebody managed to recreate Hogwarts. 🙂

Then I woke up

I had a dream last night in which my friend and I happened to be in a sketchy part of town. I was carrying my computer bag under one arm, and under the other arm I had a big box containing the device we had just invented that can be used to predict the future. My state of mind at this point in the dream, as I recall, was one of great excitement and anticipation, as we were just about to try out the device for the first time.

For some reason I needed to put the box down momentarily, and all of a sudden, it was gone! Fortunately my friend spotted a guy running off with the box. We chased the man down, and after a minor confrontation we managed to get the box back.

My feeling of relief at this point in the dream was great, yet short-lived. For in all the confusion I had put down my computer bag, and it too had been stolen away. Whoever had taken it was by now long gone. I thought sadly of all my work still on the computer, work I had not yet had a chance to transfer off, and that was now gone forever.

Then I woke up, and I felt a surge of relief to realize that it had all been a dream My computer bag and its contents were in fact safe and sound.

It took a few moments more for me to remember that the box that told the future was still trapped inside that dream. There was no way now to go back into the dream and rescue it, and I realized with sadness and resignation that my wonderful invention was as lost to me as Eurydice to Orpheus.


The New York Times crossword puzzle today had the black squares forming a giant “11”. I didn’t understand the significance at first, but now I do — it’s a reference to today’s date, November 11, 2011. Today is already quite important here in the U.S., because it is Veteran’s Day. But it is also a date that can be written 11.11.11. And for that distinction it doesn’t matter whether you are in the U.S. (where the month comes first) or Europe (where the day comes before the month).

This is probably the second to last time in your lifetime that you will experience a date with matching day, month and year, the next time being December 12, 2012. Unless, that is, you happen to stay alive long enough to see January 1, 2101.

And this is the only date in any century that can be written using only a single digit.

Once you start looking at the numerical patterns of dates, all sorts of possibilities suggest themselves. For example, if you are in the U.S. (where the month comes first) then November 23, 2058 can be written as 11.23.58, the first six number of the Fibonacci series.

I wonder how many other numerically notable dates there are.