Fallible Animals Episode 3: Progress as Error-Correction

Below is the transcript of episode 3 of my podcast, Fallible Animals. The original audio can be found on YouTube, Anchor, Spotify, and iTunes.

Hi, this is Logan Chipkin, and you’re listening to the Fallible Animal podcast. We’re continuing our deep-dive into critical rationalism, our best theory of knowledge. Last time, we covered a few core concepts of the theory — that scientific theories must be falsifiable, or testable, that all intellectual pursuits are fundamentally about solving problems, and that science in particular is about solving problems in our worldview. We do this by guessing an explanation of some aspect of Reality for which we previously had no explanation. This guess, this conjecture, is a theory. We then criticize that theory, as well as potential alternative theories, with every conceivable mode of criticism that we have. This includes, but is not limited to, experimental testing and the gathering of evidence. Those explanations that survive our criticisms, we tentatively accept to be the solution to our problem, the explanation of the phenomena of our focus.

Because all of our explanations are conjectural, there is no room for absolutely certainty in this framework. Future modes of criticism, or just novel evidence, could always render a theory problematic. But if that’s the case, does science ever really progress? Is there a direction to the growth of knowledge, or are we just spinning our wheels, forever swapping one theory for another under the illusion that we’re peering ever deeper into the Nature of Reality?

Indeed, scientific progress, and the growth of knowledge more generally, are possible. Not only is the growth of knowledge possible, but it’s been happening on Earth for a few billion years, since the first genetic code began to replicate. Genes are a form of knowledge, but that’s another story for another episode. Anyway, long after knowledge first came onto the scene in the form of genes, it began to grow via a new medium — human brains. (Naturally, I am skipping many important details in the 3.5 billion years between the origins of life on Earth and the dawn of humanity). And even after humans had spread across the entire planet, the growth of knowledge was only just beginning. During the sixteenth, seventeenth, and eighteenth centuries, knowledge grew at a faster pace than ever before, thanks to the so-called Scientific Revolution and more general Enlightenment. It was during this time that many of the foundational ideas of civilization were codified, such as individualism, the scientific method, and many others. We’ll talk more about this time period during a history episode. My point now is only to broadly outline the history of knowledge on Earth (and perhaps in the Universe, if there are no aliens out there).

But what is knowledge? Intuitively, we all have an idea by what I mean when I say knowledge, but let’s not be ambiguous, for ambiguity is one of the great enemies of understanding. Knowledge is basically a special kind of information that, once instantiated in the world, tends to cause itself to remain so. Consider Johannes Kepler’s discovery of his famous Three Laws of Planetary motions, which he published in the early 1600s. They were meant to be improvements on Nicolaus Copernicus’s heliocentric model of our solar system. While Copernicus thought that planets traced circular paths in their revolutions around the sun, Kepler’s First Law states that planetary orbits follow elliptical paths, rather than circular ones. And while our understanding of the the motion of astronomical bodies has deepened several times over since Kepler’s days, the fact that planets in our solar system follow approximate ellipses rather than circles has held true (I should caveat by saying that in fine enough detail, the planets actually follow a more complicated trajectory, but my point remains so long as we know that Kepler’s ‘Law’ is now an approximation).

So — that planets in our Solar System follow approximately elliptical orbits is a fact about Reality. This fact, when recorded in papers, books, or stored in the brains of people, is information. Now, as I’d said, this fact survived centuries of exposure, from 1609 to the time of this recording. It survived not only scrutiny, but also comparison to alternatives, such as the aforementioned Copernican idea that planets orbit around the Sun in circular paths. Kepler’s elliptical path idea has traveled across time and space, from 17th century Europe into your ears, wherever and whenever you’re listening to this. And it hasn’t been a passive traveler — it is a cause of its own propagation. Had the idea ever been shown to be false, for example, by contradicting observations of the motions of Venus or Neptune, then the elliptical path idea would’ve gone extinct, only to be found in the history books. But it’s not just in the history books — it’s in the science books. So the merits of this idea — namely, its survivability in the face of attempts to criticize it — have caused it to remain instantiated in the world.

