BASICS: "Hummingbirds.....where is the person, I ask, who, on observing this glittering fragment of the rainbow, would not pause, admire, and turn his mind with reverence..." (J. J. Audubon).
This is a blog about my summer life at the Baiting Hollow Hummingbird Sanctuary, at my winter garden, Calypso, in the Bahamas, and aspects of life in general.
This private sanctuary is now permanently closed to the general public, as a result of a lawsuit brought by a neighbor. Only my friends and personal guests may visit (

Monday, May 12, 2014

Hebbian synapses

I described in the last post how a neuron combines the signals from other neurons via connections called synapses, and sends the result, after some additional simple manipulation (analogous to "cooking") to neurons at the next level. These signals are small electrical voltages, sent over wires called "axons". When an axon reaches the vicinity of its potential target neurons, it starts to branch profusely, in 3 dimensions. These terminal branches may occupy a volume of several cubic millimeters. The target neurons also branch extensively, forming structures called dendrites. Wherever the axon branches of one neuron and the dendritic branches of another neuron happen to pass very close to each other (within a thousandth of a millimeter), a synapse can form between them. The synapse is formed as a result of a tiny fingerlike protrusion from a dendrite, called a "spine". There could be tens of thousands of target neurons within range of a given axon, though not every possible connection is permanently made - only those connections which work well survive.

The crucial issue is, which synaptic connections become permanent, and what is the strength of those synapses? This determines the special "recipe" that the neuron uses to combine the tens of thousands of possible ingredients. One possibility is that the recipe is set by a master "cook-book", which would be basically the genes of the individual to whose brain the neuron belongs. Indeed it seems likely that in many simple organisms such as worms and flies this is a major part of the process. Evolution, over millions of years, has learned what recipes work for this particular individual, regardless of personal experience, and the brain slavishly follows this standard recipe.

But the cortex seems to be much more flexible: it uses the experience of the individual rather than that of the species. This does NOT mean that each brain has an inner "genie" who records the experiences of the individual, flitting around adjusting the strengths of the trillions of individual connections. Neuroscientists believe there is no inner "genie", no "Ghost in the Machine". Indeed an individual synapse does not have access to the "experiences of the individual". What it does have access to, almost by definition, is the voltages in both the input neuron (the axon side of the synapse) and the output neuron (the dendrite side of the synapse). Typically the synapse multiplies these voltages together, and, depending on whether the result is negative, positive or close to zero, slightly decreases, increases or leaves unchanged the strength of the synapse. Remember that the current strength of the synapse determines the amount of the specific ingredient (in this case, this particular axon) contributes to the neuron's recipe.

This simple rule is known as "Hebbian learning", in honor of the canadian psychologist Donald Hebb, who first clearly proposed it. It's often summarized, rather crudely, as "Neurons that Fire Together, Wire Together".  This is the crux of the matter: thoughts are just firings of neurons, and the pattern of firings (and hence the thought) is set by the strengths of synapses, which are set in turn by the previous firings of neurons! While this might seem an absurdly trivial basis for the glories and squalors of the human mind, the fact that it's going on every thousandth of a second over one's whole lifetime, and happening at each of the quadrillion synapses (for the cognoscenti that's 10^12 X 10^15 = 10^27 or about Avogadros's number).

More to the point, it works. The reason why it works is as follows. The cortex is looking for the hidden structure in the ceaseless flow of one's experiences - this is what allows it to identify a cup as a cup. These experiences are really just vast arrays of numbers, pouring into the brain as an Amazon of data. But while these numbers almost look random, they exhibit subtle but strong structure, or "correlations".
(remember that if x and y both vary, and y tends to increase when x increases, they are positively correlated).

The Hebb rule is basically a correlation detector: it wires up 2 cells (input and output) if they fire together. In particular, since the overall output of a neuron depends (by definition) on what all the inputs are doing, then if a synapse is strengthened by the correlation between input and output, it is strengthened as a result of correlations between its various inputs. What this means is that a neuron can discover the hidden structure behind the apparently random flux of its ever-changing inputs: it can discover the meaning of the information it receives. In principle it can signal when a unique particular pattern of inputs occurs.

Well, I realize this is tough-going for the average hummingbird-lover! And there's a lot more to cover. But we got over the worst, and most important, bit: the idea of the "Hebbian Synapse".

To end up, let's me give you an analogy - a very useful and powerful one. The immense diversity and magnificence of life, ranging from the hummingbird to the tiger, and the jellyfish to the Royal Palm, is at bottom built on a very simple "trivial" rule, known as Crick-Watson base pairing. You should vaguely remember it: A goes with T and C goes with G (these are the building blocks of genes). There's now absolutely no question that the repeated application of this silly little rule over the whole earth over the last 4 billion years has generated hummingbirds, tigers, Royal Palms and us. It's much less certain that the mind is the result of the repeated application, over a lifetime and a quadrillion synapses, of the Hebb Rule. But I would bet a considerable sum (and my scientific career) that it is. And I don't find either of these conclusions depressing - indeed, as we will see, they amount to miracles.

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