Should we teach both evolution and religion in school?

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Try reading the rest of the line that you snipped off.
"It's a fact, Jack. DNA evolutionary changes are random events and if you understand introductory probability theory, joint random events don't add, you have to multiply their probabilities." And if you understood introductory probability theory, you would see the reason to think so.

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No, you wouldn’t. Not if you understood introductory probability theory. The fact that you are looking at events in hindsight does make a difference. You cannot just consider what did happen, you have to be prepared to consider other events that might have happened and did not.

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Not when it comes to understanding DNA evolution. The only variables necessary to compute the probability of a particular mutation occurring are the mutation rate and the number of replications of that variant. What other unknowns are swirling around in your imagination?

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Aside from the fact that finding the particular mutations in question and identifying the number of replications available are not trivial problems? You have to identify other beneficial mutations that could have occurred and did not. You have to identify which alternate sequences of the same mutations would work, And you have to take into account those populations - of all species - which did not get the beneficial mutations.It’s easy to get low probabilities from sequences of events. By making the sequence long enough you can get arbitrarily low probabilities. If you are defining the sequence in advance that is not a problem, but if you are looking at the sequence in hindsight it is usually a far more difficult problem. Consider the lottery. The probability that a particular person will win is low - if you can predict the winner, that would be impressive. But in hindsight - in the absence of other information that makes the win significant - the relevant probability would be the probability that someone wins the lottery, which is far higher. If you try extending that to sequences of wins in hindsight, the relevant probability becomes the probability of getting at least that many winners. If you multiply the probabilities of the particular winners winning or even the probability of the exact sequence of wins versus nobody winning you can get low probabilities but they aren’t worth anything.

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Do you think that mutations are not random events? This is really a simple binomial probability problem, does the mutation occur or does the mutation not occur.

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Because you are looking in hindsight the problem is more complex. You should know that.

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Really? Blunder again? I've put down the math for you line by line. Where's the blunder? Are you going to argue that mutations are not random events? Because if you do, that's your first obvious blunder very early in this discussion.

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It seems so. You’ve made the elementary error of failing to consider the differences between an a priori calculation and one made in hindsight.Edited by PaulK, : Tidy up

The other analogy I quite like is when you tell someone that you can guarantee doing something which has a 1 in 8.0658175e+67 chance of occurring. And then you shuffle a deck of cards.

That is not what I am doing. In fact, I published the governing equations for the Kishony experiment before Kishony ran his experiment. And when you say something like this makes me think that you do not understand introductory probability theory. What you can't do with probability theory is to predict the outcome from any random trial. What you can do with probability theory is to predict the frequency of outcomes if you do the random trial many times, that is if you formulate your probability problem correctly. So far, you haven't demonstrated that capability. You are confusing two concepts. Those two concepts are the governing mathematical laws of a physical process and the physical properties of the real world. Here's an analogy that might help you understand where you are confused on this point. I can use Newton's 2nd law to predict the stresses in a beam carrying a load but I can't predict when the beam will fail without experimentally measuring the properties of the particular material I use to make that beam. In the same way, I can't predict the number of possible beneficial mutations will exist for a particular evolutionary process, but I can predict the number of replications necessary for there to be a reasonable probability of a lineage to take any evolution trajectory to improved fitness for any number possible beneficial mutations. I can do this in the same way as using Newton's 2nd law on a beam. If you say you want to carry a load X on that beam, I can tell you to find a material with a yield stress point greater than Y if you don't want that beam to fail whether that material exists or not. I'm not defining anything in advance. No matter what drug Kishony uses in his experiment, it always works the same way. The reason is when you have a highly asymmetric binomial probability process such as DNA evolution, it's going to take a lot of random trials before you get the successful outcome (mutation) that improves fitness. The only difference between DNA evolution and a coin-tossing problem is your frequency of success. Your probability of calling the correct toss of a coin in a single toss is 0.5. Your probability of getting a beneficial mutation in a single replication is the (beneficial) mutation rate. You really aren't as good at this math as you think you are. You are looking at this problem with blindsight. Why do you think the Kishony experiment works the same way no matter which drug is used? Do you think that bacteria are saying to themselves, "Hey, we saw it work this way in the last experiment, we better do it the same way in this experiment". DNA evolution works with low frequencies of success per random trial (replication). That's because DNA replication works with very high fidelity. Then when you factor in that you must multiply the individual probabilities of success to compute the joint probability of multiple beneficial mutations occurring, it becomes clear why you need large number of random trials (replications) for each evolutionary transitional step. You just don't want to accept this fundamental fact of life for this stochastic process. That's how drug-resistance evolves, that's how cancer treatments fail, that's how the Lenski experiment works, that's how all examples of DNA evolution work. I wrote the paper which predicted the behavior of the Kishony experiment before Kishony performed his experiment. You could have as well if you actually understood introductory theory. But you don't.

