The Universe of Discourse

Addenda to recent articles 200801
Here are some notes on posts from the last month that I couldn't find better places for.

• As a result of my research into the Harriet Tubman mural that was demolished in 2002, I learned that it had been repainted last year at 2950 Germantown Avenue.

• A number of readers, including some honest-to-God Italians, wrote in with explanations of Boccaccio's term milliantanove, which was variously translated as "squillions" and "a thousand hundreds".

  The "milli-" part suggests a thousand, as I guessed. And "-anta" is the suffix for multiples of ten, found in "quaranta" = "forty", akin to the "-nty" that survives in the word "twenty". And "nove" is "nine".

  So if we wanted to essay a literal translation, we might try "thousanty-nine". Cormac Ó Cuilleanáin's choice of "squillions" looks quite apt.

• My article about clubbing someone to death with a loaded Uzi neglected an essential technical point. I repeatedly said that

      for my $k (keys %h) {
        if ($k eq $j) {
          f($h{$k})
        }
      }
  

  could be replaced with:

      f($h{$j})
  

  But this is only true if $j actually appears in %h. An accurate translation is:

      f($h{$j}) if exists $h{$j}
  

  I was, of course, aware of this. I left out discussion of this because I thought it would obscure my point to put it in, but I was wrong; the opposite was true.

  I think my original point stands regardless, and I think that even programmers who are unaware of the existence of exists should feel a sense of unease when presented with (or after having written) the long version of the code.

  An example of this error appeared on PerlMonks shortly after I wrote the article.

• Robin Houston provides another example of a nonstandard adjective in mathematics: a quantum group is not a group.

  We then discussed the use of nonstandard adjectives in biology. I observed that there seemed to be a trend to eliminate them, as with "jellyfish" becoming "jelly" and "starfish" becoming "sea star". He pointed out that botanists use a hyphen to distinguish the standard from the nonstandard: a "white fir" is a fir, but a "Douglas-fir" is not a fir; an "Atlas cedar" is a cedar, but a "western redcedar" is not a cedar.

  Several people wrote to discuss the use of "partial" versus "total", particularly when one or the other is implicit. Note that a total order is a special case of a partial order, which is itself a special case of an "order", but this usage is contrary to the way "partial" and "total" are used for functions: just "function" means a total function, not a partial function. And there are clear cases where "partial" is a standard adjective: partial fractions are fractions, partial derivatives are derivatives, and partial differential equations are differential equations.

• Steve Vinoski posted a very interesting solution to my question about how to set Emacs file modes: he suggested that I could define a replacement aput function.

• In my utterly useless review of Robert Graves' novel King Jesus I said "But how many of you have read I, Claudius and Suetonius? Hands? Anyone? Yeah, I didn't think so." But then I got email from James Russell, who said he had indeed read both, and that he knew just what I meant, and, as a result, was going directly to the library to take out King Jesus. And he read the article on Planet Haskell. Wow! I am speechless with delight. Mr. Russell, I love you. From now on, if anyone asks (as they sometimes do) who my target audience is, I will say "It is James Russell."

• A number of people wrote in with examples of "theorems" that were believed proved, and later turned out to be false. I am preparing a longer article about this for next month. Here are some teasers:
  • Cauchy apparently "proved" that if a sum of continuous functions converges pointwise, then the sum is also a continuous function, and this error was widely believed for several years.

  • I just learned of a major screwup by none other than Kurt Gödel concerning the decidability of a certain class of sentences of first-order arithmetic which went undetected for thirty years.

  • Robert Tarjan proved in the 1970s that the time complexity of a certain algorithm for the union-find problem was slightly worse than linear. And several people proved that this could not be improved upon. But Hantao Zhang has a paper submitted to STOC 2008 which, if it survives peer review, shows that that the analysis is wrong, and the algorithm is actually O(n).

    [ Addendum 20160128: Zhang's claim was mistaken, and he retracted the paper. ]

  • Finally, several people, including John Von Neumann, proved that the axioms of arithmetic are consistent. But it was shown later that no such proof is possible.

• A number of people wrote in with explanations of "more than twenty states"; I will try to follow up soon.

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