On Being Just the Right Size

Is it just chance that people are about two meters tall, or is it a result of laws of nature?

Life comes in many sizes. The smallest creatures are bacteria. The smallest of these are about one millionth of a meter long and half that wide, and weigh less than a billionth of a billionth of a kilogram. The longest and widest creature is a surprise -- not an elephant, not a whale, not a giant sequoia tree. It is a huge fungus that lives in soils in western North America, just under the ground. Some of these individuals stretch across two kilometers! If one of these giants were merely 10 cm thick, it would weight about 314,000 kilograms. These fungi live by digesting decaying vegetation in the soil, a vital role in the eternal cycling of life’s chemicals. Thank goodness, however, they have no sharp teeth or legs to walk on, or an interest in feeding on living flesh.

The heaviest organism is probably the largest of the giant Sequoia trees of California, known as the “Del Norte Titan” sequoia. It stands 94 meters high and is more than 7 meters in diameter, and weighs more than one million kilograms.

So the range of sizes of living things is huge -- in terms of weight the range is from a billionth of a billionth of a kilogram to one million kilograms. This is a range that mathematicians call 12 powers of ten or 12 orders of magnitude. In terms of length the range is from a millionth of a meter to 2 kilometers, which is nine powers of ten or nine orders of magnitude.

Among mammals, our kind of creatures, the range is smaller, but it is still large. The smallest mammal is Savi's pygmy shrew (known among scientists as Suncus etruscus). It is 3.5 centimeters long plus a 2.5_cm tail, and weighs about two grams. Though small, it has a large geographic range. This thimbleful of energy lives in the Mediterranean and is found from there to Africa and Malaysia.

The largest mammal is the blue whale, weighing in at 150,000 kilograms and 30 meters in length. On the land, the largest mammal is a male African elephant that can weigh 4,000 kilograms, so he is two million times as heavy as the smallest shrew. The range of size of mammals extends over seven powers of ten.

Out of the 12 powers of ten in weight and nine powers of ten in length, is there one that is best? The answer is: it depends — because it depends on best for what?

Take, for example, a question that has long been of interest to people -- what is the best size for a beast of burden? What we would like to get is the largest burden carried the longest distance for the least amount of food and water. Here we can take food to represent a supply of fuel or energy. So the question is the same as asking what is the most fuel efficient automobile, train engine, or airplane -- what carries the biggest load for the least fuel?

If you have been on a diet to lose or gain weight, then you might think that energy use is simply a matter of total body weight. An apple contains about 100 calories; a half kilogram of human body fat about 1000 calories. If you gain a kilogram a year, diet books will tell you that you have been eating just 50 calories too many a day — half an apple’s worth. This seems to apply to everybody, whatever one’s size. And it’s a good enough approximation for people. Even though we come in a range of sizes, the smallest adults are about half the length of the largest, and this is small compared to the ranges of all living things.

But in fact the use of energy per body cell declines with body size. This is a consequence of a rule of geometry, known as the surface-volume ratio. The ratio of surface area to volume of any three-dimensional object declines with size. This is because the volume increases with the cube of the diameter, while the surface area increases with the square of the diameter. The result is a rapid change in the ratio. You can see this by blowing up a balloon. A balloon that is one centimeter in diameter has a surface area of 3.14 square centimeters, and a volume of about half of a cubic centimeter. The surface to volume ratio is six. A 10 centimeter balloon has a surface area of 314 square centimeters and a volume of 523 cubic centimeters. The surface to volume ratio drops by a power of ten, to 0.6. By the time you have blown up the balloon to one meter in diameter, it has a surface area of 31,400 square centimeters, and its volume has expanded to 523,333 cubic centimeters. The surface to volume ratios has declined 0.6 to 0.06. The bigger an object, the less surface there is for any unit of volume.

Why does this matter for a beast of burden? The answer has to do with metabolism -- the chemical reactions that go on inside each cell that keep the organism alive. In a warm-blooded mammal, each cell produces heat as a byproduct of its metabolism. This heat keeps the animal warm, but it can also make it too warm. An imaginary animal that was as round as a balloon and 10 centimeters in diameter would have ten times as much surface area for each cell, compared to a 100-centimeter wide animal. If the two animals had the same metabolic rate, and if the only way that they could lose heat was directly from exchange at the surface with the environment, then the larger one would be much hotter.

A surface exchanges heat energy with its environment in four ways: by radiating heat energy as infrared light; by evaporating water (sweating for us), and through two methods that depend on the contact of the surface with the surrounding air or water: conduction and convection. Convection exchange is the transfer to the wind – to moving air – or to a current of water. Conduction exchange is the transfer simply due to the contact of the surface with still air or water. If the surface is warmer than the air or water, it warms the molecules of the fluid that touch it. These rise and are replaced by colder molecules, which in turn are warmed.

