9 ms·

To Save Drowning People, Ask “What Would Light Do?”

160 points by pmcpinto 9y ago

draluy 9y ago
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.
- stevemk14ebr 9y ago
  It's similar to the common problem of crossing a river + walking on shore: https://www.youtube.com/watch?v=-phqoALu_44 https://www.youtube.com/watch?v=-phqoALu_44
- supermdguy 9y ago
  In the paper[0] about Elvis, Pennings solves a general form of the problem. Look at the second page of the pdf. [0]: http://www.indiana.edu/~jkkteach/Q550/Pennings2003.pdf http://www.indiana.edu/~jkkteach/Q550/Pennings2003.pdf
- evanb 9y ago
  You need to draw some triangles and relate b to w. Assuming a still, straight shore, the answer will depend on your distance to the waterline, the ball's distance to the waterline, and the distance parallel to the shore separating your starting spot and the ball's spot.
- whack 9y ago
  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
- tzs 9y ago
  On a graph, plot b/Vb, with b on the horizontal axis and b/Vb on the vertical axis. This plot shows the time you spend on the beach if you run to b on the beach. Add to this graph a plot of w/Vw. You'll have to express w as a function of b to do this. This plot shows the time you spend in the water if you run to b on the beach and then swim to the ball. You are trying to minimize the sum of these two plots. You can see from the plots that as b increases, beach time goes up, and water time goes down. As b decreases, beach time goes down and water time goes up. If b is less than the minimizing point, water time changes more than beach time as b changes, so you can lower the total by moving b in the direction that makes water time go down. That will make beach time go up, but since water time changes more than beach time, it's a net win. When b is more than the minimizing point, beach time changes more than water time as b changes, so you can lower the total time by moving b in the direction that makes beach time go down. The will make water time go up, but since beach time changes more than water time, it's a net win. The minimizing point is the point where the rate beach time is changing and the rate water time is changing match, so that you cannot lower the time by nudging b in either direction. What you could then do is think about how to calculate the rate of change of a function. Say you have a function, f(x), and you want to know how fast it changes as x changes. To help with intuition, let's say f(x) is the position of a car at time x. The rate of change of position is velocity, so we are asking how you find the velocity at a given point x if you know position as a function of x. If the car was moving at a constant velocity, this would be easy. Just note the position at x, f(x), and then note the position a little bit later, say at x+t, f(x+t). Then the distance traveled is f(x+t)-f(x), in time t, so the velocity is (f(x+t)-f(x))/t. If the car is not moving at constant velocity that just gives you the average velocity during the time t. If the car isn't accelerating too much, the smaller t the closer the average velocity over an interval t should be to the instantaneous velocity at t. For example, suppose f(x) = x^2. Then f(x+t) = x^2 + 2xt + t^2. The average velocity is 2x + t. It's pretty obvious that as we make t smaller and smaller, this gets closer and closer to 2x, and so we can reasonably conclude that the instantaneous velocity of something whose position at time x is f(x) is 2x. Applying those same ideas to the functions involved in the ball problem, you could figure out the rates of change, and find the b that makes the beach time and the water time rates of change match. Unlike the nice x^2 car, though, the algebra would be messy and error prone. After you have done that, you might realize that this operation of take an average over smaller and smaller intervals and seeing if that converges to some fixed value as the interval goes to zero is quite useful, and start studying it. You'd then discover that while computing it directly can be a royal pain in the ass, it turns out that if your function is built up of other functions by adding, subtracting, multiplying, dividing, or applying functions to other functions, and you know how to do this operation on the component functions, then there are simple rules that you can follow mechanically do figure it out on the combined function. At that point, you've pretty much invented half of calculus as it was understood back in the days of Newton and Leibniz, and are ready to tackle all kinds of minimization and maximization problems in physics, engineering, finance, and elsewhere, plus all kinds of problems involve rates of change, such as bacteria growth, velocity of water coming from a hole in the bottom of a leaky bucket, and rocket motion.
bloat 9y ago
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 9y ago
  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_principles_in_physics https://en.wikipedia.org/wiki/History_of_variational_princip...
deleted 9y ago
[deleted]
philbarr 9y ago
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?"
- hinkley 9y ago
  Dogs are originally forest creatures. Whatever we bred into them we did initially because they were forest creatures. A few tens of thousands of years haven’t erased and in fact probably reinforce their instincts to solve pathing problems. Ravines and thickets must be circumscribed. Hillocks too, depending. Getting wet in the winter is better avoided so follow the stream and try to ford it later. It’s only preferable to going hungry. Play for time and min-max.
- LeifCarrotson 9y ago
  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_b8b9c74ac526fffbeb2d39ab038d1cd7.png https://d3chnh8fr629l6.cloudfront.net/2904_b8b9c74ac526fffbe... [2]: https://webcache.googleusercontent.com/search?q=cache:l0DmOIr4uhsJ:www.indiana.edu/~jkkteach/Q550/Pennings2003.pdf+&cd=1&hl=en&ct=clnk&gl=us https://webcache.googleusercontent.com/search?q=cache:l0DmOI...
mason55 9y ago
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?
- petters 9y ago
  Yes. It follows from the wave equation.
- tedsanders 9y ago
  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.
- abecedarius 9y ago
  You might find Feynman's popular book QED more, erm, illuminating: https://press.princeton.edu/titles/8169.html https://press.princeton.edu/titles/8169.html
whack 9y ago
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.
- jules 9y ago
  There are other particles that move at the speed of light (gluons, gravitons), so in that sense, light is not special. Classical mechanics can be formulated in Lagrangian form such that the path that a particle takes is the path of least action (for light, action is proportional to time). Don't put too much weight on light having agency because this description of how particles move is mathematically equivalent to a system of differential equations, in which the infinitesimally future position of a particle is determined by local information. Classical mechanics is just an approximation of quantum mechanics anyway. Quantum mechanics clarifies why particles move according to the principle of least action: the paths close to the path of least action have large probability amplitudes.
- tkahnoski 9y ago
  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 9y ago
    I think it is called "optical computing".
bahmboo 9y ago
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.
chrisbrandow 9y ago
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.
madmax108 9y ago
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
- azeirah 9y ago
  I'm afraid I belong to your group. I think he'd save the drowning person, he'd like the attention.
- wingerlang 9y ago
  Could be that "Light" is capitalized. I thought about the same.
- djsumdog 9y ago
  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.
- Jemmeh 9y ago
  Weeb reporting for duty. Since it's not a heart attack there's a good chance he isn't the one who wrote the name down. So being the perfect role-model student extraordinaire that he is, he'd dive in and save them...to further throw anyone off his trail, of course.
jerf 9y ago
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 9y ago
  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.
kbutler 9y ago
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-techniques/ladder-approach-step-step-procedure-successful-rescues https://www.sauvetage.qc.ca/en/lifeguarding/rescue-technique...) but don't really address the run-vs-walk choices.
- killjoywashere 9y ago
  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.
danjc 9y ago
The photo of the ants seems to be showing a route that is neither least time nor least distance
kazinator 9y ago
> 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 9y ago
  Huygens–Fresnel principle applies to waves in general. Fermat's principle follows mathematically from Huygens' principle at the limit of small wavelength.
Lramseyer 9y ago
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.
deftturtle 9y ago
This article was painful to read. Am I on the science side of Buzzfeed? /s

