Digressions&Impressions

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.  

 

 

 

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.

Maria Cunitz, the greatest astronomer between Kepler and Huygens.

It remains here to forestall suspicion, for some will ask why it is that against the custom of all expert practitioners I have written the introduction in a two-fold idiom; and it will be suspected (for men are prone to suspicion) that either through eagerness for novelty or display of Latinity I seek after a little empty glory. To these I answer that I have done this neither heedlessly nor without careful thought, but persuaded by the encouragement of two weighty authorities, of which the first is LOVE OF FATHERLAND, the other NECESSITY itself. I believe it is unknown to no one that the German Nation abounds in those of abilities suited to astronomical practice although often lacking knowledge of Latin, to whom I do not see by what pretense of duty I, being of the German Nation, could refuse or take away the benefit of my labors since it is agreed by the opinion of foreigners also that the Fatherland claims a great part of our labors as its own. And we see that most other Nations publish their writings, in particular their discoveries, in the vernacular idiom familiar to them (German: in ihrer Muttersprache). But because this work, in as much as it is intended for the universal improvement of the republic of letters, should also be imparted to other nations not proficient in our idiom, necessity itself ordained to entrust this introduction to the Latin language as being more universal and familiar to most Nations. In addition, it is also to be feared, lest perhaps kidnappers (plagiarii)—for by the wickedness of our age such shamelessness has come about that very many are found who have no scruples to translate works of some note into another language, with the authors not knowing, not consulted, not willing, rather with their names entirely suppressed, and maliciously take credit for themselves—seizing this opportunity for conveyance in the open market of their own desire, ambition, and arrogance, expose for sale, enveloped in a veil of Latinity, this my authentic progeny, honorably and freely born and raised.-- Maria Cunitz’s Beneficent Urania (1650) translated by N.M. Swerdlow (2012), Urania Propitia, Tabulae Rudophinae faciles redditae a Maria Cunitia Beneficent Urania, the Adaptation of the Rudolphine Tables by Maria Cunitz 86-7.

Editing volumes can be ungrateful work; one is at the mercy of the often deplorable time-conscientiousness of others, and one must pray for their generosity in sharing their best work. One also relies on their integrity; I have had senior scholars recycle material from earlier publications without mention. But one of its great joys is learning the unexpected in nearby areas of scholarship. While editing a draft-paper by Rhonda Martens, "Newton's Introduction to Astronomy," on the significance of early Kepler (for the forthcoming Oxford Handbook to Isaac Newton, co-edited with Chris Smeenk). Martens writes: "Kepler's second law in particular was generally avoided by astronomers before Newton's Principia. Maria Cunitz (c.1604-­‐1664)5...approved of Kepler's work but used alternatives to Kepler's second law." The accompanying footnote reads: "Maria Cunitz is notable not only for her excellent tables, but also for achieving recognition despite her gender. Swerdlow (2012) has an excellent chapter on her." Made curious by Martens' comment and knowing from personal experience that Noel Swerdlow doesn't suffer fools lightly, I asked Swerdlow to send me his paper.