Parsimony in Copernicus and Osiander

10 November 2015


William of Ockham, one of the greatest philosophers of the late Middle Ages, is remembered today primarily for his formulation of the principle of parsimony, also called Ockham's razor.

William of Ockham, one of the greatest philosophers of the late Middle Ages, is remembered today primarily for his formulation of the principle of parsimony, also called Ockham’s razor.

A medieval logician in the twenty-first century

In the discussion surrounding the unusual light curve of the star KIC 8462852, Ockham’s razor has been mentioned numerous times. I have written a couple of posts on this topic, i.e., interpreting the light curve of KIC 8462852 in light of Ockham’s razor, KIC 8462852 and Parsimony and Plenitude in Cosmology.

What is Ockham’s razor exactly? Well, that is a matter of philosophical dispute (and I offer my own more precise definition below), but even if it is difficult to say that Ockham’s razor is exactly, we can say something about what it was originally. Philotheus Boehner, a noted Ockham scholar, wrote of Ockham’s razor:

“It is quite often stated by Ockham in the form: ‘Plurality is not to be posited without necessity’ (Pluralitas non est ponenda sine necessitate), and also, though seldom: ‘What can be explained by the assumption of fewer things is vainly explained by the assumption of more things’ (Frustra fit per plura quod potest fieri per pauciora). The form usually given, ‘Entities must not be multiplied without necessity’ (Entia non sunt multiplicanda sine necessitate), does not seem to have been used by Ockham.”

William of Ockham, Philosophical Writings: A Selection, translated, with an Introduction, by Philotheus Boehner, O.F.M., Indianapolis and New York: The Library of Liberal Arts, THE BOBBS-MERRILL COMPANY, INC., 1964, Introduction, p. xxi

Most references to (and even most uses of) Ockham’s razor are informal and not very precise. In Maybe It’s Time To Stop Snickering About Aliens, which I linked to in KIC 8462852 Update, Adam Frank wrote of Ockham’s razor in relation to KIC 8462852:

“…aliens are always the last hypothesis you should consider. Occam’s razor tells scientists to always go for the simplest explanation for a new phenomenon. But even as we keep Mr. Occam’s razor in mind, there is something fundamentally new happening right now that all of us, including scientists, must begin considering… the exoplanet revolution means we’re developing capacities to stare deep into the light produced by hundreds of thousands of boring, ordinary stars. And these are exactly the kind of stars where life might form on orbiting planets… So we are already going to be looking at a lot of stars to hunt for planets. And when we find those planets, we are going to look at them for basic signs that life has formed. But all that effort means we will also be looking in exactly the right places to stumble on evidence of not just life but intelligent, technology-deploying life.

Here the idea of Ockham’s razor is present, but little more than the idea. Rather than merely invoking the idea of Ockham’s razor, and merely assuming what constitutes simplicity and parsimony, if we are going to profitably employ the idea today, we need to develop it more fully in the context of contemporary scientific knowledge. In KIC 8462852 I wrote:

“One can see an emerging adaptation of Ockham’s razor, such that explanations of astrophysical phenomena are first explained by known processes of nature before they are attributed to intelligence. Intelligence, too, is a process of nature, but it seems to be rare, so one ought to exercise particular caution in employing intelligence as an explanation.”

In a recent post, Parsimony and Emergent Complexity I went a bit further and suggested that Ockham’s razor can be formulated with greater precision in terms of emergent complexity, such that no phenomenon should be explained in terms of a level of emergent complexity higher than that necessary to explain the phenomenon.

De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus (1473–1543). The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy's geocentric system, which had been widely accepted since ancient times. (Wikipedia)

De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus (1473–1543). The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy’s geocentric system, which had been widely accepted since ancient times. (Wikipedia)

De revolutionibus orbium coelestium and its textual history

Like Darwin many centuries later, Copernicus hesitated to publish his big book to explain his big idea, i.e., heliocentrism. Both men, Darwin and Copernicus, understood the impact that their ideas would have, though both probably underestimated the eventual influence of these ideas; both were to transform the world and leave as a legacy entire cosmologies. The particular details of the Copernican system are less significant than the Copernican idea, i.e., the Copernican cosmology, which, like Ockham’s razor, has gone on to a long career of continuing influence.

