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Authors: Shimon Edelman
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BOOK: The Happiness of Pursuit: What Neuroscience Can Teach Us About the Good Life
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Concerning Computation
Given that the computer metaphor for the brain looks like it has the embarrassing (for a metaphor) quality of being literally true, we must make sure that we understand what computation is, if we ever want to be able to fully understand brains. Luckily, understanding the basic nature of computation does not require a degree in computer science. Contrary to what one is inclined to believe, most instances of computation in the universe happen without involving any kind of particularly complex, contrived, or specially engineered device. Computation is all around us; in fact, it is as common as anything can be, for the following simple reason: every physical process that unfolds over time computes something.
Think about it. How would a pebble that you release from your grasp be able to strike the ground precisely at the correct instant if it could not figure out—compute—its trajectory, given the acceleration of gravity and its initial position? How would a stove-top heating element be able to reach precisely the correct temperature if it could not figure out the current that flows through it, given the grid’s voltage and its own resistance? In a very concrete sense, a falling pebble computes its trajectory by following Newton’s laws, just as a heating element computes the current that flows through it by following Ohm’s law.
There is of course nothing mysterious about objects obeying the laws of physics: on the contrary, it would be a mystery (in other words, a sign of a subtler law at work) if they did not, or if exceptions or exemptions were possible. This situation seems to be not to everyone’s liking: riding a ski chairlift one winter day, I saw on a pylon an ad that began: GRAVITY: IT’S MORE OF A NUISANCE THAN A LAW—a bizarre notion, given that not just skiing but actually getting down at all from the mountain and seeing your loved ones ever again (rather than flying off screaming into space) would be impossible, were it not for gravity. Like it or not, the implacability of the laws of physics is what makes the world go round, so to speak, and in doing so carry out a vast panoply of computations.
Most of these computations are very limited in the spatial and temporal reach of their effects. Such is the fate of the computation performed by the pebble that I release and let fall to the ground. The law-abiding pebble faithfully computes its own trajectory and manages to arrive at its resting place at a precisely timed moment, yet this computation is pretty inconsequential: a few grains of sand may be kicked around, but once they settle the only readily discernible change in the state of affairs of the universe is that the pebble, which was previously in my hand, is now on the ground. Who cares?
That particular computation was useless, but it could have been otherwise, if only the fall of the pebble were to have some significant and enduring consequences or repercussions on other events. Here is how this could happen. Imagine that you are defending a castle. Your assigned post is immediately above the portcullis, and your duty is to drop an anvil onto the head of any attacker who comes too close to it. Your store of ammunition is limited (the besiegers just intercepted an inbound shipment of blacksmith supplies), and so you would like to time the release of each anvil so that it arrives at a certain small volume of space simultaneously with the head of the intended target. This can be easily arranged through practice with some pebbles. All you need to do is mark the position of the knight who is charging at the gate as you release the pebble; if the pebble then strikes the charging knight’s helmet (you’ll hear it), you can be reasonably sure that the next time a knight’s charge takes him through the marked position you may drop the actual anvil instead of the practice pebble.
You may be surprised to realize that what I just described happens to be a computer- controlled ballistic missile launch system. The missile is, of course, the anvil, which is ballistic by definition, because it has no onboard means of propulsion. And what about the launch-control computer? Since you are in charge of releasing and observing the pebble, you are one of its parts. Another part is the earth, whose gravity field so conveniently imparts an equal acceleration to anvils and to pebbles (as Galileo famously discovered four hundred years ago). Yet another part is the pebble that you use to simulate the anvil’s projected descent. Unlike the listless, lonely pebble from the earlier example, about whose fall nobody cares, this one is lovingly tracked and the computation it carries out (just by being itself and acting naturally) is made use of. Its use lies in serving as a stand-in for or a
representation
of the anvil: the actual fall of the pebble, as it unfolds over time, represents the potential descent of the anvil.
representation
of the anvil: the actual fall of the pebble, as it unfolds over time, represents the potential descent of the anvil.
Because the fall of the pebble is precisely analogous to the fall of the anvil that it represents (their trajectories unfold at exactly the same rate), the anvil-aiming computer of which the pebble is part is an
analog
computer. The familiar
digital
computers differ from analog ones in one key respect: they deal in representations that are made to correspond to their objects through some arbitrary but consistent rules rather than through direct physical analogy. A good example of a digital representation is the code agreed upon in April 1775 by Paul Revere and Robert Newman, the sexton of the Old North Church in Boston, for representing the mode of the expected British assault: one if by land, two if by sea.
analog
computer. The familiar
digital
computers differ from analog ones in one key respect: they deal in representations that are made to correspond to their objects through some arbitrary but consistent rules rather than through direct physical analogy. A good example of a digital representation is the code agreed upon in April 1775 by Paul Revere and Robert Newman, the sexton of the Old North Church in Boston, for representing the mode of the expected British assault: one if by land, two if by sea.
