Evo-Info 3: Evolution is not search

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Introduction to Evolutionary Informatics, by Robert J. Marks II, the “Charles Darwin of Intelligent Design”; William A. Dembski, the “Isaac Newton of Information Theory”; and Winston Ewert, the “Charles Ingram of Active Information.” World Scientific, 332 pages.
Classification: Engineering mathematics. Engineering analysis. (TA347)
Subjects: Evolutionary computation. Information technology–Mathematics.

Marks, Dembski, and Ewert open Chapter 3 by stating the central fallacy of evolutionary informatics: “Evolution is often modeled by as [sic] a search process.” The long and the short of it is that they do not understand the models, and consequently mistake what a modeler does for what an engineer might do when searching for a solution to a given problem. What I hope to convey in this post, primarily by means of graphics, is that fine-tuning a model of evolution, and thereby obtaining an evolutionary process in which a maximally fit individual emerges rapidly, is nothing like informing evolution to search for the best solution to a problem. We consider, specifically, a simulation model presented by Christian apologist David Glass in a paper challenging evolutionary gradualism à la Dawkins. The behavior on exhibit below is qualitatively similar to that of various biological models of evolution.

Animation 1. Parental populations in the first 2000 generations of a run of the Glass model, with parameters (mutation rate .005, population size 500) tuned to speed the first occurrence of maximum fitness (1857 generations, on average), are shown in orange. Offspring are generated in pairs by recombination and mutation of heritable traits of randomly mated parents. The fitness of an individual in the parental population is, loosely, the number of pairs of offspring it is expected to leave. In each generation, the parental population is replaced by surviving offspring. Which of the offspring die is arbitrary. When the model is modified to begin with a maximally fit population, the long-term regime of the resulting process (blue) is the same as for the original process. Rather than seek out maximum fitness, the two evolutionary processes settle into statistical equilibrium.

Figure 1. The two bar charts, orange (Glass model) and blue (modified Glass model), are the mean frequencies of fitnesses in the parental populations of the 998,000 generations following the 2,000 shown in Animation 1. The mean frequency distributions approximate the equilibrium distribution to which the evolutionary processes converge. In both cases, the mean and standard deviation of the fitnesses are 39.5 and 2.84, respectively, and the average frequency of fitness 50 is 0.0034. Maximum fitness occurs in only 1 of 295 generations, on average.

I should explain immediately that an individual organism is characterized by 50 heritable traits. For each trait, there are several variants. Some variants contribute 1 to the average number offspring pairs left by individuals possessing them, and other variants contribute 0. The expected number of offspring pairs, or fitness, for an individual in the parental population is roughly the sum of the 0-1 contributions of its 50 traits. That is, fitness ranges from 0 to 50. It is irrelevant to the model what the traits and their variants actually are. In other words, there is no target type of organism specified independently of the evolutionary process. Note the circularity in saying that evolution searches for heritable traits that contribute to the propensity to leave offspring, whatever those traits might be.

The two evolutionary processes displayed above are identical, apart from their initial populations, and are statistically equivalent over the long term. Thus a general account of what occurs in one of them must apply to both of them. Surely you are not going to tell me that a search for the “target” of maximum fitness, when placed smack dab on the target, rushes away from the target, and subsequently finds it once in a blue moon. Hopefully you will allow that the occurrence of maximum fitness in an evolutionary process is an event of interest to us, not an event that evolution seeks to produce. Again, fitness is not the purpose of evolution, but instead the propensity of a type of organism to leave offspring. So why is it that, when the population is initially full of maximally fit individuals, the population does not stay that way indefinitely? In each generation, the parental population is replaced with surviving offspring, some of which are different in type (heritable traits) from their parents. The variety in offspring is due to recombination and mutation of parental traits. Even as the failure of parents to leave perfect copies of themselves contributes to the decrease of fitness in the blue process, it contributes also to the increase of fitness in the orange process.

Both of the evolutionary processes in Animation 1 settle into statistical equilibrium. That is, the effects of factors like differential reproduction and mutation on the frequencies of fitnesses in the population gradually come into balance. As the number of generations goes to infinity, the average frequencies of fitnesses cease to change (see “Wright, Fisher, and the Weasel,” by Joe Felsenstein). More precisely, the evolutionary processes converge to an equilibrium distribution, shown in Figure 1. This does not mean that the processes enter a state in which the frequencies of fitnesses in the population stay the same from one generation to the next. The equilibrium distribution is the underlying change­less­ness in a ceaselessly changing population. It is what your eyes would make of the flicker if I were to increase the frame rate of the animation, and show you a million generations in a minute.

