{"id":116,"date":"2006-08-14T09:27:06","date_gmt":"2006-08-14T09:27:06","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2006\/08\/14\/big-numbers-bad-anti-evolution-crap-from-anncoulter-com\/"},"modified":"2006-08-14T09:27:06","modified_gmt":"2006-08-14T09:27:06","slug":"big-numbers-bad-anti-evolution-crap-from-anncoulter-com","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2006\/08\/14\/big-numbers-bad-anti-evolution-crap-from-anncoulter-com\/","title":{"rendered":"Big Numbers: Bad Anti-Evolution Crap from anncoulter.com"},"content":{"rendered":"

A reader sent me a copy of an article posted to “chat.anncoulter.com”. I can’t see the original article; anncoulter.com is a subscriber-only site, and I’ll be damned before I *register* with that site.
\nFortunately, the reader sent me the entire article. It’s another one of those stupid attempts by creationists to assemble some *really big* numbers in order to “prove” that evolution is impossible.
\n>One More Calculation
\n>
\n>The following is a calculation, based entirely on numbers provided by
\n>Darwinists themselves, of the number of small selective steps evolution would
\n>have to make to evolve a new species from a previously existing one. The
\n>argument appears in physicist Lee Spetner’s book “Not By Chance.”
\n>
\n>At the end of this post — by “popular demand” — I will post a bibliography of
\n>suggested reading on evolution and ID.
\n>
\n>**********************************************
\n>
\n>Problem: Calculate the chances of a new species emerging from an earlier one.
\n>
\n>What We Need to Know:
\n>
\n>(1) the chance of getting a mutation;
\n>(2) the fraction of those mutations that provide a selective advantage (because
\n>many mutations are likely either to be injurious or irrelevant to the
\n>organism);
\n>(3) the number of replications in each step of the chain of cumulative >selection;
\n>(4) the number of those steps needed to achieve a new species.
\n>
\n>If we get the values for the above parameters, we can calculate the chance of
\n>evolving a new species through Darwinian means.
\nFairly typical so far. Not *good* mind you, but typical. Of course, it’s already going wrong. But since the interesting stuff is a bit later, I won’t waste my time on the intro \ud83d\ude42
\nRight after this is where this version of this argument turns particularly sad. The author doesn’t just make the usual big-numbers argument; they recognize that the argument is weak, so they need to go through some rather elaborate setup in order to stack things to produce an even more unreasonably large phony number.
\nIt’s not just a big-numbers argument; it’s a big-numbers *strawman* argument.
\n>Assumptions:
\n>
\n>(1) we will reckon the odds of evolving a new horse species from an earlier
\n>horse species.
\n>
\n>(2) we assume only random copying errors as the source of Darwinian variation.
\n>Any other source of variation — transposition, e.g., — is non-random and
\n>therefore NON-DARWINIAN.
\nThis is a reasonable assumption, you see, because we’re not arguing against *evolution*; we’re arguing against the *strawman* “Darwinism”, which arbitrarily excludes real live observed sources of variation because, while it might be something that really happens, and it might be part of real evolution, it’s not part of what we’re going to call “Darwinism”.
\nReally, there are a lot of different sources of variation\/mutation. At a minimum, there are point mutations, deletions (a section getting lost while copying), insertions (something getting inserted into a sequence during copying), transpositions (something getting moved), reversals (something get flipped so it appears in the reverse order), fusions (things that were separate getting merged – e.g., chromasomes in humans vs. in chimps), and fissions (things that were a single unit getting split).
\nIn fact, this restriction *a priori* makes horse evolution impossible; because the modern species of horses have *different numbers of chromasomes*. Since the only change he allows is point-mutation, there is no way that his strawman Darwinism can do the job. Which, of course, is the point: he *wants* to make it impossible.
\n>(3) the average mutation rate for animals is 1 error every 10^10 replications
\n>(Darnell, 1986, “Molecular Cell Biology”)
\nNice number, shame he doesn’t understand what it *means*. That’s what happens when you don’t bother to actually look at the *units*.
\nSo, let’s double-check the number, and discover the unit. Wikipedia reports the human mutation rate as 1 in 108<\/sup> mutations *per nucleotide* per generation.
\nHe’s going to build his argument on 1 mutation in every 10^10 reproductions *of an animal*, when the rate is *per nucleotide*, *per cell generation*.
