K

By 1940 the USA is a facist state with slavery, ghettos, and concentration camps. A British agent is sent in by sub to assassinate elements in the White House who are pressing for an alliance with the Nazi regime of Germany. He uncovers plans for an American Final Solution and a German/American atomic project.

Point of divergence from our timeline: 1929

Why "K" and not "S"? Most baseball historians (and baseball websites I've browsed) seem to agree the answer comes from the very early days of baseball, back in the 1850s.

A sportswriter named Henry Chadwick created a method to keep score during a game, so he'd have something to reference whenever he wrote articles. This scoring system is the basis of modern ones that can be found in scorecards bought at baseball games.

So, why "K"? Chadwick used "S" for "sacrifice". So he used "K", which was the last letter as "struck", a then-common term for a strikeout. Makes sense.

Dwight "Doc" Gooden became known as Doctor K in his heyday as a member of the New York Mets in the '80s. Fans in an area of Shea Stadium that became known as the "K Corner" would hang placards with the letter "K" for every strikeout Gooden notched that game. This tradition has been used for other power pitchers since.

The best songs: the kick ass rockers "Hey Dude", "Knight On The Town", and "Grateful When You're Dead (before it segues into "Jerry Was There"), "303". The best Indian rock songs are "Govinda" (itself the popular chant "govinda jaya jaya") and "Tattva". Kula Shaker sounds like Pink Floyd on a few occasions: "Magic Theatre". But my favorite song is the pop/rock "Start All Over".

All the songs on this album are good. You might get bored with some of the Indian instrumental tracks "Sleeping Jiva", "Temple Of Everlasting Light", but overall the album and its tracks are exceptional.

K /K/ n.

[from kilo-] A kilobyte. Used both as a spoken word and a written suffix (like meg and gig for megabyte and gigabyte). See quantifiers.

--The Jargon File version 4.3.1, ed. ESR, autonoded by rescdsk.

Like its contemporary language J (by APL's creator, Ken Iverson), k restricts itself to the ASCII character set for interoperability (unlike APL, which had a character set tailored to its usage pattern). Because of this, the ``normal'' ASCII punctuation characters are nearly all reserved for some use (much as in J).

However, J and k are following significantly different paths, both from a technical standpoint and a marketing/purpose standpoint. Where J focuses primarily on an academic/pedagogical audience and caters to this with copious documentation and its interesting tacit definitions, k is the basis for a commercial venture rooted at http://kx.com; kdb, built on top of k, claims to be a high-performance relational database system (on the order of Oracle and Sybase) with features making it especially convenient for financial applications.

From a programming language standpoint, k's interesting deviations from J include ragged (that is, non-rectangular) arrays, zero-based indexing, and user-defined functions with any number of arguments (as opposed to a mandated 1 or 2).

Those differences aside, k shares many of J's traits (as well as those of all APL derivatives):

• Many important operations are already built into the language, like < and > (grade up and grade down for sorting), ? (list lookup), and = (group, equivalent to J's self-classify).
• Most builtins operate on vectors as well as they do scalars (if not better); x+y can be the sum of scalars, vectors, matrices, conformable ragged arrays, or even a single scalar increment to any of the above (if one operand is a scalar).
• For all of these reasons, good k programs have a very high ``meaning to length'' ratio, so a k program to accomplish a given task will often be much shorter than an equivalent (for example) C or Java program.

• cut:{1_'(&x=*x)_ x:"\t",x}: ``cut is one drop each where x equals first x cut x is tab join x''...prepend a tab to x, then cut x into pieces everywhere where it has a tab (first x), then drop the first element of each chunk (the tab).
• join:{1_,/"\t",'x}: ``join is one drop join over tab join each x''...prepend a tab to each chunk of x, join them together (accumlating over all chunks), then drop the first element (the extra tab separator).

For more details and examples, see the E2 k programming reference.

From Arthur's http://kx.com/a/k/readme.txt:

k is a high-level general-purpose programming language.
it is used for high performance database and analysis.
syntax is simple infix/prefix: x**y is x times first y
k programs are short.

 "hello world"
 +/x                            / plus OVER x (i.e. sum x)
 1_'(&x=y)_ y:x,y               / 1 drop EACH(where x=y)cut y:x join y
 @[close;stock;;price]'(|;&;:)  / amend close at stock with (high;low;close)

Originally, I was going to use this writeup to describe what I thought were two unrelated meanings of the letter K in mathematics. However, after more research, I realised that the two meanings are in fact deeply and inextricably linked. More on that later; first, here are the two meanings.

Lambda Calculus and Combinators

In the early- to mid-20th century, mathematicians, for the first time, started to analyze the expressiveness and power of maths itself. In order to do this, they needed a model of computation which could then be used to reason about the very language it was expressed in. There were a number of different approaches, Alan Turing with his machines, Marvin Minsky with his machines, Andrei Markov with his algorithms but most importantly to us, Alonzo Church's Lambda calculus. Lambda calculus is basically a convenient way to express and apply functions. It was used to reason about computation where we only had functions available to us in our mathematical vocabulary.

Combinators are used as a set of basic functions in the lambda calculus, taken as given, so that more complex expressions can be written in terms of atomic building blocks. K is one of these combinators. Intuitively it accepts two arguments, ignores the second one and returns the first one. A few more formal descriptions:

(K x) y → x

K = λx. λy. x

    fun K x y = x;

I have reservations giving C-style code due to the lack of type polymorphism.

Although this combinator seems incredibly simple and weedy, when used in conjunction with other combinators, such as S, and function application, it becomes very powerful.

Formal Logic

In propositional logic, K is a standard axiom which a lot of proofs rely on.

K:    A → (B → A)

Where → signifies inference.

This axiom can be shown to be valid from the truth table of the statements.

     A | B | A → (B → A)
    ---+---+-------------
     t | t |     t
     t | f |     t
     f | t |     t
     f | f |     t

Again, this axiom seems obvious and useless. However, when combined with other axioms and Modus Ponens, K becomes an essential part of intuitionistic logic.

The Connection

The similarity between the two Ks became apparent when I was putting the ML code fragment into an interpreter. The type it gave for fun K x y was

    val K = fn : 'a -> 'b -> 'a

The similarity between this and the logic axiom is striking

It turns out that this is no coincidence. A very deep result known as the Curry-Howard Isomorphism establishes direct correspondence between such seeminly diverse fields as second-order logic and polymorphic types, and importantly to us, minimal propositional logic and lambda calculus.

As the ML fragment given above is simply-typed lambda calculus in essence, it should be no surprise that there is such a direct connection between the K axiom and its related combinator's type.

NB, this does not mean that propositional logic is Turing complete, as lambda calculus is. It is the types of lambda expressions that are relevant, not the programmes themselves.

K

, (kay), the eleventh letter of the English alphabet, is nonvocal consonant. The form and sound of the letter K are from the Latin, which used the letter but little except in the early period of the language. It came into the Latin from the Greek, which received it from a Phenician source, the ultimate origin probably being Egyptian,. Etymologically K is most nearly related to c, g, h (which see).

In many words of one syllable k is used after c, as in crack, check, deck, being necessary to exhibit a correct pronunciation in the derivatives, cracked, checked, decked, cracking; since without it, c, before the vowels e and i, would be sounded like s. Formerly, k was added to c in certain words of Latin origin, as in musick, publick, republick; but now it is omitted.

See Guide to Pronunciation , §§ 240, 178, 179, 185.

© Webster 1913.