Genesis 3:19 speaks of Adam returning to inanimate matter - “dust” - as a result of death, therefore “dust” obviously cannot refer to a living organism. That being so, since Adam was formed from “dust” (Gen 2:7), he could not have been the offspring of any living creature.
Besides Gen 3:19, the OT speaks of returning to lifeless “dust” as a result of death in at thirteen other places (Eccl 3:20, 12:7; Psalms 22:15, 30:9, 90:3, 104:29, Job 10:9, 17:16, 30:19, 34:14-15, 40:13; Isaiah 26:19, 29:5).
Theistic evolutionists are forced to twist the meaning of “dust” in Gen 2:7 into some living creature, of which Adam was the offspring. In what mad universe would anyone use “dust” as a metaphor for a living creature?
Interpreting the evidence is always a personal opinion. How could it not be? You examine the evidence, mull it over in your mind and come to a conclusion – how is that not a personal opinion?
That is actually a very poor comparison. The earth revolving around the sun is an observable, repeating event that can be verified empirically. If Adam was the offspring of some living creature, that was an unobservable, one-of event that cannot be verified empirically – so regardless of whatever evidence exists, Adam being the offspring of some living creature is nothing more than a personal opinion.
Thank you for that information and please forgive my ignorance. Regardless, whatever known genetic similarities exist between humans and non-humans, they do little to explain the immense differences between us and them.
I think you would agree that science has a very long way to go before it can claim to have got to the bottom of understanding how genomes function.
You’re right – after all, chimps made it into space before humans did! And not only are chimps adept at building space-craft and astronauting, many of them are scientists, inventors, philosophers, musicians, poets, authors, priests, engineers, doctors, architects, computer-programmers, clothes designers, builders and tradesmen.
No doubt about it, the differences between us and them are not large at all (although, strangely enough, no chimp has ever won a Nobel Prize).
Before I get started, I assume that the other issues you brought up were satisfactorily answered in my previous post? I like to know that we’re making progress.
I’m not quite sure what you mean by “relationship of variables captured by conditional probability”, but here’s how I’m thinking about the probabilities you bring up. It should be robust enough to capture any relationship among them:
We have three probabilities: P(H), P(E), and P(H ∩ E). Each of them is a real number between 0 and 1. Therefore, ANY possible combination of them (dependent, independent, correlated, whatever) can be expressed as a set of 3 numbers, which can be graphed on a 1x1x1 cube, with each probability taking on the x, y, and z values respectively.
So any specific H, E will generate these x, y, and z values. For example, if H is “this coin flip will land heads”, and E is “the next coin flip will land heads”, then under the idealized independence assumption, this would correspond to (0.5, 0.5, 0.25). In reality, because these flips almost surely have some dependence, the values may be more like (0.500214913312, 0.5004123290300, 0.25012131), or whatever.
This is, of course, not limited to coin flips. H can be “It will rain tomorrow”, and E can be “Today was a cloudy day”, or whatever. That, along with any H and E you can think of, can be plotted onto this 1x1x1 cube (into actually a subset of the cube, but that’s a minor detail). Therefore this representation should be enough to capture any relationship among these probabilities that you want to capture.
Now, I want to consider “any given H and E”. I can perhaps define that more precisely, but I think it’s clear from the discussion so far what this space encompasses. It includes things like astrological claims, @John_Harshman 's “Gus the wombat” problem, and water molecules rotating in the Andromeda Galaxy affecting life on earth.
For every such problem, we plot its (x, y, z) coordinates in our cube. Now, it’s clear that this will create some kind of volume: For x = 0.5 and y = 0.5, z can be 0, or 0.1, or 0.123151234, or 0.25, or 0.4999234, or 0.5, or any range between them. The same is true for any other value of x and y.
But what about “independence”? What does P(H ∩ E) = P(H) · P(E) look like in this cube? It forms a surface. It’s pretty easy to visualize, or you can just plot it on some online calculator. Anything on that surface has the label of “independent events”. Things not on that surface are dependent. So our 1x1x1 cube is perfectly adequate in capturing this “relationship of the variables”, as we’ve said.
But this surface, being of a lower dimensionality than a volume, must necessarily have a probability of zero of being actualized. This is the “almost surely” idea. As we’ve said, in such a space any equation is almost surely going to end up being not equal.
Of course, all this can be projected onto a lower dimension, simply by defining a new variable, P(H|E) = P(H ∩ E) / P(E). Then we’re back down to the 2D example that we discussed earlier, where the x = y argument applies, to a 1x1 square this time, with all the same conclusions.
So with that framework - which, as I said, encompasses any possible H and E, and therefore any possible relationship between them - I can answer some of your questions:
Yes I do. It’s zero, for the reason I walked through above.
