When you have to do with a question of this type, the first thing to
ask yourself what is meant by one thing being better (or bigger, or cleverer,
or prettier, or ...) than another. You see, when you speak of say, one
piece of a fine thread being longer or heavier than another piece, everything
is simple. You either weigh the thing or stretch and measure the length, and
the bigger the number you get, the longer (or heavier or hotter...) the thing
is that you are measuring.
We say that such measurements are SCALARS. One number is all you
need, and there is not much doubt about what it is that you are measuring.
But there are other things that cannot usefully be described with a
single number; where numbers come into the matter, you need several numbers.
Suppose I want to measure the prettiness of girls (a disgusting idea if you ask
me; some things are better not measured, something the Miss World people just
don’t understand. And the same applies to dog breeders and judges at Crufts and
their opposite numbers at the Supreme Cat Show.) then I could measure their
height, and their “vital statistics” and the colour of their hair and eyes and...
whatever they measure. And I get a LOT of
numbers. We say that I get a VECTOR. If they measure say, twenty numbers, we
say that it is a twenty-dimensional vector. If the score for hair is the third number
in one girl’s vector, then hair score must be the third number in every girl’s
vector.
Right?
Now, if you have not yet studied vectors at school, then you
probably soon will, but it is important to understand that there really is a
way to measure the “size” of a vector. It is not even a very complicated
business to do so (leaving out ideas such as the scaling and weighting of
values). This gives you a single number whose size in fact amounts to a scalar.
And as you have seen, we CAN compare scalars!
These are real and important subjects, and very interesting, and I
hope you get on to them and understand them and enjoy them when you do, or
alternatively, that you already have and did and did.
The trouble is that to replace those vectors with those scalars for
the purposes of comparison means that you have lost something. For instance, if
the third and fourth numbers in the beauty contest vectors were for hair and
eyes, and one girl got a three and a
four, whereas another got a four and a three, their vectors would have the same
size (for that part of the vector anyway).
BUT THE TWO GIRLS WOULD LOOK DIFFERENT!
One’s eyes would look better and the other’s hair would look better
(if you happened to agree with the judges of course). It would be as if one
could measure beauty by adding components of beauty, as you could measure
weight by adding components of weight. (allowing for the fact that adding
vectors is not quite the same as adding scalars like weight).
And could you? Of course you could. People do it all the time,
usually rather badly.
The catch is that the results are not very useful unless you know
what it is that you really are trying to establish. It works pretty well if a
navigator wants to know how far currents and fuel will take his boat or plane,
but not if you want to know whether one camera is better than another, or than the
human eye. Professional photographers with experience say that the best camera
is...
The camera you have with you...
You can't have much success with any other camera!
Which camera do you have with you all the time?
Apart from your eye, do you want a camera with a good resolution?
Well, does that mean you are using a digital camera or a film? Do you want
automatic adjustment? None rivals the eye. Do you want versatility? I can show
you umpteen cameras that do the most fantastic things, but they could not rival
the versatility of the eye. How about the range of contrast that the eye can
manage?
Sure the eye’s receptor is small, and its area of highest acuity is
smaller. Yes, just as one girl’s hair beat the other girl’s. But what are you
comparing? As long as there are things one can do with the eye that you cannot
do with an SLR or vice versa, one can argue that the eye (or the SLR) is better.
But if you cannot say why you are right and no one else’s opinion matters, then
you demonstrate that you don’t understand the difference between comparing
vectors and comparing scalars.
In comparing cameras one would have to talk about not just the field
of focus, or its depth, or its resolution, or its contrast, or its weight, or
cost, or size, or speed, or memory etc etc, but about which is the better optic
recording and interpreting system.
And for every system you could mention, some would be better for
something, and some other for other things. And that goes for eyes and SLRs
too.
Your other question is very important and thoughtful.
“...if anything really was better than the human eye, how on earth
would we be able to tell that it is better?”
Well, to begin with, there is the problem of comparing vectors at
all. But that is not really what you wanted to know.
When Galileo Galilei told people that through his telescope he could
see moons around Jupiter, some disbelieved him. He offered to let them see for themselves.
What do you suppose they said?
Some of them refused to look. (You will find all sorts of arguments
about this, but Galileo did explicitly mention the refusal in a letter to
Kepler (I think it was) for one.) Some people pointed out that there was some
merit to their refusal because there was at the time a caution against
believing what you could only see, whereas even in those days a lot of optical
illusions were known.
But back to your question. What one can do is to compare things
under a lot of conditions. Suppose I said that my camera was better than your
eyes because it could show smaller objects. First I could photograph a lot of
objects at a lot of different magnifications. Some would be big, some smaller,
and so on down to really invisibly small objects. By measuring how much the camera enlarged the
large objects, and the smaller ones, checking each example with my eyes, I
could work out how the camera magnifies things. From that I could predict how
small an object it could make visible for me. If my prediction works, then I
have given at least one kind of evidence that in that respect the camera is
better.
And this principle we can follow in many such matters. Start with
things that we can check directly, then use those to check the things that we
can only check indirectly.
At one time I had to do some work based on such principles, and good
fun it was too!
Again,
Tell me if I have not dealt with what it was that you wanted to
know.
Go well, Jon
