A little treat for loyal CV readers: Tom Levenson is a professor of science writing at MIT, and the proprietor of the Inverse Square Blog, one of the most erudite scientifically-minded outposts in this blogosphere of ours. I’ve been enjoying how Tom writes engagingly about science while mixing in cultural and artistic references, so I asked if he would like to guest-blog a bit here at CV. This is the first of three posts he’ll be contributing; look for the other two later this week. [Here is two, and here is three.]
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Monday Isaac Newton blogging: A little light reading, Principia edition.
Update: See correction below.**
To introduce myself to the Cosmic Variance community (at Sean’s very kind invitation), let me just admit up front that I am a glutton for punishment.
Exhibit A: last year I read the Principia for pleasure.*
That’s not exactly right– it is more accurate to say that in the context of writing a book on Isaac Newton’s role as currency cop and death penalty prosecutor, I found myself reading the Principia as literature rather than the series of proofs it appears to be. Just like John Locke, who had to ask Christiaan Huygens if he could take the mathematical demonstrations on faith (Huygens said he could), I read to see what larger argument Newton was making about the ways human beings could now make sense of material experience. (This is, by the way, the only connection I can imagine that Locke and I share.)
What I got out of the exercise, more than anything else, was a reminder of how something we now mostly take for granted is in fact truly extraordinary: taken all in all, it seems genuinely remarkable that cosmology exists at all as a quantitative, empirical science.
That is: it is not obvious – or at least it wasn’t, all that long ago, that it would ever be possible to treat the universe as a whole as an object of study – especially given our very constrained vantage point from within that which we want to examine.
Most accounts of the story of modern cosmology more or less unconsciously downplay the strangeness of the claim that we can in fact make sense of the universe as a whole. They begin – mine did — with Einstein and the 1917 paper “Cosmological Considerations in the General Theory of Relativity, (to be found in English translation here.) Cosmology in this telling becomes more or less an inevitable extension of a recent advance in theoretical physics; the change in worldview precedes this extension of the apparatus of general relativity into a new calculation.
I recant: though I certainly wrote my version of this basic tale, reading Newton has reminded me of the much more radical change in the understanding of what it is possible to think about that had to precede all that cosmology (among much else) has achieved.
It certainly was not clear that the universe as a whole was subject to natural philosophical scrutiny in 1684, the year of Edmond Halley’s fortunate visit to Trinity College, Cambridge, and his more-or-less innocent question about the curve traced by a planet, assuming “the force of attraction towards the sun to be reciprocal to the square of their distance from it? that would produce an elliptical planetary orbit with the sun at one focus.
An ellipse inverse square relationship, Newton told Halley.
How did he know?
Why – he had calculated it.
By 1686, Newton had extended and revised his off-the-cuff answer into the first two books of Principia, both titled “The Motion of Bodies.” These pursued the implications of his three laws of motion through every circumstance Newton could imagine, culminating in his final demolition of Cartesian vortex physics.
But even though he had worked through a significant amount of mathematical reasoning developing the consequences of his inverse square law of gravitation, he left the ultimate demonstration of the power of these ideas for book three.
Books one and two had been “strictly mathematical,” Newton wrote. If there were any meat and meaning to his ideas, though, he must “exhibit the system of the world from these same principles.”
To make his ambitions absolutely clear Newton used the same phrase for the title of book three. There his readers would discover “The System of the World.”
This is where the literary structure of the work really comes into play, in my view. Through book three, Newton takes his audience through a carefully constructed tour of all the places within the grasp of his new physics. It begins with an analysis of the moons of Jupiter, demonstrating that inverse square relationships govern those motions. He went on, to show how the interaction between Jupiter and Saturn would pull each out of a perfect elliptical orbit; the real world, he says here, is messier than a geometer’s dream.
