Evolution Without Life

Philosopher Mark Bedau points out that, even on a dead planet, the microscopic crystallites that make up clay and mud seem to have the flexibility to adapt and evolve by natural selection:

  • Crystals reproduce in the sense that when they become large enough they cleave and pieces break off, becoming seeds for new crystals. A population of reproducing crystals can become the setting for crystal “evolution.”
  • All crystals have flaws, which are reproduced randomly and can become a source of novel information that gets expressed in “phenotypic” traits such as shape, growth rate, and the conditions that cause cleaving.
  • Each new layer of crystals copies the geometrical arrangement of atoms in the layer below, and defects can be copied in the same way. Grain boundaries and dislocations in one crystal tend to be copied to its “offspring” and subsequent generations. Over time these “mutations” can produce “species” among which nature selects.
  • A crystal’s shape, growth rate, and cleaving conditions all affect the rate at which it proliferates, and crystals with different properties will disperse and diffuse differently, which affects the rate at which they reproduce.

So a population of crystals can exhibit reproduction, variation, heredity, and adaptivity. “What is rather surprising is that, in the process, the planet remains entirely devoid of life. Thus, natural selection can take place in an entirely inorganic setting.”

(Mark Bedau, “Can Biological Teleology Be Naturalized?” Journal of Philosophy 88:11 [November 1991], 647-655. I think A.G. Cairns-Smith originated this idea in Seven Clues to the Origin of Life in 1985, and Richard Dawkins took it up in The Blind Watchmaker the following year.)

Suspense

One April Fool’s Day, when logician Raymond Smullyan was 10 years old, his brother told him, “Today I am going to trick you like you have never been tricked before.”

“Little Raymond waited, and waited, and waited, and nothing happened,” writes Ron Aharoni in Circularity. “To this very day, he is not sure whether his brother tricked him or not.”

The Value of an Education

https://commons.wikimedia.org/wiki/File:Latreille_Pierre_Andr%C3%A9_1762-1833.png

Imprisoned during the French Revolution, zoologist Pierre André Latreille found a beetle on the floor of his dungeon. He pointed out to the prison doctor that it was the rare Necrobia ruficollis, described by Johan Christian Fabricius in 1775. Impressed, the doctor sent it to a local naturalist, who knew Latreille’s work and managed to secure the release of Latreille and a cellmate.

All the other inmates were executed within a month.

Reunited

In 1884, as engineers sawed brownstone out of a quarry near Manchester, Conn., amateur paleontologist Charles Owen realized that one block contained the hind part of a skeleton. He alerted professor Othniel Charles Marsh, who managed to acquire the block, but the corresponding stone containing the skeleton’s fore part had already been carted off for use in a new highway bridge.

In the ensuing years the identity of that bridge was forgotten, but in 1967, as a new highway was being constructed, Yale paleontologist John Ostrom saw an opportunity. He surveyed 60 bridges in the Manchester area and identified one 40-foot span over Hop Creek as the likeliest candidate. Then, in 1969, as that bridge was replaced, he and his colleagues examined more than 300 likely blocks at the site.

They found two 500-pound blocks that showed distinct fossil markings, and in New Haven Ostrom determined that one of the visible bones matched a thigh bone that Marsh had recovered 85 years earlier. The complete skeleton had belonged to a member of Ammosaurus, a genus that roamed the northeastern United States 200 million years ago.

(Thanks, Glenn.)

A Century-Old Ghost

What does this mean?

PMVEB DWXZA XKKHQ RNFMJ VATAD YRJON FGRKD TSVWF TCRWC
RLKRW ZCNBC FCONW FNOEZ QLEJB HUVLY OPFIN ZMHWC RZULG
BGXLA GLZCZ GWXAH RITNW ZCQYR KFWVL CYGZE NQRNI JFEPS
RWCZV TIZAQ LVEYI QVZMO RWQHL CBWZL HBPEF PROVE ZFWGZ
RWLJG RANKZ ECVAW TRLBW URVSP KXWFR DOHAR RSRJJ NFJRT
AXIJU RCRCP EVPGR ORAXA EFIQV QNIRV CNMTE LKHDC RXISG
RGNLE RAFXO VBOBU CUXGT UEVBR ZSZSO RZIHE FVWCN OBPED
ZGRAN IFIZD MFZEZ OVCJS DPRJH HVCRG IPCIF WHUKB NHKTV
IVONS TNADX UNQDY PERRB PNSOR ZCLRE MLZKR YZNMN PJMQB
RMJZL IKEFV CDRRN RHENC TKAXZ ESKDR GZCXD SQFGD CXSTE
ZCZNI GFHGN ESUNR LYKDA AVAVX QYVEQ FMWET ZODJY RMLZJ
QOBQ-

No one knows. Cryptologist Louis Kruh discovered it in the New York Public Library’s rare book room in 1993 among some old material from the U.S. Army Signal School. In 1915 first lieutenant Joseph O. Mauborgne had created what he believed was a more secure cipher than the ones currently in use, and had offered this challenge to see if his colleagues could break it. Kruh found no solution in the archive, and he published it in both The Cryptogram and Cryptologia, inviting their readers to try their hands at it. As far as I know, none succeeded.

Mauborgne described it as a “a simple, single-letter substitution cipher adapted to military use.” He invited the director of the Army Signal School to place it on a bulletin board and allow the officers there to work on it for three months and then to post the solution “to show why the standard method of attacking a substitution cipher fails in this case.” “If any attack upon this cipher is successful, I shall be glad to hear of it,” he wrote.

