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*> From: "Willoughby Sarah" <SEW295@psy.soton.ac.uk>
*

*> Date: Wed, 1 May 1996 14:53:47 GMT
*

*> Could you please explain what an algorithm is?
*

An algorithm is a mechanical procedure that you can follow in order to

achieve a result. The example I gave in class was the formula for finding

the roots of quadratic equations (remember? "-b +/- the square

root of b squared minus 4ac all over 2a"?).

The important point is that the procedure is mechanical: You don't need

to think about it; you don't have to know what it means. You just have

to DO it; and if you do it faithfully, you will always get the right

result.

Algorithms are always formal, that is, symbolic. Symbols are just

arbitrary-shaped objects, for example, marks on paper or on a computer

screeen (like "b" or "-" or "square root"). The algorithm is just a set

of rules for manipulating those symbols, based only on their shapes, not

on what they mean. But the manipulation will give you a correct solution

to some problem. In the case of factoring quadratic equations, the

problem is finding the roots of equations -- which you may need in

order to do, say, some surveying work or some weather forecasting

(I'm just inventing what you might apply the equation to): Maybe the

way to calculate tomorrow's temperature is by finding the roots of a

quadratic equation. You apply the formula to, say, measurements of

barometric pressure and humidity, and you calculate tomorrow's

temperature.

Sharon's example of an algorithm happened to be a baking recipe,

but it's the same kind of thing: "put the sugar and butter into a bowl,

beat in the eggs, fold in the flour." Those are just words, symbols.

But if you follow them and apply them to sugar, butter, etc., they will

mechanically generate a cake.

The important thing to remember about algorithms is that (1) they are

mechanical, mindless. You can follow them without knowing what you're

doing or what the symbols mean. So a machine could perform them too.

(2) Algorithms are abstract, formal, symbolic: That means that the

physical shape of their symbols doesn't matter; it's arbitrary. I could

have said "sucre" instead of sugar, or I could even have called sugar

"X." Sharon's recipe is a trivial algorithm, but it's still an algorithm.

You could still get it wrong by not following it faithfully (for example

if you first beat the eggs and then put in the sugar and butter).

The reason algorithms are important to explaining the mind is that

anything that can be done by mechanically following an algorithm no

longer requires a homunculus: It's done mindlessly, so it is a potential

explanation of the mind. Supposing you do something, say, look at a

painting and recognise that it was painted by Michelangelo. Someone asks

you how you did it. You say: "I know that only Michelangelo uses

curved brushstrokes like that." So I ask "How did you know the strokes

were curved, and that only M. uses them?" The questions go on and on,

and as long as you reply by saying what you saw, recognised, or knew,

you have not explained HOW you saw, recognised, knew. You keep using

the mind to explain the mind. That's the homunculus problem: the little

man in your mind that's acting as your mind's mind: We need an

explanation of the mind that does not rely on yet another mind.

Now suppose someone comes up with an algorithm, a recipe that, whenever

it gets the "shadow" of a Michalengelo painting can immediately compute

that it was by Michelangelo. That's a potential explanation of how YOU

did it, and it is immune to the homunulus problem because an algorithm

works mindlessly, mechanically. You don't need to ask "how did the

algorithm know" it was Michelangelo: The algorithm didn't know

anything, it just came up with the right solution by a mechanical

procedure that works.

That's an algorithm. And algorithms are computations: mechanical

symbol manipulations, based on rules that don't "know" anything, they

simply operate on the (arbitrary) shapes of symbols: They don't care

whether they operate on real butter, or on the symbol "butter." They

don't care if you physically put something in a bowl, or you merely do it

symbolically, in a computer simulation or a virtual world. They don't

care because they are mindless and mechanical. Yet, remarkably, just

about anything that can be done at all, can be done by some algorithm or

other: There are algorithms for solving equations, forecasting the

weather, baking cakes, but also for building cars and planes, maybe

eventually even for building robots.

Now inside a car's engine, even though it can be DESCRIBED as just

following an algorithm, we know there is something else going on too,

because a real car actually moves, whereas a computer simulated car

doesn't go anywhere. Yet they are both following the same algorithms.

That means that a car engine is not just a computer, computing. It

matters what its parts are made out of and what they're shaped like and

connected to. The shapes are not arbitrary. So a car is an analog

device, not a computer; what it's made out of matters to whether or not

it really moves; it's not enough that it should just be performing the

right algorithm.

But what about us? Obviously a robot, like a car, has to move, so to

that extent, it too is not just a computer, computing the right

algorithm. But what about when it's not moving? What about when it's

just "thinking"? Could THAT be just the execution of the right

algorithm?

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