Category Archives: work

Black Hole Information Paradox

A Cafe I visit routinely on my morning commute exploded yesterday. We also took pictures of a black hole for the first time. My son used his potty for the first time.

Feeling slightly overwhelmed by the crazy confluence of scales which intersected in my life yesterday. On our weekly date, Shelley asked me about the long term structure and fate of the universe. Hard not to think, absurd as it is, about my own child careening into the future. Is some distant descendant going to look out the window at an earth which can barely support life on account of the increase in solar radiation or suffer some other painful sense of final detachment from the universe?

The owner of the cafe died in the explosion. I talked to him on Monday when I stopped to get a tea on the way to work. Now that impression of a friendly old man framed by the accoutrements of a bustling cafe has taken on a hyper-reality, like the morning light streaming in from the windows as the sun came up over the buildings across the street really was the excitation of a mysterious quantum field. One characterized by nothing more or less than handful of symmetry relations which ascended picoseconds after the universe began and whose reign will still be absolute when the universe is nothing but black holes and the distant, cooling, cosmic horizon.

A Critique of The Programming Language J

I’ve spent around a year now fiddling with and eventually doing real
data analytic work in the The Programming Language J. J is one of
those languages which produces a special enthusiasm from its users and
in this way it is similar to other unusual programming languages like
Forth or Lisp. My peculiar interest in the language was due to no
longer having access to a Matlab license, wanting an array oriented
language to do analysis in, and an attraction to brevity and the point
free programming style, two aspects of programming which J emphasizes.

Sorry, Ken.

Sorry, Ken.

I’ve been moderately happy with it, but after about a year of light
work in the language and then a month of work-in-earnest (writing
interfaces to gnuplot and hive and doing Bayesian inference and
spectral clustering) I now feel I am in a good position to offer a
friendly critique of the language.

First, The Good

J is terse to nearly the point of obscurity. While terseness is not a
particularly valuable property in a general purpose programming
language (that is, one meant for Software Engineering), there is a
case to be made for it in a data analytical language. Much of my work
involves interactive exploration of the structure of data and for that sort
of workflow, being able to quickly try a few different ways of
chopping, slicing or reducing some big pile of data is pretty
handy. That you can also just copy and paste these snippets into some
analysis pipeline in a file somewhere is also nice. In other words,
terseness allows an agile sort of development style.

Much of this terseness is enabled by built in support for tacit
programming. What this means is that certain expressions in J are
interpreted at function level. That is, they denote, given a set of
verbs in a particular arrangement, a new verb, without ever explicitly
mentioning values.

For example, we might want a function which adds up all the maximum
values selected from the rows of an array. In J:


J takes considerable experience to read, particularly in Tacit
style. The above denotes, from RIGHT to LEFT: for each row ("1)
reduce (/) that row using the maximum operation >. and then (@:)
reduce (/) the result using addition (+). In english, this means:
find the max of each row and sum the results.

Note that the meaning of this expression is itself a verb, that is
something which operates on data. We may capture that meaning:

sumMax =: +/@:(>./"1)

Or use it directly:

+/@:(>./"1) ? (10 10 $ 10)

Tacit programming is enabled by a few syntactic rules (the so-called
hooks and forks) and by a bunch of function level operators called
adverbs and conjuctions. (For instance, @: is a conjunction rougly
denoting function composition while the expression +/ % # is a fork,
denoting the average operation. The forkness is that it is three
expressions denoting verbs separated by spaces.

The details obscure the value: its nice to program at function level
and it is nice to have a terse denotation of common operations.

J has one other really nice trick up its sleeve called verb
. Rank itself is not an unusual idea in data analytic languages:
it just refers to the length of the shape of the matrix; that is, its

We might want to say a bit about J’s basic evaluation strategy before
explaining rank, since it makes the origin of the idea more clear. All
verbs in J take one or two arguments on the left and the right. Single
argument verbs are called monads, two argument verbs are called dyads.
Verbs can be either monadic or dyadic in which case we call the
invocation itself monadic or dyadic. Most of J’s built-in operators
are both monadic and dyadic, and often the two meanings are unrelated.

NB. monadic and dyadic invocations of <
4 < 3 NB. evaluates to 0
<3 NB. evalutes to 3, but in a box.

