Episode 9: Laws vs. Principles
Hello, I’m Logan Chipkin, and you’re listening to the Fallible Animals podcast. Today we’re going to talk about laws versus principles, and how constructor theory elucidates the differences between the two. We’ll be drawing on ideas talked about in previous episodes, but I’ll do my best to redefine any terms as we come across them anyway.
It’s interesting that, while constructor theory provides a natural, important, and useful demarcation between laws and principles, the notion of ‘law’ itself underwent a similar split some time ago, having previously been used to cover both man-made law and the laws of science. The ancient Mesopotamians of 5 or 6000 years ago thought that both moral laws and the laws of nature derived from divine sources. In other words, our ancestors saw no difference between the two — the gods told the winds when to blow, and they told people what behaviors were acceptable, and what the punishments would be for violating them. For a detailed account of this history, I recommend Leondar Mlodinow’s 2015 book, The Upright Thinkers.
Ancient Greeks such as Aristotle in the fourth century B.C., and ancient Romans such as the philosopher Seneca and the poet Lucretius of the first century B.C. began to treat moral law and scientific laws as applying to distinct domains, although I don’t know if they were conscious of the fact that they were delineating between two realms that had previously been thought to be one and the same.
Now, we consider the difference between legal, manmade law and scientific law so obvious that it doesn’t need stating. But that wasn’t always the case. One day, our descendants will feel the same way about the difference between laws and principles.
Sticking to science now, what do you think the difference is between laws and principles? Do you think there is one? There’s the so-called Law of Conservation of Energy, which states that total energy of an isolated system remains constant. We have Newton’s three laws of motion, including the famous ‘force equals mass times acceleration’ equation. In chemistry, we have the law of definite proportions, which states that a chemical compound is composed of elements in fixed ratios — for example, all molecules of water are composed of two hydrogen atoms and one oxygen atom. What about in areas like epistemology and biology? We’ve discussed our best theories in each, namely, critical rationalism, and evolution by natural selection, respectively. Should we consider the rules of those theories as laws, principles, merely statements about how the world works, or what? Does it matter?
Yes, it does. If Reality is as coherent as we think it is, then there must be a way to relate these laws, principles, and explanations of Mother Nature’s various pieces. But then we need an explanatory framework about how these theories, like those of physics, epistemology, and biology are interrelated. In other words, we need a theory of theories. Let’s call that theory the meta-theory, and the theories that it would explain (and maybe constrain) subsidiary theories. Not only would such a meta-theory allow for all sorts of unifications between seemingly disparate subsidiary theories, but it might provide rules of its own right that would aid us in the creation of future subsidiary theories.
This might all sound a bit abstract right now, but it’ll make more sense as we go.
Consider Newton’s theory of classical mechanics. This is a theory of motion. It provides what we might call ‘object-level’ laws — given some object or objects, whether planets or billiard balls, it explains and predicts their positions and velocities over time, given the forces acting on them. I’ve already alluded to the fact that at the core of his theory are three laws of motion. The first, for example, roughly states that an object in motion will stay in motion unless acted on by an external force. So Newton’s laws explain the motions of objects, and the laws are eminently testable, since they make predictions for the trajectories of objects given the forces acting on them. Newton’s classical mechanics forbids certain trajectories from being possible, to play on the words of Karl Popper.
Furthermore, you can prove that any system that conforms to Newton’s laws also obeys the Principle of Conservation of Energy (I’m beginning to be more precise with my terminology, as we edge ever-closer to constructor theory).
If we turn to quantum mechanics, in fact, in the 1920s, it looked for a moment as if quantum mechanical phenomena did violate the principle of conservation of energy. One of the earliest quantum mechanical phenomena to be hypothesized was that electrons in an atom ‘jump’ from one energy level to another, rather than move continuously between them. We might say that quantum mechanics provides ‘object-level laws’ that explain the weird phenomena of the subatomic world. In 1924, one of the founders of quantum mechanics, Niels Bohr, along with Hans Kramers and John Slater, guessed that energy would not be conserved during such a jump. Einstein himself scoffed at this, and eventually he would be vindicated — quantum mechanics would come to be shown to obey energy conservation, just as Newton’s theory did.
Einstein’s theory of general relativity, too, is an object-level theory — it explains the dynamics of space, time, matter, and energy on large scales, to give an extremely brief summary. And it, too, obeys the principle of conservation of energy.
Now consider the science of thermodynamics, which attempts to explain phenomena as they relate to heat, work, energy, and other such quantities. Thermodynamics is a sprawling and many-headed dragon, which we’ll explore in greater detail in a future episode. For now, I want to draw attention to the Iron Laws of Thermodynamics. As Newton’s classical mechanics has its three laws relating the concepts of motion, force, mass, and so forth, thermodynamics has four laws relating its concepts of energy, heat, entropy, temperature, and others. The second law of thermodynamics, for example, states that the entropy of an isolated system tends to increase…there are actually a few different ways of expressing this law. Another informal way of understanding it is that heat cannot, or will not, maybe, spontaneously flow from colder regions to hotter regions. Another law of thermodynamics is the zeroth law, which is effectively a reformulation of the principle of conservation of energy!
