The Universe of Discourse
           
Wed, 01 Mar 2006

Addenda to recent articles 200602
Here are some notes on posts from the last month that I couldn't find better places for.

  • Regarding my bad solution to the problem of preventing multiple simultaneous SMTP connections from the same place, Chris Siebenmann suggests that a better strategy is to centralize all SMTP access through a single server that can manage the connections in any convenient way, without IPC, and fork child processes to perform the actual SMTP transactions. I had ended my post with "duh", but this suggestion requires an even bigger "duh", because I am already running such a server and modifying it appropriately would have been even easier than the modification I did make to the SMTP program. Thank you, M. Siebenmann. Duh!

  • Regarding the 3n+1 domain, I should mention first that my use of the word "domain" is incorrect here. A domain, properly speaking, is required to have both addition and multiplication; the 3n+1 system supports only multiplication. Addition doesn't work because (for example) 1+1 is undefined in this system, 2 having been omitted.

    I may discuss this in more detail in a future post.

  • Regarding Perl's accidental s/.../.../ee feature, John Macdonald remarks that he thinks it was first discovered by Randal Schwartz, not Tom Christiansen, as I said. M. Macdonald suggests that M. Schwartz first used it in the form s/.../.../eieio in a "Just Another Perl Hacker" signature, and that M. Christiansen then invented the s/(\$\w+)/$1/ee form as a way to make real use of it.

  • Regarding Robert Hooke's mismeasurement of the frequency of G above middle C, I referred to Benjamin Wardhaugh's suggestion that the error was in the length of the pendulum he used to mention the time. Carl Witty points out that this is unlikely, for two reasons. First, Hooke would have been quite familiar with how to make a pendulum of the correct length to time a one-second interval; indeed, he probably would have had such pendulums sitting around, ready to be used. And second, the period of a pendulum is proportional to the square root of its length, so to get the error of a factor of √2 in the measurement of the frequency of the brass wire, Hooke's pendulum would have had to be twice as long as it should have been.

    In reply, I suggested several possible causes of error:

    1. Perhaps the initial wire was not vibrating at precisely 1 Hz. Synchronization with the 1 Hz pendulum might have been done by eye. Any error in the original frequency would have been multiplied by 136 in the final result.

    2. The halving of the wire might not have been exact.

    3. If the tension in the wire changed during the halving process, the shortened wire would have a frequency different from twice that of the unshortened wire.
    4. The note produced by the one-foot wire might not have been exactly G. it could have varied somewhat from true G without being detected by the musical observers.

    5. G in 1664 wasn't 384 Hz anyway. In fact, I haven't finished finding out just what Hooke meant by it, since pitches weren't fully standardized; I don't know what Hooke intended for the reader to understand from his assertion that it was 272 Hz. See Wikipedia's discussion, for example.

    6. I don't yet know that the second was accurately measured. You need a pendulum that strokes exactly 86,400 times per day. They would have had to calibrate it against sandglasses and such things. How accurate was that calibration?

    7. Even if the second was accurately measured, was it the same second that we use today? I'm not sure. I should be able to find this out by reading Hooke's lectures on gravitation (which I have handy) and seeing what he gives as the acceleration due to the earth's gravity.

    There may be some other possible causes of error that I haven't thought of. Which of these actually contributed, and how much, I do not know.

    M. Witty also wondered if the fact that apparent error in the measurement was almost exactly √2 was a coincidence. I imagine so, but I could easily be wrong.

  • Regarding non-oral reading, I said:

    Someone once told me that some famous scholar, I think perhaps Thomas Aquinas, was the only one of his contemporaries to read non-orally, that they were astonished at how the information would just fly from the book into his mind without his having to read it.
    Ricardo J. B. Signes has confirmed this, except that it wasn't Aquinas. He says that Augustine wrote of Ambrose that "When he read, his eyes travelled over the page and his heart sought the sense, but voice and tongue were silent." Thanks, Ricardo.

  • Regarding John Wilkins' artificial language, I said:

    . . . a certain bishop John Wilkins had invented a language in which the meaning of each word would be immediately apparent from its spelling.

    (I don't have an example handy, so I will make one up. All words that begin with "p" are animals. Words beginning with "pa" are birds, those with "pe" are fish, and so forth. Words beginning with "pel" are fish with fins and scales. Words for fin-fish that live in rivers and streams all begin with "pela". "pelam" is a salmon.)

    I have now obtained a copy of this book, and it uses "salmon" as an example. Wilkins' word for "salmon" is "zana". The first two letters always identify one of forty primary classifications for things; animal words begin with "z", and fish with "za". Each major group is divided into nine subgroups; the third letter identifies which of the nine subgroups the thing is in, with "n" denoting the ninth. The ninth subgroup of fish are "squamous river fish". Each subgroup is then divided into (usually) nine species, and the fourth letter identifies which of the nine species the thing is in with "a" denoting the second. The "squamous river fish" are divided as follows:

            Bigger fish
              Voracious fish
                With loose scales
                  With one fin, near the tail; wide mouths, and sharp teeth (1)
                  With two fins
                    Common to both fresh and salt water (2)
                    Common to fresh water only
                      Spotted (3)
                      Not spotted
                        More round (4)
                        More broad or compressed (5)
                With close, compact scales    (6)
              Not voracious
                Bigger
                  Those that live in standing waters (7)
                  Those that live in running waters
                    Those that are thick and round (8)
                    Those that are broad and deep (9)
                Lesser (10)
            Smallest river fish
              In the lower parts of the water
                With one fin on the back (11)
                With two fins and a broad head (12)
              In the upper parts of the water (13)
    
  • Regarding British assertions that Americans speak of nothing but dollars, John Bodoni writes in with the following quotation from Ayn Rand's book Atlas Shrugged:

    "If you ask me to name the proudest distinction of Americans, I would choose--because it contains all the others--the fact that they were the people who created the phrase 'to make money.' No other language or nation had ever used these words before; men had always thought of wealth as a static quantity--to be seized, begged, inherited, shared, looted or obtained as a favor. Americans were the first to understand that wealth has to be created."

    I looked this up, and I found that it is not true. The OED has citations back to 1472:

    • 1472 R. CALLE in Paston Lett. (1976) II. 356, I truste be Ester to make of money..at the leeste l marke.
    • 1546 O. JOHNSON in H. Ellis Orig. Lett. Eng. Hist. 2nd Ser. II. 175 Besides the monney that I shal make of the said wares.
    • 1583 T. STOCKER tr. Tragicall Hist. Ciuile Warres Lowe Countries II. 64 [They] furnished him with all the money they were able to make.
    • 1588 R. PARKE tr. J. G. de Mendoza Hist. China 45 Then may the husband afterwardes sell his wife for a slave, and make money of her for the dowrie he gaue her.

    I suppose it's possible that the phrase only became common in the United States, but Rand's assertion that "No other nation had ever used these words before" is mistaken.


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