The role of mathematics in physics

Submitted by Nicholas C. Darnton (inactive) on Monday, 2/1/2010, at 10:32 AM

A famous article by Eugene Wigner ruminating on the deep connection between mathematics and physics.  Depending on your point of view, this connection is either incredibly profound or completely trivial.  My opinion on this matter fluctuates. 

Read this before questioning me

Submitted by Nicholas C. Darnton (inactive) on Sunday, 12/13/2009, at 5:08 PM
Question authority

Here's a peer-reviewed argument that students should just shut up and listen – preferably in awe – to their professors.  So if you ever get the feeling that you'd like to disagree with me, just remember that it's pedagogically unsound for you to do so.  Your proper attitude "should be one of humility before the science being studied."

This reminds me of the bumper sticker pictured to the right.  When I first saw one of these, I immediately thought "Why?" and for years I thought these were meta-jokes.

Overhyped science

Submitted by Nicholas C. Darnton (inactive) on Tuesday, 1/6/2009, at 9:57 AM
incorrect

The Economist waxes philosophical with an article that asserts that ground-breaking – and wrong – science is more likely to get published in the higher-profile journals (read Science and Nature) than solid but accurate science.  While there is a kernel of truth to this (I've seen some ludicrously overhyped articles in Nature), I'm suspicious because "ground-breaking" means "new", and The Economist reflexively hates all things new.  The Economist is so conservative that it brings life to the adage

a true conservative is someone who hates all change – even change for the better. 

It doesn't surprise me at all that The Economist is attracted to an argument (especially one based on the law of supply and demand) that casts suspicion on newness.

Ignorance of philosophy of science

Submitted by Nicholas C. Darnton (inactive) on Thursday, 10/16/2008, at 5:54 PM

Apparently we practitioners of science are pretty ignorant of the philosophy of science.  I have captured this excerpt because the original is defended by an onerous registration barrier, but the source is longer and has comments and links to related stories:

Philosophy

Graduates [of science teaching programs], from a range of science disciplines and from a variety of universities in Britain and around the world, have a poor grasp of the meaning of simple terms and are unable to provide appropriate definitions of key scientific terminology.

... Given the numerous news stories that require an understanding of how science operates - global warming, cloning, the possible dangers posed by cell phones or the pros and cons of genetically modified crops - understanding the difference between a fully fledged scientific theory that is backed by evidence and accepted by the scientific community and a speculative guess is essential. If we, as scientists, cannot teach children what these words mean in a scientific context, how can we hope to improve scientific literacy generally? If science graduates are confused to begin with, then it is an uphill battle.

Only a few of the graduates had studied any history and philosophy of science, and therein lies the problem. The majority had high quality degrees and some had doctorates in a science discipline, so it wasn't that they were not well qualified in science. It was just that their study of science had been utilitarian, a means to an end with the end being a practicing scientist. They had not been given any grounding or instruction on what makes science 'science.' It was not their fault: history and philosophy of science was an optional part of their degree programs and many could not see the point of it.

The point is this: you must understand your discipline, know its foundations so you are able to defend it from attack by those who seek to hijack science for their own ends, such as climate change deniers, GM modification scaremongers, or creationists. A basic course in the history and philosophy of science should be a compulsory element of an undergraduate degree in any science discipline.

As a card-carrying physicist (well, not literally, because APS doesn't actually issue cards), I can't say I'm particularly surprised, and not everyone is worried about this.  I understand how the terms 'fact', 'theory' and 'hypothesis' are used in normal scientific discourse, but I picked this up without any formal training.  We don't spend any time on philosophy of science in Physics 16 and certainly don't require it for our physics majors at Amherst. 

Aristotle 1 – Newton 0

Submitted by Nicholas C. Darnton (inactive) on Thursday, 10/16/2008, at 5:35 PM
Discouraging newsDiscouraging news about trying to teach physics.  But my students aren't going to end up making "strange explanations for the fact that all objects experience the same acceleration in free fall", right?  Right?

Philosophical implications of Newton's laws

Submitted by Nicholas C. Darnton (inactive) on Thursday, 10/16/2008, at 5:34 PM
Galilean reference frame

I don't have the time or, frankly, the inclination to deal with philosophy of science in Physics 16.  Most of day-to-day physics is pretty practical, and the fact that Newton's laws work (to the precision we require in most applications) is generally justification enough to use them.  However, people with a more highly developed philosophical sensitivity than mine may be concerned that Newton's laws seem to rely on circular reasoning.  You can check out a lightweight summary of the issues involved; if that doesn't dissuade you I suggest you take it up with the Department of Philosophy.