Measuring the Size of the World
28 November 2020
Saturday
A Scientific Research Program That Never Happened
Carl Sagan liked to characterize the Library of Alexandria as a kind of scientific research institution in classical antiquity:
“Here was a community of scholars, exploring physics, literature, medicine, astronomy, geography, philosophy, mathematics, biology, and engineering. Science and scholarship had come of age. Genius flourished there. The Alexandrian Library is where we humans first collected, seriously and systematically, the knowledge of the world.”
Carl Sagan, Cosmos, 1980, pp. 18-19
Clearly, before the scientific revolution there were many intimations of modern science, but these intimations of modern science, these examples we have of scientific knowledge prior to the scientific revolution, are isolated, and almost always the work of a single individual, like Archimedes or Eratosthenes. Thus Sagan used the example of the Library at Alexandria to suggest that there was, in classical antiquity, at least an intimation of a research institutions in which scholars worked in collaboration with each other. How accurate of a picture is this of science in antiquity?
The philosopher of science Imre Lakatos used the phrase “scientific research program” to refer to a number of scholars working jointly on a common set of problems in science. These scholars need not know each other, or work together in the same geographical location, but they do need to know each other’s work in order to respond to it, to question it, to elaborate upon it, and to thus contribute together to the growth of scientific knowledge, not as an isolated scientist producing an isolated result, but as a community of scholars with shared methods, shared assumptions, and shared research goals. Did any scientific research programs in this sense exist in classical antiquity? And was the Library at Alexandria a focal point for ancient scientific research programs?
If there were scientific research programs in antiquity, I am unaware of any evidence for this. No doubt at some humble scale shared scientific inquiry did take place in classical antiquity, but no surviving accounts of research undertaken in this way describe anything like this. In Athens, and later at Rome and Constantinople, the ancient philosophical schools did exactly this, investigating common research problems in a collegial atmosphere of shared research findings, and since there was, in classical antiquity, no distinction made between science and philosophy, we can assert with confidence that scientific research institutions (Plato’s Academy and Aristotle’s Lyceum) existed in antiquity, and scientific research programs existed in antiquity (Platonism, Aristotelianism, etc.), but even as we assert this we know that this was not science as we know it today.
When universities were founded in the Middle Ages, these universities inherited the tradition of philosophical inquiry that the ancient schools had once cultivated, and they added theology and logic to the curriculum. If there is any research program in a recognizable science that extends through western history all the way to its roots in classical antiquity, it is the research program in logic, which we can find in antiquity, in the Middle Ages, and in the modern period still today. But the Scholasticism that dominated medieval European universities was, again, nothing like the science we know today. Scholars did collaborate on a large, even a multi-generational research program, in Aristotelianism and Christian theology, and in the late Middle Ages this began to approximate natural science as we have known it since the scientific revolution, but when the scientific revolution began in earnest, it often began as a rejection of the universities and Scholasticism, and the great thinkers of the scientific revolution distanced themselves from the tradition in which they themselves were educated.
One could even say that Galileo worked essentially in isolation, when, during the final years of his life, living under house arrest due to the findings of the Inquisition, he pursued his research into the laws of motion in his own home, building his own experimental apparatus, writing up his own results, and being segregated from wider society by his sentence. What is different in the case of Galileo however, what places Galileo in the context of the scientific revolution, rather than being simply another isolated scholar like Archimedes or Eratosthenes, perhaps with a small circle of intimates with whom they shared their research, is that Galileo’s work was shortly thereafter taken up by many different individuals, some of them working in near isolation like Galileo, while others worked in community (in some cases, in literal religious communities).
Alexander Koyré’s 1952 lecture “An Experiment in Measurement” (collected in Metaphysics and Measurement), details how Filippo Salviati, Marin Mersenne, and Giovanni Battista Riccioli all took up and built upon Galileo’s work. Some of the experiments undertaken by Mersenne and Riccioli demanded an almost heroic commitment to the attempt to make precision observations despite the technical limitations of their experimental apparatus. Riccioli built several pendulums and, with the aid of nine Jesuit assistants, counted every swing of a pendulum over a period of twenty-four hours. The many individuals who were inspired by Galileo to replicate his results, or to try to prove that they could not be replicated, is what made the scientific revolution different from scientific knowledge in earlier history, and this community of scientists working on a common problem is more-or-less what Lakatos meant by a scientific research program.
Since the scientific revolution we have any number of examples of the work of a gifted individual being the inspiration for others to build upon that original work, as in the case of Carl von Linné (better known today as Linnaeus), whose followers were called the Apostles of Linnaeus, and who spread out across the world collecting and classifying botanical specimens according to the binomial nomenclature of Linnaeus. During Linnaeus lifetime, another truly remarkable scientific research program was the French Geodesic Mission, which sent teams to Lapland and Ecuador in order to measure the circumference of the Earth around the equator and around the poles, to see which distance was slightly longer than the other.