The search space is “any given H and E”, and illustrated through the specific kinds of problems that we’ve been discussing. Of course, you can choose to narrow down the search space so that the probability of independence is not zero. You can, for example, say that P(H) is 1/2 then ignore any facts that can possibly show you otherwise, as @John_Harshman has done, and define that as your space. In such cases you can get a nonzero chance of perfect independence. But it’s also clear that that’s not the search space we’re discussing.
Let me know if you have any questions. I think the above framework is enough to address all your concerns.
@John_Harshman :
I hope the above explanation was helpful to you, as it touches on some of the issues you brought up in your previous post. But I doubt it. You have a far larger problem than a misunderstanding of any particular issue: you ignore facts. Nor is this problem helped at all by your tendency to simply “deny” or “claim that it isn’t”, or your declaration that the fact is simply “not relevant”. Especially after I explicitly explained why the fact was relevant, and doubly so when it’s on a problem that you yourself brought up, repeatedly.
Your problem is of immediate concern. No other discussion is possible while you continue to exhibit it. Fortunately, the remedy is easy: Stop ignoring facts. You can start by answering my original question.
I haven’t followed your discussion too closely, but I would give due consideration to @AllenWitmerMiller’s position here. I said earlier that I agree with your line of thought and favored a de novo creation of Adam and Eve. But if I were to expand on that position, I would get what @AllenWitmerMiller described above.
What immense differences are you thinking of? Of course there’s a lot we don’t know, but we know enough to say that whatever differences there are must be due to genetic differences.
Depends on what you mean. We understand in a general way, and we know some of the specifics, but not all by any means. Still, I don’t see where creationism can be hiding.
Yes, I am, despite your attempt at sarcasm. Just goes to show that a small difference in genetics and anatomy can lead to a big difference in outcome. And of course we can see all this arising gradually in the fossil record.
I’m not aware of any TE that reads the text this way because it assumes both literalism and concordism, both generally eschewed by TEs. Rather, for TEs that accept biblical inspiration and even inerrancy, “dust” is generally read as a symbol for mortality. This is why the Bible assumes we are all made from dust (e.g., Ps 103:14).
The point is that biblical interpretation is more than “the Bible says…”; it’s about what the particular author means by his words within the historical, literary, and theological contexts. In this case, genre plays a key role…and the problem is that the genre of the early chapters of Genesis is not easily discernable or obvious.
Sure, the manifold shows infinite solutions for z=xy. And you’re arguing there are infinitely more solutions to z < xy and z > xy than z=xy. I’m tracking with you there.
I understand you want to ignore the probability of independent events through the average probability of an infinitely larger search space via almost surely not.
What does not make sense is that when you select a specific set of E and H events, you have necessarily performed a dimensional reduction of the search space from a very large infinity to N = 1. This is because you have now declared the elements {z, x, y} from the infinite set. This necessarily instantiates an interpretable relationship between each variable—meaning you can no longer assume independence is almost surely zero. You actually have to test for it to know whether P(H ∩ E) = P(H) · P(E) or P(H ∩ E) ≠ P(H) · P(E).
At best, you can say, “E is almost surely evidence for H until P(E), P(H), and P(H ∩ E) are declared.”
Do you agree that specifying P(H), P(E), and P(H ∩ E) reduces the search space from infinity → 1?
You are very confused @Edgar. The GAE shows how your own reading of Adam and Eve created, without parents, is consistent with evolutionary science. Have you read it yet?
This question of Independence caught my attention, and the resolution seems to be to properly define the probability space (or sampling frame). “No two events can be completely independent” might be true in a cosmic sense, where we can trace everything back to quantum causes at the time of the Big Bang. Trying to take that literally seems a bit of a stretch - In any practical sense (and defined probability space) we can effectively have Independence where P(H) = P(H|E) + e, and e converges to zero in Distribution, if not Almost Surely.
I haven’t read your book yet–but it’s on my list. If I understand what you’ve proposed about A&E’s de novo creation, it’s inherently unfalsifiable and untestable.
I am hesitant to describe an unfalsifiable phenomenon as being consistence with a scientific theory. Do you address this concern in the book?
What should I make of it? If it’s true (which, given the way coins are often flipped, probably is not), that just means that the probability of heads might be .4999 rather than .5. OK, adjust the scenario to reflect that. Now what?
And you ignore my arguments, especially when I point out your unwarranted assumptions.
It will be much more effective in overcoming your massive confirmation bias if you learn for yourself.
The game you’re playing is, “My side says this, your side says that!” so that you can avoid the evidence and pretend it’s just rhetoric vs. rhetoric instead of rhetoric vs. evidence.
How can you have no idea, if you think 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”?
