I know that this is casting pearls before swine, but others reading this may get something out of it even if you refuse to.
It's not either-or, because both processes, selection and accumulation of greater genetic diversity, are happening at the same time. Therefore, we could work out a mathematical function of genetic diversity which incorporates the effects of both selection and the processes that increase genetic diversity such as the accumulation of genetic mutations.
Now refer to your differential calculus in which you examine the rates of change of a function with respect to an independent variable. To illustrate with a simple and intuitive example, you can develop a function of spatial displacement with respect to time, s(t); we would say "s is a function t" or "displacement s is a function of time t". If you differentiate s(t) with respect to t, you get velocity, v(t) = ds / dt. With v(t), you can determine the velocity at any point in time. If you then differentiate v(t), you get acceleration, a(t) = dv / dt.
To put that simplistically (because other factors come into play) into a practical problem, you have a rocket that needs to follow a particular trajectory, the displacement function, s(t), which yields the rocket's location at every point in time. From that trajectory, you can determine what the rocket's velocity has to be at every point in time. From that velocity function, you know how much the rocket will need to be accelerating at every point in time. From that acceleration function, you can determine how much thrust you'll need from the engines. Of course, in real life, differential calculus is often mainly used to solve problems of a more abstractly mathematical nature or to develop mathematical models of observed phenomena. The story is that Newton invented calculus to provide him the language with which to describe what he was observing.
Many functions describing the real world are multi-variant -- ie, instead of having just one independent variable, they have more than one, often several. That changes the problem to needing to determine with variables have more of an effect on the function. For that, we use
partial derivatives:
quote:
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
In short, you successively differentiate the function by each variable, then add up all the partial derivatives to get the
total derivative. The benefit of this evolution {NavySpeak} is that each term in that total derivative tells you how much each variable contributes to the total rate of change.
So returning to our mathematical function of genetic diversity which incorporates the effects of both selection and the processes that increase genetic diversity such as the accumulation of genetic mutations, I think we can safely assume that it is a function with multiple variables, which would make it a prime candidate for partial differentiation. In term, I think we can safely assume that the constituent function for selection also has multiple variables and can itself be decomposed into partial derivatives -- those multiple variables would express selection under different conditions, such as during speciation as opposed to during stasis as opposed to normal tracking of a changing environment. The partial derivative for mutation may well prove to be much simpler and nearly constant.
The bottom line is that the none of the processes involved does turn off or on, but rather each process is at work continually. It is not a simplistic either/or situation, but rather one in which one process contribute more or less than the others under certain circumstances
and, as those circumstances change ever so slightly, then so do the contributions of each process.
It is a complex interplay which can quickly outstrip the human mind's ability to imagine it. The human ability to imagine how something works is very remarkable, albeit limited. My own ability is fairly strong; coupled with my mechanical aptitude, I frequently observe a system in operation and start to analyze how it works. At a multi-day campout which started with the moon being up and spoiling our star-gazing, I visualized in my mind, coupled with some vary basic calculations based on the moon's roughly 28-day orbit, how the moon would be rising about 45 minutes later each night, and thus determined that we would have a good window of opportunity for star-gazing on the last night before the moon could rise and spoil the party.
But our ability to imagine things is limited -- a fact which you have failed to learn in your own failed geological thought experiments. In one of his most misquoted statements, Darwin described the evolution of complex organs such as the eye as being beyond human imagination, but -- he continues, which creationists always leave out in misquoting him -- if you apply reason then we can work out how the eye could have evolved. What follows varies from one edition of
On the Origin of Species to the next, but he works methodically through example after example of visual organs in then-extant species starting with a photo sensitive cell to one connected to a nerve and so on and so. In
The Blind Watchmaker, Richard Dawkins recreated that exercise, I seem to recall in Chapter 3.
