An excerpt from the extensive manuscript “Mechanics in Biology” (1920-1921), which remained unfinished. The author began work on the manuscript back in 1882, and at the same time the first part was sent for review to the great Russian physiologist I. M. Sechenov. The excerpt was processed for printing by K. E. Tsiolkovsky himself.
If a human’s stature was 180 cm, then, reduced by half, it
will be 90 cm. While maintaining the geometric similarity, the surface of the
body will decrease by four times and the volume by eight times. The body weight
and mass decrease bya similar amount. If a human weighed 64 kilos, now he weighs
8 kilos. The volume, weight and mass of the brain, like of all other organs,
also decrease by eight times, the surface by four, and the linear size, i.e.
length, width and height, by two times. The ability of logical thinking should
be significantly weakened by this, so it is unlikely that our dwarf could understand
and describe his feelings. We’ll have to do it for him ourselves. Only with
a different structure of the brain, with a different relationship between its
parts, the mind can remain strong enough, despite the decrease in the total
mass of the brain.
The total absolute heat emission will decrease by four times, which will correspond to a decrease in the surface of the body, so that its temperature seems to remain the same. But the cold will penetrate deeper into the body, and therefore the temperature of the central parts of him should decrease.
The relative volume of absorbed food, oxygen and secretions should double. If the former normal creature absorbed two kilograms of nutrient materials per day, then the dwarf will absorb half a kilo, which will be twice as much in relation to body weight. Thus, our dwarf will be more voracious than we are. He needs a relatively twice as long sausage for lunch, bread twice as large.
His mechanical work will be relatively twice as much: he can climb a mountain or a ladder twice as fast, run twice as fast (if only friction is taken into account and the resistance of the air environment is neglected). In relation to the size of the reduced body, the effect will even be four times stronger. So, a normal person ascends one growth of his body per minute, and a small person ascends four growths of his body.
The absolute strength of the muscles will decrease by 4 times, so that a fight with a giant or even with people of large stature will be impossible: the dwarf will be defeated. But the relative strength of the muscles will double: if he used to lift one person with his hands, now he will lift two equals with greater ease.
The comparative resistance of bones and cartilage to breaking will double, as will the resistance of tendons and skin to rupture. If a normal human easily carries himself and one more such human on his shoulders, then a dwarf will carry six, including himself, and without him – five ones. It will seem that a dwarf can drag a log comparatively twice as long or heavier. He can drag stones twice as bulky on the ground and drag a wagon twice as loaded and heavy. The absolute safe height of the fall is twice as large, but compared to the size of the body, it will be four times larger. If a normal human can fall harmlessly from the height of his stature, then a dwarf can safely fall from the height of his quadruplicate stature.
The work of every muscle, with one contraction, is reduced by eight times, since its tension will be four times less, and the magnitude of the contraction is half as short. As a result, the jump remains of the same absolute value, but its relative value will increase. Indeed, a human of ordinary height, preparing for a jump, straightens up by 30 cm and jumps, let us assume, by the same amount, but in total he raises the body by 60 cm. The muscles of the dwarf should also raise the same; but the straightening of his legs is only 15 cm. Then, a 45 cm rise above the soil remains, which means that the jump will be three times higher in relation to growth. If a normal person jumps on a chair, the dwarf will jump easily on the table. If the number of muscular contractions per minute remained the same during the work, then the absolute work would decrease by eight times, and the relative work would remain unchanged. But we know that the latter in dwarf is twice as large. Consequently, the number of muscular contractions per unit of time should double. In other words, the frequency of movements, the number of swings of arms, legs, head, etc. should double. It just corresponds to the acceleration of neural communications. The dwarf will not only be a strongman, an inimitable jumper and acrobat, but also very lively, fast and agile person.
The absolute height of the stones of proportional size thrown by the hand will remain the same, but in relation to stature it will be twice as large. If a human of ordinary stature throws a stone the size of his fist to a height 10 times greater than his height, then a dwarf will throw a stone the size of his little fist to a height 20 times greater than his size. If the first one will throws any thing over his dwelling, then the dwarf will throw the same thing over a house twice as large in relation to him.
The impact of the hand or foot will be proportional to its mass, i.e. eight times weaker, since the speed of the armed or unarmed hand will remain the same. So, the relative strength of the fist, hammer, saber or knife will remain unchanged, but the frequency of beats will double.
Swimming will be easy, since the energy of the dwarf is twice as much, and the absolute speed of falling in the water will decrease by almost one and a half times; the useful action of the hands and feet will double relatively, because their relative surface will also double.
This makes it clear that, the withstand the gravity is much easier for a dwarf, that he is more energetic, livelier, even faster absolutely. What prevented creatures of smaller stature from sidelining of people of normal height in the struggle for existence? First of all, dwarfs lose due to a decrease in the absolute strength of muscles: in the fight against gravity, they gain, but in the fight against larger creatures, they lose. In addition, a decrease in brain volume should be accompanied by a weakening of mental abilities.
