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.
Science & Math
Frugal
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.
A Magic Globe
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.
Speed Limit
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.
Still Life
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.
Fare Division
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:
- “Soups are a suspension of ingredients in a liquid matrix, whereas salads are a suspension of ingredients in a gaseous matrix.” Thus cereal is soup, and mixed nuts are salad. The transition between phases is continuous: Depending on how finely they’re chopped, the same set of ingredients might produce a chunky salad, a salsa, or a gazpacho. Vanilla ice cream is a “glassy” soup because it doesn’t flow at its serving temperature, but it takes on a more liquid character as it melts.
- A soup or salad becomes a sandwich when it’s enclosed in a carbohydrate. The shape and quality of the carbohydrate must vary according to the substance it encloses, but a proposed general rule is that if you can pick up a dish by the carb and eat it, it’s a 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].)
Dinner for One
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
Synopsis
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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:
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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.
Small World
Reddit user xilefakamot created this in 2020 — a “topologist’s map of the world.”
It depicts international borders and nothing else — the shapes, sizes, and distances between countries are forsaken in order to present the pattern of their borders as efficiently as possible.
“No calculations per se – I sketched out a series of networks showing which countries bordered each other, then gradually smoothed them out to make the map – all done manually.”
(Via MapPorn.)
A Bug’s Life
A bicycle has wheels of different sizes. On the rim of each wheel is a bug. As the bike travels, the bug on the smaller wheel traces a large number of small arches, and the bug on the larger wheel traces a smaller number of large arches. On a given bicycle trip, which bug travels the greater distance through space?
Remarkably, they travel the same distance. The arches are cycloids, and one revolution of a wheel produces one cycloid arch of length 8r, where r is the wheel’s radius. With each revolution the wheel travels a distance 2πr along the road. This means that during a bicycle journey of distance D, the wheel makes D/2πr revolutions, and the attending bug’s total distance through space is (D/2πr)(8r) = 4D/π. The rs have dropped out, which means that the size of the wheels doesn’t matter — the length of each bug’s path through space is 4/π times the length of the bicycle journey.
Via Doug Rohrer’s 1993 book Thought Provokers.
Somewhat similar: How much paint does my carousel need?