Darwin eventually published in his lifetime, prompted by the “Ternate essay” that Wallace sent him, but Copernicus put off publishing until the end of his life. It is said that Copernicus was shown a copy of the first edition of De revolutionibus on his deathbed (though this is probably apocryphal). Copernicus, of course, lived much closer to the medieval world than did Darwin — one could well argue that Toruń and Frombork in the fifteenth and sixteenth centuries was the medieval world — so we can readily understand Copernicus’ hesitation to publish. Darwin published in a world already transformed by industrialization, already wrenched by unprecedented social change; Copernicus eventually published in a world that, while on the brink of profound change, had not appreciably changed in a thousand years.

Copernicus’ hesitation meant that he did not directly supervise the publication of his manuscript, that he was not able to correct or revise subsequent editions (Darwin revised On the Origin of Species repeatedly for six distinct editions in his lifetime, not including translations), and that he was not able to respond to the reception of his book. All of these conditions were to prove significant in the reception and propagation of the Copernican heliocentric cosmology.

Copernicus, after long hesitation, was stimulated to pursue the publication of De revolutionibus by his contact with Georg Joachim Rheticus, who traveled to Frombork for the purpose of meeting Copernicus. Rheticus, who had great respect for Copernicus’ achievement, came from the hotbed of renaissance and Protestant scholarship that was Nuremberg. He took Copernicus’ manuscript to Nuremberg to be published by a noted scientific publisher of the day, but Rheticus did not stay to oversee the entire publication of the work. This job was handed down to Andreas Osiander, a Protestant theologian who sought to water down the potential impact of De Revolutionibus by adding a preface that suggested that Copernicus’ theory should be accepted in the spirit of an hypothesis employed for the convenience of calculation. Osiander did not sign this preface, and many readers of the book, when it eventually came out, thought that this preface was the authentic Copernican interpretation of the text.

Osiander’s preface, and Osiander’s intentions in writing the preface (and changing the title of the book) continue to be debated to the present day. This debate cannot be cleanly separated from the tumult surrounding the Protestant Reformation. Luther and the Lutherans were critical of Copernicus — they had staked the legitimacy of their movement on Biblical literalism — but one would have thought that Protestantism would have been friendly to the work of Ockham, given Ockham’s conflict with the Papacy, Ockham’s fideism, and his implicit position as a critic of Thomism. (I had intended to read up on the Protestant interpretation of Ockham prior to writing this post, but I haven’t yet gotten to this.) The parsimony of Copernicus’ formulation of cosmology, then, was a mixed message to the early scientific revolution in the context of the Protestant Reformation.

Both Rheticus and Copernicus’ friend Tiedemann Giese were indignant over the unsigned and unauthorized preface by Osiander. Rheticus, by some accounts, was furious, and felt that the book and Copernicus had been betrayed. He pursued legal action against the printer, but it is not clear that it was the printer who was at fault for the preface. While Rheticus suspected Osiander as the author of the preface, this was not confirmed until some time later, when Rheticus had moved on to other matters, so Osiander was never pursued legally over the preface.

Nicolaus Copernicus (1473–1543) -- Mikołaj Kopernik in Polish, and Nikolaus Kopernikus in German

Nicolaus Copernicus (1473–1543) — Mikołaj Kopernik in Polish, and Nikolaus Kopernikus in German

