While reading
Juliusz Słowacki's "Genesis from the Spirit", my attention was also drawn to two other sentences:
"Mathematical thought itself seems to have developed in plants (Myśl, zda się, sama matematyczna rozwijała się w roślinach)"
and
"Each tree is a great solution to a mathematical problem, a mystery of number(s) (Każde drzewo jest wielkim rozwiązaniem matematycznego zadania, tajemnicą liczby)"
This is very unusual: one might expect that a Romantic poet, looking at plants, trees, etc., would pay attention rather to the aesthetic side. However Słowacki associates this view with mathematics! This is more important to him. Isn't it brilliant? Our great romantic poet as a forerunner of a mathematical view of botany! In fact, in his era, scientists already knew a bit about the mathematics of plants or trees. Especially when it comes to the occurrence of patterns or schemes in nature based on the so-called Fibonacci sequence (Italian mathematician from Pisa [~1170 - ~1250]), i.e. a sequence of numbers starting with 0 and 1 in which each subsequent number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8... It turns out that many patterns in nature reflect numbers from this sequence. For example, the number of petals of many plants is a Fibonacci number: irises have 3 petals; buttercups and wild roses have 5 of them, delphiniums 8, certain asters 21, daisies 34, 55, and even 89 petals… Other parts of plants also follow this pattern, e.g. the arrangement of leaves on the stem (phyllotaxis), the number of flowers in the inflorescence, etc. etc. If living nature follows the Fibonacci sequence, this explains why it is not easy to find a 4-leaf clover: after all, 4 does not belong to this sequence, it is not a Fibonacci number! However, there are exceptions to this rule... When it comes to trees, their development (e.g. oak) can be schematically presented as follows:
http://leventtourne.free.fr/livreouvert ... bredor.jpg (the horizontal lines indicate subsequent years of development, and the numbers on the left are the number of branches of the tree: 1,2,3,5,8,13 - which correspond to the Fibonacci sequence) or as in the illustrations in:
https://drzewapolski.blogspot.com/2021/ ... -zota.html However, J.Słowacki was not the first to discover it: The German astronomer Johannes Kepler [1571-1630] had already thought about it, then in 1753 the Scottish biologist Robert Simson [1687-1768], the Swiss Charles Bonnet [1720-1793], Jean Louis Calandrini [1703-1758]… (the Polish poet would have some interesting topics in astronomy to discuss with Kepler. And who would benefit more from such a conversation?) Did Słowacki make this discovery on his own? I think so. Could a Polish emigrant in 19th-century Paris, who had no contacts in scientific circles, have known the works of the scientists mentioned above? (If he had read it somewhere, his friend and personal secretary St. Z.S. Felinski, who was a mathematician by education, would probably have known about it… And there is no indication of that.) Słowacki's observations are extremely insightful, even brilliant - all the more so because he was a poet, not a scientist. A great, great Poet who looks at the world, at living nature like a scientist, like a mathematician - what a rarity. I found it unfortunate that so few people in the world know about it. Especially when it comes to people interested in the history of scientific ideas - and those who are interested in the Fibonacci sequence and its representation in nature etc. etc. and write about it on their blogs (and there are quite a few of them on the Internet). Let’s see for example, the blog
https://simanaitissays.com/2019/06/09/leaf-mathematics/ which posted a note about «LEAF MATHEMATICS» which begins like this:
...HOW COME THE common Japanese shrub ‘Orixa japonica’ breaks all the rules of leaf arrangement? Basil, for instance, is decussate: Each leaf is about a quarter-turn, 90 degrees, from the last. Bamboo leaves are distichous, with leaves directly opposite each other. And spiral aloe leaves form a swirl that follows the Fibonacci sequence, the same as sunflower seeds. There’s even a phyllotaxis equation (Greek: “phyllon = leaf, “taxi” = fashion) that explains leaf arrangement. But ‘Orixa japonica’ fails to comply. Instead, its leaves follow a complex five-step pattern: The second leaf up the stem grows opposite the first one, 180 degrees away. The third leaf is 90 degrees from the second, the fourth 180 degrees from the third. And (just when you think you see a pattern) the fifth one grows 270 degrees from the fourth. Only then does the sequence repeat. Whatever do you suppose ‘Orixa japonica’ is thinking??..
(the poet noticed something similar to this - although he did not try to describe it in detail nor formalize it). So I translated these two already quoted, wonderful sentences and tried to share them on the internet. To make the following Internet search query succesufull (or easier/smoother):
"Juliusz Słowacki" Fibonacci
and/or something similar... (In the analogous way, as earlier the another search query: « Juliusz Slowacki Big Bang », see:
https://www.salon24.pl/u/edalward/13342 ... j-slowacki and
https://excathedra.pl/discussion/12363/ ... -i-to-jaki - in Polish)
On the above-mentioned blog, there was the following response:
What dear thoughts. Thanks for including them here
Some other blogs also provided nice responses, such as:
Thanks for … your wonderful comments. “Numbers are the language of the Universe”, indeed
Thanks so much… Your comment is beautifully phrased
Frumos spus... (Nicely said… - Romanian)
Häftigt! (Wonderful - Swedish)
Yes, the incredible 19th century poet Juliusz Słowacki was indeed among the first to predict mathematical botany...(see also:
https://www.salon24.pl/u/edalward/14134 ... j-botaniki )
