Digressions&Impressions

On Olaf Stapledon, Technology induced Extinction Risk, and the Awesome new Atomic and AGI power

 The First Industrial Revolution was almost entirely dependent on coal, oil and falling water, which sources occur only in certain localities. Scientists have been exploring the possibilities of deriving industrial power from the tides, from differences of temperature (which means ultimately from sun-light) and from the disintegration of atoms. It is impossible to say yet what success will be attained in these ventures. But it seems probable that the result will be at least a far wider distribution of the sources of power. It may well be that the perfected production of atomic power will involve a vast and complex enterprise undertaken under a world-wide authority, and the universal distribution of electric current derived from atomic generators. As it is certainly probable that the transmission of power in the form of electricity is going to become very much cheaper and more efficient, ample power will be available everywhere. Each village throughout the world will either tap a high tension grid or generate its own power. As to atomic energy, its frightful dangers are obvious. It is not inconceivable that the belt of minute planets, the Asteroids, between Mars and Jupiter, is the wreckage of a world which its inhabitants accidentally destroyed by the unwise use of atomic energy. It would be a pity to turn our planet into another belt of Asteroids. But atomic energy, though dangerous, promises fabulous source of power in comparison with which coal and oil are quite insignificant. It opens up the possibility of transforming the whole face of the planet according to man's needs. It could , for instance, easily render the Arctic islands and the Antarctic Continent warm and habitable. And atomic power for industrial purposes, we are told, is already “in the offing.” Meanwhile the danger of atomic warfare is increasingly frightful. Short of exploding the planet, atomic energy used as a weapon might do so much damage that the present war, in comparison, would seem an affair of flint arrows and axes. The abolition of war becomes more urgent as man's power increases.--Olaf Stapledon (1946) Youth and Tomorrow, pp. 74-5

Olaf Stapledon (1886 –  1950) is known only to aficionados of science fiction now (Last and First Men and Star Maker are classics that shaped the genre throughout the twentieth century, and arguably kept Spinozistic ideas alive in a positivist age), but in his writings he also helped invent 'futurology' and 'transhumanism.'  I hasten to add, in case you are are of more discerning taste, J.L. Borges was an admirer of Stapledon. Stapledon obtained a PhD in philosophy from University of Liverpool under Alexander Mair (hitherto unknown to me). Stapledon's first book (1929), A Modern Theory of Ethics: A Study of The Relations of Ethics and Psychology, was clearly based on his PhD. Judging by citations, it made no impact on the scholarly world of his day. 

The quoted passage is from a short book written in preparation of a post (second) world war age. In the book, Stapledon is  committed to renewed internationalism (he clearly regrets the failures of the League of Nations) and a form of democratic socialism that can avoid dictatorship (even though Stapledon is clearly very impressed by achievements of the Soviet Union). About his politics some other time more.

The passage caught my attention because it entertains the possibility of technology induced human/species extinction of the species that deploys a new technology. This extinction possibility is in the news again thanks to the (recall) impact of Parfit's writing on longtermism and (the publicity surrounding) rapid developments in AI/AGI. 

Contemplating civilizational collapse or the extinction of species are not new thoughts in the history of philosophical writing or social theory. As I have noted (recall), in book 3 of Plato's Laws, (677a-678a) Plato's Athenian stranger entertains the possibility that the Earth has experienced frequent catastrophic natural events (he explicitly mentions massive floods and pandemics, but it's easy to imagine he also assumes earthquakes and perhaps even meteorite impacts) that have wiped out whole populations of humans and other species of animals, and has set-back the technological capability of civilizations for millennia. (We know from the Hebrew Bible account of the flood and other ancient writings that Plato is not unique in this.)

It's also not new to think that civilizational collapse is endogenous to civilizational life. Arguably this is one of the the natural ways to understand the Hebrew Bible's account of the scattering after the tower of Babel; in (recall) The Great Endarkenment, Elijah Millgram suggests that the linguistic diversification and differentiation (and subsequent cultural implosion and scattering) is itself the effect of the advanced division of labor that makes the building of the tower possible. (This is the great set-piece that opens Millgram's (2015) book.) Social theory going back to Ibn Khaldun is rife with cyclical, civilizational processes in which the key drivers of expansion and success also become self-undermining.

It's also not wholly unusual to recognize the potential civilizational collapse that is endogenous to one's own civilizational life. The writings of a number of elite authors of the final century of the roman republic are pretty clear on the fact that endurance of the roman republic is threatened by its own past history of success (due to conquest imported habits of luxury and/or empowered generals to aim for political power). Of course, often the point of recognizing the potential of civilizational collapse is to create a call to political arms, or a philosophical prophecy, to prevent the collapse from occurring (we can see hints of this in Plato's story of Atlantis). But sometimes the doom is inevitable or fated (as some of the Roman authors clearly came to think).

But, as Parfit de facto notes in Reasons and Persons, there is a non-trivial difference between foreseeing civilizational collapse of one's civilization and the collapse of one's whole species. Now, absent a certain kind of ethical or axiological cosmopolitanism, it seems obvious to me that most authors of the past lamented the possible collapse of their own civilization and showed remarkable indifference to the possible collapse of larger humanity. (This is an option that Parfit does not consider, but if he had he would clearly have suggested that this shows a clear error in their implied axiology.)

Now, Stapledown's writings suggest he is a cosmic cosmopolitan. And in this respect, he clearly fits in a philosophical tradition tracing back to Fontenelle, Huygens, and Kant.  So, it's no surprise he contemplates the possibility of endogenous technologically induced extinction among aliens as an example worth avoiding in the harnessing of atomic power. There are some hints in Youth and Tomorrow that it was written during wartime, and interestingly enough he does not mention the use of atomic weapons. But just before the passage quoted at the top of this post, he claims that "the manufacture of atomic bombs necessitates organisation of production on a national scale and the danger of the misuse of these terrific weapons forces world-wide organisation upon us." (p. 73; emphasis added)

It's a bit unfortunate that Stapledown does not clarify what he means by 'misuse' of atomic weapons here. (He was a pacifist during World War I, but not during the second world war.) Does he mean their deployment, or does he worry about them falling in the hands of rogue states/actors, or does he worry about nuclear world war? But he clearly thinks that atomic power isn't merely a technological problem, but also a political problem on a global scale. After all, he thinks that a world-wide organization is required to handle it.

In the quoted passage at the top of this post, Stapledon is discussing what we now call the 'Kuiper belt' (or Edgeworth-Kuiper belt') [UPDATED: see Ken McLeod's comment below.] But was only then recently proposed by K.E. Edgeworth in a 1943 paper in the Journal of the British Astronomical Association. It would be worth trying to figure out if Stapledon knew Edgeworth personally. In Edgeworth there is no mention of an alien civilization. I am not claiming that Stapledon is the first to propose the hypothesis that the asteroids are themselves the effect of a technologically induced existential collapse, but given this timeline he has to be among the first.* Clearly the function of Stapledon's hypothesis is to alert us to avoid this fate (not, perhaps, to create a testable hypothesis for planetary explorers of the solar system).*

It is, of course, an open question to what degree global institutional control of atomic power mitigates risk or accelerates existential risk. But since this post is long enough as is, I close with the following observation: the possibility of technology induced (endogenous) extinction is, thus, not new with the possibility of AGI. Our society has lived with the possibility of technology induced (endogenous) extinction of humanity for almost eighty years now. To say that is not to underestimate the existential risk that follows from the introduction of new technology. But it is worth noting that we have a history of living with, and perhaps managing, such risk, and perhaps we can learn from this history. For, while it would be nice if there were a technological fix to the existential extinction risk of AGI, it's more likely than not we'll need institutional and social mitigation of such risk. 

