OK ok, let's go over the answer. I'll show you how there can be resolution between our two stances. The key here you needed to argue was the definitions of start and end points. The examples that I used specifically manipulated these two points, starting with a population, and making my end point all subsets of that population that are able to survive a filter. My end point ensures that 100% of the resulting subset survives, based on the definition of the filter, in a self-fulfilling manner. You were very close when you used the word "constrained", because that's how the examples were setup.
Contrast that to analyzing the PATH, and not the end result, in ways to get through the filter. Such an example would show that random mutations can take a number of random paths to get through. An example to support your idea would be placing a "filter" on answers to a simple math equation, only allowing for answers that total 10. A myriad of random combinations could achieve that: 5+5, 14-4, 100/10, etc etc. So even if the numbers are randomly generated, and the sign is randomly generated, a ton of random equations can be generated that pass the filter.
So you see you WERE partially right, if you adjust your start and end points. The problem in your reasoning, though, really does come back to application of the math. In the case of evolution, you didn't understand that the outcomes of one filter are the reactants for the next, completely educing the "random" aspect of how it got there in the first place: it doesn't matter. In other words, all the randomly generated equations that achieve an outcome of 10 don't matter once that 10 goes on to be used in a subsequent equation. You were busy looking at the reactants that made it through the filter, and claiming they are random, which they appear to be. But the real focus should have been the products, which are all exactly the same.
That's essentially how evolution works. It randomly generates solutions to an environmental challenge in a directed and constrained manner. While it's easy to claim the examples and filters I'm using are self-fulfilling non-random endpoints based on an intelligent/unnatural/conscious construct, the fact remains that natural selection ALSO produces self-fulfilling non-random endpoints without having anything to do with terms such as intelligence, naturalness, or consciousness. That's why evolution only helps and never hurts survival/reproduction in a given environment, whereas mutation alone can create any outcome. In the simplest example, antibiotic resistance, the "constraints" are black and white. In most settings however, they are not so tightly bound, but they are constraints nonetheless.
At that point, we get into a philosophical discussion of what technically defines "randomness". It's funny that the one link you did provide, a wikipedia article on that word, starts with the following line:
Wikipedia said:
Randomness has somewhat disparate meanings as used in several different fields.
which brings me back to my original point: while math is universal, not all terms can be applied across all fields equally.
You're pretty smart. You just need to lose to tude until you understand the underlying concepts instead of just spitting back the words.
Here is the problem as I see it.
You are looking at the result, and claiming that is a filter. If we pace a filter in the equation, which is possible in mathematics, than will change the results, but it will not change any other part of the equation. That is why I say that randomness cannot be removed from the result of an equation simply by filtering, because the filter is actually part of the equation.
If we were to write an equation that described evolution we would have to include a lot of factors, and I have no idea how many so please do not try to get me to attempt to define them. We both agree that mutations themselves are random, and I think we both agree that a lot of the environmental factors are random.
We also agree that there are various factors that filter the results. Where we digress is understanding how those filters work. You believe that they take the results of the equation and choose among them. Hence your examples of the different ways to get a particular answer, like 10.
That is not how they work. The filters are actually part of the equation/ A good example of this are formulas to generate psudo-random numbers. All those formulas return a result between 0 and 1 when unfiltered, but the simple application of a filter can change the range of results to fall between desired extremes.
You are arguing that natural selection filters the results of the equation, and selects for a specific result. In order for natural selection to work as a filter it has to be part of the equation, and constrain the range of the possible results.
Note: I believe that, as popularly used, natural selection is actually the result, not a filter that is part of the equation. This is actually what you are arguing, as far as I can see. The result of evolution through natural selection is nothing more what survives. It is not a selection for the stongest, or fastest, or even the smartest (though all of those factors contribute.) Ultimately, it comes down to the luckiest, which explains why we are around instead of highly intelligent relatives of the dinosaurs. That meteor strike killed them, and our ancestors survived.
If we take a large enough sample of any random event it will eventually be susceptible to statistical analysis. This often leads people to think that because these events are predictable, they are not random. thinking like this keeps places like Las Vegas and Atlantic city in business. People think that just because a quarter has come up heads 10 times in a row that it is more likely to come up tails on the next flip. The reality is that the coin has the exact same chance of coming up heads as it does tails, but it will average out in the long run.
There is plenty of evidence piling up that evolution is more constrained than we first believed, and some are even arguing that if we reset the evolutionary clock we would end up with the same result. Personally, I think that what is happening is that we are discovering that DNA is not as flexible as we thought it was.
The randomness of evolution is constrained by a number of different factors, including the fact that a chicken cannot lay an egg that will hatch an eagle. (Theoretically possible through intervention by man, but you know what I mean.) Natural selection, properly applied, can filter those results, but it cannot select for a specific result.
Let me see if I can explain this using rolls of dice. The possible results from rolling two dice vary from 2 to 12. If we arbitrarily define survival from that rang as being 4 or above, and then further reject results below 7 at the rate of 75% for 4, 50% for 5, and 25% for 6 we will have a different weighting for those numbers than we would if we did not do this, but the results will still be both random, and statistically predictable. (I could take the time to work out the numbers, but as I am pulling this example out of thin air I prefer not to.)
This is how natural selection works in reality, it weighs the results so that they favor not just survival, but a general, and slow, improvement in the results. It does not select specific results, it works to weigh the odds in favor instead of against. That is why I understand that evolution is random, and also have no problem with it selecting improvements.
I also understand that evolution is just as likely to deselect those improvements if conditions vary enough. I used to think that fish in caves de-evolved eyes and went backwards on the evolutionary scale. I now understand that evolution does not work that way, and that those fish actually evolved so that they no longer need eyes to navigate their environment. Yet fish deep in the ocean, who also never see light, have evolved ways of generating their own light to see by.
Both of these are quite normal, for evolution. I have a personal preference for sight, but those blind fish do not need it.