In my dim and distant youth, I was an ardent fan of twentieth-century physics and consumed a large quantity of popular books and articles (mostly New Scientist and Scientific American) on the subject as well as graduating to some high-grade serious history of science on both relativity and quantum physics. One of the books I read was The First Three Minutes: A Modern View of the Origin of the Universe by theoretical physicist and Nobel Laureate Steven Weinberg. This book impressed me very much, as it did the reviewers at the time, and I came away with a deep respect for Steven Weinberg as a science writer. Now in his eighties Weinberg is still highly active and this year he published his own history of science, To Explain the World: The Discovery of Modern Science. This book proved to be highly contentious because of Weinberg’s avowed presentist approach to writing history of science and its appearance generated a lot of debate some of which I collected in one edition of Whewell’s Gazette (scroll down to book reviews). This situation led me to the thought that I should read and review Weinberg’s tome for myself, a thought that for various reasons didn’t really appeal. However rescue was at hand. Chris Graney, Renaissance Mathematicus friend and more than welcome guest blogger, has taken on the task, read, analysed and reviewed To Explain the World and it is with great pleasure and some relief (I won’t have to read it after all) that I present his thoughts on Weinberg’s book to the eager readers of the Renaissance Mathematicus.
In To Explain the World: The Discovery of Modern Science, author Steven Weinberg covers science history from the Milesians of ancient times to the Standard Model of today. His emphasis is on physics and astronomy, and he includes thirty-five ‘Technical Notes’ for the mathematically advanced reader that explain the physics and mathematics of things such as ellipses, refraction, and centripetal acceleration. His treatment of science’s history is not just a re-hashing of stock stories: he gives attention to Tycho Brahe; he does not lionize Galileo. He tries to show what he thinks science is and is not. The average Joe or Jane who has a casual interest in science and history and wants an overview by a prominent scientist should read the book. He or she will learn quite a few things, most of them not wrong.
However, the Renaissance Mathematicus is about neither casual interest in the history of science, nor history in which most things are not wrong, nor deference to prominent authors. And so, having generally recommended this book, I have two big specific criticisms of it: one regards facts; and the other regards philosophizing.
Weinberg makes factual errors. For example, in Chapter 10 on Medieval Europe, he discusses how the French cleric Jean Buridan rejected the Aristotelian idea that all motion requires a mover and introduced the idea that objects remain in motion once set in motion. Buridan called this impetus. Weinberg mischaracterizes impetus, saying that it was a foreshadowing of the modern idea of momentum, not momentum itself. “He [Buridan] never identified the impetus carried by a body as its mass times its velocity,” writes Weinberg (p. 133), “which is how momentum is defined in Newtonian physics.”
This is not correct. Buridan wrote regarding impetus that a moving body is impressed with —
…a certain impetus or a certain motive force of the moving body, in the direction toward which the mover was moving the moving body, either up or down, or laterally, or circularly. And by the amount the [mover] moves that moving body more swiftly, by the same amount it will impress in it a stronger impetus… by the amount more there is of matter, by that amount can the body receive more of that impetus and more intensely.
Thus Buridan plainly says that impetus is proportional to mass and proportional to velocity. That is mass-times-velocity momentum. He differs from modern momentum only in that he does not separate angular momentum, moment of inertia, etc. He uses momentum to explain the motion of bouncing balls, vibrating strings, and falling bodies in a manner consistent with Newtonian physics. He says that in the absence of resistive forces that will corrupt momentum, an object will continue in motion forever.
The Buridan quote above is from Edward Grant’s Source Book in Medieval Science p. 276-277. Weinberg cites the Source Book twice in that chapter, but not regarding Buridan. Regarding Buridan he cites the Dictionary of Scientific Biography.
