Galileo had balls

Prompted by a post by Gene Callahan's recent post, I have thought more about Galileo's thought experiment concerning the two balls (of different mass) tied to each other.  Galileo attempted to prove the inconsistency of Aristotelian physics by arguing that two balls tied to each other are a composite object of greater mass than either, so they must fall faster than either constituent ball, but at the same time the lighter ball has a natural tendency to fall slowly and so it will try to slow down the heavier ball.  Based on this, Galileo concludes that the model is inconsistent and so the balls must accelerate at a mass-independent rate.

This is, of course, wrong in one very important sense:  In a world with air resistance things do fall at mass-dependent rates!  Yet, at the same time, we know that Galileo is right about purely gravitatinal effects.  So, how did he get that right, and was it a coincidence?

Well, first, he got it right about purely gravitational effects because of an embedded assumption of inertia.  He is assuming that the lighter ball is trying to retard the motion of the heavier ball, which means that he's assuming that it's harder to move if you're pulling something.  While that's not a fully Newtonian model, it has a general idea of inertia in there.  If you assume a mass-dependent resistance to changes in motion then adding mass to an object should slow its acceleration, which can (if the dependencies are the same) cancel the mass-dependent pull of the earth.

Galileo got this right, but it was partly a coincidence because these cancellations require that mass enter into inertial and gravitational effects in the same way, so that you can divide it out.  Still, he got the qualitative idea.  I wouldn't recommend acceptance of his theoretical arguments at a journal today, but I give him full marks for groping toward the right physical idea and making a major leap in 17th century physics.

The other reason Galileo got this right is that he made the Aristotelian assumptions explicit while keeping inertia implicit.  When your suppositions lead to a contradiction it means that at least one supposition is wrong.  If you only make one assumption explicit then you'll reject that assumption, rather than concluding that there's a tension between two assumptions and we need more investigation to figure out which is wrong.  Galileo may not have realized to what extent he was invoking an assumption of inertia.  I'd probably need to read Two New Sciences to see how well he understood inertia.

Galileo, Day 1: OK, now it gets good.

On page 63 things get interesting.  Salviati has spent a few pages talking about sun spots.  The purpose of this was that after dozens of pages discussing the notion of a perfect universe or perfect celestial objects of...whatever it was that Aristotle was smoking, Salviati has introduced sun spots as evidence that the heavens are changeable, asymmetric, and altogether imperfect.  Simplicio counters by suggesting that the sun spots are planets that are really, really close to the sun, and Salviati swats down that theory with observational evidence.

Finally, Salviati and Sagredo back Simplicio into a corner, reminding him of Aristotle's insistence that the evidence of the senses should take precedence over eloquent argument.  I have two thoughts on this:
1) It is quite ironic that Aristotle's teachings were treated as dogma by subsequent generations who tried to suppress or disregard evidence of the senses in favor of Aristotle's eloquent arguments.  This reminds me a bit of Hofstadter's final word on Dewey, whose disciples tried to institutionalize anti-institutional teaching methods.

2) If we told our students to trust their senses over even the most seemingly logical argument, we might persuade them that Newtonian mechanics is wrong (and not in the way that relativity and quantum mechanics disagree with Newtonian mechanics).  A great many physicists, from a great many pedagogical schools, have noted that when you grow up in a world with friction, air resistance, and gravity, and where most physical objects have substantial moments of inertia (i.e. they can't be treated as gravity), the abstractions of Newtonian mechanics make precious little sense.  We don't have point objects.  We don't have frictionless surfaces.  We can't really conceive of motion "in the absence of an applied force" because real objects either slow down while moving on the ground if you don't push them, or fall if you let go of them.

Moreover, the known inadequacies of freshman lab equipment once led the great teacher and author David Griffiths to make this statement:

I can explain the conservation of momentum in 15 minutes, but three hours in the lab would only convince an honest student that the law is false.

If the question is what we should do about this in the classroom, the answer is that we should do Newtonian mechanics experiments on air tables with digital timers and photogates.  However, the bigger point here is that many fallacies are rooted in real observations, and it isn't always obvious how un-systematic those observations are.  Short of a really, really good experimental investigation of Newtonian mechanics, one will almost certainly be solving mechanics problems on the basis of logical argument rather than the observations of one's own senses.  Ironic, no?  And that's not just true of Newtonian mechanics (where, in principle, a university could get some really, really good freshman lab equipment and really take the time to....HA HA HA HA HA, I made a good joke there, didn't I?), it's even more true of other branches of science.  None of us will ever personally observe, let alone conduct, more than a tiny fraction of the experiments needed to establish the foundations of our branches of science.