He worked on problems of the moon’s motion, of the issues raised by the fact that the earth is not a perfect sphere, and then, in what could have been a reasonable resting point for the book as a whole, he brought his laws of motion and gravity literally down to earth, with his famous analysis of the way the moon and the sun influence the tides.
Why not stop there? The story thus far had taken gravity from the limits of the observed solar system to the ground beneath each reader’s feet. More pragmatically – it told a story whose significance Newton’s audience would have grasped immediately: the importance of understanding the rules governing tides was obvious enough to the naval powers of the day.
No matter. Newton kept on going. The last section of his world-system turned to the celestial and seemingly impractical: the motion of comets, in an analysis of the track of the great comet of 1680.
Newton presented his findings through two different approaches: one produced by collecting all the data points he could of traveler’s observations and plotting the comet’s track against those points; and the other in which he selected just three points and calculated the path implied.
The two analyses matched almost exactly, and both showed that this comet did not complete a neat, elliptical orbit. Rather, it traced a parabola.
Newton knew what he had done. He was no accidental writer. A parabola, of course, is a curve that keeps on going – and that meant that at the end of a very long and very dense book, he lifted off again from the hard ground of daily reality and said, in effect, look: All this math and all these physical ideas govern everything we can see, out to and past the point where we can’t see anymore.
Most important, he did so with implacable rigor, a demonstration that, he argued, should leave no room for dissent. He wrote “The theory that corresponds exactly to so nonuniform a motion through the greatest part of the heavens, and that observes the same laws as the theory of the planets and that agrees exactly with exact astronomical observations cannot fail to be true.” (Italics added).
And now, finally, to get back to the point: this, I would argue, was the essential first and in some ways the most difficult step in the foundations of cosmology. With it Newton transformed the scale of the universe we inhabit, making it huge, perhaps infinite. Even more important, he demonstrated that a theory that could not fail to be true made it possible to examine one phenomenon — matter in motion under the influence of gravity — throughout all space.
That thought thrilled Newton’s contemporaries – Halley caught the mood in his dedicatory poem to the Principia, writing that “Error and doubt no longer encumber us with mist;/….We are now admitted to the banquets of the Gods;/We may deal with laws of heaven above; and we now have/The secret keys to unlock the obscure earth….” To catch a distant echo of that euphoria, just imagine what it would have been like to contemplate that ever receding comet, fifteen years into its journey towards who knew where at the time of Newton’s writing, and know that its behavior was knowable through an extraordinary act of human invention.
It’s a whole ‘nother story to ask what it would take to create a similar sense of pride and pleasure in a general audience today. But just to get the discussion going, I’d suggest that one of the oddities of contemporary cosmology as presented to the public is the degree to which the universe at large has become more homey; the very success in making the argument that there is a continuous scientific narrative to be told from the Big Bang to the present makes it harder to see just how grand a claim that is.
So, to end with an open invitation to this community: what would make current physical ideas as powerful and as intelligibly strange as Newton was able to make his story of a comet traveling from and to distances with out limit?
Last housekeeping notes: in one of the more premature bits of self-promotion in publishing history, the Newton material discussed above derives from my book, tentatively titled Newton and the Counterfeiter, coming early next year from Houghton Mifflin Harcourt (and Faber, for those of you across the pond).
Also – my thanks again to Sean Carroll for welcoming me here. If you want to see what I do when I’m at home, check out The Inverse Square Blog.
*If you are minded to pick up a copy of Principia, get this edition. Not only is it a well made book, easy to look at, well printed, with clear diagrams, it comes with the invaluable guide to reading the Principia written by I. Bernard Cohen. Accept no substitutes.
**Thanks to reader and award-winning physics teacher David Derbes for catching my inversion of the problem Halley put to Newton. Let this be a lesson to me: blog in haste; check one’s notes at leisure; repent in public.
Image: Woodcut by Jiri Daschitzsky, “The Great Comet of 1577.” Source: Wikimedia Commons.
