If you’ve ever been in a Waffle House, you’ve probably seen a sign on the wall advertising that the restaurant offers 1,572,864 ways to enjoy their hash browns. While this astronomical figure may appear at first glance to be a gross exaggeration, it’s actually a legitimate calculation of the number of different ways in which four preparation methods, three sizes, and eighteen “additional ingredients” (in addition, that is, to the potatoes themselves) can be combined. From a “truth in advertising” perspective, Waffle House is on pretty solid ground with their impressive claim.
Of course, just because there are a million and a half possible ways of eating hash browns at Waffle House, that doesn’t mean that each of these combinations is equally probable. If you look around at the plates of diners gathered during a Saturday morning breakfast rush, you’ll see far more ketchup and onions in people’s hash browns than you’ll see, say, mayonnaise and jalapenos, or mushrooms and thousand island dressing. Because of the fairly limited range of ingredients that people expect to see on their hash browns, a given twenty-four hour period at a Waffle House is likely to utilize but a tiny fraction of the potential of their extensive hash brown menu. To come anywhere near maximizing the possibilities of the menu would require a redistribution of its probabilities through a random distribution of combinations, such as might occur if a busload of drunken after-party revelers staggered in late on a Saturday night and ordered whatever ingredients their bleary eyes happened to focus on first. In this chaotic scenario, any one possible combination of ingredients would be just as likely to occur as any other, producing a far higher percentage of the 1,572,864 possible combinations than the soberer, more predictable demands of a typical collection of Waffle House diners.
A recent study of human consciousness approached relationships among networks in the human brain as collections of possible combinations, not unlike the Waffle House hash brown menu. Researchers in Canada and France used statistical mechanics—a branch of theoretical physics using probability theory to study the average behavior of a mechanical system—to analyze different patterns of electrical connectivity in the human brain during different states of consciousness. Recording the electromagnetic activity at dozens of different locations in the brains of nine people (four of whom had epilepsy), the researchers searched for “pairwise” patterns of functional connectivity between the locations during different states of consciousness.
In the subjects who had epilepsy, the connectivity patterns they exhibited during seizures were compared with patterns they exhibited when in a normal state of open-eyed alertness. In the five other subjects, the connectivity patterns they exhibited when they were asleep were compared with those they exhibited when they were awake. In addition to counting the actual number of connections recorded during each of these states of consciousness, the researchers also calculated the total number of possible connections among the networks being measured (in much the same way that Waffle House calculates the total number of possible hash brown combinations). In each case, the fully conscious states were characterized by a higher number of actual connections—close to the calculated maximum—than either the seizure states or the sleeping states.
While it may not at first glance seem surprising that full consciousness involves more extensive connectivity among brain networks than states of reduced alertness, when viewed within the context of the physical laws that govern the physical universe (of which the human brain is a physical part) this finding offers intriguing new insight into the origin of human consciousness. In the language of physics, what the researchers were actually measuring in their comparison of actual versus possible connectivity pairings was the brain’s entropy. According to the Second Law of Thermodynamics, the elements that make up an isolated physical system tend naturally toward disorder rather than order over time as those elements drift toward a state of most probable distribution. Entropy is a measure of the degree of disorder that exists among the elements of a system. To consider a familiar example, think of shuffling a deck of cards. When you first take a new deck out of the box, the cards are very precisely—and improbably-- ordered, with suits gathered together and the cards within each suit arranged in ascending or descending ordinal numbers. For each and every card in the unshuffled deck, there is one and only one possible location. The entropy of the deck is thus zero. Introduce disorder into the deck by shuffling it, however, and the probability distribution begins evening out until the likelihood of any one card being in one location is just as great as that of its being in another location. The unshuffled deck, with zero entropy, has exactly one possible arrangement of its cards. The shuffled deck, with maximum entropy, has a staggeringly large number of possible arrangements (larger even than the number of possible Waffle house hash brown combinations).
The researchers who conducted the study hypothesize that the brain, like a deck of playing cards and other physical systems in the universe, naturally tends toward a state of most probable distribution—toward a state of maximum entropy—among its connectivity configurations. Their finding that full consciousness exhibits a higher degree of entropy than states of reduced awareness suggests that human consciousness is an “emergent property” of the brain’s natural tendency toward entropy. Since the brain’s primary function is to “maintain a predictive model of the environment,” perhaps it evolved in such a manner as to “copy” this environment. And since its environment is one that is governed by the Second Law of Thermodynamics, its “global configuration” of networks similarly maximizes energy-- and information-- exchange.
Faced with the staggering complexity presented by the entropic universe in which we all live, a less entropic, more “orderly” brain would be ill-equipped to make sense it. As with the drunken after-partiers ordering random combinations off the Waffle House hash brown menu, it is the brain’s disorder rather than its order that opens us up to the full potentialities of our richly complex world.