Give that the arguments (usually called x and y respectively) are
often matrices it is natural to think of a verb as some sort of matrix
operator, in which case it has, like any matrix operation, an expected
dimensionality on its two sides. This is sort of what verb rank is
like in J: the verb itself carries along some information about how
its logic operates on its operands. For instance, the built-in verb
-: (called match) compares two things structurally. Naturally, it
applies to its operands as a whole. But we might want to compare two
lists of objects via match, resulting in a list of results. We can
do that by modifying the rank of -:

x -:”(1 1) y

The expression -:”(1 1) denotes a version of match which applies to
the elements of x and y, each treated as a list. Rank in J is roughly
analogous the the use of repmat, permute and reshape in Matlab: we can
use rank annotations to quickly describe how verbs operate on their
operands in hopes of pushing looping down into the C engine, where
it can be executed quickly.

To recap: array orientation, terseness, tacit programming and rank are
the really nice parts of the language.

The Bad and the Ugly

As a programming environment J can be productive and efficient, but it
is not without flaws. Most of these have to do with irregularities in
the syntax and semantics which make the language confusing without
offering additional power. These unusual design choices are
particularly apparent when J is compared to more modern programming

Fixed Verb Arities

As indicated above, J verbs, the nearest cousin to functions or
procedures from other programming languages, have arity 1 or
arity 2. A single symbol may denote expressions of both arity, in
which case context determines which function body is executed.

There are two issues here, at least. The first is that we often want
functions of more than two arguments. In J the approach is to pass
boxed arrays to the verb. There is some syntactic sugar to support
this strategy:

multiArgVerb =: monad define
‘arg1 arg2 arg3’ =. y
NB. do stuff

If a string appears as the left operand of the =. operator, then
simple destructuring occurs. Boxed items are unboxed by this
operation, so we typically see invocations like:

multiArgVerb('a string';10;'another string')

But note that the expression on the right (starting with the open
parentheses) just denotes a boxed array.

This solution is fine, but it does short-circuit J’s notion of verb
rank: we may specify the the rank with which the function operates on
its left or right operand as a whole, but not on the individual
“arguments” of a boxed array. But nothing about the concept of rank
demands that it be restricted to one or two argument functions: rank
entirely relates to how arguments are extracted from array valued
primitive arguments and dealt to the verb body. This idea can be
generalized to functions of arbitrary argument count.

Apart from this, there is the minor gripe that denoting such single
use boxed arrays with ; feels clumsy. Call that the Lisper’s bias:
the best separator is the space character.1

A second, related problem is that you can’t have a
zero argument function either. This isn’t the only language where
this happens (Standard ML and OCaml also have this tradition, though I
think it is weird there too). The problem in J is that it would feel
natural to have such functions and to be able to mention them.

Consider the following definitions:

o1 =: 1&-
o2 =: -&1

(o1 (0 1 2 3 4)); (o2 (0 1 2 3 4))
│1 0 _1 _2 _3│_1 0 1 2 3│

So far so good. Apparently using the & conjunction (called “bond”)
we can partially apply a two-argument verb on either the left or the
right. It is natural to ask what would happen if we bonded twice.


Ok, so it produces a verb.

 3 3 $ ''
  ;((o1&1 (0 1 2 3 4))
  ; (o2&1 (0 1 2 3 4))
  ; (1&o1 (0 1 2 3 4))
  ; (1&o2 (0 1 2 3 4)))

│     │o1          │o2          │
│right│1 0 1 0 1   │1 0 _1 _2 _3│
│left │1 0 _1 _2 _3│_1 0 1 2 3  │

I would describe these results as goofy, if not entirely impossible to
understand (though I challenge the reader to do so). However, none of
them really seem right, in my opinion.

I would argue that one of two possibilities would make some sense.

  1. (1&-)&1 -> 0 (eg, 1-1)
  2. (1&-)&1 -> 0″_ (that is, the constant function returning 0)

That many of these combinations evaluate to o1 or o2 is doubly
confusing because it ignores a value AND because we can denote
constant functions (via the rank conjunction), as in the expression


What this is all about is that J doesn’t handle the idea of a
function very well. Instead of having a single, unified abstraction
representing operations on things, it has a variety of different ideas
that are function-like (verbs, conjuctions, adverbs, hooks, forks,
gerunds) which in a way puts it ahead of a lot of old-timey languages
like Java 7 without first order functions, but ultimately this
handful of disparate techniques fails to acheive the conceptual unity
of first order functions with lexical scope.