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That is not what I am doing

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If you are going to predict that macroevolution cannot happen the calculation will work out much the same except you have to work out future conditions instead of past conditions.

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In fact, I published the governing equations for the Kishony experiment before Kishony ran his experiment

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Even if that is true, it is hardly the same issue. A very simple and very special case that can’t be generalised to all evolution.

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And when you say something like this makes me think that you do not understand introductory probability theory

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Which is more evidence that you don’t. You won’t get a useful number just by multiplying probabilities.

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You are confusing two concepts. Those two concepts are the governing mathematical laws of a physical process and the physical properties of the real world.

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Not at all. You can derive equations but without the numbers you can’t apply them.

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In the same way, I can't predict the number of possible beneficial mutations will exist for a particular evolutionary process, but I can predict the number of replications necessary for there to be a reasonable probability of a lineage to take any evolution trajectory to improved fitness for any number possible beneficial mutations

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Maybe you can do that for a particular trajectory - where the trajectory is defined by the sequence of beneficial mutations. But you still have to know how many trajectories are possible and how many populations fail to successfully follow any trajectory.Simply multiplying probabilities is not nearly enough.

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The only difference between DNA evolution and a coin-tossing problem is your frequency of success. Your probability of calling the correct toss of a coin in a single toss is 0.5. Your probability of getting a beneficial mutation in a single replication is the (beneficial) mutation rate. You really aren't as good at this math as you think you are.

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The beneficial mutation rate will be variable, depending on conditions. For instance the mutations in the Kishony experiment are beneficial because of the presence of the antibiotic. So good luck working it out.It’s looking as if this is just a rephrasing of your assertion that it will take too many replications. But writing the same argument in different terminology really does nothing to help you.

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You are looking at this problem with blindsight. Why do you think the Kishony experiment works the same way no matter which drug is used?

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Because antibiotic resistance typically requires a very narrow set of mutations and resistance to the higher doses tends to require a sequence of such mutations. And because the drug is fatal to non-resistant bacteria. The conditions do matter.

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Then when you factor in that you must multiply the individual probabilities of success to compute the joint probability of multiple beneficial mutations occurring, it becomes clear why you need large number of random trials (replications) for each evolutionary transitional step.

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Which still requires knowing the numbers. You can come up with equations but conclusions are going to require numbers.