There is nothing inherent in assault by land that dictates that it should be represented by one lantern in the belfry as opposed to two. It is in this sense that the Revere-Newman code is symbolic and arbitrary. Switching to a more modern example, consider how my notebook’s battery meter represents the remaining charge. If I have worked for an hour since the last full charge and the meter now shows “75%,” I conclude that the battery will last for three more hours. The connection between the symbols “75%” and what I take them to represent is entirely a matter of convention; the same information could have been equally well represented by the symbols “3/4.” Alternatively, I can switch the battery meter from the digital representation mode to analog, in which case it would look like a little “thermometer” whose mercury is three-quarters of the way up to the maximum mark.
What is common to all these examples of representation is that some
physical symbol
—an object, event, or process—stands in for some other object, event, or process for the benefit of a third party. Thus, some squiggles on my notebook screen represent for me the battery level; the appearance of a lantern in a belfry conveys to Paul Revere a piece of battle intelligence; the fall of a pebble tells the castle defender how the fall of an anvil would proceed. Understanding representation gives us a crucially important conceptual handle on computation. The key insight is this: useful computation hinges on the possibility of some objects or processes representing others. Indeed, the reliance on representations is the defining characteristic of useful computation, which distinguishes it from computation that merely happens as the world goes on.
No Cognition Without Representationphysical symbol
—an object, event, or process—stands in for some other object, event, or process for the benefit of a third party. Thus, some squiggles on my notebook screen represent for me the battery level; the appearance of a lantern in a belfry conveys to Paul Revere a piece of battle intelligence; the fall of a pebble tells the castle defender how the fall of an anvil would proceed. Understanding representation gives us a crucially important conceptual handle on computation. The key insight is this: useful computation hinges on the possibility of some objects or processes representing others. Indeed, the reliance on representations is the defining characteristic of useful computation, which distinguishes it from computation that merely happens as the world goes on.
Against the constant, pervasive background hum of the universe relentlessly computing its next state given its past history, the relationship of representation—two computations that always co-occur in a particular order or unfold over time in lockstep with one another—stands out as a great rarity. Merely drawing a parallel between some carefully chosen aspects of two events is not at all difficult, especially if it is numerical or otherwise abstract; finding a repeated co-occurrence or a parallel that persists over time is.
As I ponder this point, I observe nine ducks landing on a pond and am struck by the thought that their number is exactly the same as the number of months I have left until the date on which I promised to deliver this book to the publisher. What am I to make of this observation? It is this kind of coincidence, invariably noted in retrospect, that inspires popular tales of successful auguries, such as the one found in the second book of
The Iliad
. The Greeks, weather-bound at Aulis on their way to Troy, witness an omen: a snake devours a mother sparrow and its eight chicks in their nest, then turns into stone. They are told by Calchas, their chief soothsayer, that the omen means that the coming war with Troy will not be resolved until the tenth year. It is worth noting that this story betrays perfect hindsight on Homer’s part: the prophesied tenth year happens to be the very year during which the main events of
The Iliad
are set.
3
The Iliad
. The Greeks, weather-bound at Aulis on their way to Troy, witness an omen: a snake devours a mother sparrow and its eight chicks in their nest, then turns into stone. They are told by Calchas, their chief soothsayer, that the omen means that the coming war with Troy will not be resolved until the tenth year. It is worth noting that this story betrays perfect hindsight on Homer’s part: the prophesied tenth year happens to be the very year during which the main events of
The Iliad
are set.
3
The strange decision to count together the sparrows and the newly petrified snake to reach the number ten would have ruined the career of a lesser augur than Calchas (who did not seem to have had any problem convincing the Greeks at Aulis that King Agamemnon’s daughter had to be sacrificed to Artemis to break the spell of bad weather). Scholars believe that the sparrow omen story confounded Aristotle, who was otherwise a great admirer of
The Iliad
.
4
Ever since, educated people’s readiness to take such omens at face value has been steadily on the wane. Indeed, some people viewed numerological divination with great suspicion already in biblical times, as suggested by the injunction found in Leviticus: “Nor shall ye employ auguries, nor divine by inspection of birds.” One likes to think that the Old Testament lawgivers sought to protect the people from superstitiously perceiving false patterns in noise (rather than merely to protect their own monopoly on foretelling).
The Iliad
.
4
Ever since, educated people’s readiness to take such omens at face value has been steadily on the wane. Indeed, some people viewed numerological divination with great suspicion already in biblical times, as suggested by the injunction found in Leviticus: “Nor shall ye employ auguries, nor divine by inspection of birds.” One likes to think that the Old Testament lawgivers sought to protect the people from superstitiously perceiving false patterns in noise (rather than merely to protect their own monopoly on foretelling).
