The Pythagorean theorem has a reciprocal variant:
In combination with the inverse-square law, this means that identical lamps placed at A and B will produce the same light intensity at C as a single lamp at D.
Inside Out
Science & Math
Misc
- It’s illegal to enter the Houses of Parliament wearing a suit of armor, according to a 1313 statute.
- “All things in moderation” is an immoderate policy.
- If a prime number is made up entirely of 1s (e.g., 11), then the number of its digits is prime.
- The word CARBON is itself made up of element symbols (Ca, Rb, O, N). (Dmitri Borgmann)
- Interior decorator Nicholas Haslam: “All it comes down to is making a setting in which people look prettier.”
07/17/2024 UPDATE: Several readers point out, correctly, that carbon is hardly the only elemental “chemical word” — indeed, some elements can be spelled in multiple ways. I’ve assembled this list from multiple contributions:
ArSeNiC ArSeNIC
AsTaTiNe
BiSmUTh BISmUTh
CArBON CaRbON
CoPPEr COPPEr
IrON
KrYPtON
NeON
OGaNeSSON OGaNEsSON
PHoSPHoRuS PHOSPHoRuS PHOsPHoRuS PHoSPHORus PHOSPHORuS PHOsPHORuS
SiLiCoN SiLiCON SILiCON SILiCoN
SiLvEr SILvEr
TeNNeSSINe TeNNEsSiNe TeNNEsSINe
TiN
XeNON XeNoN
TiN is even a valid compound, titanium nitride.
Of these Borgmann had found arsenic, carbon, iron, neon, phosphorus, silicon, and xenon when he wrote in 1974, “surely the most unusual is CARBON which can be factored into elements not including itself.” But that property wasn’t unique even within his limited list, as can be seen above.
Many thanks to readers Gareth McCaughan, Catalin Voinescu, and Eric Harshbarger for writing in about this.
Unusual Biological Names
- Herpetologist Mark Scherz named three tiny species of Malagasy frog Mini ature, Mini scule, and Mini mum.
- Malacologist Alan Solem named a Fijian land snail Ba humbugi.
- The name of each species in the African spider genus Palindroma is a palindrome: P. aleykyela, P. avonova, P. morogorom, P. obmoimiombo, P. sinis.
- The binomial name of the crowned slaty flycatcher has 15 syllables: Griseotyrannus aurantioatrocristatus.
- Malacologist John Stanisic named an Australian land snail Crikey steveirwini.
- The Australian leafhopper genus Dziwneono, named by entomologist Irena Dworakowska, is Polish for “It is strange.”
In 1977, on receiving a package of insect specimens from a colleague, entomologist Arnold Menke exclaimed, “Aha, a new genus!” His colleague Eric Grissell responded “Ha” doubtfully. Menke was proven right and named the species, an Australian wasp, Aha ha. He ordered a custom registration plate for his car bearing the same phrase. Further odd names.
The Earth-Moon Problem
Suppose that each country on Earth has a colony on the moon and that we want to draw maps on which each nation’s territory receives a consistent color. How many colors would we need?
In 1980 Thom Sulanke showed that we might need as many as nine (above), but it’s possible that a particularly challenging map would require more than that. The problem remains unsolved.
Return Engagement
On Easter Saturday 1921, pharmacologist Otto Loewi dreamed of an experiment that would prove that the transmission of nerve impulses was chemical rather than electrical. He scribbled down the idea and went back to sleep, then discovered the next morning that he couldn’t read the note.
That day, he said, was the longest of his life. Fortunately, the dream returned to him that night, and this time he went immediately to the laboratory. Thirteen years later he received the Nobel Prize for discovering the role of acetylcholine as an endogenous neurotransmitter.
Moment
It is related of the Socratic philosopher Aristippus that, being shipwrecked and cast ashore on the coast of the Rhodians, he observed geometrical figures drawn thereon, and cried out to his companions: ‘Let us be of good cheer, for I see the traces of man.’
— Vitruvius, De architectura
Endless Variety
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.
“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
Accord
“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.)
Cotes’ Theorem
The product of the distances from N equally spaced points on a unit circle to a point M that lies on the x axis at distance x from circle origin O and on a line passing through the first point, A0, on the circle equals 1 – xN.
Discovered by Roger Cotes (1682-1716). Here’s a proof.