Copernicus’ Ockham

The most common reason adduced to preferring Copernican cosmology to Ptolematic cosmology is not that one is true and the other is false (though this certainly is a reason to prefer Copernicus) but rather that the Copernican cosmology is the simpler and more straight-forward explanation for the observed movements of the stars and the planets. The Ptolemaic system can predict the movements of stars, planets, and the moon (within errors of margin relevant to its time), but it does so by way of a much more complex and cumbersome method than that of Copernicus. Copernicus was radical in the disestablishment of traditional cosmological thought, but once beyond that first radical step of displacing the Earth of the center of the universe (a process we continue to iterate today), the solar system fell into place according to a marvelously simple plan that anyone could understand once it was explained: the sun at the center, and all the planets revolving around it. From the perspective of our rotating and orbiting Earth, the other planets also orbiting the sun appear to reverse in their course, but this is a mere artifact due to our position as observers. Once Copernicus can convince the reader that, despite the apparent solidity of the Earth, it is in fact moving through space, everything else falls into place.

One of the reasons that theoretical parsimony and elegance played such a significant role in the reception of Copernicus — and even the theologians who rejected his cosmology employed his calculations to clarify the calendar, so powerful was Copernicus’ work — was that the evidence given for the Copernican system was indirect. Even today, only a handful of the entire human population has ever left the planet Earth and looked down on it from above — seeing Earth from the perspective of the overview effect — and so acquired direct evidence of the Earth in space. No one, no single human being, has hovered above the solar system entire and looked down upon it and so obtained the most direct evidence of the Copernican theory — this is an overview affect that we have not yet attained. (NB: in The Scientific Imperative of Human Spaceflight I suggested the possibility of a hierarchy of overview effects as one moved further out from Earth.)

The knowledge that we have of our solar system, and indeed of the universe entire, is derived from observations and deduction from observations. Moreover, seeing the truth of Copernican heliocentrism would not only require an overview in space, but an overview in time, i.e., one would need to hover over our solar system for hundreds of years to see all the planets rotating around the common center of the sun, and one would have to, all the while, remain focused on observing the solar system in order to be able to have “seen” the entire process — a feat beyond the limitations of the human lifetime, not to mention human consciousness.

Copernicus himself did not mention the principle of parsimony or Ockham’s razor, and certainly did not mention William of Ockham, though Ockham was widely read in Copernicus’ time. The principle of parsimony is implicit, even pervasive, in Copernicus, as it is in all good science. We don’t want to account for the universe with Rube Goldberg-like contraptions as our explanations.

In a much later era of scientific thought — in the scientific thought of our own time — Stephen J. Gould wrote an essay titled “Is uniformitarianism necessary?” in which he argued for the view that uniformitarianism in geology had simply come to mean that geology follows the scientific method. Similarly, one might well argued that parsimony is no more necessary than uniformitarianism, and that what content of parsimony remains is simply coextenisve with the scientific method. To practice science is to reason in accordance with Ockham’s razor, but we need not explicitly invoke or apply Ockham’s razor, because its prescriptions are assimilated into the scientific method. And indeed this idea fits in quite well with the casual references to Ockham’s razor such as that I quoted above. Most scientists do not need to think long and hard about parsimony, because parsimonious formulations are already a feature of the scientific method. If you follow the scientific method, you will practice parsimony as a matter of course.

Copernicus’ Ockham, then, was already the Ockham already absorbed into nascent scientific thought. Perhaps it would be better to say that parsimony is implicit in the scientific method, and Copernicus, in implicitly following a scientific method that had not yet, in his time, been made explicit, was following the internal logic of the scientific method and its parsimonious demands for simplicity.

Andreas Osiander (19 December 1498 – 17 October 1552) was a German Lutheran theologian who oversaw the publication of Copernicus' De revolutionibus and added an unsigned preface that many attributed to Copernicus.

Andreas Osiander (19 December 1498 – 17 October 1552) was a German Lutheran theologian who oversaw the publication of Copernicus’ De revolutionibus and added an unsigned preface that many attributed to Copernicus.