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what would make current physical ideas as powerful and as intelligibly strange as Newton was able to make his story of a comet traveling from and to distances with out limit?
To answer that open question I think the way to make current physical ideas as powerful as they first seemed to people at the time of their discoveries is to make us remember what it was like for them, to make us see through their eyes.
Schoolkids are told facts about our universe, that the sun is at the center of our solar system with these planets including ours going around them and the star is just one sun in a whole galaxy etc, etc… They see the photos, they know the earth is obviously round and so on.
So naturally they don’t see how amazing it is that we can comprehend so much about these things so far removed us, it’s just fact to them. What they need is to rethink things from first principles, go back to a time when nothing was known and all one could do was look up at the sky and wonder at the motions of heavenly bodies then build up from there.
The fascination of physics comes not from being taught facts but from how those facts are deduced, but if those facts aren’t deduced from principles people can relate to then their meaning is lost. Explaining the standard model of particle physics to a layman won’t get that feeling of discovery across, he’ll just know a lot of useless terminology about “quarks” and “mesons” and the LHC searching for some “higgs” which might as well be called “foobar” for all it matters.
In short I think that instead of telling the general public “this is the universe, it started with a big bang, isn’t it amazing!” it should be more like “put yourself in the shoes of someone 10 000 years ago and look a the sky, what do you see?” then build up that picture to our modern day understanding. That’s where the sense of awe comes from, not from empty statements and facts.
It took me an embarrassingly long time before I finally figured out the point of the story of Newton and the apple. Who needs to discover gravity? It’s everywhere, surely people knew about it.
But understanding that it’s the same gravity that pulls the apple and governs the motion of the planets is quite a leap.
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Understanding how “inverse square law” is applicable in today’s world, would be interesting enough comparison to what you ask?
Knowing where the basis of where these thoughts arose then, would be as important as showing Sir Isaac Newton with all his frailties in the quest for a psychological perspective, to defining statements, that have become experimental principals endowed? I am glad this psychological quest was never introduced. 🙂
Newton, Isaac. 1687, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy and his System of the World), trans. by A. Motte and revised by F. Cajori (University of California Press: Berkeley, 1934) or The Principia: Mathematical Principles of Natural Philosophy Trans. I. Bernard Cohen and Anne Whitman, with the assistance of Julia Budenz (University of California Press: Berkeley, 1999)?
Newton tacitly assumed c=infinity. EM was unified by Maxwell; general relativity appeared. Mercury’s perihelion excessively precesses and light falls at twice the acceleration of matter. Somebody looked.
All physics assumes isotropic vacuum and the Equivalence Principle. String theory demands BRST invariance. Teleparallel gravitation wholly contains GR for EP = true plus consistent and detectable cases of EP = false.
Do left and right shoes vacuum free fall identically? Not in a massed sector chiral vacuum background. Metaphoric socks and left shoes fit unremarkably, right shoes are heresy. A parity Eötvös experiment opposing single crystal test masses of space group P3(1)21 (right-handed screw axes) and P3(2)21 (left-handed screw axes) quartz could expose knowledge masquerading as truth. Somebody should look. Newton would be amused.
Super post – that was indeed a treat as advertised!
One minor comment : re the statement
“It is not obvious – or at least it wasn’t, all that long ago, that it would ever be possible to treat the universe as a whole as an object of study – especially given our very constrained vantage point from within that which we want to examine”.
I think this view is still common among the general public. I’ve noticed in public lectures that the real surprise for lay audiences is the concrete evidence for the BB model, etc, i.e. the idea that cosmology exists as a quantitative, empirical science as good as any other.
This is probably interesting for philosophers of science – after all, only a few decades ago, most physicists also regarded cosmology as a speculative branch of their profession!
great post
“what would make current physical ideas as powerful and as intelligibly strange as Newton was able to make his story of a comet traveling from and to distances with out limit?”
