by Isaac Asimov
But let us be practical. Is there really danger of replacement?
In the first place, we must ask whether intelligence is a one-dimensional variant, or whether there may not be qualitatively different kinds of intelligence, even very many different kinds. If dolphins have intelligence similar to ours, for instance, it seems nevertheless to be of so different a nature from our own that we have not yet succeeded in establishing communication across the species line. Computers may, in the end, differ from us qualitatively also. It would certainly not be surprising if that were so.
After all, the human brain, built of nucleic acid and protein against a watery background, has been the product of the development of three and a half billion years of biological evolution, based on the random effects of mutation, natural selection, and other influences, and driven forward by the necessity of survival.
The computer, on the other hand, built of electronic switches and electric current against a semiconductor background, has been the product of the development of forty years of human design, based on the careful foresight and ingenuity of human beings, and driven forward by the necessity of serving its human users.
When two intelligences are so different in structure, history, development, and purpose, it would certainly not be surprising if their intelligences were widely different in nature as well.
From the very start, for instance, computers were capable of solving complex problems involving arithmetical operations upon numbers, of doing so with far greater speed than any human being could, and with far less chance of error. If arithmetical skill is the measure of intelligence, then computers have been more intelligent than human beings all along.
But it may be that arithmetical skill and other similar talents are not at all what the human brain is primarily designed for—that such things, not being our metier, we naturally do very poorly.
It may be that the measure of human intelligence involves such subtle qualities as insight, intuition, fantasy, imagination, creativity—the ability to view a problem as a whole and guess the answer by the “feel” of the situation. If that is so, then human beings are very intelligent, and computers are very unintelligent indeed. Nor can we see right now how this deficiency in computers can be easily remedied, since human beings cannot program a computer to be intuitive or creative for the very good reason that we do not know what we ourselves do when we exercise these qualities.
Might we someday learn how to program computers into a display of human intelligence of this sort?
Conceivably; but in that case we might choose not do so out of a natural reluctance to be replaced. Besides, what would be the point of duplicating human intelligence—of building a computer that might glow with a faint humanity—when we can so easily form the real thing by ordinary biological processes? It would be much like training human beings from infancy to perform “mathematical marvels” similar to those a computer can do. Why, when the cheapest calculating device will do it for us?
It would surely pay us to continue to develop two intelligences that were differently specialized, so that different functions could be performed with the highest efficiency. We might even imagine numerous classes of computers with different types of intelligence. And, by the use of genetic engineering methods (and the help of computers), we might even develop varieties of human brains displaying different species of human intelligences.
With intelligences of different species and genera, there is the possibility at least of a symbiotic relationship, in which all will cooperate to learn how best to understand the laws of nature and how most benignly we might cooperate with them. Certainly, the cooperation will do better than any intelligence variety on its own.
Viewed in this fashion, the robot/computer will not replace us but will serve us as our friend and ally in the march toward the glorious future—if we do not destroy ourselves before the march can begin.
Appendix
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Mathematics in Science
Gravitation
As I explained in chapter 1, Galileo initiated science in its modern sense by introducing the concept of reasoning back from observation and experiment to basic principles. In doing so, he also introduced the essential technique of measuring natural phenomena accurately and abandoned the practice of merely describing them in general terms. In short, he turned from the qualitative description of the universe by the Greek thinkers to a quantitative description.
Although science depends so much on mathematical relationships and manipulations, and could not exist in the Galilean sense without it, I have nevertheless written this book non mathematically, and have done so deliberately. Mathematics, after all, is a highly specialized tool. To have discussed the developments in science in mathematical terms would have required a prohibitive amount of space, as well as a sophisticated knowledge of mathematics on the part of the reader. But in this appendix, I would like to present an example or two of the way in which simple mathematics has been fruitfully applied to science. How better to begin than with Galileo himself?
THE FIRST LAW OF MOTION
Galileo (like Leonardo da Vinci nearly a century earlier) suspected that falling objects steadily increase their velocity as they fall. He set out to measure exactly by how much and in what manner the velocity increases.
The measurement was anything but easy for Galileo, with the tools he had at his disposal in 1600. To measure a velocity requires the measurement of time. We speak of velocities of 60 miles an hour, of 13 feet a second. But there were no clocks in Galileo’s time that could do more than strike the hour at approximately equal intervals.
Galileo resorted to a crude water clock. He let water trickle slowly from a small spout, assuming, hopefully, that it dripped at a constant rate. This water he caught in a cup; and, by the weight of water caught during the interval in which an event took place, Galileo measured the elapsed time. (He also used his pulse beat for the purpose on occasion.)
