Tuesday, August 9, 2011

Why naming an axiom may seem pompous but is not

My friend Joe, a biology professor at a US public university, gave me some great feedbacks after I emailed him my essay “The second axiom of construction and the second axiom of biology” as posted here on July 9, 2011. Below, I post his email feedbacks and my responses, which deal with axioms and the random nature of natural selection.

My essay: “The Second Axiom of Construction and the Second Axiom of Biology posit that any system can allow a certain degree of random noises or errors in its building blocks, and such limited degree of random errors may confer zero, negative, or positive values to the functioning/survival of the system under certain random environmental circumstances.

This axiom underlies the whole of the modern evolution theory composed of Neo-Darwinism and Kimura’s Neutral theory and is the foundation for microevolution and population genetics where there is no change in system complexity over time. (In contrast, the First Axiom of Biology is the foundation for macroevolution where there is change in system complexity over time.)”

Joe’s comments: “This is true, but I fail to see why you are trying to put a name to it. This is a given, known to everyone. The concept that any system has a certain amount of tolerance for noise is an accepted concept for any endeavor or study. The only thing people would argue about with this is how much tolerance any particular system has under what conditions. Calling it the “Second Axiom of Construction” is just going to make you sound pompous and aggrandizing unless you are just using them to basically abbreviate a later discussion by listing a few basic concepts accepted by everyone and showing how they apply to the main point. Besides, I expect engineers have already put a name to this concept long ago.”

My response: Your reaction is absolutely natural. My wife, a PhD biologist, strongly urged me not to use the word axiom in my university websites and grant applications. She thinks that people will not take it well, if only for psychological reasons. I fully recognize this type of concerns. I wish there is a way out of it. The reason I put a name like axiom to it is pretty sound. First, it is a given, known to everyone, as you correctly said. But that is precisely what an axiom is, a self-evident truth that everyone can see. There is always a straight line connecting two dots, which is Euclid's first axiom. Second, just because every one can see it does not mean it is unnecessary to formally make it a law or axiom. It is only when a self evident idea is being actually utilized to describe nature in a scientific way, it is formally recognized as a law or axiom. So, putting a name to such an idea marks the beginning of a branch of science. There are many other self-evident ideas yet to be incorporated into science and hence yet to be called an axiom. An axiom may be obvious to everyone but its specific connection to a branch of science is not obvious before it is made (even though it is always obvious in hindsight). Thus, the inventor of an axiom always deserves credit for making such a connection, which may seem trivial but is really not and takes a rare kind of creativity. Third, I expect as you did that people in the past should have already put a name to both the first and second axiom of construction as in my nomenclature. But as far as I know no one did in the past 5000 years of human history. This is not unexpected however because the scientific value of such axioms is not evident until one has an appreciation for DNA as the building blocks of life, which of course only becomes possible in the last 60 years.

So here is something I would like to hear your suggestions. How to avoid being perceived as pompous and aggrandizing when it is really a purely scientific practice to call some self evident idea an axiom, which is merely meant to be an abbreviation for a concept, or as you correctly pointed out: I am “just using them to basically abbreviate a later discussion by listing a few basic concepts accepted by everyone and showing how they apply to the main point.” One may try to use intuition in place of axiom. But while that may avoid being viewed as pompous, it is against the standard practice in science since the time of Euclid all the way to Newton and to today. Even some philosophers like Spinoza used the word axioms to label their ideas in order to make them more law like or science like. In the last analysis, truth/history and I could care less if I appear grandiose or over confident so long I am right. To some people, one will always be perceived as grandiose the moment he is suggesting that he has better ideas than someone like Darwin. Being mis-perceived by some in the beginning is always a part of the package of striving to be a revolutionary.

My essay: “For the neutral errors that confer zero values to the functioning/survival of the system under a certain random environmental circumstance, the accumulation of such errors is determined by random drift and linearly related to time, as described by Kimura’s neutral theory. For the non-neutral errors that confer either negative or positive survival values, the survival values are dependent on the environmental circumstances, which are and can only be random in nature. Thus, the accumulation of non-neutral errors is determined by random natural selection by random environmental circumstances. Since natural selection is overall a completely random process (see my post on April 9, 2009 and other posts on the random nature of natural selection), the fixation of non-neutral mutations by natural selection is effectively no different from that of neutral mutations and is therefore also linearly related to time given long enough time that allows for multiple rounds of selection and de-selection.”

