{"id":406,"date":"2007-05-02T21:05:36","date_gmt":"2007-05-02T21:05:36","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2007\/05\/02\/using-bad-math-to-create-bad-models-to-produce-bad-results\/"},"modified":"2007-05-02T21:05:36","modified_gmt":"2007-05-02T21:05:36","slug":"using-bad-math-to-create-bad-models-to-produce-bad-results","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2007\/05\/02\/using-bad-math-to-create-bad-models-to-produce-bad-results\/","title":{"rendered":"Using Bad Math to Create Bad Models to Produce Bad Results"},"content":{"rendered":"

An astute reader pointed me towards a monstrosity of pompous bogus math. It’s an oldie, but I hadn’t seen it before, and it was just referenced by my old buddy Sal Cordova in a thread on one of the DI blogs. It’s a “debate” posted online by Lee Spetner, in which he rehashes the typical bogus arguments against evolution<\/a>. I’m going to ignore most of it; this kind of stuff has been refuted more than enough times. But in the course
\nof this train wreck, he pretends to be making a mathematical argument about search spaces and optimization processes. It’s a completely invalid argument – but it’s one which is constantly<\/em> rehashed by creationists, and Spetner’s version of it is a perfect demonstration of exactly what’s wrong with the argument.<\/p>\n

<\/p>\n

Let’s look at the relevant parts of Spetner’s argument. Spetner basically repeats himself over and over, so I’ll just quote the first repetition; you can go look at the full document to see others.<\/p>\n

\n

The principle message of evolution is that all life descended with modification from a
\nputative single primitive source. I call this the grand sweep of evolution. The mechanism
\noffered for the process of modification is basically the Darwinian one of a long series of
\nsteps of random variation, each followed by natural selection. The variation is generally
\nunderstood today to be random mutations in the DNA.<\/p>\n

…<\/em><\/p>\n

For the grand process of evolution to work, long sequences of beneficial<\/em>
\nmutations must be possible, each building on the previous one and conferring a selective
\nadvantage on the organism. The process must be able to lead not only from one species to
\nanother, but to the entire advance of life from a simple beginning to the full complexity
\nof life today. There must be a long series of possible mutations, each of which conferring
\na selective advantage on the organism so that natural selection can make it take over the
\npopulation. Moreover, there must be not just one, but a great many such series.<\/p>\n

The chain must be continuous in that at each stage a change of a single base pair
\nsomewhere in the genome can lead to a more adaptive organism in some environmental context.
\nThat is, it should be possible to continue to climb an adaptive<\/em> hill, one base
\nchange after another, without getting hung up on a local adaptive maximum. No one has ever
\nshown this to be possible.<\/p>\n

Now one might say that if evolution were hung up on a local Maximum, a large genetic
\nchange like a recombination or a transposition could bring it to another higher peak. Large
\nadaptive changes are, however, highly improbable. They are orders of magnitude less
\nprobable than getting an adaptive change with a single nucleotide substitution, which is
\nitself improbable. No one has shown this to be possible either.<\/p>\n<\/blockquote>\n

So – he’s trying to do the usual thing of modeling evolution as a search of a fitness landscape. It’s pretty common to model evolution that way – both real scientists and creationist bozos do it – but it is worth pointing out that while search is a useful model of evolution, it’s far from a perfect one. The classic formulation of search over a fitness landscape requires an unchanging<\/em> landscape. But the “fitness landscape” that’s being traversed in an evolutionary process is not<\/em>: it’s constantly changing.<\/p>\n

He takes advantage of that flaw in the model of the fitness landscape to build a key part of his argument. Throughout the argument, he keeps making claims about getting “hung up on a local maximum”. The passage quoted above contains an example; in the full document, he comes back to that point again and again.<\/p>\n

But it’s a completely invalid point. Even if we assume that there are<\/em> local maxima where things can get hung up, the landscape is constantly changing. So a local maximum today is not<\/em> necessarily a maximum tomorrow, and is almost certainly not<\/em> a maximum 100 years from now. So even if we pile together his bunch of bogus assumptions without argument, we still<\/em> wind up with his argument being completely and thoroughly wrong<\/em>, because it’s based on the invalid assumption of an unchanging fitness landscape.<\/p>\n

