Quite obviously, the fact that we share 98% of our DNA with a chimp doesn’t account for the immense gap between the two organisms. We also share about 40% of our DNA with bananas. This means of course that our knowledge of genetics has a very long way to go before it can explain the differences between humans and other organisms. The secret may lie in regulatory genes.
Non sequitur.
Being made in the image of God suggests a very special creation - hence Gen 2:7, which describes life being created where there was no life and describes God Almighty himself breathing life into a lifeless form to produce “a living being” - Adam. Jesus did essentially the same thing when he raised a dead Lazarus to life.
How so? Are you understanding what de novo means?
You haven’t explained how. You are simply making a claim.
One more time: the GAE idea allows for Adam to have been de novo created. Adam could have been created directly from dust and humans today can be evolved from the same ancestors as other primates–because Adam’s descendants could have married outside of their Adamic family, just as Genesis tells us about Cain.
So is interpreting the evidence of a heliocentric planetary system no more than a “personal opinion”?
I’m sure you don’t realize it, but you have used two entirely different and incompatible measures of genetic similarity. The 98% (really 98.7%) similarity between humans and chimps is the percentage identity between aligned sites. The 40% similarity between humans and bananas is the percentage of genes that have recognizable homologs. You need to learn some basic biology rather than just parroting something you saw on a creationist web site.
This is sort of true, in that differences in gene regulation are responsible for most morphological differences. But most of that isn’t in genes proper but in transcription factor binding sites.
More importantly, the differences between chimps and humans are not large and whatever gaps you see are spanned by fossils. I’m sure you dismiss all fossils as either obvious humans or obvious apes, but I’m also sure that no two creationists assign fossils to those two groups in quite the same way. It’s almost as if there were no sharp dividing line. Now what could be the reason for that?
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Even more obviously, that wasn’t my question. What is it in numbers of orthologous genes? That’s why I noted that you might learn something.
What are the numbers for regulatory genes, then? Not percent, but numbers of orthologs.
And if the secret may lie there, which creationist biologists are working on them?
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@chris_doesdna2018 , @John_Harshman :
On the question of my position on dependence/independence: you’re pretty close, but let me add in a word to clarify it: no two events are PERFECTLY independent (or, at least have a zero probability of being so).
“Independent events” is a useful idealization, like similar ones used in many other fields. “Frictionless pulleys” and “massless springs” in physics, “perfect equilateral triangle” in geometry, “pure H2O” in chemistry, etc. These things do not exist in real life, yet they help us learn the subject and organize our thinking, so they’re taught in our schools to simplify things for our students.
Of course, a naive geometry student may say, “what do you mean, there’s no equilateral triangles? I learned about them in school! There’s a picture of one, right here in my textbook!”, but of course, upon sufficiently close examination the shape will turn out to be imperfect in some way. The same is true for “independent events”.
Of course, often times it’s perfectly fine to make some approximations, like pretending that a shape is really a perfect triangle. The results you get by doing so lead to negligible differences, and it makes the calculation easier. The same is true for “independent events”. Sometimes, it’s okay to pretend that P(H) = P(H|E)
But what are you doing when you’re making that decision? You’re actually EVALUATING the evidence, THEN deciding that it’s negligible. You are NOT rejecting it categorically from the beginning. Of course, this is exactly what I’ve said since the beginning, in discussions involving astrology, or in the original article, in discussing the possible non-existence of a historical Adam and Eve.
So: no two events are PERFECTLY independent (or, at least have a zero probability of being so). I’ve given numerous reasons to think so: from considering all possible distributions (and distribution of distributions, etc.), to the calculation showing that everything on earth is affected (that is, not independent of) a single water molecule at intergalactic distances. My work above can effectively constitute a proof of the statement that no two events are perfectly independent, or at least a pretty firm outline of one.
Thus, I have already done this. So “the assumption of dependence” is not in fact an assumption: it is very explicitly my conclusion. In fact, a trivially simple re-tooling of my arguments applies directly to P(H ∩ E) ≠ P(H) · P(E), just as it was applied to P(H) ≠ P(H|E)
Also note the following about that formula, that P(A ∩ B) = P(A) · P(B): this is a definition, not a law. Meaning, it isn’t simply true for all A and B. Contrast that with Bayes’ rule, which is a law, and true for any H and E. What does this mean for our purposes? It means that we must see if this definition applies, for any individual case, to see if the “independent” label applies. To do so, we must evaluate the left hand side and the right hand side separately, then see if they’re equal. Of course, it would be an incredible (in the most literal sense of the word) coincidence if they actually turned out to be EXACTLY equal, although they’re often close enough for an approximation. In fact, if you stick around you may see this exact procedure being carried out. In any case, it’s not a formula that you can simply point to and say “see, independence!” about.