Now, for Darwin's work, "reason", let's substitute "math". When I read Dawkins' description of his WEASEL program in Chapter 3, "Accumulating Small Change", of
The Blind Watchmaker, I didn't believe it. So, using his description of it as my specification (he did not provide any source listing and I think it was written in BASIC anyway), I wrote a Pascal program to implement it (since rewritten in C). It worked phenomenally, which still made no sense to me. Even with my maybe-better-than-average ability to imagine a solution in my head, I simply could not understand how Dawkins' WEASEL, now my
MONKEY, so named as an homage to Eddington's perennial misquote:
quote:
... If I let my fingers wander idly over the keys of a typewriter it might happen that my screed made an intelligible sentence. If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favourable than the chance of the molecules returning to one half of the vessel.
(A. S. Eddington. The Nature of the Physical World: The Gifford Lectures, 1927)
The misquote is that creationists (and others) keep misrepresenting it as referring to the probabilities of evolution, whereas in fact he was talking about thermodynamics, as in the probability that the random motion of a gas in a container could ever result in all the molecules having moved to one side of the container -- see
Infinite monkey theorem.
Because I simply could not imagine how my own MONKEY program could produce such results,
I analyzed it mathematically. It was only then that I could finally understand it. Human imagination had failed me completely, but it was mathematics which showed me the truth of what was happening.
Faith, on this point, your imagination has failed you. It is time to turn to reasoning and then to mathematics. Figures don't lie, although liars can figure.
The ultimate solution with WEASEL and MONKEY lies completely in the probability models used.
My apologies, but I am decades out or practice with the academic definitions. Most probability models are based on "this happening AND this happening AND this happening AND ... ". For example, assuming a fair coin (normally impossible since heads is usually ever so slightly heavier) such that heads would have a probability of 0.5 (50%), what is the probability of tossing 10 heads in a row? That would be the product of the probability of each and every independent event, which in this case would be 0.5
10, which would be 0.0009765625 or 9.765625×10
-4. 100 times in a row would be 0.5
10, which would be about 7.89×10
-31. Practically all creationist probability arguments follow this model.
The problem with creationist probability arguments is that they have nothing whatsoever to do with evolution nor with how it works -- the latter being the far stronger argument.
Let's return to that coin toss sequence. One coin, one thumb, one single series of attempts. Now let's look at how evolution would need to work. One population.
Multiple members of that populations, hence multiple parents and multiple sets of progeny. Immediately, we see the typical creationist format providing only one single path, whereas in reality life itself follows multiple parallel paths. So instead of ANDing (Boolean multiplication, BTW) each step, we need to be ORing (Boolean addition, BTW) each step.
I explain all this in my analysis of MONKEY,
MONKEY PROBABILITIES (MPROBS) -- I have been informed of an error therein: in calculating the Markovian chain probabilities for each step of a given scenario, I was off by one iteration. When you open the page, search for "de Morgan Theorem". As part of my training as a computer electronics technician, I was taught
Boolean algebra, which was later supplemented by a university electrical engineering course in logic design. "De-Morganizing" a circuit or Boolean expression was an every-day skill for us.
Here is the section on Wikipedia about the engineering use of de Morgan's Theorem:
https://en.wikipedia.org/wiki/De_Morgan%27s_laws#Engineering. Basically, to de-Morganize a Boolean expression, you invert all the Boolean variables and replace the ANDs with ORs and the ORs with ANDs.
Here is how I applied that to the probability model. Please note that for every probability, P, of something happening, there is also the probability, Q, of it not happening, such that Q = (1.0 - P) -- BTW, probability values range from 0 (absolute impossibility) to 1.0 (absolute certainty).
Now, here is the bottom line from MPROBS and the ultimate reason why both MONKEY and WEASEL succeed so inevitably. For MONKEY to fail, it would require every single parallel path to fail. When we work out the probabilities of that happening, such complete and utter failure is so small as to be deemed "virtually impossible", which by inversion ( P = (1 - Q) ) , renders the probability of success virtually inevitable.
I could not ever have possibly
imagined that outcome! But the mathematics shows it to be virtually inevitable.
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