Thinking
The problem of indoctrination is this: in a modern democratic society, the desired goal of education is that each student develop a set of beliefs that are rationally grounded and open to change when challenged by better-grounded beliefs. In order to develop such students, however, it would seem that they must acquire a belief in rational methods of knowing which must itself be beyond challenge, i.e., held in a manner inconsistent with its own content. Thus, students must be indoctrinated in order not to be indoctrinated: a pedagogical dilemma or paradox.
— Charles James Barr Macmillan, “‘On Certainty’ and Indoctrination,” Synthese 56:3 (September 1983), 363-372
Tat-a-Tat
A visual palindrome by Basile Morin. The image is symmetrical.
The Münchhausen Trilemma
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.
The Math of Christmas
I know this is early, but I just bumbled into it on the Wikimedia Commons (by user GB fan):
Unquote
“In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite!” — Paul Dirac
Translation Table
“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.
In a Word
zetetic
adj. proceeding by inquiry
astucious
adj. subtle; cunning; astute
consectary
adj. following logically
‘Who did you pass on the road?’ the King went on, holding out his hand to the Messenger for some more hay.
‘Nobody,’ said the Messenger.
‘Quite right,’ said the King: ‘this young lady saw him too. So of course Nobody walks slower than you.’
‘I do my best,’ the Messenger said in a sulky tone. ‘I’m sure nobody walks much faster than I do!’
‘He can’t do that,’ said the King, ‘or else he’d have been here first.’
— Lewis Carroll, Through the Looking-Glass, 1871
A Second Try
In a 1977 letter to Nature, University of Malaya geologist N.S. Haile observed the poor quality of an 1818 paper by one P.B. Shelley and presented this improvement:
Twin limb-like basalt columns (‘trunkless legs’) near Wadi Al-Fazar, and their relationship to plate tectonics
Ibn Batuta and P.B. Shelley
In a recent field trip to north Hadhramaut, the first author observed two stone leg-like columns 14.7 m high by 1.8 m in diameter (medium vast, ASTM grade scale for trunkless legs) rising from sandy desert 12.5 km southwest of Wadi Al-Fazar (Grid 474 753). The rock is a tholeiitic basalt (table 1); 45 analyses by neutron activation technique show that it is much the same as any other tholeiitic basalt (table 2). A large boulder 6 m southeast of the columns has been identified as of the ‘shattered visage’ type according to the classification of Pettijohn (1948, page 72). Granulometric analysis of the surrounding sand shows it to be a multimodal leptokurtic slightly positively skewed fine sand with a slight but persistent smell of camel dung. Four hundred and seventy two scanning electron photomicrographs were taken of sand grains and 40 are reproduced here; it is obvious from a glance that the grains have been derived from pre-cambrian anorthosite and have undergone four major glaciations, two subductions, and a prolonged dry spell. One grain shows unique lozenge-shaped impact pits and heart-like etching patterns which prove that it spent some time in upstate New York.
There is no particular reason to suppose that the columns do not mark the site of a former hotspot, mantle plume, triple junction, transform fault, or abduction zone (or perhaps all of these).
Haile added, “I pass this on in the hope that it will be of value to authors in preparing papers for publication.”
Doubly True
Leonard J. Gordon discovered this remarkable cryptarithm in 1990 — each letter corresponds to a digit:
NINE × FOUR + FIVE = FORTYONE
9895 × 3074 + 3865 = 30421095
(Leonard J. Gordon, “Literary Cryptarithmetic by Computer,” Word Ways 23:2 [May 1990], 67-70.)