Should we teach both evolution and religion in school?

You better tell Taq that he is making an error because he thinks that fish evolve into mammals and they are only 4 nodes apart.

I've shown you how to do the mathematics of DNA evolution and even got the results peer-reviewed, published and these papers are in the National Library of Medicine. I've published the mathematics of random recombination, the mathematics for the Kishony and Lenski experiment and I've explained why combination therapy works for the treatment of hiv. Can't any of you halflings do anything for yourselves?

Too bad you can't nail the physics and mathematics of evolution. But if you want, you can explain to us how fish evolve into mammal and reptiles evolve into birds. We need some amusement in this discussion.

If you want to see immediate steps, take a look at the Kishony experiment. Do you want to see those clades again? Here they are:
https://www.youtube.com/watch?v=plVk4NVIUh8
Check out after 1:44 in the video, those are real evolutionary clades showing the immediate steps.And why am I picking out fish? Haven't you ever heard a good fish story? You heard about the one-armed fisherman? Someone asked how big the fish was that he caught. He stuck out his arm and said it was that long.

The mathematical jabs are even more effective. They keep hitting home. Of course, if you think that evolution works differently than the way I've published, feel free to post your mathematical explanation. Explain to us how the Kishony and Lenski experiment works. You won't because you can't.And you should stop indoctrinating naive school children with your mathematically irrational nonsense. You are failing to prepare them to deal with the problems of drug-resistant infections and failed cancer treatments. That is quite harmful.

Read this paper which shows how the multiplication rule of probabilities applies to DNA evolution.
Just a moment...
This paper shows why it takes 3e9 replications for each evolutionary step. Microbes, weeds, and a few other replicators attain the population sizes necessary for a (small) DNA evolutionary process. Check out this link if you want to get an idea of population sizes for different organisms.
Lists of organisms by population - Wikipedia

It's correct if the mutation rate is e-9. And you need to explain why hiv can't evolve in parallel when subject to three selection pressures targeting only two genes. Or are you arguing that combination selection pressures won't work for treating hiv because evolution occurs in parallel? Read this paper if you want to understand what happens when evolution must work in parallel to multiple simultaneous selection pressures:
Just a moment...And selection pressures can target one or more genes and the math still applies. This is why this math works for the Lenski experiment because every gene in every metabolic pathway that requires energy will be acted on by his starvation selection conditions. And beneficial mutations at any one of these genetic loci obey this math. The beneficial mutations don't have to occur in any particular gene, all they have to do is improve reproductive fitness.

You either have not followed or understood my discussion with Taq on the "Do you really understand the mathematics of evolution" topic. If you have 2 possible beneficial mutations, the number of replications required is still over a billion replications. Msg 92 in that thread shows you how to do the probability calculation if you have more than 1 possible beneficial mutation. But what happens after that first beneficial mutation occurs? Are there many beneficial mutations for the next and ensuing evolutionary steps for that selection pressure? The answer is no! Read this paper and find out why.
Darwinian Evolution Can Follow Only Very Few Mutational Paths to Fitter Proteins
The reason why this happens is that whatever evolutionary trajectory has been taken by a lineage, each step on that evolutionary trajectory must give improved reproductive fitness because it takes replications for there to be a reasonable probability of the next beneficial occurring and that is on the order of a billion replications for each evolutionary step for each variant of each lineage on any evolutionary trajectory. The point is that hiv can't traverse any possible evolutionary trajectory to improved fitness in the typical lifetime of a patient taking 3 drug therapy. It takes too many replications for the virus to get the beneficial mutations necessary to occur on a single lineage even though the mutation rate for this virus is on the order of e-5.Another point you are failing to understand is that all lineages on their own particular evolutionary trajectories must accumulate their own particular beneficial mutations. And when those mutations occur at a frequency of e-9, that's going to require about a billion replications for every variant on each evolutionary step no matter which evolutionary trajectory they are on. It is quite likely that there are multiple possible evolutionary trajectories to improved fitness for the Kishony experiment but no matter which trajectory, the variant from that particular lineage on that evolutionary step must still form its colony of about a billion members before the next beneficial mutation has a reasonable probability of occurring. Do you think that the intensity of selection is "hard" in the Kishony and Lenski experiments? It takes only 1 beneficial mutation to give improved fitness in either of these experiments. What "hardens" or makes it more difficult for a population to follow an evolutionary trajectory is the number of mutations required to give improved fitness. That's why the Kishony experiment won't work if the step increase in drug concentration is too large requiring more than a single mutation to give improved fitness. It is the same mathematical situation if Kishony were to use 2 drugs at lower concentrations where some member of the colony in the lower drug concentration region must get two mutations before they are able to grow in the next higher drug-concentration region. The difference between your explanations and my explanations is that I publish my mathematical explanations and they predict the behavior of real evolutionary processes. Hard mathematical science is passing up your vague, unsubstantiated explanations. You just don't know it.

Your clique has no mathematical discipline.

It is not apparent to you and other members of your clique but it is apparent to the peer-reviewers and publishers of my papers and to the librarians at the National Library of Medicine.