Well, some of us contemplate that our ‘universe’ is a bubble in an inflating phase of matter containing other, different, ‘universes.’ I think the idea that we could confirm this picture, and say something about what the other ‘universes’ look like, qualifies as “intelligibly strange.” What it would take to do this is of course an open question — but one that some of us are taking the very first scratches at.
Newton was the first to apply symmetry principles to physics as well. The first law tells us physics is properly observed on an inertial frame. The third law tells us that physics is invariant with displacement and rotation of one’s frame, and the second law gives the dynamics which obeys these principles.
The second law is a bit odd, for it says a dynamical quantity F is equal to a kinematical quantity m times a geometric quantity a.
Lawrence B. Crowell
This is a cynical view of things, I’m afraid, but is it possible that Newton’s ideas were “powerful and intelligibly strange” only to a relatively scant number of people, even among those literate Englishmen who’d heard of his ideas way back then? I don’t actually know the answer, but I’d warrant most people that heard he’d solved the motion of the planets simply shrugged, and got on with their lives.
In my experience, there are many more highly intelligent people than there are those brights that also find science to be fascinating and intelligible. And of course, high intelligence is a rarity among the population as a whole. Thus, contemplation of the universe as an object of study was, and will always be, an activity for those who are smart enough and temperamentally inclined to do it. I don’t believe it is possible to invent a radically new way of presenting science that would dramatically increase the number of people who find science, much less cosmology, to be interesting.
great post, btw.
I find it helpful to at least imagine the process of demonstrating these “facts” for myself. If we believe everything our teachers tell us, we could believe almost anything. To really know things, we need to be more critical – and then our knowledge will become more precious and more exciting.
For example: how, from my back yard, could I prove the Earth is round? How,
using household gadgets and perhaps a car and a phone, could I measure the diameter of the Earth?
I would never call Newton “the first cosmologist”, much as I revere him. What about Eratosthenes? To measure the radius of the Earth is no mean feat! He measured it quite accurately back around 200 BC. In fact, the main reason we don’t know how accurately he measured it is that he measured it in “stadia”, and we don’t know the size of the stadium in his home town!
If anyone thinks measuring the size of the Earth doesn’t count as “cosmology”, they are blind to how the “cosmos” keeps getting more interesting, they more we know of it.
In short: making people stand on their own two feet, instead of accepting facts by the authority of “experts”, is the best way of making them realize how cool the world really is.
In my limited experience, I’ve found success with explaining how humans are contiguous with the rest of the universe. What I mean is to emphasis that we are not separate from the universe, that the history of the universe is our own history. For my own street lectures, this culminates in repeating Carl Sagan: “We are made of star stuff.”
I’ve never found strangeness to be a great attractor of the attention of the public. If a topic is too strange, like quantum mechanics and string theory, then most members of the public shrug it off and let someone else deal with it. But, point to a star and say, “That’s where you came from!” occasionally you can get someone to stop and ponder their place in the universe.
Standing on one’s own feet. Hmmmm….. as a layman I am trying to learn to be like a scientist.
I guess if the totality of all that science has to offer could be contained in each individual, then the scope of such a move to “super cosmological views” would have to include what is taking place at LHC?
Theoretical definitions embedded as well?
So, Christopher Columbus may of eventually thought the world was a pear shape? Yet ,not forgetting the history Tom is introducing of showing Inverse Square Law.
Such analogies to the journey, are like paving the way for new processes in science . There had to be “some philosophical foundation” with which such explanations about the current state of the universe could be held accountable too?
It rests then on the inductive/deductive definitions with which science must be introduced to phenomenological order, under the guise of implementing the Aristotelean Arche? What is “self evident” as we are lead by science?
This would go to show Sir Isaac Newton’s method of approach? Although Francis Bacon came much later to show the “value of science,” then what did Sir Isaac Newton do by such “inferences to a mathematical basis?”
