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TINY GIANTS
What are the proportions which will merit your esteem?â1 By thus questioning those who despise insects, the French historian Jules Michelet emphasizes how, by the standards of common sense, people characterize insects first of all by their physical smallness. Measurement nuances the first impression without contradicting it. A field guide instructs that insects range from âunder 1/4 mm to about 30 cm long and from 1/2 mm to about 30 cm across the wings.â2 An Australian phasmid, whose thin body and filiform legs span nearly thirty centimeters, and moths with similar wingspans are exceptions.3 If we stick to European fauna, the maximum width reached, that of the deathâs-head hawkmoth, is 12 centimeters, and the length of the stag beetle (Lucanus cervus) does not exceed 5 centimeters.4 So, when reflecting upon insects, it is impossible to escape the point that the largest insects are ten times smaller than we areâand these are extreme and rare cases.
THE FAMILIAR YET COMPLEX CONCEPT OF SIZE
Size, which plays a decisive role here, demonstrates some astounding characteristics. These become evident when we compare size with two other spatial determinations: position and form.5 In the absence of some special type of intervention, changing the position of a solid object does not necessarily change the object: my pencil remains the same whether I hold it vertically or lay it down horizontally on the table. On the other hand, when I modify the form of an object I transform it, whether that form refers to its external profile or to its internal structure. Size is more related to the object than position is, but less than shape is. This means it is possible to consider an object as being the same as another that is smaller or larger. This difference in size combined with an equivalent form is found in elementary geometry, where rational beings group together similar triangles and other homothetic figures. It can also be found in tales and myths that our imagination fills with dwarfs and giants. Contemporary literature has not abandoned this approach. The surrealist poet Robert Desnos writes about âan ant thatâs eighteen meters long.â It amuses people as it âpulls along and tows / Penguins and ducks in a carriage load,â speaking Latin, French, and Javanese. Smurfs, which were created in Belgium to appeal to a family audience, are little blue elves whose houses are the size of a large mushroom.6 American cinema has made accidental gigantism of insects the premise for several fantasy films. For example, in Gordon Douglasâs 1954 movie Them!, authorities call on the expertise of an entomologist to fight giant ants. The title itself expresses how a change in size is enough to make the so-called familiar insect strange and threatening.
Use of the imagination does not necessarily imply the presence of narrative elements. In a fragment of Blaise Pascalâs PensĂ©es, the philosopher wants us to feel that we are suspended between two infinities. After showing the earth as lost in the universe, he focuses our attention on a mite. Through this tiny animalâtoday mites are classified as arachnids and not as insects7âwe are invited to consider âinfinites,â and, in these, animals, including mites, âin which he [we] will find again all that the first had.â And Pascal marvels that âour body, which a little while ago was imperceptible in the universe, itself imperceptible in the bosom of the whole, is now a colossus, a world, or rather a whole, in respect of the nothingness which we cannot reach.â8 If for a moment we forget the extreme terms of whole and nothingness to focus on progressive reduction, we are struck by the purely fictitious nature of these tiny animals that contain worlds inhabited by replicas of those very animals. Mites, which inhabit flours and cheeses and are considered by the French LittrĂ© dictionary to be the smallest animal visible to the naked eye, seem to exist at any scale in Pascalâs writing.9
Change in size with invariance in form can be found a century later in Gulliverâs Travels. Jonathan Swiftâs hero travels to several countries, the first of which, Lilliput, is populated by tiny beings, and the second, Brobdingnag, by giants. Mathematicians who serve the king of Lilliput rate Gulliverâs size as twelve times their own. They very rightly deduce that his body has a volume 1,728 times greater than their own and that it is therefore necessary to provide him with food and drink in proportion.10 Swift does not give such a precise number for giants, but he tells us that when his hero is placed on a table he is thirty feet from the ground. Knowing that our tables have an average height of two and a half feet, we can deduce that the giants are twelve times larger than we are.11 Gulliver is to the giants what the Lilliputians are to him, which is to say that his size is the geometric mean of the size of the giants and that of the Lilliputians.
Twenty-six years later, other giants appear, with satirical intention, in Voltaireâs philosophical novella MicromĂ©gas.12 The inhabitant of Sirius is eight leagues high. The companion said that the giant met on Saturn is only six thousand feet tall. Their form and behavior are similar to ours; only their lifespan, which is linked to the size of their stars, is commensurate with their gigantism. In the first chapter we learn that at the end of his childhood, or around the age of 450, the inhabitant of Sirius had been charged with heresy for having written a book on insects, whose diameter was a little less than a hundred feet.
The nature of big and small seems so relative that the same character can successively shrink or grow in size. During her trip to Wonderland, Alice unwisely drank the contents of a bottle and shrank to a mere ten inches tall. One cake makes her bigger, but other cakes make her shrink again.13 Her creator, logician and mathematician Charles Dodgson, better known by his pseudonym Lewis Carroll, gives a playful flavor to these spectacular changes.
These size-related thought experiments are not only used as a support for a meditation on nothingness and the infinite, and as a pretext for social criticism, they also constitute one of the favorite approaches used in popularizing rhetoric on insects.
