The title of an article from the author, J.B.S. Haldane's first collection,
Possible Worlds. This will be a
cut-and-paste writeup, altered for e2 by your humble hard-linker. My reasons for this are as follows:
- This explaination of the physics and developmental biology behind the size of an organism was published back in 1927 and is thus in the public domain.
- It is a very well written and relevant populist science essay which is as pertinant today as when it was written. Yes, it is long - stick with it. It's an easy read and I guarantee you'll learn something. If you don't, /msg me.
So, in it's entirety -
On Being the Right Size
The
most obvious differences between different animals are differences of size, but for some reason the zoologists have paid singularly little attention to them. In a large textbook of zoology before me I find no indication that the eagle is larger than the sparrow, or the hippopotamus bigger than the hare, though some
grudging admissions are made in the case of the mouse and the whale. But yet it
is easy to show that a hare could not be as large as a hippopotamus, or a whale
as small as a herring. For every type of animal there is a most convenient size,
and a large change in size inevitably carries with it a change of form.
Let us
take the most obvious of possible cases, and consider a giant man sixty feet
high - about the height of Giant Pope and Giant Pagan in the illustrated
Pilgrim's Progress of my childhood. These monsters were not only ten times as
high as Christian, but ten times as wide and ten times as thick, so that their
total weight was a thousand times his, or about eighty to ninety tons.
Unfortunately the cross sections of their bones were only a hundred times those
of Christian, so that every square inch of giant bone had to support ten times
the weight borne by a square inch of human bone. As the human thigh-bone breaks
under about ten times the human weight, Pope and Pagan would have broken their
thighs every time they took a step. This was doubtless why they were sitting
down in the picture I remember. But it lessens one's respect for Christian and
Jack the Giant Killer.
To
turn to zoology, suppose that a gazelle, a graceful little creature with long
thin legs, is to become large, it will break its bones unless it does one of two
things. It may make its legs short and thick, like the rhinoceros, so that every
pound of weight has still about the same area of bone to support it. Or it can
compress its body and stretch out its these two beasts because they happen to
belong to the same order as the gazelle, and both are quite successful
mechanically, being remarkably fast runners.
Gravity,
a mere nuisance to Christian, was a terror to Pope, Pagan, and Despair. To the
mouse and any smaller animal it presents practically no dangers. You can drop a
mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a
slight shock and walks away, provided that the ground is fairly soft. A rat is
killed, a man is broken, a horse splashes. For the resistance presented to
movement by the air is proportional to the surface of the moving object. Divide
an animal's length, breadth, and height each by ten; its weight is reduced to
a thousandth, but its surface only to a hundredth. So the resistance to falling
in the case of the small animal is relatively ten times greater than the driving
force.
An
insect, therefore, is not afraid of gravity; it can fall without danger, and can
cling to the ceiling with remarkably little trouble. It can go in for elegant
and fantastic forms of support like that of the daddy-longlegs. But there is a
force which is as formidable to an insect as gravitation to a mammal. This is
surface tension. A man coming out of a bath carries with him a film of water of
about one-fiftieth of an inch in thickness. This weighs roughly a pound. A wet
mouse has to carry about its own weight of water. A wet fly has to lift many
times its own weight and, as everyone knows, a fly once wetted by water or any
other liquid is in a very serious position indeed. An insect going for a drink
is in as great danger as a man leaning out over a precipice in search of food.
If it once falls into the grip of the surface tension of the water - that is to
say, gets wet - it is likely to remain so until it drowns. A few insects, such
as water-beetles, contrive to be unwettable; the majority keep well away from
their drink by means of a long proboscis.
Of
course tall land animals have other difficulties. They have to pump their blood
to greater heights than a man, and, therefore, require a larger blood pressure
and tougher blood vessels. A great many men die from burst arteries, greater for
an elephant or a giraffe. But animals of all kinds find difficulties in size for
the following reason. A typical small animal, say a microscopic worm or rotifer,
has a smooth skin through which all the oxygen it requires can soak in, a
straight gut with sufficient surface to absorb its food, and a single kidney.
Increase its dimensions tenfold in every direction, and its weight is increased
a thousand times, so that if it is to use its muscles as efficiently as its
miniature counterpart, it will need a thousand times as much food and oxygen per
day and will excrete a thousand times as much of waste products.
Now if
its shape is unaltered its surface will be increased only a hundredfold, and ten
times as much oxygen must enter per minute through each square millimetre of
skin, ten times as much food through each square millimetre of intestine. When a
limit is reached to their absorptive powers their surface has to be increased by
some special device. For example, a part of the skin may be drawn out into tufts
to make gills or pushed in to make lungs, thus increasing the oxygen-absorbing
surface in proportion to the animal's bulk. A man, for example, has a hundred
square yards of lung. Similarly, the gut, instead of being smooth and straight,
becomes coiled and develops a velvety surface, and other organs increase in
complication. The higher animals are not larger than the lower because they are
more complicated. They are more complicated because they are larger. Just the
same is true of plants. The simplest plants, such as the green algae growing in
stagnant water or on the bark of trees, are mere round cells. The higher plants
increase their surface by putting out leaves and roots. Comparative anatomy is
largely the story of the struggle to increase surface in proportion to volume.
