#AdlerWall 03: Look for Patterns

by Shane L. Larson

(L) John Trusler (R) William Blake

In August of 1799, the Reverend John Trusler commissioned a pair of watercolors to illustrate the concept of “malevolence.” As a philosophical construct, we often regard concepts such as malevolence as being aspects of human behaviour that are part of our free will, not as natural phenomena that are able to exist independent of our free thinking. Does malevolence exist outside of humans, in Nature itself? Philosophers may differ, and certainly artists’ interpretations may vary widely. Perhaps not surprisingly, Trusler was not happy with the first painting he received.

Blake’s painting of “Malevolence.” [From the collection of the Philadelphia Museum of Art]

The painter commissioned by Tusler was none other than the great English artist, William Blake.  The two shared a contentious exchange in a pair of letters that month about Blake’s depiction. In a letter on August 23, Blake admonished Tusler that we all see the world differently, writing:

“The tree which moves some to tears of joy is in the eyes of others only a green thing that stands in the way. Some see Nature all ridicule and deformity…and some scarce see Nature at all. But to the eyes of a man of Imagination, Nature is Imagination itself.”

Blake’s exhortations to Trusler dance around an interesting and lovely conundrum — what is Nature and how do we separate what Nature is from what we perceieve or think of it?

Consider clouds. In your high school science class, you may have once been told that clouds are suspensions in the Earth’s atmosphere, huge agglomerations of tiny water droplets and ice crystals. Most of the familiar clouds form in the troposphere, the lowest part of the Earth’s atmosphere where weather happens. Gossamer and diaphanous, they are pushed around by the winds of the world, carrying weather and moisture to the far flung corners of our planet. Meteorologists, partnered with amateur cloud watchers, have categorized a large number of cloud types, though if you restrict your attention to the most common there are only ten or so that you encounter most often (see NOAA’s “Ten Basic Cloud Types”).

The most common types of clouds, only a few of the more than 60 types classified. [Image: Wikimedia Commons]

But many of us have, at some point in our lives, wasted away an afternoon staring at clouds in the sky. Part of those lazy gazings is calling out shapes and figures we see in the clouds — bunnies, turtles, ships, books, hands.

There are clearly patterns in the clouds. Nature made the clouds, so Nature made the patterns. After many long years of staring at the sky, we have elucidated some regular, recurring shapes and forms that Nature creates over and over again, and we’ve given them names: cumulonimbus, altostratus, cirrus, and so on. By a similar token, the shapes and figures we recognize as bunnies and sailing ships are also patterns we have elucidated from staring at the sky. What’s the difference between our observations and Nature’s patterns? What’s the difference between afternoon figures and the cloud archetypes?

Some clouds seen from airplanes. What do you see? On the left I see a trilobite, a kid blowing a bubble, and cauliflower. On the right I see a poodle, and a shaking fist.

One of the great realizations we have made about the world is that it is predictable. The world does not evolve randomly, changing each day in unpredictable and unexpected ways. Quite the contrary — when I throw a water balloon up in the air (or, possibly, at someone) it always comes back to the ground. The Moon moves through a steady progression of phases every 29 days, always in the same order, just as it has for all of recorded history. A popsicle always melts when left on the kitchen counter. All of these happenings, and the many others that surround us in the natural world, occur according to precise sets of rules that we call the Laws of Nature. The fact that we can recognize patterns, that we can deduce and use the Laws of Nature to improve our lives, provides the impetus for one of the great endeavours of our species — science.

When we look at the clouds, there are two sets of patterns in play. One set of patterns are the recognizable shapes and forms of the basic cloud types. Each of these different forms is governed by a particular realization of the Laws of Nature. They are predicable and repeatable, appearing anytime the same physical conditions appear in the atmosphere. Consider “Kelvin-Helmholtz clouds.” They can form when layers of wind are sliding across one another, with the upper layer moving faster than the lower layer, creating turbulence at the boundary between them.