I'm giving you the correct mathematics for a series of microevolutionary changes to occur. And the probabilities of these joint events occurring don't add, you must multiply these probabilities. That's why it takes on the order of a billion replications (of the particular variant) for each evolutionary step in the Kishony experiment, the Lenski experiment, for any DNA evolutionary process where the mutation rate is e-9. That's how you correctly do the mathematics of a series of microevolutionary changes whether you are talking about bacteria accumulating mutations to adapt to an antibiotic selection pressure, bacteria accumulating mutations to adapt to a starvation selection pressure, or for some non-limbed replicator to accumulate the coding and regulatory genes necessary to produce limbs. The same math applies to all examples of DNA evolution. If you have a real, measurable, and repeatable example of DNA evolution that doesn't follow this mathematical pattern, show it. You won't. The Lenski experiment obeys this math, hiv obeys this math, weeds and cancers obey this math, human DNA evolution obeys this math. I missed your publication on the explanation of the mathematical behavior of the Kishony and Lenski experiments. In fact, none of the fish evolve to mammals clique have correctly described the mathematics of either of these two simple evolutionary experiments. What's the matter? Is your clique having difficulty doing the math for these two "specialized experiments"? The problem for you is that we now are getting the numbers and the numbers are fitting the model that I've presented, not your model. You really need to do some exercise on the effect of the multiplication rule on stochastic processes like DNA evolution. Then you will understand why the numbers fit my model and not yours. Sure, lots of variants fail to successfully follow an evolutionary trajectory, that's called extinction. But any lineage that doesn't go extinct, the joint probability of each mutational evolutionary step will be calculated by multiplying the individual probabilities. Otherwise, you are simply getting divergence of the population. You still don't get it, the mutation rate is a minor factor in the DNA evolutionary process. The multiplication rule is the dominant factor. hiv has a mutation rate of about e-5 yet it still can't evolve efficiently to just 3 selection pressures targeting only two genetic loci. The reason is that three instances of the multiplication rule is being applied to the virus at each evolutionary step. Each additional selection pressure on a replicator imposes another instance of the multiplication rule on each evolutionary step. It takes very large populations to adapt to a single selection pressure. Each additional selection pressure forces the population size to go up exponentially in order to have a reasonable probability of adaptation to those selection conditions. I'll start going over the mathematics for that in the "Do you really understand the mathematics of evolution?" thread today. I'm telling you how many (not too many) replications it takes for a mutational step on an evolutionary trajectory. And we have the numbers for example, with humans:
How Many People Have Ever Lived on Earth? | PRB
There have been about 110 billion people that have ever lived. 98% of those people have lived in the last 10,000 years. What kind of adaptive evolutionary trajectory could have been followed by humans in the last 10,000 years? And what kind of adaptive evolutionary trajectory could have been followed for those 1.2 billion that ever lived before that time? You can get some evolutionary divergence but you don't have the population sizes necessary to do any type of evolutionary adaptation. And the coding and regulatory genes to make limbs require any kind of mutation you can imagine? And in case you didn't know, that's what selection pressures do, kill or impair the replication of some or all members of a population. It doesn't matter whether it is an antibiotic, thermal stress, starvation, you name the selection pressure. That's what these stressors do to populations. And unless any of the survivors of these stressors can replicate sufficiently, they will have a low probability of getting another adaptive mutation. It is all about the multiplication rule. Go back to your probability theory textbook and read about it. We have plenty of information on population sizes of different replicators that are alive today. Take a look at the numbers from this page:
Along With Humans, Who Else Is In The 7 Billion Club? : The Two-Way : NPR
So, unless you think that drift in some small population can cause legs to appear in some legless replicator, you are going to have a hard time coming up with the population sizes necessary for adaptive evolution to operate and do this kind of genetic transformation.

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The same math applies to all examples of DNA evolution. If you have a real, measurable, and repeatable example of DNA evolution that doesn't follow this mathematical pattern, show it. You won't. The Lenski experiment obeys this math, hiv obeys this math, weeds and cancers obey this math, human DNA evolution obeys this math.

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Given that you’ve offloaded all the work into getting the probabilities it might be the same (although there are issues like co-option and preadaption and recombination to consider). However, your argument will rely on the numbers and you don’t have those.

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The problem for you is that we now are getting the numbers and the numbers are fitting the model that I've presented, not your model.

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The problem is that the numbers you are getting are very likely not applicable to most of the evolution we’re interested in. We can’t expect pressures like antibiotics to be ubiquitous drivers of evolution.

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Sure, lots of variants fail to successfully follow an evolutionary trajectory, that's called extinction. But any lineage that doesn't go extinct, the joint probability of each mutational evolutionary step will be calculated by multiplying the individual probabilities. Otherwise, you are simply getting divergence of the population.

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Diverging populations is fundamental to evolution. But that isn’t the issue. Some lineages are going to do better than expected. And in fact those we see will be those that did. There’s a selection effect there, and that even applies if you’re calculating the average replications required.

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You still don't get it, the mutation rate is a minor factor in the DNA evolutionary process.

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The rate at which beneficial mutations appear is the one you want and that will be quite variable since the number of available beneficial mutations also varies.