@John_Harshman:
So, in the face of all the argument I presented above, you “deny that they do”, and “claim that it isn’t”? I suppose this is a good time to move on to the next topic of our discussion, about the probability of a coin flip.
I see that you’re preparing your list of "what if"s already. I will, in fact, claim that every wombat has some influence on every event in the universe, including the event of a coin landing “heads”. Can I take your preparation of “what ifs” as you accepting that claim? That will make things easy, and I can get to your “what ifs” right away.
On the question of P(H) = 1/2, what do you make of the fact that coins sometimes land on their edge? This, by the way, isn’t just some cheap “gotcha”. I’m not just going to say “see, you were WRONG about P(H) = 1/2!” I promise that it points to far deeper ways in which you were wrong.
@Mercer :
Hi! I had left you behind from your earlier comment!
Anyway, I just wanted to say that your earlier comment did shift my thinking: astrology does in fact have trouble with testability, and that does contribute to the fact that it’s bunk. And the fact that your comment - despite the fact that it’s just hearsay from someone I don’t know on some internet forum - had the power to do that, means that it was evidence. Because everything is evidence.
This is so, so good. We need a banner/GIF/cool graphic of this that people can share.
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But, you are mathematically excluding the events which are independent. This is confusing to me because you are saying “no two events are independent” but you are also accepting the mathematical precept of independence in your argument.
This statement, which you hold is true for your argument:
P(H | E) ≠ P(H)
is the algebraic representation of Bayes’ when dependence is met:
P(H ∩ E) ≠ P(H) · P(E)
I’ve given numerous reasons to think so: from considering all possible distributions (and distribution of distributions, etc.), to the calculation showing that everything on earth is affected (that is, not independent of) a single water molecule at intergalactic distances.
I don’t think you’ve adequately argued this position–at least from what I can tell reading through the posts here. Providing some mathematical clarification would be helpful.
There are an unlimited number of solutions for P(H | E) = P(H) as all that is required for this to be true is P(H ∩ E) = P(H) · P(E).
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As I suggested before, I think your claim here is quite wrong. That is, what you state is not a good model for how humans assess the truth of claims. “Categorically” is precisely how we often assess evidence. We routinely dismiss entire categories of information as being irrelevant. We rely on heuristics, on stereotypes, on categories, on unexamined assumptions imparted by the society around us – they’re all part of our mental map of how the world works. It’s that map that we rely on most of the time to decide whether something is likely to be true or no, not the evidence for and against a particular claim.
I don’t dismiss astrology because I have evaluated studies of it, nor because I’ve heard about studies that falsified it. In practice, I dismiss it because I have a network of ideas about what entities are real and how causation works (based in part but only in part on direct knowledge of astronomy and physics), ideas about how humans come up with explanations for events and fool themselves about their validity, ideas about the history of ideas.
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No science is perfect. Therefore we should abandon all science.
That seems to be the implication of what you are arguing. And it is absurd.
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No. Just going along for the sake of argument.
I’m ignoring that fact. But if you like, substitute a quantum random number generator for the coin, one that outputs either zero or one.
I guess I’m confused about what you’re confused about? I mean, yeah, you can still use probabilities even if no events are perfectly independent, just as you can do geometry even if no triangles are perfectly equilateral, etc. You can still do science even if the models are imperfect. I go over examples like this in my previous post. And yes, I agree that dependence can be written in both of the ways that you described. Which is why I said that you can use the proof of one statement to prove the other.
The only thing I would point out is that, while you’re entirely correct that there’s an unlimited number of solutions for independence (either of your equations is fine), there’s infinitely more (in fact, infinitely more by a larger infinity) ways for that equation to NOT work out. That was much of what the previous discussion was about, with the “almost surely” and “distribution of distributions” and all that.
So… maybe we’re mostly agreed? I think there’s still something that I’m not quite understanding about your post.
