Popular Science Monthly/Volume 22/April 1883/Dwarfs and Giants
A BELGIAN philosopher, M. Stas, declared, two years ago, that "no science to which measure, weight, and calculation are not applicable can be considered an exact science; it is only a mass of unconnected observations, or of simple mental conceptions." I agree to this without reserve. Undoubtedly, vain imaginations and crude theories, which have form without solidity, should be banished from science; but it does not follow that we must define science as a collection of weights and measures, and calculations upon them, or as consisting of combinations of algebraic formulas from which other formulas may be deduced. These matters of weight, measure, and calculation must have some synthesis or useful purpose in view. They should throw light upon some law, and that a law which is an idea, or which is susceptible of being converted into an idea. It is the philosophic thought penetrating them that gives interest to the statistical labors of Quetelet. The cry of the positivists of the day is for "facts!" To that I oppose another cry: "Ideas! give us ideas!" A fact without an idea is a body without a soul, a useless incumbrance to the memory. I come to the defense of speculation. While I view with impatience volumes of figures, operations, and formulas, of which the signification and bearing can not be perceived, I am inclined to be grateful to the man who throws out a new idea, though it be a thousand times false. There is always more to be learned from the thinker who talks nonsense logically than from the observer who does not reason at all. From nothing, nothing can come, but error may bring forth the truth at the price of its own death.
Laying aside these generalities, let us consider an example of the way in which we can weigh and measure, submit the results to calculation, and draw from them conclusions which are formally quite legitimate, and still be all the time on the wrong track; then examine how we may be set upon the right road, and led to a new conclusion more plausible and more in harmony with the rest of our knowledge.
It has been discovered that the flea can leap two hundred times its length. Our admiration at this is changed to astonishment when it is demonstrated by calculation that, if nature had endowed the horse with a degree of strength similarly proportioned to his weight he would have been able to clear the Rocky Mountains at a bound, and that with a like effort a whale would be able to leap to a height of two hundred leagues. What can be more unassailable than these conclusions, founded on weight, measure, and calculation?
It is true that, if, instead of comparing the weights of the horse and the flea, we had compared their heights, we should have found that the horse's leap would not measure more than three hundred metres. Why is preference given to the weight? Because it is its whole body with its three dimensions and its density that the flea hurls to two hundred times its height, and it is the same feat of strength that we demand in vain of the horse. Calculations have also been made to show that, if a man could move with a speed proportioned to that of certain insects, he would be able to travel more than ten leagues in a minute, or sixty times as fast as a railroad-train.
The Amazon ants, going to battle, travel from two to two and a half metres a minute. The Amazons of antiquity, to be even with them, if we judge by the relative heights, should have traveled eight leagues an hour. We have, however, in this case, to compare the forces with which given masses move themselves, and should take account of weights or volumes. If we proceed by this rule, we shall obtain formidable numbers, that stagger the boldest imagination. The warlike inhabitants of the banks of the Thermodon would have to get over fifty thousand leagues in an hour. Yet, who can deny the truth of the observations, the rigor of the measurements, or the justice of the reasoning?
The authors of these interesting calculations have not had in mind only to make known some figures of comparison, good to store up, even if they are never used, but they have endeavored to set forth the idea that certain insects are much better endowed with powers of leaping and speed than the vertebrates, and especially than man. The persons who express this conclusion have failed to conform to the precept that they must not extract more from their facts than is rigorously contained in them, and are the victims of a scientific illusion, which is quite wide-spread, but not hard to dissipate. What is in question? It is the valuation of the labor necessary to raise a certain weight to a certain height. The labor increases in proportion to the weight and the height. When, then, two animals of different masses leap to the same absolute height, each one performs a work precisely proportional to its mass; and, when a man leaps over an obstacle sixty centimetres from the ground, he accomplishes, other conditions being the same, a task as considerable again as that of the flea or the grasshopper, which can not spring much above thirty centimetres.