The more complex a set of observations, the more likely it is to give rise to ghost “patterns,” or correlations that arise by chance—an apparent signal in a sea of random noise. Skepticism toward such correlations is the only reasonable default stance in science, and it can only be assuaged through the application of science’s single most powerful ghost-busting tool: statistical analysis of data. Patterns that withstand statistical scrutiny are still suspect: they need to be
explained
, that is, integrated into a wider framework or theory that makes sense of as much data as possible, in the simplest possible terms. This is how observations (themselves usually guided by informed guesses or hypotheses) get distilled into laws of nature.
explained
, that is, integrated into a wider framework or theory that makes sense of as much data as possible, in the simplest possible terms. This is how observations (themselves usually guided by informed guesses or hypotheses) get distilled into laws of nature.
Now that we are armed with the scientific method, let us return to the problem of telling apart reliable from unreliable representations—that is, true co-occurrences between events from chance ones. The first hypothesis to be let go is the one stating that a bunch of objects represents another bunch of different objects simply because their number is the same. As if to prove this point, my nine ducks on a pond are joined by another; I rush home and open my mail to see if the deadline for my manuscript has receded by a month, only to find out that, alas, it is still only nine months away. Apparently, the number of ducks on that particular pond does not, after all, represent the time frame of my contract with the publisher. More generally, attaching wide-ranging representational significance to patterns of bird flocking is empirically unwarranted, as one can quickly learn by observing the efficacy of the hypothesized representations over time.
It would be even better if we could tell ahead of time, from first principles, whether or not one thing—object, event, process—is going to be representative of another. Thanks to the understanding of the natural world that has already been gained by science, it is possible to do so. What is it then that singles out valid instances of representation? There is just one principle that can ensure the validity of a representation:
causation
, as it is embodied in the various laws of nature.
5
The fall of a pebble and the fall of an anvil are caused and governed instant by instant by the same universal law—the law that Newton is said to have discovered when he intuited that the motion of the celestial bodies is not any different from the motion of terrestrial ones. Because of that common causality, falling pebbles are representative of falling anvils (and apples and penguins, but not ducks). We may think of the relation between processes that all obey the same mathematical equation as representation by causally justified analogy.
causation
, as it is embodied in the various laws of nature.
5
The fall of a pebble and the fall of an anvil are caused and governed instant by instant by the same universal law—the law that Newton is said to have discovered when he intuited that the motion of the celestial bodies is not any different from the motion of terrestrial ones. Because of that common causality, falling pebbles are representative of falling anvils (and apples and penguins, but not ducks). We may think of the relation between processes that all obey the same mathematical equation as representation by causally justified analogy.
There is another way in which causality can give rise to a valid representational relation: one event may simply cause the other. This is how the lighting of a lantern in the belfry of a church on the eve of the Battle of Lexington and Concord represented the redcoats’ advance (through the mediation of one Robert Newman). Representation that is underwritten by causality in this direct manner is much more versatile than causal analogy: whereas falling objects representative of each other must all resemble each other in certain respects (heft, flightlessness), smoke represents fire by virtue of being caused by it, not by resembling it. Moreover, it does not matter how far from the represented event the causal chain leads before it reaches the representing event, as long as the chain is reliable; thus, a blaring fire alarm represents fire even if it is activated by smoke.
The principle of representation of one event by another through a causal chain whose reliability is guaranteed by the laws of nature is extremely powerful. Once it is discovered by evolution
6
and unleashed into the biosphere, it becomes a force that can change the face of the planet. Whereas computation as such permeates the very fabric of the universe, only those rare physical systems that harbor representations of their environment are capable of sustaining
cognitive
computation, whose distinctive feature is that it is about something other than itself. In a typical cognitive system, the representing processes are separated from the represented ones by being safely ensconced inside a contraption that keeps the rest of the world at bay while sensing its surroundings, computing a course of action, and carrying it out, all at the same time. The most familiar naturally occurring contraption of that kind is an embodied brain.
6
and unleashed into the biosphere, it becomes a force that can change the face of the planet. Whereas computation as such permeates the very fabric of the universe, only those rare physical systems that harbor representations of their environment are capable of sustaining
cognitive
computation, whose distinctive feature is that it is about something other than itself. In a typical cognitive system, the representing processes are separated from the represented ones by being safely ensconced inside a contraption that keeps the rest of the world at bay while sensing its surroundings, computing a course of action, and carrying it out, all at the same time. The most familiar naturally occurring contraption of that kind is an embodied brain.
BOOK: The Happiness of Pursuit: What Neuroscience Can Teach Us About the Good Life
4.21Mb size Format: txt, pdf, ePub
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