Mr. K. hit after a mosquito

Mr. K. hit a mosquito. He did not hit it. This prompted him to the following consideration: "Why was the mosquito able to escape from me? I hit it really fast. But it got away from the target area so quickly and skilfully that I could no longer adjust my striking movement.

Mosquitoes have been around for 400 million years. When they developed, no one ever struck after them. Well, 40 million years ago, horses and elephants began to wag their tails to scare away insects. But to strike at them specifically? Mosquito killing is a modern phenomenon. Six million years ago, the first dry-nosed monkeys began to walk upright. So they had their hands free to strike at mosquitoes. But why should they? In the wild it is hardly helpful to kill a single mosquito. You can scare them away, or dress them. Only the advent of closed rooms, in which one could dress more easily and yet not want to fear bites, provided the occasion for the targeted mosquito killing. The first houses were built 20,000 years ago. Since then, people have been deliberately beating for mosquitoes. In comparison to the entire habitat of mosquitoes, closed rooms make up a negligible percentage, even though it may sometimes seem different in a house by a lake. Even today there is hardly any evolutionary selection pressure to give the mosquito the ability to avoid targeted strikes, and the low selection pressure that currently exists has existed for a negligible period of time compared to the evolutionary history of this insect. So why can the mosquito do something it does not have to do?

But is it not so similar with music? Why can we humans make music? One can hardly construct an evolutionary selection pressure here. Well, the need to move rhythmically in groups may be conducive to group cohesion and thus have an evolutionary background. But primitive percussion instruments would have sufficed for this. There was no evolutionary pressure for a fugue. This is also shown by the fact that music came up relatively late, perhaps 60,000 years ago, while the genetic potential of humans had existed for millions of years.

Didn't I read recently that even sea anemones carry information in their genome that later led to the construction of much more complex structures like those of vertebrates? Maybe the development of vertebrates is not due to external influences, so that depending on the situation, something completely different could have come out of it. Perhaps the emergence of vertebrates rather followed an inner necessity, and living beings on other planets with different environmental conditions, if we could get in touch with them more than ever before, would be surprisingly different, but in part also surprisingly similar. Perhaps they would make music. Perhaps their language would be subject to a grammar that is partly similar to our grammar.

My friend M. thinks that it would be necessary to find the necessary concepts, according to which language is structured, but also according to which the brains of humans arrange themselves so that they speak and understand this language. The same would have to be done for music. And just as there are perhaps also necessary principles of order in the construction of tissue animals, which inevitably lead to vertebrates, there is perhaps also an inevitable grammar of mosquito flight. The concept of flying leaves no other solution stable than that which at the same time allows to avoid a targeted strike.

Mr. K. had delved so deeply into the implications of the successful flight of the mosquito that he did not notice its renewed approach. The bite of the mosquito called him irrevocably out of his reflections, and in an excitement and desire for revenge that was completely surprising in view of the depth of these reflections, and despite the obvious senselessness of this undertaking, which came too late and was not worthy of his intellect, he subsequently concentrated all his physical and mental strength on the subsequent mosquito killing.

- Christian Kaernbach -

 

Jupiter, viewed in light

Jupiter, viewed in light
Finally all the parts he had ordered had arrived. He carefully cleaned the main lens. It was important not to leave any fingerprints on it. This was difficult, especially when it came to placing the lens on the front of the tube and inserting the clamping ring. But he found out that he had to wear gloves when assembling the telescope, then it worked.

In a moment he would point his brand-new telescope at this bright spot in the sky. He was the first person to point a telescope at the night sky. As the first observation object he had thought up Jupiter. Jupiter had been known since ancient times, certainly even earlier, but he had no evidence of it. But what did people know about Jupiter? Sure, it seemed to be closer than the stars, because it had a slightly different position in the starry sky depending on the place of observation on Earth, and from this parallax it followed that it had to make its orbits in front of the fixed star sky. But what exactly was Jupiter? Soon he would point his telescope at it, and then he would know more.

Stop! Not so fast! A careful scientist would not simply look through the telescope. Before he would have to formulate hypotheses. Without such hypotheses, one ran the risk of subsequently thinking up explanations for the results of his research, and if one was clever enough, one could bend any result to one's liking. It was better to have sorted out beforehand what one could expect and under which assumptions this could be expected. Then the explanation of the findings found in the end would no longer be subject to the suspicion that one had let oneself be guided by the results when forming one's theory. It applied to formulate thus as complete a picture as possible of the conceivable views, which would offer themselves to it directly by the telescope.