 

Spinoza, Hume, and the Story of Thales and his Olive Presses

Most courteous Sir,—When Professor N. N. visited me recently, he told me that he heard that my Theologico-Political Treatise has been translated into Dutch, and that someone, whose name he did not know, was about to have it printed. I earnestly beg you to inquire carefully into the business, and, if possible, prevent the printing. This is the request not only of myself, but of many of my friends and acquaintances, who would be sorry to see the book placed under an interdict, as it undoubtedly would be, if published in Dutch. I do not doubt, but that you will do this service to me and the cause.

A short time ago one of my friends sent me a pamphlet called "Homo Politicus," or Political Man, of which I had heard much. I have read it, and find it to be the most pernicious work which men could devise. Honor [eer] and riches are the author's highest good; he adapts his doctrine accordingly, and shows the means to acquire them; to wit, by inwardly rejecting all religion, and outwardly professing whatever best serves his own advancement, also by keeping faith with no one, except in so far as he himself is profited thereby. For the rest, to feign, to make promises and break them, to lie, to swear falsely, and many such like practices call forth his highest praises. When I had finished reading the book, I debated whether I should write a pamphlet indirectly aimed against its author, wherein I should treat of the highest good and show the troubled and wretched condition of those who are covetous of rank and riches; finally proving by very plain reasoning and many examples, that the insatiable desire for honor and riches must bring and has brought ruin to states.

How much better and more excellent than the doctrines of the aforesaid writer are the reflections of Thales of Miletus, appears from the following argument [redenering]. All the goods, he says, are in common among friends; wise men are the friends of the gods, and all things belong to the gods; therefore all things belong to the wise. Thus in a single sentence, this wisest of men accounts himself most rich, rather by generously [edelmoedig]  despising riches than by sordidly seeking them. In other passages he shows that the wise lack riches, not from necessity, but from choice. For when his friends reproached him with his poverty he answered, "Do you wish me to show you, that I could acquire what I deem unworthy of my labour, but you so diligently seek?" On their answering in the affirmative, he hired every oil-press in the whole of Greece -- for being a distinguished astronomer he knew that the olive harvest would be as abundant as in previous years it had been scanty --, and sub-let at his own price what he had hired for a very small sum, thus acquiring in a single year a large fortune, which he bestowed liberally as he had gained it industriously, &c.--Spinoza to Jarig Jelles, The Hague, 17 Feb., 1671. Translated by R. H. M. Elwes (with modest modifications).+ [Here is the Dutch version in De Nagelate Schriften.]

In today's post, I am primarily interested in the third quoted paragraph (although the first two are definitely fascinating). I have noted before (recall) that in his Natural History of Religion, David Hume explicitly treats Thales as an "atheist" and, by implication, a proto-Spinozist, who treats cosmogeny without recourse to a deity. Presumably Hume's account of Thales was influenced by Diogenes Laertius, who presents Thales as a kind of pantheist (although not a monist about gods) and Cicero, who, in De Divinitatio (1:111), treats Thales as an exemplary natural philosopher with the skill to have rational foresight of nature.

This matters because Hume treats Thales kind of as the founder of philosophy, especially natural philosophy.* In this -- that Thales is the first real philosopher -- he kind of follows the presentation of Diogenes Laertius, who also attributes to Thales the saying, 'know thyself.' 

And, as regular readers know (recall) I am quite fond of the story of Thales, and its variants in Aristoteles, about Thales' monopolizing oil-presses. Thales shows up in these digressions more regularly (recall here; here; here; here; here); and even in my scholarship (and also here). 

I was reminded of the quoted passage by Spinoza by a Dutch learned (non academic) correspondent, Marco van Heugten, in response to a handbook chapter I published on "Spinoza and Economics."  Van Heugten correctly noted I had missed its significance. This is a shame because it could have nicely supported the general claims in the chapter in which I had argued that that Spinoza thought the open‐ended pursuit of wealth is a species of madness (Ethics 4, p44S), even though he did not reject moderate desire for the conveniences of life (Ethics 4, p45c2s). (Most of my chapter is on how he diagnoses a political problem of luxury, and the institutional mechanisms by which it can be managed.)

Spinoza's version of the story of the olive presses is close to Aristotle's version. In one important respect Spinoza's version of the Thales story deviates from Aristotle's. Aristotle very strongly implies that Thales knowledge of the heavens is irrelevant to his source of wealth (regardless what Thales and his friends or the common people may have thought). Monopoly is a decidedly terrestrial feature (and, as Aristotle claims, knowledge and use of it widespread), and any correlation between celestial phenomena and harvests an irrelevant aside. As it happens this nicely fits Aristotle's tendency to treat the heavens and terrestrial matters as relatively distinct.

Spinoza, who lived in an age of commerce, and whose Political Treatise is full examples that he understands the nature of monopoly, the role of incentives, and mechanism design just fine, does not treat Thales' astronomical knowledge as an aside. Post Galileo and Descartes, one may say, the heavens and earthly matters are re-integrated and so the idea that one could forecast (the directionality of) harvests based on astronomical observations was not wholly implausible. (Of course, Spinoza also recognizes that Thales was a monopolist.)

The point of the previous passage is nicely illustrated by Gassendi's (1649) treatment of the anecdote in volume 2 of the Animadversiones. My former (Ghent) colleague, Steven Vanden Broecke called my attention to it.+ Gassendi, who is a critic of judicial astrology, cannot take the relative decoupling of the heavens and terrestrial matters for granted because the new science is re-integrating them (which opens the door to certain forms of astrology still familiar to casual readers of the newspaper). And so he adds more detail about the kind and historical basis of empirical knowledge Thales would have possessed.

As an aside, if I were Justin Smith, I might report to you the contents of seventeenth century almanacs on seasonal forecasting here. But I'll stick to what I know and mention that in the nineteenth century, the economist-logician, Jevons, tried to model, like a modern Thales, the correlation between sun spots and grain harvests. As I learned from my friend Sandra Peart, Jevons thought that the sun spots shaped economic moods (and expectations). Jevons treats Thales as "the father of philosophy."

Interestingly enough, Spinoza does not treat the anecdote about Thales to criticize the vulgar who mock the learned (which is common feature in the story about Thales). Rather, in his rendering it's Thales' own circle of friends who need persuading. And this makes me think that the letter to Jelles was partially intended for Spinoza's circle. 

This suspicion is strengthened by the fact that I have been unable to find the source of the 'argument' attributed to Thales, who is presented here as an exemplary, generous wise man (and it seems to me worth comparing it with (Ethics IV, P45S)). Since Spinoza lived a life very much in the spirit of the 'argument,' it was undeniably important to him. It's psychologically interesting that Spinoza volunteers the story after suggesting he will write a pamphlet (which he never did) against the doctrines of Homo Politicus. And the implication is that he, too, could be rich if he had wanted to be. This would have appealed to Jelles, who was a merchant, but who had turned his back on the business world and had been devoted to his studies. But judging by Spinoza's request to him (in the first paragraph), Jelles was taken to be still influential in worldly affairs. 

So, let me wrap up. Of course, in Spinoza the real point is that if one has wealth one should bestow it on noble causes. This echoes the account of liberality in Book IV (I think, please correct me) of Aristotle's Nicomachean Ethics. And this is either a hint to his friend (who was wealth), or, perhaps more kindly, a thank you to his generous friend. 

We know that Adam Smith very much lived in the spirit of the argument attributed to Thales by Spinoza. (I don't have any reason to think Smith was influenced by Spinoza's depiction of Thales on this score.) But Hume does not. Hume explicitly defends the pursuit of (non-excessive) riches for the wise man and offers himself as an exemplar in his autobiography.

