[Smt-talk] Classical Form and Recursion

[Dmitri Tymoczko]

On Apr 16, 2009, at 12:48 AM, Fred Lerdahl wrote:

> The competence-performance issue is not important to me, or  
> generally to practitioners of cognitive science in language or  
> music, except as a marker of the study a mental capacity according  
> to certain simplifying idealizations. The value of the results  
> reveals the usefulness of the idealizations. Dmitri questions the  
> idealizations but offers nothing in return. Meanwhile progress is  
> being made using them.

"The value of the results reveals the usefulness of the  
idealizations" -- if this means "match of theory with experiment  
always proves that a model is correct," it's false.  Science is  
(unfortunately for us!) more difficult than that.

Ptolemeic astronomy explained the motion of the planets using  
epicycles -- circular orbits within circular orbits, all centered  
around the earth.  It fit the data pretty well, but was completely  
wrong.  It held sway for hundreds of years -- during which much  
progress was made on the theory.  Students learned it from their  
teachers without making objections.  The question is whether TPS is  
analogous -- a complicated theory that fits some data reasonably  
well, but is based on incorrect assumptions.  To ask this question is  
not to attack you or cognitive science more generally; it's part of  
the normal give-and-take of science.  (Which nowadays can occur on  
email lists as well as in published articles!)  In fact, it's our  
duty as responsible consumers of science to be tough on theories.

What I think I'm offering is a suggestion for an alternative  
direction: construct a theory that is more realistic about human  
perceptual abilities.  Incorporate Cook's results about long-term  
closure, Huron's about voice denumerability in polyphonic music, the  
7 +/- 2 limits on short term memory, and so on.  Or else, explain in  
a more detailed way how TPS's assumption of complete perceptual  
transparency is consistent with our demonstrated limitations in ear- 
training experiments.  This isn't a full-blown rival theory, to be  
sure, but it is a suggestion about how to start constructing one.

> Dmitri seems to have trouble with two points that are foundational  
> in cognitive science: the distinction between explicit and implicit  
> knowledge, and the amazing complexity of implicit knowledge. Both  
> points are beyond dispute within the field. It would be better to  
> move on to issues that are indeed under investigation--for  
> instance, the structures and principles involved in a capacity's  
> mental representation (my interest), the role of statistical  
> learning (see Huron, "Sweet Anticipation," Oxford, 2006), the  
> different roles of representation and processing and their neural  
> instantiation (Patel), or neuropsychological evidence of what music  
> and language do and do not share (Peretz & Coltheart, 2003).

I recognize that some knowledge is implicit, and it is sometimes  
complex, but this does not mean that every theory that proposes  
complex implicit knowledge is correct.  My worries about TPS arose  
because I sensed a contrast between the idealizations in TPS and  
those in other areas of cognitive science.

We could, if you wanted to, explore the contrast in more detail.   
David Marr proposes various algorithms that explain how we construct  
high-level 3D objects from low-level retinal sense data.  We know  
some such story must be right, because we do experience objects in a  
3D world.  Linguistics proposes rules by which we parse strings of  
sounds to extract the meaning of sentences; we know that some such  
story must be true because we do in fact understand what people say.   
In neither case do these theories propose subconscious computations  
with high-level data that go far beyond the sorts of abilities humans  
can demonstrate in simple tests.

TPS proposes that we calculate "tension" by performing complex  
unconscious calculations with very high-level data -- essentially,  
the musical score.  Unlike the cases mentioned above, there is no a  
priori reason to think that some such story has to be true.  We could  
calculate tension in a more low-level way (based on timbre, loudness,  
dissonance, etc.), or with different kinds of high-level data  
(rhythm, schemas, etc.).  Furthermore, the abilities it attributes to  
us go far beyond what people can typically demonstrate in experiments  
or ear-training tests.  Students have trouble, even in very  
simplified and controlled situations, identifying intervals  
correctly.  But TPS proposes that they do so effortlessly,  
accurately, and at extremely high speed -- constructing on this basis  
elaborate mental representations of musical structure.

Note also that when learning to see and speak, people have multiple  
opportunities to receive feedback that helps them correct their  
mental models.  We move through the world, and this helps us improve  
our abilities at edge-detection and object recognition.  We speak and  
listen to others, and this helps us improve our linguistic  
perceptions.  But many listeners receive no musical training  
whatsoever.  Furthermore, even if they receive training in  
performance, this usually has nothing to do with developing the kinds  
of models postulated in TPS.  (Play this note now!  Nope, that's a  
little sharp!  Whoops, your rhythm is wrong!)  You never hear "your  
model of the basic space has only four levels instead of five!"  (And  
indeed, if we like playing or listening to music, but have the  
"wrong" mental model, it's not obvious what pressure there is to  
change.)  So TPS proposes that all listeners spontaneously converge  
on the same set of complex unconscious high-level mental  
representations, even without any explicit training -- or even  
incentive -- that would help them do so.

These are specific reasons to worry about TPS in particular --  
responding with general facts about science, or cognitive science in  
particular, doesn't really address them.  My one regret about ending  
this discussion here is that I was hoping was to get you to explain  
your particular responses to these kinds of issues.  I suspect that  
you have lots to say about these specific criticisms -- that you've  
thought about them carefully, and have more to offer than simple  
generalities about science or cognitive science.  What I've been  
trying to do, not totally successfully, is get you to share these  
responses.  Maybe some other time ...

DT

PS. For those of you listening in at home, here's a fascinating  
subtext: Fred has perfect pitch and I don't.  So we may have very  
different ideas about what is and is not realistic to assume about  
listeners!

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)
http://music.princeton.edu/~dmitri