The Difference Between Mathematics and Biology?

As part of my daily diet of news sites and blog reading I keep an eye on various creationist websites. This is done partly as opposition research. It's always good to know what the crazy people are getting excited about. But it is also because they frequently link to interesting articles I might have overlooked otherwise.

Over at Uncommon Descent, Denyse O'Leary helpfully linked to this article by Carl Zimmer from the November 10 issue of The New York Times. The article discusses recent developments in genetics, and how hey are changing long-held notions of what a gene is. It's fascinating stuff, but O'Leary seemed especially taken with the following excerpt:

But these exceptions did not seem important enough to cause scientists to question their definitions. “The way biology works is different from mathematics,” said Mark Gerstein, a bioinformatician at Yale. “If you find one counterexample in mathematics, you go back and rethink the definitions. Biology is not like that. One or two counterexamples -- people are willing to deal with that.”

That seems like an odd thing to say.

In mathematics, a counterexample is something that refutes a proposed conjecture. Someone says, “I believe it's true that assumptions A, B and C imply that D is true as well.” A counterexample is then an example in which A, B, and C are all seen to hold, but D is sadly false. Presented with such a counterexample, you conclude merely that your intuition is not yet as finely honed as it might be.

There is a sense in which a counterexample might lead you to rethink your definitions. Presumably you have some concrete scenario in mind, and you are devising an abstract model of it. Typically your understanding of the scenario guides your construction of the model, and that includes the definitions of the basic terms you will be using. If you then discover that things that really ought to be true turn out not to follow from your definitions and assumptions, you might then conclude that these definitions need to be tweaked.

This is not really comparable to the situation in biology, or any other science for that matter. There we have some theory that successfully accounts for a great deal of experimental data. That gives us confidence that our theory represents at least some part of the truth about nature. But since even our best scientific theories are mere approximations of reality, as opposed to perfect descriptions of it, there are always anomalies that are not covered by the theory. But a few anomalies are not going to lead scientists to abandon a theory that has consistently proven itself to be useful in the field and the lab.

That aside, the article makes for fascinating reading. It goes without saying, of course, that O'Leary's description of it is farcically wide of the mark. For example, she writes:

Earlier, I called attention to this longish but very informative article by Carl Zimmer, “Now: The Rest of the Genome” (The New York Times, November 11, 2008). It pretty much blows the genetic reductionism I grew up with out of the water. The “gene” - that little coil of sugar that ran our lives back then - is a dead idea.

In this earlier post she comes to the bizarre conclusion that somehow Lamarck's ideas are being rehabilitated, and that new research makes it unreasonable to talk about “genes for” various traits.

This is all perfectly absurd. As Zimmer notes at the start of his article, in reference to the word “gene:”

The word was coined by the Danish geneticist Wilhelm Johanssen in 1909, to describe whatever it was that parents passed down to their offspring so that they developed the same traits. Johanssen, like other biologists of his generation, had no idea what that invisible factor was. But he thought it would be useful to have a way to describe it.

Given O'Leary's rather outre ideas about body/mind dualism, it is possible she thinks heredity is based on some sort of bizarre, nonmaterial whatizzit that somehow interacts with matter. But as long as we are okay with heredity having some physical basis, the idea of the gene is not going anywhere.

What is dying, or, more correctly, is dead, is the idea of one gene one protein, or the idea that merely knowing the sequence of letters in a person's DNA is enough, if only in principle, to explain their physical form. The idea that a gene is just a stretch of DNA that codes for a protein is no longer adequate. Turns out there are other factors involved in heredity:

But it turns out that the genome is also organized in another way, one that brings into question how important genes are in heredity. Our DNA is studded with millions of proteins and other molecules, which determine which genes can produce transcripts and which cannot. New cells inherit those molecules along with DNA. In other words, heredity can flow through a second channel.

Also interesting is the role evolution is playing in helping scientists understand some of these new findings:

David Haussler, another Encode team member at the University of California, Santa Cruz, agrees with Dr. Birney. “The cell will make RNA and simply throw it away,” he said.