Here, we’re basically in full agreement. In fact I’ve already basically said almost exactly what you’re saying:
I guess I just want to make two clarifications, to make the agreement complete: All the things you brought up, in your network of ideas, heuristics, etc. - they’re all considered as evidence in my model, and they’re to be taken into account. And when I said “categorically”, I meant that some people will reject things before they even consider THAT level of evidence. Like, I guess, they’d just reject a whole field that they’d never even heard of before? I’m not sure how that would even work - it was such a strange idea that I couldn’t even describe it adequately, which has lead to this confusion. But that is indeed what I’m discussing with the others, because their rejection of our view of evidence continued even after I made it absolutely explicit, as I have in the post I just quoted.
I don’t see how you got that from what I’ve said in my post. In fact I go to some lengths to express the exact opposite idea, that even if the real world doesn’t conform to our useful idealizations, we can still get results and make decisions using perfectly fine approximations.
Okay, this is a party foul. I’m talking about this gus/coin flip problem explicitly because YOU brought it up repeatedly and YOU wanted to talk about it, because it was a concrete example. And now you want to just ignore facts?
If you just don’t want to talk, that’s fine. Have a nice day, and a nice weekend!
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It sounds like you are making two contradictory claims:
- You are mathematically claiming independent events do not exist
- You are then suggesting there are at least some solutions to P(H | E) = P(H) which is the mathematical definition of independence
Any P(H ∩ E) that results in P(H | E) = P(H) represents independent H and E events, by definition. I’m not sure how else to simplify this.
Claims 1 and 2 are logically contradictory and cannot simultaneously be true. I am hoping that you will:
a. clarify your position so that you are not making two logically incompatible claims
b. provide mathematical evidence that the events you are describing meet the assumption of dependence
The only thing I would point out is that, while you’re entirely correct that there’s an unlimited number of solutions for independence (either of your equations is fine), there’s infinitely more (in fact, infinitely more by a larger infinity) ways for that equation to NOT work out.
I’m not sure that’s true and I don’t think you’ve demonstrated it to be the case. The relationship of H and E can be defined in an infinite number of ways that satisfy P(H ∩ E) = P(H) · P(E). Can you explain why P(H ∩ E) = P(H) · P(E) is necessarily a smaller infinity than P(H ∩ E) ≠ P(H) · P(E)?
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It’s really not relevant to the question, is it? It’s just a distraction from the actual point. I have no idea why you even brought it up unless you actually want to create a distraction.
Even if it is, why should that matter? It would matter only if we were choosing systems at random from the full set of possibilities, and what reality does that model?
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I don’t find it to particularly matter at all–but it does seem to be the crux of his position. The earlier arguments presented for this position are premised on plugging in values to the theorem. That is the incorrect approach as we are only concerned with the relationship between the events–i.e. there are an infinite number of non-correlating and correlating slopes for two variables. The two sets should be same size, I think.
Thank you for bringing up this question. It made me down a rabbit hole in thinking about the nature and types of infinity, and lead me to learn some new things about them.
It turns out that I was wrong - or at least, I’m not certain that I was right. P(H ∩ E) = P(H) · P(E) is NOT necessarily a smaller infinity than P(H ∩ E) ≠ P(H) · P(E), as far as I know.
This has no bearing on there rest of my claims, as this was literally just a parenthetical remark in my post. As long as P(H ∩ E) = P(H) · P(E) is infinitesimally smaller than P(H ∩ E) ≠ P(H) · P(E), everything I said holds. And this second fact is easy to see: ANY equation over infinite space is infinitely more likely to be false than to be true. The equation y = x has infinitely many ways to be true, but those solutions are an infinitesimally small portion of all possible values of x and y. The first set forms a line, the second set forms a plane. Therefore, for any x and y, the probability of them having the same value is zero. This is the central idea behind the concept of “almost surely”, which came up multiple times in the discussion so far. I strongly suggest you read it, if you haven’t already. The “throwing a dart” example is particularly apt.
I guess I’d also like to know what level of math I should be discussing things at? Like, I don’t know whether you’re interested in power sets of possible distributions and their cardinality, or just simple probability theory - please let me know!
Anyway, the idea behind “almost surely” can easily resolve what you perceive to be a contradiction: I am not saying that independent events do not exist; I’m saying that they’re infinitesimally rare, to the point of having zero probability. This seems strange, that you can specify a possibility (“independent events”), and yet have the probability for that possibility be zero. But if that possibility requires an exact alignment out of infinite possibilities, then that’s what probability theory says will happen.
Maybe another example from geometry will help. Have you seen these “sometimes, always, never” questions? They were fairly common where I went to school. So you would say, for example, that a triangle:
- can sometimes have an area greater than 1,
- will always have three sides
- can never have its angles add up to 100 degrees.