Kruh, who died in 2010, noted that “it was probably solved or otherwise deemed unsuitable for use because there is no knowledge of a new cipher being adopted by the Army around that time.” If a solution was found, I don’t believe anyone alive today knows what it is.

(Louis Kruh, “A 77-Year-Old Challenge Cipher,” Cryptologia 17:2 [April 1993], 172-174.)

Lightning Strikes

In 1998, the BBC reported that four card players at a whist club in Bucklesham, Suffolk, had each been dealt one suit from a shuffled deck. Hilda Golding found herself holding 13 clubs, Hazel Ruffles held 13 diamonds, and Alison Chivers held 13 hearts (and won, as this was trumps). The dummy hand, face down on the table, held 13 spades.

Though there were 55 people in the village hall at the time, some of whom claimed to have witnessed the event, it’s vastly more likely that this was some misunderstanding or a false report. In 1939 Horace Norton of University College London calculated the odds of such a deal arising naturally to be 1 in 2,235,197,406,895,366,368,301,599,999.

In The Mathematics of Games (2013), John D. Beasley writes, “A typical evening’s bridge comprises perhaps twenty deals, so a once-a-week player must play for over one hundred million years to have an even chance of receiving a thirteen-card suit. If ten million players are active once a week, a hand containing a thirteen-card suit may be expected about once every fifteen years, but it is still extremely unlikely that a genuine deal will produce four such hands.”

(Martin Gardner points out somewhere that anecdotal reports of four perfect hands are strangely more frequent than reports of two perfect hands, which is more likely — though, I guess, less newsworthy.)

(Via Martin Cohen, 101 Philosophy Problems, 2002.)

Love Triangle

https://commons.wikimedia.org/wiki/File:Side_Blotched_Lizard_(d23b9bbd-8831-4be1-973f-d5196a3c16e9).jpg

Male side-blotched lizards compete for mates using a three-sided strategy that resembles a game of rock-paper-scissors. Orange-throated males, the strongest, don’t form strong pair bonds but establish large territories and fight blue-throated males outright for females. The blue-throated males, middle-sized, are less aggressive and tend to pair strongly with individual females. Yellow-throated males, the smallest, have a coloration that resembles that of females; this allows them to approach females in the territories of orange-throated males — though this won’t work with females that have formed strong pair bonds with blue-throated males.

So, broadly speaking, orange beats blue, blue beats yellow, and yellow beats orange, an equilibrium of sorts in which each variety has an advantage over another but not over the third.

Van Schooten’s Theorem

https://commons.wikimedia.org/wiki/File:Satz_von_van_schooten.svg
Image: Wikimedia Commons

A pleasing little theorem by Dutch mathematician Frans van Schooten:

Inscribe equilateral triangle ABC in a circle. Now, from a point P on that circle, the length of the longest of segments PA, PB, PC equals the sum of the lengths of the other two segments (in this example, the length of segment PA equals the sum of the lengths of PB and PC).

Extra-ordinary Magic

From Lee Sallows:

A recent contribution to Futility Closet showed an atypical type of 3×3 geometric magic square in which the 4 pieces occupying each of its nine 2×2 subsquares are able to tile the same rectangle. A different square with the same property is seen in the figure here shown, where the nine tiled rectangles appear at right.

sallows extra-ordinary magic 1

As in the earlier example, the square is to be interpreted as if drawn on a torus, the relations among its peripheral cells then being the same as those that result if the square is surrounded with copies of itself, as seen in the following figure showing four such copies, one in each quadrant:

sallows extra-ordinary magic 2

The figure makes it easier to identify the different 2 × 2 subsquares, exactly nine distinct examples of which can be identified. A brief commentary on the square pointed out that the number of ‘magic’ conditions it satisfies is one greater than the eight conditions demanded by a conventional 3 × 3 magic square. Hence the title of the piece, ‘Extra Magic.’

It was while perusing this diagram that an alternative division of the cells into sets of 4 suggested itself. Instead of 2 × 2 subsquares, consider the four cells defined by a cross that can be centered on any chosen cell. The above figure shows a yellow-shaded example, along with a rectangle tiled by its four associated shapes. It is interesting to note that, as before, there are just nine distinct crosses of this kind to be found in a 3 × 3 square. An obvious question thereby prompted was whether or not a new 3 × 3 magic square could be found based upon such crosses rather than 2×2 subsquares? The answer turned out to be yes, but in the process of scrutinizing an initial specimen I noticed that although it embodied nine cross-based sets of 4 rectangle-tiling pieces, as required, it also included a couple of additional rectangle-tiling sets contained within 2 × 2 subsquares. Clearly the maximum number of such surplus sets would be nine, one for each cross, but could a specimen showing nine cross-based and nine subsquare-based rectangle-tiling sets really exist? I lost no time in seeking an answer.

Regrettably, I was unable to find one. However, the figure below shows a close approach to perfection. It is the same 3 × 3 square with which we started, but now shown alongside no less than eight additional rectangles, each of them tiled with a set of 4 pieces belonging to a cross. Note that the missing rectangle is the one belonging to the non-magic central cross, a show of symmetry that seems appropriate.

sallows extra-ordinary magic 3

So whereas a 3 × 3 magic square, numerical or geometric, satisfies at least 8 separate conditions (3 rows + 3 columns + 2 diagonals), the square here shown satisfies no less than eight more.

(Thanks, Lee.)