Buridan is not the only instance of Weinberg getting things wrong. He says a number of weird things about the appearance of stars, mostly because he insists on discussing the stars in modern terms of brightness, rather than of size as they were traditionally viewed. He tries to explain the term magnitude (p. 88), never drawing the connection to size. This creates problems in a number of places, most notably when he wonders how Copernicus could speak of the Sun, Moon, planets, and stars all being seen to be circular in shape — “how could [Copernicus] know anything about the shape of the stars?” Weinberg asks (p. 155; I wonder how he thought Copernicus might know anything about the shape of the planets?). The answer is found by looking at the sky with good eyes. Then one sees that Copernicus (like Ptolemy and Tycho and many others) was right and that all these bodies do appear round to the eye. They appear as little round dots — the more prominent ones look like larger round dots, the less prominent like smaller round dots. Thus the term magnitude — size — and thus Copernicus’s comments.
There are other examples of, if not errors, at least odd phrasing:
- Weinberg tries (p. 58) to distinguish a gnomon (“simply a vertical pole, placed in a level patch of ground open to the Sun’s rays”) from a sundial (“different from a gnomon; its pole is parallel to the Earth’s axis rather than to the vertical direction, so that its shadow at a given hour is in the same direction every day. This makes a sundial more useful as a clock, but useless as a calendar.”). But all shadows fall in the same direction at a given hour, and so both the vertical pole and the sundial pole can be used to keep time; and all shadows vary in length with the seasons, and so both can be used to mark the time of year.
- He cites Newton as noting that “the observed phases of the five planets other than Earth show that they revolve around the Sun [p. 237]”, but Jupiter and Saturn show no observable phases, and Mars only shows a gibbous phase consistent with it having a certain position relative to Sun and Earth. Only the phases of Venus and Mercury prove their motions around the Sun. Newton did talk about phases of all five planets (in his Phenomena), but Weinberg’s phrasing is odd.
- He says the Inquisition gave a public formal order censoring Copernican books (p. 184), but according to Maurice Finocchiaro, the historian who translated and published the relevant documents, the Inquisition took no formal action; it was the Congregation for the Index (which Weinberg does mention elsewhere) that issued the censoring order.
- Weinberg states that Kepler made a case for heliocentrism “based on mathematical simplicity and coherence, not on its better agreement with observations [p. 172]”, but Kepler seems to indicate otherwise. “It behoves us,” Kepler wrote, “to whom by divine benevolence such a very careful observer as Tycho Brahe has been given, in whose observations an error of 8′ of Ptolemy’s computation could be disclosed, to recognize this boon of God with thankful mind and use it by exerting ourselves in working out the true form of celestial motions….”
Almost all the errors/oddities that I have pointed out here could have been fixed with relatively little effort, and without substantially changing the book. I have read complaints from historians concerning Weinberg writing about history as a non-historian, and in particular writing as a scientist who judges the past by his own standards as a scientist of today (see Steven Shapin’s review in the Wall Street Journal; there was an editorial about this in Physics in Perspective). In my opinion, Weinberg is clear about his approach, often stating “I think this” or “I don’t think that”. An example is found in his discussion of Descartes, where he both praises Descartes (“This was Descartes at his best as a scientist [p. 209]”) and criticizes him (“The writings of Descartes on scientific method have attracted much attention among philosophers, but I don’t think they have had much positive influence on the practice of scientific research…. [p. 213]”). I have no complaint with what Weinberg is doing. His position is clear. The reader can consider accordingly. But Weinberg is obligated to get the historical facts right.
Weinberg peppers To Explain the World with comments related to philosophy and religion, some of which are problematic. For instance, at one point Weinberg writes “whatever the final laws of nature may be, there is no reason to suppose that they are designed to make physicists happy [p. 165]”. But then later we find, “We learn how to do science, not by making rules about how to do science, but from the experience of doing science, driven by desire for the pleasure we get when our methods succeed in explaining something [p. 214].” And so apparently science exists because indeed the laws of nature are designed to make physicists happy — a sentiment Weinberg repeats elsewhere (p. 248, 255).
Weinberg also writes, “Modern science is impersonal…; it has no sense of purpose; and it offers no hope for certainty…. We learn not to worry about purpose…. We learn to abandon the search for certainty [p. 254-255]”. But then later we find, “…the Standard Model provides a remarkably unified view of all types of matter and force (except for gravitation) that we encounter in our laboratories, in a set of equations that can fit on a single sheet of paper. We can be certain that the Standard Model will appear as at least an approximate feature of any better future theory [p. 264].” And so apparently there is hope for certainty after all.