Animation 2. As the mutation rate increases, the equilibrium distribution shifts from right to left, which is to say that the long-term mean fitness of the parental population decreases. The variance of the fitnesses (spread of the equilibrium distribution) increases until the mean reaches an intermediate value, and then decreases. Note that the fine-tuned mutation rate .005 ≈ 10–2.3 in Figure 1.

Let’s forget about the blue process now, and consider how the orange (randomly initialized) process settles into statistical equilibrium, moving from left to right in Animation 1. The mutation rate determines

  1. the location and the spread of the equilibrium distribution, and also
  2. the speed of convergence to the equilibrium distribution.

Animation 2 makes the first point clear. In visual terms, an effect of increasing the mutation rate is to move equilibrium distribution from right to left, placing it closer to the distribution of the initial population. The second point is intuitive: the closer the equilibrium distribution is to the frequency distribution of the initial population, the faster the evolutionary process “gets there.” Not only does the evolutionary process have “less far to go” to reach equilibrium, when the mutation rate is higher, but the frequency distribution of fitnesses changes faster. Animation 3 allows you to see the differences in rate of convergence to the equilibrium distribution for evolutionary processes with different mutation rates.

Animation 3. Shown are runs of the Glass model with mutation rate we have focused upon, .005, doubled and halved. That is, uʹ = 2 ⨉ .005 = .01 for the blue process, and uʹ = 1/2 ⨉ .005 = .0025 for the orange process.

An increase in mutation rate speeds convergence to the equilibrium distribution, and reduces the mean frequency of maximum fitness.

I have selected a mutation rate that strikes an optimal balance between the time it takes for the evolutionary process to settle into equilibrium, and the time it takes for maximum fitness to occur when the process is at (or near) equilibrium. With the mutation rate set to .005, the average wait for the first occurrence of maximum fitness, in 1001 runs of the Glass model, is 1857 generations. Over the long term, maximum fitness occurs in about 1 of 295 generations. Although it’s not entirely accurate, it’s not too terribly wrong to think in terms of waiting an average of 1562 generations for the evolutionary process to reach equilibrium, and then waiting an average of 295 generations for a maximally fit individual to emerge. Increasing the mutation rate will decrease the first wait, but the decrease will be more than offset by an increase in the second wait.

Figure 2. Regarding Glass’s algorithm (“Parameter Dependence in Cumulative Selection,” Section 3) as a problem solver, the optimal mutation rate is inversely related to the squared string length (compare to his Figure 3). We focus on the case of string length (number of heritable traits) L = 50, population size N = 500, and mutation rate uʹ = .005, with scaled mutation rate uʹ L2 = 12.5 ≈ 23.64. The actual rate of mutation, commonly denoted u, is 26/27 times the rate uʹ reported by Glass. Note that each point on a curve corresponds to an evolutionary process. Setting the parameters does not inform the evolutionary search, as Marks et al. would have you believe, but instead defines an evolutionary process.

Figure 2 provides another perspective on the point at which changes in the two waiting times balance. In each curve, going from left to right, the mutation rate is increasing, the mean fitness at equilibrium is decreasing, and the speed of convergence to the equilibrium distribution is increasing. The middle curve (L = 50) in the middle pane (N = 500) corresponds to Animation 2. As we slide down the curve from the left, the equilibrium distribution in the animation moves to the left. The knee of the curve is the point where the increase in speed of convergence no longer offsets the increase in expected wait for maximum fitness to occur when the process is near equilibrium. The equilibrium distribution at that point is the one shown in Figure 1. Continuing along the curve, we now climb steeply. And it’s easy to see why, looking again at Figure 1. A small shift of the equilibrium distribution to the left, corresponding to a slight increase in mutation rate, greatly reduces the (already low) incidence of maximum fitness. This brings us to an important question, which I’m going to punt into the comments section: why would a biologist care about the expected wait for the first appearance of a type of organism that appears rarely?

You will not make sense of what you’ve seen if you cling to the misconception that evolution searches for the “target” of maximally fit organisms, and that I must have informed the search where to look. What I actually did, by fine-tuning the parameters of the Glass model, was to determine the location and the shape of the equilibrium distribution. For the mutation rate that I selected, the long-term average fitness of the population is only 79 percent of the maximum. So I did not inform the evolutionary process to seek out individuals of maximum fitness. I selected a process that settles far away from the maximum, but not too far away to suit my purpose, which is to observe maximum fitness rapidly. If my objective were to observe maximum fitness often, then I would reduce the mutation rate, and expect to wait longer for the evolutionary process to settle into equilibrium. In any case, my purpose for selecting a process is not the purpose of the process itself. All that the evolutionary process “does” is to settle into statistical equilibrium.

