gistfile1.txt

NEWTON is riding his bicycle in Lincolnshire when he comes across
SOCRATES on the road.

SOCRATES: For what purpose do you return to Woolsthorpe my dear sir?
NEWTON: Cambridge has been closed due to the plague.
SOCRATES: By Zeus! Closed?
NEWTON: Indeed.
SOCRATES: And so what are you doing with your time here? Surely not
farming.
NEWTON: Good heavens! No. I am developing many insights into the
problem of planetary motion.
SOCRATES: I have heard that your knowledge of the mathematics of motion
is greater than that of any other man. For this reason, I am eager to
become your pupil. Tell me, by the god of friendship, will you share
your knowledge with me?
NEWTON: I can teach you many things of which the majority has no
knowledge.
SOCRATES: Is it true that the speed of something is simply the
distance it travels divided by the time it takes to travel that distance?
NEWTON: Yes, that is so. For if I travel fifty yards on this
bicycle in ten seconds then my speed is five yards per second.
SOCRATES: So every second, you travel five yards.
NEWTON: Yes, indeed.
SOCRATES: And in two seconds, you travel ten yards.
NEWTON: Of course.
SOCRATES: Is it not possible that one second you might travel four
yards and then next second you might travel six yards?
NEWTON: I suppose that is possible.
SOCRATES: So in two seconds, you have travelled ten yards. From what
you have taught me so far, that is a speed of five yards per
second.
NEWTON: You understood what I said very well, Socrates.
SOCRATES: That is because I am so desirous of your wisdom, and I
concentrate my mind on it, so that no word of yours may fall to the
ground. But tell me, would you not say that if you travel four yards
in one second then your speed is four yards per second?
NEWTON: Yes.
SOCRATES: But how can that be seeing as you agreed that if you
travelled four yards in one second and six in the next that your speed
must be five yards per second. So we must investigate again from the
beginning what speed is, as I shall not willingly give up before I
learn this. Would it be true to say that the *average* speed was five
yards per second, even though in any given second, the distance
travelled may be more or less than five?
NEWTON: That seems to be so.
SOCRATES: By the gods, so how do we ever find the actual speed at any instant
and not just the average?
NEWTON: I do not understand what you mean.
SOCRATES: We have already seen that if you travel ten yards in two
seconds it does not mean you were always travelling five yards per
second as it is possible that in the first second you travelled four
yards and then in the next second you travelled six.
NEWTON: I think, Socrates, that you could say the your speed for the
first second was four yards per second.
SOCRATES: But this again is only average speed. Is it not possible
that part of that second you were travelling slower than four yards
per second and part of the time you were travelling faster?
NEWTON: I see now what are you saying. In the first half-second I
might travel one-and-a-half yards (that is, a speed of three yards per
second) and in the second half-second I might travel two-and-a-half
yards (that is, a speed of five yards per second).
SOCRATES: But, my dear friend. Even these are just averages. And if
you measure half the time again, it will still only be an average for
that time.
NEWTON: I'm afraid so. I could keep halving the time for which I
measure the distance and it would still only be an average.
SOCRATES: I came to you seeking wisdom, great Newton, but you have
taught me nothing!