As regular readers know, I think Spinoza is not very far from Hume's pre-occupations at key points in his works. Paul Russell has offered solid reasons for thinking that this idea is a natural effect of the presentation of the Treatise.** In that light it is worth remarking, again, that in Hume's hands, at the start of his own philosophical project, Thales is treated as a natural philosopher and not a moral philosopher. This is, in fact, revisionary because it goes against Thales as one of the exemplary Greek wise men (and the presentation in Diogenes Laertius). And so a Spinozist, free-thinking reader of the Treatise is also alerted to the fact that Hume is no slavish follower at all.  

 

 

 

RIP: Noel Swerdlow (1941-2021)

My graduate school classmate at The University of Chicago, Matt Kerrigan Frank, alerted me to the fact that Noel Swerdlow recently passed away. (See this obit.)

I met Noel on one of the first days in graduate school back in September 1995. The seminar room was busy filling up with faculty and graduate students from philosophy and history of science for one of the many, weekly joint seminars I would attend during the next seven years. I was trying to impress David Malament with my knowledge of the Huygens/Newton debate which I had been researching under the guidance of George Smith (one of my undergrad gurus). An old crank -- I now realize he was then barely older than I am now-- interrupted my narrative to tell me that Huygens' objections to Newton's inverse law were primarily metaphysical. I tried to explain to the guy that Koyré's view had been refuted (by George and me). I never get a chance. I asked David, "who is that old man?" and he informed me it was Noel Swerdlow.

Over the next few years I saw Noel in action at the various joint seminars: often abrasive and impatient, but at times quite brilliant. Some of his exchanges with visiting scholars could be quite spirited. (His exchange with Motti Feingold was legendary, but they were or became close friends.)

My relationship with Noel evolved once he spent some time away at Dibner (where George had become director). After we met again on campus, he told me with a big smile "you could have told me about all the archival research that went into the Huygens paper [see here]. I thought you were just bluffing. It's really marvelous work--I love the argument with the maps." I meekly tried to say, "i tried." But something had changed, I was now on his good side. And to receive a compliment from Noel (or anyone in graduate school) was one of the highlights of my graduate career.

He was famous for his work on Babylonian astronomy (he was a student of the legendary Otto Neugebauer), but I have to admit that as a PhD student I loved learning about Copernicus and his (obscure to me) peers from Noel. I also have a memory of him playing piano, but I have not seen this mentioned in any obituary so maybe I am confused. We discovered our shared love for opera at the Lyric, and I always looked forward to seeing him there. (He was very learned on opera.)

When I was nearly done with my PhD, I had the luminous idea to ask him to read Adam Smith's posthumous "History of Astronomy" with me. This piece was central to my dissertation. I was delighted he agreed, and even more that he had never read it before. (I always assumed Noel pretty much had read everything.) I expected that Noel would be extremely critical of Smith as a historian (as the editors of the Oxford edition are). But Noel was, in fact, quite impressed with Smith's historical acumen and, more importantly, gave me a graduate seminar on all the possible sources Smith could have consulted during the 18th century. He also flattered my vanity in assuming that I was intimately familiar with all the works of Regiomantus, Riccioli, and Peuerbach. Often after our reading group at The Medici I had to go to special collections to figure out what he was saying. (This was before the age of google.books!)

Later, when I realized I had bombed out on the job-market first time around, he even helped me apply (and wrote a letter) for a project on Smith as historian of astronomy. But that was not funded.

At the time, i assumed it was normal for historians of astronomy to have a position in an astronomy department.  So, I later used that as an argument for my paper on "philosophy and a scientific future of the history of economics" But I have learned it is much less common (although archeoastronomy is sometimes practices by professional astronomers). 

That paper was part of a rather contentious symposium. organized by Paola Tubaro & Erik Angner. To be clear the symposium was lovely but our audience of established historians were underwhelmed. I think referees managed to prevent bublication of some of the papers.
Anyway, my core idea was that the history of economy theories could play an evidential role in present day economics as the custodians of the theories and data of the past. This was not well received at all. But it let to an invitation by Bertram Schefold to reflect on the possibilities and significance of economic history. I did not know much about the practice of economic history. But as I was musing about the invite, I wondered what the oldest economic data might be. The hunch being that if you have data very far apart this might help you to calibrate important measures.  So on a lark I googled (!) "Babylonian economics" and I was directed to Alice Louise Slotsky The Bourse of Babylon Market Quotations in the Astronomical Diaries of Babylonia, which I read and loved.

I was astonished to learn that the very clay tablets with astronomical data Noel had studied also had economic data on them! I started drafting one of the craziest and fun papers I ever wrote, "Prophecy, eclipses and whole-sale markets: A case study on why data driven economic history requires history of economics, a philosopher’s reflection." [published in Jahrbuch für Wirtschaftsgeschichte/Economic History Yearbook 50.1 (2009): 195-206.]

With some trepidation I sent an early draft to Noel. Rather than scolding me for my amateurishness (this was the initial response of some of my Leiden colleagues who were experts on ancient Mesopatamia--I think they really thought I was crazy), he wrote lengthy letters on the quality of the data that I wanted to use. (The published version of the paper includes excerpts from his letters to me. ) Nobody seems to have read this paper, but it was good enough for me that Noel (who called my attention to relevant other scholars) took it seriously enough to try to help me improve it.

In later years, Noel would always read works I sent him. Sometimes even my blog. Even when I relied on impeccable scholarship of others, he would correct mistakes that had crept into now famous scholarly works. My favorite letter, however, is this one-liner, "Take it down; it's nonsense!--Noel."

On the Epicurean Conception of Gravity, and Newton

[T]here is a second aspect of Newton’s thought that is relevant: there are numerous instances in which both Newton and his followers reject action at a distance in strong terms. Newton’s apparent rejection of distant action in the correspondence with Bentley has been subject to considerable debate, but Newton makes similar points elsewhere, even in unpublished works that cannot be read as involving a hedging of his bets. For instance, in the unpublished corollaries to propositions 4 through 9 of Book III to the Principia, written in the early 1690s, when Newton thought a second edition of his text might appear, he writes:

For two planets separated from each other by a long empty [vacui] distance do not attract each other by any force of gravity or act on each other in any way except by the mediation of some active principle [movente principio] interceding between them by which the force is transmitted from one to the other.[1]

Unlike the Bentley correspondence, this is a direct expression of Newton’s own understanding of gravity, one that is entirely independent of the questions about Newton’s views of the essence of matter and his attempts to distance himself (perhaps) from what were then called “Epicurean” conceptions of atoms in the void (cf. Henry, 2011). There cannot be a clearer statement of his views: two planets do not act on each other in any way except through some mediating item.--Andrew Janiak (2013) "Three concepts of causation in Newton." Studies in History and Philosophy of Science Part A 44.3 (2013): 403

As regular readers may recall, I am one of Janiak's targets in context.* And I have to admit that when I first read Janiak's paper I thought his evidence was so strong that I had to concede that after the publication of the Principia, Newton did not return to the position that I attributed to him (here; here) based on my reading of the posthumously published Treatise of the System of the World, an early version of what became book III of the Principia.