Contrast this with Copernicus’s rival idea that planets revolve in circular paths. That idea has been cast to the history books, since it eventually failed in the face of criticism — in this case, it failed to account for the data as compared with Kepler’s idea.

To reiterate, then, knowledge is sticky information: once it’s instantiated in the world, it causes itself to remain so. Like all good definitions, this refines and reshapes our intuitive notion of knowledge into workable, physical terms.

Finally, I should say that this definition emerges naturally in our deepest theory in physics, which is constructor theory. We’ll switch gears in the next episode and talk much more about this theory, but I thought I’d mention it now. I’ve added a link to the foundational paper on the theory, which was published in 2013, in the show notes page.

Can this thing we call knowledge grow? Is our own knowledge of how Reality works increasing — are we really understanding evermore of the world as our admittedly conjectural theories rise and fall over the centuries?

Consider the example we’d just discussed when teasing out the definition of knowledge. Copernicus conjectured that the Sun was the center of our solar system, and that the Earth, and the other planets, revolved around it. This was itself an improvement upon the previous prevailing theory, but for now we’re focused on the successor to Copernicus, not his predecessor. So from 1543, when Copernicus published the heliocentric model in his book, On the Revolutions of the Celestial Spheres, until 1609, when Kepler published his first two laws in his book, Astronomia nova, our best theory of the solar system was that planets resolved around the Sun in circular orbits. Crucially, while Kepler contradicted Copernicus with respect to the shape of the planets’ trajectories, crucially, he kept Copernicus’s idea that the planets revolve around the Sun in the first place!

While Kepler was scrutinizing astronomical data, crunching numbers, and ascertaining the patterns underlying the planets’ movements, the Italian Galileo Galilei was not only gazing at celestial bodies with his telescope but also studying more terrestrial phenomena, such swinging pendulums and the the dynamics of falling objects. Galileo is famous for a host of contributions, one of which is the popularization of experimental testing as a crucial step in the scientific method. He called such a test a cimento, which translates to “ordeal”.

Actually, although Kepler and Galileo never met, they did correspond and bond over their mutual acceptance of the heliocentric model of our solar system. Their dispositions stood in stark contrast — Kepler was motivated by a religious and even mystical faith that God created an orderly, mathematical universe. For Kepler, the sacred and the mathematical were one and the same. Galileo was much more grounded in his approach to science, working to solve problems for their own sake, rather than for some divine purpose. And while Kepler had almost become a Lutheran minister, making him quite literally the churchboy of the pair, Galileo had always been a heretical type — he never finished his degree but nevertheless became a brilliant academic lecturer, becoming known for his wild, biting lectures. He also had a taboo love affair with a much younger woman. Kepler, meanwhile, was too physically impaired to even work most jobs, owing to a smallpox episode from childhood. Small wonder it was Galileo and not Kepler who famously clashed with the Catholic Church. In one of his letters to Kepler, Galileo wrote, “I wish we could laugh at the extraordinary stupidity of the mob. What say you about the foremost philosophers of this University, who with the obstinacy of a stuffed snake, and despite my attempts and invitations a thousand times they have refused to look at the planets, or the moon, or my telescope?”

Galileo’s contributed to a wide array of fields, including astronomy, engineering, and importantly for our purposes, the scientific method itself and the physics of falling bodies, both of which I’d mentioned earlier. Although probably apocryphal, the stories goes that by dropping objects of various weights from the Leaning Tower of Pisa, Galileo demonstrated that objects accelerate, or speed up, at the same rate as they fall towards the earth, reaching the earth’s surface at the same time if they fall from the same height simultaneously. This was significant in the history of ideas because it was a refutation of one of Aristolte’s many theories, this time of his theory of motion, which posited that heavier objects should fall faster than lighter ones, and that a net force on an object is what causes it to move with a constant speed. This was one of several episodes during the Scientific Revolution and Enlightenment period in which an idea of the Great Aristotle was challenged and overturned by innovative thinking and rigorous scientific methodology.

