This blog post is a book review of sorts for the following two books:
To Explain the World: The Discovery of Modern Science by Steven Weinberg (2016)
The Knowledge Machine: How Irrationality Created Modern Science by Michael Strevens (2020).
Both books cover (in different proportions) the history and philosophy of science. By the end of this post, I will also discuss my thoughts. Trigger warning: I will end up comparing science to the blockchain and finding positive aspects of the dreaded “reviewer 2”.
Both books attempt to answer the question of “why and how did the scientific revolution happen?”. Strevens describes this conundrum as follows:
“[If you were a citizen of ancient Greece], you could enjoy just about every cultural invention that makes life worth living today. You could delight in the poetry of Homer and Sappho, visit the theater to relish Oedipus Rex and other masterpieces of ancient drama… You could live in cities regulated by law and a system of courts shaped by the architects and sculptors who built some of the seven wonders of the world and governed in accordance with political models that have lasted to this day: monarchy, oligarchy, sweet democracy.”
The point Strevens makes is that while obviously, a lot has changed in culture and society since 300 BC, the change has not been so drastic as to make life unrecognizably different. In contrast, science and technology have undergone drastic changes in the same period, with most changes occurring in the last few centuries. Weinberg quotes the historian Herbert Butterfield, who claimed that the scientific revolution “outshines everything since the rise of Christianity and reduces the Renaissance and Reformation to the rank of mere episodes.”
If you are the type of person who prefers data to quotes from historians, there is no shortage of graphs demonstrating this point, including the following:
One distinguishing property of science (compared to activities such as religion, philosophy, art, political thought, sports etc.) is that it simultaneously satisfies the following three properties:
- Consensus: While scientists don’t agree about everything, they generally agree on much, and the scientific literature does seem to converge toward consensus in the long run. Perhaps most importantly, even when scientists disagree on interpreting facts, they agree on what these facts are and agree on the forum where these should be discussed. In contrast, there is much less consensus in other spheres of human activities. Often, there isn’t even a consensus on what forum to hold the debate or even if to hold it at all. As far as I know, there isn’t a Science or Nature journal of theology where clergypersons of all faiths debate with one another. Indeed, with the polarized media these days, there are fewer and fewer forums where Democrats and Republicans debate with one another.
- Change: The consensus is not just frozen in time but instead evolves. Scientists today generally agree with one another, but their views have radically changed over time. While, as Strevens notes, in art and religion, millennia-old texts are still very much relevant, in Machine Learning, when I recommend my students “read the classics,” I mean papers written before 2018 🙂
- Correlation with reality: Science does not merely change but also progresses, in the sense that with time we gain a better understanding of nature. While some radical subjectivists might dispute that external reality exists or that science gets to know more of it, most people who have ever flown in a plane, were administered a vaccine, or read a blog post over the Internet, will agree that science did advance. Science’s path may be a random walk, but that walk is biased towards progress.
Science did not always possess the above properties, and the distinction between science and philosophy was much murkier in the past. Both Strevens and Weinberg trace the birth of modern science to the Scientific Revolution of the 16th and 17th centuries. Both books describe the history of science and attempt to answer what changed since ancient times and why.
Strevens: Modern Science as a result of Newton and the “Iron Rule”:
Strevens begins by explaining the philosophies of Karl Popper and Thomas Kuhn. I found this part very informative since I have never read a proper philosophy of science book. (He also describes their fascinating personal histories.)
For Popper, progress in science happens via refutations. At a given point in time, there is a collection of hypotheses H₁,…,Hₖ that are currently consistent with known experiments. Then an experiment happens which refutes some of these, narrowing down the set of potentially feasible theories.
According to Strevens, Popper is an absolutist. Once a theory has been falsified, it’s dead, and all theories that have not been yet falsified will “forever remain … conjectures”. That is, Popper was not a Bayesian and did not assign any likelihood to theories based on how many true predictions they made. The only question was whether they still survive or have been refuted.