In his 1798 Essai sur lâhistoire des Fourmis de la France (Essay on the history of ants in France), the French zoologist Pierre-AndrĂ© Latreille describes an anthill as a âpyramid, contrasting in its grandeur the smallness of the architect.â14 Thirty years later, the French entomologist Martial Ătienne Mulsant, author of an introductory book for the female audience, Lettres Ă Julie sur lâentomologie (Letters to Julie on entomology), echoes the idea put forward by Carl Linnaeus the previous century: if an elephant were proportionally as strong as a stag beetle, it could move rocks and flatten a mountain.15 In 1858, Michelet judges that beetles, which wear formidable armor and yet move with agility, âreassure us only by their size,â and he adds: âWere a man proportionally strong, he might take in his arms the obelisk of Luxor.â16 Closer to home, German evolutionary biologist Bert Hölldobler and his coauthor Edward O. Wilson write, in their quite scholarly popular book Journey to the Ants, about an ant nest unearthed in Brazil whose construction âis easily the equivalent in human terms, of the building of the Great Wall of China.â17 The Austrian ethologist Karl von Frisch, famous for his work on bee behavior,18 which earned him the Nobel Prize for Medicine in 1973, also authored a short introductory book on entomology entitled Zehn kleine Hausgenossen (Ten little housemates), published in 1955. He indicated that a fleaâPulex irritansâcan jump 10 centimeters high and more than 30 centimeters in distance. To give meaning to these figures, he adds that âan adult man wanting to compete with a flea would have to clear the high-jump bar at about 100 metres and his long jump would have to measure about 300 metres.â19 To simplify the analysis, we will limit ourselves to height, but the same reasoning applies to distance. This reasoning is based on the equality of two ratios. The first is that which relates the size of the insect and that of man. This ratio is about one to one thousand. The second is between the performance observed in the insect, a jump of 10 centimeters, and that which is calculated as equivalent for humans, here a fantastic jump of 100 meters. It is this calculated term that at the same time serves as the imagined term.
CHANGING SCALE
Attractive as the imagination may find these comparisons that seem to satisfy reason, those who implement them forget that these size ratios involve changes of scale. In short, if one ignores air resistance, an animal that doubles in size would see its muscle strength (which depends on a section of the muscle and therefore on a surface area) multiplied by four and its weight by eight (since it depends on volume). Similarly, if the size of a flea were multiplied by a thousand, its muscle strength would be multiplied by a million, and its weight would be multiplied by a billion. In other words, if it were larger, the flea would certainly be stronger, but, above all, it would be much heavier. In the end, it is useless to lend our size to fleas or grasshoppers, as it would not allow them to jump any higher.
The same type of explanation applies to the seemingly exceptional force of an ant carrying burdens bigger than itself. As with jumps, we like to imagine the weight we would have to carry to compete with the insect. At first glance, again, the calculation seems quite simple, the weight we would carry would be to the weight carried by the ant what our size is to the size of the ant. This is an illusion that does not take into account the physical consequences of a change in size.
Entomological literature did not always attempt to maintain this illusion, and some authors undertook occasionally difficult demonstrations, even for the general public.
Among the works of the punctilious French entomologist Charles Ămile Blanchard, is a popular book titled MĂ©tamorphoses, mĆurs et instincts des insectes (Metamorphoses, manners, and instincts of insects), the second edition of which was published in 1877. After making the usual comparisons to highlight insect performance, he refers to the measurements of muscle strength made by the physician Felix Plateau and then posits that ârelatively speaking, the strength of small species is still much greater than that of larger ones,â which he explained in one sentence: âbody weight increases in proportion to the cube, while strength measured by muscle section only increases in proportion to the square.â20
We find the same didactic audacity in Belgian author Maurice Maeterlinckâs 1930 The Life of the Ant. The poet warns us against âthe error into which we all instinctively fall when we see ants carrying objects three or four times their own size.21â For him, this error comes from the fact that âwe do not think of the insectâs weightâ but only of its length, which is directly perceptible to us. Maeterlinck develops his analysis by referring to an article published in the literary journal Le Mercure de France in 1922 and entitled âRemy de Gourmont, J.-H. Fabre, and the Ants.â Its author, Victor Cornetz, myrmecologist at Algiers University, refers to a text by Yves Delage that was published in the Revue scientifique in July 1913.22 Supported by the scientific authority of two authors, the second of which was a renowned biologist, Maeterlinck can thus explain to the reader that an antâs weight is proportionally the cube of its size, while its muscular strength depends on the square of its size. This is why, according to Delage, an ant âwhich can carry a grain of wheat ten times its own weight would be able to carry only a hundredth part of its own weight if it were enlarged to a thousand times its present size.â23 Ants benefit from what physicists call a scale effect.
Although the scale effect is generally ignored by even the knowledgeable public, it has necessarily been known for a long time in technical fields, as it conditions the solidity of constructions. An echo of this empirical knowledge can be read in the passage from Politics in which Aristotle asserts that there exists âa determinate size to all cities as well as everything else, whether animals, plants or machines.â24 This applies to the size of a boat that cannot sai...