My book club is currently reading Dolnick’s The Clockwork Universe. To some extent it’s about Newton and the development of calculus, but the way in which Dolnick introduces and develops his story makes it seem, to me, to be about much more than that – really, about the great paradigm shift from knowledge as something handed down by authority, to knowledge as something discovered by experiment. He makes it clear that the founders of the Royal Society were far from iconoclasts; they generally believed that the ancients had possessed all knowledge. Much of it was lost, and their efforts to retrieve it ranged from poring over different translations of the Bible to discover hidden codes, to performing experiments which gradually became more rigorous and repeatable. Gradually (or so it seems to me; I haven’t finished the book yet) the inquiring minds that made up the British Royal Society shifted focus from authority to experiment. Their motto early on was Nullius in verba, or “Don’t take anybody’s word for it,” but they grew into that motto by fits and starts. It may have helped that the Society was something of a boy’s club: they liked experiments, particularly those involving loud noises or explosions.
They believed in God; they also believed that God was a mathematician, and that the laws of nature could be mathematically expressed. They did not realize, at the beginning of this intellectual journey, that discovering the laws governing moving objects would require them to invent a new kind of mathematics. (Invent, or discover? Mathematicians still debate which they’re doing.)
And what’s all this got to do with writing fiction? Well, a lot of science fiction and fantasy novels portray societies teetering on the transition between authority and reason. And far too often, we writers think of the transition as far more simple and clear-cut than it actually was. I think that studying Dolnick’s book will help me to widen and deepen my portrayal of imaginary societies in transition and the forces that moved them. When you realize that the idiot who searched the Chaldean translation of the Bible for hidden meanings was also the idiot responsible for Boyle’s Law, it’s hard to settle for the simplistic view of “authority bad; science/magic good” that we so often fall into.
As for the title – “the ghosts of departed quantities” was a phrase used by Bishop Berkeley, who did not think much of the early formulations of calculus. He’s best known as the guy whose argument about the non-existence of matter was answered by Dr. Johnson’s kicking a stone and saying, “I refute it thus.” But I’ve always had a soft place in my heart for the good bishop on account of his ingenious tying of Christian apologetics to calculus; I can’t find the reference tonight, but my father claimed that Berkeley said that anybody who could believe in Newton’s “fluxions” should have no problem whatsoever with believing in the Resurrection.
Let’s have some twisty thinkers like that to enliven our stories.
Mad Genius Club 
36 responses to “The Ghosts of Departed Quantities”
Literally it means “At the word of nobody,” because nullius is in the genitive case. But obviously the non-literal translation is smoother.
But it is also a scholarly joke, because they are riffing on the poet Horace’s line, “Nullius addictus jurare in verba magistri,” which literally means, “Handed over to be bound” (as a slave or prisoner) “to the word of no teacher of nobody.”
This is taken to mean that he isn’t obliged by any sworn allegiance to a philosophy school; but it also riffs on the fact that Horace was a freedman’s son, and that he himself had narrowly escaped execution for leading troops for Brutus.
The line comes from Horace’s first epistle (in poetic form), which is addressed to Maecenas, his friend and sorta patron. Horace says that he is dropping fun poetry like an old horse that is ready to die, and will now write serious stuff about philosophy. So the line right before this one is, “Ac ne forte roges quo me duce, quo Lare tuter,” which means, “But if perchance you should ask me who guides me, whom I would protect like a household Lar god….”
The line continues, “Quo me cumque rapit tempestas, deferor hospes,” which literally means, “And so, where a storm steals me away, a guest disembarks.” (ie, me, Horace).
Horace admits a certain lack of consistency but then praises virtue, and tells Maecenas that he needs to work as hard at that as at business. He then says all of Rome is too money-hungry, and praises the poor as living a more satisfying life.
Such as himself with his tattered clothes. (He was not poor, although he probably had lost a good chunk of his dad’s money, and was not in a position to do well in business while basically alive on probation. Hence the Sabine farm.)
He dispraises his own inconsistency of thought, praises Maecenas’ kindness in not laughing at him, and points out that a wise man has more freedom of action than anyone except Jupiter, and is the “king of kings.”
So it is a piece that all educated men studied in school, and the quote would be recognized.
Things are always complicated. Or should be.
Otherwise you end up with a single genius going from believing in a flat world to planning a space program so they can escape from their moon of a gas giant before it breaks up. I wish I were kidding. . . .
But on a more realistic and wide-spread level, there are actual arguments for Earth being stationary. Learn them.
oops
Mary Catelli
Historically the reason Copernicus first created the heliocentric model of the solar system wasn’t because he believed that the Earth orbited around the Sun, but because he discovered that it made modelling the solar system simpler. At the time this was horribly counter-intuitive because everyone knew that the Sun orbited the Earth – they could see it pass overhead every day, and a common theological position was that man, as the pinnacle of God’s creation, was situated at the centre of the universe.
