In 1831, in the appendix to a book on the raising of trees for shipbuilding, Scottish grain merchant Patrick Matthew suggested that, over great expanses of time, “the progeny of the same parents, under great difference of circumstance, might, in several generations, even become distinct species, incapable of co-reproduction.” He’d struck on the central idea of natural selection nearly 30 years before On the Origin of Species:

As the field of existence is limited and pre-occupied, it is only the hardier, more robust, better suited to circumstance individuals, who are able to struggle forward to maturity, these inhabiting only the situations to which they have superior adaptation and greater power of occupancy than any other kind; the weaker, less circumstance-suited, being prematurely destroyed.

On learning of this, Darwin allowed that Matthew “briefly but completely anticipates the theory of Nat. Selection.” In a letter to the Gardeners’ Chronicle, in which Matthew had pointed out his early observation, Darwin wrote, “I freely acknowledge that Mr. Matthew has anticipated by many years the explanation which I have offered of the origin of species, under the name of natural selection.”

But modern observers point out that Matthew didn’t pursue the idea and may not have realized the breadth of its import. Historian of science Peter Bowler writes, “Simple priority is not enough to earn a thinker a place in the history of science: one has to develop the idea and convince others of its value to make a real contribution.” Darwin called Matthew’s note “a complete but not developed anticipation … Anyhow one may be excused in not having discovered the fact in a work on Naval Timber.”

Among electric fish, those that live in freshwater have their generating cells arranged “in series”; in saltwater they appear “in parallel.”

Seawater conducts better than fresh water, so freshwater fish need to generate a high voltage to overcome the resistance of their medium. Their electricity-producing cells are arranged in series.

Marine fish operate at higher currents but lower voltages, so their electrocytes appear in parallel.

William Stokes’ Pictorial Multiplication Table of 1866 promised to teach multiplication facts to a child of average ability in less than half an hour. It did this by representing each digit with an object:

A TREE means 1, from one trunk springs.
A BIRD means 2, it has two wings.
A BOAT is 3, three sails are shown.
ANIMALS 4, four legs they own.
A MAN means 5, five fingers he.
A HOUSE means 6, six windows see.
A CHURCH means 7, not windows less.
A LADY 8, see eight-flounced dress.
A BRIDGE is 9, nine lamps are found.
A BOY means 0, see hoop so round.

Now each fact can be represented by a picture. Here’s the “twice” table:

These are the products of 2 with the first 12 integers, in order. The second box, representing 2 × 2, depicts a dog, which is an ANIMAL with 4 legs, so 2 × 2 is 4. The sixth box, representing 2 × 6, depicts a TREE and a BIRD, so 2 × 6 = 12. And so on. The first box, which covers the fact that 2 × 1 = 2, is omitted because we’ve already mastered the fact that 1 × 2 = 2 (in the “once” table). The 10th and 11th boxes are blank because multiplication by 10 and 11 are considered so easy that no mnemonic is needed.

How can we remember the “twice” table itself? Stokes provides a verbal rhyme that sums it up:

Twice — Dog, Cot, Reader, Nest, and Bird flying;
Giraffe, Inn, Shower, and Camel dying.

In this way a student can master every fact up to 12 × 12 by memorizing 59 simple pictures (and 12 rhymes). How well this worked, and whether the images could be carried accurately in one’s head through a lifetime, is less clear.

On a glass door in the mathematics department at the University of Erlangen–Nürnberg in Germany, this determinant is printed:

Sure enough, X · I – IV · II = II.

Pass through the door and regard it from the other side and you see a different equation:

But this too is true: II = VI · II – X · I.

(Burkard Polster, “Mathemagical Ambigrams,” Proceedings of the Mathematics and Art Conference, 2000.)

Commonly we demonstrate the truth of a proposition by providing proof. But our doubter might then turn his skepticism on the proof in its turn. It seems there are only three ways to reach the end of the business:

• by a circular argument, in which the proof of a proposition presupposes its truth
• by a regressive argument, in which each proof requires a further proof, and so on forever
• by a dogmatic argument, in which precepts are asserted rather than defended

This is called the Münchhausen trilemma after Baron Münchhausen, who tried to lift himself and his horse out of a mire by pulling on his own hair. Any attempt to justify knowledge must start from a position of ignorance. Without firm ground to stand on, it seems, there’s no way to “bootstrap” ourselves into confident assertions.

I know this is early, but I just bumbled into it on the Wikimedia Commons (by user GB fan):

“A Glossary for Research Reports,” by C.D. Graham Jr., from Metal Progress, May 1957:

It has long been known that …	I haven’t bothered to look up the original reference
… of great theoretical and practical importance	… interesting to me
While it has not been possible to provide definite answers to these questions …	The experiments didn’t work out, but I figured I could at least get a publication out of it
The W-Pb system was chosen as especially suitable to show the predicted behaviour …	The fellow in the next lab had some already made up
High-purity … Very high purity … Extremely high purity … Super-purity … Spectroscopically pure …	Composition unknown except for the exaggerated claims of the supplier
A fiducial reference line …	A scratch
Three of the samples were chosen for detailed study …	The results on the others didn’t make sense and were ignored
… accidentally strained during mounting	… dropped on the floor
… handled with extreme care throughout the experiments	… not dropped on the floor
Typical results are shown …	The best results are shown
Although some detail has been lost in reproduction, it is clear from the original micrograph that …	It is impossible to tell from the micrograph
Presumably at longer times …	I didn’t take time to find out
The agreement with the predicted curve is excellent	… fair
… good	… poor
… satisfactory	… doubtful
… fair	… imaginary
… as good as could be expected	… non-existent
These results will be reported at a later date	I might possibly get around to this sometime
The most reliable values are those of Jones	He was a student of mine
It is suggested that … It is believed that … It may be that …	I think
It is generally believed that …	A couple of other guys think so too
It might be argued that …	I have such a good answer to this objection that I shall now raise it
It is clear that much additional work will be required before a complete understanding …	I don’t understand it
Unfortunately, a quantitative theory to account for these effects has not been formulated	Neither does anybody else
Correct within an order of magnitude	Wrong
It is to be hoped that this work will stimulate further work in the field	This paper isn’t very good, but neither are any of the others in this miserable subject
Thanks are due to Joe Glotz for assistance with the experiments and to John Doe for valuable discussions	Glotz did the work and Doe explained what it meant

See Progress.