Why are you talking about “our knowledge of genetics” when you have so little knowledge of genetics, particularly when interacting with geneticists?
@chris_doesdna2018 :
I think you and I are pretty much in complete agreement. Let me see if I can summarize your points:
Before you specify H and E, the probability of independence is almost surely zero.
After you specify H and E, you actually have the x, y, z values, so you can directly test for independence. That will tell you whether they events are independent. And, of course, this can be done more than once, which means that it’s possible to get a set of H and E that are independent.
Do I have that right? I absolutely agree with all of that. The only thing I would point out is that I’ve only been arguing for #1 this whole time, over the set of “any given H and E”, as I’ve defined before.
@Dan_Eastwood :
I absolutely agree with you. In fact, I’ve repeatedly brought up applications of your idea, that often times approximations are good enough, that you can have evidence that’s so weak that you don’t find it meaningfully convincing (e.g. astrology), that even in the original article we talked about the position where a historical Adam and Eve didn’t even exist, because some people considered Genesis to be this level of evidence.
But in my current discussion, the debate very much seems to be over the absolute sense of independence. Because when I specifically worked through the astrology example, as a low level of evidence (which would rise from approximate independence), it was rejected. I furthermore brought up the cardinality of the real numbers multiple times, indicating infinite resolution, and my claim was still contested.
Actually, this may be a good time to check in again: hey @John_Harshman , would you agree with the following statement? “P(H) and P(H|E) are almost surely not equal, for any given H and E. Therefore, everything is evidence. But in practical situations, any given evidence may be too weak to be convincing, or even weak enough to be approximated as zero”.
@John_Harshman :
If you answer the above question in the affirmative, then I think we can chalk this up to a misunderstanding. Otherwise, here’s two follow-up to the coin flip question:
Here’s the first follow-up: so, you say that P(H) is 0.4999. But there’s bound to be some uncertainty around that. I mean, I’m sure that you’re not claiming that P(H) is 0.499900000… with infinite precision, right?
This uncertainty implies a probability distribution. As far as you know, the actual value of P(H) may be 0.4999000, or 0.4969320632, or 0.50012312, or some other such number. Are you with me so far?
The other follow up is just another acknowledgement of fact: what do you make of the fact that, in one of the more extensive empirical study of coin flips, the coin landed heads 5067 out of 10000 times?
No. I would think that for any given H and E, if you are pulling hypotheses at random from the world rather than from a simple distribution of real numbers, it’s most likely that the two are independent. That is, most facts about the world are not evidence for or against astrology. My cat is orange; the capital of Ethiopia is Addis Ababa; Vesta is the second-largest asteroid: none of those has any relevance to astrology.
Yes. I just don’t see the relevance. Sure, our estimates of probability are not completely precise. And in fact coins are probably not perfectly balanced. (Incidentally, how many times did it land on edge, your previous obsession?) But what does that have to do with wombats? The estimate is equally imprecise regardless of whether Gus is there or not. Until you have something to say about the influence of Gus on P(H|E), you have said nothing relevant.
I think that’s an accurate summary. I suppose I’m more curious now.
If H is almost surely dependent on E only up until we employ the calculation, at which point the search space for independence is reduced to a binary operator, why go through the trouble of holding the premise?
In order to calculate any specific posterior probability, the search space for independence will always be binary. In other words, any specific calculation obviates the leading explanation of “Any E is evidence for H.”
Maybe phrased as a question: What utility do you see in stating “any E is evidence for H” when that’s not the case once a specific calculation is performed?
It seems that this all comes down to what we think the a priori likelihood of independence of two variables.
@naclhv is arguing that everything is connected, so true total independence is rare. He is arguing this is because there are infinitely more ways for variables to be correlated (because there is an infinite number of correlations), and only one way not to be correlated. This argument, I am not sure about at all, but it might be true that ultimately everything is dependent on everything.
Except, even in his example, he talks about the independence of events that are distant from one another under which not enough time has passed for light to reach us from them. That seems to undermine entirely the proposition he makes. There are large classes of interactions that are not interacting. Randomly pick two atoms from the universe at randomly chosen times, and most likely they are not interacting in any way. (@dga471 and @PdotdQ might refine this claim).
Aside from that, there seems to be another issue. Perhaps in an ideal conceptualization of the problem a relationship of R^2 = 0.000001 is not independent, but in the vast majority of cases correlation is practically indistinguishable from R^2 = 0.0. So though technically the two events are not independent, it might as well be independent, and in fact should be treated as independent in most our reasoning.
That means “independent” is not really R^2=0.0, but |R^2| < epsilon. That means there are an infinite number of ways that to variables can be independent (in this analysis), undermining the argument in a different way.
