Sunday, September 26, 2021

Greetings from Thumbelina


Some time ago, I posted a Darwin video about Thumbelina. This is a very old story, continually reappearing in new children’s books, about a young woman who is so small that she can hitch a ride on the back of a swallow or hide inside of a tulip (to use the two examples from our public library). We all know it is impossible to have a human being this small, but why is this so? 

Organisms can be very small. If you define an organism as something that can actively maintain constant internal conditions, and can reproduce itself, then the smallest organisms on Earth are bacteria and archaea. Viruses are smaller, but they cannot maintain constant internal conditions, or reproduce, by themselves; they have to outsource these processes to the cells that they parasitize. Astrobiologists (scientists who generate fact-based speculations about possible life on other planets) have lively disagreements about what the smallest life forms could be.

How small could a vertebrate be? A vertebrate is an animal that has (in addition to vertebrae) whole systems of organs that maintain constant internal conditions. Vertebrates are so complex that they could not possibly be microscopic.

But they can be pretty small. Scientists recently discovered a frog, Paedophryne amaneusis, that is so small that it can comfortably sit on a dime. X-rays reveal that it has a complete skeleton. It does not have a tadpole stage, but it attracts mates with ultrasonic peeps. I suspect that it does not need to have as much anatomical complexity to maintain internal conditions; for example, it probably absorbs most of the oxygen that it needs through its skin.

This image is from the source in this link.

Humans have seventy trillion cells. Would Thumbelina need to have seventy trillion very tiny cells? Probably not. She could have tiny organs that did everything that they needed to do, each organ with fewer and smaller cells.

But there is one organ that would need to have a minimum size: the brain. While Thumbelina could metabolize as she rode around on the back of a swallow, she would not be able to enjoy it, or even know what was happening. Since no one knows how to define consciousness, we cannot say how big a brain has to be to be conscious; but Thumbelina’s brain would definitely be too small.

Probably everyone has heard about the homunculus. This is supposedly a tiny complete person that lives inside of a sperm head, made famous by the Nicolaas Hartsoecker drawing (1695). According to many scientists of the late seventeenth century, that is where people came from: a little person inside a sperm grows up by consuming the food inside the egg. Some of the sperm had little men, some had little women, as in the drawing. Even more amazing, the male homunculi had sperm, with homunculi inside of them, with homunculi inside of them, with…how far can you go? Forever? Scientists at the time knew no reason to doubt it.

The reason that you cannot have an infinite regression of smaller and smaller objects is that everything is made of atoms. Although atoms are incredibly small, they are not infinitely small. This places a lower limit on the size of anything made out of atoms.

We must be careful to avoid the argument from incredulity: If I cannot believe it, then it cannot exist. Not long after I post this essay, a computer scientist might create a qubit structure that could fit inside Thumbelina’s head and impart a reasonable level of intelligence. But the principle remains unchanged: there is a lower limit of brain size for human intelligence, and Thumbelina is probably below that limit.

There are upper limits also. A very large walking vertebrate could not exist, since volume (weight) increases as the cube of the linear dimension while the strength of a leg increases only as the cross-sectional area (the square). An animal twice as big in linear dimensions would have legs four times as strong but would weigh eight times as much. This is true only for animals that walk on land. Whales can be much larger, but their weight is supported by the buoyant force of the water that they displace.

None of this will make any difference to people who are enjoying the new King Kong vs. Godzilla movie, or to my granddaughter who enjoys the Thumbelina books. But, I suspect, human imagination is limited—not by size, but by our evolutionary heritage. We imagine things that our evolved brains allow us to imagine, and nothing more.


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