A classic example of Kelvin-Helmholtz clouds, created when different layers of wind slide across one another. [Image: Wikimedia commons]

By contrast, the picture patterns that you can pick out staring up at the sky are unique to your own experiences and interpretations. You can certainly point them out to friends and get them to see what you see. But left to your own devices, you may see a turtle whereas your dearest friend may see a hoagie sandwich.  These are patterns made by your mind; the difference between them and the patterns made by Nature is that the patterns of the natural world are predictable and subject to rules. Our job as scientists and observers of the world is to figure out what those rules are.

The #AdlerWall this week exhorts us to “Look for patterns,” and that “patterns can be man-made or found in Nature.”

So what kinds of patterns can you find around you? There are clearly patterns that humans make, usually quite deliberately. Our brains crave the regularity and dependability of patterns. One of the most obvious places we encounter patterns is in woven textiles. There are global patterns — stripes, dots, space cats — that you can see standing next to your friend with the loud and colorful shirt. But there are smaller, more subtle patterns you can see if you look closely, notably the interwoven fibers that cross up and over one another to give the fabric its structure. The interlocking up and down, over and under pattern of individual fibers is a human invention, though who thought of it and when is now lost to history; the oldest known woven textile fibers date to about 6000 BCE.

There are many patterns to be seen in textiles, all of them made by humans. The patterns your eye can see, as well as the underlying patterns in the weave of fabric. Patterns occur on all levels. [Images: S. Larson]

Carpets are another great place to see human-created patterns. These grace the floors in the Salt Palace Convention Center in Salt Lake City. I want to know whose job it is to make up these patterns!

In a similar way, there are impressive patterns visible in Nature too. On cold winter days, frost ferns can form on your windows. These beautiful displays of symmetry look almost organic in nature, but result from water molecules binding to other water molecules. As a large structure forms, the molecules are forced to remain near the cold surface of the glass, and the structure of the fern emerges. Frost ferns exhbit fractal structure — a repeating pattern that appears on many many different size scales. We see fractal structure in tree branches and clouds as well.

A classic frost fern that formed on my sliding glass door this spring. [Image: S. Larson]

There are other patterns in Nature that you can notice. I just popped outside, and with a few quick sweeps found this rock on the gravel path next to my house. I could have picked up any old rock and found something interesting, but this one has a clear structural pattern. Look closely at the exposed, broken surface. It is comprised of a myriad of interlocking small crystal structures. I’m not a robust rockhound (I just pick up cool rocks and carry them around in my pockets), but this looks like a quartzite of some kind. Quartzite is a metamorphic rock — a rock that has formed by transformation under extreme heat. In the case of quartzite, extreme pressure and heat on sandstone variety rocks causes the glassy minerals in the sand to break down and reform in crystalline arrays, not unlike the one you see on the surface of this rock.

An everyday rock, picked up off a gravel path, shows a jumble of quartz crystals on its surface. [Image: S. Larson]

You can see much more robust crystal formation in a kind of rock known as a geode. Geodes are roughly spherical rocks with a hollow core, where crystals have slowly grown inside the core. Beautiful (and expensive!) specimens can be bought, but breaking open common geodes will reveal a beautiful little garden of crystals. Crystals are a special pattern of matter that arises from molecules that have regular geometric shapes that are preserved when the molecules are stacked together. The regular geometric shape of the crystal that you can see with your eye is a clue to the microscopic alignment pattern of the molecules that your eye cannot see.  Salt crystals and sugar crystals are other examples.

Geodes are known for their crystal structures. The crystals are macroscopic manifestations of the underlying molecular shapes — large patterns building from small patterns. [Image: S. Larson]

Another example of patterns, where human and Nature’s patterns collide is in the layout of city streets. I grew up in the American west, on the fringes of the Great Plains of North America. There the landscape is vast and flat, and humans could have laid their streets out willy-niIly in any way they wanted.  But a quick glance on satellite shows the roads are usually in a nearly perfect grid, roads running straight north-south or straight east-west. This is not true everywhere. In central Pennsylvania, the rolling landscape of the Appalachian Mountains strikes across the state from the southwest to the northeast. If you look at a town along the rolling, folded ridges you see that the roads and streets are aligned parallel to the mountains — humans patterns have been influenced and shaped by the natural patterns of the world around them.