But before I was going to throw in the towel, I wanted to check out the wider context of the passage quoted by Janiak. It reads as follows:

The Epicureans making a distinction of the whole of nature into body and void, denied the existence of God, but very absurdly. For two planets separated from each other by a great expanse of void do not mutually attract each other by any force of gravity or act on each other in any way except by the mediation of some active principle that stands between them by means of which force is propagated from one to the other. [According to the opinion of the ancients, this medium was not corporeal since they held that all bodies by their very natures were heavy and that atoms themselves fall through empty space toward the earth by the eternal force of their nature without being pushed by other bodies.] Therefore the ancients who grasped the mystical philosophy as Thales and the Stoics more correctly taught that a certain infinite spirit pervades all space, and contains and vivifies the entire world; and this supreme spirit was their numen; according to the poet cited by the Apostle: In him we live and move and have our being. Hence the omnipresent God is recognized, and by the Jews is called 'place'. To the mystical philosophers, however, Pan was that supreme numen...By this symbol, the philosophers taught that matter is moved in that infinite spirit and by it is driven, not at random, but harmonically, or according to the harmonic proportions as I have just explained.[2]

As McGuire notes (1968: 169), the manuscript probably dates from the mid-1690s when Newton became eager to situate his own work in light of ancient epicureanism. (I have tried to explain why this would be so here.) Here the mediating active principle just is the Stoic world soul, which appears to be an electric spirit of some sort. So, at first glance the wider context seems to support Janiak’s position.

And before I address the position, I have to note a complication. A very natural reading of the General Scholium, which was drafted a decade or two later, of the Principia is that he denies that God is a world soul (Newton 1999: 940; recall last week's discussion.) Rudolf De Smet & Karin Verelst have convincingly argued that here (and in a few other places of the General Scholium) Newton is echoing Lipsius's attack, inspired by Philo, on the old stoic notion  of anima mundi. So, we are by no means required to accept this manuscript as authoritative expression of Newton’s all-things-considered views. But because I have expressed some doubts that Newton really does reject the world soul altogether, this move is not entirely open to me.

However, and more controversially, I now think Janiak was wrong to think that the manuscript offers "a direct expression of Newton’s own understanding of gravity, one that is entirely independent of the questions about Newton’s views of the essence of matter and his attempts to distance himself (perhaps) from what were then called “Epicurean” conceptions of atoms in the void." In fact, now I deny that we are supposed to treat the key sentence – “For two planets separated from each other by a great expanse of void do not mutually attract each other by any force of gravity” – as really expressing Newton’s own position. For, he could be expressing the Epicurean position here. In fact, I think it is a natural reading of Epicurus' physics as expressed in the "Letter to Herodotus" reproduced in Book X of Diogenes Laertius Lives of Eminent Philosophers.  

Epicurean gravity is directed down to a privileged place (Epicurus, Letter to Herodotus, section 61). And this is so in infinite worlds (section 45). In a void atoms, which constitute bodies, do not interfere with each other unless they accidently deflect each other from their path (Epicurus, Letter to Herodutus, section 44). So, in Epicurean cosmology, the atoms on a planet move down, barring deflection and the swerve, and planets do not attract each other. So, a natural way to read the Epicureans is that two planets separated from each other by a great expanse of void do not “mutually attract each other by any force of gravity.” The atoms that constitute such planets have a tendency to press toward the center of each planet. But there is no reason to think they attract each other across the void. 

So, if one is antecedently convinced that Newton rejects the possibility of action at a distance, then, indeed taken in isolation --- "for two planets separated from each other by a great expanse of void do not mutually attract each other by any force of gravity or act on each other in any way except by the mediation of some active principle that stands between them by means of which force is propagated from one to the other" -- seems like a smoking gun. But the sentence before it and the sentence after it discuss ancient theories. In fact, the following sentence ("bodies by their very natures were heavy and that atoms themselves fall through empty space toward the earth by the eternal force of their nature without being pushed by other bodies") just conveys the Epicurean position. 

So, a natural reading of the first three sentences of the manuscript is as a description of a debate between Epicurean atheists and ancient (mystical-theist) critics. And I am willing to believe that Newton agreed with the critics that the Epicurean position was absurd. Not just because the Epicureans could be taken to deny God's existence, but also because Newton himself has established that Jupiter and Saturn did influence each other (Principia, Book III, Proposition 18, Theorem 18; Newton 1999: 818)

 

 

On Newton's Third Rule of Reasoning and Rational Theology (or on Brading on Newton's Philosophy of time), pt I

I agree [with Schliesser] that [I] Newtonian absolute time (p.18) should not be conflated with Newtonian true time. I agree that, for [II] the purposes of the Principia, Newton does not need his time parameter to extend from infinity to infinity. I agree that [III] the spatial reach of Newton’s time parameter in the Principia is an empirical matter. However, I do not think that, [IV] for Newton,“absolute” and “true” mark Schliesser’s distinction between a spatially limited empirical time parameter and a theologically motivated, infinitely extended “time.”
Initial doubts about Schliesser’s interpretation arise when we notice that in the scholium Newton does not make the positive assertion that absolute, true, or mathematical time are eternal in duration, nor does he assert that space is infinite, and nor does he assert that each moment of time extends from infinity to infinity. We are familiar with these claims from other places in Newton’s writings, but in this part of the text, where Newton is setting out what is needed for the project of the Principia, no such positive claims are made.
Moreover, the distinction that Schliesser draws is not one that we find doing work for Newton in his argument in the Principia, such that he has reason to mark it by means of a terminological distinction. As evidence for this, consider that Newton has just as good reasons to think that his absolute time extends to the physics of the distant stars and to the planetary systems around distant stars (if any such exist) as he does to think that his laws of motion and law of universal gravitation apply to such bodies, and he does not make the solar system the boundary of applicability for these latter.
Newton worried about how we extend our knowledge to bodies beyond the reach of our experiments, and this worry is explicitly addressed in his Rule 3 of Reasoning, added to Book 3 in the second edition of the Principia (Newton 1999, 795):

Those qualities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.

This rule plays a crucial role in enabling Newton to extend results from terrestrial experiments to the celestial bodies of the solar system. In applying Rule 3 to bodies beyond the solar system, we would certainly be wise to be tentative given the flimsiness (even non-existence) of our empirical evidence, but there is nothing in Newton’s writings to indicate a sharp cutoff at the outer edges of the solar system such that we should not consider distant stars to be bodies. On the contrary, the possibility of other worlds around other Suns, governed by the same laws, is very much part of Newton’s thinking. For example, there is a manuscript in which Newton (p.19) asserts that the fixed stars are bodies just like our Sun: they are formed into spheres by their own gravity, and since they are bodies, they are, by definition, subject to the laws of motion. It seems to me that the distinction Schliesser draws is not important for Newton’s purposes.
Finally, the contexts in which Newton extends moments of time to spatial infinity are generally also those in which he is talking about God’s presence in the world, rather than those in which he is concerned with methods of reasoning from the phenomena.
In my opinion, we have good reason to suspect that Newton was careful not to overreach empirically when he was setting out his accounts of time and space in the scholium (i.e., at the outset of the empirical project of the Principia). There is therefore reason to doubt that the inclusion of “true time” is an “unnecessary addition” (Schliesser 2013, 91). In the following section I propose an alternative interpretation of the terminology, in which each of his three distinctions—absolute versus relative, true versus apparent, and mathematical versus common—are relevant and important for the project of the Principia.--Katherine Brading (2017) "Time for Empiricist Metaphysics" in Metaphysics and the Philosophy of Science: New Essays edited by Matthew Slater and Zanja Yudell [emphases added for ease of discussion.]

While it's pretty baffling to be told by a referee#2 to cite [fill in your name + year], there is, in academic life, no stranger feeling than to publish a scholarly paper about which one thinks firmly, 'this has to be wrong' and one simultaneously believes in exhilarated fashion, 'I am on to something really important.' So far I have only thought that once, when my Newton's Philosophy of Time (2013) appeared in print (thank you Adrian and Heather for seeing it through!)