So if the number of possible beneficial mutations is X and the probability of one of those beneficial mutations occurring is 0.6, then if there are 2*X possible beneficial mutations then that probability goes to 1.2? It is easy to see why you think that fish evolve into mammals and reptiles evolve into birds. Learn what the difference is between additive and complementary events. You might not make so many mathematical blunders. Of course, thousands of possible beneficial mutations exist to a given selection pressure. But they only exist in your mind. You obviously didn't understand the link to the Weinreich paper about "Darwinian Evolution Can Follow. Only Very Few Mutational Paths to Fitter Proteins" which means you don't know where Weinreich makes a mathematical error in his paper. The only thing that I've learned from our previous interactions is that you don't understand introductory probability theory. How do you think the Lenski experiment will work if he runs the experiment at a non-optimal temperature? In other words, both starvation and thermal stress simultaneously? Do you think you will get the same mutations for adaptation to the thermal stress as you would get for the starvation stress? I get the "transitional" argument made by believers in the fossil record story. The problem with that story is that you can say nothing about the genetics based on gross anatomy. DNA evolution must be measured on the molecular level because that's where these events happen. And the most common erroneous argument made on this subject is that a series of microevolutionary changes add up to a macroevolutionary change. Microevolutionary changes are not linked by the addition rule. Mutations are random events so the joint probability of these events are linked by the multiplication rule. You won't understand this because you don't understand the theorems and axioms of probability theory. You demonstrated that above when you applied the addition rule to complementary events. Really???? So the Lenski experiment has hard selection since variants in his populations go extinct and selection in the Kishony experiment is soft because none of his populations go extinct? Is the use of combination therapy for the treatment of hiv soft selection because you don't drive the population to extinction? The reason you can't quantify selection is that you don't understand how it works. Combine that with the fact that you don't understand introductory probability theory means you have a lot of homework to do if you want to understand the physics and mathematics of evolution.

None of those peer-reviewers were mathematical wizards like you. They didn't know that the number of replications needed for a beneficial mutation to occur was between 1 and an indeterminant amount. Such brilliance on your part. You should publish your findings.You can publish a series of papers. The number of replications required for 2 beneficial mutations to occur is between 2 and 2*an indeterminant amount. Your contribution to society is innumerable (that is the number of drug-resistant infections and failed cancer treatments).

Every replication of every living thing gives a potential transition. That's because mutations occur with replication. If it is a short genome bacteria, then in most cases you will get an exact clone of the parent and no transition is made. With longer genome replicators, you can expect that one or more mutations with each replication so they become transitional forms. But then you have to ask, transitions to what. Is it a transition to just a more divergent form of the parents? Is it a transition to a new species? You can't use the fossil record and gross anatomy to make that determination because gross anatomy tells you nothing about the genetics. Trying to use gross anatomy to describe evolution is like trying to use classical physics to describe quantum mechanics. You have to analyze and understand what is happening on the molecular scale if you want to understand evolution and what it takes for evolutionary transformation. Looking for fossils that fit your theory is not how you explain evolution. You study real, measurable, and repeatable examples of evolution such as the Kishony and Lenski experiments. You measure how many replications it takes to make a transitional evolutionary step. When you do that, you now have some real evidence of how evolution works. Watch this video from the Kishony experiment where they actually draw the clades at the end of the video showing the lines of descent. At 1:44 they draw in the nodes and complete the clades. Each mutation represents a new node (transition).
https://www.youtube.com/watch?v=plVk4NVIUh8
What I've presented is the mathematics which describes those clades (evolutionary trajectories). That is how you do the mathematics of evolution correctly. And note that at each of the nodes is a colony with a huge number of members (billion). The reason for that is with a mutation rate of e-9, you need huge numbers of replications (billions) for the correct transitional form to occur to the environmental selection conditions. This principle applies not only to bacteria but to every replicator including Tiktaalik at each evolutionary transition. That's not correct. My mathematical model is in conflict with your interpretations of reality. My model fits perfectly with real, measurable, and repeatable examples of evolution. You can start with the Kishony and Lenski experiments but try to find any empirical example of evolution that contradicts the math I've presented. You won't, you can only present your interpretation of the fossil record which is in direct contradiction to real examples of evolution. There are lots of unusual life forms and I understand the desire to categorize things. But you can't use gross anatomy to explain evolution. Try sending your photograph into ancestry.com and ask them based on that photo, who you are related to. Actually, I'm simply correctly quantifying Darwinian evolution. I'm doing that by starting with the definition of the mutation rate and deriving the probability of a particular evolutionary trajectory occurring. And surprise, surprise, it predicted the behavior of the Kishony experiment before he ran the experiment. It is you with your misinterpretation of the fossil record that I'm overturning. Do you really have that big of a problem with understanding how DNA evolution actually works? Don't you think it is worthwhile to correctly explain the evolution of drug-resistance and why cancer treatments fail? There may be some people interested in correctly understanding how evolution works since our society must deal with drug-resistant microbes, herbicide-resistant weeds, pesticide-resistant insects, and failed cancer treatments. The rest of you can amuse yourselves by making up stories about fossils and have absolutely no idea how evolution works. Of course, those suffering from drug-resistant infections and failed cancer treatments might not find that so amusing.And it appears that you aren't going to compare my model of DNA evolution with Felsenstein's model and use it to predict the behavior of the Kishony experiment. It's smart that you don't. Felsenstein's model is incorrect.

I totally understand your desire to change the subject since you don't have the mathematical skills or experience to explain the evolutionary transitions of very, very close ancestors. When you learn that, you can tell us how fish evolve into mammals and reptiles evolve into birds.Don't any of the posters on this forum understand introductory probability theory? Because that is what is needed to understand stochastic processes (like DNA evolution).

I have, that's why I don't use the addition rule for complementary events. Only those who don't understand introductory probability theory do that.But if you think you do understand probability theory, explain to us what is wrong with Felsenstein's model of DNA evolution.
F81 model (Felsenstein 1981)
If you think the model is correct, predict the behavior of the Kishony experiment using this model.