The consequence of this is that small mammals, like a Savi's pygmy shrew, have to have a very fast metabolism to keep from freezing to death, and to keep as warm as a large animal. If you pick up a puppy or kitten, you can feel its rapid heartbeat, indicating its very high metabolism. Meanwhile, a large mammal, like an elephant, has to keep its metabolism much slower so that it doesn’t overheat. So if you live in a cold climate and you want to stay warm, there are benefits to being large. If you live in a hot climate and want to keep cool, there are benefits to being small.

If you think all this is complicated, you are in good company, because it has fooled some good scientists. In the 1960s, when psychedelic drugs were fashionable, several scientists experimented with the effects of LSD on an elephant. They published their results in the prestigious American journal, Science — the journal of the American Association for the Advancement of Science.

These scientists had calculated the dose based simply on body weight, not on the surface to volume ratio. First they found how many milligrams of LSD put a cat into a rage. Then they took that number and multiplied it by the ratio of the weight of the cat (2.6 kilograms) to the weight of the elephant. This resulted in a dose of 297 mg of LSD. By comparison, a dose of 0.2 milligrams puts a human being on a “trip.”

Unfortunately, the elephant died immediately after he received this 297 mg dose, and the authors of the scientific article concluded that elephants were especially sensitive to LSD. But they made a fundamental mistake. In his marvelous book, How Animals Work, the American scientist, Knut Schmidt-Nielsen, explained the mistake. The scientists assumed that the dose of a drug was simply a matter of body weight. In reality the proper dose of anything depends on metabolic rate, and since this decreases with body size, the elephant should have received a dose of 3 mg of LSD to get the same “trip” that a person receives from 0.2 mg. So the poor elephant was given an overdose 99 times too large!

Let us imagine the highly unlikely procession of two million shrews employed by their human owner to carry a tonne of material, and compare this with a single elephant pulling the same weight. Not only would it be pretty much impossible to organize two million shrews to work together to pull the load, but their metabolic rates are so high that they would eat much, much more than the single elephant, and they would be an extremely inefficient way to move material. Based strictly on the brawn required to move a burden, the bigger the better. One big draft horse will eat less than two smaller horses whose combined weight equals his.

But, of course, we humans find much more to life than pulling around heavy weights efficiently. And there is much more to life on Earth as well. So to try to answer the question: what is the best body size for a living organism? We have to return to the question best for what tasks?

Suppose we consider a more fundamental concern: what is it that living creatures do that is necessary to maintain life on Earth? The fossil record provides a clue. Life has existed on the Earth for three and a half billion years. But for the first two billion years the only forms of life were bacteria and their ancient relatives. All the time since — 1.5 billion years -- the time of animals, plants and fungi, the time of the dinosaurs, and the time of human beings, is shorter. This tells us that very small creatures can persist quite well, for a very long time, without the help of the rest of us. There must be something to being very very small – a billionth of a billionth of a meter or slightly bigger. Is small then the best size, except for carrying burdens?

For life to persist, living things require an input of energy (mostly from sunlight, converted by plants, algae, and certain bacteria, through photosynthesis to sugars and then to other organic compounds), and a supply of 22 chemical elements that are nutritionally necessities. In that first two billion years of a bacterial world, bacteria did all the necessary chemical reactions. Some captured sunlight and carried out photosynthesis. Others converted chemical elements from inorganic forms unuseable directly by life into forms that living cells can use.

For example, all proteins contain nitrogen, and all life requires protein. But nitrogen exists in our atmosphere in its simply molecular form, as N2, that is, as a molecule of two nitrogen atoms. But the chemistry inside cells cannot use nitrogen in this pure form. It must be converted either to nitrate or ammonia. Before people came along and discovered modern chemistry, only bacteria did this – except for a small amount of nitrogen oxides produced by lightning. Bacteria take pure nitrogen and convert it to nitrate and to ammonia.

Chemical elements have to cycle, and so not only is it necessary for pure nitrogen to be converted to nitrate or ammonia, but also eventually nitrogen has to return to the atmosphere in its pure form, so that it is available to be used again. Only bacteria carry out the final decomposition of nitrogen, converting nitrate and ammonia back to molecular nitrogen. Bacteria still do most of the important chemical reactions necessary to maintain life on the Earth.

Since bacteria lack teeth, mouths, claws, and other weapons, they exchange chemical elements with their environment by simple diffusion through their cell surfaces. This brings us back to the all important surface to volume ratio. If your primary goal is to take up chemical elements, convert them into organic chemicals, and then release them again, it is efficient to have a rapid rate of exchange, and therefore to have a high surface area relative to the volume of living tissue. It is best to be very small.

