From Lee Sallows:
(Thanks, Lee!)
Science & Math
Outcry
A curious observation by a British ornithologist during World War I:
The Zeppelin raids … were nearly always heralded in this country by the crowing of pheasants, and the sensitiveness of this species to distant sounds was frequently a subject of comment. There seems no reason to suppose that pheasants have keener powers of hearing than men; it appears more probable that these birds are alarmed by the sudden quivering of the trees, on which they happen to be perched, at the time of an explosion … During the first Zeppelin raid in January 1915, pheasants … thirty-five to forty miles from the area over which the Zeppelins flew, shrieked themselves hoarse. In one of the early battles in the North Sea … Gamekeepers on the east coast used to say that they always knew when enemy raids had commenced, ‘for the pheasants call us day and night’.
On the Western Front, a starling learned to imitate the whistle that warned of enemy aeroplanes. One artillery officer wrote, “It was great fun to see everyone diving for cover, and I was nearly deceived myself one day.” A gun commander wrote of an owl, “The beastly bird learnt to imitate the alarm whistle to a nicety; on several occasions he turned me out in pyjamas and, when the crew had manned the gun, gave vent to a decided chuckle.” See Onlookers.
(Joy Damousi, Deborah Tout-Smith, and Bart Ziino, eds., Museums, History and the Intimate Experience of the Great War, 2020.)
The Peirce-Putnam Paradox
Divide line interval AD at point P and separate the halves by a short distance.
What’s happened to point P? Did it become point B or C? It seems wrong to say that it’s neither of these, or that it’s only one of them.
But if the single point P has “become” the two points B and C, how can we say it was a dimensionless object?
(Hilary Putnam, “Peirce’s Continuum,” in Kenneth Laine Ketner, ed., Peirce and Contemporary Thought: Philosophical Inquiries, 1995, via Piotr Łukowski, Paradoxes, 2011.)
Keep Away
A notable adaptation: The forewing tips of the Atlas moth, Attacus atlas, resemble the heads of snakes.
When the moth encounters predators in its native Asian forests, the movement of its wings exaggerates the resemblance.
Fair and Square
From Lee Sallows:
(Thanks, Lee!)
Spuds Illustrated
I just found this visual explication of the potato paradox — if potatoes are 99 percent water by weight, and you start with 100 pounds of potatoes and let them dehydrate until they’re 98 percent water, what’s their new weight?
The surprising answer is 50 pounds. Blue boxes represent water, orange non-water. So to double the share of the non-water portion we have to halve the amount of water.
(I had thought it was the setting that made this so confusing, but it turns out real potatoes are 80 percent water! So it’s not as outlandish as I’d thought.)
Sideways Music
It’s sometimes contended that time is one of four similar dimensions that make up a single manifold that we call spacetime. The four dimensions are orthogonal to one another, and though humans view one of them, time, as distinct from the others in various ways, it’s not intrinsically different.
Philosopher Ned Markosian offers a novel argument against this view: If aesthetic value is an intrinsic feature of an item, and if the four dimensions of spacetime are indeed similar, then rotating an object shouldn’t change its value. Turning a van Gogh painting 90 degrees doesn’t alter its beauty (though we may now have to turn our heads to appreciate it).
But turning a piece of music “out” of time, so that the notes of its melody, for example, occur all at once, changes the aesthetic value of the piece. “Whereas the original series of events had some considerable positive aesthetic value … the resulting series of events has either no aesthetic value or, more likely, negative aesthetic value. … Hence we have a powerful modus tollens argument against The Spacetime Thesis.”
(Ned Markosian, “Sideways Music,” Analysis 80:1 [January 2020], 51-59; and Sean Enda Power, Philosophy of Time: A Contemporary Introduction, 2021.)
Anagram
Corresponding with Leibniz about his method of infinite series in 1677, Isaac Newton wanted to advert to his “fluxional method,” the calculus, without actually revealing it. So he used an unusual expedient — after describing his methods of tangents and handling maxima and minima, he added:
The foundations of these operations is evident enough, in fact; but because I cannot proceed with the explanation of it now, I have preferred to conceal it thus: 6accdae13eff7i3l9n4o4qrr4s8t12ux. On this foundation I have also tried to simplify the theories which concern the squaring of curves, and I have arrived at certain general Theorems.
That peculiar string is an inventory of the letters in the phrase that Newton wanted to conceal, Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa, which means “Given an equation involving any number of fluent quantities to find the fluxions, and vice versa.” So “6a” indicates that the Latin phrase contains six instances of the letter A, “cc” means that there are two Cs, and so on. In this way Newton could register his discovery without actually revealing it — the fact that he could present an accurate letter inventory of the fundamental theorem of the calculus proved that he’d established the theorem by that date. (More details here.)
Robert Hooke had used the same resource in 1660 to establish priority for his eponymous law before he was ready to publish it. And Galileo first published his discovery of the phases of Venus as an anagram. The technique today is known as trusted timestamping.
(Thanks, Andy.)
Cause and Effect
When we are praying about the result, say, of a battle or a medical consultation, the thought will often cross our minds that (if only we knew it) the event is already decided one way or the other. I believe this to be no good reason for ceasing our prayers. The event certainly has been decided — in a sense it was decided ‘before all worlds.’ But one of the things taken into account in deciding it, and therefore one of the things that really causes it to happen, may be this very prayer that we are now offering. Thus, shocking as it may sound, I conclude that we can at noon become part causes of an event occurring at ten a.m.
— C.S. Lewis, Miracles, 1947
Lewis adds, “Some scientists would find this easier than popular thought does.” In his 2016 book Time Machine Tales, physicist Paul J. Nahin writes, “It is a view that does find much support in the block universe interpretation of Minkowskian spacetime. Lewis never mentions the block concept by name, but it is clear that he believed in the idea of God being able to see all of reality at once.” See Asking Back.
Eight Flights
From Lee Sallows, a geomagic square with a staircase theme:
(Thanks, Lee!)