100 Essential Things You Didn't Know You Didn't Know (25 page)

Should we feel safe if robots were created in large numbers with these four laws programmed into their electronic brains? I think not. It’s all a question of timing. The precedence of the Zeroth Law over the First means that the robot may kill you because you are driving a gas guzzling car or not recycling all your plastic bottles. It judges that your behaviour, if it continues, threatens humanity. It might become very concerned about its duty to act against some of the world’s political leaders as well. Asking robots to act for the good of humanity is a dangerous request. It seeks something that is not defined. There is no unique answer to the question ‘What is the good of humanity?’ No computer could exist that prints out a list of all actions that are good for humanity and all actions that are harmful to it. No programme can tell us all good and all evil.

You might feel safer without the Zeroth Law than with it. Still, there is another worrying consideration that could put you at risk from all the harmful direct actions that the First, Second and Third Laws were conceived to protect us from. Advanced robots will have complicated thoughts, thoughts about themselves and us as well as about inanimate objects: they will have a psychology. Just as with humans, this may make them hard to understand – but it may also lead them to suffer from some of the psychological problems that humans can fall victim to. Just as it is not unknown for humans to be deluded into thinking they are robots, it may be that a robot could think it was a human. In that situation it could do what it likes because it no longer believes that the Four Laws of Robotics apply to it. Closely linked to this problem would be the evolution of religious or mystical beliefs in the robot mind. What then of the Third Law? What robotic existence is it that must be preserved? The material fabric of the robot? The soul in the machine that it perceives itself to have? Or, the ‘idea’ of the robot that lives on in the mind of its maker?

You can carry on asking questions like this for yourself, but you can see that it is not so easy to trammel the consequences of artificial intelligence by imposing constraints and rules on its programming. When that ‘something’ that we call ‘consciousness’ appears, its consequences are unpredictable, with enormous potential for good or evil, and it is hard to have one without the other – a bit like real life really.

79

Thinking Outside the Box

Many people would rather die than think; in fact, most do.

Bertrand Russell

It is easy to get trapped into thinking about a problem in one set way. Breaking out and being ‘imaginative’ or original in solving a problem can require a different way of thinking about it rather than just a correct implementation of principles already learned. Simple problems that involve the application of fixed rules in a faultless way can usually be conquered by the second approach. For example, if someone challenges you to a game of noughts and crosses you should never lose, regardless of whether you move first or second. There is a strategy whose worst outcome is a draw, but it will give you a win only if your opponent deviates from that optimal strategy. Alas, not all problems are as easy as finding the best move in noughts and crosses. Here is an example of a simple problem whose solution will almost certainly take you by surprise.

Write down a 3×3 square of nine dots. Now pick up your pencil and
without lifting the pencil point from the paper or retracing your path
, draw four straight lines that pass through all the dots.

Here’s one failed attempt. It misses out one of the points in the middle on the left-hand edge:

Here’s another. It’s also one point short because it doesn’t go through the central point:

It looks impossible doesn’t it. I can do it with four straight lines only if I retrace the pencil path, going down the diagonal and then going back and forth along the intersecting lines. But that requires the drawing of far more than four lines, even though only four appear to be present when you have finished:

There
is
a way to draw four lines through all the points without lifting the pencil or retracing its path, but it requires breaking a rule that you imposed on yourself for no reason at all. It wasn’t one of the restrictions imposed at the outset. You were just so used to playing by a certain type of rule that you didn’t think to step outside the box and break it. The solution that you want simply requires that you draw straight lines that (literally) extend beyond the box of nine points before they turn back in a different direction.

Think outside the box!

80

Googling in the Caribbean – The Power of the Matrix

Cricket is organised loafing.

William Temple

Most sports create league tables to see who is the best team after all the participants play each other. How the scores are assigned for wins, losses and draws can be crucial for determining who comes out on top. Some years ago, football leagues decided to give three points for a win rather than two, in the hope that it would encourage more attacking play. A team would get far more credit for winning than for playing out a draw – in which each team earns only one point. But somehow this simple system seems to be rather crude. After all, should you not get more credit for beating a top team than one down at the bottom of the league?

The 2007 Cricket World Cup in the Caribbean gives a nice example. In the second phase of the competition, the top eight teams played each other (actually each had played one of the others already in the first stage, and that result was carried forward so they only had to play six more games). They were given two points for a win, one for a tie and zero for a defeat. The top four teams in the table went on to qualify for the two semi-final knockout games. In the event of teams being level on points they were separated by their overall run-scoring rate. Here is the table:

But, let’s think about another way of determining the team rankings that gives more credit for beating a good team than a bad one. We give each team a score that is equal to sum of the scores of the teams that they beat. Since there were no tied games we don’t have to worry about them. The overall scores look like a list of eight equations:

A = SL + N +SA + E +W +B + I

SL = N + W + E + B + I

N = W+ E + B + I + SA

SA = W + E + SL + I

E = W + B + I

W = B + I

B = SA

I = B

This list can be expressed as a matrix equation for the list
x
= (A, N, W, E, B, SL, I, SA) with the form
A
x
= K
x
, where K is a constant and A is an 8×8 matrix of 0’s and 1’s denoting defeats and wins, respectively, and is given by:

In order to solve the equations and find the total scores of each team, and hence their league ranking under this different point-scoring system, we have to find the eigenvector of the matrix A with all its entries positive or zero. Each of these solutions will require K to take a specific value. This corresponds to a solution for the list x in which all have positive (or zero – if they lost every game) scores, as is obviously required for the situation being described here. Solving the matrix for this, so-called ‘first-rank’ eigenvector, we find that it is given by