\nSo what does that tell us if we’re looking at horses? Well, according to a research proposal to sequence the domestic horse genome, it consists of 3×109<\/sup> nucleotides. So if we go by wikipedia’s estimate of the mutation rate, we’d expect somewhere around 30 mutations per individual *in the fertilized egg cell*. Using the numbers by the author of this wretched piece, we’d still expect to see 1 out of every three horses contain at least one unique mutation.
\nThe fact is, pretty damned nearly every living thing on earth – each and every human being, every animal, every plant – each contains some unique mutations, some unique variations in their genetic code. Even when you start with a really big number – like one error in every 1010<\/sup> copies; it adds up.
\n>(4) To be part of a typical evolutionary step, the mutation must: (a) have a
\n>positive selective value; (b) add a little information to the genome ((b) is a
\n>new insight from information theory. A new species would be distinguished from
\n>the old one by reason of new abilities or new characteristics. New
\n>characteristics come from novel organs or novel proteins that didn’t exist in
\n>the older organism; novel proteins come from additions to the original genetic
\n>code. Additions to the genetic code represent new information in the genome).
\nI’ve ripped apart enough bullshit IT arguments, so I won’t spend much time on that, other to point out that *deletion* is as much of a mutation, with as much potential for advantage, as *addition*.
\nA mutation also does not need to have an immediate positive selective value. It just needs to *not* have negative value, and it can propagate through a subset of the population. *Eventually*, you’d usually (but not always! drift *is* an observed phenomenon) expect to see some selective value. But that doesn’t mean that *at the moment the mutation occurs*, it must represent an *immediate* advantage for the individual.
\n>(5) We will also assume that the minimum mutation — a point mutation — is
\n>sufficient to cause (a) and (b). We don’t know if this is n fact true. We don’t
\n>know if real mutations that presumably offer positive selective value and small
\n>information increases can always be of minimum size. But we shall assume so
\n>because it not only makes the calculation possible, but it also makes the
\n>calculation consistently Darwinian. Darwinians assume that change occurs over
\n>time through the accumulation of small mutations. That’s what we shall assume,
\n>as well.
\nNote the continued use of the strawman. We’re not talking about evolution here; We’re talking about *Darwinism* as defined by the author. Reality be damned; if it doesn’t fit his Darwinism strawman, then it’s not worth thinking about.
\n>Q: How many small, selective steps would we need to make a new species?
\n>
\n>A: Clearly, the smaller the steps, the more of them we would need. A very
\n>famous Darwinian, G. Ledyard Stebbins, estimated that to get to a new species
\n>from an older species would take about 500 steps (1966, “Processes of Organic
\n>Evolution”).
\n>
\n>So we will accept the opinion of G. Ledyard Stebbins: It will take about 500
\n>steps to get a new species.
\nGotta love the up-to-date references, eh? Considering how much the study of genetics has advanced in the last *40 years*, it would be nice to cite a book younger than *me*.
\nBut hey, no biggie. 500 selective steps between speciation events? Sounds reasonable. That’s 500 generations. Sure, we’ve seen speciation in less than 500 generations, but it seems like a reasonable guestimate. (But do notice the continued strawman; he reiterates the “small steps” gibberish.)
\n>Q: How many births would there be in a typical small step of evolution?
\n>
\n>A: About 50 million births \/ evolutionary step. Here’s why:
\n>
\n>George Gaylord Simpson, a well known paleontologist and an authority on horse
\n>evolution estimated that the whole of horse evolution took about 65 million
\n>years. He also estimated there were about 1.5 trillion births in the horse
\n>line. How many of these 1.5 trillion births could we say represented 1 step in
\n>evolution? Experts claim the modern horse went through 10-15 genera. If we say
\n>the horse line went through about 5 species \/ genus, then the horse line went
\n>through about 60 species (that’s about 1 million years per species). That would
\n>make about 25 billion births \/ species. If we take 25 billion and divided it by
\n>the 500 steps per species transition, we get 50 million births \/ evolutionary
\n>step.
\n>
\n>So far we have:
\n>
\n>500 evolutionary steps\/new species (as per Stebbins)
\n>50 million births\/evolutionary step (derived from numbers by G. G. Simpson)
\nHere we see some really stupid mathematical gibberish. This is really pure doubletalk – it’s an attempt to generate *another* large number to add into the mix. There’s no purpose in it: we’ve *already* worked out the mutation rate and the number of mutations per speciation. This gibberish is an alternate formulation of essentially the same thing; a way of gauging how long it will take to go through a sequence of changes leading to speciation. So we’re adding an redundant (and meaningless) factor in order to inflate the numbers.