160 points by pmcpinto 9y ago

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.

stevemk14ebr 9y ago
It's similar to the common problem of crossing a river + walking on shore: https://www.youtube.com/watch?v=-phqoALu_44 https://www.youtube.com/watch?v=-phqoALu_44
supermdguy 9y ago
In the paper[0] about Elvis, Pennings solves a general form of the problem. Look at the second page of the pdf. [0]: http://www.indiana.edu/~jkkteach/Q550/Pennings2003.pdf http://www.indiana.edu/~jkkteach/Q550/Pennings2003.pdf
evanb 9y ago
You need to draw some triangles and relate b to w. Assuming a still, straight shore, the answer will depend on your distance to the waterline, the ball's distance to the waterline, and the distance parallel to the shore separating your starting spot and the ball's spot.
whack 9y ago
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
tzs 9y ago
On a graph, plot b/Vb, with b on the horizontal axis and b/Vb on the vertical axis. This plot shows the time you spend on the beach if you run to b on the beach. Add to this graph a plot of w/Vw. You'll have to express w as a function of b to do this. This plot shows the time you spend in the water if you run to b on the beach and then swim to the ball. You are trying to minimize the sum of these two plots. You can see from the plots that as b increases, beach time goes up, and water time goes down. As b decreases, beach time goes down and water time goes up. If b is less than the minimizing point, water time changes more than beach time as b changes, so you can lower the total by moving b in the direction that makes water time go down. That will make beach time go up, but since water time changes more than beach time, it's a net win. When b is more than the minimizing point, beach time changes more than water time as b changes, so you can lower the total time by moving b in the direction that makes beach time go down. The will make water time go up, but since beach time changes more than water time, it's a net win. The minimizing point is the point where the rate beach time is changing and the rate water time is changing match, so that you cannot lower the time by nudging b in either direction. What you could then do is think about how to calculate the rate of change of a function. Say you have a function, f(x), and you want to know how fast it changes as x changes. To help with intuition, let's say f(x) is the position of a car at time x. The rate of change of position is velocity, so we are asking how you find the velocity at a given point x if you know position as a function of x. If the car was moving at a constant velocity, this would be easy. Just note the position at x, f(x), and then note the position a little bit later, say at x+t, f(x+t). Then the distance traveled is f(x+t)-f(x), in time t, so the velocity is (f(x+t)-f(x))/t. If the car is not moving at constant velocity that just gives you the average velocity during the time t. If the car isn't accelerating too much, the smaller t the closer the average velocity over an interval t should be to the instantaneous velocity at t. For example, suppose f(x) = x^2. Then f(x+t) = x^2 + 2xt + t^2. The average velocity is 2x + t. It's pretty obvious that as we make t smaller and smaller, this gets closer and closer to 2x, and so we can reasonably conclude that the instantaneous velocity of something whose position at time x is f(x) is 2x. Applying those same ideas to the functions involved in the ball problem, you could figure out the rates of change, and find the b that makes the beach time and the water time rates of change match. Unlike the nice x^2 car, though, the algebra would be messy and error prone. After you have done that, you might realize that this operation of take an average over smaller and smaller intervals and seeing if that converges to some fixed value as the interval goes to zero is quite useful, and start studying it. You'd then discover that while computing it directly can be a royal pain in the ass, it turns out that if your function is built up of other functions by adding, subtracting, multiplying, dividing, or applying functions to other functions, and you know how to do this operation on the component functions, then there are simple rules that you can follow mechanically do figure it out on the combined function. At that point, you've pretty much invented half of calculus as it was understood back in the days of Newton and Leibniz, and are ready to tackle all kinds of minimization and maximization problems in physics, engineering, finance, and elsewhere, plus all kinds of problems involve rates of change, such as bacteria growth, velocity of water coming from a hole in the bottom of a leaky bucket, and rocket motion.

