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You're definitely correct, this article overhypes the mysteriousness. It's a shame, though, and a missed opportunity to go deeper, because it is a surprising fact that almost all of physics is most elegantly expressed in terms of least action principles, where it really does seem like the universe conspires to minimize some quantity.

In classical physics, the Lagrangian formulation is merely useful for some calculations, and can be fairly viewed as a mathematical trick that is equivalent to using Newton's law directly; similarly in E+M it's a compact and often useful way to express Maxwell's equations, but not particularly fundamental.

When you reach quantum field theory, though, it's all but impossible to do anything without a Lagrangian/action, and theories are almost always described in that form. String theories are the same. General relativity is not always presented that way, but gravitational dynamics are stunningly simple in that form: in a vacuum, nature abhors curvature.

Principles of least X are fascinating and incredibly useful, and the ex-physicist in me believes that they describe the actual universe so concisely that they are truly fundamental in some sense. But you have to really dig in to get any sort of appreciation for that, and I agree that this article didn't go anywhere near deep enough.

Thats pretty interesting.. I wonder though -

Does the universe seem to prefer minimizing some quantity, or do human brains gravitate towards theories that identify quantities that are minimized/maximized?

Couldn't physical theories be expressed in many different ways, maybe with completely different fundamental concepts than mass/energy etc? Where the theories describing nature would not be so clean?

That's the same thing here, though, since physics is a scientifically descriptive endeavor. Our conceptualization of the universe is limited by our perception of it, and thus the whole idea of "what the universe does" is fundamentally entangled in what we see it doing and how we can talk about it.

So that the universe "optimizes" something must be true, given that only one past is observed. It has to have been optimizing for the past that we see. (It is perhaps more remarkable that we can make accurate predictions of the future, but this more or less seems to be a side-effect of optimization requiring some notion of continuity.)

Our descriptions of nature are clean because they are based on observations of the past, which are the exact phenomena the universe appears to be optimized to produce. All other possible results are merely counterfactuals in our brains, and having those encoded in our theories would make them noisy and inaccurate. (And the best evidence for such counterfactuals being 'real' does exactly this by introducing quantum indeterminacy into the theory.)

> it really does seem like the universe conspires to minimize some quantity.

But there's only one min/max isn't there? Otherwise all values may be permitted, and we'd have entropy.

The vast body of physics may concern behavior simple enough to be expressed, but much of reality behaves in complex ways?

Hence the challenge of 6D (2,0) superconformal field theory.

There is a small problem with your explanation: refraction can happen with single photons, which means that the "minimum path length" rule continues even as the wave formulation breaks down. If you say "the photon travels along all paths at the same time, finally choosing one path to have 'really' gone down," then you have to explain how it was able to move faster than light to collapse down to the single point where you found it on your camera's sensor.

There is indeed a mystery here. In fact, since the only option I know of that eliminates spooky FTL signalng and spooky hidden (unobservable) mechanics has spooky alternate universes, I feel safe in concluding that at least one spooky thing has to be happening, even though we don't know which one it is.

Thinking about photons is bad for you, especially if you are doing quantum-optics. It is almost always better to think about quantum fields, and in this case the quantumness adds nothing to the physics.

The "photon" is just a quantum of excitation of the optical medium (in this case the EM compled with the electromechanical state of matter in it). These exictations obey wave equations, just as classical waves do, and hence Snell's law.

It's true that you can also (almost) think of photons as point-particles travelling over every possible path in time-space and then do infinite-dimensional path-integrals. That point of view is important for a physicist to understand, but it is not needed to explain refraction.

I'd say the last model is necessary for explaining refraction, but not for describing it (where a simpler wave model suffices).

Huygens explained refraction using classical wave velocities only. Though I agree there is a similarity between his notion wave-sources everywhere and path integrals. (Which is odd since path-integrals are a very particle oriented way of thinking).

What Huygens' explanation leaves slightly mysterious, is why (beyond a mathematical coincidence) this result just happens to also give the minimum-time result. Path integrals explain that very nicely.