Popper is said to have been inspired by Einstein, who was willing to put his theory to the test and said, “if the redshift of spectral lines due to the gravitational potential should not exist, then [my] general theory of relativity will be untenable.” Indeed, a classical story of testing a theory via refutation is Eddington’s expedition to check Einstein’s predictions during the 1919 total solar eclipse. Specifically, due to the curvature of space, the effect of the sun’s gravity on the light shining from stars would be double the effect predicted by Newton’s theory.
A priori, the Eddington expedition seems like a textbook Popperian refutation: an experiment is set out to test conflicting predictions of two theories, after which only one of them will survive. However, as Strevens points out, the truth is murkier. The expedition took three measurements: one on the island of Principe, off the coast of West Africa, and two in Brazil. The weather in Principe was cloudy, and the resulting photos were blurry. In Brazil weather was good, but the measurements were taken using two different telescopes that gave conflicting results. Concretely, one of the Brazil telescopes’ measurements conformed with Einstein’s predictions, while the other conformed with the Newtonian theory. Eddington argued that the second Brazil telescope had a systematic error, and hence Einstein’s theory was confirmed. This was accepted by the Royal Society and made big headlines at the time. While Eddington probably made the best conclusion given the data, Strevens claims that he also had extra-scientific motivations to endorse Einstein’s theory: a desire to unite British and German science after WW-I. Einstein’s response to the experiment was also famously non-Popperian: When asked what he would have done if the investigation had the opposing results, he said, “Then I would feel sorry for the dear Lord. The theory is correct anyway.”
Thomas Kuhn famously saw scientific progress as not so much a process of incremental refutation as periodic revolutions and paradigm shifts. A paradigm consists not just of mere factual predictions but also ways of thinking and determining truth. As such, paradigms are internally self-consistent, and one cannot “refute” them as much as step away from them, when they outlive their usefulness and cannot handle “anomalies”. Geo-centrism is a good example. While Strevens doesn’t say this, it is impossible to refute a geocentric point of the world (we can always say that the sun rotates around the earth but just does it in a very complex path). And of course, as Earth-based scientists, making it the center of the universe is a very natural prior assumption. Therefore, Helio-centrism did not arise from refuting geo-centrism but through switching to a different paradigm.
For Popper, scientific theories die in a duel with one another. For Kuhn, they die of old age. As scientists struggle ever more to get useful results out of their current paradigm (maybe fine-tuning it more and more to fit the data), they get the sinking feeling that it’s a dead end, and are ready to accept a new paradigm. While some of Kuhn’s radical followers believed there is no such thing as scientific progress and all paradigms are equally valid, Strevens says that (at least later in life) Kuhn did not agree with this view. Thus, for Kuhn, while switching paradigms is not as much a rational deliberation as a “leap of faith,” it typically results in improved understanding and predictive power.
If the Popperian scientist is a refutation machine, according to Kuhn, the vast majority of scientists are confirmation machines. They cannot see beyond the current paradigm, but rather because of their belief in it, they continue to push it forward, accumulating more and more data until its natural demise. Popper thought of scientists as always keeping an open mind and never believing in anything not proven. Kuhn thought that blind faith (and the pleasure of “puzzle-solving”) keeps scientists going in what 99% of the time is a slog to do more experiments and produce more data.
Strevens has his own view on the philosophy of science. In particular, he pinpoints the beginning of the Scientific Revolution to a single person – Isaac Newton. To Strevens, Newton’s theory was so different from what came before because it gives precise predictions without claiming to explain the deeper reasons. Newton gave the equation for gravity without explaining why objects can act on each other at a distance. In his postscript to the Principia, Newton said,
“I have not as yet been able to deduce from phenomena the reasons for these properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena … [has] no place in experimental philosophy. … It is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.”
In other words, Strevens sees Newton as saying, “shut up and calculate,” and indeed believes that Newton would have had no trouble with quantum mechanics’ famous “measurement problem.”