We can even show why<\/em> the fixed fitness landscape is wrong. Suppose we had a
\nfixed fitness landscape with local maxima. Then we’ll find organisms “climbing” towards
\nthose maxima. And when they reach<\/em> a maximum, they stop moving. What this means is
\nthat we’ll see multiple<\/em> organisms climbing towards the fitness maxima; and over
\ntime we’ll see things clustering around the maxima. With this clustering at the maxima, eventually, there will be competition for resources – meaning that the maximum isn’t a maximum anymore<\/em> – suddenly it’s a hotbed of competition with some<\/em> changes producing winners, and some losers. So the fitness landscape can’t<\/em> be a fixed with true local maximums that become traps.<\/p>\n

What else does he get wrong? As bad as the “fixed landscape” bogosity is, it’s not the worst of his slimy mathematical sloppiness. <\/p>\n

Because, you see, the chances of there being an actual local maximum in an evolutionary fitness landscape is something amazing close to nil. Sure, there are probably some<\/em>, sometimes. But the thing is, “fitness” in the evolutionary sense is really a function of not just one or two variables, but of dozens, or hundreds, or even thousands of variables. We’re not talking about a two-dimensional counter where there are hills and valleys. An evolutionary fitness landscape is a surface with dozens of dimensions. To be a true local maximum – that is, a point in the landscape with no<\/em> smooth upward paths out requires the surface to be at a maximum in all dimensions at the same point<\/em>: it means that if you slice a plane through the surface to get a two-dimensional view, no matter how you orient the plane in those dozens of dimensions, it will always produce a hill shape with the maximum at the same place. Why would all of the dimensions coincide on a maximum like that? If we’re playing probability games – and this argument of his is ultimately probabilistic – then the deadlocking local maxima are incredibly<\/em> improbable – less likely than the things that he’s ruling out as being too<\/em> unlikely.<\/p>\n

And even that isn’t his worst mistake. Suppose you’re looking at evolution as a search
\nover a landscape. So you’ve got an organism at some point in the landscape. To consider
\nwhere it can go in its traversal of the landscape, you need to consider how it can “move”: where can it go in one step from its present location?<\/p>\n

Spetner requires<\/em> that the only<\/em> permissible “motions” are single point changes<\/em> which produce immediate<\/em> effects. He explicitly disallows
\nconsideration of multiple concurrent changes; he disallows consideration of changes that don’t present an immediate<\/em> benefit; he disallows consideration of any change other than single-base changes – no duplications, no rearrangements, no changes of any kind except single-base point mutations. In other words, he deliberately creates a search model that does not match observed reality<\/em>, and then uses it to conclude that his search model cannot match observed reality<\/em>. (Where’s Dr. Egnor when you need him? This is exactly the kind of tautology that Dr. Egnor claims to like to knock down!)<\/p>\n

And even that<\/em> isn’t his worst mistake. If you look at how Spetner formulates the search, he basically treats an evolutionary search as if it’s a single organism<\/em> traversing the fitness landscape. He demands that changes work in a strict stepwise fashion. One<\/em> change happens; that one change<\/em> produces a selective advantage; the selective advantage causes that change to propagate and become fixed in the population; and then the next change can occur. That is not<\/em> an accurate model of reality: reality is a population of many individuals, with many changes happening at the same time – some neutral, some beneficial, some harmful – and those changes accumulate and propagate through the population, with some individuals surviving, and some not. In other words, it’s an even more blatant example of the Egnor error: create a model that does not match observed reality, claim<\/em> that it’s an accurate model of the theory you want to criticize, and then declare triumph when the predictions of your model cannot match reality. <\/p>\n

Pure bogosity. Pure slop. Pure bad math.<\/p>\n","protected":false},"excerpt":{"rendered":"

An astute reader pointed me towards a monstrosity of pompous bogus math. It’s an oldie, but I hadn’t seen it before, and it was just referenced by my old buddy Sal Cordova in a thread on one of the DI blogs. It’s a “debate” posted online by Lee Spetner, in which he rehashes the typical […]<\/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":[31],"tags":[],"class_list":["post-406","post","type-post","status-publish","format-standard","hentry","category-intelligent-design"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-6y","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/406","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=406"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/406\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=406"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}