Some of the methods of increasing the surface are useful up to a point, but not
capable of a very wide adaptation. For example, while vertebrates carry the
oxygen from the gills or lungs all over the body in the blood, insects take air
directly to every part of their body by tiny blind tubes called tracheae which
open to the surface at many different points. Now, although by their breathing
movements they can renew the air in the outer part of the tracheal system, the
oxygen has to penetrate the finer branches by means of diffusion. Gases can
diffuse easily through very small distances, not many times larger than the
average length traveled by a gas molecule between collisions with other
molecules. But when such vast journeys - from the point of view of a
molecule - as a quarter of an inch have to be made, the process becomes slow. So
the portions of an insect's body more than a quarter of an inch from the air
would always be short of oxygen. In consequence hardly any insects are much more
than half an inch thick. Land crabs are built on the same general plan as
insects, but are much clumsier. Yet like ourselves they carry oxygen around in
their blood, and are therefore able to grow far larger than any insects. If the
insects had hit on a plan for driving air through their tissues instead of
letting it soak in, they might well have become as large as lobsters, though
other considerations would have prevented them from becoming as large as man.
Exactly
the same difficulties attach to flying. It is an elementary principle of
aeronautics that the minimum speed needed to keep an aeroplane of a given shape
in the air varies as the square root of its length. If its linear dimensions are
increased four times, it must fly twice as fast. Now the power needed for the
minimum speed increases more rapidly than the weight of the machine. So the
larger aeroplane, which weighs sixty-four times as much as the smaller, needs
one hundred and twenty-eight times its horsepower to keep up. Applying the same
principle to the birds, we find that the limit to their size is soon reached. An
angel whose muscles developed no more power weight for weight than those of an
eagle or a pigeon would require a breast projecting for about four feet to house
the muscles engaged in working its wings, while to economize in weight, its legs
would have to be reduced to mere stilts. Actually a large bird such as an eagle
or kite does not keep in the air mainly by moving its wings. It is generally to
be seen soaring, that is to say balanced on a rising column of air. And even
soaring becomes more and more difficult with increasing size. Were this not the
case eagles might be as large as tigers and as formidable to man as hostile
aeroplanes.
But it
is time that we pass to some of the advantages of size. One of the most obvious
is that it enables one to keep warm. All warmblooded animals at rest lose the
same amount of heat from a unit area of skin, for which purpose they need a
food-supply proportional to their surface and not to their weight. Five thousand
mice weigh as much as a man. Their combined surface and food or oxygen
consumption are about seventeen times a man's. In fact a mouse eats about one
quarter its own weight of food every day, which is mainly used in keeping it
warm. For the same reason small animals cannot live in cold countries. In the
arctic regions there are no reptiles or amphibians, and no small mammals. The
smallest mammal in Spitzbergen is the fox. The small birds fly away in winter,
while the insects die, though their eggs can survive six months or more of
frost. The most successful mammals are bears, seals, and walruses.
Similarly,
the eye is a rather inefficient organ until it reaches a large size. The back of
the human eye on which an image of the outside world is thrown, and which
corresponds to the film of a camera, is composed of a mosaic of 'rods and
cones' whose diameter is little more than a length of an average light wave.
Each eye has about a half a million, and for two objects to be distinguishable
their images must fall on separate rods or cones. It is obvious that with fewer
but larger rods and cones we should see less distinctly. If they were twice as
broad two points would have to be twice as far apart before we could distinguish
them at a given distance. But if their size were diminished and their number
increased we should see no better. For it is impossible to form a definite image
smaller than a wave-length of light. Hence a mouse's eye is not a small-scale
model of a human eye. Its rods and cones are not much smaller than ours, and
therefore there are far fewer of them. A mouse could not distinguish one human
face from another six feet away. In order that they should be of any use at all
the eyes of small animals have to be much larger in proportion to their bodies
than our own. Large animals on the other hand only require relatively small
eyes, and those of the whale and elephant are little larger than our own. For
rather more recondite reasons the same general principle holds true of the
brain. If we compare the brain-weights of a set of very similar animals such as
the cat, cheetah, leopard, and tiger, we find that as we quadruple the
body-weight the brain-weight is only doubled. The larger animal with
proportionately larger bones can economize on brain, eyes, and certain other
organs.
Such
are a very few of the considerations which show that for every type of animal
there is an optimum size. Yet although Galileo demonstrated the contrary more
than three hundred years ago, people still believe that if a flea were as large
as a man it could jump a thousand feet into the air. As a matter of fact the
height to which an animal can jump is more nearly independent of its size than
proportional to it. A flea can jump about two feet, a man about five. To jump a
given height, if we neglect the resistance of air, requires an expenditure of
energy proportional to the jumper's weight. But if the jumping muscles form a
constant fraction of the animal's body, the energy developed per ounce of
muscle is independent of the size, provided it can be developed quickly enough
in the small animal. As a matter of fact an insect's muscles, although they
can contract more quickly than our own, appear to be less efficient; as
otherwise a flea or grasshopper could rise six feet into the air.