Emergence

The brain is often described as the most complicated device in the known universe.^[1] The basic units of information processing in the brain are neurons and glial cells. Yet, neurons and glial cells aren’t generally considered to be terribly intelligent on their own. At a certain level of description, on which you’ll read more later, neurons and glials cells could be thought of as dominoes, reacting simply to local conditions around them. Somehow, though, putting together 86 billion neurons and a similar number of glial cells—about 200 billion dominoes—produces something REALLY intelligent. How?

To understand your brain is to understand the concept of emergence. Stephen Hawking, a brilliant modern physicist, has called the study of emergence the science of the 21st century.^[2] Emergence is often described by the mantra “the whole is greater than the sum of the parts”.

Water is a canonical example of emergence. You could define water as H₂0, a molecule composed of two hydrogen atoms and one oxygen atom. However, this would be an incomplete description. To understand this, think about the following:

Liquidity is a property of the interaction of H₂O molecules. Emergence is often found when you have many things (like H₂O molecules) interacting. Let’s reflect on what is emerging here. Nothing about your knowledge of hydrogen or oxygen would allow you to predict the myriad of properties of water, including surface tension (which allows leaves and bugs to sit on the surface), a high capacity to hold heat (which buffers the earth from large temperature fluctuations, and is also why temperatures are more temperate near a large lake than further away), and the feeling of wetness. Most importantly, water provides a medium for molecules to dissolve, chemical reactions to occur, and materials to be transported—all properties which make water essential to life on earth. Clearly, the whole (water) is greater than the sum of the parts (hydrogen and oxygen atoms).

Two other illustrative examples of emergence are diamonds and graphite. Diamonds and graphite (which can be found on the end of a pencil) are chemically identical. Both are collections of interconnected carbon atoms. And yet they appear quite distinct: graphite is opaque, diamonds are transparent; graphite is soft, diamonds are hard. The key difference is how the carbon atoms interact—carbon atoms are arranged differently in diamonds and graphite, as shown below, and those different arrangements account for the diametrically opposed properties of the two substances!

Interactions amongst a large number of elements are the critical factor in emergence. Interacting H₂O molecules give rise to properties much different than a single H₂O molecule, or either hydrogen or oxygen atoms. Different interactions of carbon atoms give rise to radically different types of material. Likewise, the sophistication of the brain emerges out of the interactions of relatively simple neurons. Interactions are crucial for intelligence.

Because interactions are so critical, it is important to gain greater familiarity with the wonder of emergence, and the types of patterns and behaviors that can be generated by different types of interactions. Activity 1.1 is a straightforward example of emergence that a group of people can demonstrate. Before doing the demonstration, try to predict what the results would be!

Activity 1.1 illustrates an important principle: even very simple rules of interaction can give rise to unexpected—and sometimes complex—patterns. The rules defined the nature of your interactions, which catalysed the emergent patterns.

Cellular Automata

Emergence can be systematically studied using a class of computer models called cellular automata. Computer models are important for studying emergent systems (like the brain) because the results of having a large number of interacting agents (like neurons) are often difficult to predict and hard, if not impossible, to work out by hand.

By way of introduction to cellular automata, imagine a square on a piece of graph paper (see Activity 1.2 below). That square can either be filled-in with a pencil, or left white. Which state the square is in (filled-in or blank) depends on the states of the square’s neighbours: simple rules link the state of a square to the state of that square’s neighbours. In a so-called “one-dimensional (1-D)” cellular automaton, the fate of a given square depends on just three neighbours: the square immediately above it, the square one up and one to the left, and the square one up and one to the right, as in the box in Activity 1.2 below (those three squares form a short line, which is 1-dimensional, hence the cellular automaton’s description as a 1-D cellular automaton). The figures in Activity 1.2 represent one possible rule set for linking the state of the bottom square to the states of its three top neighbours. Our rule set must indicate whether the bottom square should be filled-in black (“B”) or left white (“W”) for every possible combination of the states of the three squares above it. Since each of the top squares can be in two states, and there are three squares, there are 2³ = 8 combinations of top squares. For each of the eight combinations, the rule set below shows what the bottom square should be (B or W). To see which pattern emerges from this rule set, do Activity 1.2.

As you can see, a simple rule iterated repeatedly gave rise to quite an unexpected pattern. Indeed, the pattern you derived is known as a fractal. Fractals are patterns that repeat themselves at multiple scales. In the image that you generated, within the larger triangle were a few smaller triangles, within which were a few smaller triangles, etc. Trees are another classic example of a fractal: trees have a large trunk with branches coming off of it, each branch has a main trunk with branches coming off of it, etc. If you were looking at a close-up of a single branch without contextual clues, it would be unclear if you were looking at a small tree, or the smaller branch of a large tree. Your body is also composed of a lot of fractal structures. Blood vessels are fractals (using the same reasoning as for trees), your respiratory system is fractal, and dendrites (the receiving ends of neurons) are fractals. Fractals are important biologically because complete structures can be produced with simple rules. Your DNA generates complex structures like your cardiovascular, respiratory, and nervous systems by encoding the simple rules of production for those systems, rather than exactly what the end structure should look like. In other words, fractals give you a lot of bang for your genetic buck. This helps explain in part how it can be that humans have the same number of genes as the much smaller mouse!

Activity 1.2 represents just one rule. We could have chosen the opposite state for each of the bottom squares. B could have been W and vice-versa. Because each of the eight combinations of the three top squares can map onto two possible states of the bottom square, there are 2⁸ = 256 possible rule sets. In other words, there are 256 ways that four squares—which can only be blank or filled-in—can interact! The sheer number of possible patterns emerging from these rules dramatizes why computer models are important. Let’s turn to a computer model to see these other rule sets (do Activity 1.3).

Now let’s get a little more concrete, and see an example cellular automaton which models a real world phenomenon. In the next Activity (1.4), you’ll see how cellular automata can reproduce different fur coloration patterns—from the striping of zebras to the spotting of Dalmatians. This cellular automaton is more complex than the last one—now the state of a cell is a function of the cells above it, below it, and to the sides. In other words, this is a two-dimensional cellular automaton.

Note the striking qualitative similarity in the images below. The top image was generated using the Fur model in Netlogo. The middle image shows a similar striping pattern in a zebra’s coat. Finally, the bottom image depicts stains of “ocular dominance columns” in the primary visual cortex of a macaque monkey. The white stripes correspond to cortex with cells dedicated to processing visual input from one eye and the black stripes correspond to cortex with cells dedicated to processing visual input from the other eye. This qualitative similarity between images suggests similar dynamic interactions are at work in all three. What differs are the kinds of cells doing the interacting!

Both computers and brains are kinds of cellular automata.^[7] Rather than B or W, imagine that the two possible states are 0 or 1. You have all probably heard that computers, at bottom, run on a series of 0s and 1s. What this means physically is that a particular electronic component either does or does not have electricity flowing through it. Whether or not electricity is flowing through a particular component is a function of whether or not electricity was flowing through some combination of its neighbors. Neurons can be thought of similarly. Whether a neuron is firing an action potential (1) or not (0) is a function of the activity of the neighboring neurons feeding into it. Just as 1-D and 2-D cellular automata generated unexpected and sophisticated patterns based on simple rules, so too are networks of neurons capable of unexpected and sophisticated processing, as you’ll see in the next chapter.