Instead of 1.8 m, a human’s stature will be 3.6 m. Volume,
mass and weight will increase eight times. Instead of 64 kilos, our giant will
weigh 512 kilos. The absolute strength of the muscles and locomotor parts of
the body will increase fourfold. Compared with the weight of the body, it will
decrease by half. If a man could previously carry only one person equal to him
on his shoulders, then a giant will not carry anything on himself: all his muscular
strength will be absorbed by the eight-fold increased mass of his body. For
work, for carrying weights, for the making of lodgements, there is no longer
enough strength. The giant himself will barely drag himself: the slightest pressure
on him will knock him down.
The giant’s brain gains considerable strength, though. But what does it mean, accompanied by physical impotence, in the absence of efficiency and aggravation of all forces by the weight of one’s own body?! The physicality of a giant can be compared with the physicality of an ordinary, but strong and healthy person, overloaded with weight to exhaustion, without hope of getting rid of it.
The work of the giants necessary to withstand the gravity increases to the fourth power of their growth, because the loads corresponding to the size increase eight times, and the height of their lifting increases twice, in total, the work increases 16 times. Meanwhile, the absolute power increases only four times. Consequently, the energy in relation to withstand the gravity has fallen fourfold. With a further increase in growth, he loses the ability to walk, even lift or move the organs of movement and mechanical work. The ability to move fingers, tongue and other small organs remains the longest; but they also disappear when the giant reaches sufficient height, because he will no longer be able to overcome their heaviness. An even greater increase in growth will be accompanied by rupture of blood vessels, destruction of all organs and death.
The possibility of observance of similarity for internal organs
is hardly feasible here, but we will suppose it. Now we are dealing with a real
Lilliputian. Its stature is 10 mm, the surface is 10,000 times smaller, and
the volume, mass and weight are a million times less than at normal one. Namely,
its weight will be 0.063 g, i.e. it weighs a little more than an ordinary drop
of water. The relative strength of his muscles will increase by 100 times. He
will lift loads 100 times more compared to the mass of his body. The relative
strength of his bones, cartilage, skin and other supporting parts will increase
a hundred times. You can pile on him 200 creatures equal to him, and not a single
bone will crack, not a muscle will tremble, he will carry them with the same
ease as a normal human carries one more human.
The withstanging the gravity is made 10,000 times easier. A Lilliputian will dig 10,000 dugouts corresponding to his stature, when a normal one will dig only one. The channel he dug at the same time with a normal person will be 10,000 times longer compared to the growth of the body.
The relative work of muscular contraction will remain the same, but the apparent magnitude of the jump in relation to the body size will increase by 100 times, while lifting above the ground – by 200 times. The Lilliputian will jump over a twenty-story “skyscraper” and puddles, which he imagines to be lakes, without a run. The range and height of throwing stones will remain the same, but relative one will increase a hundred times. Swimming is not worth the slightest effort, since the relative strength of the muscles and the surface of the palms increases 100 times. The air will seem to the Lilliputian a hundred times thicker in comparison with the mass of his body. The wind will also seem 100 times stronger. But the midget is not helpless even against the strongest wind, as his tenacity and muscle strength increases a hundred times.
Our Lilliputian can fall from any height. The air resistance will not allow him to get smashed, since the relatively large surface of his body does not allow him to acquire speeds of more than 3-4 m per second. In addition, the resistance of his bones and other organs to destruction increases a hundred times. Even with a much larger magnitude, it can fall even from the clouds.
Small wings, taken in the hands of our Lilliputian, give him the full opportunity to fly. It can fly even with a relatively very large load.
The question arises again: why did man not turn into a midget in due course of evolution, if the benefits of small sizes are so great?
Firstly, the absolute strength of organs in large creatures is still greater, and in their struggle with small ones, the latter are in trouble. Secondly, the mental abilities of large creatures still prevail. This adds to the winning chances in the fight.
If there were a different gravity on our planet, the size of the most perfect people, as well as all other creatures, would change. For example, with a decrease in gravity by 6 times (as on the Moon), a person’s stature could increase by 6 times, mass by 216 times, muscle strength by 36 times; the brain would increase accordingly. Such a person, thanks to the strength of his muscles (and an extensive mind), would be the winner, despite the fact that in the fight against dead nature, small people would have more physical advantages. This giant of 10 m in height would have turned out (subject to internal and external similarity) to be a clumsy creature, although freely moving and jumping like a man on Earth, only six times slower in relation to his size. But the absolute power of muscles and mental strength would have subdued all living things of a smaller size to him.
On the contrary, if the gravity increased by 21/2 times, as on Jupiter, then the human race would have to decrease by 21/2 times. Otherwise, the own weight of people on Jupiter would take away their working capacity and even the ability to move with their muscular forces. A person would be 72 cm tall, have a brain 16 times smaller in volume and weight, and would probably be a very mentally limited being. All other animals must also decrease, and therefore man, perhaps, would still remain the master of a small living nature. But the higher progress associated with machines, inventions, science, would probably be very weak. It would be impossible to expect the development of technology that is now being observed on Earth and which, we hope, will increase over time to an unimaginable magnitude. On Mars, Mercury and other small planets and moons, one would expect a large stature of land animals and the strongest development of the brain, if other unfavorable conditions did not prevent it: high or low temperature, atmosphere unsuitable for life, scarcity of water and other elements useful for the development of life, etc.
The original Russian article and photocopies of author's
manuscript may be found here
Translated by Pavel Volkov, 2021