I don't have any particular issue with Westergaard, I just couldn't make it through the book. Perhaps with more more effort I could but I'm lacking motivation due to low expectancy. It was a long time ago that I attempted the book, but If I had to pinpoint why, there are few things I stumbled over:

The biggest problem was that I have poor aural skills. I cannot look at two lines and imagine what they sound like so I have to play them on a piano. Add in more lines and I am quickly overwhelmed.

A second problem was the abstractness of the first half of the book. Working through counterpoint exercises that didn't really sound like music did not hold my attention for very long.

A third problem was the disconnect between the rules I was learning and my intuition. Even though I could do the exercises by following the rules, too often I felt like I was counting spaces rather than improving my understand of how musical lines are formed.

I think that your comparison is very interesting because I would predict that a phrasebook is much more useful than a grammar text for learning a language. The Pimsleur approach, which seems to be a decent way to start to learning a language, is pretty much a phrase book in audio form with some spaced repetition thrown in for good measure. Of course the next step, where the actual learning takes place, is to start trying to communicate with native speakers, but the whole point of Pimsleur is to get you to that point as soon as possible. This important because most people use grammatical rules implicitly rather than explicitly. Certainly grammar texts can be used to improve your proficiency in a language, but I highly doubt that anyone has actually learned a language using one. Without the critical step of communication, there is no mechanism for internalizing the grammatical rules.

(Sorry for taking such a long tangent into language acquisition, I wasn't initially planning on stretching the analogy that far.)

Thanks for your feedback on the Westergaard text. I think many of your problems will be addressed by the material I plan to write at some indefinite point in the future. It's unfortunate that ITT is the only exposition of Westergaardian theory available (and even it is not technically "available", being out of print), because your issues seem to be with the book and not with the theory that the book aims to present.

There is considerable irony in what you say about aural skills, because I consider the development of aural skills -- even at the mo... (read more)

Bad Concepts Repository

by moridinamael 1 min read27th Jun 2013204 comments


We recently established a successful Useful Concepts Repository.  It got me thinking about all the useless or actively harmful concepts I had carried around for in some cases most of my life before seeing them for what they were.  Then it occurred to me that I probably still have some poisonous concepts lurking in my mind, and I thought creating this thread might be one way to discover what they are.

I'll start us off with one simple example:  The Bohr model of the atom as it is taught in school is a dangerous thing to keep in your head for too long.  I graduated from high school believing that it was basically a correct physical representation of atoms.  (And I went to a *good* high school.)  Some may say that the Bohr model serves a useful role as a lie-to-children to bridge understanding to the true physics, but if so, why do so many adults still think atoms look like concentric circular orbits of electrons around a nucleus?  

There's one hallmark of truly bad concepts: they actively work against correct induction.  Thinking in terms of the Bohr model actively prevents you from understanding molecular bonding and, really, everything about how an atom can serve as a functional piece of a real thing like a protein or a diamond.

Bad concepts don't have to be scientific.  Religion is held to be a pretty harmful concept around here.  There are certain political theories which might qualify, except I expect that one man's harmful political concept is another man's core value system, so as usual we should probably stay away from politics.  But I welcome input as fuzzy as common folk advice you receive that turned out to be really costly.