Sanity check of some claims in the book

Unfortunately, the most important thing to know about the Glass model is something that cannot be expressed in pictures: fitness has nothing to do with an objective specified independently of the evolutionary process. Which variants of traits contribute 1 to fitness, and which contribute 0, is irrelevant. The fact of the matter is that I ignore traits entirely in my implementation of the model, and keep track of 1s and 0s instead. Yet I have replicated Glass’s results. You cannot argue that I’ve informed the computer to search for a solution to a given problem when the solution simply does not exist within my program.

Let’s quickly test some assertions by Marks et al. (emphasis added by me) against the reality of the Glass model.

There have been numerous models proposed for Darwinian evolution. […] We show repeatedly that the proposed models all require inclusion of significant knowledge about the problem being solved. If a goal of a model is specified in advance, that’s not Darwinian evolution: it’s intelligent design. So ironically, these models of evolution purported to demonstrate Darwinian evolution necessitate an intelligent designer.

Chapter 1, “Introduction”

[T]he fundamentals of evolutionary models offered by Darwinists and those used by engineers and computer scientists are the same. There is always a teleological goal imposed by an omnipotent programmer, a fitness associated with the goal, a source of active information …, and stochastic updates.

Chapter 6, “Analysis of Some Biologically Motivated Evolutionary Models”

Evolution is often modeled by as [sic] a search process. Mutation, survival of the fittest and repopulation are the components of evolutionary search. Evolutionary search computer programs used by computer scientists for design are typically teleological — they have a goal in mind. This is a significant departure from the off-heard [sic] claim that Darwinian evolution has no goal in mind.

Chapter 3, “Design Search in Evolution and the Requirement of Intelligence”

My implementation of the Glass model tracks only fitnesses, not associated traits, so there cannot be a goal or problem specified independently of the evolutionary process.

Evolutionary models to date point strongly to the necessity of design. Indeed, all current models of evolution require information from an external designer in order to work. All current evolutionary models simply do not work without tapping into an external information source.

Preface to Introduction to Evolutionary Informatics

The sources of information in the fundamental Darwinian evolutionary model include (1) a large population of agents, (2) beneficial mutation, (3) survival of the fittest and (4) initialization.

Chapter 5, “Conservation of Information in Computer Search”

The enumerated items are attributes of an evolutionary process. Change the attributes, and you do not inform the process to search, but instead define a different process. Fitness is the probabilistic propensity of a type of organism to leave offspring, not search guidance coming from an “external information source.” The components of evolution in the Glass model are differential reproduction of individuals as a consequence of their differences in heritable traits, variety in the heritable traits of offspring resulting from recombination and mutation of parental traits, and a greater number of offspring than available resources permit to survive and reproduce. That, and nothing you will find in Introduction to Evolutionary Informatics, is a fundamental Darwinian account.

1,439 thoughts on “Evo-Info 3: Evolution is not search”

  5. phoodoo,

    Well what do we do Allan, do we ignore unibrows? Or are they just as important as DMD?

    If the allele for unibrows is not tightly linked to that for DMD, they can be treated separately. I don’t know if they are or not.

  6. If we are going the linkage route, we’d have to believe that every single allele were tightly linked to every other. Clearly, given the fact that the genome occupies physical space, and is not a dimensionless singularity, that is not possible.

    [eta – of course, there are genomes where linkage is complete. But those are not the ones one treats at ‘allele’ level. There is a reason for the allele view, and that reason is recombination. ]

  7. Allan Miller: If the allele for unibrows is not tightly linked to that for DMD, they can be treated separately. I don’t know if they are or not.

    Right they are treated separately. So then do both hold equal weight in counting the fitness of an individual?

  8. phoodoo,

    Right they are treated separately. So then do both hold equal weight in counting the fitness of an individual?

    An individual with both a unibrow and DMD would have its reproductive output added to both the ‘unibrow’ and the ‘DMD’ statistics. It is a carrier of both (and of course of all other alleles it possesses). But unless the two are tightly linked, it will not be the case that all individuals with the one will be carriers of both. So, you just add them separately.