Strevens sees this as key to modern science: giving up on deeper explanation and focusing only on empirical predictions. He admits scientists take other considerations, including the beauty of theories, into account in their motivations. But he claims that the “rules of engagement” are that all scientific disputes should be settled based on empirical evidence alone and within the domain of the formal scientific literature. He calls this the “Iron Rule of Explanations.” Strevens also sees Newton as science personified, in the sense in which Newton was an archetype of the modern scientific professionalism, formalism, and compartmentalization of thought. While Newton was very interested in both alchemy and biblical studies, unlike prior philosophers, he completely separated those interests from his work on physics. In that, Strevens says, Newton anticipated the modern universities, with its focus on specialization.
“Breaking down silos” is a common slogan these days, but Strevens argues that specialization and compartmentalization were crucial to science’s success. He says that “whatever is lost through detachment and disregard for the grand view of life is more than recompensed by the narrow, tightly focused beam that searches out the diminutive but telling fact.”
Weinberg: Science history through modern eyes
Weinberg’s is a gem of a book. Weinberg does not merely describe the works of ancient scientists, but he redoes their calculations, explaining what they got right, what they got wrong, and whether or not they could have done better with the data available. The book contains 35 technical notes, including everything from reworking Aristarchus’ derivations of the sizes and distances of the sun and the moon, through Descartes’ derivation of the law of refraction, to Newton’s calculations showing that the moon’s motion can be explained by the same gravitational force we see here on earth.
Weinberg places the beginning of the scientific revolution with Copernicus. While the choice of starting point might seem immaterial, this betrays a nearly opposite philosophical stance to Strevens’. While Strevens sees the reduction of science’s goal to empirical predictions as key, Copernicus’ heliocentric theory was actually a step back in terms of predictive power. The theory fitted the data worse than the prior geocentric theory of Ptolemy. Ptolemy introduced epicycles to adjust Aristotle’s clean but wrong geocentric theory to fit the data better. Today we know that epicycles correspond to the Fourier decomposition, and hence with enough of them, one can fit any periodic function. So, Ptolemy’s theory was the quintessential “shut up and calculate” theory: a good fit with observed data, but ugly and with several “fine-tuned” aspects that didn’t have any explanations. This has troubled astronomers for ages. The following words of the 12th-century Muslim scholar Ibn Rushd about Ptolemy’s theory could have been written about quantum mechanics today: “The astronomical science of our days surely offers nothing from which one can derive an existing reality. The model that has been developed in the time in which we live accords with the computations, not with existence.” [A side note is that quantum mechanics is very different from Ptolemy’s theory in the sense that while it does not offer a satisfactory story about reality, it is not “fine-tuned” and has its own sense of beauty, even if seeing this beauty is an “acquired taste”.]
Thus Copernicus’ contribution was not to find a more predictive theory, but rather a more beautiful one. As Weinberg says, this theory “provides a classic example of how a theory can be selected on aesthetic criteria, with no experimental evidence that factors it over other theories… [this is] a recurrent theme in the history of physical science: a simple and beautiful theory that agrees pretty well with observation is often closer to the truth than a complicated ugly theory that agrees better with observation.” [This might be a point to make a side note: while Popper, Kuhn, and (to some extent) Strevens often consider experiments as having discrete or logical outcomes – either true or false – for Weinberg quantities are always continuous or approximate, and every experiment always has a measure of uncertainty.]
Not surprisingly, while Strevens calls Francis Bacon’s extreme-empiricist book “one of the most significant books ever written on scientific inquiry”, Weinberg says that Bacon is one of the individuals “whose importance in the scientific revolution is most overrated” and that “it is not clear to me that anyone’s scientific work was actually changed for the better by Bacon’s writing.”
That is, as far as Weinberg is concerned, the novel parts of Bacon’s writing– the extreme empiricism– are false, and the true parts— plain-old experimentalism— are not novel and were known to scientists before Bacon’s time.
