Let My Textbooks Go!

There are three problems with prescribed textbooks:

1. A generally low standard: Feyman's anecdote. Has anything changed since the 60's?
   
2. An inflated sticker price: A NY Times article explains how textbook publishers are like big pharma.
   
3. Limited content: So learn how to search the interweb!
   

Textbooks are starting to be given away for free. One free one that I have bought -- because I wanted a dead leaves version -- "one of the great classics of Computer Science" - Paul Graham.

This is free as in free beer, which addresses point 2. Point 1, the generally low standard, might be helped by more collaborative work on the content, taking a leaf out of the free software movement.

We'll see ...

Academic Cross-Training

Cross-training is not a new idea.

In most professional sports cross-training is incorporated into the usual training regime. Although weight-training and swimming are popular there are more exotic options around. Some Australian Rules footballers have even dabbled in ballet.

In cultures that emphasize the development of the individual as well as excellence, breadth and depth are valued. And for those who like the etymological definition of philosophy -- love of learning -- this is a bit of a no-brainer.

Now, if you are focussed on a narrow goal over a wide-ranging journey the diversions of breadth may prove a waste of time. But if the converse holds you will find that there is much to learn by exploring other disciplines. Here's what happened when physicist Richard Feynman ventured into biology.

If two academic disciplines are dealing with similar material at a deep level, chances are that each has something to offer an individual who crosses over from the other side.

Of course forcing everyone to compulsorily study X, usually leads to resentment from a significant proportion of those so conscripted, so when I say should study, I really mean should be encouraged to study.

In terms of excellence, someone should make a list of people who have achieved excellence after switching fields.

* * *

In sports, it is well-known that gymnasts do well after switching to diving and ski-jumping. From this I infer that gymnastics teaches transferable skills.

What are the nominations for the gymnastics of academic disciplines?

Is Law a Branch of Computer Science?

I studied Law as well (as Science) early in my University career before relinquishing it on account of near-terminal boredom during Contracts (the content of the first third of which ironically proved quite useful to me subsequently).

I remember a visiting lecture by a Government draftsperson, whose job it was to draft legislation. He also happened to be blind. Aha, I thought, this is why legislation is so appallingly structured. That was undoubtedly unfair.

Later I came to the view that lawyers should study programming in order to learn how to structure large descriptions about processes and contingencies.

Now, Dave has come along with this brilliant comparison of legal language and programming languages. It is funny because there are several truths in there.

So, perhaps in the 21st century it is time to include a compulsory "programming for lawyers" unit, along with "legal process" as an introductory subject?

This would extend the wider view of Computer Science as a Natural Science, to cultural endeavours such as Law.

Calculus? Which Calculus?

In high school and University I learned Calculus, by which I mean the Differential and Integral Calculus of Newton and Leibniz, and their extensions. I do not think that I really grasped the meaning of a continuous function until I studied metric topology.

I like calculus, I have used it professionally, and it is a glory of the modern age, but I do question the cost/benefit of teaching it to millions (billions?) of children on account of its difficulty.

What makes calculus hard?
I would say the relatively high level of abstraction, and in particular becoming comfortable with with either limits or infinitesimals (hello: non-standard Analysis). These things strain our intuition.

Why is calculus taught in high-school? My guesses:

• It is essential for physics and engineering, and other quantitative fields
  
• It is very beautiful and powerful (but you will not see that at high school)
• It is challenging
  
• It has a filtering effect on students
  
• Tradition

Since it has to be re-taught at College / University, I wonder whether it might be time to start teaching other Calculi in high school, just to mix things up a bit.

Perhaps a progressive school could hold a "calculus bake-off" and try to gauge the suitability and broad benefits of teaching and learning the various calculi?

Which other calculi could be taught?
Some might opt for the predicate calculus (also known as first-order logic), but my vote goes to the lambda calculus, which is fundamental to the theory of computing, and useful in practice. In fact there are computer languages such as Scheme (a Lisp dialect), ML, and Haskell that are essentially souped-up forms of the lambda calculus.

And if high-school sounds a bit late to get started with such an important subject, here is a game designed for eight year-olds that introduces the essential ideas.