
To Save Drowning People, Ask “What Would Light Do?” - pmcpinto
http://nautil.us//blog/-to-save-drowning-people-ask-yourself-what-would-light-do
======
jerf
This is a particularly egregious example of the pop-sci genre "making things
sound more mysterious than they really are". How does light choose the fastest
path to its destination when light can't "choose"? 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. It so happens
that solution also matches how to get to the eventual point in the shortest
time, but that adds an unnecessary concept of "intention to arrive at a given
point". Light has no such preference or intention, it just arrives where it
arrives.

We _could_ hypothesize dogs are working out calculus problems, or we could
just hypothesize that the dog tried it one way, then another, and eventually
over the course of its lifetime works out how to get to the ball the most
quickly, which in comparison to the difficulty of manipulating all of its
dozens of muscles to perform the running optimally in the first place is a
frankly insignificant challenge. 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.

We _could_ hypothesize that the ants have a simple pheromone-based
optimization system that naturally mathematically converges on the same
solution as Snell's Law when, after all, faced with the same problem, but...
uh... actually it's not at all clear to me how the article manages to make
this sound mysterious after what is a fairly effective solution to the
problem. If nothing else, the ants taking the most optimal path will make more
to-and-from trips than other ants, thus laying thicker trails; that plus an
initial shotgun approach are adequate to explain.

This is particularly egregious since none of the math here is very
complicated, and it is completely unsurprising that when the same problem is
given to several optimizing agents in several domains that the same solution
pops out. There is not very many bits of information in this problem.

~~~
whatshisface
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.

~~~
adrianratnapala
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.

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

~~~
adrianratnapala
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.

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madmax108
So weird that the moment I read the title, I started thinking of DeathNote,
and the morality of saving drowning people from the perspective of Light
Yagami. :D

~~~
djsumdog
I'm glad I'm not the only one! I thought this was going to be an article that
was a philosophical/thought experiment, but nope. The author meant actual
light. Pretty disappointed.

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philbarr
For the dog optimising when to jump in the water, I think it's fairly easy to
see how it does it. It's constantly optimising as it runs. It doesn't "choose"
the path and then run it.

It's just repeating the same question as it moves, "is it worth running along
the shore a bit more or should I just jump in now?"

~~~
LeifCarrotson
This would be more interesting if, instead of throwing the ball while standing
at the water's edge, the human stood further back up the beach as in the
lifeguard illustration. [1]

This would require the dog to decide on the path to take at the start, or run
in a path that wasn't a straight line. Anecdotally, when performing this
experiment in the past, my dog typically runs directly towards the ball along
the straight-line path Lifeguard->A, then turns somewhat along the edge of the
beach to plunge in somewhere between A and C.

I'm also curious if there is a confounding factor in the dog's motivation.
Pennings states [2] that:

> _By the look in Elvis’seyes and his elevated excitement level, it seems
> clear that his objective is to retrieve itas quickly as possible rather
> than, say, to minimize his expenditure of energy._

There is obviously a value that the dog ascribes to the expeditious retrieval
of the ball, but when the ball is not present there's also a value to be had
in simply running joyously on the sand, and, of course, there's little better
than being in the water. We may therefore need to calculate the ideal path
based on a static value (perhaps 100 dog-utilitons) for retrieving the ball,
plus 2 du/m running in the sand, and 12 du/m when swimming in the water. This
complicates the mathematics somewhat.

Finally, the author's method of running ahead with a tape measure may work
when measuring the performance of a short-legged subject, but I would be
unable to use these methods to measure the performance of my larger and faster
(Newfoundland) dog. Aerial drone videography may be more suitable instead.

[1]:
[https://d3chnh8fr629l6.cloudfront.net/2904_b8b9c74ac526fffbe...](https://d3chnh8fr629l6.cloudfront.net/2904_b8b9c74ac526fffbeb2d39ab038d1cd7.png)

[2]:
[https://webcache.googleusercontent.com/search?q=cache:l0DmOI...](https://webcache.googleusercontent.com/search?q=cache:l0DmOIr4uhsJ:www.indiana.edu/~jkkteach/Q550/Pennings2003.pdf+&cd=1&hl=en&ct=clnk&gl=us)

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bloat
This is also a plot point in Ted Chiang's story "The Story Of Your Life" which
was the basis of the movie "Arrival".

~~~
mudita
Through this short story I also learned that Fermat's principle is just one
example of a variational principle. I'm not an expert, but if I understand it
correctly, many physical laws can be restated as variational principles.

See e.g.
[https://en.wikipedia.org/wiki/History_of_variational_princip...](https://en.wikipedia.org/wiki/History_of_variational_principles_in_physics)

------
whack
It's interesting to note how light has become more and more "special" over the
past century. It used to be that light was just another entity, similar to
sound. That the speed of light was just another constant, like the speed of
sound.