A few figures will make the matter plain. Take a grasshopper weighing six decigrammes (nine grains), and a man weighing sixty kilogrammes (one hundred and fifty pounds). The man is equivalent in weight to a hundred thousand grasshoppers. But a hundred thousand grasshoppers grouped into a single mass could only raise that mass thirty centimetres, while the man can lift his own mass sixty centimetres. All the advantage, then, is on the side of the man. Here is a wide variance from the strength which has been exacted of the horse to make him a rival of the flea.
The basis of the comparison was vicious. The height or volume of the agent who handles a weight has nothing to do with the estimation of the labor. A sack of meal is no heavier on the shoulders of a man than on the loins of a horse. The labor and the effort have been confounded. The labor is a defined and absolute quantity; the effort a vague and variable sensation.
The deductions respecting speed have no better foundation. The ant, as a moving body, is a little mass of matter on which a determined force impresses a speed of two and a half metres a minute. To impress the same speed on a mass of fifteen millions of ants—which I take to represent the volume of a man—would require a force fifteen millions greater. This force is developed by a man going two and a half metres a minute, while in the same space of time he can easily accomplish a hundred metres and more. In this case, then, if we take notice of any one of the data, the man manifests a strength forty times greater in proportion than that of the ant. This is a very different result from the one arrived at by the other method. Other data, however, com in to complicate the comparison and considerably modify the result.
A little closer study of the phenomena of walking will show us that it absorbs a considerable quantity of force that does not appear in speed. It is not simply a uniform transportation of the body along an horizontal line; but at each step the body is raised, and falls again. The incessant repetition of the lifting is a great cause of fatigue. Hence, walking on an uneven road tires us greatly. In the best paths, the differences of level which have to be overcome correspond with a notable quantity of force lost from speed. The ant, however, being a creeping thing, and supported on six feet, has to raise only a very small part of its weight at each step, and is therefore more advantageously formed than the man, who, having only two feet, gives to his whole body a double oscillation—sidewise, and up and down. On the other hand, the ant feels even the slightest inequalities of the ground. When it goes over the space that represents a man's step, and requires only a single lifting of his body, it has to lift its own perhaps a thousand times. The sum of all these little lifts would probably give us a considerable one.
The conclusion we have just reached, that man is relatively forty times stronger than the ant, deserves, then, a closer examination; and it may be that the just interpretation of our facts will cause us to believe that the energetic capacity of muscular fibers is nearly uniform in all animals.
There is another illusion in these matters, which we might call psychological. The agility of some animals surprises us. The monad in a drop of water moves so nimbly that we can hardly follow it; and we naturally make a comparison between the distance which an animal can cover in a certain time and its dimensions. The reasoning of this comparison presents a problem somewhat difficult of solution. It is enough to know that we can not draw from the illusion the consequences which we like to see in it.
If I were to attempt an explanation of this agility, which gives small animals so great facility in escaping their enemies, I should look for it in the small momentum of their mass when in flight, by reason of which only a slight effort is required to enable them to change their direction. Incontestably, we can run much faster than mice; nevertheless, it is not easy to catch a mouse in a closed room. Our own mass is an impediment to our agility. By the time we have made a spring in one direction, the mouse has changed his, and we put our hand, too late, where he was. It is very hard even to lay hold of a bird in a narrow cage.
The part of our question that remains to be treated is no less arduous or obscure than that which we have gone over. I will try to throw what light is possible upon it, but I can not flatter myself that I shall fully succeed. M. Plateau some seventeen years ago measured, with the aid of ingenious harnessings and other devices, the muscular force of insects. He deduced from his experiments that, aside from the power of flight, insects have, as compared with vertebrates, an enormous strength in proportion to their weight; and that in the same group of insects the strength varies, as between different species, inversely as the weight, or, in other words, that the smallest insects are the strongest.