While there were, in classical antiquity, curious individuals who traveled widely and who attempted to gather empirical data from many different locations, there was no community of scholars, inside or outside any institution, that, prior to the scientific revolution, engaged in this kind of research. We can imagine, as an historical counter-factual, if other scholars in antiquity had been sufficiently interested in Eratosthenes’ estimate of the size of the Earth that they had sought to replicate Eratosthenes’ work with the same passion and dedication to detail that we saw in the work of Mersenne and Riccioli. Imagine if the Library at Alexandria had conducted Eratosthenes’ experiment not only in Alexandria and Syene, but also had sent teams to the furthest reaches of the ancient world — the great cities of Asia, Europe, and North Africa — and had repeated their investigations with increasing precision with each generation of experiments.
If Eratosthenes’ determination of the circumference of Earth had been the object of such a scientific research program in classical antiquity, there would have been no need of the French Geodesic Mission two thousand years later, as these results would already have been known. And given that Eratosthenes lived during the third century BC, the stable political and social institutions of the ancient world still had hundreds upon hundreds of years to go; the wealth and growth of the ancient world was still all to come in the time of Eratosthenes. There was, in the post-Eratosthenean world, plenty of wealth, plenty of time, and plenty of intelligent individuals who could have followed up upon the work of Eratosthenes as Mersenne and Riccioli followed up on the work of Galileo, and the Apostles of Linnaeus followed up on the first research program of scientific botany. But none of this happened. The scientific knowledge that Eratosthenes formulated was preserved by others and repeated in a few schools, but no one picked up the torch and ran with it.
Why did no Eratosthenean scientific research program appear in classical antiquity? Why did scientific research programs appear during the scientific revolution? I cannot answer these questions, but I will note that these questions could constitute a scientific research program in history, which continues today to be weak in regard to scientific research programs. History today is in a state of development similar to natural science in medieval universities, before the scientific revolution. This suggests further questions. Why was there was scientific research program into logic that has been continuous throughout the history of western civilization (including the Middle Ages, which was particularly brilliant in logical research)? Why has history escaped, so far, the scientific revolution?
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More on the Unfinished world
12 August 2009
Wednesday
Yesterday in The Unfinished World I attempted, however awkwardly, to draw a distinction between a common conception of the world becoming more rigid, inflexible, and closed as mature institutions dominate progressively greater areas of life, and the world becoming more unpredictable, changeable, and open as novel developments open new possibilities to us. I am not denying that the mature institutions of contemporary civilization do indeed conspire to confine us within ossified categories, but exclusively interpreting the world in this way does an injustice to the world.
I was bothered by the fact that my exposition of yesterday was as awkward as it was, because this is an issue of paramount importance. Whether one conceives of the world as finite, closed, bounded, finished, and completed on the one hand, or as infinite, open, unbounded, unfinished, and incomplete on the other hand, is one of those frighteningly clear points where one’s Weltanschauung — and not merely any aspect of one’s world-picture, but one’s intellectual world-picture, one’s ontological orientation, one’s personal metaphysic — comes into direct if not poignant contact with life. How one acts, and how one understands that action — with hope or fear, optimism or fatalism — will depend crucially on one’s conception of the world: what it is, how it is, and whether there is any “why” behind it.
Traditional institutions that are as old as civilization itself — law, economic organization, political hierarchy, privilege and subordination, hold before our eyes the image of a world that, if not eternal, is as close to eternal as anything sublunary can be. Even the sciences constructed to study these institutions — the social sciences — while often critical nevertheless end up recapitulating and regurgitating the society that they study, whatever shortcomings are found in it. It is this sort of attitude that must have inspired Marx to write in the last of his Theses on Feuerbach (which also appears on his tombstone), “The philosophers have only interpreted the world in various ways; the point is to change it.”
What shows us a very different world, a transient world in which all things solid melt into air, and what ought to excite us, are those institutions that have emerged since the advent of modernity: modern science, modern industry, modernism in the arts, the city as megalopolis, and all the things that are condemned by moralists and self-appointed defenders of the old order.
Hermann Weyl
As Hermann Weyl formulated it in his Yale lectures of 1932 subsequently published as The Open World:
Modern science, in so far as I am familiar with it through my own scientific work, mathematics and physics make the world appear more and more as an open one, as a world not closed but pointing beyond itself.
Weyl was not the only one inspired by contemporary science to imagine a world no longer subject to the dead weight of tradition. Bertrand Russell, one of the greatest logicians of the nineteenth and twentieth centuries, turned his later career to expressing his skepticism about traditional society that he had earlier expressed regarding traditional logic. Russell was an iconic iconoclast and was often unsparing in his attacks on traditional institutions.
Bertrand Russell lecturing at University of California Los Angeles in 1939; Russell was one of the great iconoclasts of recent philosophy, and he often expressed his iconoclasm in compelling prose.
Not precisely describing an open world, but definitely a modern and non-classical world view (perhaps we could call it a quantum world view), Russell, in one of my favorite passages from his writings painted this picture of the world for us:
“Academic philosophers, ever since the time of Parmenides, have believed that the world is a unity. This view has been taken over from them by clergymen and journalists, and its acceptance has been considered the touchstone of wisdom. The most fundamental of my intellectual beliefs is that this is rubbish. I think the universe is all spots and jumps, without unity, without continuity, without coherence or orderliness or any of the other properties that governesses love. Indeed, there is little but prejudice and habit to be said for the view that there is a world at all.”
