The Quantization of Thought

According to what has become known as the neuron doctrine, proposed by Spanish histologist Santiago Ramón y Cajal in the late 19th century, the neuron is the basic structural and functional unit of the nervous system. There are an estimated 10¹¹ (100 billion) neurons in the average human brain, and each of those is capable of forming about 7,000 synaptic connections with other neurons, making the total connections possible on the order of 10¹⁴ (100 trillion), a truly staggering number.

Neurons communicate electrochemically, functioning essentially as switches that are either on or off at any given moment. Signals are sent when electrical impulses travel over the synapses from one neuron to another. At the neuronal level, then, the total amount of information that can be transmitted by a single nerve cell at one time should be one bit. If a thought can be said to be finite, meaning that it is a discrete entity with a beginning and an end, there are finitely many neurons activated during the course of that thought sufficient to render it within our brains.

Thoughts, then, have fixed information content. I believe that we can learn much from analyzing the mechanics of thought, basing our interpretations not only on the location of neuronal activity within the brain but also on the total information content transmitted by the neurons.

This turns out to be a challenging task. No living brain is ever truly quiet. Even while we are in a deep, dreamless sleep, neurons continue to fire within our brains without any conscious thought being the result. An effort therefore needs to be made to establish a baseline of neuronal activity for a normal, resting brain (and, for the moment, we will cautiously ignore what it means to be both normal and resting). Building up from this baseline, we can observe the neuronal activity of conscious thought and begin to quantify the information content of individual thoughts.

One of the stalwart methods of measuring electrical activity in the brain is the electroencephalograph (EEG), a machine that produces the familiar images of brainwaves that we see in textbooks. The different types of brainwaves (alpha, beta, theta, delta, etc.) correspond to different levels of electrical activity in the brain, and we can usually make fairly sound judgments about the state of consciousness of the person whose brainwaves are being monitored.

What these brainwaves don’t tell us, however, is where in the brain the activity is taking place or exactly how many neurons are involved. For the location of activity within the brain, a typical method of measurement is positron emission tomography (PET), which employs sugar molecules built with radioactive carbon atoms to measure glucose consumption in the brain. When the carbon atoms go through radioactive decay, the gamma rays they produce show up on the scanning equipment, and the results can be displayed graphically to give a picture of which areas of the brain are eating the most sugar at any given moment. The idea is that the area of the brain that is most hungry is the area that is most active. The use of PET has greatly advanced our knowledge of what areas of the brain are responsible for particular tasks.

It is tempting to perform a thought experiment—and a bit of imaginary engineering—in order to get a better picture of the internal activity of the brain. All electrical impulses, no matter how transient, produce an electromagnetic field. Considering active neurons as single point sources of fixed charge, it is possible to apply Coulomb’s law to determine the field produced by a single neuron’s firing. The field produced by multiple neurons would simply be the vector sum of the fields produced by individual neurons.

Could we, then, with sensitive enough equipment, map with precision the neuronal firing patterns of individual thoughts? It is tempting to think that we could, and the imaging technique known as magnetoencephalography comes closest to the application of the idea I mention above. But it is even more tempting to perform the following hypothetical experiment.

With our “baseline field” information handy, we would establish the neuronal firing patterns that result from fixed stimuli. For instance, what is the brain’s neuronal response to a single image of a black dot on a white background, displayed for one second? Assuming this response is uniform (and this is a hefty assumption), we can create first principles from which we can expand a greater theory of human thought and cognitive science.

For example, if we discover that the neuronal response to the aforementioned stimulus spans, say, ten neurons, then we know that the processing of that image or concept requires ten bits of information within the brain. By building an informational vocabulary with stimuli of increasing complexity, we can then begin to analyze thoughts of unknown content by mapping and quantifying their corresponding neuronal activity and comparing that content to the responses engendered by known stimuli.