Now, the “almost surely / almost never” category is like a sub-category under “sometimes”. Yes, it’s “possible”, in that you can give examples of it happening. But it requires such exactitude that its probability is zero. For example, a triangle:
- can sometimes be an equilateral triangle, but the chance of any specific triangle being perfectly equilateral is zero.
So, when it comes to your statement about my position:
No; I am NOT saying independent events do not exist. That is, I am NOT saying that two events will NEVER be independent.
I AM saying that two events can SOMETIMES be independent, but that the chances of that is zero.
Or, to summarize it all, two events are almost surely not independent. Again, the concept behind “almost surely” is crucial here.
Also, in the real world (as opposed to pure mathematics), I’ve said that two events can often be approximated as being independent, and that this is often a practical and adequate solution. So the math behind independent events is indeed quite handy.
Yes, I’m in full agreement with you. No arguments against this point at all.
And, because the two statements are fully equivalent, that’s why I don’t need to provide ADDITIONAL “evidence that the events you are describing meet the assumption of dependence”: I’ve already given ample evidence that P(H | E) != P(H). That should also count as evidence of dependence, because they’re the same statement.
I hope that clears things up?
@John_Harshman :
Here is why any facts related to the gus/coin flip problem is relevant:
If you want to start dealing in facts again, please answer my question about P(H).
The hole in your logic happens right before the conclusion, when you implicitly assume that values of x and y are chosen at random from some range of real numbers. Without that assumption, you have nothing.
Again, that depends on how you arrive at that specific triangle. You are correct if we’re choosing at random from the space of all triangles.
So in the real world, one of those events is not evidence for the other, for all practical purposes. You are thus making a mathematical point with no relevance to the real world, even if your assumption is true.
What question? About the coin landing on edge? I say it’s a distraction, and that the name of a wombat has no effect on the probability of a coin landing on edge.
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Right–but that’s not the relationship of variables captured by conditional probability. There are an infinite number of ways for the intersection of the variables to give you zero information about the state of the other variable. Plugging in values for x and y is not the same as extrapolating the relationship between the variables. The reasoning provided here is not mathematically valid for this context.
Solutions for P(H ∩ E) = P(H) · P(E) exist outside of P(H) = P(E). P(H ∩ E) = P(H) · P(E) may be satisfied using any combination of numbers where P(E) > 0.
Additionally, y = x may also be a solution to P(H ∩ E) ≠ P(H) · P(E).
This is the central idea behind the concept of “almost surely”, which came up multiple times in the discussion so far.
Yes, I read the Wiki–which is one of the reasons I responded. This logic relies on knowing the probability of the diagonal. You do not know the probability of P(H ∩ E) = P(H) · P(E).
I guess I’d also like to know what level of math I should be discussing things at?
Whatever you feel is necessary to adequately explain the position. I can always ask questions.
This seems strange, that you can specify a possibility (“independent events”), and yet have the probability for that possibility be zero.
You are making the claim that this probability is almost surely zero on the premise of y = x. This premise conflates the relationship of two variables with plugging in values to the theorem. I am suggesting that you need to consider the scope of relationships between variables where P(H ∩ E) = P(H) · P(E).
Again, the concept behind “almost surely” is crucial here.
I’m not convinced this concept applies here as it requires that you know the search space a priori. I suppose I am asking you to justify, mathematically, the a priori without committing to the error of discarding the variables’ relationships.
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The 40% number is still incorrect regarding orthologs.
We have ~25% gene orthologs with bananas (and about 20% sequence similarity with bananas).
https://lab.dessimoz.org/blog/2020/12/08/human-banana-orthologs
Where did the 40% figure come from? Apparently
The article goes on to explain that this 41% figure comes from a blast search between protein sequences of human and banana. They found about 7,000 hits, and the average percent identity of these hits was 41%. He goes on to note:
“This is the average similarity between proteins (gene products), not genes… Of course, there are many, many genes in our genome that do not have a recognizable counterpart in the banana genome and vice versa.”
So when we get to the bottom of it, the 50% figure is actually 40% average amino acid percent identity between 7000 blast hits of human and banana.
So the original 40% figure was wrong on multiple levels.
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I’m not sure why one would require orthologs or how at that remove one could distinguish orthologs from paralogs.
It sounds fine, as it would seem to be the average percent identity of protein sequence between recognizable orthologs. What’s wrong is conflating two unrelated measures of similarity.