You're describing quantum mechanics, but the phenomena here are classical. There is no mystery with Fermat's law, even if you do not accept wave optics and want a theory of light particles. At each instant in time a light particle can determine how its trajectory will bend based on purely local information. The bending of light is determined by the local variation in the index of refraction. Snell's law is what you get if the index of refraction jumps discontinuously. This is analogous to how in classical mechanics the trajectory of a particle is determined by the local variation in the potential energy function (or more generally, the Lagrangian), and how a particle's trajectory has a kink if the potential energy has a discontinuous jump. The particle bounces back if the jump is too high, which corresponds to reflection of light.

Well, here's why I wanted to bring up QM: the principle of least time is really most at home in geometric optics where beams of light are arrows and everything is steady-state. In that view, things are indeed nonlocal: I can alter the arrows drawn for a beam of light going from A to B by doing something over at point C. Wave optics would understand this as interference, but if we insist that we want to keep the arrows then we have to introduce the path integrals.

Essentially, geometric optics lets us draw arrows and assert refraction, QM lets us draw arrows and derive refraction, but wave optics doesn't really involve arrows at all.

Things aren't nonlocal in geometrical optics though. Something happens at C at the instant in time when the particle is at C. You can start a ray at any point in any direction, and just follow a straight line until you hit something. Then you determine what happens next based on local information at that point, and you continue. Ordinary tennis balls have the same property that the path from A to B can be altered by putting a wall at C.

By the way, wave optics is already QM in some sense. Maxwell's equations are the analogue of the Schrödinger equation for light. Geometrical optics is the analogue of classical mechanics.

Look at Bohm's interpretation of quantum mechanics and subsequent formulations for quantum field theory.

Hidden variables are possible for quantum mechanics, they just necessitate that the Universe is fundamentally non-local, offering a possible explanation for quantum entanglement results.

Von Neumann's rejection of hidden variables was not an absolute one but a conditional one; if the universe is local, then hidden variables cannot be invoked to explain the weirdness of the quantum world. Non locality opens the door to hidden variables.

AIUI photons are an observational phenomenon, the photon isn't travelling any path, the probability distribution is occupying all possible paths, the observation collapses the wavefunction and makes it so we can find the photon in a general locality.

I think the physics of QM is too far displaced from our natural ideas of how mechanical things work to be able to reason about in the way we would like.

I’m not a fan, but DeBB/Pilot Wave interpretation is also compatible with the predictions of QM.

> We could hypothesize dogs are working out calculus problems, or we could just hypothesize that the dog tried it one way, [...] Or, to put it into a human reference frame, we do not do calculus problems to catch things. We "just" catch them. Neurons are built to solve this problem.

But the point remains that you are solving a calculus problem.

I mean, I agree that some of this is over-hyping things, but I think it is actually a really important realization that a lot of people are lacking, often because they are stuck in some completely nonsensical notion of dualism, that your body does a lot of computation.

Just because you are not consciously manipulating numbers does not mean you aren't computing the trajectory of your arm and the necessary activation of muscles to execute that trajectory. It's not that thinking is a prerequisite of computation, but rather computation is a prerequisite of thinking. Your arm doesn't catch a ball by thinking, but rather your arm catches the ball by computation--just as your brain thinks by computation.

It's been found that to catch a fly ball (as pros do) your brain has to solve (approximately but accurately) a third-degree calculus equation, and does.

http://www.icr.org/article/plants-math-ration-food-use/

This is a really cool example of plants using math too.

Yeah it's almost akin to asking "If I put hot coffee in a thermos, the thermos keeps it hot, but if I put cold lemonade in there, the thermos keeps it cold. How does the thermos know the difference? Well because quantum, that's how!"

Except "why does Snell's law over a continuous gradient effect the path of shortest time?" is equivalent to asking "why is the universe quantum?"

It's plenty bizarre that electricity follows the path of least resistance, light the shortest path, etc.

Bizarre in comparison to what?

Let me put it this way: never have I heard an explanation in terms of classical mechanics. In my intuition, the billiard ball model of physics makes perfect sense. But a current taking the path of least resistance really seems like it "knows" the best way. And it's amazing.

That's a misconception. Electricity takes ALL paths in amounts proportional to each path's conductance.

If you have a 1000 Ω path and a 10 Ω path (in parallel), current will go through both paths. However, much more current will go through the 10 Ω path.

