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10/22/2021

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Kenneth Pearce

I think you are clearly right about what Newton is up to. This is definitely the point of his remark. But given that Newton's laws do in fact render the solar system unstable, how does the system of providence have any advantage over the system of fate, unless because God will institute the needed reformation? Is it just an argument against the eternity of the world?

E.S. Schliesser

I doubt Newton has any reason to think his laws create an unstable solar system. (That's a very hard problem.) And he can always claim that his laws are not final word.

Kenny Pearce

But then I'm confused. What's actually going on in the quote? Don't the 'irregularities' mentioned there occur in Newton's own system?

E.S. Schliesser

I am denying that this is the intended meaning. I think the General Scholium suggests these motions have been finetuned.

I do think it's possible Newton believes the system is not eternal, but that is orthogonal to this argument.

Kenny Pearce

Oh, I see. Your thought is: in order for the perturbations not to destabilize the system it has to be even more fine-tuned. On the one hand, it seems to me that that's not the most straightforward reading of what he says here. On the other hand, this is clearly a possible reading, and it makes the relevance of the remark to its context much clearer. I had been a bit puzzled by what looked like an irrelevant aside, that actually seems to undermine his argument. Your reading does not have that problem, at least!

E.S. Schliesser

Yes, I don't think he is giving his own views at all in that sentence. Also, the existence of 'irregularities' is inconsistent with blind fate *and the PSR*, but no problem for Newton.

Mike Jacovides

But Newton certainly knew that the the planets are almost, but not perfectly, on the plane of the ecliptic and that their orbits are almost but not quite circles. Aren’t these (especially the second) minor irregularities from a solar system in which the planets move in the same way in concentric orbs? And the introductory remark on the eccentricity of comets tells us that that’s the sort of irregularity he has in mind?

Eric Schliesser

From his perspective these are not *irregularities* at all! (I agree with you Mike that this is what he has in mind.) He has explained it. His point is that the system of fate must treat these motions as without sufficient reason and so as irregularities .

Kenny Pearce

Clarke would say: from a human perspective those are irregularities, but from a divine perspective they're not.

Eric Schliesser

Hi Kenny, that's another way to go. (I don't think it's Newton's.) But then again Clarke actually accepts the PSR (so maybe it's natural for him to treat them as irregularities), whereas I suspect Newton does not.

Mike Jacovides

I think it’s less strained to say that blind fate can’t explain why the planets move in the same direction, in nearly the same plane, and in nearly concentric circular orbits. The minor irregularities are an objection to this argument from design, which he replies to by explaining them in his system. If you think that the non-circular paths of the planets are the inconsiderable irregularities he has in mind and that these are explained by the pull of planets and comets, then I don’t see how you can avoid saying that Newton thinks that, given this explanation, the deviations will increase until a reformation is needed

Marius Stan

I always thought that the "irregularities which are apt to increase" but are "inconsiderable" *for now* are the perturbation effects in the Solar System: the sun isn't the only source of gravity on a planet. Every other planet is -- and so are comets. They attract each other, but much more weakly that the sun attracts them all -- hence, "inconsiderable."

But, these perturbation effects are of two kinds, 'secular' and 'periodic.' The latter cancel out over time -- they go one way first, then exactly the other way the second time around, so they add up to zero in the long run. 'Secular' perturbations are small, but add up. They don't cancel out, they're cumulative. E.g., the precession of the perihelion of Mercury.

I always thought that, by the 'inconsiderable for now but are apt to increase' passage, Newton meant secular perturbations. Which he thought would add up until they destabilize the orbits -- some planets will fall into the sun, others will escape its pull and wander off into space, etc.

Of course, he doesn't have the math to prove that, and when exactly in the future the destabilization will occur. He's just taking an informed guess. The math to work that out only became available in the late 20th century.

Eric Schliesser

Wait, now, Mike, you are moving to fast. First, my main argument is that in context the natural reading of the passage is simply a reductio of the system of fate. It's only because of Leibniz's letter (and Clarke's weird way of responding to it) that this passage becomes somehow a description of Newton's own views.
Second, on Newton's the system of fate cannot explain the visible patterns (only his non-mechanical laws can).
Third, Newton can explain why the orbits are ellipses, and also why there are interaction effects between planetary orbits comets. <--From his point of view the deviation of the ellipse is not an irregularity at all, but to be explained by the interaction. However, from the perspective of the system of fate, these interactions are themselves a further source of irregularity.
Fourth, he thinks that these planetary and comet orbits jointly exhibit finetuning of some sort.
Fifth, in the general scholium he makes clear that he thinks that what cause a solar system collapse is the nearby presence of another solar system. And he gives this as evidence for God's design (by putting them far apart).
Finally, if you look through the Opticks and the Principia, Newton never describes, I think, *the motions that he has brought under law as 'irregular'.* (This is an important contrast with the copernican scholium.)

Eric Schliesser

Yes, Marius, that's pretty much what I take to be the standard reading. And if you project the discussions of Euler, Clairaut, d'Alembert, and Laplace back onto Newton that is a super natural reading. (Basically Cohen and Smith do that in the Principia translation.) But I don't think he has that future debate in mind at all in this particular context. (And one reason to think that in addition to the fact that he is offering a reductio, is that after he rejected the Copernican Scholium, he has no reason to treat such motions as 'irregular.)