bloat 9y ago

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 9y ago
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_principles_in_physics https://en.wikipedia.org/wiki/History_of_variational_princip...

deleted 9y ago

[deleted]

philbarr 9y ago

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?"

hinkley 9y ago
Dogs are originally forest creatures. Whatever we bred into them we did initially because they were forest creatures. A few tens of thousands of years haven’t erased and in fact probably reinforce their instincts to solve pathing problems. Ravines and thickets must be circumscribed. Hillocks too, depending. Getting wet in the winter is better avoided so follow the stream and try to ford it later. It’s only preferable to going hungry. Play for time and min-max.
LeifCarrotson 9y ago
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_b8b9c74ac526fffbeb2d39ab038d1cd7.png https://d3chnh8fr629l6.cloudfront.net/2904_b8b9c74ac526fffbe... [2]: https://webcache.googleusercontent.com/search?q=cache:l0DmOIr4uhsJ:www.indiana.edu/~jkkteach/Q550/Pennings2003.pdf+&cd=1&hl=en&ct=clnk&gl=us https://webcache.googleusercontent.com/search?q=cache:l0DmOI...

mason55 9y ago

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?

petters 9y ago
Yes. It follows from the wave equation.
tedsanders 9y ago
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.
abecedarius 9y ago
You might find Feynman's popular book QED more, erm, illuminating: https://press.princeton.edu/titles/8169.html https://press.princeton.edu/titles/8169.html

whack 9y ago

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.

jules 9y ago
There are other particles that move at the speed of light (gluons, gravitons), so in that sense, light is not special. Classical mechanics can be formulated in Lagrangian form such that the path that a particle takes is the path of least action (for light, action is proportional to time). Don't put too much weight on light having agency because this description of how particles move is mathematically equivalent to a system of differential equations, in which the infinitesimally future position of a particle is determined by local information. Classical mechanics is just an approximation of quantum mechanics anyway. Quantum mechanics clarifies why particles move according to the principle of least action: the paths close to the path of least action have large probability amplitudes.
tkahnoski 9y ago
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 9y ago
  I think it is called "optical computing".

bahmboo 9y ago

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.

chrisbrandow 9y ago

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.

madmax108 9y ago

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

azeirah 9y ago
I'm afraid I belong to your group. I think he'd save the drowning person, he'd like the attention.
wingerlang 9y ago
Could be that "Light" is capitalized. I thought about the same.
djsumdog 9y ago
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.
Jemmeh 9y ago
Weeb reporting for duty. Since it's not a heart attack there's a good chance he isn't the one who wrote the name down. So being the perfect role-model student extraordinaire that he is, he'd dive in and save them...to further throw anyone off his trail, of course.

jerf 9y ago

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 9y ago
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.

kbutler 9y ago

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-techniques/ladder-approach-step-step-procedure-successful-rescues https://www.sauvetage.qc.ca/en/lifeguarding/rescue-technique...) but don't really address the run-vs-walk choices.

killjoywashere 9y ago
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.

danjc 9y ago

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

kazinator 9y ago

> 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 9y ago
Huygens–Fresnel principle applies to waves in general. Fermat's principle follows mathematically from Huygens' principle at the limit of small wavelength.

Lramseyer 9y ago

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.

deftturtle 9y ago

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