This crossed my mind today...
There is Schrödinger's cat and Newton's apple.
Are there any other famous animals/plants featured in physics in a similar way?
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Arhytas made the first known steam powered toy in the shape of a pigeon, see The steam-powered pigeon of Archytas.
Priestley put a mint plant in a closed container with a burning candle. The candle flame went out after using up the oxygen, but after 27 days Priestley re-lit the candle, demonstrating that mint produces oxygen of its own.
Kekulé claimed, 25 years later, that he discovered the shape of the benzene molecule after having a dream of a snake biting its own tail. As with the apple, there are doubts that this actually happened.
Snake biting its own tail is an alchemic symbol called the ouroboros. It is sometimes also associated with Wallis's symbol for mathematical infinity (he did not make this association).
Pavlov's dog became a common metaphor for psychological conditioning after Pavlov's experiments with causing salivation in dogs by associating food with turning on a light bulb.
Asimov (who is a biochemist, in addition to the science fiction author) wrote a story about a goose that lays golden eggs, by transmuting oxygen-18 to gold-197 via an enzyme-catalyzed nuclear process. The goose can not reproduce due to heavy metal poisoning of the eggs, and a biopsy of the liver needed to uncover its secret would kill it. Asimov's riddle is to figure out how to make it reproduce (there is a scientific solution).
Parfit's “people who divide like an amoeba” illustrate a conundrum associated with brain transplants:
"My brain is divided, and each half is housed in a new body. Both resulting people have my character and apparent memories of my life. What happens to me?"
Jackson's Mary, the color scientist, who knows everything about the physics of colors, but grew up in a colorless room, sees a red tomato for the first time, and learns something new nonetheless. This illustrates the problem with explaining the so-called qualia.
A related earlier illustration is due to Wittgenstein, who imagined that everyone has a box where they keep a "beetle". That is everybody calls it "beetle", but "no one can look into anyone else's box, and everyone says he knows what a beetle is only by looking at his beetle". The point is to dispel the idea of a special non-physical entity, "mind".
Many of these sorts of things, featuring creatures or not, are what Mach called thought experiments, and there is extensive literature on them.
There's "Buridan's ass" in logic, which says that a "hungry donkey" will not be able to decide "between two completely alike bales of hay" (Duhem 2018 p. 13) and thus will starve. It's attributed to medieval physicist John Buridan (1295-1360), but a physics (not logic) version of it can be found in Aristotle's De Caelo 295b32 [375.]:
the man who, though exceedingly hungry and thirsty, and both equally, yet being equidistant from food and drink, is therefore bound to stay where he is
A good treatment of Buridan's ass can be found in Nicholas Rescher's Scholastic Meditations (ch. 1) or Studies in the History of Logic (ch. 7), "Choice without Preference: The Problem of Buridan's Ass".
the first paper where the graphs that are now called penguins were considered in the weak decays appeared in JETP Letters in 1975, and there they did not look like penguins at all. Later on they were made look line penguins [...] The penguin name came in 1977, as follows. [...] That summer, there was a student at CERN, Melissa Franklin who is now an experimentalist at Harvard. One evening, she, I and Serge [Rudaz] went to a pub, and she and I started a game of darts. We made a bet that if I lost I had to put the word penguin into my next paper. She actually left the darts game before the end, and was replaced by Serge, who beat me. Nevertheless, I felt obligated to carry out the conditions of the bet. [...] For some time, it was not clear to me how to get the word into this b quark paper [then I] visit some friends living in Meyrin where I smoked some illegal substance. Later, when I got back to my apartment and continued working on our paper, I had a sudden flash that the famous diagrams look like penguins.
So not only animals are involved in this story, but also a plant, I suppose..., maybe this also answers to another question on hsm even if we cannot say that this was a "mathematical breakthroughs".
Another Feynman diagram whose name derives from the similarity with an animal is the tadpole diagram.
Biological similarity are more often used in mathematics and computer science, see for example butterfly diagrams (in fast Fourier transforms), onion diagrams/models and spider diagrams (in Euler-Venn diagrams), ...
In mathematics (with relevance to physics), Émile Borel in 1913 illustrated concepts of probability with monkeys, this lead to what's now called the "Inifinite Monkey theorem". He wrote:
Concevons qu’on ait dressé un million de singes à frapper au hasard sur les touches d’une machine à écrire et que, sous la surveillance de contremaîtres illettrés, ces singes dactylographes travaillent avec ardeur dix heures par jour avec un million de machines à écrire de types variés.
Let us imagine that a million monkeys have been trained to strike at random on the keys of a typewriter and that, under the supervision of illiterate foremen, these typing monkeys work eagerly ten hours a day with a million typewriters of various types.
Borel, Émile. „La mécanique statique et l’irréversibilité“. Journal de Physique Théorique et Appliquée 3, Nr. 1 (1913): 189–96. https://doi.org/10.1051/jphystap:019130030018900
Descartes allegedly developed coordinate systems after observing a fly on the ceiling of his bedroom; he realised he could define its position by counting the number of wooden panels from two adjacent walls. This is ascribed to Descartes in many popular maths books, but so far I have not been able to find a definite primary source.
(It's maths, but clearly very relevant to physics...)
In 1780, Luigi Galvani experimented with frog legs, mounted on iron or brass hooks, and saw the leg twitch when touched with a probe made of another metal. They would also jump when hanging on a metal fence in a lightning storm.
Galvanized, Alessandro Volta realized that the crucial feature of Galvani’s experiments was the two dissimilar metals – the iron or brass hook - and the probe of some other metal. The metals were generating the current.
To show that the generation of an electric current did not require animal parts, he built a stack of alternating zinc and silver discs, separated by brine-soaked cloth, in imitation of the electric organ of the torpedo fish.
When a wire was connected to both ends of the pile, a current flowed. He found that different types of metal could change the amount of current produced, and he could increase the current by adding disks to the stack.
The battery was a huge success. In 1800 Nicholson and Carlisle used its current to decompose water into hydrogen and oxygen. In the 1830s Faraday used a battery in his studies of electromagnetism. Other inventors made improvements on Volta’s design, and soon it was powering telegraphs and doorbells.
The monkey and hunter thought experiment on the effect of gravity on projectile motion.
If human bodies are allowed there is, for example: