Can Wolfram’s Cellular
Automata Capture
the Greased Recursive Piglet of Human Brain Evolution?
(Written to spark debate among my fellow participants of the Woframscience Forums)
PDF VERSION AVAILABLE: http://www.nyu.edu/pages/linguistics/CA/HCF.pdf
Prof. Ray
C. Dougherty
Linguistics
Department
A recent article in Science (The Faculty of
Language: What Is It, Who Has It, and How Did It Evolve) by Mark Hauser, Noam Chomsky, and W. Tecumseh Fitch (HCF) – three scholars
counted among the world’s leading specialists in linguistics, animal
intelligence, and human brain functions and mechanisms – discusses several
computational aspects of human intelligence that are shared between animals and
humans and one uniquely human mental characteristic: recursion. This brief essay aims to douse students of machine
learning, inductive processes, and Cellular Automata (CA) - who lack
familiarity with ideas from linguistics and ethology
– with a recursive bucketful of my thinking about HCF’s
recent thinking about scholarly thinking about thinking in humans and thinking
animals. Recursion can often lead to redundancy and ambiguity in language and
‘nesting’ and ‘repetition’ in Wolfram’s Cellular Automata. Redundancy and
ambiguity are the symptoms (like spots) of an underlying computational
recursive process (like measles).
http://www.sciencemag.org/cgi/reprint/298/5598/1569.pdf
HCF argue that the study of
the faculty of language requires us to field a motley team of researchers.
Their first sentence on the first page is this:
We argue that an understanding of the faculty of
language requires substantial interdisciplinary cooperation. We suggest how
current developments in linguistics can be profitably wedded to work in
evolutionary biology, anthropology, psychology, and neuroscience. (HCF: 1569)
Reflecting on ‘substantial interdisciplinary cooperation’,
I find it odd that Konrad Lorenz and Niko Tinbergen who won the Nobel
Prize in the 1970s for their studies of the role of ‘releasers’ in animal
intelligence are not mentioned in the text or footnotes. This seems unusual
since concepts of ‘constituent structure’ and ‘syntax’ seem to play a crucial
role in their Nobel prize winning work on animal intelligence, and in
particular, in analysis of the innate versus learned aspects of duck, goose,
and wolf languages. Perhaps what’s-his-name with the funny hair
who made phoney Campbell’s soup cans said it
all: We will all be famous for fifteen seconds. Nobel prize
winners, perhaps for seventeen. Then, out of sight, out of mind and out of
recent studies of the minds of humans, animals, and Martians.
More to the point for enthusiasts of Wolfram’s
Cellular Automata and Crutchfield’s views of Inductive Emergent Machines (or
whatever the system currently is called), this Science paper opens up a window on human brain mechanisms,
functions, and data structures into which formal computational theory can shine
a light. I feel rather strongly that Crutchfield’s definitions and
formalizations of problems of learning machines remain unsurpassed among
current proposals, but I think statistics offers no solution to the problems
posed by HCF but simply uses a ‘lossy algorithm’ to
restate a complex problem in a new notation. Quite possibly the solutions to
problems posed by Crutchfield’s learning machines should be sought in the
computational ‘processing’ formulations of Wolfram’s cellular automata. Using
such a system, we could not only describe, but even partially explain why
‘minds’ and ‘brains’ work as they do to churn through perceptions to distill
knowledge and ferment the whole to yield a yogurt of insight flavored with
chunks of understanding. Such figurative speaking, I hope to show, can achieve
a concrete realization in the systems of Wolfram and Crutchfield. Such
computational systems would provide the underpinnings of the notions of
‘complexity’, ‘recursion’, and so on which spill out of the Science paper through various leaks in
logic and design and here and there by intention of the authors.
Hauser & Co. hold that
the definitive difference between humans and ‘animals’ derives from the fact
that the human mental apparatus utilizes ‘recursion’ but ‘animals’ do not. BUT!
To understand this, we must grasp ‘recursion’, a well-oiled pig that has been
wrestled to the ground by able mathematicians, cyberneticists, and
computationally inclined folk only squirm free of sloppy notations and suddenly
to pop from our definitional grasp – owing to lack of formalisms generally –
and bolt free. According to Chomsky, Humboldt in the 1800s merely grabbed the
fleet pig by the tail, but as Chomsky acknowledges in somewhat different words
than ours, Humboldt was the first to grab the oinker at all. Alas, slipping
though the fingers of the elderly German scholar, it lived to oink on and taunt
future generations who sought to understand how humans could make infinite use
of finite means.
The recursive pig grunts in three distinct recursive
dialects, only distinguishable in large sentences: The least complex dialect
offers: (oink oink oink oink oink), the normal dialect
offers: (((((oink) oink) oink) oink) oink) or (oink (oink (oink (oink
(oink))))); and rumors abound that the recursive pig could say (oinka (oinkb
(oink) oinkb) oinka),
but in fact this ‘self-embedded nesting’ squeal is never heard. In a very
strange argument, sort of like the dog that didn’t bark (perhaps because the
dog was really a cat, or a finite state grammar), the fact that center embedded
recursion never occurs in any human language provides proof that the structure
(and computational capacity) exists in all languages but is not used by any
speaker. Loosely speaking, Chomsky says this self-embedded recursion remains a
grammatical utterance for the recursive piglet, but is not used by the pig.
Others, like me, think that human language structures are defined by a finite
state grammar running on a rather simple push down storage machine with a fixed
(small) number of registers, some of which are content addressable – hence
center-embeddings are all but impossible to process except using registers.
This is a subject for a later essay, but anyone interested can e-mail me and
get an earful. See some figures illustrating ‘recursion’ in Chomsky’s grammar
in PROLOG here:
http://www.nyu.edu/pages/linguistics/f0719w5.html (left and right recursion)
http://www.nyu.edu/pages/linguistics/f0801w5.html (coordinate structure)
http://www.nyu.edu/pages/linguistics/f0802w5.html (subordinate structure)
See
also: f0718w5, f0721w5, f0808w5, f0809w5, and look around.
HCF claim that ‘Despite their
attractive simplicity, such rule systems [finite-state grammars] are inadequate
to capture any human language.’ (HCF: 1577) I strongly disagree. To see an
alternative view, search INTEX on Google. The INTEX
finite state grammar forum is hosted at NYU, administratively by me but contentwise by Max Silberstein. Check also the pages of Cedrick Fairon, who was a post-doc
with me for two years. All such proofs were offered in the 1960s or earlier and
crucially hinged on the assumption that a language is a set. Since this
assumption has been abandoned by HCF (I think), the proofs are no longer
relevant for any research – presumably including that of HCF - that does not
assume a human language is a set. If you understand the mathematics I am
referring to and want to work with me to review and analyze all proofs that
attempt to show that the complexity of a human language exceeds the powers of a
finite-state grammar, e-mail me. Currently this is my highest priority research
project. I particularly need fluent German speakers since self-embedded
recursion takes on a special meaning in languages that can place the verb at
the end of the sentence. Papers by Kuno in the
1960-70 period neatly define the special problems of
verb-final languages. Anyway, enough about me and my projects, on with the
pursuit of the prancing dancing peccary!
Perhaps Wolfram’s computational approach can wrestle
down the recursive pig so we can slice and dice it into hocks and chitlins until we find the origins of its language
capacity, and the dream of Hauser et al, the very source of the recursively
echoing oink – apparently the current Holy Grail of brain science. My belief is
that a combination of the ‘problem statements’ and the definitions of
Crutchfield about ‘learning machines’ reanalyzed into the computational CA
formalisms of Wolfram will offer a conceptual grasp of ‘recursion’ (as opposed say
to ‘iteration’) that will relate directly to the concept of ‘recursion’ used by
Hauser et. al. in their analysis of the fine
distinction between human and non-human intelligence. The problem statement by
Crutchfield and his group of the dazzling array of difficulties faced by a
‘learning machine’ far surpasses in detail and elegance anything to be found in
previous literature. Although Quine and his chums
write about ‘inductive learning’ in wittier prose, they have significantly less
to say than does Crutchfield whose papers electrify those interested in the
mechanical, logical, mathematical, linguistic, computational, whatever
representation of a ‘learning machine.’ I thoroughly enjoy reading
Crutchfield’s works. Two especially relevant to the Hauser et.
al Science paper and this essay are listed
here. I am quite familiar with Crutchfield’s papers and might be able to point
you to a specific one if you are interested in statistical modeling of learning
machines.
The
Evolution of Emergent Computation: (my
students liked this one)
ftp://ftp.santafe.edu/pub/CompMech/papers/wlboac.pdf
When
Evolution is Revolution – Origins of Innovation:
http://www.santafe.edu/projects/evca/Papers/evrevinno.html
Roughly speaking, one might say that
‘recursion’ introduces a sort of ‘redundancy’ (and ‘ambiguity’, ‘equivocation’,
etc.) into a language’s structural complexity. Crutchfield’s statistical
methods and machines measure the quantity of the redundancy, but not the
quality or type, since the redundancy in the primary data ‘loses’ something as
the statistical algorithms are not ‘loss-less’ compressions or extractions of
redundancy parameters. Wolfram’s Cellular Automata measure (or characterize as
computations) the quality of the redundancy and are ‘loss-less’. What is
crucial for the study of redundancy (recursion) in linguistics is more the quality
than the quantity of redundancy. A child de-multiplexing the adult
language continuously moves through stages at which it reformats the redundancy
structures of the language altering the quality
of the redundancy.
Quite possibly both Wolfram’s ‘discrete’ CA devices
and also Crutchfield’s ‘continuous’ statistical induction strategies could
characterize in a notation the syntactic and semantic properties of a human
language as they are discussed in HCF. Wolfram’s devices might be able to
capture ‘how’ a child acquires a language by passing through stages, but I do
not see how Crutchfield’s devices can do that. Crutchfield’s inductive
procedures would be ‘derailed’ if any process or data structure existed at an
early stage of language acquisition but was abandoned and rejected at a later
stage. For ‘commercial’ purposes, a Crutchfield-type learning machine might do
well, but for studying the unfolding of genetically based maturationally
emergent behavior one sees in human language, the complexity of a CA seems more
appropriate.
The Science
article reads more technically than my humble oblique view. My goal here is not
to eat and digest the meat, rather, I aim to sink chompers into the jugular. Wolfram-ites
should bare their canines and leap to bite into the article when they eye
succulent meaty passages like this morsel, given here totally out of context:
We believe that if explorations into the problem of
language evolution are to progress, we need a clear explication of the
computational requirements for language, the role of evolutionary theory in
testing hypotheses of character evolution, and a research program that will
enable a productive interchange between linguists and biologists. (HCF: 1570)
The total regularity (deductive, deterministic,
algorithmic…) in the irregularities and jumps in behavior that dominate Class
III and
…The evolutionary puzzle, therefore, lies in working
out how we got from there to here, given this apparent discontinuity [in
computational capacity and behavior, RCD]. A second issue revolves around
whether the evolution of language was gradual versus saltational;
this differs from the first issue because a qualitative discontinuity between
extent species could have evolved gradually, involving no discontinuities
during human evolution. Finally, the ‘continuity versus exapation’
issue revolves around the problem of whether human language evolved by gradual
extension of preexisting communication systems, or whether important aspects of
language have been exapted away from their previous
adaptive function (e.g., spatial or numerical reasoning, Machiavellian social
scheming, tool-making). (HCF: 1570)
Let us ignore crucial distinctions
as well as fundamental concepts that underlie the Science formalization in order to get right to the main point. HCF
define the Faculty of Language –
narrow sense (FLN), which ‘is the
abstract linguistic computational system alone, which is independent of the
other systems [of the brain] with which it interacts and interfaces’. (HCF:
1571) They offer a definition of
recursion while discussing FLB. Basically FLN is the recursive
computational component of FLB:
FLB includes a sensory-motor system, a conceptual-intentional system, and [FLN, RCD] the computational mechanisms for recursion, providing the capacity to generate an infinite range of expressions from a finite set of elements. (HCF: 1569)
They give the heart and soul of human mentation and point out the nature of the gulf between
human and animal cogitations:
…We hypothesize that FLN only includes
recursion and is the only uniquely human component of the faculty of language.
(HCF: 1569)
..the core recursive aspect
of FLN currently appears to lack any
analog in animal communication and possibly other domains as well. This point,
therefore, represents the deepest challenge for a comparative evolutionary
approach to language. We believe that investigations of this capacity should
include domains other than communication (e.g., number, social relationships, navigation). (HSF: 1571)
…In contrast, we suggest that FLN – the computational mechanism of recursion – is recently
evolved and unique to our species…(HSF: 1573)
…But only those mechanisms underlying FLN – particularly its capacity for
discrete infinity – are uniquely human. (HSF: 1573)
The above computationally
titillating passages brought a broad, but short lived grin to my face. This
next passage almost caused me to choke on my croissant. If you are easily upset
by people who glibly pass from recursive rewrite rules to rudimentary finite
state processors, be forwarned in order that you do
not choke. ‘Complexity’ and ‘computational capacity’ are less than well-defined
in the Hauser et al. article. To hire two workers each with an IQ of 70 is not
the same as hiring one worker with an IQ of 140. But anyway, let us rush on.
Continuing to quote them out of context, we see they state at some point in
their extremely well-thought out and logically arranged essay:
At present, however, we see little reason to believe
either that FLN can be anatomized
into many independent but interacting traits, each with its own independent
evolutionary history, or that each of these traits could have been strongly
shaped by natural selection given their tenuous connection to communicative
efficiency (the surface or phenotypic function upon which selection presumably
acted). (HSF: 1574)
I can imagine how the recursive processes underlying
human language structures can be atomized into a few (buffers mainly)
independent but interacting computational mechanisms. Students, colleagues, and
fellow travelers could work with me to develop ‘interfaces’ to the NKS
and Mathematica software to permit CA
experiments to see the levels of ‘possible complexity’ in models that implement
finite state grammars – not on universal machines – but on machines with
limited depth, buffer types (structural, content addressable where content can
be ‘meaning’ or ‘sound’), and machine architectures (how do the buffers work to
pass information around). Of great interest to me is Wolfram’s discussion of
how the ‘carry digit’ in a CA adder gets ‘moved’, or perhaps ‘moves by itself’
to the left. This ‘leftward movement’ of a ‘carry digit’ might well bear on the
questions involving the ‘odd’ properties of what linguists call ‘wh-‘ movement. I have not had sufficient time to
examine the problem, and worse, I do not quite understand what Wolfram says
about the issues. The ‘carry digits’ in a multiplier ‘move leftward’ in a far
‘jumpier’ way than they do in an adder, or anyway, so it seems. What would be
‘carry digits’ in a CA that ‘took square roots’? Would they move to the right?
This, to me curious, property of CA that leads to ‘movement’ of complex structures apparently drew Lawrence Gray to use CA to study traffic movement patterns in which cars, and groups of cars, move jerkily as jams form and dissipate for no apparent reason and in response to nothing, although of course, sometimes in response to an accident. While I thoroughly enjoyed Kurzweil’s review of Wolfram’s book (check the web), the most intriguing by far to linguists and cognitive scientists would be that of Gray, which in fact is quite readable.
Gray, Lawrence. (2003) A Mathematician Looks at Wolfram’s
New Kind of Science. Notices of the AMS, Journal of the American
Mathematical Society, Vol. 50, N. 2.: 200-211.
Getting back to the Science article, the
intermediate stages would be finite state grammars with simple push down
storage buffers, and the ‘degree’ of intermediacy would be the order of the
Markov processes and the nature and architecture of the buffers. Experiments
with children and the ill do I not do, preferring to leave such research to the
more skilled, the kinder, and the gentler.
But I think that one can observe the specific forms of ‘garblement’ in the data structures defined by various sorts
of Markov processes aided by an assortment of different memory buffer types
when one studies the ‘errors’ of children and the brain damaged. Such people
produce a different sort of ‘error’ and ‘deviance’ than do adult second
language learners with presumably normal adult Markov processes and the full
array of normal memory buffers, albeit aligned and calibrated to the data
structures of their first language.
Extremely strange to select ‘recursion’ (which smacks
of infinity) as ‘the’ mental property of humans, especially when in any and all
data that have been – or ever can be - observed, the ‘recursive processes’
rarely go much beyond a dozen or so. Twelve nested push down buffers, or
thirteen for Bakers, would permit a dozen levels of ‘recursion’. Since with
pencil and paper one can do giant recursions, one might think that ‘recursion’,
relying on external aids for ‘deep’ cases, reflects performance. Who cares? I
do. I study these things.
So, why do I like Wolfram’s CA?
Mainly because CA enables us to see that perhaps the issue of
‘saltation’ (jumps) verus
‘continuity’ reflect an underlying Class III or IV automaton – and our
lack of understanding of the computational processes of human cognition – more
than any ‘real’ discontinuity in the data. Questions to be looked at include
such exciting cocktail party conversation openers as: (A) What
is recursion in Cellular Automata and how does it differ from iteration? (B) A
personal favorite to kick off a conversation: How do Cellular Automata fare
when characterizing the stages of signal processing capacity for a time domain
multiplexer? (C) What would be the ‘complexity’ of a language that was defined
by a Markov grammar with order 0, 1, 2, 3, 4… and with 0, 1, 2, 3… memory
buffers (to handle center-embeddings)? While such questions might bring stars
to the eyes of those who have Wolfram’s Summer Institute 2004 circled on their
calendar, they do not normally generate interest. I read these questions aloud
and people moved away from me on the subway. Wolfram’s stuff, despite its
‘best-seller’ aura, still has not reached the level of popular banter. But
that, perhaps, is because using existing language structures, people only talk
to people and do not try to lower their levels of recursion in order to permit
discussions with squirrels, rodents, fish, birds, and pigeons – the latter
often approach us squawking iteratively but not recursively, perhaps? Perhaps? Perhaps trying to engage us in non-recursive
discourse structures? To rub elbows and sip suds with CA enthusiasts who keep
conversation churning late into the night by asking questions like the above,
be sure to attend NKS2004. I thoroughly enjoyed the NKS2003 shindig in
http://www.wolframscience.com/conferene/2004
So what do I want to find students
to do? Simple. I am interested in finding students
who, as said in the Science article,
think ‘that an understanding of the faculty of language requires substantial
interdisciplinary cooperation.’ (HSF: 1569) I need folks who can understand how
to ‘formalize’ the ideas of biologists, ethologist,
psychologists, linguists, and so on into the problem statements posed today
mainly by Crutchfield in term of ‘learning machines’, but earlier in terms of
‘self-reproducing machines’ by Weiner, von Neuman,
and so on. When the problems are ‘properly formulated’ –usually in terms of
data structures and
statistics – we will offer possible ‘solutions’ in terms of cellular automata
and computational processes.
Wolfram’s system enables one to formalize the
computational mechanisms that underly the possible
‘continuous’, ‘saltational’, ‘regular’, ‘discontinuous’,
and so on data structures one observes in development of animal and human
intelligence in a single organism
moving from the egg to the grave. A swimming pollywog has three degrees of
freedom of movement, a frog only two –it cannot go straight up. A creepy crawly
caterpillar has two degree of freedom of movement, but when linearly,
deductively, and deterministically metamorphosed into a butterfly by a genetic
Wolfram-like Cellular Automata commands three. The cognitive system of the ‘wog loses a degree as it loses it tail, but the ‘pillar
gains a degree as it sheds its many legs for wings. The sensory system of a
caterpillar involves taste and touch, but a butterfly orients itself by
‘stereoscopic smell’ having a ‘nose’ at the end of each antenna. Such cognitive
saltations – in a single animal and governed by
DNA/RNA (
There seems to be no ‘scale’ of ‘developmental
complexity’ in emergent behavior and structure in a single egg-to-grave animal
generally accepted by all, but if there were, and 0 meant ‘simplest’, perhaps
an amoeba splitting, then as we passed the normal animal kingdom and dealt with
the ‘wog/frog type animals, this metamorphosis
problem might be called a ‘lulu’. Going farther out, we encounter
genetically governed maturationally emergent behavior
in the human passing from toddler to taxpayer, and this would define the multiplex
problem, a ‘lalapalooza’. I wish to develop such a scale of complexity
by incorporating into cognitive study the formalisms from cybernetics,
following the lead of Konrad Lorenz and Niko Tinbergen, and to use the
mathematics of communication theory (Shannon, Weiner) and self-reproducing machines
(von Neuman, Weiner) to study the relation of adult
human language to the semiotic performance data available from children, the
ill, and the leaping and creeping of the animal kingdom. While I agree with
much of Wolfram’s analysis of these people, here and there I think his view
offers only an oblique glimpse of their work. When I read Wolfram’s summaries
of previous researchers that looked at data like his, I often think back to the
letters from the 1600’s in which the Pope discussed Martin Luther. It is a
style that discusses other people and points out that even if they are right
they are wrong, not because they are wrong, but because they cannot be right.
But this is for another time.
For those not in the know and who could not
immediately define any and all terms in this essay, you should run, not walk,
to get: Richard L. Gregory. (latest paper edition). The
To do justice to the ideas presented in this essay one
would have to cast the whole business in the Semiotic and Pragmatic perspective
of C.S. Peirce. An excellent introduction to Peirce,
is the biography by Joseph Brent. 1993. Charles
Sanders Peirce: A Life.
Rumor has it that when Kant was first told about
Newton’s theory of gravity and planetary movements, he responded that Newton’s theory
had nothing to do with the solar system but told us how our minds grapple with
data concerning movements. According to some biographers, Kant first
interpreted the gravitation theory as a theory of human perception and
cognition, not as a theory of ‘things’ and how they ‘really’ moved. I
thoroughly enjoy reading Wolfram’s notes, but disagree here and there a little,
some places a lot, and almost totally with much of the gab on 1125-1127. Quite
possibly Wolfram has a theory of human/animal perception and cognition (the CA
being the primitive operators) and not a Cartesian-like theory of the mechanism
underlying ‘things’ outside us. The recent translation of Descartes’ works by Cottingham et al. from
Cottingham, Stoothoff,
Murdoch, and Kenny. 1991. The Philosophical Writings of Descartes,
Vol. I, II, and III.
Gaukroger, 1995. Descartes: An
intellectual biography.
I also like the Logical Based
language (PROgramming in LOGic,
PROLOG), see http://www.nyu.edu/pages/linguistics/anlcbk.html
and massively parallel processors. I published an introductory book (Natural Language Computing, Erlbaum
Press) showing how to program Chomsky’s grammar into PROLOG. All the software
(free) is on the website. This savvy book, a paragon of excellence that cleanly
merges form and function, neatly defines all technical terms in a witty piquant
sauce full of facts and examples – although some bigoted and biased reviewers
less objective than I am did not see it this way. I concede, however, that some
did have a point. Eons ago, I published a book, quite formal and mathematical
for those that like formalisms, dealing with ‘digital/analog interfacing’:
Stanley, William, Gary Dougherty, and Ray Dougherty. 1984. Digital Signal
Processing. Prentice Hall.
I enjoyed the Wolfram Bash 2003 in
Jenkins,
Lyle. 2001. Biolinguistics: Exploring The
Biology of the Brain.
Putting it all together, I want, or
need, students who can do my work for me program Wolfram’s automata onto
parallel processors - using PROLOG perhaps - in order to solve what once were
called problems in ‘self-reproducing machines’ but slyly pass today under the
moniker ‘computer and machine learning’ or as ‘animal intelligence’. Basically,
I think that a human language presents a multiplex data base (three levels of
multiplexing), the adult is a multiplexer (hence all the redundancy, ambiguity,
and regularity among the irregularities in adult language) and the child
(passing through stages of selective structure blindness) is a time domain
de-multiplexer. Roughly speaking, the 2nd level of multiplexing is
‘coordinate’ structures (iteration) and the 3rd level is
‘subordinate’ structures (recursion). We must differentiate coordinate (He smokes but is not dead yet) recursion
from subordinate (Although he smokes, he
is not dead yet) recursion. In German, with obwohl, the verb jumps to the
end, hence, subordinate, but with aber does
not, and so on into linguistic arcana. According to
the psychologist Luria, there are brain damaged
patients that can understand ‘but’ constructions but not ‘although’
constructions, and that can understand ‘John’s brother’ but not ‘the brother of
John’. One (coordination, iteration, juxtaposition) is ‘less complex’ than the
other (subordination, recursion, embedding).
If my ideas were sketched by a cartoonist, I would have a grinning but terrified well-oiled pig running into a conceptual net (a crisp definition of ‘learning machines’) held taught by Crutchfield, and have Wolfram perched ready to stab and butcher it with a spear that morphs into a knife looking all the while like the behavior of a Class III cellular automata, with Hauser, Chomsky, and Fitch pointing and yelling, ‘Gavagai! Lo, the recursive pig!’ Perhaps Quine looking down from a cloud searchingly at the horizon might say: ‘Was that Noam Chomsky calling “Gavagai!”? Was ‘Gavagai’ used appropriately in context?’
On good days, when my research progresses nicely, I imagine the pig looking more terrified with less of a grin. But on days when even Wolfram’s computational tools for dealing with the incomprehensible seem to leave pockets of incomprehensibility amid the order – giving me the sensation that I have eaten a delicious but sandy oyster – I imagine the piglet with a toothy sneering grin and a less terrified mellower demeanor. Although the greased pig may escape to pose challenges for future generations of computational linguists, I have the feeling that we are much closer to catching the rascal than in the past. If, as Chomsky claims (sort of) Humboldt working alone managed to grab the tail single handedly a century ago, quite possibly the unlikely SWAT team of Hauser, Chomsky, Fitch, Crutchfield, and Wolfram may each be able to seize a leg, enabling one of them to more firmly grasp the tail, or crunchingly grab some other part that might truly impede its motion and hinder its escape.
Me, myself, and I
Personally: I have a BS and MS in
Electrical Engineering, and studied control, guidance, and navigation systems
at the MIT Instrumentation Lab way back then when the I-Lab still was. I
studied cash flow accounting related to bond and currency trading at
There are strong parallels between the work and career
trajectories of Rene Descartes and Wolfram, but that I leave for a future essay
should there be anyone interested in 17th century math, science, and
Descartes’ sweaty unbridled wild passion (for math and science), gossip, and turmoil
in the years when the recursive pig roamed free and undetected merely leaving
footprints and soil in various manuscripts. I have gathered all the dirt and am
ready to share it with you. Let me know if you have any interest in, for
instance, Pascal and the pig: ray.dougherty@nyu.edu.
In any and all e-mail, place the sequence ‘greased-pig’ in the subject line,
and do not use the words ‘increase’ or ‘enlarge’ anywhere in your letter,
although ‘decrease’, ‘diminish’, ‘shrink’ and various cognates, synonyms, and
hyponyms will not be speared by the NYU Spam detector.
I teach graduate and undergraduate
classes on the above topics at New York University Linguistics Department (linguistics@nyu.edu). I wrote this essay
in response to letters I have received from the Wolfram forum from CA
enthusiasts who wanted to know what I did with the automata. I adopted the
style of writing of the essay in response to a lunch I had with some NYU film
students who wondered if anyone could ever make an interesting movie about
anything in linguistics. While I thought cognitive science abounded with
classical ‘hero’ types and one might simply make an encyclopedic documentary or
a Platonic epic, most students thought we would need some ‘external’ – like the
spelling spider in
http://www.nyu.edu/pages/linguistics/CA/G611025.pdf
How to lose friends
and alienate everybody with your, their, our whose? computer
Or
How interdisciplinary
research on brains snags on interdepartmental barriers
Or
An ‘Iceberg’ warning
blast to fellow professors
Over the years I have used computers
in my research and teaching (Fortran, Algol, C, AWK, SED, UNIX, LISP, HTML, CGI, PERL, PROLOG,
and on and on). In all past cases, my students could share usage of a PC or MAC
with other students. After 15 or so minutes, a student programming in LISP for
example, could stop and let another student use the machine, and then later
come back to what they were doing. One might even politely compile C code in
the background while other students glacially ran foreground tasks. PROLOG,
utilizing mainly massive exhaustive searches of data bases, often taxed the
machine, but still one student could share usage with another. If you have
students in a class all trying to run Wolfram’s NKS or Mathematica
to experiment with Cellular Automata, be forewarned that even a ‘simple’ (this
might not be definable in CA research) experiment can run on a fast machine for
an hour – and you cannot interrupt it without loss of everything, and it does
not run in the background. Also, if one runs an experiment overnight to search
out a thousand or so iterations, the file produced ends up in the gigabyte
range, and, AND!: As one should have been able to guess reading the book, the
file is almost guaranteed not to compress using any known algorithm. Hence, a
student almost needs a dedicated machine with an immense hard drive (200 gig) to run this stuff if they are going to do serious
research on the types of questions raised in this essay. And these only scratch
the surface. Write me for some real brain teasers.
Until students get the hang of it
(six weeks for stone cold beginners, two weeks for a LISP programmer), the
student often has to sit in front of the machine for the hour(s) it computes
since at any time the MathKernel may suffer some
injustice and flash you a message that
you must respond to in order to continue.
Although participants from assorted
departments show enthusiasm for studying ‘recursion’ – an apparent focal point
of modern brain studies at Harvard and MIT - the persons in charge of
department computer resources balk at ‘outsiders’ coming in to their department
and hogging all the CPU time and disk space running ‘alien’ software. My own
research and teaching has hit this iceberg
floating between departments that crushes and sinks efforts at
interdisciplinary research: Which department must fund the resources to host
the computer programs? Which department is ready to allocate 2 hours of CPU
time per student per day and dedicate 10 or 20 gigabytes of disc space per
student to students from another
department or school? One could easily have a class of twenty students. Posed
thusly, while rabidly endorsing interdisciplinary research in the abstract,
department chairs will not all raise their hands at once. I completely
understand.
For reasons I agree with totally,
the NKS software in the Linguistics
Department at NYU will be removed from the computers in the syntax-semantics laboratory
Nov. 10, a few weeks before final exams, so that the machines will be usable by
everyone. In many smaller colleges, students would be at a loss – sunk by the
interdepartmental iceberg. Luckily NYU, a major research university, offers
extensive resources. Fortunately the Courant Institute at NYU, and some other
divisions, have immense computer power that our
students can use. NKS research is
massively computer and memory intensive if one begins to investigate questions
involving the relative complexity of various finite state grammars with an
assortment of memory buffer structures.
When you decide to use NKS – and you should must if you
want to begin to grasp the materials in the Hauser, Chomsky, and Fitch paper –
think seriously of asking the dean, that generous soul, for a $2,000 computer.
I can give you specific advice about the particular configuration I use. NYU
provided me with basically a 2.8 gig Pentium 4, 1 gig ram, two built in 80 gig
drives, 10 external 200gig firewire drives, 3 external
USB drives, a dual head graphics card, and two 19 inch monitors connected as
one big screen. The machine was built optimized for video editing, which is not
surprising since CA amounts basically to a visual system. This does a slick
job. If you go external hard drives, go firewire
and not USB. Although they must daisy chain, each becomes basically a
network drive. If students want to run programs and save their work, you should
think of a R/W DVD drive, but this writing process is
s-l-o-w. An external 40-80 gig USB drive runs about $100, and suits most
students very well. Some of my students have bought such devices already for
backups and so on.
Anyway, do not think you will simply load the NKS software on the IBM PC’s in your
department and all will be honky dory. What will happen in your department when
students from other departments and divisions start to use all of your
department’s computer resources? This tiny NKS
program thinks big.
My recommendation for professors who
want to get their feet wet with students but not step on the toes of their
colleagues is this. Buy one or more portables (Toshiba Satellite: 2455-S305,
$1899 list (really 1600) is superb and writes DVDs). One portable will serve
5-8 students if they work on projects in groups. You need no dedicated space,
and further, students can learn to give presentations on the portable. I
recently supervised the installation of 5 of these Toshibas and can heartily
recommend them without any qualification. I personally use Compaq/HP portables
in my own research since I am basically a ‘hardware’ person and admire the
circuit design and board configurations of the Com/HP devices. I have bought
Dell equipment, but beware, it is hard to upgrade Dell
equipment without buying Dell products. You cannot just easily buy a 200gig
Maxtor and plunk it in. I am one of the sorry folks who struggled with the
infamous Dell L800r, a Pentium III 800 gig machine that was condemned by its
designers to have a max limit of a 10 gig hard drive and no possibility of installing
a second hard drive. I now have a $700 door stop. Dell?
Once burned, twice shy.
Currently my Wolfram-stuff classes
only have 3-4 students who seriously
use the software and perhaps another 20-30 that dabble. If I had 20 students
working on finite state grammars, I do not know what machines they could use.
I’m looking into this and would welcome suggestions.
I do not offer any ‘correspondence’
type courses, and never will, although I am happy to help students with their
research over the Internet. There is little doubt in my mind however that one
could develop a graduated web-based soup-to-nuts correspondence course to teach
Wolfram’s CA, and in particular, to show how CA play a role in explicating
theories of mind and language. In such a situation, each student would
presumably have their own computational devices.
NYU Linguistics
Department
NYU
is in the heart of
NYU’s Common
Recently
President John Sexton of
President
Sexton states:
Knowledge
creation requires subjecting ideas to scrutiny and review - and the university
provides the broadest, deepest and most immediate forum for a rich array of
conversations and criticism. Even as it observes and enforces the established
norms of the disciplines, the university by its very nature is a rebuke to
intellectual silos, in its essence insisting on the widest and most rigorous
exploration and testing of ideas. The methods of research integral to one field
carry over to others; what is taken as orthodoxy within one discipline must be
revisited in the light of insights gained elsewhere. So, for example, the
disciplines of philosophy, linguistics and psychology were seed ground for
cognitive science, only to find themselves transformed in turn by it. This is
not unusual; indeed, the general lesson is that when disciplines engage
seriously with each other, the influence typically is reciprocal and the
benefits mutual.
And there is something more, an explicit connection
of knowledge creation to knowledge transmission. The great researcher is in
command of advanced materials and a subject at an advanced level, and that
command is tested and developed in an ability to convey it not only to peers
but to students at all levels. Teaching is not merely a matter of passing on
information; it is the act of engaging students in a field, in a frame of mind,
in a spirit of inquiry and the excitement of the creative endeavor. As
knowledge creators hone their thoughts in teaching students, both advanced and
novice, so also students delight in witnessing knowledge creators at work. And
through their interactions with leading scholars and artists, students at
research universities have direct access to new breakthroughs as they occur —
with some even joining the creative process early in their careers. This is a
defining premise of the research university: the affirmative integration of
knowledge creation and knowledge transmission at all levels in a rich and
synthetic engagement, a multilayered immersion in the world of ideas and the
growth of knowledge. (Sexton: 4)
Following President Sexton’s Common
Enterprise Initiative, we are forming a research group composed of
undergraduate and graduate students, post-doctoral students, alumni, and
faculty from NYU and outside colleges to facilitate the involvement of students
into the processes of creation and transmission of knowledge in the cognitive
sciences. We expect to host the Journal of Psycholinguistic Research in
the Linguistics Department, and students will work to process the submitted
manuscripts, reviewers’ comments, and so on to gain a hands-on understanding of
the professional process of dissemination of information via refereed journals.
We plan events at which current students can interact informally with recent
and less recent alumni to help them become involved in ongoing research and to
facilitate the transition from student to professional, from students of the
professor to peers of the professor, to colleagues engaged in the creation and
dissemination of knowledge. Many alumni of the Linguistics Department are
actively engaged in research and hold major research positions or are
Professors at colleges in the New York Metropolitan area.
Prof. Ray Dougherty (NYU Linguistics), Prof. Robert Rieber (John Jay Psychology), and Prof. Murray Alpert (NYU
Medical) - and alumni too numerous to mention - constitute the current
organizing committee. Initially this triumvirate plus alumni will do the
organizing, but as soon as possible, we hope to have it become totally governed
by alumni from cognitive science departments in the New York Area. A main
mandate of the group is to set up informal situations in which undergraduate
and graduate students can interact one-on-one with alumni who are professionals
in the field the students are contemplating entering. We are currently forming
this group, and if you would like to become an active part, or simply be on our
mailing list, contact rwrieber@yahoo.com
or rcd2@nyu.edu with the phrase ‘students-alumni’
in the subject field.