Now, between (ca) 2007 and 2015, I was immersed in a collegial community of Newton scholars, which -- thanks to email and a steady stream of workshops -- shared papers and ideas regularly  (Brading's letters were often at the root of my papers); and many of the best ideas in my Newton's Philosophy of Time paper originated with or had been commented on by them. And, in fact, the (2013) paper's core starting point, that we ought not assume that absolute and true time are identical, originates in reflecting on a paper by Nick Huggett, who had claimed that absolute and true motion should not be treated as the same concept in the famous scholium to the definitions of the Principia.

Somewhat strangely, while there is huge sophisticated literature on Newton's philosophy of space, there are only a few papers on Newton's philosophy of time. There is, however, a general presumption that Newton's treats them in more or less identical or at least symmetrical fashion as was more common in early modern world (Geoff Gorham has explored this). And Newton invites the idea when he writes, in the scholium to the definitions, 'Just as the order of the parts of time is unchangeable, so, too, is the order of the parts of space.'

In the scholium to the definitions, Newton tells us that space and time are both abstract "quantities" and that these can be distinguished "into absolute and relative, true and apparent, mathematical and common."

But alerted by Huggett's paper, I had noticed something quirky. Compare the following two sentences (they are both the first sentence of the respective paragraphs in which these quantities are explained):

[A]: Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration.

[B] Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable.

'True, and mathematical' are absent in [B]! Now look at what Newton says about the relevant contrast (in the next sentence of each paragraph):

[A*] Relative, apparent, and common time is any sensible and external measure a (precise or imprecise) of duration by means of motion; such a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time.

[B*] Relative space is any movable measure or dimension of this absolute space; such a measure or dimension is determined by our senses from the situation of the space with respect to bodies and is popularly used for immovable space, as in the case of space under the earth or in the air or in the heavens, where the dimension is determined from the situation of the space with respect to the earth.

Again, "apparent, and common" are absent in [B*].+ In addition, there is a further asymmetry in the measures.  When the (regular) motion of bodies are used (qua measure of time), something physical is deployed to track an abstract quantity (viz. absolute time, etc.) But when the situation of one body relative to another body is used,  it looks like the very abstraction you are trying to track is already in the measure. (Of course, this is also true of motion, qua measure, which presupposes the very abstract regularity you are trying to track.) But to put the point informally, Newton is proposing to treat a part of space as the measure of space. He treats something that is prima facie not time as the measure of time.+ 

This is not the place to recount what I did with these initial observations. You can infer some of what I claimed in my paper from some of Brading excellent criticisms quoted above. As I said above, I had strong feeling that something had gone wrong in my argument. And, as it happens, in the piece I partially quoted above, Brading has articulated the version of Newton's position that I would have expected to articulate myself (except that she does so much better than I could imagine myself doing) before I had started writing my own paper. And when I first heard her paper, and than read it when it appeared, I was both pleased she agreed with me on [I-III] and convinced she is right about the remaining differences between us, that is [IV]. 

But as she guessed in a recent note to me, I don't really believe in the inner recess of my heart that I am wrong about [IV]. And so here I want to begin spelling out why. And, rather than going to the heart of the matter, I start by sorting out some preliminary disagreements. Today I tackle two such disagreements. I fully agree with Brading that rule 3 "plays a crucial role in enabling Newton to extend results from terrestrial experiments to the celestial bodies of the solar system." And that, while there are epistemic risks, the rule also encourages to project "to bodies beyond the solar system." But notice that in the quote from Rule 3, Newton mentions bodies, or as David Miller has emphasized, systems or, as I (influenced by Chris Smeenk) would say, interactions among bodies in rule 3. He does not mention space or time in the rule. 

And, in fact, in the Opticks, Newton had queried “it may be also allowed that God is able to create particles of matter of several sizes and figures, and in several proportions to space, and perhaps of different densities and forces, and thereby to vary the laws of nature, and make worlds of several sorts in several parts of the universe.” (Query 31; emphases added.) This passage is interesting for what Newton thinks about the nature of the laws of nature (see my (2017) piece with Zvi Biener, which engages with Brading's influential views on laws).  But here I use it to note an important contrast: for Newton it is quite conceivable that bodies and the laws they obey could be different whereas he does not think space could be different. And, in fact, for Newton it is conceivable, as a speculative matter, that in solar systems (what he calls "worlds") far from ours bodies and their laws are different (such that the galaxy is populated (by "worlds of several sorts in several parts of the universe"). Such speculations are not to be used in active research (which is, in fact, governed by rule 3).

As an aside, because solar systems are so far apart, and separated by empty space, there is negligible interaction among them. (According to the general scholium, this is a providential thing because it prevents the solar systems from collapsing onto each other.) I say 'negligible' because light does reach us from afar. And there is no reason to think it obeys different laws. 

But crucially, space cannot be created differently by God. And that is, as Newton explains in the general scholium,“by existing always and every where, [God] constitutes Duration and Space . . . ’Tis allowed by all that the supreme God exists necessarily; and by the same necessity he exists always and every where.” So, space, and time, are unchanging because they are constituted by God. In effect, they are privileged attributes of God. So, while time is not mentioned in the passage quoted from Query 31, it seems natural to read Newton as claiming that fundamentally time is necessarily unchangeable, while bodies could be different. 

Okay, this puts me in position, to mark a second (less important) misconception (for which my terminology may be to blame). Brading appears to think that when I use 'rational theology' I mean unempirical. Now, it is true that I argue that unlike absolute time, true time is of no use in Newton's dynamics or the physics proper of the Principia. But by this I do not mean that true time is thereby unempirical. For, Newton is quite explicit in the general scholium that theology is, in part, an empirical enterprise: "to treat of God from phenomena is certainly a part of "natural" philosophy.""

But rather by 'rational theology' I meant (by way of analogue to 'rational mechanics') that there are features of Newton's theology that, while attentive to the phenomena, rely on conceptual moves and (what I have called (recall) Newton's 'modal metaphysics' [see also here; here]) from those phenomena and that (those moves) are not overdetermined by the empirical findings. So, for example, what grounds (true) time in God is a constitution relation governed by a species of necessity.

Now this second misconception is not just a terminological matter because for Brading Newton's contribution to metaphysics (and its history) is precisely to allow the kind of distinctions between true and absolute time to "become empirically tractable in the context of the project of the Principia (or some such project)." I think she is right about this, but that she also has a tendency to downplay the extra-empirical conceptual/metaphysical moves (e.g., constitution, necessity, etc.) Newton makes from the phenomena. (That is she turns Newton into an empiricist of a sort I don't think he is.) But I have gone on for too long today.

Notice that everything I have said thus far is compatible with Brading being right about how we should distinguish between true and absolute time in Newton and also that both kinds of time have a place in Newton's physics, that is, the project of the Principia proper. But to settle these matters it is not sufficient to nitpick about her criticism of my view, but I must engage with her "alternative view." [To be continued...]

On Eugenics, Armed Robots, and Sparta; (Asimov's Libertarian Utopia)

Now Sparta in its hey day consisted of a relatively small number of Spartiates, the only full citizens, plus a somewhat larger number of second class individuals, the Perioeci, and a really large number of outright slaves, the Helots. The Helots outnumbered the Spartiates a matter of twenty to one, and the Helots were men with human feelings and human failings. In order to make certain that a Helot rebellion could never be successful despite their overwhelming numbers, the Spartans became military specialists. Each lived the life of a military machine, and the society achieved its purpose. There was never a successful Helot revolt.

Now we human beings on Solaria are equivalent, in a way, to the Spartiates. We have our Helots, but our Helots aren’t men but machines. They cannot revolt and need not be feared even though they outnumber us a thousand times as badly as the Spartans’ human Helots outnumbered them. So we have the advantage of Spartiate exclusiveness without any need to sacrifice ourselves to rigid mastery. We can, instead, model ourselves on the artistic and cultural way of life of the Athenians, who were contemporaries of the Spartans...