He put the telescope from the hand. He took a fresh sheet of paper from a stack. He had not yet quite gotten used to this new invention; he preferred parchment. But it was so expensive, and from his meager lecturer's salary he could not afford so much parchment. For the fair copy he could use parchment. First of all, it was important to collect and record ideas. He took off his gloves and picked up a freshly carved pen in his hand. The inkwell was well filled, and he carefully dipped the tip of the pen into it.

"Opinatio prima" ... yes, what was his first hypothesis? Ah, of course: Jupiter appeared to the naked eye like a dot. And if you looked through the telescope, what would you see? Maybe just a dot. That was certainly a good starting hypothesis. You would not have won anything. Or would they? What would that mean? Maybe Jupiter was too far away to see more than one point in the telescope. Or maybe... it was one point? A luminous point... why not? What did people know about what was orbiting up there? Some people thought that the planets must be spheres, like the Earth. But it was probably best to take as a starting hypothesis what you could see with the naked eye, namely a point. That was safer than immediately sticking to one of the many theories that were in circulation. He quickly wrote down the hypothesis, but was deliberately a bit vague as to why Jupiter would appear as a point in the telescope, because if this result actually came about, it would be so disappointing that he did not expect an extensive discussion of the possible causes. So why bother to think through this ungrateful case in detail, only to be attacked by younger colleagues at this unimportant point?

Fine, but then what was the second most obvious idea? Should he come with the bullet now? That would produce a circular picture. But it was only one of many theories. It was safer to orientate oneself on a systematics of conceivable phenomena, then his field of hypotheses would become more comprehensive, and it would be less likely that he would see something in the telescope that he had not previously suspected. So what could be the second most simple appearance after a point? Certainly a line. Well, there were many possibilities why Jupiter could look like a line. For example, it could be as flat as a discus, and turn its narrow edge towards the earth. Or it could be stock-shaped. Would the line always maintain a fixed orientation? There were several possibilities. It could turn slowly, quickly, or not at all, have preferred directions or not, move systematically, or irregularly. He already saw: Hypothesis two, as simple as it was, required several sub-hypotheses.
 

It was early morning, and daylight was dawning when he was finally finished with Hypothesis Two. He had tried several possibilities to finally wisely limit himself to the smallest possible set of sub-hypotheses, and in his opinion, this included the case that the line always had the same orientation (with the sub-cases "orientation to the North Star", "orthogonal to the orientation on the North Star", and "different orientation"), and that it moved (with the sub-cases "regular" and "irregular"). As for the speed of the motion, he only recorded two possibilities: so fast that it could be seen with the naked eye, or so slow that only observation over several days would reveal the motion. He was tired, because after all, he had just spent a night, a night in which he actually wanted to observe stars. He cleaned the feather, carefully laid out the last sheet of paper written on it to dry, cleared his desk a little more, and then, with a tender and almost melancholy gesture, he put the telescope in its case. There it was stored dust-free, and he would be able to use it tomorrow, if he had written down the remaining hypotheses.

It turned out differently. He also spent the next night formulating hypotheses. It took him quite a long time to formulate his third hypothesis. He rejected several approaches. First, he had thought of combinations of strokes, and wanted, for example, to list the plus sign as the simplest combination as his own sub-hypothesis. But after some time he realized that he had not done himself any favors. For there were so many possibilities to combine strokes, strokes of the same length, of different lengths, in right angles or in crooked angles, with fixed angles or with variable angles, that he could have filled many pages with the sub-hypotheses for the hypothesis "combinations of strokes" alone. Finally, he added only a small sub-hypothesis to hypothesis two, that instead of a single line, there could have been several. No further details, that was better. But how to continue? Then he finally saw the light: it occurred to him that a stroke can be regarded as a dodecagon. Via the equilateral triangle, the square, the regular pentagon and so on, one would approximate the circle. In this way he had found a natural way to incorporate the spherical shape of Jupiter (and the resulting circular appearance), which some of his colleagues had suspected, in a canonical way into his systematics of the conceivable appearances of Jupiter. He preferred this so much rather than jumping directly to the spherical hypothesis. The advantage was obvious: what if Jupiter really did look like an equilateral triangle? He would never have jumped from the sphere hypothesis to the triangle hypothesis, he was sure of that. But since he based his hypothesis building on a systematics of all conceivable manifestations, such an omission could not happen to him, just as he had now begun. This flash of knowledge of course still needed to be worked out. Thus, in addition to the regular polygons, the irregular polygons also had to be considered, and again the temporal behavior of the alignment had to be recorded. It could also happen that the number of corners would change over time. Everything had to be considered. But at the end of the night, the third hypothesis with all possible sub-hypotheses was written down on twelve closely written pages. It was again early in the morning when he let go of his pen, but no trace of regret about the missed starry night clouded his contentment and peace radiating face: too obvious and too important was the progress made in the formation of the hypotheses.
 

