Mach 2

I am just starting chapter 2.  After delving deep into assumptions in the first third of chapter 1, he had some dull discussion of how ideas move from tentative to accepted, and then a historical summary of fluid statics that was interesting for its tidbits in a field that most physicists don't pay much attention to, but was not very deep in its unpacking of assumptions.  It feels to me like Mach wanted to be encyclopedic, and not just give  analytical Commentary on key issues.

Chapter two opens with a a declaration that dynamics (the study of moving objects) began with Galileo.  Aristotle simply isn't worth Mach's time.  It will be interesting to see how this plays out.  His encyclopedic goals seem to be balanced by an editorial perspective on significance.  Also, he is so encyclopedic that he even goes into an early effort of Galileo's (soon discarded) in which he hypothesized that velocity was proportional to distance.  The sheer level of familiarity with primary sources displayed in this work marks Mach as something of a historian as well as a physicist and philosopher.

Perpetual motion Mach-ine

On pages 24-26, Mach lays out Stevinus's argument for how forces on inclined planes work.  The freshman treatment of inclined planes is technical, it teaches important skills, and it is understandable, but it is also as dull as George W. Bush in a grammar class.  Stevinus, on the other hand, proves that if inclined planes worked differently than we know them to work then perpetual motion devices would be possible.  That is a gem of reasoning.

Mach-ing sense

I haven't gotten very far in Mach, but I like something that he said on page 13:  "In fact, we regard a phenomenon as explained when we find in it known simpler phenomena."  That's an important statement of what physicists value in our theories and derivations.  We want to start from as few assumptions as possible, and then show that that small set of assumptions is sufficient to derive the phenomenon of interest.  Mach applies this to the derivations of the law of levers throughout history, from Archimedes to Galileo and others.  He takes them to task by unpacking their derivations and showing that in each one there was a hidden assumption that went farther than the assumptions enumerated at the start.  I admire this effort of Mach's.  Personally, I think I can come up with a derivation of the law of the lever that starts from a few explicitly stated assumptions, but still a list that is (in keeping with Mach's argument) longer than the one assumption stated by Galileo and others.  However, it requires a lot drawing, so I will probably do it by hand, scan it, and post it at some point.

Also, before I post this I need to do an experiment at home with a hanger, string, and ruler.

Next Reading Project: Mach

I don't know how far I'll get with this, but I'm going to attempt to read Ernst Mach's The Science of Mechanics.  Although (according to the introductory preface) Mach was not necessarily a fan of Einstein's general relativity, the questions asked by Mach had an impact on Einstein and many others, so Mach is worth understanding.

Here goes nothing.

Two quick observations

1) I just read Inventing the Flat Earth by Jeffrey Burton Russell.  It's a fairly short book (about 70 pages) but it makes the interesting observation that educated people have known since ancient Greece that the earth is round, and certainly in Columbus's Day people knew that the earth is round.  That knowledge was never lost from the educated classes in the Western world, even in the Middle Ages.  Indeed, the entire system of Aristotelian and Ptolemaic astronomy was built upon concentric spheres, with the earth being the sphere at the center.  Russell claims that the myth that the Church and the educated classes used to believe in a flat earth comes from 19th century critics of religion, who invented the idea that the Medieval Church believed in a flat earth as a way of arguing that the Church was backwards.  (Considering all of the other things that one might use to make such a claim, it is strange that they would reach for fictional claims.)

2) This weekend I had occasion to be reminded of the excellence of my university's programs in business and related fields.  The purpose of these programs is to train people for management in a wide variety of settings and industries.  What is interesting is that my colleagues in business and management programs mostly do not seem to speak of some sort of moral imperative in getting students into their programs, even though their programs are a path to the managerial class.  On the other hand, my colleagues in science and engineering very much see it as a social and ethical mission to get students into science and engineering, even though claims of labor shortages (and hence abundant opportunities) are rather dubious.