“Civilizations have always been pyramidal in structure. As one climbs toward the apex of the social edifice, there is increased leisure and increasing opportunity to pursue happiness. As one climbs, one finds also fewer and fewer people to enjoy this more and more. Invariably, there is a preponderance of the dispossessed. And remember this, no matter how well off the bottom layers of the pyramid might be on an absolute scale, they are always dispossessed in comparison with the apex. For instance, even the most poorly off humans on Aurora are better off than Earth’s aristocrats, but they are dispossessed with respect to Aurora’s aristocrats, and it is with the masters of their own world that they compare themselves.

“So there is always social friction in ordinary human societies. The action of social revolution and the reaction of guarding against such revolution or combating it once it has begun are the causes of a great deal of the human misery with which history is permeated.

“Now here on Solaria, for the first time, the apex of the pyramid stands alone. In the place of the dispossessed are the robots. We have the first new society, the first really new one, the first great social invention since the farmers of Sumeria and Egypt invented cities.”--Isaac Asimov (1957) The Naked Sun

The passage is quoted from a speech Quemot, a sociologist sought by the main protagonist, Elijah Bailey, a detective from (future, post-Nuclear apocalypse) Earth invited to investigate a murder on Solaria.* Solaria is a very wealthy society in which robots vastly outnumber humans and in which eugenics has been perfected.

In an interesting and potentially far-seeing twist, in this society people avoid nearly all direct (they call it seeing) contact with each other, and if they must interact at all, they do so entirely through remote devices (viewing). [This is also true for married couples, which meet at scheduled moments to do the deed if they have clearance to have children.] In fact, from a young age kids are socialized not just to experience the world through viewing, but to feel intense disgust being around each other in person (there is no such disgust when viewing such that they completely lack a taboo on nudity).  

As an aside, there is an unintentional irony in noticing that a novel set in the future treats sociology as the queen of the human sciences. Bailey seeks out Quemot because on his home planet, the sociologists are the leading experts to government -- no surprise because it must keep a huge human population, which is literally holed up underground quiet --, and he thinks it useful to get some useful background to Solarian society. On Bailey's Earth, sociology is a sophisticated mathematical science, but in his militarily and economically advanced society, Quemot shows little interest in it.

Solaria approaches the character of a community of wise people because there is very little in the way of organized government, yet it flourishes. (I say approaches because philosophy is clearly absent.) There is no need for government due to the lack of 'friction.' I call it a 'libertarian utopia' (somewhat jokingly) because initially uninhabited, Solaria was founded without original sin violence by very wealthy individuals who appropriated the land and turned this planet of holiday villas into a self-supporting, exclusive gated community. There is no exploitation on Solaria because the robots do nearly all the work. (From the perspective of a robot-ethicist the previous sentence may require considerable modification.)

One may correctly quibble in calling Solaria 'libertarian' because of the existence of three important constraints: (i) estates are not allowed to be divided or sold; (ii) estates are not inherited (and on the whole parents do not know who their kids are); (iii) the population of Solaria is held constant (at relatively small number of 20,000). Once an estate-holder dies (after many centuries), one of society's genetically optimized kids, who are reared communally at a planetary wide center, takes possession. So, while there is some inequality among the estates, this is wholly due to luck. One may suspect that these three constraints are a limitation on people's choices. But the narrative strongly implies that the constraints are fully consensual, agreed upon at the original founding and not disputed by any of the Solarians. Of course, a libertarian may well object to the collective brainwashing of kids even if their parents and society decide to do so.

The reason why these constraints are not disputed is because Solarians lack (what we may call) drive; they do not desire accumulation nor desire each other. They also lack competitive emulation. However, they do have pride in their genetic make-up (see here; and here), which is notable given that they possess this without any personal merit. 

It is notable that in a society full of robots, the Spartans are seen as machine-like. The implication is that each Spartan fulfilled a singular functional--that is, military hegemony over the more fully rounded human-Helots through self-mastery. Quemot does not stop to consider that his own people are machine-like in their singular devotion to disease-free, longevity without signs of aging.** 

Asimov's robots obey the three laws of robotics. These are meant to prevent the foreseeable, inductive risk of robots being deployed to harm humans. The Naked Sun relies on the distinction between reason and logic, and this distinction is exemplified by illustrations of how in virtue of robots's reliance on logic, they can be tricked into unknowingly harming humans. In a society in which humans are vastly outnumbered by robots the most dangerous taboo centers on weaponizing robots that can be knowingly and without effort be used to harm other humans without the robots realizing they do so. With the development of fully autonomous weapons systems, we can say that humans are crossing a disastrous threshold.

 

On the Ancient Wisdom of the Babylonians;

    A modern trigonometric table is a list of right triangles with hypotenuse 1 and approximations to the side lengths sin θ and cos θ, along with the ratio tan θ = sin θ/ cos θ . We propose that P322  is a different kind of trigonometric table which lists right triangles with long side 1, exact short side β and exact diagonal δ– in place of the approximations sin θ and cos θ. The ratios β/δ or δ/β (equivalent to tan θ) are not given because they cannot be calculated exactly on account of the divisions involved. Instead P322 separates this information into three exact numbers: a related squared ratio which can be used as an index, and simplified values b and d for β and δ which allow the user to make their own approximation to these ratios.
    If this interpretation is correct, then P322 replaces Hipparchus’ ‘table of chords’ as the world’s oldest trigonometric table — but it is additionally unique because of its exact nature, which would make it the world’s only completely accurate trigonometric table. These insights expose an entirely new level of sophistication for OB mathematics. We present an improved approach to the generation and reconstruction of the table which concurs with Britton, Proust and Shnider (2011) on the likely missing columns. We present the generally accepted reconstruction of the table both in sexagesimal form as P322(CR) and also in approximate decimal form as P322(CR-Decimal8). We show that in principle the information on P322(CR) is sufficient to perform the same function as a modern trigonometric table using only OB techniques, and we apply it to contemporary OB questions regarding the measurements of a rectangle.
    We then exhibit the impressive mathematical power of P322(CR-Decimal8) by showing that P322 holds its own as a computational device even against Madhava’s sine table from 3000 years later. This is a strong argument that the essential purpose of P322 was indeed trigonometric: suggesting that an OB scribe unwittingly created an effective trigonometric table 3000 years ahead of its time is an untenable position.
    The novel approach to trigonometry and geometrical problems encapsulated by P322 resonates with modern investigations centered around rational trigonometry both in the Euclidean and non-Euclidean set-tings, including both hyperbolic and elliptic or spherical geometries (Wildberger, 2005, 2013, 2010). The classical framing of trigonometry and geometry around circles and angular measurement is only one of a spectrum of possible approaches, so perhaps we should view angular trigonometry as a social construct originating from the needs of Seleucid astronomy rather than a necessary and intrinsic aspect of geometry.--D.F. Mansfield, N.J. Wildberger (2017) "Plimpton 322 is Babylonian exact sexagesimal trigonometry," Historia Mathematica, 2. [Ht Dan Schneider & Sam Rickless]

About a decade ago, I was contemplating an argument that suggested economic ideas needed to be tested on data-sets far removed, temporally and culturally, from the present (see here for the fruits of my research; and especially here). I googled, and stumbled on a dissertation, The Bourse of Babylon, by Alice Slotsky (now twenty years old). To simplify, because all dissertations are complex entities, it presented and interpreted ancient tables, going back many millennia, with price data alongside astronomical data (the  latter being more familiar to historians of science). These price data alone has inspired quite a bit of fascinating research by economic and political historians. But none of the research I found (except for Slotsky's) really addressed the question why the ancient scribes of the temple of Marduk would put sophisticated astronomical data alongside detailed market data in the very same tables. While we cannot completely rule out that the tables were used to generate or predict omens, I think part of the answer has to do with the fact that these very same tables also include natural phenomena important to agriculture. That is, I thought, and still think, these tables represent a basket of goods (useful both for comparing purchasing power as well as for thinking about insurance purposes) that [A] allowed the ancient Babylonians to try to find, or manipulate, patterns in prices related to natural (astronomical and agricultural) cycles and, perhaps, political disturbances. Let's call [A] a hypothesis about Babylonian scientific mind-set in which earthly and celestial patterns may have an intricate connection. Of course, it is unclear what exactly is the content of [A] until the clay-tablets are studied with an open mind. (When I was a PhD student I got hints of the excitement surrounding these tablets from Noel Swerdlow.)