Some of his single results were really surprising. While a horse weighing six hundred kilogrammes can hardly support four hundred kilogrammes, or two thirds of his weight, he found May-bugs, weighing a sixth of a gramme, able to support sixty-six times their own weight, or more than ten grammes. Here, then, was a humble and stupid beetle a hundred times as strong in proportion as the proud and sturdy horse. Another little insect, weighing half a decigramme could move a hundred times its weight. By this standard we men ought to be able to struggle with weights of six thousand kilogrammes (or fifteen thousand pounds), and elephants should move mountains. We can not dispute the accuracy of the experiments or the calculations, nor impeach the sincerity or judgment of the experimenter. The facts are, moreover, conformable to observations. A caterpillar in the closed hand will make prodigious efforts to open his prison; and who has not seen ants carrying things three or four times as large as themselves? Various attempts have been made to escape the consequences that were deduced from these experiments, but they still stand, apparently defying criticism. Must we, then, resign ourselves to being a hundred or two hundred times weaker than a beetle? Are insects really, in physical force, kings of creation?
Not yet. An important element has been neglected. No account has been made yet of the time it takes the insect to perform its wonderful feat. Whenever we raise a given weight to any height, by whatever method, the labor performed is in proportion to the weight multiplied by the height; and this product always gives the measure of that labor. The same product, under certain restrictions, furnishes the measure of the force that is utilized in the work. A dog is not as strong as a horse, but both animals expend precisely the same force in raising a kilogramme a metre. Whatever the kind of work he may wish to calculate, even though it be horizontal, it is always reducible to the elevation of a certain weight to a certain height, and is in practice measured by a formula of which these are the terms.
While, however, the quantity of force that must be expended for a determined work is invariable, this is not the case with the manner in which that expenditure may be distributed. If I wish to strike a single strong blow, I execute a quick movement. If my muscular power is weak, I must have more time. It is possible, then, for time to supply a deficiency of power. I can make such a substitution applicable in two ways, by dividing the resistance, or by using a machine as a lever, which, when everything about it is considered, is nothing more or less than a device by means of which we replace power with time.
Accurately to compare the strength of a May-bug with that of a man, we must take into the account the time which the insect requires to perform the work exacted of it. Suppose a horse harnessed to a load of half his weight, and a May-bug drawing a tray fifty times as heavy as itself: the beetle's load will be relatively a hundred times as heavy as the horse's. But if the horse needs only a second to raise his load a metre, while the insect takes a hundred times as Ions; to produce the same effect, then the efforts of which they are both capable are proportionably the same. The case is the same, only the appearance is changed, when the force is spent in maintaining the weight at an equilibrium.
In a similar manner we may account for the power manifested by the insect which I cover with a board a hundred times as heavy as itself, and which gets its head under the edge, raises it, and escapes. You know that, if we should put a horse under a bell weighing sixty thousand kilogrammes, it could not make its cover move at all. That is because the animal can not insinuate itself under the edge of the bell, and is not formed to raise weights with its head. But fix a lever under the edge so that the horse can work conveniently at its longer arm, and require him to raise the weight, not to a proportionate, but to an equal height with that to which the insect raised his board in the same time, and he would not fail to achieve the task.
The interest of the problem before us does not lie singly in learning why insects are capable of efforts which appear enormous as compared with their size. The important thing is to discover whether Nature, as has been said, has regarded them more favorably than it has the vertebrates and man, and has endued them prodigally with muscular force, while it has been parsimonious to the other animals. We need not believe anything of this kind. The prodigies of force that astonish us are due to a very simple cause, and can be accounted for under the common law that, of two muscles having the same mass and the same energy, the shorter one is capable of raising the more considerable weight. We may figure muscular fiber as a spiral spring, habitually relaxed, which, under nervous action, flies back upon itself. Suppose this fiber to be a decimetre long and capable of contracting to half its length, and that it has attached to it a weight, say, of a centigramme. Under the nervous action, it will raise this weight half its length, or five centimetres. Now, if we replace this single fiber, a decimetre long, by a muscular bundle weighing just as much but composed of ten fibers a centimetre long, we can attach a centigramme weight to each of these fibers, or ten centigrammes to the whole bundle; but the weight will be raised, under the contraction of the muscle, only five millimetres instead of five centimetres. What we have gained in power we have lost in extent of motion. That is the rule. We have hence a right to conclude, that short muscles have the peculiarity, as compared with long muscles of the same volume, that they act more slowly but can move more considerable masses. Consequently, small animals perform, absolutely, slower motions, but, in compensation they can move proportionately heavier masses. We can thus comprehend how our insect can move masses a hundred times heavier than itself, without having to infer that it is a hundred times stronger than a horse. Introducing its head and corselet under the obstacle it desires to remove, it stretches its six legs, raises its body, and develops an apparently surprising force. Really, it has lifted the obstacle only in the slightest degree, but enough to allow it to escape. Its strength has been furnished by the short and thick muscles of its six legs and its neck. These considerations furnish the key to all the Herculean labors performed by small animals. The smaller the animal, the more capable it is of great efforts; only it loses in speed what it develops in force. Hence the strongest insects are generally the slowest.
