Synopsis: After 1650, more scientists take as a given that theory must be based on empirical observation.
Opening line: "Something very curious happens at this point in time. And it'll show up in this course because almost everything we read from now on in the last five weeks of this course and throughout almost all the second semester, is going to look like modern science to an extent, n... read moreothing we've read so far."
Something very curious happens at this point in time. And it'll show up in this course because almost everything we read from now on in the last five weeks of this course and throughout almost all the second semester, is going to look like modern science to an extent, nothing we've read so far.
Even quite Kepler looks like modern science. Kepler and Astronomia nova look like modern science, but that's probably the only place we've seen it. And so there's a natural question, why did things change at this juncture? And that's what I want to end by thinking about, and giving you at least a partial answer.
The first step is look at who dies between 1642 and 1655. It's really extraordinary figures of the generation of the people working in the sciences other than Kepler in the 17th century. Galileo dies in January of 1642. Torricelli five years later. Very young. Mersenne in 1648, a year after Torricelli.
Descartes two years later in 1650. Gassendi manages to make it to 1655. But the generation, almost all the names up there behind these things, other than Fermat's and Riccioli's, they're all have died by 1651 or shortly thereafter. And one of the elements here, I'll come back to this, is the next generation didn't care to fight the battles that the prior generations had fought.
They treated them as settled and wanted to go on beyond them. And what are those battles? Well, that's what I'm listing here as breakthroughs, and they're worth noting, and who's responsible for them. That full recognition that a parent celestial motions are consistent within incompatible alternatives about what is moving in orbit about what.
Now, look, Appolonius was the first to point this out. It's all through Ptolemy, but I don't think anybody appreciated how radically wrong we could be from appearances before Copernicus. At that juncture, Copernicus, Tycho, Ptolemy challenge really made it clear that the same apparent motions could be treated in really radically, radically different ways.
And that opened the question, seriously, how are you to suppose to establish what the actual motions are? Kepler was trying to do that of course. Second thing, a battle that people that didn't want to fight anymore. The only battle here is to give up the idea that it's trivial to go from appearance to the actual motions.
Second one, the importance given to discrepancies in calculated verses observed longitudes and latitudes in astronomy. Those have been ignored from Ptolemy up to Tycho with an attitude, we don't have anything to learn from the discrepancies since they're away from opposition. They're away from the interesting phenomenon. They're not gonna tell us anything.
Tycho and Kepler and Horrocks, though remember, he hasn't been recognized but by a handful of people until 1661, they showed very conclusively how instructive small discrepancies can be. And Horrocks sorta topped it all off by taking Kepler's successes and taking very small discrepancies in them, and achieving a significant advance on Kepler.
So it's now I think more and more widely recognized by 1651, these discrepancies are informative. Third difference, the shift in compounding curvilinear motions out of circular motions to compounding them out of rectilinear motions. Now, you might not think of it yet as rectilinear motions, but there's a motion along the radius, and a motion along the tangent.
That's what produces curve and linear motion. Descartes doesn't quite say that, okay? Because he doesn't have the motion toward the center, but he's very close to it. The person I know of who says it that way totally clearly first is Robert Hooke. And you'll see it in a letter he wrote Newton, but we'll come to that.
But the idea of doing that, of focusing on rectilinear motions as primary and asking how curvilinear motions can arise out of it, that seems to have managed to be settled with Descartes being the principle person that Galileo and Gassendi. Galileo's, of course, parabola is very much a product of two rectilinear motions.
So that's become standard, or at least commonplace. The increased emphasis on designing and developing experiments that address comparatively specific questions. Mersenne probably does that more than anyone. Marsenne's work on musical instruments and the experiments he did on them, which are often very highly contrived. This is in Harmonie universelle.
They're remarkable experiments and extraordinarily informative about things like vibration, the relation of sound to vibration, how pitch works, et cetera. A lot of progress was made. The thing I'm emphasizing here is these are experiments that are very far removed from things occurring in nature. They are contrived. And that comes to be appreciated by Mersenne, Galileo.
And I give Riccioli credit for this because of all the work he did with the pendulums dropping objects, etc. A marked relaxation of the strictures of classical mathematics, opening the way to a wide range of new mathematical methods for solving problems. The three keys there are from an earlier date, he's closer to a contemporary of Tycho's, in fact he is a contemporary of Tycho's.
Then Descartes And Fermat. Descartes and Fermat are normally credited with the development of analytic geometry as was sort of the reverse for both of them. But both are very important. Fermat came up with ways to calculating tangents that are getting very, very close to the calculus. But all of these are no longer working under the strictures of classical mathematics.
You're making moves that classical mathematics would have said they're not really math any more, okay? But that's been relaxed. And finally, the stress on efficient causation over its Aristotelian alternatives and answers to why and how questions about changes that occur in nature, all of these. And that Francis Bacon, whom I've barely mentioned because he didn't do science so much as describe how it ought to be done, but he's gonna become very important in the influence he had in England.
And then, of course, Mersenne who made a huge deal throughout his career against both renaissance naturalism and its pseudo causes, and against skepticism focusing on efficient cause. And, of course, Mersenne and Gassendi, I think I've told you, they had ran this rump seminar. In the nights, they would teach scholasticism in the daytime and then night teach their rump seminar, telling you what the truth is and that what they told you in the classes was wrong.