Yes, it’s true that only a small minority of people have the background to really understand Newton’s contributions. But I still think Newton’s ideas have inspired millions of people throughout the years. And different people have different relationships to science. I know many nonscientists who find the big ideas of science fascinating even if they’re turned off by the details.
I agree with John: if education focused more on the process of discovery (without excluding the traditional learning methods), people would better understand how awesome the universe really is.
Thanks for the comments all…
Just to pick up on a couple. On Laurence Crowell’s post at number 10 — Frank Wilczek wrote a very nice three part essay (or series of essays) on the culture of force. They were published in Physics Today in late 2004 and earl7 2005. (Go here: and scroll down to the bottom).
Also: to Mark Harrison — I’ve done the “you come from stars” thing with great pleasure in the NOVA film I did with Neil Tyson on Origins; you’re right. It works. I’d venture to say, though, that the strangeness quotient in both the thought and the underlying physics is pretty high — which is part of its appeal.
I blew the link to the Wilczek series. It’s here: http://xserver2.lns.mit.edu/~csuggs/physics_today/wilczekpubs.html. Scroll to the bottom for the three articles in quesiton.
…….Although Francis Bacon came much later to show the “value of science,” then what did Sir Isaac Newton do by such “inferences to a mathematical basis?”
Newton’s inverse-square (1/r2) law is a cornerstone of General Relativity.
I was going to include the mathematical derivative as well, in case there were other layman like myself reading.
Given that Newton and his contemporaries made the first big successes of basing physics and similar sciences on specific mathematical laws, maybe the biggest turnaround today or hereafter would be unassailable evidence that fundamental laws were statistical and random.
Not saying I believe that, and probably the vast majority of scientists today don’t either (although there was a recent ArXiV paper that made a fair stab at predicting the cosmic proportions of mass types, on a similar assumption of a random ensemble of laws).
No doubt for a long time scientists would assume the randomness was a consequence of underlying deterministic laws, and seek “hidden law” theories analogous to now discredited hidden variable theories in QM. But perhaps that idea would eventually become as anachronous and unfruitful as astrology did after Newton (who dabbled in the occult himself). And consider how popular all that hocus pocus still is today, although unlike that the by-then old-style deterministic science would still of course be useful for most practical purposes.
I look forward to your book on Newton and the Royal Mint, Tom. But let’s hope you’re not too harsh on the cantankerous old coot – As you must be all too aware, after researching for the book, “the past is another country”. In Newton’s case it was one with no police force to speak of, hardly any social security, general illiteracy and poverty, and prisons so insanitary they were death traps in themselves.
So inevitably, the law in those days was harsher than many today can imagine. Practically every crime was a felony, and almost every felony was a capital offence (over 300 a mere two hundred years ago!). As well as death, conviction meant forfeiture of all goods and chattels; so a condemned man’s family, if any, would end up literally on the street!
Some of the offences were considered ridiculous even then, and for most types of offence only about 20% of death sentences ended up being carried out – If a person of standing, like the local vicar or squire, put in a good word for a condemned felon, a reprieve was more than likely (this mercy being a form of social control in itself, a kind of carrot to go with the stick).
But one crime for which conviction meant almost certain death was forgery. Also, forgery of precious metal coinage was treason, which meant the execution was more grisly: Men were hanged, drawn, and quartered, and women were burned at the stake, and this happened quite often, almost into the 19th century. Although most forgers were male, their womenfolk were often implicated when the authorities found forgery equipment in their possession. (Unluckily for the women, one can’t be an accessory to treason.)
Well, I hope that didn’t go too far off on a tangent, and will look forward to buying the book.
that’s an awesome post
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Tom Levenson on Jun 4th, 2008 at 10:39 am
I blew the link to the Wilczek series. It’s here: http://xserver2.lns.mit.edu/~csuggs/physics_today/wilczekpubs.html. Scroll to the bottom for the three articles in quesiton.