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The multiplication rule is the dominant factor. hiv has a mutation rate of about e-5 yet it still can't evolve efficiently to just 3 selection pressures targeting only two genetic loci. The reason is that three instances of the multiplication rule is being applied to the virus at each evolutionary step. Each additional selection pressure on a replicator imposes another instance of the multiplication rule on each evolutionary step.

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That’s only true of hard selection. Reality is more complex. There will be cases where the baseline population is adequately fit and a mutation gives an advantage. That sort of selection works perfectly well in parallel.

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I'm telling you how many (not too many) replications it takes for a mutational step on an evolutionary trajectory. And we have the numbers for example, with humans

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You’re telling me your guess. But you haven’t got real numbers for, say, the evolution of birds.

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There have been about 110 billion people that have ever lived. 98% of those people have lived in the last 10,000 years. What kind of adaptive evolutionary trajectory could have been followed by humans in the last 10,000 years? And what kind of adaptive evolutionary trajectory could have been followed for those 1.2 billion that ever lived before that time? You can get some evolutionary divergence but you don't have the population sizes necessary to do any type of evolutionary adaptation.

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Ten thousand years isn’t a lot of time in evolutionary terms. And large interbreeding populations aren’t an ideal situation for evolutionary change. But there are some interesting adaptions around and I wonder how you account for those. White skin and adult lactose tolerance are two notable examples.

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And the coding and regulatory genes to make limbs require any kind of mutation you can imagine?

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We certainly have a few intermediates for that transition. But of course there is no reason to believe that was the only evolutionary trajectory available - or that it is true that all mutations need to be equally targeted.

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We have plenty of information on population sizes of different replicators that are alive today.

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And what numbers do you have for the number of possible beneficial mutations ?

Not bragging, just stating a fact: science does not deal in proofs. Neither do plumbers. Neither do bus drivers.Science does not deal in proofs. You should have understood that before you claimed to know anything about science.Edited by ringo, : Fixed attribution

You're not making any sense. It isn't mathematics that treats infections and cancer. And the treatments that DO work are not discovered by mathematics.

It is mathematics that relates the variables involved in evolutionary processes and if you don't understand this math, it will increase the risk that the selection pressures used to treat infectious diseases and cancers will fail. Now the simple-minded muddlers in your fish evolve into mammals clique might recognize that using two selection pressures will be more likely to drive these infections and cancers to extinction. However, with this kind of vague understanding of evolution, you won't understand when and why more than a single selection pressure has to be used to achieve a successful treatment.

Real science is based on evidence. We can test and repeat and observe and etc. That is proof in a sense. There is no proof in any sense whatsoever for the whopper fables of origin so called sciences.
If you knew the limits of science and what it is really all about you would know that.

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However, with this kind of vague understanding of evolution, you won't understand when and why more than a single selection pressure has to be used to achieve a successful treatment.

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Who really cares about selection pressure when it comes to what was created or not? Who cares about why creatures needed to adapt and evolve after being created? If there was a creation, then who could really know what was here already, and what all came as a result of evolving from that starting point?If fish needed to adapt to land in the far past, well, big deal. If God created some fishy like thingies that were suited to both, that is fine also. Who really knows?

You're only hurting your own credibility by repeating that nonsense over and over again. It isn't a clique. It's practically everybody who has studied biology.Even IF your math had any value (and it doesn't seem to have any) you have a responsibility to behave like an adult instead of a petulant teenager. Smarten up and talk science and leave your immature insults in the playpen.

Yes, and you have no evidence for your claims. You don't know what you think you know.Edited by ringo, : Spellig.

But I do, you can start with the Kishony and Lenski experiments. And then you can go on to every real, measurable, and repeatable example of DNA evolution. The only evidence that you have is what your fossil tea-leaf readers give you and that tells you absolutely zilch how evolution works. It is you and the rest of your fish evolve into mammals clique that has no real evidence. And you harm people with drug-resistant infections and failed cancer treatments with your ignorance of the mathematics and science of evolution.

Keep blowing smoke. Too bad you haven't enough smoke to cover your busted beliefs that you thought were sciencey.