One difficulty was, however, that a falling object dropped so rapidly that Galileo could not collect enough water, in the interval of falling, to weigh accurately. What he did, then, was to dilute the pull of gravity by having a brass ball roll down a groove in an inclined plane. The more nearly horizontal the plane, the more slowly the ball moved. Thus Galileo was able to study falling bodies in whatever degree of slow motion he pleased.
Galileo found that a ball rolling on a perfectly horizontal plane moves at constant speed. (This supposes a lack of friction, a condition that could be assumed within the limits of Galileo’s crude measurements.) Now a body moving on a horizontal track is moving at right angles to the force of gravity. Under such conditions, the body’s velocity is not affected by gravity either way. A ball resting on a horizontal plane remains at rest, as anyone can observe. A ball set to moving on a horizontal plane moves at a constant velocity, as Galileo observed.
Mathematically, then, it can be stated that the velocity v of a body, in the absence of any external force, is constant k, or:
v = k.
If k is equal to any number other than zero, the ball is moving at constant velocity. If k is equal to zero, the ball is at rest; thus, rest is a “special case” of constant velocity.
Nearly a century later, when Newton systemized the discoveries of Galileo in connection with falling bodies, this finding became the First Law of Motion (also called the principle of inertia). This law can be stated: Every body persists in a state of rest or of uniform motion in a straight line unless compelled by external force to change that state.
When a ball rolls down an inclined plane, however, it is under the continuous pull of gravity. Its velocity then, Galileo found, is not constant but increases with time. Galileo’s measurements showed that the velocity increases in proportion to the lapse of time t.
In other words, when a body is under the action of constant external force, its velocity, starting at rest, can be expressed as:
v = kt.
What is the value of k?
That, it was easy to find by experiment, depends on the slope of the inclined plane. The more nearly vertical the plane, the more quickly the rolling ball gains velocity and the higher the value of k. The maximum gain in speed comes when the plane is vertical—in other words, when the ball drops freely under the undiluted pull of gravity. The symbol g (for “gravity”) is used where the undiluted force of gravity is acting, so that the velocity of a ball in free fall, starting from rest, was:
v = gt.
Let us consider the inclined plane in more detail. In the diagram:
the length of the inclined plane is AB, while its height at the upper end is AC. The ratio of AC to AB is the sine of the angle x, usually abbreviated as “sin x.”
The value of this ratio—that is, of sin x—can be obtained approximately by constructing triangles with particular angles and actually measuring the height and length involved. Or it can be calculated by mathematical techniques to any degree of precision, and the results can be embodied in a table.
By using such a table, we can find, for instance, that sin 10° is approximately equal to 0.17365, that sin 45° is approximately equal to 0.70711, and so on.
There are two important special cases. Suppose that the “inclined” plane is precisely horizontal. Angle x is then zero, and as the height of the inclined plane is zero, the ratio of its height to its length is also zero. In other words, sin 0° = 0. When the “inclined” plane is precisely vertical, the angle it forms with the ground is a right angle, or 90°. Its height is then exactly equal to its length, so that the ratio of one to the other is just 1. Consequently, sin 90° = 1.
Now let us return to the equation showing that the velocity of a ball rolling down an inclined plane is proportional to time:
v = kt.
It can be shown by experiment that the value of k changes with the sine of the angle so that:
k = k' sin x
(where k' is used to indicate a constant that is different from k).
(As a matter of fact, the role of the sine in connection with the inclined plane was worked out somewhat before Galileo’s time by Simon Stevinus, who also performed the famous experiment of dropping different masses from a height—an experiment traditionally, but wrongly, ascribed to Galileo. Still, if Galileo was not the very first to experiment and measure, he was the first to impress the scientific world, indelibly, with the necessity to experiment and measure, and that is glory enough.)
In the case of a completely vertical inclined plane, sin x becomes sin 90°, which is 1, so that in free fall
k = k'.
It follows that k' is the value of k in free fall under the undiluted pull of gravity, which we have already agreed to symbolize as g. We can substitute g for k' and, for any inclined plane:
k = g sin x.
The equation for the velocity of a body rolling down an inclined plane is, therefore:
v = (g sin x) t.
On a horizontal plane with sin x =0°, the equation for velocity becomes:
v = 0.
This is another way of saying that a ball on a horizontal plane, starting from rest, will remain motionless regardless of the passage of time. An object at rest tends to remain at rest, and so on. That is part of the First Law of Motion, and it follows from the inclined plane equation of velocity.
Suppose that a ball does not start from rest but has an initial motion before it begins to fall. Suppose, in other words, you have a ball moving along a horizontal plane at 5 feet per second, and it suddenly finds itself at the upper end of an inclined plane and starts rolling downward.
Experiment shows that its velocity thereafter is 5 feet per second greater, at every moment, than it would have been if it had started rolling down the plane from rest. In other words, the equation for the motion of a ball down an inclined plane can be expressed more completely as follows:
v = (g sin x) t + V
where V is the original starting velocity. If an object starts at rest, then V is equal to 0 and the equation becomes as we had it before:
v = (g sin x) t.