Thanks, interesting. Frank pondered these problems in his youth. It took me a bit more time to ponder this. This funniness in F = ma is one motivation for eliminating force from the foundations of physics. I also think that physics needs to liberalize the idea of inertial frames, or to remove the dichotomy between accelerated and inertial frames.
It is hard to know who was the first cosmologist. For that matter we could argue over whether Galileo or Newton get the title of the first physicist. Galileo figured out some simple rules for motion on Earth. Kepler found the rules for planetary motion. Newton with his F = ma assumed a gravity law of the form F = GMmr^n, equated this to the centripetal acceleration and found that n = -2 recovered Kepler’s laws. So we might say that Newton unified a physics (protophysics) with a cosmology, which extended out to Saturn.
That all of this early solar system is amazing has to be seen in the light of how long it took to actually figure it out. Watching the sky leads one to a quick conclusion that everything does go around the Earth. What could be more natural? The problem lay in those pesky planets, they just didn’t seem to fit the rule. It took some time to begin to understand the motion of the planets against the sky and how the solar system was heliocentric. It is also fortunate that the ancient Hebrews made little commentary about the sky or stars. In fact they admonished against astrology, which is what the story of the Tower of Babel is about. Galileo challenged Papal scholarship and not so much the core of theology.
Biology is less fortunate, for Darwin is more of a direct challenge to theology, as seen in the continued silly fuss in the United States with evolution vs creationism.
Lawrence B. Crowell
I was afraid the scientific basis of Sir Isaac Newton may be clouded by the character he enshrined? Sometimes, things are allowed to go by the way side because of the character flaws or directions reputable scientists may go, after leading a scientific life. Character, is not excusable either?
Reading John’s Ramsden reasons for the
“primitive alchemical work or astrology” in what he relates to the “time and the country,” are important I think, and this leads into what is of value in our culture if we understood the value to the EQ instead of the IQ.
Not so much the process of astrology for sure here, because we may have never had understood it’s alchemical relations but by the woodcuts that we had been shown previous, by the assumption of the culture people of that time.
I do not know if this leads into Tom’s new post above, but the relevant basis of, “calculus by invention” is a testament to “looking past” the work and history of the character of Sir Isaac Newton. Fully acknowledging the work any of us to do with what “is” primitive in us.
This does not discount the roles to validation, but points out the work to bypass the emotive realizations that existed with Sir Isaac Newton, as we work together, what ever your arena as an “subjective valuation” and hence repugnant to what is intelligent today by elevating the genius standard, while discounting the creative valuations one might assign to new theories, any group that gathers in front of the blackboard under the basis of this emotive consideration.
Scientist or not. There is a conduciveness to growth in science and technologies that works it’s way into the social network by nurturing. The emotive valuations must be understood by learning to know what makes one tick in emotive response.
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Levenson expresses his admiration for Book III of the Principia. And he says, with good sense, that Newton brought cosmology to science. I would like to add a short comment concerning the “moon test” that appears in Proposition IV of Book III.
The world is supposed to be composed of two classes of bodies: terrestrial and celestial. The force of gravity (g = 9.8 m/seg^2 ) acts upon terrestrial bodies, and the force GMm/r^2 acts upon celestial bodies. He showed, beautifully, that those two forces are not two forces, but one and the same force. That was the first example of unification of forces in the history of physics.
Now, since there is no difference between the two forces, there is no difference between terrestrial and celestial bodies. He showed that the Moon gravitates, so that it is like terrestrial bodies. But what impresses me most is the other, parallel idea: that the apple is like celestial bodies. We, terrestrial beings, are part of the Universe, just as the planets are. Before Newton the world was supposed to be a cosmos (terrestrial and celestial bodies obeying different laws); after Newton the world is a universe (all bodies obeying the same rules).
Notice that Newton´s proof depends crucially on a detail that he does not mention explicitly in Proposition IV: that the force exerted by the Earth is as if all its mass was concentrated in the center of the sphere.