Do we have thoughts that stream megabytes of information? Is our processing of images fundamentally different from our processing of concepts? Is it even possible to construct a theoretical vocabulary of neuronal patterns? I don’t know the answers to any of these questions, but I do surmise that this is a case wherein the advance of technology and a solid application of theory can serve to unlock some of the most profound mysteries about what makes us uniquely human.

The Evanescing American Dream

A recent study suggests that the rags-to-riches American Dream is a myth . . . at least in America. But that does not stop millions of people from trying to come to this country for an opportunity at a better life.

The recent debate on illegal immigration has stirred great controversy with the suggestion of making felons out of those who come to this country without first going through the proper channels. In other words, crossing an invisible line in the sand will in most cases become a worse offense than beating the shit out of your kids.

It's tempting to go back to first principles when dealing with such an issue. Instead, let's go back to 1885, when the French gifted us the Statue of Liberty. (Yes, those wacky French, who became the people we love to hate when they objected to our plans to invade a sovereign nation under false pretenses. Theirs being the first nation to officially recognize our existence after the Revolutionary War, which we won partly because of French military assistance, is a bit of trivia we seem to have forgotten.)

The Emma Lazarus poem "The New Colossus," an excerpt of which adorns a plaque at the base of that statue, includes the line:

Give me your tired, your poor,
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.
Send these, the homeless, tempest-tossed, to me:
I lift my lamp beside the golden door.

On that plaque, there is no asterisk that links to a paragraph of legalese: "Aforementioned huddled masses restricted to those who have completed and notarized Forms XYZ-1041-3H and INS-347-5(a), shown proof of immunization, and filed Application Form LMI-1313-B. Further restrictions apply."

In short, what the hell has happened to this place?

Cellular Automata: Complexity from Simplicity

Cellular automata is a fascinating field of research that spans several scientific disciplines. The idea is simple: Very basic mathematical rules can eventually produce extraordinarily complex behavior. A cellular automaton is defined as a "state machine that consists of an array of cells, each of which can be in one of a finite number of possible states." The idea is that a cell is switched on or off according to rules based on the state of its neighbors. If you think of a cell as being a square on an infinite sheet of graph paper, imagine its neighbors as being the eight squares that border it.

There is a game (and it is only loosely a game) called "Life," which was developed by mathematician John Conway. It follows three simple rules. (Note: A filled-in square is considered "alive," and a blank square is considered "dead.")

1. A dead cell with exactly three live neighbors becomes a live cell (birth).
2. A live cell with two or three live neighbors stays alive (survival).
3. In all other cases, a cell dies or stays dead (overcrowding or loneliness).

Simple as those rules are, the complexity of the interactions (considering that each neighbor also has a neighborhood that influences its behavior) presents a situation wherein it is essentially impossible to predict the outcome of an initial state (the initial state being some choice of live cells arranged on the grid).

If you go to this site, there is an applet that will run the game of Life on your computer in a separate window (you don't have to download anything). All you have to do is click on a few squares here and there to make an initial image and then click "Go." The computer will then apply the rules over successive generations, and your initial image will evolve. It will either stabilize into several groups of "still life" images that remain constant when the rules are applied, produce "gliders" that will move off indefinitely, produce "oscillators" that stay fixed in their positions, or the squares will blink out of existence altogether. There is also the possibility that the scene will evolve indefinitely and chaotically (this was originally not thought to be possible).

Try it out for yourself. After you try a few images of your own (hitting "Clear" to start over), try starting with the shape known as the r-pentomino, shown here:

You will be surprised to see how this one simple image of only five filled-in squares evolves over successive generations, not stabilizing until generation 1,103.

What is the point of all this? Well, some people, including Stephen Wolfram, theoretical physicist and creator of the Mathematica software, believe that cellular automata can go a long way toward explaining the evolution of complex systems—including perhaps life and the universe itself—based on simple rules. A simple one-page explanation of the principle in PDF format can be found here.

Play with it and have some fun! Prepare to become addicted.