Galileo on Aristotle

I am a third of the way through the first of the four dialogues.  It consists largely of showing how cumbersome and inconsistent Aristotelian physics is.  It is a hard slog. We owe Galileo a debt for taking down Aristotle, cleaning the slate, and then starting to fill it in with new physics so that Newton could complete mechanics.

There is a little bit of actual physics.  Early in this part of the book (page 26) Salviati uses ideas equivalent to energy conservation on the inclined plane, and Sagredo readily agreed without demanding experimental proof.  Then they segue to other topics.  I think they return to it in a subsequent dialogue.

Next Book: Dialogue concerning the two chief world systems

After enjoying excerpts from Galileo's dialogues, I've decide that my next reading project will be the full text of Dialogue Concerning the Two Chief World Systems.  This one will probably take a while, but so be it.

The "two cultures" problem of the academic world, in which it is considered barbaric to have no interest in art or literature or history but quite acceptable to laugh and say "Yeah, I never got math or science", is well-illustrated by Galileo's position in the Western canon, or perhaps his lack of a position in the Western canon.  Every educated person knows his name and a few anecdotes (and probably apocryphal anecdotes) but there are far more educated people who have read Plato than have read Galileo.  (For the record, I've read Plato's Symposium and the Republic.)  This is a strange thing when you consider that our modern view of the universe owes so much to him, and that Galileo's view of the relationship between science and religion remains controversial (to both secularists and believers) in the modern world, yet is also an apt description of the views of many of the religious believers working in the sciences today.  It is strange that the writings of such a pivotal figure in the development of modern science and Western culture are not nearly as widely-studied as those of Western thinkers outside the sciences.

Bullship

If I'm reading pages 228-229 correctly, Galileo never actually dropped a rock from the top of the mast of a ship, and is just asserting what the outcome of the experiment must be.  That is...not what I was expecting from Galileo.

The words of the prophets are written on...?

I'm on chapter 8 of The Essential Galileo now.  Chapter 5 was letters from Galileo to supporters, largely arguing that a figurative interpretation of Biblical verses on natural phenomena need not be a threat to faith.  Countless scientists throughout the ages have been followers of religious faiths and would agree with him.  I find it interestingly that Galileo did not mention the Gospels, which are full of parables, as evidence that the Bible is awash in figurative language.  Also, in two of his letters he says (paraphrase) that if God only wanted us to learn about the natural world from the Bible then He would not have given us the ability to observe and reason.  Countless scientists who are also religious agree whole-heartedly with our illustrious predecessor on this point.

Chapter 6 is largely documents and testimony from Galileo's first trial, in 1615.  These documents are consistent with a distinction that a historian friend of mine drew:  Galileo didn't get in trouble for heliocentric theory so much as for public statements concerning the Church's authority on astronomical questions.  The testimony of the witnesses is less about heliocentrism vs. geocentrism and more about Galileo proclaiming that his heliocentric-compatible interpretation of Scripture is superior to the Church's.  Also, the witnesses refer ominously to "disciples" of Galileo.  They feared his theory less than his ability to persuade people to favor his teachings over those of the Church.

Chapter 6 ends with a 1616 edict adding several books to the Index of forbidden books.  Nothing by Galileo was on the list, but Copernicus' work made the list.  What else got banned in that year?  Well, it will be no surprise that a book on Calvinism made the list (poor Puritans :( ), nor that some books on law and politics got banned.  But it is amusing that a book called Scotanus Redivivus, or Erotic Commentary in Three Parts, was banned alongside Kepler.  A quick Google search mostly returns pages about Galileo and Copernicus, which is rather disappointing.  (Though there is a link to Fark!)  I could get my freshmen more interested in physics if I did a comparative study of Copernicus' writings and those of his contemporaries.

Chapter 7 was boring, so I skipped it.  Something about comets and disputes with contemporaries.

Chapter 8 is a series of excerpts from Dialogue on the Two Chief World Systems.  I haven't gotten very far in that chapter, but I like this quote from his preface:

Many years ago I had occasion to say that the unsolved problem of the tides could receive some light if the earth's motion were granted.  Flying from mouth to mouth, this assertion of mind has found charitable people who adopt it as a child of their own intellect.

Yeah, that burns.