| +HP+++++++++++++++++++++++++ø SUN.APR,950409 ø++++++++++++++++++++++++++++
  Published in the NYC ACM/SigAPL Newsletter ` BigAPL '

        A memorable article by my great old Professor, Donald T.
Campbell, (who gave me my first paying APL task analyzing
discontinuities in time series) was titled "The Fish Scale Model of
Collective Omniscience." In that spirit, I accept Ed Shaw's invitation
(Big Apple APL, <<95 2>>) to cover the lacunae in his view of APL94,
which are to me what made the trip worth its cost:

        Antwerp is a <<ancient>> party port. Arriving Saturday afternoon,
I consumed much of my 6 hours' jet lead sampling my capacity of the
reported 330 brews, each in its proprietary goblet, with some of the
locals at the Cafe Breughel near the hotel. Costs ranged

          | 40 70  x  0.034 |>| 1.36 2.38 | US$,   <<e |950506>>

which is a deal to a Manhattanite for a beer like Duval that runs $10
per 6-pack around Chicago. I also learned of the local spirit,
"Genever," and that women have to walk past the men's urinal trough to
reach their <<private>> potty.

        Without question, what made the conference worth its cost was
the chance to hear and discuss with Arthur Whitney his "K" language.
It's ironic to cross an ocean to get a glimpse of what someone is
creating and using across town, but when it's a proprietary language
functioning as the heart of an international investment bank, it's more
understandable.

        At his workshop, Arthur handed out a 2-sided, 8-panel, K
Language Summary card, which displays a remarkable breadth and depth of
understanding of the fundamental invariants of programming.

        Within the ken of APLers, K is based on the observation that
multidimensional <</(depth 1)>> APL objects are just special cases of lists
of lists of lists.., where the lengths of all lists at each depth are
equal. Thus the verbs of K are all 1-dimensional, with <<`>>Each (denoted by
`' ) reaching into succeeding dimensions (levels of nesting).
 From the world beyond, Arthur brings the recognition that symbols and
executable expressions must be syntactically denotable. For instance, a
function may be defined by expressions of the form

           avg  :  { ( +/ x ) % # x }
or
           .[  `avg  ;  ()  ;  { ( +/ x ) % # x }  ]

where the form .[ ; ; ] amends a tree--which I won't try to explain
further. << ( Note the use of the tik (`) to mark symbols. I think this is
also the least obtrusive way to distinguish transiterations for e-mail, etc.)
>>

        Arthur's concepts, and particularly the question, "Does 0th axis
suffice?" pervade my own extensions of CoSy:APL nowadays. It certainly
is simpler to construct.

        The last night of the conference, I took a tram to Groen Plaats,
near the area where the women metallically tap the pane of their red-lit
windows as you pass them up, and <<wandered on to>> <<"De Vagant">> at
Reyndersstraat 25, "Het Begrip in Jenever" ("The Understanding of Gin"),
<<to do>> my best to taste their 220 brands. I must have made a dent: I've
enjoyed receiving the restaurant's mailings from the proprietor, Ronald
Ferket, ever since.

        Since the trams did not start running again until dawn (much
less a deprivation than being stuck on the wrong side of the open
bridges of St. Petersburg), I was lucky to bump into Sasha Skomorokhov
and wife (who had courageously upheld the tradition of Evening Seminar
throughout the conference) as they were boarding the tour bus to Paris.
I seized the opportunity to present him a copy of DeVagant's 25 page
menu<< I had kept >> to show him there is more in this world than just
Russia's "Little Water".