Slowing Down

When I started to backup files on my primary PC I noticed that this was my first backup since January. I'm becoming very slack; yet another sign of my antiquitiy!

Wittgenstein's Tractatus

I bought a copy of Wittgemnstein's Tractatus Logico Philosophicus more than 60 years ago. From time to time I have dipped into it, puzzling over a few remarks here and there, but I'd never read the complete work until now. A few days ago I started from the beginning and, reading a few pages each day, I finished yesterday.

As the title suggests the Tractatus is primarily concerned with philosophical logic. In it Wittgenstein affirms that all logical truths are truth functional tautologies, so no apparatus of proof is necessary, since the truth of a tautology is in all cases obvious. That thesis is false as are a number of Wittgenstein's remarks about Mathematics.

Among philosophical works the Tractatus is unusual in containing so many statements which are clearly false.

My edition has the German original and an English translation on opposite pages, and would be useful to an English speaker wishing to learn the vocabulary to discuss philosophical logic in German, or to a German speaker wishing to discuss such matters in English. Someone looking for an introduction to the subject matter would be wise to look elsewhere.

Imperial Measure.

Noticing suggestions that we should in some way rehabilitate Imperial Measure, I tried to see how much I could recall about it. After writing this I shall check, but first I want to see what I can remember.

I remember spending a lot of time at the primary school performing complicated calculations with imperial measures. There were definitely sixteen ounces in a pound, 112 pounds in a hundred weight and 20 hundredweights in a ton. There were also stones and quarters. A stone were a multiple of 7 pounds - I'm strongly inclined to think there were 14 pounds in a stone, but am not quite sure. My memory of the quarter is much vaguer. If it was a quarter of a hundredweight it might have been two stones.

There was also the bushel, but that may have been a measure of volume. There was also more than one ounce I think there were Troy ounces and Avoirdupois ounces - I have an idea that gold may have been weighed in smaller ounces than boiled sweets.

Ounces too were subdivided; there were drams, which may or may not have been the same as drachms, and there were also grains. I think that one of the ounces may have been divided into 480 grains. While I was preparing this reminiscence a comment in an Internet forum reminded me of the scruple, which I believe was intermediate beteen a dram and an ounce. Perhaps a quarter of an ounce, perhaps an eighth.

When I was 10 years old, in my last year at the primary school, we were given horrid calculations on the lines of:

"Multiply 7 hundredweight five stones eleven pounds thirteen ounces by 37". We had no calculators in those days. I doubt if any of us ever had to perform such an absurd calculation later in our lives

Lengths had 12 inches in a foot, three feet in a yard, 22 yards in a chain, 10 chains in a furlong and 8 furlongs in a mile. Areas were usualy square inches. feet or miles. I don't recall encountering square chains or square furlings, but an acre, 4840 square yards = 10 square chains = one tenth of a square furlong = 1/640 of a square mile

Then there were volumes. The obvious measure of volume is the cube of the unit of length. Although cubic feet were used from time to time, the common measures of volume were pints and gallons.

Few, if any, enthusiasts for the Imperial system could convert gallons into cubic inches. The most knowledgable could do not better than stall by asking which of the three gallons one had in mind, replacing one question they couldn't answer by three, all of which still baffled them.

A pint was 20 fluid ounces, and the fluid ounce was the volume of an ounce of pure water, at some temperature and pressure that I never heard specified. Hence:

"A pint of clear water weighs a pound and a quarter"

Five fluid ounces also had a special name which I can't recall, though there was something called a gill. Eight pints made a gallon. We weren't taught any other imperial measures of volume, though I think bushels were rather larger than gallons, and minims rather smaller than fluid ounces.

Finally I recall mention of rod, pole and perch. I have an idea they might all be the same and be units of area, but we weren't taught about them at school, so I shan't be sure until I do my check.