Joe’s comments: “As long as you are saying that you are discussing long term responses and can’t predict a priori how the environment may change and drive specific natural selections, you may be able to get away with saying natural selection is random, but once the parameters are set, natural selection is the antithesis of random. It is very much a directed responses and not a random process from that point. Probabilistic yes, but not random. The two are very different. You need to make sure you are clarifying your proper frame of reference for this assertion.”

My response: You are right to say natural selection the process is not random. You are also right to say that if one cannot predict the environment, then natural selection is random. I have written several entries in my blog to argue why one should call natural selection random. The key point here is that a non-random process does not guarantee a non-random outcome. In evolution, what really matters is the cause and the effect. If the cause is random, then the effect is random, regardless whether the process from cause to effect is random or not. For example, a mutation event in a gene at the level of DNA is random. However, the biochemical process from this mutation to the manifestation/expression of mutant protein/phenotype is not random. And yet, we always call the mutant phenotype (the final outcome following the random mutation in the beginning) randomly caused. In the same way, the outcome of natural selection is always random because the environmental change in nature is always random. It is helpful to contrast natural selection (NS) with artificial selection (AS). The environmental change in artificial selection is not random, and hence the outcome of it is not random. If you call NS non-random, then what are you going to call AS? NS and AS are complete opposites. To say natural selection the process is not random is not wrong but is a trivial and irrelevant truth to say because the end result is what we care. To say NS is non-random must exclude the environmental change in the concept of NS, but then NS is no different from AS. But everyone understands that NS is different from AS, and that difference lies strictly in whether the environmental change is random or intentional. So calling NS non-random is flawed even from a purely logical or linguistic point of view and is guilty of sophism or disguised displacement of concept.

In fact, the random drift process per se, which led to the fixation of neutral variations, is in fact not random in the same way that NS the process is not random. Imagine a fraction of population randomly drifted into a new geographic location and then an earthquake killed all of the individuals in the old location. The genotypes that survived in this case would be a result of random drift rather than natural selection. However, the dying process per se of the individuals located in the earthquake zone, from earthquake to the death of individuals, which may involve bleeding to death, crushing to death, etc, is anything but random or fully predictable. So, this example illustrates that even random drift of neutral variations may involve a non-random process. Thus, calling natural selection non-random because natural selection the process is not random should equally justify calling random drift non-random. The bottom line is that both the results of natural selection and random drift are random because the environmental changes are always random.

Joe’s comments: “I disagree anyway. If this was true, that there is no difference between neutral and selected mutations, the neutral theory would work just fine. Positive mutations have a chance of increasing, but negative mutations will by necessity be eliminated over time unless they are in some way tied to a positive mutation that has a contribution that outweighs the negative. Thus, negative mutations will decrease over time while positive ones will increase on average. Because they have different vectors, they can’t be random even if they are not determinant, but probabilistic. Moreover there is plenty of evidence that mutation rates are neither random nor clocklike. Several other studies have found mutation rates in E. coli increasing in response to high selective pressure, and if I am not mistaken, even the locations of such mutations are not necessarily random. Now over the long haul, what may be a positive trait now may be a negative trait later as the environment changes, but it is unlikely that this can be an across the board assumption. Some traits are going to be positive in almost every situation, while some negative traits will be negative no matter where you put them.”

My response: It is true that mutation rates may vary depending on environmental selections. But the positive and negative selections cancel each other out so that the average mutation rate would be similar to the mutation rate under neutral selections. I agree with you that "Now over the long haul, what may be a positive trait now may be a negative trait later as the environment changes, but it is unlikely that this can be an across the board assumption. Some traits are going to be positive in almost every situation, while some negative traits will be negative no matter where you put them." However, I think that such traits that are positive in almost every situation is extremely rare. They would have little impact on the clock like divergence which is contributed or determined by the average mutations that are more abundant and can be either positive or negative depending on environments. In fact I can’t think of any traits that are always positive. The Chinese yin-yang philosophy, which I believe is fundamentally correct, says that every fundamental trait has opposites yin and yang which are never absolute and neither can exist without the other. Too much of goodness is bad and too much badness is good. Is being rich always good? Absolutely not. Is being top of the class in school always good? Absolutely not. Is being at the top of the food chain always good? No. Is being at the bottom always bad? No.

So, in sum, if we correctly view natural selection as random, then most fixed mutations that contribute to genetic distance are randomly fixed, regardless whether the process is by random drift or natural selection (both of which may involve a non-random process). Thus they in turn should behave like a clock, which is what we actually observe. We can test this by performing two divergence experiments, one by artificial selection and one by natural selection. The prediction would be that within a fixed time, AS should produce a large genetic distance while NS would not.

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