[plt-scheme] Re: Why "lambda"?

On Sat, May 30, 2009 at 9:46 PM,  <hendrik at topoi.pooq.com> wrote:
> On Sat, May 30, 2009 at 09:38:49PM -0400, Marco Morazan wrote:
>> Ok, I guess I will chime in at this point. I feel rather uncomfortable
>> with the notion that using alpha and beta are more complex than using
>> A and B. Frankly, we can use two different squiggly lines as far as I
>> am concerned.
>>
>> The simple fact is that the use of a variable is a form
>> of (low-level) abstraction. Who cares if the symbol used for the
>> variable representing the abstraction is latin, greek, russian, or
>> mayan? If you understand the abstraction it does not matter, period.

In my previous life as a linguist, I became convinced that Chomsky and
his followers (and his detractors, for that matter) would often
introduce Greek letters, just to make things seem more technical than
they needed to be. I remember arriving late to a syntax class where
the professor was talking about some ideas from Chomsky's 1986
monograph Barriers. There were two or three very official looking
statements involving Greek letters and the class was looking at
several examples to see how they applied. After watching for about
twenty minutes, I apologized and asked what the definition for one of
the terms was, assuming it had been defined before I got there. The
professor said that, in fact, Chomsky had provided no definition and
needled the rest of the class--mostly undergrads--for not challenging
that fact. I guess that's a case of not seeing the trees for the Greek
letters.

I think the point that a lot of people who devolve into dense notation
seem not to realize is that the point of such notation is to elucidate
the concept under discussion by boiling it down to its essence, not to
make it seem more complicated than it really is.

The problem for many students is that they're not willing to make the
jump from an intuitive understanding of a concept to its formal
statement, and this is just as true in basic algebra as it is in the
study of automata. It's always a balance to include enough formalism
to make one's point clear, but not so much that people who could
benefit from the concepts are turned off by the exposition. (Stephen
Hawking, I think, mentioned in the preface to A Brief History of Time
that his publisher warned him that every equation in the book would
cut the readership in half.)

The problem for many researchers seems to be that they're too willing
to jump to a formalization, before deciding if the concept they're
describing is important enough to deserve such treatment.

Todd