And then Descartes put an enormous stress on efficient causation cuz it's the only form of causation for him. So that's a change that was slow to happen but it has happened at this point. Now, the interesting question is why I date this as of 1651. And any date's arbitrary.
I gave it to you in your assignment paper two as two reasons. It's the date of the publication of Riccioli's New Almagest and it's also the date of Huygens' first publication, which is actually what we would call the integrals under hyperbolas, it's the quadrature of hyperbolas. Huygens, for a brief period, knew more about the logarithm function and the hyperbola and it's various functional properties than anybody in the world.
Time and again there was a period when he knew more than anybody in the world. Then he went on to another problem, and other people picked up from where he left off. That's going to be Huygens. And what you can't quite appreciate yet is for the next 40 years, from 1651 on, surely from 1655 on when Huygens comes to Paris for the first time and starts participating in intellectual life there, Huygens is the dominant figure in the sciences in the world and recognized by everybody to be such.
Now he is just so dominant in fact, that we just see it again and again. He's the sole charter member of both the Royal Society in England and the Royal Academy in Paris, which is wonderful because he's neither French nor English. And nobody else from Holland is in either of them.
He's just the dominate figure. He dominates for a 40 year period. I have a favorite quote about, I'll throw it out now, I'll throw it out again next week. There's a quote that I started using in this class and kept searching for a moment to put it in print.
Then I get invited to do a Physics Today article, which meant I have 40,000 physicists as my audience, so I used it. I won't quote myself exactly cuz I don't remember, but Holland has suffered the misfortune of producing two of the greatest stars in the history of science, Huygen's and Lorentz, only to see each of them eclipse by a supernova in their own lifetime.
And it's the one quote that physicist's always throw back at me from that article because they're so competitive and the idea of Newton and Einstein eclipsing these two extraordinary. But both of them were dominant figures, Lorentz and Huygens, for a long period. So, that's one reason Huygens comes on the scene finally at age 22 in 1651.
I don't think that's the best reason, though. I think the Riccioli reason is the best because we think of him as the last of the defenders of Ptolomy, but you've seen enough already to know that's a complete misrepresentation. He's taking on all of Galileo's claims and trying to evaluate them.
How? Not by turning to scriptures, not by turning to Aristotle, by turning to observation. So he does all that effort to test free fall. Okay? He could've argued it from Aristotle, he could've argued in any number of ways. He thought the only appropriate way to argue it was to go out and measure and conclude Galileo was right.
He did the same thing with New Almagest. He concludes that Venus and Saturn are definitely, excuse me, Venus and Mercury, are definitely going around the sun. So is Mars. It's unclear whether Jupiter and Saturn, their orbits are centered on the earth or on the sun. They go around both, just as Galileo says.
So in the first edition, he leaves it as open, and in the second addition, it becomes they go around the sun. He is empirically driven and that leads me to my last slide. What I think happens at this time, and this is the best phrasing I can come up with, is there's an increasing respect for the idea that the empirical world ought, somehow or other, to be the ultimate arbiter of all questions about it.
That respect was just not there until sometime around the middle of the century. After this that respect is very, very widespread. Okay if there's some way that the empirical world can solve the questions about it that ought to be the way. That ought to dominate anything else. And that's a really sea change versus 1500 years before it.
Now I'll end with why that should be the case. There's a social context to this, and I'll just run it off. In England, there was a civil war. The upshot of the civil war is the Puritans took over and the Church of England got ousted. And King Charles I lost his head.
One of the nice things about that is the universities in England had been ruled by the Church of England which was, in all respects, the same as Rome except for the papacy. It was as Aristotelian as it could be. What happened when the Church of England was forced out of the universities?
All of the sudden there was an enormous relaxation of the curriculum. And, more important, discussion groups formed, particularly a discussion group that involved Oxford and London to such an extent that Robert Boyle finally started describing it as the invisible university. And they were totally committed to doing empirical research, that's England.
France is a more complicated story. Mersenne started this discussion group in the late 1830s and regularly had meetings talking about things, that's where the learned ladies comes from, because it was fortunately not men only. It was very much aimed at advancing what we now call science, or at least empirical research at the time.
That group became more and more powerful. When Mersenne died, Gassendi took it over. When Huygens came in 1655, Gassendi introduced Huygens to that group. And Huygens started presenting his work to that group. They were the first to see what he was doing anywhere. That group ended up being the foundation for the Royal Academy ten years later after Gassendi died.
But again, and you have a nexus of intellectuals very much committed to empirical research. And finally, even in Italy, number one the church starts doing things to do astronomical measurement. You'll see that week after November 11th, our holiday. But Bologna, where of course Riccioli and Grimaldi are, there's both Jesuits, but they're Jesuits doing really serious empirical research.
So in all three countries, there's this increasing respect for settling questions empirically side by side with an unwillingness to fight the battles that have been fought for the first half century all over again. Let's treat them as largely settled and go on, okay? But it's a really abrupt looking change when you look at the literature.
Before 1650, it looks one way. After 1650, it looks very different and that's where we're gonna go from here on. We will do a little astronomy from the 1640s, but almost everything for the rest of the course is gonna be after 1650s.