Now, Aristotle was familiar with [A] because in the Politics he reports a version of [A] as a fable about Thales:

"so the story goes, because of his poverty was taunted with the uselessness of philosophy; but from his knowledge of astronomy he had observed while it was still winter that there was going to be a large crop of olives. So he raised a small sum of money and paid round deposits for the whole of the olive-presses in Miletus and Chios, which he hired at a low rent as nobody was running him up; and when the season arrived, there was a sudden demand for a number of presses at the same time, and by letting them out on what terms he liked he realized a large sum of money, so proving that it is easy for philosophers to be rich if they choose, but this is not what they care about. Thales then is reported to have thus displayed his wisdom, but as [20] a matter of fact this device of taking an opportunity to secure a monopoly is a universal principle of business; hence even some states have recourse to this plan as a method of raising revenue when short of funds: they introduce a monopoly of marketable goods.." (Aristotle, Politics 1; 1259a)

What's interesting about Aristotle's response is that he offers an unmasking of the story. Aristotle shows that Thales exploits a universal mechanism (local monopoly) that drives up prices. Aristotle is not interested in exploring either (a) an error theory, that is, why would people have thought this about Thales nor (b) the possibility that the story is, in fact, a true report of Thales's beliefs. (In both cases, Aristotle's unmasking can still be the true explanation of the observed price rise.)+ In other research, I have explored the significance of Thales as the original exemplar of philosophical wisdom (including Aristotle's rejection of the Socratic idea -- recall Theaetetus, [174a] --that Thales contained secret, esoteric wisdom in Nicomachean Ethics, 6.7.5)[recall this post] and Hume's insistence that Thales is the origin of Spinozism (recall). Both (a) and (b) take the historical significance of [A], the Babylonian mind-set seriously in a way that Aristotle's move rules out.

That is to say, while we find in Plato, especially, occasional nods to older knowledge in Egypt and Mesopotamia and some invitation to explore it, Aristotle's philosophy, with its enormous interest in empirical observation, shows a remarkable tendency to exclude the very possibility of eastern, ancient knowledge and removes [A] from serious consideration. While Newton scholars are not unfamiliar with the fact that the Platonic impulse recurs throughout history, where it gets merged and touched with Hermetic and even Protestant ideas (for a great book that I have  been reading on the topic, see Levitin's massive Ancient Wisdom in the Age of Science); the touchstone for knowledge are the concepts and ideas familiar from, and developed out of, Greek science and philosophy. (The previous sentence allows, of course, that this development also involves a series of revolutionary rejections of modes of thought found in Greek science and philosophy.)

The significance of this is two-fold: first, our philosophical tradition has an original rejection of what I (and, recall, Justin Smith) have called 'rustic wisdom' (recall here). We can (recall) understand the significance of David Graeber's work as, in part, a reflection on the consequences of this rejection:  our inherited, urbane traditions of philosophy fail to recognize that our manners (note the plural) of theorizing are itself conditioned by particular and peculiar circumstances. In particular, these circumstances presuppose the violent eradication of alternative ways of thinking.

[Update: this paragraph inserted:]* The Babylonians represent, of course, an urbane philosophy (not rustic wisdom). What I had not previously grasped is that the original rejection of rustic wisdom was accompanied by a de-mystification and consequently lack of interest in the Babylonian scientific mind-set.

Second, and this reinforces the first, there is, thus, a recurring tendency to trace our origins to a clean slate that involves the starting-point of knowledge and, thus, a denial of other ways of knowing. This move is a recurring temptation at macro and micro levels. Sometimes these other ways are, of course, unimpressive or just crap. But the denial also always entails the genuine possibility of a version of (what we now call) a Kuhn-loss; the historical forgetting of previous knowledge that is, in some senses, superior to ours. Given my commitments, I should not be surprised that this process is even possible in mathematics. But I am surprised by Mansfield & Wildberger's findings.

I leave the final word today with Mansfield & Wildberger interpretation of P322:

Artifacts from ancient civilizations offer us a glimpse at their complex social and scientific achievements. Sophisticated artifacts offer us a larger window, and P322 is undeniably complex. Through P322 we see a forgotten ancient approach to trigonometry that is based on exact sexagesimal ratios.
The approximate nature of modern trigonometry is so culturally enshrined that we give it no second thought. It comes as a complete surprise, then, to find that the OB culture developed a trigonometry that actually only contains exact information, and so any imprecision is a consequence of using the table rather than inherent in the table itself.
P322 should be seen as an exact sexagesimal trigonometric table text...No other explanation has achieved this level of cohesion with the
evidence.
P322 is historically and mathematically significant because it is both the first trigonometric table and also the only trigonometric table that is precise. Irrational numbers and their approximations are seen as essential to classical metrical geometry, but here we have shown they are not actually necessary for trigonometry. If the dice of history had fallen a different way, and the deep mathematical understanding of the scribe who created P322 not been lost, then very possibly ratio-based trigonometry would have developed alongside our angle-based approach.
This new interpretation of P322 significantly elevates the status of Babylonian mathematics, and the vast number of untranslated tablets are likely to contain many more surprises waiting to be found. The discovery of trigonometry is attributed to the ancient Greeks, but this needs to be reconsidered in light of the much earlier, computationally simpler and more precise Babylonian style of exact sexagesimal trigonometry. In addition to being historically significant, P322 also brings the founding assumptions of our own mathematical culture into perspective. Perhaps this different and simpler way of thinking has the potential to unlock improvements in science, engineering, and mathematics education today. (24)

 

On Saving the Hebrew Bible from Analytical Theology

Swinburne’s account of revelation reflects a common view of what is taking place when an Israelite prophet tells us he is speaking words that have been taught to him by God. But...this view is mistaken as an interpretation of what is meant by God’s speech in Hebrew Scripture.[15] One obvious indication that there is something wrong with this interpretation is the fact that the biblical prophets explicitly reject the second plank of Swinburne’s account, namely, the supposition that the prophet’s words have to be taken on authority or faith because their truth cannot be tested by those that hear it. Indeed, Moses himself is presented as rejecting Swinburne’s position in what is perhaps the most significant passage concerning the nature of prophecy in all of Scripture, the law of the prophet in Deuteronomy:

I will raise them up a prophet from among their brethren… and put my words in his mouth…. And if you say in your mind, “How will we know the word that the Lord has not spoken?” Know that if a prophet speaks in the name of the Lord, and the thing is not, nor does it come, that is a thing that the Lord has not spoken, but the prophet has spoken it out of presumption, so do not fear what is from him.[16]

In this passage, Moses hands down God’s law respecting the recognition of prophets by the broader public. Earlier, Moses has already rejected appeals to signs or miracles as being a legitimate means of authenticating the prophet’s message.[17] Here he tells the people that if they wish to distinguish God’s word from what has been spoken presumptuously, the test is whether the things that are spoken really come to pass: If “the thing is not, nor does it come,” then anyone can know that what has been said in God’s name “is a thing that the Lord has not spoken.” ...Moreover, there are numerous additional passages that suggest that the wisdom in God’s teaching can in principle be recognized by anyone, from any nation;[19] and that the people of Jerusalem would be able to distinguish right teaching from wrong if only they would make a careful comparison using their own senses and judgment.[20] Together, these passages suggest that in Hebrew Scripture—or at the very least, in some of its most prominent texts—God’s word is not at all something that must be accepted on faith due to the credibility or authority of the prophet. On the contrary, the prophet bearing a teaching that is truly God’s word is supposed to be recognizable by anyone, using conventional human experience as the basis for judgment.[21]

If this is right, then a reasonable account of God’s word as it appears in Hebrew Scripture will not be able to include Swinburne’s third plank either, which calls for a sharp distinction between knowledge that has been “revealed,” and the products of philosophy and science that are derived from conventional human experience. As the empiricism of the Mosaic test of the prophet’s message suggests, Israelite prophecy was a forerunner and family relation of what later generations knew as philosophy and science.--Yoram Hazony, Jerusalem Letters: What is Revelation?