  10. phoodoo: Yes, that’s all well and good if we want to use common sense as a measure of fitness.

    That is all I am asking for.

    phoodoo: But common sense isn’t part of Allan’s definition of fitness. […] So whose view do we take, what thinking people know about fitness, or do we go with what Allan says all evolutionary biologist understand?

    For now, let’s stick with “Allan’s definition of fitness” in situations where we can agree it is consonant with “what thinking people know about fitness”.

    Since we now both agree that people with severely debilitating diseases tend to have few children (even compared to people sporting a unibrow), could we not also agree that this is a plausible explanation for the fact that mutations that cause these diseases are typically very rare? As Allan remarked, this is already argued by many Creationists anyway; “bad mutations” do not spread.

  11. phoodoo,

    So you disagree with Corneel that DMD has a more important role in fitness then?

    No.

    I would be pretty sure that the ‘unibrow’ bin had a higher mean fitness than the ‘DMD’ bin, even though unibrow+DMD individuals would count towards both bins. Unless all unibrow individuals are DMD, which is why I add the qualifier on linkage.

  12. Allan Miller:
    phoodoo,

    No.

    I would be pretty sure that the ‘unibrow’ bin had a higher mean fitness than the ‘DMD’ bin, even though unibrow+DMD individuals would count towards both bins. Unless all unibrow individuals are DMD, which is why I add the qualifier on linkage.

    You mean there are probably more people with a unibrow than people with DMD, so they would be more fit?

    Allan Miller: An individual with both a unibrow and DMD would have its reproductive output added to both the ‘unibrow’ and the ‘DMD’ statistics.

    But I didn’t ask you about what the statistics are for DMD and what the statistics are for unibrows. I said, which counts more towards the fitness of an individual? They count equally? If DMD’s have less mean fitness, but unibrows have more mean fitness, what does that mean for the individual, do they cancel each other out?

  14. phoodoo: If DMD’s have less mean fitness, but unibrows have more mean fitness, what does that mean for the individual, do they cancel each other out?

    That depends on their relative contribution to fitness. Do you understand that sentence?

    It depends on HOW MUCH those alleles affect fitness, compared to non-carriers. Given how debilitating DMD is, unibrows would have to make you extremely reproductively successful to cancel out the negative effect of DMD.

    So no, they are very unlikely to cancel each other out (and I’m of course assuming for the sake of argument that unibrows have a positive rather than negative effect on fitness). So having DMD will make you much less successful, supposing unibrows are really sexy, it would probably still not outweigh the negative effect of DMD.
    But to get an actual number, we need the actual mean fitness of those two alleles. We need actual numbers. Once we have actual numbers, a calculation can be made.

    There’s this thing called math, and there’s this thing called the real world, and the real world can be observed, and things in the real that we observe can be counted, and the numbers we get from counting we can do math with. Amazing shit, I know. I’ll blow your mind when you learn it.

  15. Rumraket: That depends on their relative contribution to fitness

    I am pretty sure nobody understands that sentence, because we have no way of measuring that Rumraket, and that is the point.

    What is it relative to? To an individual? To all individuals on the planet?

    Tell me how you are going to measure it.

  16. phoodoo: You mean there are probably more people with a unibrow than people with DMD, so they would be more fit?

    Probably more without a unibrow, so unibrow would be less fit too.

  17. newton,

    Right. And there is a much higher percentage of people that are gay than have green eyes. In fact there are probably even more people that are gay than have blue eyes. So clearly having green eyes is a much bigger detriment to reproductive success than being gay is.

  18. phoodoo,

    Enough with the hair colour and the eye colour and the eyebrows and what-have-you. Let’s talk business.

    Do you agree that mutations that cause severy debilitating diseases will not spread because patients suffering from those tend to have few children?
    In other words: do you accept that purifying selection works for these specific examples?

    Come to us, phoodoo!

  19. Corneel,

    I don’t have an opinion about that, because I think the reasons genes exist in the population are much more complicated and unknown then evolutionists are willing to admit.

  21. Allan Miller: The fact one can dream up exceptional scenarios – hurricanes…

    It wasn’t dreamed up Allan, it actually happened to them. More than once. Read the freaking book.

  22. Corneel,

    Why hair colors, why eye colors, why are some dominant and some recessive. Why does a combination of genes affect a phenotype, what made it work out that way? Why are there mutations on the X chromosone but not on the Y? Why do some gene expressions skip generations? Why do mice remember bad things that happened to their ancestors?

