Should Empirics Determine the Curriculum?

I agree with Arnold on the importance of statistics, but I'm curious as to how he would rate data mining techniques, such as neural networks, trees and other machine learning methods, compared to statistics.

You need basic calculus (integration, sequences, etc.) to do anything above rudimentary statistics. So if you want to do anything with statistics yourself (rather than just understand when people use the words 'significant at the x% level) you will need basic caculus.

Statistics may also be harder to teach than calculus. To teach stats well, you need a very clear understanding of the link between the mathematical formalism and the real-world situation you are modelling. Not very many people can do this well (fewer than can teach calculus as a pure math class). Kahneman and Tversky showed that even mathematical psychologists fail on fairly simple problems of applying statistics (see "Judgment under Uncertainty"), so I think it would be difficult to find enough people to teach stats well to make a class worthwhile.

Do you know of any data on the relative efficacy of different college courses? My experience is that academics (nearly as much as students) think shoddily about this issue. I commonly here people say "if I hadn't been forced to take this class then I never would have read X, which I loved reading". But if you hadn't been forced to take that class you would've have read something else which might have been even better than X!

For stats teachers, I highly recommend the Electronic Textbook at this web site: http://www.statsoft.com/textbook/stathome.html

Yes. Statistical analysis applied to everything is very important. I took statistics in 1970. It was one of my favorite courses. For the uninitiated, statistical analysis can be an eye-opener concerning the analysis of the efficacy of every paradigm.

It was statistics that provided me the breakthrough that permitted the formulation of Robertson's Law:

No matter the problem, no matter the solution, if it's an exclusively empirical solution applied to the real world, the resulting biproducts of the processes of empirical reason will give rise to problems tenfold that of the original problem.

It is also statistics that will show those who have no health insurance actually live longer than those who do. (There's definitely something nefarious implied there.)

It is also statistics that has demonstrated cell phone users do indeed incur a higher risk of brain cancer. (Don't worry. I'll have long since passed away before I have to look at all those bloated heads walking up and down the street asking, Is that my phone or yours?)

It is statistics that will eventually demonstrate that while the lifespan of the average American has increased over the years, it has reached its peak, and will begin to decline, mostly because statistical analysis has already shown greater indebtedness, longer working hours and a greatly decreasing standard of living due to increasing competition for the illusive ideals Americans seek, freedom, wealth, and respect.

What goes around, America, is generally what comes around.

As a postscript I'd like to add:

The Boston area is the intellectual colostomy bag of an intellectually ill nation.

I know. I went to school in Boston and lived there for twenty years.

You can feel sorry for the horrific depravation of all those Harvard kids. Harvard professors are so high on ego, they walk on clouds to keep from stepping in the ubiquitous dog poop in Cambridge.

Don Robertson, The American Philosopher
Limestone, Maine

An Illustrated Philosophy Primer for Young Readers
Precious Life - Empirical Knowledge
The Grand Unifying Theory & The Theory of Time
http://www.geocities.com/donaldwrobertson/index.html
Art Auctions:
http://www.artbyus.com/auctions.php?a=6&b=4807