In context, Hazony is criticizing an important distinction (reason vs revelation) that he takes to be underwriting a key hermeneutic move common in (Protestant) analytical theology/metaphysics:  that the authority of Biblical prophets ultimately rests on faith. While this is an important issue, it is part of a larger project (with which I have considerably affinity) in which Hazony defends the integrity of what he calls the Hebrew Bible from Christian reinterpretation (one of his targets his Plantinga) in which some of the Biblical prophets have as much claim to wisdom as Greek philosophers. (A key part of this move is that history and social analysis are integral to philosophy.) One consequence of Hazony's move is that a central part of the Hebrew Bible becomes continuous with what later became known as "philosophy and science." I call this Hazony's continuity thesis.

Hazony's continuity thesis position was not un-common among a strain of seventeenth and eighteenth century English, protestant natural philosophers with a fondness for King Salomon, Jeremiah, and Ecclesiasticus, especially. This strain includes Bacon (recall), Clarke (recall), and -- the biggest prize of all, Newton (e.g., the General Scholium).* This is useful to keep in mind because it allows us to recognize that Hazony's continuity thesis is also available to non-Jewish readers of the Hebrew Bible. It also raises the very important historical-conceptual question of why the continuity thesis fell out of fashion among the Protestant learned. (This presumably has something do with theological responses to the Enlightenment thought of Hume and Kant.) 

Here I raise a problem for Hazony's position. For, with his appeal to Deuteronomy 18:18, he has left the reader without enough resources to distinguish between true and false prophets. (Hazony accepts the distinction because he treats Parmenides as a false prophet, although "not entirely false.") A true prophet speaks "truly God’s word." Let's grant, for the sake of argument, that "whether the things that are spoken [prophesied] really come to pass," that is, predictive accuracy, is a necessary condition for true prophecy. It is not sufficient. Because as the Hebrew Bible recognizes false prophets are also capable of accurate prediction--Balaam is the exemplar in this category.** To put the point anachronistically, not all predictively accurate science is moral science.

This is why in addition to predictive accuracy the Hebrew Bible also adds a content restriction on true prophecy. So, for example, at Deuteronomy 13:2-3, in the midst of discussion of prophecy, the Bible remarks that if a predictively accurate prophet also adds "Let us go after other gods, which thou hast not known, and let us serve them; [then] thou shalt not hearken unto the words of that prophet, or that dreamer of dreams." So, Hazony needs to explain the evidential basis for the authority of such content restriction(s). If Hazony wishes to deny faith and revelation a role here, he is presumably left with either an appeal to tradition or an appeal to the principle of sufficient reason. The former is not shared by everyone, while the latter goes against his empiricist sensibilities; presumably I have overlooked some options, but I would welcome learning which ones.

Huygens and Newton on Beauty and Design (and Kant)

But such diversity and beauty of things is available on the other planets like our Earthly realm, surely they wouldn't lack a spectator! As the elegance and artful workmanship of the animals, and the colors and scents of the flowers seem to be made available for human admiration and delight, will there not be beings on these planets who [could] enjoy so many and so pleasing spectacles? ["Quod si igitur similis quaedam rerum varietas ac pulchritudo in caeteris planetis atque in Terra hac nostra viget, nunquid spectatore carebunt! an non ut animalium elegantia et artificiosa fabrica, florum colores atque odores ad hominum admirationem aut voluptatem comparata videntur, ita et in istis existent aliqui qui tantis spectaculis tamque jucundis fruantur."--Christiaan Huygens (ca 1689).

In the first edition of Newton's Principia (1686), God is mentioned only once, deep into the technical details of Book 3: ''Therefore God placed the planet at different distances from the sun so that each one might, according to the degree of density, enjoy a greater or smaller amount of heat from the sun'' (Book 3, proposition 8, corollary 5; quoted from the Whitman/Cohen translation, p. 814). This claim was removed in subsequent editions of the Principia, and Newton moved his natural theology -- without this particular argument -- to the new conclusion of the Principia, his General Scholium.

At least one person discerned the significance of Newton's remark in Book 3 of the Principia. As Bernard Cohen argues in his (1690) Discourse on Gravity, Huygens comments on proposition 8 that it showed what kind of gravity ''the inhabitants of Jupiter and Saturn would feel,'' (quoted from Cohen's long introduction to the translation of the Principia p. 219). We know that Huygens had empirical reasons to doubt Newton's argument for the inverse-square law as a universal quality of matter, but Huygens certainly accepted an inverse-square rule for celestial gravity that governed the planets.

As an aside, despite the fact that the argument was removed after the first editions, Kant, who knew his Huygens, also saw Newton's point: ''Newton, who established the density of some planets by calculation, thought that the cause of this relationship set according to the distance was to be found in the appropriateness of God's choice and in the fundamental motives of His final purpose, since the planets closer to the sun must endure more solar heat and those further away are to manage with a lower level of heat,'' (UNH, Part 2, section 2, 284–85 (271)).

The Book of Jashar (in Newton and Spinoza)

And the sun stood still, and the moon stayed, until the nation had avenged themselves of their enemies. Is not this written in the book of Jashar? And the sun stayed in the midst of heaven, and hasted not to go down about a whole day.--Joshua 10:13

After the rise of Copernicanism, the quoted passage became very central. While there are other non-Copernican passages in Scripture, this one is significant because it is associated with a purported miracle, which shows God's favor to the Ancient Israelites in their war of conquest. (The whole chapter is very violent.) For example, Galileo's treatment of "the famous passage in Joshua" is central in his attempt to reconcile revelation and science in his Letter to Christina. The distinguished Newton scholar, Andrew Janiak,* has argued that Newton builds on, and subtly revises, Galileo's position. According to Janiak, Newton treats the Bible as literally true of the appearances.  That is, "if scripture...proclaims that the sun once miraculously stopped moving, we should not understand this as a change in what Newton calls its “true” motion, which would obviously have to be accompanied by various dynamical effects but, rather, as a change in its apparent and relative motion, which need not be accompanied by such effects." (Janiak, 429) In this way, Newton delivers on his promise (in the scholium to the definitions of the Principia) of avoiding doing "violence to the Scriptures" (recall this post).

One striking fact about the passage from Joshua 10:13 is that it appeals to the "Book of Jasher [sic]." [סֵפֶר הַיׇּשׇׁר]  Evidently, the Biblical narrative treats the "Book of Jashar" as an authoritative source.+ This book is mentioned once more in the Hebrew Bible, 2 Samuel 1:18ff, where it is cited as the source for an extended poetic quote (David's lamentation over Saul and Jonathan), which closes with a famous line: "how the mighty fallen, and the weapons of war perished."