    I mean just take a look at some of the research for how a “gay gene” might be acquired (hint they don’t really know, but its a combination of mother to son, father to daughter, several genes, plus environmental factors affecting those genes during development, and, and..we don’t know).

  23. Mung: It wasn’t dreamed up Allan, it actually happened to them. More than once. Read the freaking book.

    Yea, but it doesn’t count, because, because…we are off to see the wizard…

  24. Corneel: Why are the populations in the simulations not reaching maximum attainable fitness, if not because of deleterious mutations?

    According to the OP the populations are not reaching maximum attainable fitness because evolution doesn’t maximize fitness.

    Do you think that absent deleterious mutations that evolution would maximize fitness?

  25. phoodoo: Why hair colors, why eye colors, why are some dominant and some recessive. Why does a combination of genes affect a phenotype, what made it work out that way? Why are there mutations on the X chromosone but not on the Y? Why do some gene expressions skip generations? Why do mice remember bad things that happened to their ancestors?

    I mean just take a look at some of the research for how a “gay gene” might be acquired (hint they don’t really know, but its a combination of mother to son, father to daughter, several genes, plus environmental factors affecting those genes during development, and, and..we don’t know).

    Coming from a genetics background, I will happily agree that the genetics of living organisms can be pretty daunting (though I daresay I can answer a few of those questions). But I fail to see how this prevents you from forming an opinion about purifying selection.

  26. Mung: Do you think that absent deleterious mutations that evolution would maximize fitness?

    In Tom’s simulation? Yes, it would. Because the correct alleles would “latch” into place and not budge again.

    In real life: no. The Darwinian demon can not be attained.

  27. Phoodoo, think of the Polar Bear. It’s fur is white. Suppose it was black, or red. Would that, on average, have any effect on the reproductive success of a bear living in the Arctic?

    Would it make it more likely for an arbitrary bear living in the arctic snow, to catch prey if the bear was black(or red) and living in white surroundings?

    Do you think this is an unanswerable question that couldn’t possibly be assessed neither in theory nor practice?

  28. Rumraket:
    Phoodoo, think of the Polar Bear. It’s fur is white. Suppose it was black, or red. Would that, on average, have any effect on the reproductive success of a bear living in the Arctic?

    You think polar bears in the Arctic don’t get eaten by others because they can’t be seen?

    Or that seals don’t see them coming?

  29. phoodoo: You think polar bears in the Arctic don’t get eaten by others because they can’t be seen?

    I happen to think they’re camouflaged so they can get close to their prey. Do you think this is an unimaginable stretch on my part?

  30. phoodoo: I mean just take a look at some of the research for how a “gay gene” might be acquired (hint they don’t really know, but its a combination of mother to son, father to daughter, several genes, plus environmental factors affecting those genes during development, and, and..we don’t know).

    Much easier to just say design

  31. Rumraket: I happen to think they’re camouflaged so they can get close to their prey. Do you think this is an unimaginable stretch on my part?

    Yes, but if you are an evolutionist, you should be saying there were brown ones and red ones and blues that all accidentally occurred, but the blue and red and brown ones were not good at catching anything to eat, so after a few hundred thousand years they disappeared.

    Maybe we will find their fossils one day.

    Only one problem though, the arctic isn’t always white.

  32. phoodoo: Yes

    So you say yes as in, yes it is an unimaginable stretch that it is a help to the polar bear that it is white, while living in the arctic?

    but if you are an evolutionist, you should be saying there were brown ones and red ones and blues that all accidentally occurred, but the blue and red and brown ones were not good at catching anything to eat, so after a few hundred thousand years they disappeared.

    Polar bears evolved from brown bears, and their ranges overlap in some arctic regions. Some brown bears (grizzlies) some times get mutations so they are white.
    Why is it that the polar bears are white, do you suppose?

    Incidentally, this is one of those “microevolution” things even the most obtuse and staunch creationists accept.

    Not you, however. Not you. The polar bear being white is an impenetrable mystery that has nothing to do with it’s environment.

    I suppose the same is true for insects that look like sticks and thorns, or frogs that look like leaves, and so on. There’s just no reason to think these things have any bearing on their ability to avoid predators and catch prey. So why they are why they are… well, who knows? And it’s obviously also impossible to find out.

    Only one problem though, the arctic isn’t always white.

    And there are some times bushes in the desert, so wearing camouflage that looks like sand and small rocks is useless. And the forest ends where the road is and city is. Call all the worlds militaries, they’re wasting time and resources.

