Let's start with those imaginary folks. Not too long ago we watched the Spanish film Fermat's Room. Pierre de Fermat, a 17th century lawyer and mathematician, has his place in history for posing a mathematical puzzler unresolved for over 350 years. In the movie a man who calls himself ‘Fermat' lures four very clever people to a meeting of minds in a remote warehouse. The purpose? To solve a great ‘enigma'. The bait? In order to attend, each individual must first determine how the following numbers are ordered: 8 5 4 9 1 7 6 3 2. What's the pattern?
Most of us find that kind of question irresistible. People are, in fact, pattern-recognizing and pattern-forming creatures. In order to make sense of the world, we look for repeating qualities in phenomena around us; we try to discern the reasons behind repeating events and processes. On a very simple level, we may group things by color, or shape, or texture, or number or according to qualities of sound, smell, taste, touch or properties of movement. Or we may group them according to purpose, function or any one of many conceptual organizers-as in the number puzzle just posed. (Does it help if we say we've transcribed the puzzle into English?)
While that puzzle may have us scratching our heads, a lot of pattern recognition comes to us naturally. According to psychologist Alison Gopnik and colleagues, day-old infants will gaze with intensity at the edges and stripes. Strong visual lines and color contrasts are first clues to the existence of discrete objects. Along with tactile, auditory and movement information, these clues coalesce into patterns with which we first parse the world around us. Babies also respond to the eyes-nose-mouth pattern of the human face and seem to prefer, too, the pitches and rhythms of parental ‘baby talk'. By their first birthday they recognize or privilege that repertory and begin to babble in the sound patterns of what will become their native tongue. (1)
The drive to recognize and form patterns can be a spur to curiosity, discovery and experimentation throughout life. Many artists, from Leonardo da Vinci to M.C. Escher, have purposefully looked for familiar patterns in wood grain, stone walls, stains, clouds, even man-made objects. Da Vinci found this "Way of Stimulating and Arousing the Mind to Various Inventions" so invaluable that he applied it not only visually, as a means of inventing landscape or battle scenes, but in musical matters as well. (Da Vinci was also a fine musician.) "It happens with this confused appearance of walls," he observed, "as it does with the sound of bells in whose jangle you may find any name or word you can imagine." (2)
Scientists also play the pattern game. And some have played it as da Vinci suggested. Take, for instance, the efforts of birders and biologists to recognize and understand the communication of birds. Spend a bit of time listening to a woodland chorus, and you can discern the auditory patterns of different species. You can tell the difference between a robin, say, and a bluejay. Spend a bit more time and you can tell the difference between the robin's call at seeing a hawk and the call it gives when mobbing an owl. Go one step further, and you might even recognize that the robin's call in each of these instances shares fundamental similarities with that of the blackbird and other song birds.
In fact, the sonograms of these calls look very much the same. For zoologists such as Charlotte Uhlenbroek the song patterns of different birds fall into larger cross-species patterns because needs and constraints across species are so similar. The alarm call, for instance, must signal danger to fellows without alerting the predator to the whereabouts of the alarm caller. "The solution," she writes, "is to produce a distinctive call whose source is very difficult to locate...the calls are high-pitched and pure-toned; they start quietly, get louder and then fade very quickly..." (3) The evolutionary result is that different birds ‘understand' each other's alerts.
Of course, what we understand about bird song depends an awful lot on the patterns we recognize and form. In Why Birds Sing David Rothenberg takes a look at a wide variety of patterns people have found in bird song and rendered in a wide variety of ways. In addition to the sonogram, bird song has
been transformed into musical notations as well as words and phonemes. When we listen to bird song we hear music and poetry as well as science. (4)
Indeed, the more patterns we recognize, the wider our imaginative and creative scope. Which brings us back to Fermat's Room. Chances are good that if you've been thinking beyond mathematics, you've already recognized the organizing principle behind the sequence of numbers in ‘Fermat''s puzzle. If so, you get to attend his meeting-though you may not want to! In the movie, our four clever people are locked in the room and presented with increasingly difficult puzzlers which they have only minutes to solve. When they fail, the walls start closing in and-well, you see the story pattern, don't you? In Fermat's Room patterning is a vital skill. It's vital for babies, birders and the rest of us, too.
PUZZLE SOLUTION: In Fermat's Room one of the characters struggles for days to find the pattern in 8 5 4 9 1 7 6 3 2. Our parenthetical aside that the puzzle has been translated into English provides a clue similar to the offhand remark that sparks the aha! of pattern recognition in the film. The pattern is not numerical, but alphabetical. In the movie the numbers are alphabetized in Spanish. Here, we've arranged them according to their English spellings.
© Michele and Robert Root-Bernstein 2011
(1) Alison Gopnik, Andrew Meltzoff & Patrician Kuhl. 1999. The Scientist in the Crib, What Early Learning Tells Us About the Mind. New York: Perennial, pp. 66-70, 152.
(2) Cited in Robert & Michele Root-Bernstein. 1999. Sparks of Genius, The Thirteen Thinking Tools of the World's Most Creative People. New York: Houghton Mifflin, p. 97.
(3) Charlotte Uhlenbroek. 2002. Talking with Animals. London: Hodder & Stoughton, p. 67-68.
(4) David Rothenberg. 2005. Why Birds Sing, a journey through the mystery of bird song. New York: Basic Books. See also http://www.whybirdssing.com/
Fermat's Room, 2007. Written and directed by Luis Piedrahita and Rodrigo Sopeña.
Blackbird alarm call at http://www.fssbirding.org.uk/blackbirdsonogram.htm
Hermit thrush song at http://www.math.sunysb.edu/~tony/birds/music/hermitB.html