Not only is there an advantage, as a chemical processing form of life, to being small, but early life could not be very big. That was because the early Earth had no free oxygen in the atmosphere. Free oxygen allows rapid combustion. The early Earth had little free oxygen in its atmosphere, but the atmosphere is now about 20 percent oxygen. Before the Earth’s atmosphere became high in oxygen, complete “burning” of food as fuel was not possible. Bacteria living in an oxygenless atmosphere obtain energy by such reactions as fermentation – the same reactions that yeast use to give us bread and wine. The product, alcohol, is a very good fuel, as automobile race car drivers know. If the end product of the attempt to use energy is still a good fuel, this means that the end product contains a lot of energy, and that fermentation is not the most efficient way to get energy from organic compounds.

With only non-oxygen means of energy use, bacteria could not get very big. They could not form three-dimensional bodies of many cells, because the interior cells could not get enough raw materials fast enough to maintain their metabolism. Life was restricted to single cells, or to strips of cells one cell thick. It was life restricted to a plane, to two dimensions. The existence of animals and plants, with their large and complex bodies, had to wait for an atmosphere high in oxygen.

How did our atmosphere change from having no oxygen to being rich in oxygen? The photosynthetic bacteria did it. The process of photosynthesis releases oxygen. For early life, evolved and adapted to an oxygenless environment, that free oxygen was toxic. As a toxic waste, it was simply dumped into the environment by the bacteria. There were no pollution control laws to prevent this dumping – there were no sentient creatures with the ability to conceive of society, laws, and writing.

Over a very long time, free oxygen dumped by bacteria as a waste increased in the atmosphere. Once it reached approximately its modern level, then animals, plants, and fungi, with complex and large bodies, could evolve, and they did. It is necessary to have bacteria for all life to be sustained, and they are most efficient as small creatures.

So far, we have arrived at two answers to the question: what is the best size for an organism? To carry a burden, be big. To be a chemical factory that creates and then decomposes the necessary chemicals for life, be small. But what about us, and our consciousness, spirituality, poetry, art, music, literature and technology? Is there a best size for these qualities?

The short answer to this question is that we are not sure whether there is a single perfect size for a sentient being. But we can put some constraints on the range of sizes. To have a brain with which to think, we must have a complex body, in three dimensions, with many cells. So we cannot be very small.

But could we be as small as a shrew or as large as an elephant and still have our human qualities? We know that our brain is very large, and that many of the largest creatures that have lived on the Earth have had tiny brains by comparison. It seems unlikely that sentient creatures could be as small as shrews or mice. This is once again a consequence of the surface to volume ratio. As a general rule, longevity is proportional to metabolic rate. The faster the metabolic rate, the shorter the lifetime. Shrews, mice, and small birds live a short time. The average lifetime for many songbirds is less than one year, and the lifetime of a songbird that lives to reproduce can be as short as a few years. Pet owners know that dogs and cats live much shorter lives than we do. It is unlikely that creatures that live such short times could have time to gain the knowledge and skills to create civilization, technology, and to learn the arts. So we can begin to put some lower bounds on the “best” size for intelligent, sentient, thinking beings. It would seem necessary to be able to live a number of decades, and therefore to be as large as say the larger, longest-lived dogs.

But could we be much larger? Could there be an elephant civilization, as in the children’s storybooks about Barbar the elephant? We can’t say for sure. But there are pressures of evolution and ecology that would tend to work against being both very large and very smart. The game of biological evolution is to win by having more offspring than one’s competitors, and this forces species to focus their resources. Given the million and a half named species, and probably many more yet unnamed, if you are going to put a lot of your energy and material resources into a brain, it is better to not expend your energy and chemical resources in other ways. On the other hand, If you don’t want to be eaten, it’s not a bad idea to be big and powerful. But perhaps the fact that people were not the largest, nor the fastest, nor had the biggest teeth or sharpest claws, helped force the evolution of our brains.

At this stage in our understanding of life, we can’t say for sure what the absolute “best” size is for a thinking creature that can create civilization, technology, and arts, and can appreciate beauty and philosophy. Most likely there is a range – small perhaps – that would work well. We can say that it would have to be a creature that could live a relatively long time and put its resources into brains rather than brawn. That suggests that it is not an accident of evolutionary history that people are between one and two meters in length. But it leaves unanswered the question: how much bigger might intelligent life on another planet be, or how much smaller? The range would most likely be from one meter and larger, but we cannot at this time answer this question with completeness.

And so we can make a few generalizations about being the best size for being alive. We can say that to do the chemistry required for life, it is best to be very small; while to carry burdens it is best to be very big; to think it is necessary to be not too small, but just how small or how large is a question that will have to wait much scientific research about cognition, a science only in its early stages. Meanwhile, be happy that those ancient and tiny bacteria created an oxygen atmosphere for us three-dimensional, complex creatures and that they, along with algae and green plants, still do so. And be thankful that our size makes us use our wits, not simply our brawn, so that the universe is not empty of music, art, literature, philosophy, architecture, or of beings that can ask the question: are they the best size?

Copyright © 2000 Daniel B. Botkin
written for Le Temps Strategique