In the meantime, many weeks had passed. He had given up the unhealthy habit of writing at night. During the day it was brighter, and that helped him to think. He was also more rested, and so the stream of his thoughts flowed cheerfully in pages after pages of closely written explanations. Once, after three weeks, when he looked at the whole thing again from the front, he was close to despair for a moment. For he had the impression that he had not grasped very important possibilities of how Jupiter could also show itself in the telescope with its systematic approach, or, what was worse, that he could not grasp them at all. That evening he drank plenty of good wine to calm himself down. He slept soundly and calmly until the middle of the night, then he jumped up, was wide awake, and had the solution of how he could expand his system so that there would never be any such omissions again. He wrote for twenty hours straight, then he went back to bed dead tired but happy. He had not eaten or drunk anything that day, and he had not missed anything.

His stroke of genius at that time was very fruitful: the further he progressed with his work, the clearer it became to him that he had indeed laid down a masterly systematics of systematics here, which was invaluable not only for the present case but also for future observations of nature. Because of the importance of this fundamental work, he decided not to write his manuscript on parchment but to take it to a printer. This novel invention would help his work reach the audience it deserved. On the advice of the printer, however, he chose a pseudonym, because after all - as a pure provocation of the church - he had, among other things, built in the hypothesis that it was possible that Jupiter would appear in the telescope as a god hurling lightning in a war chariot. However, he had not guessed that letterpress printing would be such a time-consuming business. Again and again the printer called him in to clarify details of the depiction, and that was a good thing, because it was important to him that his readers would understand the beauty of the systematics of his hypotheses and also recognize in it the overriding principle that would enable them to construct such beautiful hypothesis buildings. Despite the many visits to the printer, he would now have had enough time to point his telescope at Jupiter at night after the compilation of the hypotheses had been completed. But he was a systematic man: first finish one thing, and then, one night, with the freshly printed work at his side, point the telescope at Jupiter. He was eagerly awaiting the completion of his new book.

Then, one day, the printer showed him a font that had just been brought to him. "Sidereus Nuncius", the messenger of the stars, a small, short writing of an unknown professor of mathematics from Padua, reported on observations that this Galileo had made in the night sky with the help of a telescope. Disgusting. Completely without hypotheses, not even pretending to have had any before, let alone publishing them in a separate paper, just as he was about to do himself, simply despicably pointing the telescope at Jupiter. He could have had that too. But such a theory-free approach was beneath his dignity. This Galileo spoke of a "disk" when Jupiter supposedly appeared. He himself had foreseen this round disk as one possibility in his hypothesis building, as the end point of the third hypothesis. That would have been clean: first build such a hypothesis building, and then confirm the finding "disk" and thus hypothesis 3. But to point the telescope at Jupiter and then speak of a disk without any theoretical preliminary work was something anyone could do. Then it was no science. And then Galileo wanted to have seen "moons" - pah, such a typical post hoc explanation. Certainly Galileo had never said a word about moons before. It struck him that he hadn't even thought about the possibility of seeing more than one object. For a moment he doubted his own approach. His systematics of all conceivable appearances had not provided for this case. But the touch of doubt lasted only briefly. Then his face brightened up, and he hurried to the printer and dictated a new page into the typesetting box, to be inserted after page one, with an extension of the first hypothesis, Jupiter's one point, which had come up a bit short anyway: It could also be that Jupiter did not appear as one point but as two, three or more points. Then a few additional thoughts about the temporal behavior of the points, and the page was already full. Almost full, it was just enough for the theorem that this variant of Hypothesis One should be applied in the same sense to all following hypotheses. Thus, the effect observed by this Paduan was elegantly taken from Hypothesis Three using Hypothesis One A). However, the printer also wanted additional money for this additional page. He had no cash in the house at the time, but light-heartedly he gave the printer his new, unused telescope in exchange. His work on the theory of science was much more important than any knowledge he or any other person could think to gain with a shaky telescope at night. It was light during the day and dark at night, he liked the idea. This aptly expressed the intellectual superiority of the theory of science over nocturnal observation. Now he had finally found the title for his new œuvre:

"Jupiter, seen in light"

- Christian Kaernbach -