\n>Q: What’s the chance that a mutation in a particular nucleotide will occur and
\n>take over the population in one evolutionary step?
\n>
\n>A: The chance of a mutation in a specific nucleotide in one birth is 10^-10.
\n>Since there are 50 million births \/ evolutionary step, the chance of getting at
\n>least one mutation in the whole step is 50 million x 10^-10, or 1-in-200
\n>(1\/200). For the sake of argument we can assume that there is an equal chance
\n>that the base will change to any one of the other three (not exactly true in
\n>the real world, but we can assume to make the calculation easier – you’ll see
\n>that this assumption won’t influence things so much in the final calculation);
\n>so the chance of getting specific change in a specific nucleotide is 1\/3rd of
\n>1\/200 or 1-in-600 (1\/600).
\n>
\n>So far we have:
\n>
\n>500 evolutionary steps\/new species (as per Stebbins)
\n>50 million births\/evolutionary step (derived from numbers by G. G. Simpson)
\n>1\/600 chance of a point mutation taking over the population in 1 evolutionary >step (derived from numbers by Darnell in his standard reference book)
\nThis is pure gibberish. It’s so far away from being a valid model of things that it’s laughable. But worse, again, it’s redundant. Because we’ve already introduced a factor based on the mutation rate; and then we’ve introduced a factor which was an alternative formulation of the mutation rate; and now, we’re introducing a *third* factor which is an even *worse* alternative formulation of the mutation rate.
\n>Q: What would the “selective value” have to be of each mutation?
\n>
\n>A: According to the population-genetics work of Sir Ronald Fisher, the chances
\n>of survival for a mutant is about 2 x (selective value).
\n>”Selective Value” is a number that is ASSIGNED by a researcher to a species in
\n>order to be able to quantify in some way its apparent fitness. Selective Value
\n>is the fraction by which its average number of surviving offspring exceeds that
\n>of the population norm. For example, a mutant whose average number of surviving
\n>offspring is 0.1% higher than the rest of the population would have a Selective
\n>Value = 0.1% (or 0.001). If the norm in the population were such that 1000
\n>offspring usually survived from the original non-mutated organism, 1001
\n>offspring would usually survive from the mutated one. Of course, in real life,
\n>we have no idea how many offspring will, IN FACT, survive any particular
\n>organism – which is the reason that Survival Value is not something that you go
\n>into the jungle and “measure.” It’s a special number that is ASSIGNED to a
\n>species; not MEASURED in it (like a species’ average height, weight, etc.,
\n>which are objective attributes that, indeed, can we can measure).
\n>
\n>Fisher’s statistical work showed that a mutant with a Selective Value of 1% has
\n>a 2% chance of survival in a large population. A chance of 2-in-100 is that
\n>same as a chance of 1-in-50. If the Selective Value were 1\/10th of that, or
\n>0.1%, the chance would be 1\/10th of 2%, or about 0.2%, or 1-in-500. If the
\n>Selective Value were 1\/100th of 1%, the chance of survival would be 1\/100th of
\n>2%, or 0.02%, or 1-in-5000.
\n>
\n>We need a Selection Value for our calculation because it tells us what the
\n>chances are that a mutated species will survive. What number should we use? In
\n>the opinion of George Gaylord Simpson, a frequent value is 0.1%. So we shall
\n>use that number for our calculation. Remember, that’s a 1-in-500 chance of
\n>survival.
\n>
\n>So far we have:
\n>
\n>500 evolutionary steps\/new species (as per Stebbins)
\n>50 million births\/evolutionary step (derived from numbers by G. G. Simpson)
\n>1\/600 chance of a point mutation taking over the population in 1 evolutionary
\n>step (derived from numbers by Darnell in his standard reference book)
\n>1\/500 chance that a mutant will survive (as per G. G. Simpson)
\nAnd, once again, *another* meaningless, and partially redundant factor added in.
\nWhy meaningless? Because this isn’t how selection works. He’s using his Darwinist strawman again: everything must have *immediate* *measurable* survival advantage. He also implicitly assumes that mutation is *rare*; that is, a “mutant” has a 1-in-500 chance of seeing its mutated genes propagate and “take over” the population. That’s not at all how things work. *Every* individual is a mutant. In reality, *every* *single* *individual* possesses some number of unique mutations. If they reproduce, and the mutation doesn’t *reduce* the likelihood of its offspring’s survival, the mutation will propagate through the generations to some portion of the population. The odds of a mutation propagating to some reasonable portion of the population over a number of generations is not 1 in 500. It’s quite a lot better.