Marius Stan

A question about method: not sure how we adjudicate claims about what Newt/any past figure had in mind. Never been able to answer that question.

Second, the musing about 'apt to increase' is in the Queries. Overall, they're agenda setting for future research. So, doesn't the context indicate Newton invites his peers to figure out if perturbation effects do in fact destabilize the solar system?

Mike Jacovides

I guess I agree with your second and last point. The third point is the crux of the matter. What are the 'irregularities' Newton is referring to when he writes 'some inconsiderable irregularities excepted'? I say that they are the non-circular paths of the planets (and the like) and that Newton explains these by the pull of planets and comets. Whatever they are, they have to be actual, or they wouldn't be exceptions to the more basic fact that all the planets move in the same way in concentric orbits

Eric Schliesser

On the first, that's tricky, Marius. But my claim can also be restated as, there is an existing debate about the relative merits of the system of fate, materialist system, and system of providence. Readers of the time are very familiar with that. After 1688, Newton realizes he is being mistaken for an advocate of the system of fate, and so starts criticizing it. That's the context of the sentence. Leibniz recognizes that context, but then uses that against Newton (in order to suggest that Newton is either a Spinozist or an inconsistent theological voluntarist).
We agree that the Queries are agenda setting. But I don't think this sentence is describing Newton's way of framing the agenda for how to figure out perturbation effects. The whole paragraph and wider context of that Query is about the status of the design argument not about how to set up a careful analysis of n-body stability!

Marius Stan

Fair about the wider context. Makes Newton look quite weird -- inserting a line of thought re design arguments in the middle of an agenda for empirical investigation.

Still, I feel a bit cheated by that whole correspondence. What *is* the considered answer to Leibniz's charge? 1) No, the solar system is stable. 2) Yes, the system is unstable, but that's what the theory implies, so take your objections elsewhere, GW.

Your post seems to suggest Newton thought, "Actually, *I* never said that."

Eric Schliesser

Yes, I claim 'I never said that' is the right answer, Marius. I think he would say something like: "in so far as you are a necessetarian vortex theorist, your system is unstable and will implode unless you appeal to God (etc)." [The real system, go read Book 3 of Principia. It's going to be tough to turn that into a determinate question about stability.]

Marius Stan

Thanks, Eric.

George Gale

What Eric said at 04:42PM. But I must admit to being very sympathetic to what Marius says, too. I am totally NOT a Newton guy. But I know Leibniz pretty well, and I've spent some serious time in the Leibniz-Clarke. Let me make a very general, pretty sophomoric (IMHO) comment that might be relevant to Newton vis à vis this thread. In Leibniz (certainly after '86) there is *always* a manifest tension between his philo-theology and his mathematico-physics. Sometimes one aspect leads, sometimes the other, sometimes the conflict is just never resolved. But the tension is always there. Surely the same sort of tension is present in Newton? Mathematico-physically, he most certainly was aware of the awesome complexity of the n-body problem of the planets (let alone the comets)--he was no Pascal, methinks. Surely he knew that ultimately the whole shebang was doomed (as Milne and McCrea showed in 1935). Intuitively, he *had* to know that. But Newton the philo-theologican would have been in tension with that intuition--at least, were he Leibniz, he would have been. Is that what you're implying in your position in that argument at 04:42, Eric? or did I completely misunderstand what's going on?

Alan Nelson

I wonder whether Leibniz (and Clarke?) were thinking about interplanetary ether as well as perturbations. If ether produces any frictional force at all, the orbits of the planets will decay without divine intervention or ongoing influence.

E.S. Schliesser

Hi Alan,
I think that's right.
Eric

Marius Stan

What we haven't seen yet is any solid proof that Leibniz himself would be safe from the tu quoque objection from Spinozism. In general, does the combo of PSR and God-as-perfect-watchmaker leave you any wiggle room away from 'the system of fate'?

Marius Stan

I don't think Leibniz would grant there are perturbation effects. Empirically, he was on safe ground. The Great Inequality (of Jupiter and Saturn) was not yet an empirical problem. The planets' pull on the Sun was not measured until the early 20th-century. The return of Halley's Comet was in 1759, and the 30-day delay (between Clairaut's predicted time of arrival at perihelion and its actual time) needed lot of work (much later) to be matched with expected perturbations from the planets it passes on the way. So, Leibniz can wave that off. Just as he can the precession of the perihelion of Mercury (571 arcseconds per century -- not a real source of headaches unless you're Newton, who cared about empirical agreement to the last decimal place).

Maybe a better reading of the Correspondence -- and Eric's flagged passage in particular -- is externalist: Leibniz bet the farm that he could outwit Clarke and that Newton would stay away. A sharper court theologian would have replied right away, "No, YOU're the one who undermines public piety, Gottfried! Your God is a *deus otiosus,* 'cause you left him with nothing to do after creation; so you give comfort to the much reviled deists. And, we say matter is passive and inert, but you say it's full of vis viva, which is dangerously close to making nature self-sufficient, in no need of divine assistance. With friends like you, believers need no enemies!"

Or words to that effect.

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