4 ms·

This was the 1942 experiment cited in the OP: "The subjects were asked to respond "yes" or "no" to say whether or not they thought they had seen a flash. The

by baking 9y ago

This was the 1942 experiment cited in the OP: "The subjects were asked to respond "yes" or "no" to say whether or not they thought they had seen a flash. The light was gradually reduced in intensity until the subjects could only guess the answer. "They found that about 90 photons had to enter the eye for a 60% success rate in responding. Since only about 10% of photons arriving at the eye actually reach the retina, this means that about 9 photons were actually required at the receptors. Since the photons would have been spread over about 350 rods, the experimenters were able to conclude statistically that the rods must be responding to single photons, even if the subjects were not able to see such photons when they arrived too infrequently." In other words, they lowered the intensity of the light until the subjects guesses were no better than random then concluded that 9 photons were spread over 350 rods. The 1972 experiment assumed about 6 photons were entering the retina.

joeyo 9y ago
> "until the subjects guesses were no better than random" Crucially, no: They analyzed performance at 60% and made their argument based on the photons delivered at that light intensity. If your objection is about that statistical argument (" ... the photons would have been spread over about 350 rods"), such an indirect method was necessary because the experimenters didn't have an apparatus that could emit single photons in 1942. The 2016 article mentioned upthread [1] improves on this by providing the simple and direct experiment: emit single photons and check if the subjects can beat a coin-toss over large numbers of trials. 1. https://www.nature.com/articles/ncomms12172 https://www.nature.com/articles/ncomms12172
- baking 9y ago
  Have you ever heard of the Birthday Paradox? 23 people in a class, the odds of two having the same birthday = 1-(364/365)^(23x22/2) = 50.5% Well, the odds of two out of nine photons hitting the same rod out 350 is 1-(349/350)^(9x8/2) = 9.79% so there's your 10% improvement over a wild guess. Factor in that two photons should have a much higher chance of hitting neighboring rods which would substantially increase the chance of a hit (at the synaptic level) the question really should be "Why is it so much worse than random?"
  - joeyo 9y ago
    I agree the authors should have used the improved odds calculation you mention. However, doing so would only explain the missing 10% if two photons hitting a single rod led to 100% correct response rate, and it seems unlikely for the response to be so nonlinear. Anyway with such an experiment, we don't know why the subjects are above chance, and can only make inferences. As I point out above, you really need single photon emission to know for sure. I went back to the original paper [1] and the authors' conclusions are much more measured than précis we are all discussing. From page 838: ... the range of 54 to 148 quanta at the cornea becomes an upper limit of 5 to 14 quanta actually absorbed by the retinal rods. [ed: I presume this is where the figure of 9 comes from] 3. This small number of quanta, in comparison to the number of rods (500) involved, precludes any significant two quantum absorptions per rod [ed: oops], and means that in order to produce a visual effect, one quantum must be absorbed by each of 5 to 14 rods in the retina. 4. Because this number of individual events is so small, it may be derived from an independent statistical study of the relation between the intensity of a light flash and the frequency with which it is seen. Such experiments give values of 5 to 8 for the number of critical events involved at the threshold of vision. 1. http://www.cns.nyu.edu/~david/courses/perceptionGrad/Readings/HechtShlaerPirenne-JGeneralPhysiol1942.pdf http://www.cns.nyu.edu/~david/courses/perceptionGrad/Reading...

by baking 9y ago

joeyo 9y ago

> "until the subjects guesses were no better than random" Crucially, no: They analyzed performance at 60% and made their argument based on the photons delivered at that light intensity. If your objection is about that statistical argument (" ... the photons would have been spread over about 350 rods"), such an indirect method was necessary because the experimenters didn't have an apparatus that could emit single photons in 1942. The 2016 article mentioned upthread [1] improves on this by providing the simple and direct experiment: emit single photons and check if the subjects can beat a coin-toss over large numbers of trials. 1. https://www.nature.com/articles/ncomms12172 https://www.nature.com/articles/ncomms12172

baking 9y ago
Have you ever heard of the Birthday Paradox? 23 people in a class, the odds of two having the same birthday = 1-(364/365)^(23x22/2) = 50.5% Well, the odds of two out of nine photons hitting the same rod out 350 is 1-(349/350)^(9x8/2) = 9.79% so there's your 10% improvement over a wild guess. Factor in that two photons should have a much higher chance of hitting neighboring rods which would substantially increase the chance of a hit (at the synaptic level) the question really should be "Why is it so much worse than random?"
- joeyo 9y ago
  I agree the authors should have used the improved odds calculation you mention. However, doing so would only explain the missing 10% if two photons hitting a single rod led to 100% correct response rate, and it seems unlikely for the response to be so nonlinear. Anyway with such an experiment, we don't know why the subjects are above chance, and can only make inferences. As I point out above, you really need single photon emission to know for sure. I went back to the original paper [1] and the authors' conclusions are much more measured than précis we are all discussing. From page 838: ... the range of 54 to 148 quanta at the cornea becomes an upper limit of 5 to 14 quanta actually absorbed by the retinal rods. [ed: I presume this is where the figure of 9 comes from] 3. This small number of quanta, in comparison to the number of rods (500) involved, precludes any significant two quantum absorptions per rod [ed: oops], and means that in order to produce a visual effect, one quantum must be absorbed by each of 5 to 14 rods in the retina. 4. Because this number of individual events is so small, it may be derived from an independent statistical study of the relation between the intensity of a light flash and the frequency with which it is seen. Such experiments give values of 5 to 8 for the number of critical events involved at the threshold of vision. 1. http://www.cns.nyu.edu/~david/courses/perceptionGrad/Readings/HechtShlaerPirenne-JGeneralPhysiol1942.pdf http://www.cns.nyu.edu/~david/courses/perceptionGrad/Reading...