However, both Strevens and Weinberg agree on the significance of Newton. Newton’s innovation was not showing that gravity induces a uniform acceleration on objects. As Weinberg describes, already in 1603 Galileo did experiments showing that an object in free fall undergoes uniform acceleration, and showed that the distance it undergoes under gravity is proportional to the square of the time. Newton’s crucial insight was that the same relation is enough to explain the motion of the moon around the earth. He then saw that the ratio between the gravitational acceleration on earth and the one applied on the moon corresponds to the square of the distance between the two objects, and so (through Kepler’s law and his own invention of calculus) used this relation to explain the motion of all planets around the sun.
This was an astounding achievement. Not because Newton dared use a calculation without understanding the underlying mechanism: that was already done thousands of years before by Ptolemy and many others. Rather the impressive feat was that Newton formulated a simple law that works equally well on falling apples here on earth as well as moving stars in space. By doing this, Newton gave us the reason to hope that there are simple mathematical laws that govern all objects in the universe, and truly initiated modern science.
I enjoyed reading both books and highly recommend them. Personally, I am more inclined toward Weinberg’s view than Strevens’. I think the history of science is fascinating and can teach us a lot about science even today. The philosophy of science, whether Bacon’s, Popper’s, Kuhn’s, or Strevens’, is nice to know but is of second-order importance. That said, I think Strevens does make an essential point that the scientific “rules of engagement” may well have been key to maintaining the balance between progress and consensus that made science so successful. In particular, he believes that much of science’s success can be explained by its emphasis on formal publications, with their insistence on a “sterile language” and spelling out all details of experiments or calculations, maintained through the peer review process and generations of “reviewers 2”. This might be something to keep in mind in our era, where social media, including blogs, Twitter, and company websites, sometimes replace formal venues as the main medium for conveying scientific results.
My own view is that truth in science is not settled as much by debates as by momentum. Whether the scientific consensus is X is not determined by some committee of experts, but rather by scientists, and especially students, “voting with their feet”. It is not so much a result of a debate between two distinguished scientists, but a result of a new generation of students abandoning what they think of as dead ends. (This is also known as Planck’s Principle, sometimes grimly expressed as “science progresses one funeral at a time”.) For example, in Computer Science, scores of papers and Ph.D. dissertations would be rendered meaningless if P=NP. This is stronger proof that the consensus is P≠NP than any poll of Turing laureates.
In that sense, science reminds me of the blockchain of bitcoin and other cryptocurrencies. The blockchain is a history of transactions of the form “User A paid X amount to user B”. User B will only be able to use this amount if there is consensus on this history. The blockchain is decentralized, and so several “forks” of it can exist simultaneously, but if users work on a “dead-end fork” that will not end up as part of the consensus history then their work will be for nothing. This motivates users to ensure that they are on the “right side of history” and only work on extensions of the chains that they believe will be part of the future consensus. This also means that we have more assurance of the veracity of an entry in the blockchain the further back it is, since there has been more work done that is built on this entry.
Similarly, scientists can be said to mine natural and artificial reality for scientific credit (not credit in the crass CV-padding or citation-counting way, but in terms of impact on the long-term direction of the field). But they will not get any such credit if their assumptions are eventually invalidated. Hence scientists are incentivized to ensure that they are always on the “right side of history”. They don’t want to work on a “dead-end fork” that will never get “merged” into the future main scientific discourse. A corollary is that if the truth of a particular proposition P is irrelevant to the way people do science then science will never need to form a consensus on whether P is true or false. For example, as long as the choice of interpretation of quantum mechanics remains irrelevant to actual papers, debates between the Many-Worlds, Bohm and other interpretations will continue to take place in “cheap talk” outside the formal literature (whether over beer, in blog comments, or the popular press) and science will not need to form a consensus on which interpretation is correct. In particular, I don’t think science will ever need to form a consensus on whether any view of the philosophy of science, including my own, is the true one.
Acknowledgments: Thanks to Scott Aaronson for recommending Weinberg’s book to me and Ludwig Schmidt for recommending Strevens’ book. Thanks also to Scott, Ludwig, and Preetum Nakkiran for useful comments on an earlier draft of this post.