Such contradictions arise because Weinberg juxtaposes an insistence on purposelessness with an insistence that science is purposeful and inevitable because it uncovers a beautiful (i.e. makes physicists happy) reality, or at least it approaches that reality over time (p. 252, 254, 268). He describes the Standard Model (p. 264-265) as impersonal, lacking element of purpose, not being deduced from mathematics or philosophical preconceptions, and not following straightforwardly from observation of nature, yet he then states that it is a product of guesswork and aesthetic judgment, validated by its successes. Is there nothing personal, purposeful, and philosophically preconceived in aesthetic judgment? In closing the last chapter Weinberg writes, “Still, we have come a long way on this path, and are not yet at its end…. It is toward a more fundamental physical theory that the wide-ranging scientific principles we discover have been, and are being, reduced [p. 268]”. Is there nothing personal, purposeful, and hope-filled about being on a path, moving toward some fundamental end but not yet being there? The point here is not to argue for purpose in science or for a nature designed to make physicists happy, but to illustrate the contradictions in Weinberg’s philosophical musings.
Unfortunately, where Weinberg is more consistent in his philosophizing is on religion, and there he does a disservice to science. To Explain the World is not especially hard on religion as these things go, but Weinberg does insert comments that seem religion-unfriendly, and entirely disposable. There is a comment about the Copernican “demotion of earth” (p. 156) being a problem for all religions; a comment about the works of Descartes being placed on the Index of books forbidden to Roman Catholics (p. 213); a comment about how even if Galileo had been mistaken it would still have been wrong for the church to sentence him to imprisonment and deny his right to publish, just as it was wrong to burn Giordano Bruno for being a heretic (p. 187-188).
Each of these are isolated remarks that do not tie in with the rest of the text, and each can be debated. Kepler thought the Copernican system actually elevated Earth’s position up from the sump of the universe. As for the church being wrong about censorship and treatment of Galileo, well, Weinberg is clear on judging the past by the standards of today, and no, we do not do such things today. But he is selecting what to judge. It was also wrong to execute people for who-knows-what crime and to stick their heads on pikes by the dozen on the town bridge for everyone and their toddler to see, as was done at the time, and we do not do such things today. Yes, some church people in the seventeenth century behaved like ogres. But at that time a lot of other people behaved like ogres in many ways, too. To insert comments about these ogres but not those ogres is to select your data points, and, as judged by the standards of the modern scientist, that is poor practice.
Impaled heads on the south gate of London Bridge,
from Claes Visscher’s Panorama of London in 1616.
This selecting of data points extends more deeply than just throwaway comments. Weinberg’s discussion of figures such as Kepler, Boyle, and Newton omits just how large religion loomed in their thinking. The Kepler discussion is the most egregious example of this (Weinberg does include some references to religion regarding Boyle and Newton). Kepler was an astronomer who wrote about how he originally wanted to be a theologian but how he was able to glorify God through astronomy; who saw the Holy Trinity reflected in the Copernican universe, with the Sun representing God the Father and thus properly placed at the focus of elliptical orbits; whose Mysterium Cosmographicum (which Weinberg discusses) was an effort to uncover the mathematical rationale God used in building the solar system. But none of this is in To Explain the World. Weinberg portrays Kepler as simply a Platonist who applied to historical accidents an interest in mathematical oddities (p. 163-164). Perhaps most annoying is the following Kepler quote, which Weinberg includes (p. 179) to illustrate how Kepler challenged opponents of Copernicus:
Advice for Idiots. But whoever is too stupid to understand astronomical science, or too weak to believe Copernicus without affecting his faith, I would advise him that, having dismissed astronomical studies, and having damned whatever philosophical opinions he pleases, he mind his own business and betake himself home to scratch in his own dirt patch, abandoning this wandering about the world.