Anyway, by the time Kepler and Galileo had been laid to rest in thee 1630s and 40’s, respectively, we had not only Kepler’s Three Laws describing the motion of the planets, but also Galileo’s contributions to our understanding of motion of terrestrial objects, including the fact that objects fall with a constant acceleration and at a rate independent of their mass. And Galileo formulated other important principles, such as the so-called principle of relativity — that the laws of motion are the same for all non-accelerating frame of references.

Enter Isaac Newton and his epoch-defining three-book work, Principia Mathematica. Published in 1687, the Principia is a detailed account of so-called classical mechanics, humanity’s first successful universal theory. It includes not only Newton’s famous laws of motion and his law of gravitation, but it also shows explicitly how the theory accounts for disparate phenomena such as the dynamics of the ocean tides and the orbits of comets. Crucially, Newton derived Kepler’s three Laws. So while Kepler merely found pattern in data and guessed an equation that seemed to hold true for the planets, Newton postulated deeper, more general laws, and derived Kepler’s “Laws” as consequences of his theory. Similarly, Newton’s theory accounts for Galileo’s observations in exact, elegant terms. Although the concepts of Newton’s theory such as force, momentum, and mass had been developed before him, he unified them into one grand explanation of matter’s motion, from swinging pendulums to firing cannonballs to falling objects on Earth to the orbits of celestial bodies beyond. Kepler’s and Galileo’s work turned out to be special cases that held true under particular circumstances for which Newton’s theory accounted.

The story behind the impetus of Newton finally writing and publishing Principia Mathematica is actually pretty funny. But that’ll be a story for another episode.

Newton’s theory, classical mechanics, not only explained the phenomena and corresponding mathematical patterns discovered by Kepler and Galileo, but it also explained more phenomena that no one had previously been able to explain. For any isolated system, if you knew the initial state of the system and all of the forces acting on it, Newton could in principle tell you its state at any later point in time. For example, if you know the initial velocity of a baseball after hitting it with a baseball bat, and you know perfectly well the magnitude and direction of forces due to gravity and air resistance acting on the ball, you could predict the ball’s position and velocity and any future point in time. This was a new way of thinking, a new mode of explanation.

Not only did Newton’s theory unify Galileo’s and Kepler’s ideas, and not only did it explain more than either ever could alone, but, importantly, Newton corrected their errors. While Kepler’s Laws describing orbital motion constituted a creative feat, they were rather rudimentary explanations — little better than mapping data to equations that seemed to work. And contrary to some unfortunate currents in some academic circles these days, raw equations do not constitute an explanation. For instance, from Kepler’s Laws alone, we have no idea whether or not they should, or do, apply to other solar systems, hypothetical or otherwise. Newton elegantly resolved this gap providing a universal theory of gravity — that is, a theory about how any object with mass will impose an attractive force on any other object with mass. So one of Kepler’s errors that Newton resolved was the lack of universality in his admittedly impressive mathematical descriptions. Every fundamental theory proposed since Newton has had this universal character. This feature so prevalent that it’s rarely ever made explicit, but it’s worth remembering that once upon a time, scientists merely tried to explain one or a handful of phenomena at a time. One of Newton’s brilliant strokes was to consider how the world would act if a few universal statements held true — if *entire classes* of phenomena conformed to particular rules.

And notice that Kepler’s contribution instigated further questions. For instance, and related to the whole universality business we’d just discussed, why do his Laws apply to celestial bodies, but not terrestrial ones? Why, in other words, do cannonballs and clouds and ships not follow Kepler’s Laws? These questions would have even been conceivable before Kepler produced his Laws. And then, when Newton answered these questions and others, questions were raised about *his* theory. What is this gravitational force of which he speaks?