Dr. Haussler bases his argument on evolution. If a segment of DNA encodes some essential molecule, mutations will tend to produce catastrophic damage. Natural selection will weed out most mutants. If a segment of DNA does not do much, however, it can mutate without causing any harm. Over millions of years, an essential piece of DNA will gather few mutations compared with less important ones.

Only about 4 percent of the noncoding DNA in the human genome shows signs of having experienced strong natural selection. Some of those segments may encode RNA molecules that have an important job in the cell. Some of them may contain stretches of DNA that control neighboring genes. Dr. Haussler suspects that most of the rest serve no function.

Go read the whole article. The picture that emerges is the familiar one of scientists gradually devising clearer and clearer pictures of how nature works using current theories as a springboard for further research, as opposed to the last word on the subject.

And off to the side, making noise loud enough to be annoying but not substantive enough to be interesting, are folks like O'Leary, who think that anytime scientists revise some bit of accepted wisdom it is time to argue that the whole edifice is crumbling. She writes, for example:

One thing about this article, it is mercifully free of rubbish about evolution.

We actually don't know what most of the stuff in the genome does. So why not wait until we do know before we begin to describe its history? That will save a lot of rewrites down the road, maybe inconvenient ones.

Apparently she missed the part I quoted above. More to the point, however, is that evolutionary theory, at least in the big picture, actually doesn't care all that much about the precise physical mechanisms of heredity. The difference between “Heredity is governed entirely by DNA,” and “Heredity is governed not just by DNA but also by other physical factors linked to DNA,” is not the difference between “Evolution proceeds largely through the accumulation of small, inherited variations,” and “Evolution is nonsense that must be replaced by the Magic Man theory.”

The old notion of genes mutating, leading to new variations, that are then sifted by natural selection, is not going anywhere. As Zimmer notes, those ideas have been marvelously successful at explaining a great many things. They are simply being supplemented with many new ideas as well. Far from being harmful to evolution, these sorts of discoveries are a great boon. They show that scientists have been needlessly limiting themselves in the sorts of explanations open to them in explaining the evolutionary process.


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When dealing with O'Leary, it is good to keep in mind that she is to writing, what Sarah Palin is to speaking...

Hey Typo McTyperson: The Difference Between Mathemaitcs and Biology?

Unless you are inventing a new word, mathemaitcs.

You can delete this when you fix it.


It seems to me that one of what creationists saw as their strengths was that if evolution was governed by undirected mutation, it didn't explain the clear indications of design in the process - thereby giving them an opening to insert their deities into the mix. But if it's beginning to look like life forms have found ways to manipulate their own evolutionary changes, the creationists would have to see that as a setback. So this sort of deliberate misinterpretation of new findings would continue to be a priority.

What would be the consequences if some of these "genetic side-channels" (ie non-DNA-based heredity) featured blending rather than discrete inheritance?

The difference between Mathematics and any of the Natural Sciences, surely?

It's a bit depressing
1. when this is news (to IDers), and
2. it is thought to apply only to Biology, as if it were somehow different to the other sciences.

The difference is the inherent uncertainty of evidence in biology (or any other science), as opposed to that in mathematics.

Interesting that I commented on the very same O'Leary post at Pharyngula, where I cited it in agreement with PZ's thought that UD is no longer even provocative enough to be interesting.

Same old, same old - as you say, the UD folks once again find some new discovery (or an article about old knowledge that they *think* is a new discovery) and misinterpret it as "Evolution is in its death throes!" I recall a DaveScot post about another Zimmer article (one concerning Tiktaalik), and another DS gem re horizontal gene transfer among bacteria as being particularly mind-boggling. (E.g., the horizontal gene transfer post said a "Tree of Life" and thus evolution had been proved impossible. Buried under a ton of pseudo-erudite verbiage, the simple but nevertheless lame point was that a tree's branches never reattach to each other or the main trunk, and this reattachment to a branch or trunk was what horizontal gene transfer did. In other words, DaveScot was contending that showing some inadequacy in an inexact metaphor (Tree of Life) was the death of the thing (evolutionary theory) itself.)