Human patterns [streets] often follow Nature’s patterns [terrain]. (L) Fort Morgan, Colorado is in the Great Plains and streets run N-S and E-W, oriented to the cardinal directions defined by the spin of the Earth. (C) In central Pennsylvania the Appalachians form long ridgelines and valleys. (R) Cities like State College, PA have street grids aligned parallel to the terrain of the mountains in the area. Click to enlarge. [Images: Google Maps]

But seeking patterns in everything is a dangerous proposition — while we certainly believe that the laws of Nature govern everything, recognizing repeating and organized patterns is not always so easy. One of the classic examples of this is the tale of wealthy Bostonian Percival Lowell, whose imagination was captured in 1877 by the announcement of Italian astronomer Giovanni Schiaparelli that he had observed canali (Italian, “channel” or “groove”) on Mars. Many people’s inexperience with the Italian language caused them to map the word onto the English word “canal” which has a definite connotation of being an artificial and constructed edifice. (This erroneous mapping of words between one another is a failure to correctly match patterns!).

Lowell was entranced by the idea of canals on Mars, and spent a not inconsiderable amount of money constructing what is now known as the Lowell Observatory in Flagstaff, Arizona. He himself spent many long hours at the eyepiece, staring at Mars and sketching what he saw. Looking at his sketches and records we find Lowell saw what he wanted to see — canals. Lots and lots of canals. Looking at Lowell’s exquisite maps of Mars a century later, after our robotic spacecraft have returned tens of thousands of pictures of Mars, we see none of it. The interwoven pattern of canals which Lowell saw appear to be a dramatic case of scotoma — the mind sees what it wants to see.

(L) Percival Lowell observing on the 24-inch Clark Refractor at Lowell Obseratory. (R) Lowell’s map of the canals he thought he was seeing on Mars, now a classic example of seeing patterns that are, in fact, not there at all. [Images: Wikimedia commons]

Which carries us back to the tale of Blake and Trusler. We all see the world through our own eyes. The goal of collecting knowledge and one of the purposes of doing science is to capture the world as it really is, and to use that knowledge to improve our lives. No single one of us can do it all on our own; it requires all minds on deck. No single one of us ever gets it right on first glance; we have to look at the world, examine what we have seen, ponder its meaning, and, if necessary, let go of what we once thought in favor of a more real picture of what Nature has laid out before us.

So head out and look for the subtle patterns in the Cosmos; it’s all there for you to see.  See you out in the world — I’m the guy trying to take a picture of the repeating tile pattern on the cafeteria floor! 🙂

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This post is part of an ongoing series about the #AdlerWall. I encourage you to follow along with the activities, and post your adventures, questions and discoveries on social media using the hashtag #AdlerWall.  Links to the entire series are here at the first post of the #AdlerWall Series.

grant us peace

by Adam Johnston

It was with the Vienna Boys Choir that I first sang Dona Nobis Pacem — Grant Us Peace.

Okay, I was never really a member, but I did sing with the Vienna Boys Choir. We were in the same concert hall and we were directed to sing at the same time. It just so happened that I was shoulder to shoulder with the boys of my own elementary school choir, and the Austrians were on the stage. We sang together, as directed, and it was beautiful. It was a big deal at the time. It didn’t create world peace, obviously, but it didn’t hurt, either.

I’ve been thinking about that canon lately. At Christmas, especially, I find myself poking it out of the keys of the piano, the pedal heavy on sustain. The tune, the progression of the chords, the simplicity of the sequences of notes, it all draws me.