Astronomers of the day constructed models of planetary motion using only circular orbits. To get more complicated motion they pictured the planet orbiting in a circle around a focus that was also in a circular orbit – and added as many circles as was needed.
Copernicus realised that if everything orbited around the sun he would need significantly fewer circles to describe everything than he would need if everything orbited around the Earth. It was much later (decades at least) before scientists realised that the physics backed him up.
– AC Young
Of course, the Earth-centered Solar System came from the Ancient Greeks and it was the Ancient Greeks that insisted that orbits must be circles (not elliptical).
Oh, the Ancient Greeks showed that the Earth wasn’t flat and most educated people in Copernicus’s time knew it wasn’t flat.
By the way, Columbus’s sailors weren’t worried about “sailing off the edge of the world”. They were worried about running out of food and water. (Columbus was badly wrong about the distance that he’d have to sail to get to China.)
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Paul (Drak Bibliophile) Howard
To be utterly just, Columbus knew that stuff had been blown ashore in the Canaries that could not have survived the generally accepted (and correct) distance to China. He just didn’t consider that that didn’t mean it was from China.
Plus, he may have heard stories from Northern European fishermen who may
have sighted North America while fishing near North America.
Hearing stories about the Norse settlements in Vinland may be a long
shot but not impossible.
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Paul (Drak Bibliophile) Howard
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I’ve read that apparently some few, a very few, American Indians made it across the Atlantic in their boats. They were either dead or they died almost immediately after being found but they seem to have been written about in a few Norse sagas and some accounts originally by Irish monks.
Actually, what his system gained in fewer epicycles, it lost in accuracy. The real innovation was Kepler’s ellipses.
And Kepler (at least at first) “believed” in the Earth-centered solar system.
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Paul (Drak Bibliophile) Howard
Apparently they were better innovators than they were Latinists; if you assume that you can use verbum to mean “word” in this idiom, you get “ut nullus verbum” from the online translators for the short form, with “pro eo” as the equivalent of “for it”. Meanwhile, a translation of the meaning (take nobody’s accuracy for granted) rather than the idiom gets you “ut nullus accurationem praesumpseram”
It makes more sense if you understand that it’s extracted from Horace:
Nullius addictus iurare in verba magistri.
-Margaret
Okay, we didn’t study him in school. My teachers favored Caesar, Virgil, Cicero (boooooooo) and St Jerome’s Vulgate.
Which most of us have to accept on authority. 0:)
I just wish I wasn’t living in a society that’s undergoing a forced transition from reason back to authority. Yeah, I’m looking at you, Mr. ‘I Am Science’ Fauxi. And the
Ministry Of Truth‘Disinformation Governance Board’ and all the recently revealed government meddling in every form of online communication. Thou Must Only Trust The Government, not anybody else, nor even your own personal experience!———————————
“The Science Is Settled!!” we are told, again and again — but then ‘The Science!’ changes every week, and somehow it’s always exactly what the politicians need it to be.
*Shrugs* we’re living through the late stages of a long running trend, going back to at least early/mid 20th century, to fetishize the trappings of science at the expense of the scientific method.
Just like the Soviet Union in the 1930’s where you could be killed for discussing Le Maitre’s theory that the Universe had a Day with No Yesterday.
My current WIP series set in a faux-Georgian/Regency makes use of these various societies of scientists, thinkers, etc., since the primary character functions as a great discoverer of what makes one part of the powers of wizards function (the part that is guild-specific (environment-specific) — the traditional skills (arcana) of each guild), and then extends that to prove that all people (eventually all beings) have some trace of the power and are capable of using something which is, in the end, microbiome based. Whether they or any creature can use it effectively (strongly or at all) is a separate genetically&educationally-bound issue.
His activities in direct practical microbiota experimentation (effectively bacterial cultivation) and the proofs of his theories essentially create a new competitive industry with both a wizardly and a practical component (analogous to the beginnings of the coal tar chemical industry). The wizard-component focus for Book 5, for example, will essentially be the development of “mauve” at the the bacterial cultivation level. (… raising the world-building & plot question of whether it is (defensible in fiction as a “what-if”) economically more efficient to produce mauve industrially from coal tar waste products or from inexpensive bacterial cultivation, once the particular (trade secret) bacteria is discovered?)
So I’ve been digesting (for world-building purposes) some of the social aspects of the various “scientific societies” in the real world, their memberships & gatherings & their spillovers into practical industry, as a significant part of the social and practical environment for my wizard-related society.