So three object-level theories — classical mechanics, quantum mechanics, and general relativity — can be shown to obey the meta-level principle of conservation of energy. Meanwhile, thermodynamics asserts this principle outright! What’s going on?
What if there were principles that all object-level theories and their laws had to obey? Such principles would be ‘laws about laws’: All object-level theories, remember, are theories about, well, objects, tangible things — particles, stars, heat, space. A meta-level theory, on the other hand, would be a theory about theories, not objects! Just as object-level theories are composed of laws that objects and phenomena must obey, so too, a meta-level theory is composed of principles that all object-level theories must obey.
That all hitherto created object-level theories in physics seem to obey the principle of conservation may not be a coincidence. Maybe all object-level theories that we could ever create and accept will always conform to the principle. Energy conservation would be a principle for all object-level theories every created.
That’s just one such principle. Can we think of others? We’ve discussed the principle of testability, which comes out of critical rationalism, our deepest theory in epistemology. The principle holds that all object-level theories must make predictions which, if shown to be false, would render the theory false, or at the very least problematic. Like the principle of conservation of energy, no object-level theory makes direct reference to the principle of testability. However, every successful object-level theory yet produced has conformed to it!
That makes two principles that had already been widely accepted even before the genesis of constructor theory. Logically speaking, it could have been the case that all object-theories so far created just happened to conform to these two principles, and that future object-level theories will be shown to violate either the principle of conservation of energy, or the principle of testability, or both. Then, they wouldn’t have been principles at all, at least in the sense defined here of being laws about laws. Such patterns would merely have been strange coincidences that were doomed to fail.
But, if the opposite is true — if these principles really are timeless, really are universal — then they can help us in the creation of new object-level theories. For any object-level theory that did not conform to these principles would have to be ruled out on the basis of violating deeper rules of Reality. For example, if someone conjectures a new object-level theory with the goal of unifying quantum mechanics and general relativity, and that theory was shown to violate the principle of conservation of energy, then we would be right to discard the new theory, since we already hold that the principle is true for all object theories, both those of established repute and those freshly minted.
Just as, once you lay the groundwork for an object-level theory, you then work out the mathematics to expose its predictions and implications for how Reality ought to behave, the same should be true for a meta-level theory, except that instead of producing predictions and implications for how objects and physical phenomena should behave, mathematical exploration of a meta-level theory should yield predictions and implications for how object-level theories should behave.
Recall constructor theory’s fundamental principle (I said principle, not law): that all of the other laws of physics can be expressed in terms transformations that are possible, transformations that are impossible, and why. At the outset, constructor theory is a different mode of explanation than were previous physical theories. It quite explicitly tells us that it’s not an object-level theory, not a theory about dynamical systems. No, it’s a theory of principles, of ‘laws about laws’.
As constructor theory is developed, and its underlying mathematical structure elucidated, we should expect new principles to emerge that would never have been conceivable beforehand. Remember that the few principles we did have before constructor theory were pretty ad hoc, accepted for independent reasons and not at all integrated with the rest of our knowledge. Just as the mathematics of classical mechanics allow one to derive all sorts of object-level relationships in Nature, such as that planets move faster as the distance to their central star decreases, so too the mathematics of constructor theory may allow for the derivation, and conjecture, of all sorts of principles of Nature yet unknown.
How could such a meta-theory, such a coherent set of principles, ever be testable? We know how an object-level theory is tested — for some controlled experiment, we compare recorded data against what the theory predicts the data should be. If the data and the prediction are the same, the object-level theory is said to have been corroborated. What if the data and the prediction don’t match? Recall from our discussion of critical rationalism that this whole testing business is not as straightforward as it might seem. Experimental testing is most helpful when we have more than one candidate theory that purport to explain the same phenomena, and that make different predictions for the same physical event.
(As a quick technical but interesting aside: constructor theory allows us to express this situation in exact terms: each candidate theory forbids some unique class of transformations, or tasks, from being possible. The crucial experiment, then, necessarily reveals some transformation to be possible, which then contradicts the predictions of all theories but one.)
Anyway, the point is that a theory is only ever refuted, or falsified, when we have a rival theory that survives the crucial experiment. Then we accept that theory at the expense of the other candidate theories whose predictions were contradicted by the outcome of the crucial experiment.
Now, consider the principle of conservation of energy once again. Let’s imagine that it is rendered even more rigorous and exact under a constructor theoretic formulation. In other words, if constructor theory is true, then it follows that this principle must also be true. Fine. Now imagine that two rival object-level theories are proposed to explain some newfound phenomena in Nature. Before we go about conducting a crucial experiment to determine which of these theories is false, we explore both theories mathematically and discover that only one of them conforms to the principle of conservation of energy. Finally, we conduct the crucial experiment, and only the object-level theory that violates the principle of conservation of energy survives! This would falsify the principle, and perhaps the entire edifice of constructor theory.