Osiander’s Ockham

Osiander was bitterly criticized in his own time for his unauthorized preface to Copernicus, though many immediately recognized it as a gambit to allow for the reception of Copernicus’ work to involve the least amount of controversy. As I noted above, the Protestant Reformation was in full swing, and the events that would lead up the Thirty Years’ War were beginning to unfold. Europe was a powder keg, and many felt that it was the better part of valor not to touch a match to any issue that might explode. All the while, others were doing everything in their power to provoke a conflict that would settle matters once and for all.

Osiander not only added the unsigned and unauthorized preface, but also changed the title of the whole work from De revolutionibus to De revolutionibus orbium coelestium, adding a reference to the heavenly spheres that was not in Copernicus. This, too, can be understood as a concession to the intellectually conservative establishment — or it can be seen as a capitulation. But it was the preface, and what the preface claimed as the proper way to understand the work, that was the nub of the complaint against Osiander.

Here is a long extract of Osiander’s unsigned and unauthorized preface to De revolutionibus, not quite the whole thing, but most of it:

“…it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as for the past. The present author has performed both these duties excellently. For these hypotheses need not be true nor even probable. On the contrary, if they provide a calculus consistent with the observations, that alone is enough. Perhaps there is someone who is so ignorant of geometry and optics that he regards the epicyclc of Venus as probable, or thinks that it is the reason why Venus sometimes precedes and sometimes follows the sun by forty degrees and even more. Is there anyone who is not aware that from this assumption it necessarily follows that the diameter of the planet at perigee should appear more than four times, and the body of the planet more than sixteen times, as great as at apogee? Yet this variation is refuted by the experience of every age. In this science there are some other no less important absurdities, which need not be set forth at the moment. For this art, it is quite clear, is completely and absolutely ignorant of the causes of the apparent nonuniform motions. And if any causes are devised by the imagination, as indeed very many are, they are not put forward to convince anyone that are true, but merely to provide a reliable basis for computation. However, since different hypotheses are sometimes offered for one and the same motion (for example, eccentricity and an epicycle for the sun’s motion), the astronomer will take as his first choice that hypothesis which is the easiest to grasp. The philosopher will perhaps rather seek the semblance of the truth. But neither of them will understand or state anything certain, unless it has been divinely revealed to him.”

Nicholas Copernicus, On the Revolutions, Translation and Commentary by Edward Rosen, THE JOHNS HOPKINS UNIVERSITY PRESS, Baltimore and London

If we eliminate the final qualification, “unless it has been divinely revealed to him,” Osiander’s preface is a straight-forward argument for instrumentalism. Osiander recommends Copernicus’ work because it gives the right results; we can stop there, and need not make any metaphysical claims on behalf of the theory. This ought to sound very familiar to the modern reader, because this kind of instrumentalism has been common in positivist thought, and especially so since the advent of quantum theory. Quantum theory is the most thoroughly confirmed theory in the history of science, confirmed to a degree of precision almost beyond comprehension. And yet quantum theory still lacks an intuitive correlate. Thus we use quantum theory because it gives us the right results, but many scientists hesitate to give any metaphysical interpretation to the theory.

Copernicus, and those most convinced of his theory, like Rheticus, was a staunch scientific realist. He did not propose his cosmology as a mere system of calculation, but insisted that his theory was the true theory describing the motions of the planets around the sun. It follows from this uncompromising scientific realism that other theories are not merely less precise in calculating the movements of the planets, but false. Scientific realism accords with common sense realism when it comes to the idea that there is a correct account of the world, and other accounts that deviate from the correct account are false. But we all know that scientific theories are underdetermined by the evidence. To formulate a law is to go beyond the finite evidence and to be able to predict an infinitude of possible future states of the phenomenon predicted.

Scientific realism, then, is an ontologically robust position, and this ontological robustness is a function of the underdetermination of the theory by the evidence. Osiander argues of Copernicus’ theory that, “if they provide a calculus consistent with the observations, that alone is enough.” So Osiander is not willing to go beyond the evidence and posit the truth of an underdetermined theory. Moreover, Osiander was willing to maintain empirically equivalent theories, “since different hypotheses are sometimes offered for one and the same motion.” Given empirically equivalent theories that can both “provide a calculus consistent with the observations,” why would one theory be favored over another? Osiander states that the astronomer will prefer the simplest explanation (hence explaining Copernicus’ position) while the philosopher will seek a semblance of truth. Neither, however, can know what this truth is without divine revelation.