Cdesign proponentsist said:
"little coil of sugar"


Since when does sugar have phosphorus, nitrogen, double helix structure......?

Here's a question. Does anyone here ever comment over at Uncommon Descent? I tried a couple times under a couple names, endeavoring as best I might to be more polite every time, and all my comments were moderated out. I swear, I was trying to start small with my arguments - keep the kid gloves on.

Do I wear a bad deodorant, or are they simply unwilling to engage in serious debate with people who can actually respond in real time? I know it's easier to argue with an article that can't talk back, but come ON. Some of them have PhDs and I don't. They didn't teach you how to shut down an undergrad at Creationist U?

Why is the evidence for the Bible so quickly swept under the rug? What about kings who were named by name 200 years before they were even born (Isaiah 45). Psalm 22 says they have pierced My hands and My feet. This was 800 years before crucifixion was even practiced and 1100 years before Christ came to earth. The mathematical odds for Jesus to fulfill 7 prophecies (keep in mind He fulfilled hundreds) would be the same odds as you covering the entire earth in 4inchX4inch white tiles, with a gold star hidden underneath only one tile, and you walking up on the very 1st try and finding it. Oh by the way you are blindfolded! Now you may say well that is impossible, can you imagine what the odds are for Jesus to fulfill all the prophecies He did?! They are astronomical, they cannot be fathomed. Only God knows perfectly the future and has shown that He certainly knows by predicting with pin point accuracy events well into the future. 1/4 of the Bible is prophetic and of all the prophecies that have to do with past events all have come true. not one of them has failed. God's Word has a 100% track record when it comes to pronouncing what will take place. How can one disbelieve when there is that much evidence??

I am God and there is no other, I am God and there is no one like Me. Declaring the end from the beginning, and from ancient times things which have not been done.
Isaiah 46:9-10

Chris. you're a dumbass if you think the Bible is historically accurate.
a couple of lessons for you:

Posted by: Blake Stacey | November 20, 2008 10:31 AM

The Book of Daniel is the one which confuses Rome with Cyprus [Chittim], and which erroneously states that Belshazzar was the son of Nebuchadnezzar, when he was actually the son of Nabonidus, no relation. In fact, the very first verse in Daniel is an anachronism Jehoiakim was not king in Jerusalem when Nebuchadnezzar came to power in Babylon. I dont think we have to worry about its prophetic value when it cant get history right.

Its extremely probable that Daniel was written circa 165 BCE. Parts of it are written in Aramaic, which points to a late date of composition, when Aramaic was widely spoken; references to earlier times are vague or just wrong, suggesting that the writer was working with a loose grasp of history, but knew his more recent past much better (as is only natural).

Ezekiel doesnt really have a good track record, either. In chapter 29, he predicts that Egypt will be destroyed, which didnt happen.

29:9 And the land of Egypt shall be desolate and waste; and they shall know that I am the LORD: because he hath said, The river is mine, and I have made it.
29:10 Behold, therefore I am against thee, and against thy rivers, and I will make the land of Egypt utterly waste and desolate, from the tower of Syene even unto the border of Ethiopia.

29:11 No foot of man shall pass through it, nor foot of beast shall pass through it, neither shall it be inhabited forty years.

29:12 And I will make the land of Egypt desolate in the midst of the countries that are desolate, and her cities among the cities that are laid waste shall be desolate forty years: and I will scatter the Egyptians among the nations, and will disperse them through the countries.

29:13 Yet thus saith the Lord GOD; At the end of forty years will I gather the Egyptians from the people whither they were scattered:

29:14 And I will bring again the captivity of Egypt, and will cause them to return into the land of Pathros, into the land of their habitation; and they shall be there a base kingdom.

