Connotations of Color

Check out this infographic displaying the symbolic meanings of colors in various regions of the world. (And see more visualizations made by Dave McCandless at his website, Information is Beautiful.)

The only color connotations consistent across cultures appear to be black for evil, and red for both passion and heat.

Sleep, Wake, Repeat

In modern society, there is a standard opinion on the matter of sleep: we need, we think, eight straight hours of it each night. Get less than eight and you'll be dozy the next day; wake up for a long time during the night and you have insomnia.

But recently, the results of all those sleep studies your friends have been doing for extra cash have nixed this picture of the ideal sleep pattern. It turns out that the best night of sleep doesn't happen all at once. As Jesse Gamble asserts in the following video, the most natural, restful sleep is instead "biphasic" - it comes in two stages of equal length, separated by one or two hours of quiet, meditative wakefulness in between. This is the pattern humans eventually fall into when freed of the arbitrary structure of artificial lighting.

More shocking than the notion that we're doing it all wrong is the fact that we used to do it right. Until the relatively recent advent of electricity, biphasic sleeping was the norm. From an article by the historian A. Roger Ekirch:

Until the modern era, up to an hour or more of quiet wakefulness midway through the night interrupted the rest of most Western Europeans. ... Families rose from their beds to urinate, smoke tobacco, and even visit close neighbors. Remaining abed, many persons also made love, prayed, and, most important, reflected on the dreams that typically preceded waking from their "first sleep." Not only were these visions unusually vivid, but their images would have intruded far less on conscious thought had sleepers not stirred until dawn. The historical implications of this traditional mode of repose are enormous, especially in light of the significance European households once attached to dreams for their explanatory and predictive powers. In addition to suggesting that consolidated sleep, such as we today experience, is unnatural, segmented slumber afforded the unconscious an expanded avenue to the waking world that has remained closed for most of the Industrial Age.

Erkich presents a great deal of historical evidence in support of his claim, leaving, in my opinion, little doubt that our predecessors were biphasic sleepers. But there are still many open questions on this topic. First, why the societal shift? Even if artificial lighting has something to do with our newfound tendency to sleep through the night, why did we so quickly forget about the "first sleep" and "second sleep" of old?

Furthermore, besides the convenience of a midnight bathroom break and a heightened ability to recall dreams, what true biological benefit does biphasic sleeping bestow?

Scientists will soon be able to answer the latter question by studying the biphasic and polyphasic sleep patterns of other animals, and by conducting further sleep studies on unemployed post-adolescents. In the meantime, why not try out biphasic sleeping yourself? If you do, please report back!

The Silk Renaissance

Read my feature article, "The Silk Renaissance", here at SEED Magazine.

Self-Organized Criticality

Most learned people are aware that there is some sort of a connection between financial markets and biological evolution, between earthquakes and stock market crashes. They know it all has something to do with fractals and chaos, and that such connections are the subject of the relatively new realm of science called "complexity theory."

But the general understanding rarely seems to go much deeper. Few truly grasp the common thread tying together all these various phenomena, and scientists themselves clearly have trouble explaining the thread in terms that don't sound vague or wishy-washy. There was a time when complexity theory actually was somewhat wishy-washy; when scientists saw the similarities and patterns between various fields of study but were at a loss as to how or why they arose.

But that time has passed. At this point there is an explanation available that grants a huge amount of clarity about the common processes of the natural world. And unlike the complex systems it explains, the theory isn't all that complicated. Systems as disparate as world economies, rivers, forest fires, earthquakes, the human brain, and even the internet all display a behavior known as self-organized criticality (SOC). Understand SOC, and you will understand a great deal about the relationship between all these different types of systems.

The canonical example of a system that displays SOC is a pile of sand. (The three scientists who "discovered" SOC, Bak, Tang, and Wiesenfeld, used a sandpile model to present their theory to the world in the late 1980s, and it has remained the most straightforward presentation.) You may have noticed, or it may seem right when you think about it, that when you pile up sand at the beach, the slope of the cone of sand you make is always the same no matter how big or small the cone is. Gather up some sand, move your hands away, and the sandpile spontaneously falls into a very regular shape, always with the same slope.