Osiander’s Ockham is the convenience of the astronomer to seek the simplest explanation for his calculations; the astronomer is justified in employing the simplest explanation of the most precise method available to calculate and predict the course of the heavens, but he cannot know the truth of his theory unless that truth is guaranteed by some outside and transcendent evidence not available through science — a deus ex machina for the mind.

Copernicus stands at the beginning of the scientific revolution, and he stands virtually alone.

Copernicus stands at the beginning of the scientific revolution, and he stands virtually alone.

The origins of the scientific revolution in Copernicus

Copernicus’ Ockham was ontological parsimony; Osiander’s Ockham was methodological parsimony. Are we forced to choose between the two, or are we forced to find a balance between ontological and methodological parsimony? These are still living questions in the philosophy of science today, and there is a sense in which it is astonishing that they appeared so early in the scientific revolution.

As noted above, the world of Copernicus was essentially a medieval world. Toruń and Frombork were far from the medieval centers of learning in Paris and Oxford, and about as far from the renaissance centers of learning in Florence and Nuremberg. Nevertheless, the new cosmology that emerged from the scientific revolution, and which is still our cosmology today, continuously revised and improved, can be traced to the Baltic coast of Poland in the late fifteenth and early sixteenth century. The controversy over how to interpret the findings of science can be traced to the same root.

The conventions of the scientific method were established in the work of Copernicus, Galileo, and Newton, which means that it was the work of these seminal thinkers who established these conventions. Like the cosmologies of Copernicus, Galileo, and Newton, the scientific method has also been continuously revised and improved. That Copernicus grasped in essence as much of the scientific method as he did, working in near isolation far from intellectual centers of western civilization, demonstrates both the power of Copernicus’ mind and the power of the scientific method itself. As implied above, once grasped, the scientific method has an internal logic of its own that directs the development of scientific thought.

The scientific method — methodological naturalism — exists in an uneasy partnership with scientific realism — ontological naturalism. We can see that this tension was present right from the very beginning of the scientific revolution, before the scientific method was ever formulated, and the tension continues down to the present day. Contemporary analytical philosophers discuss the questions of scientific realism in highly technical terms, but it is still the same debate that began with Copernicus, Rheticus, and Osiander. Perhaps we can count the tension between methodological naturalism and ontological naturalism as one of the fundamental tensions of scientific civilization.

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Updates and Addenda

This post began as a single sentence in one of my note books, and continued to grow as I worked on it. As soon as I posted it I realized that the discussions of scientific realism, instrumentalism, and methodological naturalism in relation to parsimony could be much better. With additional historical and philosophical discussion, this post might well be transformed into an entire book. So for the questioning reader, yes, I understand the inadequacy of what I have written above, and that I have not done justice to my topic.

Shortly after posting the above Paul Carr pointed out to me that the joint ESA-NASA Ulysses deep-space mission sent a spacecraft to study the poles of the sun, so we have sent a spacecraft out of the plane of the solar system, which could “look down” on our star and its planetary system, although the mission was not designed for this and had no cameras on board. If we did position a camera “above” our solar system, it would be able to take pictures of our heliocentric solar system. This, however, would be more indirect evidence — more direct than deductions from observations, but not as direct as seeing this with one’s own eyes — like the famous picture of the “blue marble” Earth, which is an overview experience for those of us who have not been into orbit to the moon, but which is not quite the same as going into orbit or to the moon.

Paul Carr also drew my attention to Astronomy Cast Episode 390: Occam’s Razor and the Problem with Probabilities, with Fraser Cain and Pamela Gay, which discusses Ockham’s razor in relation to positing aliens as a scientific explanation.

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Grand Strategy Annex

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