Yadda, yadda. Suffice to say that there has never been a forty-year period in which Egypt was an uninhabitable wasteland.

While were at it:

Nebuchadnezzar did lay siege to Tyre for thirteen years, but he failed to sack the city. After thirteen years, the Tyreans under Ithobaal II worked out a compromise treaty and got off with paying Nebuchadnezzar tribute. Alexander the Great managed to conquer the city centuries later, but he was too busy conquering the rest of the known world to bother destroying it utterly. After his death, his former general Antigonus, founder of the Antigonid Dynasty, had to besiege and conquer Tyre again in 315 BCE.

St. Paul spent a week in Tyre after visiting Cyprus on his third missionary journey (Acts 21:3). Crusaders captured Tyre in the 1100s and held a few coronations there; the PLO used it as a military base in the 1980s; etc., etc.

That was ALL Blakes comments, another guy chimed in as well:

Posted by: Tim H | November 20, 2008 11:42 AM

Hey guys, i was wondering if you could destroy this for me; it was written by some evangelical wingnut named phillysoul (sorry about the length):
-Historical Accuracy-
Sir William Ramsey (one of the most eminent authorities on geography and history of ancient Asia Minor) with much skepticism undertook an extensive research of the Gospel of Luke and acts later stated, I take the view that Lukes history is unsurpassed in regard to its trustworthinessyou may press the words of Luke in a degree beyond any other historians and they stand the keenest scrutiny and the hardest treatment.

Luke isnt historically accurate.

Lets look at the nativity story in chapters 1 & 2.
John the Baptist is conceived when Herod (presumably the Great, but maybe not) is king of Judea. Jesus is conceived about 5 1/2 months later. Jesus is born in Bethlehem due to the Census ordered by Rome. We will assume a normal 9 month gestation period for Jesus.

The first census in Judea was taked about 8 years AFTER the death of Herod the Great, and AFTER the death or deposition by Rome of his successor. Herod and his successor were cient kings. Rome set up client kings to have cooperative border states that they themselves wouldnt have to manage. Client kings kept the peace, followed Roman foriegn policy and paid some tribute in return for Roman support and internal freedom of action. Rome not only would not take a census in a client kingdom, they had no right to.
It was the failure of Herod the Greats succesor to rule effectively that prompted Rome to kick him out and take over Judea directly. (They attached it to Syria.) Thats when and why they took a census.
Not to mention the census method described in Luke is brain-dead, and the Romans werent brain-dead on administrative matters.


Excuse me if I preach to the choir a little presenting my take on Mark Gerstein's remark that you quote. (I haven't time to track down my NYT registration to read the full piece or O'Leary's take on it, so I'm working from what you have presented.)

Regards what Mark (Gerstein) said, I would consider who he is talking to and for. Isn't he talking to a journalist and for a general audience?

If so, he is probably presenting it within Joe Public's view of mathematics as something rigourous, where one thing wrong in an "equation", forces you to revise it.

Leaving aside "inherent uncertainty" of biological data (which to me is another way of saying "complex" or "approximate") and that we have to accept theories as imperfect explanations, the point Mark is probably trying to make is that a few outright exceptions to any rule in biology are to be expected and tolerated. This, preaching to the choir here!, follows from seeing that "evolution is a tinkerer" (to quote Francois Jacob). The "universal" genetic code is an easy example. (The nature of this tolerance of exceptions will change if you drop to the level of "strict" biophysics and biochemistry, as the rules of physics and chemistry come in to play.)

O'Leary trying to rark up Lamarckism is par for her course. Her trying to say that people should "understand the genome" first sounds a little like a reworked version of confusing that evolution occurs being very widely accepted with debates concerning the precise details of how it occurs (as is commonly seen with creationists).

Footnote: interestingly the new update of scienceblogs doesn't like some unicode characters by the looks of it. (I'm having to use a plain 'c' in Francois.)

By Heraclides (not verified) on 17 Jan 2009 #permalink