By the way, this kind of argument is always used by skeptics of many of our best theories, both now and historically. The argument goes along the lines of, “But your theory can’t explain X,” or “Your theory can’t define Y, even though it makes reference to it.” If this reminds you of the God of the Gaps argument, that’s because that argument is a special case of the one to which I’m referring. That argument is a fallacy in which someone claims that because we don’t have a naturalistic explanation for some phenomenon, therefore God is necessary to explain said phenomenon. I’m exposing the more general fallacy of someone pointing to the shortcomings of a theory as reason to reject the theory entirely. But theories must be judged by their ability to solve problems as compared with their rivals. The culprit of this fallacy, let’s call it the Perfectionism Fallacy, compares a given theory against some Utopian Theory that has no shortcomings, no errors, is capable of explaining everything. But there never will be such a theory. All of our best explanations are, and forever will be, fallible.

So in explaining what, exactly, our solar system was, and what was happening in it, civilization’s best explanation evolved towards better and better explanations, each with fewer errors than its predecessor. One paradigmatic leap was that from a geocentric model in which the earth was the center, to the Copernican, heliocentric model, which occurred in 1543. Notice that even here, where Copernicus fix the error of having the Earth in the center of the system, the geocentric model wasn’t completely false. For example, every subsequent theory has kept the knowledge that the solar system consists of bodies revolving around other bodies — so even here, the geocentric theory that is so often mocked had more knowledge embedded in it than people give it credit for. Then with Kepler, the Copernican model was improved by fixing a few of Copernicus’s errors, such as the assumption that planets traced circular paths in their revolutions around the Sun. But this still left to be explained why the planets should move in such a way at all. In 1687, Newton solved this problem with his great edifice called Classical Mechanics. Among many other things, he resolved Kepler’s error of not seeking and applying universal laws in deducing the motion of *particular* objects, such as the planets of our solar system.

But while Newton’s theory could explain the motions of celestial bodies in terms of gravity, he left an explanation of gravity unresolved. That gap in understanding would have to wait nearly 230 years to be resolved.

I could have begun this ever-improving chain of explanations earlier in the history of civilization, and I could have ended it in present-day, but I think I’ve made my point. In explaining some aspect of Reality, we conjecture a theory, an explanation. Even if successful, that explanation will inevitably have gaps, errors, and shortcomings. Those gaps, in turn, require a new explanation that accounts for everything that its predecessor could account for, plus a resolution of the errors of its predecessor. This new, deeper theory has fewer errors than its predecessor, but errors remain, some that could not have even been detected when its predecessor reigned supreme. And so our theories grow ever deeper, our knowledge accounting for more and more phenomena with every improvement in our worldview.

Last episode, I said that I wanted to cover the rival theories to critical rationalism and explain why they’re wrong, and I will get to that soon, but I think we’ve covered enough ground today. For the next episode, I want to mix it up and switch from epistemology to physics. We’ll return to critical rationalism and this business about its rivals soon, I promise. But I’d like to introduce our deepest theory in physics, constructor theory. It’s more all-encompassing than any theory that has come before it, and I’d like to tell you about it.

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In the show notes, I’ve included links to both the foundational paper on constructor theory, and the transcript of a lecture Karl Popper gave entitled, ‘Objective Knowledge.’

Thank you for listening. I’m your host, Logan Chipkin. You can follow me on twitter @ChipkinLogan, and you can read some of my articles on www.loganchipkin.com. If you liked this episode, please consider subscribing and sharing. Let’s get these ideas out there. Have a great day.

Transcript of Karl Popper’s lecture entitled ‘Objective Knowledge’ — https://pdfs.semanticscholar.org/845d...

Foundational Paper on Constructor Theory (preprint) — https://arxiv.org/pdf/1210.7439.pdf

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