\nWhy partially redundant? Because this. once again, factors in something which is based on the rate of mutation propagating through the population. We’ve already included that twice; this is a *third* variation on that.
\n>Already, however, the numbers don’t crunch all that well for evolution.
\n>
\n>Remember, probabilities multiply. So the probability, for example, that a point
\n>mutation will BOTH occur AND allow the mutant to survive is the product of the
\n>probabilities of each, or 1\/600 x 1\/500 = 1\/300,000. Not an impossible number,
\n>to be sure, but it’s not encouraging either … and it’s going to get a LOT
\n>worse. Why? Because…
\n**Bzzt. Bad math alert!**
\nNo, these numbers *do not multiply*. Probabilities multiply *when they are independent*. These are *not* independent factors.
\n>V.
\n>
\n>Q. What are the chances that (a) a point mutation will occur, (b) it will add
\n>to the survival of the mutant, and (c) the last two steps will occur at EACH of
\n>the 500 steps required by Stebbins’ statement that the number of evolutionary
\n>steps between one species and another species is 500?
\nSee, this is where he’s been going all along.
\n* He created the darwinian strawman to allow him to create bizzare requirements.
\n* Then he added a ton of redundant factors.
\n* Then he combined probabilities as if they were independent when they weren’t.
\n* and *now* he adds a requirement for simultaneity which has no basis in reality.
\n>A: The chances are:
\n>
\n>The product of 1\/600 x 1\/500 multiplied by itself 500 times (because it has to
\n>happen at EACH evolutionary step). Or,
\n>
\n>Chances of Evolutionary Step 1: 1\/300,000 x
\n>Chances of Evolutionary Step 2: 1\/300,000 x
\n>Chances of Evolution Step 3: 1\/300,000 x …
\n>. . . Chances of Evolution Step 500: 1\/300,000
\n>
\n>Or,
\n>
\n>1\/300,000^500
\n*Giggle*, *snort*. I seriously wonder if he actually believe this gibberish. But this is just silly. For the reasons mentioned above: this is taking the redundant factors that he already pushed into each step, inflating them by adding the simultaneity requirement, and then *exponentiating* them.
\n>This is approximately equal to:
\n>
\n>2.79 x 10^-2,739
\n>
\n>A number that is effectively zero.
\nAs I’ve said before: no one who understands math *ever* uses the phrase *effectively zero* in a mathematical argument. There is no such thing as effectively zero.
\nOn a closing note, this entire thing, in addition to being both an elaborate strawman *and* a sloppy big numbers argument is also an example of another kind of mathematical error, which I call a *retrospective error*. A retrospective error is when you take the outcome of a randomized process *after* it’s done, treat it as the *only possible outcome*, and compute the probability of it happening.
\nA simple example of this is: shuffle a deck of cards. What’s the odds of the particular ordering of cards that you got from the shuffle? 1\/52! = 1\/(8 * 1067<\/sup>). If you then ask “What was the probability of a shuffling of cards resulting in *this order*?”, you get that answer: 1 in 8 * 1067<\/sup> – an incredibly unlikely event. But it *wasn’t* an unlikely event; viewed from the proper perspective, *some* ordering had to happen: any result of the shuffling process would have the same probability – but *one* of them had to happen. So the odds of getting a result whose *specific* probability is 1 in 8 * 1067<\/sup> was actually 1 in 1.
\nThe entire argument that our idiot friend made is based on this kind of an error. It assumes a single unique path – a single chain of specific mutations happening in a specific order – and asks about the likelihood that *single chain* leading to a *specific result*.
\nBut nothing ever said that the primitive ancestors of the modern horse *had* to evolve into the modern horse. If they weren’t to just go extinct, they would have to evolve into *something*; but demanding that the particular observed outcome of the process be the *only possibility* is simply wrong.<\/p>\n","protected":false},"excerpt":{"rendered":"

A reader sent me a copy of an article posted to “chat.anncoulter.com”. I can’t see the original article; anncoulter.com is a subscriber-only site, and I’ll be damned before I *register* with that site. Fortunately, the reader sent me the entire article. It’s another one of those stupid attempts by creationists to assemble some *really big* […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[16,61],"tags":[],"class_list":["post-116","post","type-post","status-publish","format-standard","hentry","category-debunking-creationism","category-statistics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-1S","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/116","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=116"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/116\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=116"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}