Well it just so happens that this is the "critical slope" of the pile. Sandpiles, like many other naturally-occurring aggregates of a vast number of individual units, are attracted to their so-called "critical point". Without fine-tuning or careful arrangement, they just fall into that state. The critical point is where complex systems like sandpiles want to be.

At the critical point, sandpiles behave in a very peculiar way. If you perturb a pile by dropping a single grain of sand anywhere onto it, literally anything could happen. The grain could either slide down the pile a short distance and stop, it could knock a few grains down with it, or it could cause a huge avalanche and cave in the entire side of the sandpile.

In other words a sand avalanche of any scale is possible, and at the critical point, the severity of an avalanche exactly correlates with how likely it is to occur. Explicitly, the added grain of sand is 10 times more likely to knock 10 grains down the side of the pile than it is to displace 100 grains, and a 100-grain avalanche is in turn 10 times more likely than an avalanche involving 1000 grains. Small avalanches occur more often than big ones, but any size avalanche can and will happen if you spend long enough dropping grains onto the pile.

Slightly more technically speaking, the size of an avalanche is inversely proportional to its frequency. If you dropped grains of sand onto the pile over and over for days and recorded the size of each of the resulting avalanches, then graphed the results, the size-frequency proportionality would emerge. This correlation is known variously as 1/f noise, power law or fractal behavior, and scale-invariance. It occurs because, at the critical point, an infinity appears in the equation governing the behavior of the system, rendering such behavior unknowable. (Those interested in the math of critical points should read more here.)

SOC behavior is exhibited all over nature, wherever small perturbations (like the addition of single grains of sand) happen to large systems (like sandpiles). For example, small vibrations of tectonic plates can cause earthquakes of any size, with a severe earthquake being much less likely than a small one. The price drop of a single stock can have little or no effect on the stock market as a whole, or it can spur a chain of events that leads to a major stock market crash and economic depression. The extinction of a single biological species can bring down five others with it, or five hundred. The firing of a neuron in the brain can die down without effect, or it can cascade and grow into a conscious thought. A military skirmish can lead to a couple of others, or world war. In all these cases, "avalanches" of any size are possible, and with self-organized critical systems there's really no predicting what size avalanche will occur as a result of a given perturbation.

To use one more example, I am "perturbing" the internet by posting this article. I can be confident that this post is more likely to generate a few hundred hits than a few thousand, but who knows. With a chain reaction of Facebook shares and Tweets, anything is possible: thus the allure of blogging!

The brain, the internet, sandpiles, tectonic plates, the weather, stock markets, ecosystems, and literally countless other systems exhibit SOC, but there is as yet no general theory as to what exactly constitutes a system which causes it to self-organize around its critical point. This question occupies many minds and blackboards around the world.

My final observation on the matter of self-organized criticality concerns its relevance. Despite the fact that it explains so much about the way the world works, SOC isn't part of the general lexicon. People don't talk about it. Apart from complexity theorists, even most scientists don't talk about it. This is because scientists are in the business of predicting events in the world around us, and scientific theories have always been valued according to how well the predictions they make match reality. SOC turns this completely on its head. SOC is a theory about the impossibility of prediction. Not only can't SOC tell you how severe the next San Francisco earthquake is going to be, it is telling you that the question isn't answerable. That the earthquake could be any size. That we might as well stop trying to guess.

This kind of message is hard to swallow if you're judging science by its old standards. Self-organized criticality, and complexity theory as a whole, is certainly a new kind of science. It is more relevant than any theory before it as an explanation of how nature works, but not because it provides a means of determining what is going to happen in the future. It can't predict the next event that will occur in a complex system. Instead it predicts the pattern of events spanning the past, present, and future all at once, in no order.

Math on the Walls

Wallpaper comes in an infinite variety of patterns, from repeating peacocks to intertwined flowers to Escher creatures to simple stripes. Mathematically, though, there are only a finite number of distinct types of wallpaper. It turns out that all the elaborate patterns of the world's walls can be stripped down to their bare bones, analyzed for which symmetries they display, and identified as one or another of exactly 17 so-called wallpaper groups. (Yes, 17 - it appears again.)