But at some point, the speed of light became so special that it became a
constant from all reference frames, regardless of how fast the observer
herself is traveling. And now we believe that light is so special, that it can
be viewed to have agency. That it _" decides which is the shortest time, or
the extreme one... smell the nearby paths, and check them against each
other... and chooses that path"_

As someone who's knowledge of physics maxed out at Newton's laws, it's
interesting to see how today's perspective of the universe is so different and
"light-centric" as compared to centuries past.

~~~
tkahnoski
Just triggered the thought that we should be trying to exploit the property of
light to pursue the shortest path as a means to calculate hard problems. No
idea how this would actually work... but I would gander someone already
thought of this and it didn't pan out.

~~~
xaedes
I think it is called "optical computing".

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Lramseyer
I was a little disappointed by the lack of explanation on how light refracts.
It references Snell's law and mentions how light travels slower in water, but
it did not go into how it's an effect of parts of the wavefront changing
velocity at slightly different times as a result of the light entering the
medium at an angle (or at least that being a simple way of understanding
refraction.)

However, it was cool to see them reference "Do dogs know calculus?" I actually
saw Pennings give a presentation on it in high school because my calc teacher
was one of his students. He started out the talk by telling us that his dog
knew calculus. He then proceeded to ask his dog the derivative of x^3. The dog
did nothing, and he told us that dogs don't know calculus.

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kbutler
Interesting math story problem, but probably not much use for real lifeguards.

Is there any observational evidence that lifeguards choose paths this way,
rather than the direct line or shortest water path?

Perhaps they do some optimization, particularly for very oblique angles, but
in real "shoreline" situations, I expect wave and current action will dominate
the optimization, rather than the delta between running and swimming speed.

Guidelines for lifeguards talk about avoiding water entry if possible and
definitely avoiding direct contact from the victim if at all possible
([https://www.sauvetage.qc.ca/en/lifeguarding/rescue-
technique...](https://www.sauvetage.qc.ca/en/lifeguarding/rescue-
techniques/ladder-approach-step-step-procedure-successful-rescues)) but don't
really address the run-vs-walk choices.

~~~
killjoywashere
Funny that both top level comments about current got down-voted, while a
fifth-level comment about _electrical current_ go up-voted.

Seriously, as someone going surfing tomorrow morning, current was my first
though on this. And rips. The catching the rip will save more time than any of
this.

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chrisbrandow
I figure that animals and humans are very good at assessing the amount of
“work” that a given path requires and that we are likewise very sensitive to
minimizing the work function, due to evolutionary training.

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mason55
It wasn't clear to me from the article. Do we know the mechanism by which
light is able to find the path of least time?

~~~
tedsanders
Yes. (Or at least we have a good model.) One description is that a photon
takes all paths simultaneously and the paths that are not the shortest in time
end up mostly cancelling out. The light's behavior is consistent with
locality.

------
kazinator
> _When light travels from one place to another, it always takes the path of
> least time._

Refraction is seen in other kinds of waves and media, like sound or even waves
on the surface of a liquid (which refract when traversing from a deeper to
shallower place).

Is this "least time" principle true for all kinds of waves, or just light?

~~~
xaedes
Huygens–Fresnel principle applies to waves in general. Fermat's principle
follows mathematically from Huygens' principle at the limit of small
wavelength.

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draluy
Does anyone know how to solve the tennis-ball formula? All I can muster is
that the distance on the beach (b) divided by the speed on the beach (Vb) +
the distance on water (w) divided by the speed on water (Vw) should be
minimized. So I should find the minimum of b/Vb + w/Vw , but I have no clue as
how.

~~~
whack
You got the first equation right, in expressing time-taken in terms of b and
w.

Now you need the second equation, which expresses b in terms of w (or vice-
versa). Hard to describe it here over text, but I believe using the following
set of equations, it should be possible to express b in terms of w.

\------------------

Yb = vertical-distance from start-point to water (constant)

Yw = vertical-distance from water to end-point (constant)

Xb = horizontal-distance between start and point-of-contact with water

Xw = horizontal-distance between end and point-of-contact with water

X = horizontal-distance between start/end points (constant)

Ob = angle taken when running towards the water

Ow = angle taken when swimming towards the end point

=>

X = Xb + Xw

cos(Ob) = Yb / b

sin(Ob) = Xb / b

cos(Ow) = Yw / w

sin(Ow) = Xw / w

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danjc
The photo of the ants seems to be showing a route that is neither least time
nor least distance

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deftturtle
This article was painful to read. Am I on the science side of Buzzfeed? /s

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bahmboo
This is all definitely math and physics interesting but a real beach has
waves, currents and rocks. The lifeguard has spent weeks or months staring at
it for hours on end. Probably has a good idea best way to save someone.
Otherwise continue.