Let us finish our argument with an imaginary illustration embodying the principles and the consequences derived from them. An adventurous explorer, visiting the countries in which Gulliver traveled, brings back a Lilliputian and a Brobdingnagian. The giant is thirty feet high, the dwarf four inches. Since one is about a hundred times as large as the other, their respective masses, and consequently the masses of their muscles, must be in the proportion of a million to one. If a common man weighs sixty kilogrammes, or 150 pounds, the Brobdingnagian should weigh 15,000 kilogrammes, or about 38,000 pounds, and the Lilliputian only fifteen grammes. They agree to compete with each other in the gymnasium. At the pulleys, the Brobdingnagian can easily raise a weight of 10,000 kilogrammes, or 2,500 pounds, as high as his shoulders. Looking to the Lilliputian, we would at first sight not expect him to be able to raise more than ten grammes to his shoulders. Pie really proves able to lift a hundred times as much, or one kilogramme, or the equivalent of seventy-five times his weight. This is because the distance to his shoulders is a hundred times less than the distance to his rival's shoulders, and he is able to apply against the weight the advantage which he derives from the relative shortness of the distance.
They next try leaping at the bar. The Lilliputian gracefully clears the pole at a metre from the ground. Will the Brobdingnagian be able to make a bound of a hundred metres? Not at all. He can hardly clear the bar at five or six metres. This is not because he is lacking in suppleness. Compare his mass with that of his little rival, consider that he has raised the center of gravity of that mass to the height of about a metre as the other has done with that of his inferior mass, and it will not be hard to do justice to his agility.
They are next started on a foot-race. A course of a thousand metres is laid out. The Brobdingnagian runs it in five minutes by steps of four metres each per second. The Lilliputian's steps are only four centimetres each, but he makes a hundred of them in a second; so he likewise goes over the track in five minutes. You give all praise to the Lilliputian, but do an injustice to his competitor. Think of what the giant has to do to move his legs! They are a million times as heavy as the Lilliputian's. But while he may have a million fibers, or a thousand in the diameter of a transverse section, the Lilliputian will have ten fibers in the corresponding diameter, or a thousand in all. Thus, while the masses are in the proportion of a million to one, the proportion as to the motive fibers is a million to a hundred. The Lilliputian, then, has the advantage. It may be objected that a hundred steps can hardly be made in a second. The objection is, however, only specious, for the wings of insects show us what is possible in this matter.
We are authorized by the aid of these illustrations to draw the important conclusion that the minute world is not, and can not be, in all respects a proportional reduction of a larger world. There is an impossibility in the matter which I can only indicate, but which depends on the constitution of time and space.
If the views I have expressed are true, we have a right to infer that all animals as to their energy stand upon the same line, or, in other words, that a muscular fiber possesses the same properties, whether it belong to a vertebrate, an articulate, or a mollusk. Such a conclusion is more satisfactory at the first view than those which I have criticised, for our mind is fond of discovering unity and uniformity in nature. I am not certain that it is exact. That can be determined only by experiments. The question is now put into the hands of investigators who are endowed with the genius for patient and minute researches. Let them attack it with their instruments of observation and precision. The arguments they will deduce will be those before which we shall be forced to bow.
The main object of my remarks has been, however, to plead the cause, which in these days has been somewhat compromised, of Speculation, the mother of ideas, which allures us more frequently than it instructs us, but which stimulates, guides, and pushes us forward, and sometimes gives us a glimpse, if it does not permit us to contemplate them, of brilliant and grand horizons.
- From an address before the Royal Academy of Belgium. Translated for "The Popular Science Monthly."