Wallpaper is only the historical point of reference for a more general statement about all two-dimensional repeating patterns, including things like tessellations, honeycomb, checkerboards, and chain-link fences too. Long before mathematicians rigorously classified planar patterns as "p4g", "pmm", or any of the other wallpaper groups, the ancient Egyptians discovered and plastered all 17 of them up on the walls of their rooms and tombs.

The classification of the wallpaper groups is based on how individual segments of a pattern, called unit cells, fit together. To determine how they fit, and which group they fit into, you test how you can transform the pattern and still end up with it looking how it did before. You test whether you can translate it (by shifting the unit cells over one place and ending up with the same thing), rotate it, reflect the pattern across a line, or "glide reflect" it, which means reflecting it across a line and simultaneously shifting it.

Based on those four types of symmetries, and which of them a given pattern possesses, it can be categorized in one of the 17 groups. Sometimes it is obvious that two wallpaper patterns are members of the same group, as in this case:

(Group cm - reflections and at least one glide reflection along an axis other than the reflection axes)

And sometimes patterns within the same group look very different:

(Group pmg - two centers of 180 degree rotation, a reflection axis, perpendicular glide reflection axes)

The mathematical proof of there being exactly 17 groups gets rather hairy, but fortunately someone wonderful has created an Applet allowing you to study the wallpaper groups directly: by designing wallpaper patterns of your own in mere seconds. It's fun!

Escher Web Sketch

It Isn't Facism

Oliver Sacks, author of such brain disorder bestsellers as The Man Who Mistook His Wife for a Hat, has just written a fascinating piece for the August 30th issue of the New Yorker about his own neurological abnormality. Along with an estimated 6 to 8 million people in America alone, Sacks suffers from a condition called "prosopagnosia", or face-blindness.

Sacks cannot recognize people. Even the faces of his nearest and dearest seem like those of total strangers when seen out of context. To recognize family members and friends he must look for characteristic moles, familiar clothing, or haircuts - concrete traits rather than the subtle details to which the rest of us are so well attuned.

Because knowing your friends from your enemies is so important in our species, we have evolved a part of our brains called the "fusiform face area" which is solely responsible for storing and recalling information about human faces. Some people have a really, really heightened face sensitivity; they pass a woman at the supermarket and immediately remember seeing her at a nearby table at a restaurant a week earlier.

At the other end of the spectrum are people like Oliver Sacks. The fusiform face areas of their brains don't work very well, and so to them there is nothing much special about a face. This is my comparison rather than Sacks's, but it seems that for prosopagnosia sufferers, distinguishing between two people's faces is rather like distinguishing between their feet. Of course you can tell two pairs of feet apart if you really look, but bring in a couple more pairs and the clarity fades. We are all basically foot-blind, but some people are face-blind too.

The main interest of Sacks's article for me was a detail about the ways in which we are all partially prosopagnosiac. Recently a psychologist named Olivier Pascalis conducted a study on face recognition in babies. It found that at six months, babies are able to recognize a wide variety of types of faces - those of their own race, other races, and even individual faces within other species of animals. At nine months, however, they have lost some of the diversity in who they will recognize, as if the workings of their fusiform face areas have restricted themselves to face-types most often observed.

The consequence, in Sacks' words, is that "to a Chinese baby brought up in his own ethnic environment, Caucasian faces may all, relatively speaking, 'look the same,' and vice versa."

It is a phenomenon we have all experienced. When I was studying abroad in Ghana, West Africa, nearly every time I was in public with a white friend, no matter how different I thought we looked, someone would invariably ask us if we were twins or at the very least, siblings. They couldn't recognize the distinctions between our European faces. I would feel surprised, but then would find myself assuming the same about many pairs of Ghanaians I met as well.

Thankfully there is a neurological explanation for our foreign-face-blindness, rather than one rooted in inherent racism. It is difficult to tell people apart who are of a race other than our own simply because we didn't develop the skill as babies. Subtle awareness of deviances from an average face takes a great deal of mental resources, and these, of course, must be parsed.