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Old 22-February-2006, 09:16 PM
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Alright, I do not know if this has been dealt with in later editions (I have a first edition). I found a pretty significant error, though.

On page 101, near the end of chapter 10, the book is talking about the reason stars appear white. The book says this is because it is too dark for the color-sensetive cones to operate and the rods that are still operating cannot differentiate color. Although it is true that rods can only see black and white and it is true that they are active well below the light intensity where the frequency-sensetive cones no longer operate, it is not and cannot be the reason stars appear white. It is a very commonly-told myth that is believed by many people, but it is still wrong.

Want proof? Look right at a star. Do you see it? Then you are not using your rods. You can roughly break the retina into three sections: the fovea, the optic disk, and everything else. The optic disk is where the neurons and blood vessels from the retina leave the eye, this has no receptors and thus you are blind there. The majority of your retina is like what most people think of when they think of the retina: a mix of rods and cones (far more rods than cones, incidentally). The fovea is the center part of the eye, it is in the center of your visual field and what you are using when you look right at something.

The fovea is important because it is the region where your visual acuity is the greatest. Try a simple experiment. Grab a book, any book. Now, hold it so the distance between the book and your face is a foot or less (you don't need to be that exact). Focus your vision on a word at the very center of a page of text. Now, without moving your eyes, try reading text on either side, above and below where your eye is focused. How far you can you read? Not very far. The actual area where your visual acuity is good enough to identify any sort of detail, the fovea is very small, with a diameter of about 10 degrees of your entire visual area. The fovealo, with the highest acuity (the sort you probably need to read at that distance), is much smaller yet.

So what does this have to do with seeing stars as white? Well, there are a number of problems with rods when you compare them to cones. Cones have superior properties in every way compared to rods. They are better as seeing fast changes, they are better at seeing small details, they can handle much higher light intensities before they shut down (in fact, unlike rods, you will go blind before your cones shut down). The only advantage rods have is that they are sensitive to light intensities far below the minimum threshold for cones. For this reason, rods in the fovea would greatly reduce your visual acuity right where you need it most. That gets us to the problem: the fovea has no rods whatsoever. It only has cones. Rods are only found in the area outside the fovea. If you look right at something, you are using your fovea and thus cannot be using rods. In extreme dark your fovea is literally blind, if you want to see something in that sort of condition you are much better off focusing your eyes a little bit to the side, above, or below what you want to see. So when you are looking at a star, you are using your cones not your rods.

Here is an image showing this:

(all images are hosted by the University of Flordia, a large state university, although these exact same pictures appear in my Quantitative Physiology notes on vision. This conforms to the rules on hotlinking images)

Most people don't realize this, but the minimum threshold for cones is actually very low. Starlight, although approaching the threshold for cones, is still well within the level cones can detect (from the figure I am looking at starlight appears to be almost an order of magnitude, 10x, above the cone threshold). Moonlight is several orders of magnitude above the threshold for cones, and is actually closer to the point where rods start getting overwhelmed by too much light and shut down.

The real reason is more complicated, but I will explain it as I understand it (you will want to confirm this). The issue with cones is that cones do not detect color. Cones actually have a broad range of color sensitivity. There are three cones, each one possessing a single type of pigment molecule with a different frequency sensitivity. They each are sensitive to a wavelength range of several hundred nanometers (the entire human visual range is around 300-400 nanometers, depending on what book you are using). However, over their range their response to a particular frequency changes. You can see that below:



The black curve is rods, and the other three are the three types of cones. As you can see, they have a peak sensitivity at some frequency and their sensitivity drops off on either side (the image show absorbance, but for a large number of photons this is proportional to the output of each receptor at a given frequency). Note that when you look at a given sensitivity, it crosses each receptor's curve twice. All the nervous system knows is each receptor's output. However, the same output of a given receptor can be triggered by two different frequencies. By looking at the output from a single receptor type it is impossible to tell which frequency is present. However, notice how the sensitivities overlap? This is the key. Although a pair of frequencies stimulating the L receptor (the red one with a peak at longer wavelengths) might trigger the same output in that receptor, those same two frequencies triggering the M receptor (the green one with a medium peak sensitivity) will trigger two completely different outputs. So by comparing the response from different types of receptors with overlapping frequency sensitivities allows two colors that would be indistinguishable to one receptor to be differentiated. This is why people with color blindness have problems, they are missing one or more receptors so much of this overlap is lost and their ability to tell apart certain frequencies is thus also lost.

This brings us to stars. The reason this sensitivity system works is due to the absorbance and stochastic (i.e. random) nature of the pigments that actually detect the light. Given a photon impact, a pigment molecule may or may not actually get triggered. The chance of it getting triggered is proportional to its absorbance at that frequency. The more the absorbance, the more likely the pigment is to respond to a given photon. An individual pigment molecule's response is all-or-nothing. Either it gets triggered or it doesn't. At high light levels with a very large number of photons the random nature of the pigment molecules gets averaged over a huge number of photons and a huge number of pigment molecules, so the absorbance (which is basically a probability in this case) is, within measurable limits, proportional to the sensitivity of the pigment molecule at that frequency (this is called “the law of very large numbers”, and comes into play when doing many trials of an experiment to determine the actual probability of an event occurring). The problem is when there are very few photons. There are simply not enough photons triggering a given receptor to get a good measure of the spectral content of the light. The random nature of the pigment changes overwhelms the normal frequency sensitivity, the exact same group of photons hitting the exact same receptor could trigger very different responses due to the randomness of the pigment responses. What is more, starlight inherently contains a broad range of frequencies. A given receptor will not get very many photons, and which of the available frequencies a given photon has is entirely random. This means that at different points of time the exact same receptor looking at the exact same star will get a significantly different distribution of photon frequencies. This all comes together so that there is not enough information in the receptor activity for the cortex to be able to determine what color the starlight is. Due to various properties of the retina and central nervous system this input gets perceived as white.
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Last edited by TheBlackCat; 23-February-2006 at 12:18 AM.
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