Endless Variety

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Image: Wikimedia Commons

In 2022, amateur mathematician David Smith discovered a remarkable tile that will cover an infinite plane but only in a nonperiodic way.

This solves an open problem in mathematics — for years researchers had been seeking an aperiodic monotile, or “einstein,” from the German for “one stone.”

Technically Smith’s tile, known as the “hat,” must be used in combination with its mirror image. But last year his team found another nonperiodic tile, known as the spectre, which is strictly chiral — that is, not only will it tile the plane without its mirror image, but it must be used in that way.

| Science & Math

“Unified Field Theory”

In the beginning there was Aristotle,
And objects at rest tended to remain at rest,
And objects in motion tended to come to rest,
And soon everything was at rest,
And God saw that it was boring.

Then God created Newton,
And objects at rest tended to remain at rest,
But objects in motion tended to remain in motion,
And energy was conserved and momentum was conserved and matter was conserved,
And God saw that it was conservative.

Then God created Einstein,
And everything was relative,
And fast things became short,
And straight things became curved,
And the universe was filled with inertial frames,
And God saw that it was relatively general, but some of it was especially relative.

Then God created Bohr,
And there was the principle,
And the principle was quantum,
And all things were quantified,
But some things were still relative,
And God saw that it was confusing.

Then God was going to create Furgeson,
And Furgeson would have unified,
And he would have fielded a theory,
And all would have been one,
But it was the seventh day,
And God rested,
And objects at rest tend to remain at rest.

— Tim Joseph

| Poems · Science & Math

Accord

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“Everyone believes in the normal law, the experimenters because they imagine that it is a mathematical theorem, and the mathematicians because they think it is an experimental fact.” — Gabriel Lippmann, in a letter to Henri Poincaré

(Thanks, Tom.)

| Science & Math

The Dim Effect

In 2006, German entomologist Jochen-P. Saltin discovered a new species of rhinoceros beetle in Peru, which he dubbed Megaceras briansaltini.

Remarkably, the insect’s horn closely resembles that of Dim, the blue rhinoceros beetle in the Disney film A Bug’s Life, which was released eight years earlier.

“I know of no dynastine head horn that has ever had the shape of the one seen in M. briansaltini, and so its resemblance to a movie character seems like a case of nature mimicking art … or what could be referred to as ‘the Dim Effect,'” wrote entomologist Brett C. Ratcliffe.

“There are numerous examples of art mimicking nature (paintings, sculpture, etc.), but that cannot be the case here, because there had never been a known rhinoceros beetle in nature upon which the creators of Dim could have used as a model for the head horn. In my experience, then, Dim was the first ‘rhinoceros beetle’ to display such a horn, and the discovery of M. briansaltini, a real rhinoceros beetle, came later.”

(Brett C. Ratcliffe, “A Remarkable New Species of Megaceras From Peru [Scarabaeidae: Dynastinae: Oryctini]. The ‘Dim Effect’: Nature Mimicking Art,” The Coleopterists Bulletin 61:3 [2007], 463-467.)

| Oddities · Science & Math

Watercolor

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Absolutely hands down one of the most beautiful places to see from space is the Caribbean. You see an entire rainbow of blue. From the light emerald green to the green-blue to the blue-green to the aquamarine to the slowly increasingly darker shades of blue down to the really deep colors that come with the depths of a really deep ocean. You can see all that at one time from space. It’s very curvy, it’s not harsh geometric lines. It’s swirls and whirls and all kinds of wavy lines. It looks like a piece of modern art.

— Astronaut Sandra Magnus, quoted in Ariel Waldman, What’s It Like in Space?, 2016

| Science & Math

Seasick

Swedish botanist Elias Tillander (1640–1693) was so “harassed by Neptune” during a trip across the Gulf of Bothnia from Stockholm to Turku that he made the return journey overland and changed his name to Til-Landz (“to land”).

Linnaeus named the evergreen plant Tillandsia after him — it cannot tolerate a damp climate.

(From Wilfrid Blunt, Linnaeus: The Compleat Naturalist, 2001.)

| Science & Math

Capacity

In the 1967 Star Trek episode “The Trouble With Tribbles,” a small furry alien species is introduced on board the Enterprise and after three days grows to 1,771,561 individuals. In 2019 University of Leicester physics undergraduate Rosie Hodnett and her colleagues wondered how long it would take for the creatures to fill the whole starship. Using Mr. Spock’s estimate that each tribble produces 10 offspring every 12 hours and assuming that each tribble occupies 3.23 × 10-3 m3 and that the volume of the Enterprise is 5.94 × 106 m3, they found that the ship would reach its limit of 18.4 × 109 tribbles in 4.5 days.

A separate inquiry found that after 5.16 days the accumulated tribbles would be generating enough thermal energy to power the warp drive for 1 second.

(Rosie Hodnett et al., “Tribbling Times,” Journal of Physics Special Topics, Nov. 18, 2019.)

| Entertainment · Science & Math

Catch 22

From reader Chris Smith:

Pick a three-digit number in which all the digits are different. Example: 314.

Now list every possible combination of two digits from the chosen number. In our example, these are 13, 14, 31, 34, 41, and 43.

Divide the sum of these two-digit numbers by the sum of the three digits in the original number, and you’ll always get 22. In our example, (13 + 14 + 31 + 34 + 41 + 43) / (3 + 1 + 4) = 176/8 = 22.

This works because 10a + b, 10a + c, 10b + a, 10b + c, 10c + a, and 10c + b sum to 22a + 22b + 22c = 22(a + b + c), so dividing by a + b + c will always give 22.

(Thanks, Chris.)

06/08/2024 Reader Tom Race points out that essentially the same trick can be performed using the entire number: If you add all six permutations of the original 3 digits, then divide that total by the sum of the 3 digits, the answer is always 222.

For example, using 561:

561 + 516 + 156 + 165 + 651 + 615 = 2664

5 + 6 + 1 = 12

2664 / 12 = 222

“This works because in the first sum each of the three digits (a, b and c) occurs twice in each of the three columns, so the sum is 222a + 222b + 222c = 222(a + b + c).” (Thanks, Tom.)

| Science & Math