(Roughly) Daily

“No law of nature, however general, has been established all at once; its recognition has always been preceded by many presentiments.”*…

Laws of nature are impossible to break, and nearly as difficult to define. Just what kind of necessity do they possess?

… The natural laws limit what can happen. They are stronger than the laws of any country because it is impossible to violate them. If it is a law of nature that, for example, no object can be accelerated from rest to beyond the speed of light, then it is not merely that such accelerations never occur. They cannot occur.

There are many things that never actually happen but could have happened in that their occurrence would violate no law of nature. For instance, to borrow an example from the philosopher Hans Reichenbach (1891-1953), perhaps in the entire history of the Universe there never was nor ever will be a gold cube larger than one mile on each side. Such a large gold cube is not impossible. It just turns out never to exist. It’s like a sequence of moves that is permitted by the rules of chess but never takes place in the entire history of chess-playing. By contrast, if it is a law of nature that energy is never created or destroyed, then it is impossible for the total energy in the Universe to change. The laws of nature govern the world like the rules of chess determine what is permitted and what is forbidden during a game of chess, in an analogy drawn by the biologist T H Huxley (1825-95).

Laws of nature differ from one another in many respects. Some laws concern the general structure of spacetime, while others concern some specific inhabitant of spacetime (such as the law that gold doesn’t rust). Some laws relate causes to their effects (as Coulomb’s law relates electric charges to the electric forces they cause). But other laws (such as the law of energy conservation or the spacetime symmetry principles) do not specify the effects of any particular sort of cause. Some laws involve probabilities (such as the law specifying the half-life of some radioactive isotope). And some laws are currently undiscovered – though I can’t give you an example of one of those! (By ‘laws of nature’, I will mean the genuine laws of nature that science aims to discover, not whatever scientists currently believe to be laws of nature.)

What all of the various laws have in common, despite their diversity, is that it is necessary that everything obey them. It is impossible for them to be broken. An object must obey the laws of nature…

But although all these truisms about the laws of nature sound plausible and familiar, they are also imprecise and metaphorical. The natural laws obviously do not ‘govern’ the Universe in the way that the rules of chess govern a game of chess. Chess players know the rules and so deliberately conform to them, whereas inanimate objects do not know the laws of nature and have no intentions.

Scientists discover laws of nature by acquiring evidence that some apparent regularity is not only never violated but also could never have been violated. For instance, when every ingenious effort to create a perpetual-motion machine turned out to fail, scientists concluded that such a machine was impossible – that energy conservation is a natural law, a rule of nature’s game rather than an accident. In drawing this conclusion, scientists adopted various counterfactual conditionals, such as that, even if they had tried a different scheme, they would have failed to create a perpetual-motion machine. That it is impossible to create such a machine (because energy conservation is a law of nature) explains why scientists failed every time they tried to create one.

Laws of nature are important scientific discoveries. Their counterfactual resilience enables them to tell us about what would have happened under a wide range of hypothetical circumstances. Their necessity means that they impose limits on what is possible. Laws of nature can explain why something failed to happen by revealing that it cannot happen – that it is impossible.

We began with several vague ideas that seem implicit in scientific reasoning: that the laws of nature are important to discover, that they help us to explain why things happen, and that they are impossible to break. Now we can look back and see that we have made these vague ideas more precise and rigorous. In doing so, we found that these ideas are not only vindicated, but also deeply interconnected. We now understand better what laws of nature are and why they are able to play the roles that science calls upon them to play.

What is a Law of Nature?,” Marc Lange explains in @aeonmag.

* Dmitri Mendeleev (creator of the Periodic Table)


As we study law, we might send inquisitive birthday greetings to Federico Cesi; he was born on this date in 1585. A scientist and naturalist, he is best remembered as the founder of the Accademia dei Lincei (Lincean Academy), often cited as the first modern scientific society. Cesi coined (or at least was first to publish/disseminate) the word “telescope” to denote the instrument used by Galileo– who was the sixth member of the Lincean Academy.


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