  33. Allan Miller: So … when Creationists argue that ‘all mutations are bad’, what are they doing that differs from the ‘neo-Classical’ view of an allele’s effects affecting its spread?

    Straw Man

  36. Phoodoo’s reasoning in this thread seems to be “I get confused thinking about multiple traits and varying environmental conditions. Therefore nature gets confused too and selection can’t work.”

    It’s just you, phoodoo.

  37. Rumraket: There’s just no reason to think these things have any bearing on their ability to avoid predators and catch prey.

    No, I would say there is no reason to believe it happened by accident. Again, and again and again, with each accident making a frog look more and more like a leaf with each successive accident. A mutation for a leaf vein that makes the frog better than frogs without the leaf veins, then another accident for a stem, which makes it better than frogs without the accidental stem…

  38. Corneel: Do you agree that mutations that cause severy debilitating diseases will not spread because patients suffering from those tend to have few children?

    Wouldn’t it depend on whether the mutation was in the germ line?

  40. Rumraket: I happen to think they’re camouflaged so they can get close to their prey. Do you think this is an unimaginable stretch on my part?

    LoL. Yes, I do.

    Believe it or not, their hair isn’t actually white! Their long outer hairs, which protect their soft, thick undercoat, are mostly hollow and transparent. The thinner hairs of their undercoat are also colorless. Polar bear hair looks white because the air spaces in the hairs scatter light of all colors.

  43. Mung: LoL. Yes, I do.

    The mechanism that gives the appearance of being white is secondary with respect to the point. The fact is they appear white, and I think that has a pretty substantial long-term reproductive benefit to them in their environment.

    So whether they are white because of scattering, or white because they emit complementary wavelengths, doesn’t seem to me to be what is important. We are talking about whether there is any such thing as natural selection, and whether such a thing as a phenotype can change in frequency due to a selective pressure.

    Phoodoo seems to say no, do you agree with his assessment?

  44. Mung: Genetics.

    Yes, but why aren’t they brown? They evolved from brown bears. Why didn’t they stay brown? Even if you believe God had to cause the mutations for white appearance to happen, why did he do so? Is it a help to the bears in any way?

    If I say yes, it is a help to the bears, do you consider that a preposterous and untestable statement?

  45. phoodoo: No, I would say there is no reason to believe it happened by accident.

    I don’t care if it happened by accident.

    Do you think polar bears being white is of any help to them? If you don’t think it is, why are they white then if they evolved by (guided?) evolution from brown bears? Why did the designer guide them to whiteness?

  46. Rumraket:I happen to think they’re camouflaged so they can get close to their prey. Do you think this is an unimaginable stretch on my part?

    Mung:LoL. Yes, I do.

    “Believe it or not, their hair isn’t actually white! Their long outer hairs, which protect their soft, thick undercoat, are mostly hollow and transparent. The thinner hairs of their undercoat are also colorless. Polar bear hair looks white because the air spaces in the hairs scatter light of all colors”.

    That was Salvador Cordova quality flappery, Mung.

    Well done.

  47. Woodbine: That was Salvador Cordova quality flappery, Mung.

    Well done.

    It just needs a “Bwahaha!”. And the quote should be introduced with “From Dr. Blah, PhD, one of the most brilliant biochemistry laboratories in the world…”.

  48. Woodbine:

    [Mung]“Believe it or not, their hair isn’t actually white! Their long outer hairs, which protect their soft, thick undercoat, are mostly hollow and transparent. The thinner hairs of their undercoat are also colorless. Polar bear hair looks white because the air spaces in the hairs scatter light of all colors”.

    That was Salvador Cordova quality flappery, Mung.

    Well done.

    I think you could probably say that most “white” things are in fact colorless. The “pigment” titanium dioxide that is used in paints both for white and as an (light-colored) opacifier is simply a colorless substance whose refraction (not “air space,” that’s idiotic) scatters the light so that a layer of titanium dioxide looks white. That it’s highly refractive means less is needed to be “white.” And of course the snow that the polar bear is camouflaged to blend into is also colorless (slightly blue, but certainly not very blue) and merely looks white due to refraction and reflection by many crystals.

    It’s bizarre how people think that they make a point in saying that something is “really colorless” and not white when it’s the colorlessness that makes it white, as many structures are reflecting and refracting the light to produce a white surface.

    Glen Davidson

  49. It is all the more bizarre given how the particular optical mechanism that yields the whiteness is entirely besides the point of the question I asked.

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