This is not precisely what you are asking for, since the number one
hundred is not mentioned, but I found a lecture by James Willis which
contains an interesting discussion of the human mind's difficulty in
comprehending large numbers.
The entire lecture may be found here:
http://www.sparks.co.uk/progress/fulton.html
An excerpt:
"In his novel Watership Down, Richard Adams created a picture of what
the world might seem like to a colony of rabbits.
Apart from the necessary artistic licence of allowing the rabbits to
speak, he adhered faithfully to what is known, and what can be
guessed, about the way rabbits think. In doing so he created a book
which can be read in a number of different ways. It is an exciting
adventure. It is an excellent Natural History text and it is a
celebration of the beauty of the North Hampshire countryside. But most
of all, for me, it was a powerful insight into our own thinking. The
point that I want to pick out from Watership Down is the idea, appar-
ently supported by some experimental evidence, that rabbits are unable
to count beyond the number four.
Rabbits can count up to four. Any number above four is Hrair - 'a lot'
or 'a thousand'.
There were probably more than five rabbits in the litter when Fiver
was born, but his name, Hrairoo, means 'Little thousand', i.e. the
little one of a lot or, as they say of pigs, 'the runt'.
-Richard Adams Watership Down
This is the thing which is so fascinating to imagine. When Hazel (the
hero of the story) and his friends thought of a number between one and
four, they had a clear idea what it represented, but any number larger
than that merged into a vague concept called Hrair which meant
something like "a lot". Now while we can only make educated guesses at
the thought processes of rabbits, we can be certain from our own
experience that there are limits to the size of numbers that we
ourselves can understand. Thus, for every one of us there is a limit
above which numbers mean little more than "a lot"; perhaps the number
is "a thousand million"; perhaps it is much less.
Let's think about the way we understand numbers for a moment. Often,
we compare a figure with something we can picture; sometimes we count
on our fingers; sometimes we imagine patterns of dots. Perhaps we
recall the memory of a school which we know contained 1,500 people, or
of a football crowd of 30,000.
However good we are at doing this (and some are better than others)
na- ture contains numbers large enough to defeat us all. To take a
grand example, we are unable to begin to comprehend the numbers of
stars in the universe. There is no problem about working out the
figure; by a convenient chance (I suppose) there are about the same
number of stars in an average sized galaxy as there are of galaxies in
the universe. It also happens to be about the number of neurones in
the human brain. It's rather an easy number to remember - one hundred
thousand million (1011) of each. All you have to do to obtain the
answer to the number of stars in the universe is to multiply the two
together 1011 X 1011 = 1022 - Easy!
One with twenty two noughts - not exact of course - but roughly right.
Now what kind of words shall we use to describe such a number - to
enable us to understand it and to communicate that understanding? Is
it a BIG number? Is it an ENORMOUSLY big number? ("Enormous" sounds as
if it means "a bigger number than normal" and it is certainly that!).
Perhaps it would help if we used a calculator to work out an
illustration. For example - as blood contains five million red cells
per cubic millimetre I calculate that it would take a cube of blood
1.5 kilometres on a side - 2.25 cubic kilometres of blood - to contain
as many red cells as there are stars in the universe. NOW do we
understand?.
Well... actually... no we don't!
Another Adams, Douglas Adams, appreciated the fundamental problem here
in his classic radio play , The Hitch Hikers Guide to the Galaxy:
"Space," it says, "is big. Really big. You just won't believe how
vastly, hugely, mindbogglingly big it is. I mean, you may think it's a
long way down the road to the chemist, but that's just peanuts to
space. Listen..." and so on.
The point that I am making is that, above a certain size of number, we
are as vague in our understanding as are the rabbits in Watership
Down. The difference is not in the nature of the mental processes
involved but in the order of magnitude of numbers at which the
transition occurs.
External appearances
With my pocket computer, of course, there is no such problem. It can
store 500,000 characters in its internal memory (about ten lectures
like this) and one million characters in each of its two memory cards
(fifty of these lectures). I know that because I paid for that much
and it says its capacity on the outside. I could have paid more,
incidentally, and had two million characters internal memory and four
million in each memory card - making nearly five hundred of these
lectures.
These are big numbers and you could be forgiven for not guessing them
from external appearances, or indeed by entering facts into the
machine and then recalling them one at a time.
With human minds, of course, it is even more difficult. They don't
have their capacity written on the outside, and there is no equivalent
of pressing a few keys and getting the answer that this lecture
contains 55,575 characters. So, even it they actually contained
amounts of information which we could only call astronomical if we
could count it up, we simply wouldn't have any way of knowing it. All
we would get would be occasional glimpses. We might find ourselves,
for example, saying in astonishment from time to time, "Good gracious,
what a small world it is" even when we knew, in a very definite,
physical sense that the opposite was true and it is actually an
inconceivably big world." |
