In Dante’s Purgatorio, souls are surprised to see that their visitor casts a shadow and thus is not dead:
When they perceiv’d that through my body I
Gave way not for the rays to pass, their song
Straight to a long and hoarse exclaim they chang’d;
And two of them, in guise of messengers,
Ran on to meet us, and inquiring ask’d:
“Of your condition we would gladly learn.”
That’s a bit of a puzzle, note Roberto Casati and Patrick Cavanagh. “To be visible, supernatural entities must reflect light (if they do not emit it). But as a consequence they must be opaque to at least some light, and thus they should cast shadows.”
(Roberto Casati and Patrick Cavanagh, The Visual World of Shadows, 2019. Related: Why do ghosts wear clothes?)
The prime factorization of 255987 is 33 × 19 × 499.
That’s not very interesting. But when this is expressed in binary, it reads:
111110011111110011 = 1111 × 10011 × 111110011
Each side of that equation comprises the same string of digits.
In 1884, zoologist William Hay Caldwell sent a historic cable from Australia to his colleagues at the British Association for the Advancement of Science:
MONOTREMES OVIPAROUS, OVUM MEROBLASTIC
In four words this manages to proclaim that the platypus lays eggs and that the early stages of its embryo formation resemble those seen in birds and reptiles rather than mammals.
In 1917, W.S. Andrews inscribed a sphere with five circles of latitude and six of longitude.
Then he arranged the numbers 1 to 62 on the intersections such that each of the 11 circles bears 12 numbers totaling 378.
We think of light speed as dizzyingly fast, but it’s still disastrously slow given the roomy universe we find ourselves in. NASA astronomer James O’Donoghue designed these videos to illustrate. If we could bend it around Earth, light would orbit the planet in 0.13 seconds:
And it takes only 1.255 seconds to reach the moon:
But it takes fully 3 minutes to reach our neighboring planet Mars at its closest approach:
Light from the sun takes more than 8 minutes to reach Earth. To reach the closest star takes more than 4 years.
The programming language efghij is literally object-oriented — its logic is expressed by arranging ordinary items in meaningful tableaus:
In this example, the tray and the cutting board constitute code blocks. The oblong plate, however, has a clothes peg on it, which expresses a for loop. The fork is a local variable. The fork variable is initialized to 1 within the for loop’s initial-value expression. The sauce with the rubber band indicates that the number of iterations is equal to the function’s argument. The stuff on the cutting board is the loop body. Using a stapler, the fork is multiplied by the sauce and the result assigned to the fork using a drinking glass. A hammer decrements the sauce, which demonstrates that the function’s parameter can be used as a local variable too. Finally, the toilet roll indicates that the return value is the final value of the fork.
That produces a factorial. The program below outputs the phrase “Hello, world!” — it’s just a pillow bearing a piece of paper on which those words are written.
There are four states in which matter can exist: solid, liquid, gas, and plasma. Similarly, in an April Fools’ Day paper in 2022, Harvard’s Madelyn Leembruggen and Caroline Martin proposed that foods can be classified as soup, salad, or sandwich:
Further investigation is needed into some edge cases (e.g., lasagna vs. baked ziti), but in most cases a lot of ground can be covered by just asking “Is this a soup, a salad, or a sandwich?” “Most of the time, the answer you blurt out with the least amount of thought is the most true.”
“Finally, to remove any of the reader’s lingering uncertainty: yes, a hotdog is a sandwich.”
(Madelyn Leembruggen and Caroline Martin, “What’s for Lunch? A Systematic Ordering of Foods in the Soup-Salad-Sandwich Phase Space,” arXiv preprint arXiv:2203.16580 [2022].)
In humans, each eye has a small blind spot corresponding to the point where the optic nerve leaves the retina. Normally this isn’t noticeable because the brain can fill in the gap with information from the other eye. But by closing one eye and positioning the target at the appropriate angle, it’s possible to invoke the gap deliberately.
“When the famous physiological psychologist Karl S. Lashley was forced to endure an irritating dinner guest, he amused himself by bringing his blind spot over the person’s head, neatly decapitating the person.”
— Jearl Walker, The Flying Circus of Physics, 2006
Mazes are designed to be tortuous, so even a published solution can be hard to follow. A “straight-line diagram” dispenses with the windings and converts the essential puzzle in a simple map that’s easy to interpret:
This example summarizes the hedge maze in Barcelona’s Parc del Laberint d’Horta.
The same can be done with any meandering route — many subways have adopted stylized maps that dispense with geography and focus on the order of stops, the most important detail for most commuters.
.PNG){kind=link}
.PNG){kind=link}