The current through each path ends up being the voltage applied across the path, divided by its resistance.

Yep. Came here to say exactly this (electricity takes all paths) and then saw your reply.

> Well, we could hypothesize light is conscious and is making globally-optimal calculations, or we could just observe that if you work through the wave equations on what waves do when encountering a speed change, that's what happens

"Explanations exist; they have existed for all time; there is always a well-known solution to every human problem — neat, plausible, and wrong."

- H L Mencken

Well, quantum mechanical explanations for why light refracts may be in some sense wrong, since we know QM still hasn't been harmonized with relativity very well, but "neat" and to some extent "plausible", definitely not, at least by the person on the street's standard.

I suggest you think a bit more before you fling a quote at somebody as if it's the last word on a topic; at the very least you should make sure it is actually applicable to the topic at hand.

> I suggest you think a bit more before you fling a quote at somebody

I suggest you think a little more before sanctimoniously talking down to people. I was making a supportive reply, in agreement with what you wrote.

> at the very least you should make sure it is actually applicable to the topic at hand.

It is perfectly applicable. Light "being conscious and making decisions" is a neat explanation, but wrong.

The last bit is what got me too---pheromones are pretty simple to understand, really. you drop 2 ants, one walks 30 cm and another walks 10 cm. the one that walked 10 cm will be back sooner, can signal where he went, and others can follow his (fresher) pheromones.

Why is this mysterious?

> This is a particularly egregious example of the pop-sci genre

This is the model of Nautilus, Quartz, and a bunch of other online publications. It's fun to read so what's wrong with it?

On the one hand, I like that they're doing old physics. There is a tendency to do only cutting edge physics such as modern quantum mechanics research, particle physics, even string theory. There is little chance to convey an accurate understanding of this to a layperson. Every part of physics was at the cutting edge at one point in time. The physics that is now hip will be old in 100 years, and it will be no longer interesting for science journalists. Celestial mechanics, classical optics, classical electrodynamics were at the cutting edge some time ago, and they're still super interesting. They also have the advantage of being thoroughly understood, so there's a chance to convey genuine understanding. In that sense, this article is great: it truly explains Fermat's principle as a physics college student would learn it. It would be even greater if it had more physics and less metaphysics. On the other hand, would that have reached the front page of HN? Probably not.

That this model exists is OK; that it dominates pop science is a problem. I wish there were a lot more books like the one by Feynman that I linked to in another comment, which focus on real understanding. We can't all be Feynman, but we can try to do better.

(I haven't read the OP because it sounds like things I already know.)

I think it's the same reaction that police or lawyers have with watching crime procedurals, or why software engineers get disgusted by how "hackers" are portrayed in most popular media.

However, I think this sort of simplified shorthand, with a bit of innocent embellishment (the whole mystery aspect of how nature does it) keeps people interested.

It could be something that gets someone interested in discovering more. I think any simplification could be viewed as misleading, but I think these sorts of articles really do more to educate than if they were to only be clicking celebrity gossip or worthless listicles.

They don't educate anything. They generate crackpots who spread more pseudoscience. True science can be explained simply and clearly with good understanding and good communication (think Terrence Tao's blog) without dumbing it down.

Thank you for the response, and I will Google Terrence Tao for the link, but maybe adding a link will help others?

I don't disagree with you, but honestly, Id rather argue science with a crackpot that only has 50% of the info than the crackpot who refuses to, and can't understand anything above 0%.

It's like literacy. I'd far rather live in a world where most people have a 50% literacy rate rather than in a world where 0.5% has a genius level of literacy and the rest are illiterate.

Sure it's a weird, cold calculation, but in the pragmatic part, I'm happy to accept the compromise.

This was my thought. I think the article reads almost like a children's Did You Know? kind of book: it presents the problem and just enough background information to understand it, then leaves the mystery for the reader to go and find out more.

I could see the argument that there is a fine line between leaving a bit of mystery and just plain lazy writing.

> then leaves the mystery for the reader to go and find out more.

When the reader is interested by the mystery and really goes to find more on his own, isn't that wonderful?

Because it is dull, long winded and misleading.

Perhaps it is fun for people who like being misled?