Music is one of those things I try to teach in classes. “The Music of Physics,” I call it, rather than the converse, not simply to be witty but to make that point that what we study can be both about the beauty of nature and the nature of beauty. That’s a heavy load to bear, but one I think we regularly try to carry in physics class.

The physics of “good” music is a tricky thing. We would like to believe and even teach that the beauty of the music comes from the relationships between the frequencies. An octave is defined by a factor of two in frequency between two notes. Thirds, fourths, fifths, and all other intervals you hear in chords and scales are each defined by factors, so that each major key may be made up of distinct notes, but the same proportions from one note to the next. When played together, the difference between any two notes becomes another unique “beat frequency.” So, for example, the difference between two notes separated by an octave is the same as the lower note (delta = y-x where y=2x, so delta = 2x-x=x). We think of an octave’s difference as really being the same note simply shifted up or down — so the baritones can sing in unison with the sopranos. On a piano keyboard this just shows up as a different place on the array of keys, but the same note within the pattern of repeating white and black. This is wonderful consequence of this geometry.

What’s really splendid is that this doesn’t have to be. It’s amazing, come to think of it, that this could work at all. Why would two notes with completely different frequencies, ever have any chance to be the “same,” or in “tune” with one another? I suppose the brain hears each note, and hears the difference between these notes, forms the beats in some physiological and mental way. Hearing two notes an octave apart, there’s a pattern that’s detected that creates that beat frequency that’s exactly equal to the base, bass note. Other differences between notes (as well as differences between harmonics heard on a singular note of a singular instrument) that sound good together are created by similar geometry. The difference in frequencies is itself a frequency that is in phase with the notes themselves.

That’s one thing I think about when I’m playing Dona Nobis Pacem on the piano. This chord progression is almost the least complicated one can imagine. A garage band of 17-year-olds could be cranking away on the three chords and we’d scoff or grin at the simplicity of it. And, because the three lines can be sung in unison or in round, they are each modeled after the same pattern. (Pull out your dusty guitar and strum G-D-G-D-C-G-D-G; repeat two more times and you can accompany my colleagues from Vienna.) It’s all so fulfilling that we go to the trouble to re-create it in contraptions like tubas and cellos and pianos. Considering all the design work put into the inner workings of my piano, I realize that these simple patterns are something we are driven to re-create. Not only are the patterns there in nature, but we’re hard-wired and compelled to construct them over and over.

So, I think understand how the difference between two notes produces a beat that itself is in tune with either of the notes; and this geometry of the physics of the music makes it pleasant, interesting, coherent. And then we play with patterns in this, both in the sequences in time as well as the audial space. In class, during that “music of physics” unit, I teach this with a tuning fork, a keyboard, a microphone, and an oscilloscope. I swing a tube over my head to play a series of harmonics that emulates “Taps” and they all laugh at my cleverness, or silliness — or perhaps out of sympathy for the bizarre instructor. I can get an organ tube to resonate with a piece of wire mesh and a blowtorch; and this phenomenon can be used to calculate the temperature of the room. I know where to stroke a violin bow on a piece of aluminum in order to play that octave’s difference, and we can see the standing wave set up by sprinkling some corn meal on the surface of the metal. I’m delighted with how much we can understand, as well as what we can do with it.

But then I throw my hands up and turn up the music. I’ve been known to tear up when, for example, Brandi Carlile sings Hallelujah. When Clapton has his hands on a guitar I understand why anyone called him God, and I believe. When Bach is played on a church organ I forgive him for all the pieces I had to learn in his name (though I still curse him, the asshole, when my fingers return to those pieces). Or when I find the right notes for peace, for prayer, on a piano. My left hand finds a way to march up a scale and meet my right hand in the middle, and I think, maybe, this is what I was meant to learn from it all. The physics of the harmonics and the physicality of sound is all beautiful, but it’s only as beautiful as we choose to make it. Dona Nobis Pacem. It’s stunning, and maybe my own version and belief in a miracle, that such a sentiment can come out of three chords. Grant us peace.