— Karen Myers
” a common theological position was that man, the pinnacle of God’s creation, was situated at the centre of the universe.”
Nope. See, for example, Dante’s Inferno. Earth was as far one could get from Heaven, the true center of the Universe. The center of the earth was occupied by Hell; Dante puts Satan smack in the middle.
Based on their writings, medieval schoolmen were far more humble and aware of their limitations than Newton or Galileo, say.
As a suggestion, I recommend CS Lewis’s “The Discarded Image” as an intro to medieval thought. If you can find it.
Btw, this is Jasini.
I was going to comment on that as well.
Earth was the basest (densest) material. We were looking up at everything else, like from the bottom a well.
“societies teetering on the transition between authority and reason” I know you’re talking about fiction at this point, but I think it’s worth mentioning that, historically, there’s only *one* case of the transition from, as Mike Flynn more accurately put it, science as art appreciation to science as the tool to subdue nature: Western Civ, traditionally referred to as Christendom.
As David Stove (an atheist philosopher) observed – nobody in history was a ruthlessly logical as the medieval schoolmen. As Aquinas himself put it: “arguments from authority are the weakest kind.” His teacher Albertus spent hours drawing detailed pictures of plants, believing that careful observation was key to understanding the world. In the 14th century, Oresme was already inventing graphing, and getting right to the brink of concepts like inertia…
…when the Black Death came along and put a damper on things. Then, in the next couple centuries of political chaos, quaintly called ‘the Renaissance,’ no advances in these areas or science in general were made. We did get some beautiful if highly derivative art out of it.
Finally, the likes of Galileo and Descartes come along – and pick up right where Oresme left off 150+ years earlier. The rest, as they say, is History – as written by Enlightenment historians, ‘the Enlightenment’ being as egregious a self-flattering contrary to fact name as the Renaissance.
I mention all this in the spirit of more interesting fiction. When authors write of alien societies conquering their ignorant reliance on authority with the pure light of reason, as an all but inevitable step in Progress – it’s passed from science fiction into fantasy, and certainly damages my appreciation of the work. Now, if somebody were to write a story where the supposed bad guy said, as Robert Bellarmine said of Galileo “I say that if there were a true demonstration that the sun is at the center of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them, than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me,” I for one would be thrilled.
Kuhn famously notes that Bellarmine was right – the evidence for heliocentrism was circumstantial, Galileo had nothing like proof or demonstration. This is why, centuries later (1851), Foucault’s Pendulum was a sensation, as it provided the first direct evidence of the earth’s rotation.
Of course, the Catholic Church didn’t use scripture to say the Earth was the center of the solar system.
They (and others) pointed to the Ancient Greeks who believed in an Earth centered solar system. 😉
Sure. In Scripture, the earth is flat, and the sky a solid dome above. This is important, for the understanding of the educated in, say, 1300, would already have concluded that the literal understanding of Scripture is, in any cases, wrong – that, in accordance with, among others, Augustine writing in the 5th century, Scripture must not be read as what we would now call a science text. Thus, it shook no educated Catholic’s faith to note that the world is round, not flat, and that that fact made no difference to the inerrancy of Scripture. It’s not affecting your faith and morals, in other words.
Interesting historical tidbit: prior to around 1550, the Church was pretty uninterested in the scientific theorizing going on in the Schools. Just scholars shooting the breeze, no big thing. But once Luther, Calvin, et al decided that they could interpret Scripture without the guidance of the Church, things got hairy. The Church realized that, in that environment, any reinterpretation was at least potentially a threat to Church teachings, and as such must be carefully vetted.
This is partly why Copernicus, who had a cushy Church job that allowed him to think and write, got into no trouble for his writing – in fact, the current Pope ordered his works published. BUT a few year’s later, when Galileo directly challenged traditional literal interpretations of Scripture, Bellarmine among others insisted that, before allowing a layman to interpret Scripture on his own, they needed to see the kind of proof that had caused all educated men to agree that the world was round – logically compelling proof.
And while Galileo had what might be called a lot of compelling circumstantial evidence, his arguments lacked the logical rigor Bellarmine was looking for. Bellarmine said: present the demonstration that shows you’re right, and I’ll lead the charge on reinterpreting Scripture. BUT – if you can’t, we’re sticking with the traditional interpretation because – here’s the important part – we see no compelling reason to do so. You can theorize all you want, but you can’t teach heliocentrism as TRUE, only as a mathematically convenience.
Galileo was never the kind of guy who could shut up. And he could not produce the required demonstration.
Galileo was also a jerk.
He publicly insulted his patron (the guy who paid his bills) and to make things worse, his patron was the Pope. 😈
And he did the insulting in the book the Pope paid him to write, so he’d have a chance to lay out all sides of the argument.
