Should we teach both evolution and religion in school?

That's not at all what I'm saying. Every mutation and variant represents a transition. But a transition to what? What the Kishony and Lenski experiments demonstrate how these transitions work and how many replications are necessary to accumulate a specific set of mutations to increase fitness in a particular environment. Certainly, other mutations are occurring in their populations and those variants on different evolutionary trajectories. Those variants on those trajectories are not improving fitness to the given environment, that is they are drifting. So Tiktaalik is a transitional form but transitioning to what? Most likely, it is transitioning to another Tiktaalik but it might be transitioning to a mutant variant of a Tikaalik. But if you think it is transitioning to another species, for a mutation rate of e-9, it's going to take 3e9 replications of each variant on that evolutionary trajectory for each evolutionary step to that different species. It is no different than the way the Kishony and Lenski populations accumulate their particular mutations. I'm telling you how many replications are required for each transitional (mutational) step on that evolutionary trajectory. And this math correlates with the empirical evidence and is derived based on first principles. The math is not that difficult. Start with the definition of mutation rate and then do the probability calculation of at least one occurrence of a particular mutation. That's exactly how DNA evolution works and that's why it correctly predicts the behavior of the Kishony and Lenski experiments. I'm telling you with mathematical precision how likely a transitional step is to occur. Do you understand why it takes a billion replications for each transitional step in the Kishony experiment? Do you think that in a couple of replications Tiktaalik is going to transition into a tetrapod? Tell us how many replications of Tiktaalik will be needed to transform it into a tetrapod. Make sure you show your math. Prove to us you are not one of those who say, "given enough time, anything can happen".

The closest node to mammals is Amniota: Fish are much more distant. Mammals evolved from reptile-like ancestors, also known as Synampsids:Synapsida

So you agree, fish evolve into mammals. And it only takes 4 evolutionary transitions. Did recombination do it?

Well gosh, you found something on the web, great evidence! Peer reviewed, documented, and everything.Everyone can see that your "evidence" DOES NOT show mammals evolving from fish. Of course not. You just demonstrated that you will continue telling porkeys about how evolution works. I think I will just point out your mistakes.Now that I have pointed out one of your errors in what biologists think about the phylogeny of vertebrates, what is your hypothesis where mammals and birds came from?

It's self-contradictory statements like that which make us wonder if you understand what you are talking about. That is why we have to ask you what you understand about the "multiplicative rule" and how it is to be applied.Yet you do everything you can to avoid answering our questions. As if you are unable to answer them. As if you truly do not know what you are talking about.OK, little man, let's put that same question this third way (since the first two simple questions went completely over your little head: That question is key to your repeated claims.For a superior mathematical genius such as you claim to be (or rather crow incessantly about being), that should be a very easy question to answer. But if you are nothing but an imposter and a poser, then you will of course dodge the question yet again.

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?

You nailed it :-)

The step just before mammals was synapsids which were reptile-like. Usually when someone says A evolved into B they are asking about the immediate steps. Do mammals have fish ancestors? Yes. Mammals also have reptile-like ancestors, amphibian-like ancestors, jawless vertebrate ancestors, and single celled eukaryotic ancestors. Why are you picking fish out of that list?

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.

Message 143We do need amusement, but lets respect each other enough to keep our verbal jabs playful rather than caustic.
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Yes, you have and all of your colleagues have ignored you. Why?Such a fantastic revelation as you think you provide that could revolutionize entire fields of study remains unrecognized, discarded, by the thousands of really smart people whose life's work is to study and master this stuff. Why?There is an answer to these questions.We've seen this kind of phenomenon here before. In other forums we have seen this same phenomenon in the field of physics. The one lone genius who holds the key to overthrowing general relativity or evolution. I imagine such haunts every field.You're a crack pot, Kleinmen, to be ignored hoping you'll go away.Edited by AZPaul3, : No reason given.

Kleinman’s verbal jabs are a tactic. Along with the evasion and the misdirection. At some level he knows his arguments are no good - that’s why he’s so reluctant to spell them out.

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.