If we next consider an object with some initial velocity on a horizontal plane, so that angle x is 0°, the equation becomes:
v = (g sin 0°) + V
or, since sin 0° is 0:
v = V.
Thus the velocity of such an object remains its initial velocity, regardless of the lapse of time. That is the rest of the First Law of Motion, again derived from observed motion on an inclined plane.
The rate at which velocity changes is called acceleration. If, for instance, the velocity (in feet per second) of a ball rolling down an inclined plane is, at the end of successive seconds, 4, 8, 12, 16… then the acceleration is 4 feet per second per second.
In a free fall, if we use the equation:
v = gt,
each second of fall brings an increase in velocity of g feet per second. Therefore, g represents the acceleration due to gravity.
The value of g can be determined from inclined-plane experiments. By transposing the inclined-plane equation, we get:
g = v / (t sin x).
Since v, t, and x can all be measured, g can be calculated, and it turns out to be equal to 32 feet per second per second at the earth’s surface. In free fall under normal gravity at earth’s surface, then, the velocity of fall is related to time thus:
v = 32t.
This is the solution to Galileo’s original problem—namely, determining the rate of fall of a falling body and the manner in which that rate changes.
The next question is: How far does a body fall in a given time? From the equation relating the velocity to time, it is possible to relate distance to time by the process in calculus called integration. It is not necessary to go into that, however, because the equation can be worked out by experiment; and, in essence, Galileo did this.
He found that a ball rolling down an inclined plane covers a distance proportional to the square of the time. In other words, doubling the time increases the distance fourfold; tripling it increases the distance ninefold; and so on.
For a freely falling body, the equation relating distance d and time is:
d = ½gt2
or, since g is equal to 32:
d = 16t2.
Next, suppose that instead of dropping from rest, an object is thrown horizontally from a position high in the air. Its motion would then be a compound of two motions—a horizontal one and a vertical one.
The horizontal motion, involving no force other than the single original impulse (if we disregard wind, air resistance, and so on), is one of constant velocity, in accordance with the First Law of Motion, and the distance the object covers horizontally is proportional to the time elapsed. The vertical motion, however, covers a distance, as I have just explained, that is proportional to the square of the time elapsed. Prior to Galileo, it had been vaguely believed that a projectile such as a cannon ball travels in a straight line until the impulse that drives it is somehow exhausted, after which it falls straight down. Galileo, however, made the great advance of combining the two motions.
The combination of these two motions (proportional to time horizontally, and proportional to the square of the time vertically) produces a curve called a parabola. If a body is thrown, not horizontally, but upward or downward, the curve of motion is still a parabola.
Such curves of motion, or trajectories, apply, of course, to a projectile such as a cannon ball. The mathematical analysis of trajectories, stemming from Galileo’s work, made it possible to calculate where a cannon ball would fall when fired with a given propulsive force and a given angle of elevation of the cannon. Although people had been throwing objects for fun, to get food, to attack, and to defend, for uncounted thousands of years, it was only due to Galileo that for the first time, thanks to experiment and measurement, there was a science of ballistics. As it happened, then, the very first achievement of modern experimental science proved to have a direct and immediate military application.
It also had a
n important application in theory. The mathematical analysis of combinations of more than one motion answered several objections to the Copernican theory. It showed that an object thrown upward will not be left behind by the moving earth, since the object will have two motions: one imparted to it by the impulse of throwing, and one that it shares along with the moving earth. This analysis also made it reasonable to expect the earth to have two motions at once: rotation about its axis and revolution about the sun—a situation that some of the non-Copernicans insisted was unthinkable.
THE SECOND AND THIRD LAWS
Isaac Newton extended the Galilean concepts of motion to the heavens and showed that the same set of laws of motion apply to the heavens and the earth alike.
He began by considering that the moon might be falling toward the earth in response to the earth’s gravity but never struck the earth’s surface because of the horizontal component of its motion. A projectile fired horizontally, as I said, follows a parabolically curved path downward to intersection with the earth’s surface. But the earth’s surface curves downward, too, since the earth is a sphere. A projectile given a sufficiently rapid horizontal motion might curve downward no faster than the earth’s surface and would therefore eternally circle the earth.
Now the moon’s elliptical motion around the earth can be split into horizontal and vertical components. The vertical component is such that, in the space of a second, the moon falls a trifle more than 1/20 inch toward the earth. In that time, it also moves about 3,300 feet in the horizontal direction, just far enough to compensate for the fall and carry it around the earth’s curvature.
The question was whether this 1/20-inch fall of the moon is caused by the same gravitational attraction that causes an apple, falling from a tree, to drop 16 feet in the first second of its fall.