That is the kind of dumb that suggests incredibly high intelligence, because they ain’t got no sense.
If anybody has missed it, huuuuge story (well written and fun, too!) is here:
https://tofspot.blogspot.com/2013/10/the-great-ptolemaic-smackdown-table-of.html
I haven’t read Kuhn so I don’t know exactly what he said. The evidence for heliocentrism is a bit complex. What Galileo showed in his last work about Two New Sciences, was that, dynamically and mechanically, you cannot have a system with a large object being dragged about by a small one.
Newton said, “Force equals Mass times Acceleration” but he got it from Galileo. And Galileo already understood this principle, but hadn’t taken the time to show and prove it to people, until he got shot down. (See Stillman Drake)
Foucault provided the first mechanical proof of the earth’s revolution, but in the 1700’s there were several serious efforts made to prove heliocentrism one way or another. According to John Heilbrun in a book called The Sun in the Church, there was a complex optical proof done with the help of holes in church roofs, combined with meridian lines built into the floor of various churches. The meridian line in some Parisian church saved it from destruction during the French Revolution because someone argued that the church was really a gigantic scientific instrument.
Michael Flynn has a big blogpost series on Galileo’s mess. It is very informative.
The British Royal Society did something great in the 1980’s. Dr. John O’Keefe, NASA scientist, spent years arguing science things about the moon with Dr. Harold Urey (yes, that one). After twenty-five years O’Keefe convinced Urey that he was right about some point and they wrote a joint paper. But no-one would publish it. Urey said to O’Keefe’s wife that he had done her husband great damage because he had not confined himself to scientific arguments with O’Keefe, but also tried to trash his reputation. Karma, when no one would publish him because he was associating with O’Keefe. Anyway, the Royal Society invited O’Keefe to come and give a lecture on the subject. This meant that the paper would be part of the Proceedings of the Royal Society, hence published…
…If you give a talk at the Royal Society supposedly they want you there an hour early and then they lock you into a room with a crystal, a clock, and a seashell. You are supposed to be as clear as crystal, finish on time, and stick to the point like a limpet.
The Two New Sciences are based on observations on earth. The principle/assertion of Uniformitarianism – that the same laws that are discovered on earth apply everywhere else – had not yet been established. That had to wait for Newton. I’m not sure Galileo himself ever made that claim. His arguments I’ve seen were based on tides (wrong), and on observations of the phases of Venus (also wrong – Venus’s phases demonstrated heliocentrism *might* be true, but not that it *must* be true).
What was going on from a fundamental s cientific POV: instead of using the strict logic of the Schoolmen, after Galileo, scientists were proposing that good clean math trumps rock-solid logic, that it was reasonable to believe (as almost every scientist came to believe after Galileo) that the earth rather than the sun moved, because the math was so beautiful, even if they couldn’t tie down every logical objection with proof. Thus the principle seen across the 19th and 20th centuries: Einstein, etc. comes up with some beautiful math, and then everybody sets out to see if it’s true. In many ways, the opposite of observation and experimentation.
You would probably enjoy Mike Flynn’s series The Great Ptolemaic Smackdown, which begins here: https://tofspot.blogspot.com/2013/08/the-great-ptolemaic-smackdown.html
Note that in general relativity, there is no absolute reference frame, not the sun, and not even the center of the Milky Way Galaxy.
So, yes, the math is much easier when you use the sun as a reference system instead of the earth when doing calculations in the solar system, but the whole solar system is small compared to the Milky Way, so it makes sense to think of our solar system as rotating around the center of the Milky Way. And so on…
Don’t forget that every body has a gravitation pull on every other body; your impact on another planet’s orbit is negligible, but the earth’s effect is small but noticeable. Of course, the sun has by far the largest impact.
Schrodinger seems to have rebutted Dr. Johnson. (grin)
I wonder if one of the (to me unfortunate) side effects of the vehement “faith or reason – pick one!” arguments in the 20th Century is that Those In Authority decided that reason should win, and then proceeded to make Reason and Sciencism their faith. Which then trickled back into how the history of science was taught in schools, so that we have “the martyr to science” Galileo (and Girodano Bruno, of all people [eye roll here]) and falsely pitting the Catholic Church “against” science. “All the good people went for science, and the oppressive, backward people in the Church opposed it.”
If anything, it was an offshoot of Protestantism that developed in the late 1800s and coalesced with the publication of “The Fundamentals” that was the must skeptical about science and theories.
Tell them that Bruno thought it self-evident that blacks belonged to a separate species.
I generally focus on the “small, inconvenient detail” that he got in trouble for denying the Trinity and other things, not primarily because of supporting a heliocentric solar system.