Stated generally, if some object-level theory contradicts a principle, but we have no choice but to except the object-level theory, then the principle can be said to have been falsified. This could be detailed further, but the logic of the situation has many parallels with the logic of standard experimental testing that we’ve already covered in previous episodes, so I think it’s best to move on for now.
I’ve been arguing for the usefulness of constructor theory in providing principles that constrain the ‘behavior’, if you like, of object-level theories that themselves can be written in mathematical languages. Classical mechanics, quantum mechanics, general relativity, and most theories of traditional physics are typically summarized by a few tagline equations. (These equations should always be accompanied by verbal explanations of why the equations hold, what the terms mean, and so forth, but I digress.). My point is, what about theories that have failed to be expressible in mathematical terms? Darwin’s theory of evolution by natural selection, and Popper’s theory of critical rationalism come to mind (in fact, economics also comes to mind, but we haven’t covered that yet, so hold that thought) — there is no equation that can deterministically tell us, say, which species will rise from the Earth’s muck, nor which future theories will be discovered in our scientific investigations. In this sense, both evolution and critical rationalism explain fundamentally unpredictable domains of Reality.
In the fields of physics I’d just mentioned, we can use their equations to predict what will happen, given what has happened. Another way of saying this is that their equations allow us to predict the future state of some system so long as we know its initial conditions. This is not so in evolution nor in critical rationalism, but not all hope is lost. What if, instead of positing object-level laws that explain what happens, we instead search for meta-level principles that constrained what could possibly happen in these theories’ domains of applicability?
For example, we could imagine as-yet unknown principles that, while not telling us where and when life will emerge, maybe there is hope that we might discover principles that tell us under what conditions life could possibly emerge, and conversely, under what conditions it is impossible for life to emerge. In fact, such work has already begun. I’ll link to Chiara Marletto’s research paper in the show notes page, in which she demonstrates how life could be possible in our universe, given that the biosphere’s apparent design is not explicitly encoded in the fundamental laws of physics.
Economics, too, is inherently unpredictable, since it is all about people and their creative actions in a world of scarce resources. I won’t say much about this now, since we’re going to dive into economics soon. Just notice that, once again, no object-level may be written down that could predict with certainty the future state of an economy given some initial state. It may well, be, though, that there exist constructor theoretic principles that tell us what economic phenomena, such as the growth of wealth or so-called economic calculation, are possible and which are impossible, and each under what conditions. More on this after we cover the fundamentals of economics.
So constructor theoretic principles could still help us in explaining Reality and solving problems in our worldview, even when the phenomenon of interest is intrinsically unpredictable. Notice that this flies in the face of those who insist that science is fundamentally about prediction, rather than explanation.
Let’s summarize what we’ve covered today. Just as the difference between moral law and scientific law required development of a more coherent and deeper worldview for our ancestors to flesh out, so too the difference between law and principle had been either unknown, poorly understood, or ill-defined before the creation of constructor theory. This theory provides a natural and elegant distinction between law and principle — a theory composed of laws, or object-level laws, as I’ve been calling them, describes, explains, and predicts phenomena in Nature. A theory of principles, or meta-level principles, as I’ve been calling them, constrains the structure of object-level theories themselves. To repeat our favorite example, the principle of conservation of energy constrains any object-level theory and its laws such that no object-level theory and its laws, both past and future, may violate the principle. Constructor theory may help us to develop future object-level theories by providing many such principles to which all object-level theories must conform. Finally, while inherently unpredictable phenomena, such as those of biology, economics, and epistemology cannot be explained in terms of what will happen given what has happened, which is doable for many phenomena covered in traditional physics, we might still solve problems in each field by resorting to constructor theoretic principles that tell us what can possibly happen, and what cannot possibly happen in each.
Let’s stop there. In case you prefer written form, I’ll upload the transcript of this episode to my medium account, as I do for every episode.I haven’t decided yet what we’ll cover next week, but I have a few ideas in mind. If you have suggestions, let me know. You can contact me on Twitter @ChipkinLogan.
Also, I recently published an article called ‘Economic Creationism’ with The Libertarian Institute if you’re into that sort of thing. The link to the article can be found at my website, www.loganchipkin.com.
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Also, please consider donating to the show through my patreon page, the link to which I’ve included in the show notes page. I would greatly appreciate your support. The more money I earn from the podcast, the more time I can spend on it, and the more knowledge I can get out there. I’m so grateful that I get to do this at all, and with your help, I can invest even more resources, including time, into the show. Thank you so much, and have a great rest of your day. See you next time.
My patreon page — https://www.patreon.com/Fallibleanimals
Economic Creationism — https://libertarianinstitute.org/articles/economic-creationism/
Twitter — https://twitter.com/ChipkinLogan
Articles — www.loganchipkin.com
Foundational Paper on Constructor Theory — https://arxiv.org/pdf/1210.7439.pdf
Constructor Theory of Life — https://arxiv.org/pdf/1407.0681.pdf
The Upright Thinkers — https://www.amazon.com/Upright-Thinkers-Journey-Living-Understanding/dp/0307908232