Furthermore, I suggest that nothing whatsoever would be lost (except
J‘s interesting historical development) by collapsing these ideas
into the more typical idea of closure capturing functions.

Other Warts

Weird Block Syntax

Getting top-level2 semantics right is hard in any
language. Scheme is famously ambiguous on the subject, but at
least for most practical purposes it is comprehensible. Top-level has
the same syntax and semantics as any other body of code in scheme
(with some restrictions about where define can be evaluated) but in
J neither is the same.

We may write block strings in J like so:

blockString =: 0 : 0 
Everything in here is a block string.       

When the evaluator reads 0:0 it switches to sucking up characters
into a string until it encounters a line with a ) as its first
character. The verb 0:3 does the same except the resulting string is
turned into a verb.

plus =: 3 : 0

However, we can’t nest this syntax, so we can’t define non-tacit
functions inside non-tacit functions. That is, this is illegal:

plus =: 3 : 0
  plusHelper =. 3 : 0
  x plusHelper y

This forces to the programmer to do a lot of lambda lifting
manually, which also forces them to bump into the restrictions on
function arity and their poor interaction with rank behavior, for if
we wish to capture parts of the private environment, we are forced to
pass those parts of the environment in as an argument, forcing us to
give up rank behavior or forcing us to jump up a level to verb


Of course, you can define local functions if you do it tacitly:

plus =: 3 : 0
    plusHelper =. +
    x plusHelper y   

But, even if you are defining a conjunction or an adverb, whence you
are able to “return” a verb, you can’t capture any local functions –
they disappear as soon as execution leaves the conjunction or adverb

That is because J is dynamically scoped, so any capture has to be
handled manually, using things like adverbs, conjunctions, or the good
old fashioned fix f., which inserts values from the current scope
directly into the representation of a function. Essentially all modern
languages use lexical scope, which is basically a rule which says: the
value of a variable is exactly what it looks like from reading the
program. Dynamic scope says: the valuable of the variable is whatever
its most recent binding is.


The straight dope, so to speak, is that J is great for a lot of
reasons (terseness, rank) but also a lot of irregular language
features (adverbs, conjunctions, hooks, forks, etc) which could be
folded all down into regular old functions without harming the
benefits of the language, and simplifying it enormously.

If you don’t believe that regular old first order functions with
lexical scope can get us where we need to go, check out my
tacit-programming libraries in R and Javascript. I
even wrote a complete, if ridiculously slow implementation of J‘s
rank feature, literate-style, here.


1 It bears noting that ; in an expression like (a;b;c)
is not a syntactic element, but a semantic one. That is, it is the
verb called “link” which has the effect of linking its arguments into
a boxed list. It is evaluated like this:


(a;b;c) is nice looking but a little strange: In an expression
(x;y) the effect depends on y is boxed already or not: x is always boxed regardless, but y is boxed only if it wasn’t boxed before.

2 Top level? Top-level is the context where everything
“happens,” if anything happens at all. Tricky things about top-level
are like: can functions refer to functions which are not yet defined,
if you read a program from top to bottom? What about values? Can you
redefine functions, and if so, how do the semantics work? Do functions
which call the redefined function change their behavior, or do they
continue to refer to the old version? What if the calling interface
changes? Can you check types if you imagine that functions might be
redefined at any time? If your language has classes, what about
instances created before a change in the class definition. Believe or
not, Common Lisp tries to let you do this – and its confusing!

On the opposite end of the spectrum are really static languages like
Haskell, wherein type enforcement and purity ensure that the top-level
is only meaningful as a monolith, for the most part.

Prime Industrial Space

In their enthusiasm, they built roads
for which they had no buildings, through forest,
or through meadow. But to drive them, empty
and spacious, is a kind of luxury.
You have passed from, at fifty miles per hour,
reality; prime industrial space.

And into what? At an empty crossroad,
kids have knocked down the “road closed” barriers,
the black circles of their tires crossing,
crisscrossing, looping across that square of
white concrete. With the barriers down
you can drive right through to where the road ends,