Bertrand Russell, The Scientific Outlook, Part One, Chapter IV. Scientific Metaphysics
While I am ready to countenance “the view that there is a world at all” (though with the caveat, as I wrote in my Variations on the Theme of Life, that the world is a metaphor for a concept that cannot be made literal), of which Russell here appears skeptical, on the whole I enthusiastically approve and applaud the world-picture that Russell draws in this passage.
In this semi-popular work by Russell he criticizes the idea of the unity of the world in clever and immediately comprehensible terms, but unlike much that Russell wrote for a popular audience this radical criticism of the unity of the world was also something that he developed in his technical philosophical writings. There is one particular passage in his lecture “On Scientific Method in Philosophy” that always strikes me as incredible each time I read it, though it is not widely quoted:
The philosophy which I wish to advocate may be called logical atomism or absolute pluralism, because, while maintaining that there are many things, it denies that there is a whole composed of those things.
The whole composed of logical atoms would presumably be the world, hence Russell’s skepticism about the world mentioned above. Russell’s “logical atomism” went on to enjoy a stellar career within philosophy, spawning one of the great movements of twentieth century thought. Unfortunately, the idea of absolute pluralism got lost in the logical shuffle that led to what we may call orthodox analytical philosophy. If Russell’s technical work in the philosophy of logic and mathematics had come to be called absolute pluralism instead of his other moniker, logical atomism, the history of twentieth century though might have been different.
One of the classics of intellectual history of the twentieth century is Alexander Koyre’s From the Closed World to the Infinite Universe, which characterizes the emergence of modernity in history as precisely the opening up of the closed conception of the world that dominated ancient and medieval thought into the infinite universe of modern science.
Alexander Koyre
Instead of imagining the world as described in the passage I quoted yesterday from Tamim Ansary — “…over the centuries, even those cracks [in established precedent] grew narrower, because once an eminently qualified scholar weighed in on some subject his pronouncements also joined the canon. ” — in which novelty is being squeezed out and the scope of human action narrowed to insignificance, we ought to make an effort to imagine the world as opening up ever greater vistas, so that history shows us a widening human future that only gets larger the closer we approach it.
Ernst Friedrich Ferdinand Zermelo
Even if one conceives of the world as an open world — and according to Koyre, most Westerners since the renaissance so conceive of it — that does not settle all questions and leave us all in agreement. The world, open by consensus, remains a complex and mysterious place, and it will still be variously conceived by different persons. Weyl, for example, as a constructivist, conceives of the infinitude of the world differently than someone like Ernst Zermelo, who was an unabashed advocate of the actual infinite. Zermelo wrote:
Purely “finitistic” mathematics in which, as a matter of fact, nothing has been left to be proved because everything could be verified already by a finite model, would no longer be mathematics in the true sense. Rather, a true mathematics is genuinely infinitistic and based on the assumption of infinite domains; it can directly be called the “logic of the infinite.”
The open and infinite world of Zermelo is distinct from the open and infinite world of Weyl. Thus even if we can agree with Weyl’s elevated statement near the end of his lectures that, “…mind is freedom within the limitations of existence; it is open toward the infinite” (and I do agree), the infinite recognized by Weyl is not necessarily the infinite we recognize, and therefore the quality of freedom is distinct as well. Again, this is important, though it sounds like mere scholasticism to point out the importance of something that will be dismissed by most as overly-subtle and without human interest or personal relevance.
Zermelo built upon the work of Georg Cantor, who was one of the great intellectual revolutionaries of all time.
I find Zermelo’s uncompromising defense of infinitistic domains and infinitistic reasoning to be refreshing. Cantor, of course, preceded Zermelo and made Zermelo possible, but it is interesting to notice the analogy between the response of the scientific establishment to Darwin and Cantor, both of whom put forward a radical and simple idea and changed history. In both cases, after the initial shock wore off, the research program initiated by each took off and rapidly bore fruit, but not long after Darwin many distanced themselves from the mechanism of natural selection, while after Cantor many distanced themselves from Cantor’s realism and his more imaginative use of infinitistic methods.
Darwin, like Cantor, was an intellectual revolutionary because he formulated an idea that changed all subsequent thought and opened up new domains of inquiry.
Radical innovations like those of Cantor and Darwin made the mind of the mind immeasurably larger than they were before. The world of man is expanding, and it is expanding at a faster rate than ever before in history.
We know now that the universe is not only expanding, but that its expansion is accelerating: the world is getting bigger faster.
It was not until the twentieth century that Hubble proved the existence of galaxies outside the Milky Way. Up until that time, the world was quite small. Now we know better. Subsequent discoveries in astronomy have forced us to repeatedly expand our conception of the world. And only at the end of the twentieth century did we learn that the expansion of the universe is speeding up. From the first formulation of the big bang theory, that assumption had been that the expansion of the universe was slowing down. now we know that is not the case. There is not yet any satisfactory explanation for this. We have more than ever to learn, and more than ever before to explain.
The world is more unfinished than ever.
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Grand Strategy: The View from Oregon 