Now look at Kepler’s words in a larger context:
So everything the psalmodist said of the world relates to living things. He tells nothing that is not generally acknowledged, because his purpose was to praise things that are known, not to seek out the unknown. It was his wish to invite men to consider the beneﬁts accruing to them from each of these works of the six days.
I, too, implore my reader, when he departs from the temple and enters astronomical studies, not to forget the divine goodness conferred upon men, to the consideration of which the psalmodist chieﬂy invites. I hope that, with me, he will praise and celebrate the Creator’s wisdom and greatness, which I unfold for him in the more perspicacious explanation of the world’s form, the investigation of causes, and the detection of errors of vision. Let him not only extol the Creator’s divine beneﬁcence in His concern for the well-being of all living things, expressed in the ﬁrmness and stability of the Earth, but also acknowledge His wisdom expressed in its motion, at once so well hidden and so admirable.
But whoever is too stupid to understand astronomical science, or too weak to believe Copernicus without affecting his faith, I would advise him that, having dismissed astronomical studies and having damned whatever philosophical opinions he pleases, he mind his own business and betake himself home to scratch in his own dirt patch, abandoning this wandering about the world. He should raise his eyes (his only means of vision) to this visible heaven and with his whole heart burst forth in giving thanks and praising God the Creator. He can be sure that he worships God no less than the astronomer, to whom God has granted the more penetrating vision of the mind’s eye, and an ability and desire to celebrate his God above those things he has discovered.
To talk about Kepler as a Platonist while leaving out this aspect of Kepler is to select the data points. (Note — “Advice to Idiots” is a marginal note in Kepler’s book, not part of the text itself.)
My real job is to be a community college professor — to, ahem, Bring Science to The Community — and I absolutely hate the sort of thing Weinberg is doing. Not only is selecting the data not in the spirit of science, it does a disservice to science in general, and makes my job harder in particular. Why? Because Weinberg is in the USA (Texas, specifically), and here in the USA (especially Texas) we have many flare-ups over religion, science, school textbooks, and the like. See the March issue of National Geographic, whose cover story is “The War on Science” for a recap. I experience this issue directly with a number of my students. Weinberg, by choosing to highlight books on the Index or the troubles of Galileo, while being silent on the deep religious motivations of people like Kepler, skews the story of science in such a way as to add fuel to those flare-ups, when he could instead help to cool them down (he is not alone in this regard). Kepler is obviously a possible point of connection between “science people” and “religion people”. It is in science’s interest to emphasize such points of connection, as science is not winning in “The War on Science”. We need what allies (or at least non-enemies) we can get. Science needs prominent writers like Weinberg to talk up Kepler’s religion just as much as they talk up the Inquisition. Weinberg’s philosophy comments and selecting the data points on religion is a missed opportunity for science.
Read it — but with eyes open
The problems with facts and philosophizing are significant in To Explain the World, but they will not prevent its readers from learning a good deal about science and its long history. Indeed, the amount of history touched upon is at times itself a drawback. Chapter 9 on Arab scientists is a particular example of this. Here Weinberg introduces one scientist after another — in two pages of text (p. 110-111) we meet, and leave, Omar Khayyam, Ibn Sahl, Jabir ibn Hayyan, al-Kindi, al-Razi, and Ibn Sina. But, most readers probably know nothing about any of these scientists, and after finishing the book they will know something. And, the problems with facts and philosophizing will not prevent readers from picking up some technical details on physics and mathematics — although those readers should be aware that Weinberg occasionally includes mathematical material that many readers will not follow. For example, his discussion of the derivative, which includes invoking the idea that squares and cubes of small terms can be neglected (p. 223), will likely be useless to readers not already familiar with that material. The readers can just wade through and continue on, knowing they will likely learn something about the derivative no matter what. The problem regarding technical material is not aided by the absence of any illustrations in the main text, where they are often needed — where Weinberg describes Kepler’s nesting of Platonic solids, for instance (p. 162).
The problems with Weinberg’s book will not prevent readers from learning a good deal about science and its history, and will not prevent them from getting a scientist’s perspective on this subject. Read To Explain the World. Just keep your eyes open for its problems.