Though, I must say, assuming a uniform distribution of correlations (as is being done here) isn’t the right way to reason about the problem any way. There needs to be some specification of the domain and method of sampling of variables. From that specifications, we will have different distributions of R^2 between randomly sampled variables, and it most likely will not be a uniform distribution.
I think it runs into the same issues. R2 doesn’t innately tell you if two variables are dependent or independent. There are situations where R2 = 0.0 but the variables are otherwise dependent, just not linear and you need a different model. And we always have that painful axiom, “correlation is not causation.”
I still think the best solution is to check for dependence rather than assume it through infinite search space.
You can’t be serious. I alluded these rather obvious difference in my previous post. How many scientists do you know are chimpanzees or bananas?
As yet, genetics cannot explain the immense (intellectual… or even physical) differences between humans and chimps, for example.
… so goes the story, at least.
“Biochemists and biologists who adhere blindly to the Darwinism theory search for results that will be in agreement with their theories and consequently orient their research in a given direction, whether it be in the field of ecology, ethology, sociology, demography (dynamics of populations), genetics (so-called evolutionary genetics), or paleontology. This intrusion of theories has unfortunate results: it deprives observations and experiments of their objectivity, makes them biased, and, moreover, creates false problems.” Pierre-Paul Grasse
@swamidass :
About events separated by greater-than-speed-of-light distances - I anticipated this may come up. This is why I said earlier that:
I think the cleanest solution here is to let the context of the discussion define the space of “any given H and E”, and limit ourselves to cases like those. Not because I can’t address your example, but because doing so would rapidly expand the discussion topics to unwieldy branches, and away from the intent behind my original claim.
Here’s an example of what I mean: If “any two atoms at any two time and space in the universe’s history” is in play, then so is “any two SETS of atoms in any combinations of time and space in the universe’s history” - nearly all of which will have causal effects on one another. And over that space, it becomes pretty clear that the original, singular example has negligible weight. But if we went down this path, I’d have to get into defining exactly what “any given H and E” means, in mathematical terms, which would take us pretty far from my original point. I could also bring up things like the “spooky action at a distance” of the EPR paradox, and the fact that the universe was (probably) all causally connected at some point in the past, so that even if one atom can’t directly affect another atom in a region that’s currently causally disconnected, the information about one atom can still serve as evidence about the other.
Or, here’s another class of H and E that may be really independent: H may be a fact in pure mathematics, like “1 + 1 = 2”. Then the discussion would lead to philosophy of mathematics and whether math is “real” or discovered or invented, etc.
But I’m not interested in talking about these things just for the sake of talking about them. My goal, this whole time, was to back up one of the first statements I made here:
The esoteric discussions that come up in the more expanded space of “any given H and E” would not lead to a productive discussion about my original point. So, again, I think that defining the space from the examples that came up during the discussion is the best way forward.
As an aside - consider the strength of evidence you needed to even come up with a single counterexample, out of infinite possibilities, that had even a remote chance at contesting my claim: you needed relativity - one of the greatest scientific achievements ever. That speaks to the robustness of my claim. If anyone else has another theory of relativity in their back pocket that can apply to the space defined by the examples used in the discussion so far, I’d be glad to hear it.
Next:
I’ve already addressed this, in multiple past posts. Here’s the latest one, from my last post:
And the scope of the current discussion was confirmed by @John_Harshman in his latest post.
Next:
I’ve already addressed this as well:
@John_Harshman :
I had this whole thing set up to be really thorough, but it looks like this thread is reaching a length where people are just jumping to the end without reading what’s come before. So let’s wrap this up:
You’re right: coins are not perfectly balanced. Due to this fact, coins that are spun on the edge (as opposed to flipped) show a remarked bias in how they land, depending on their imbalance. This bias is known for specific coins.
The coins that land on their edge show a similar dynamic; if they end up not quite making it exactly on their edge, they’ll fall in the direction of their imbalance.
Of course, this imbalance is caused by gravity. Stronger gravity amplifies its effect. Gus, being a wombat, exerts gravity. Even just the name, when it is spoken, written, or thought, exerts gravity, due to energy-mass equivalence.
Thus, not only can we say that P(H) != P(H|E) in your particular example, we can even name the direction of the change: the coin is more likely to land with the side that it favors when it is spun on its edge.
Of course, this should not come as a surprise to you. After all, I already demonstrated, through an explicit calculation, that even the rotation of a single water molecule in another galaxy will affect macroscopic events here on Earth. This Gus problem, and the others you bring up, will obvious have much greater effects, although one may not necessarily be able to calculate the exact value, or the direction of the change.
No doubt you’ll continue on with your endless string of "what if"s. I suggest trying to think through some of them for yourself before you ask them, although I’m willing to engage a few more rounds with you.
This is a question that gets at the heart of what I said at the very beginning. Thank you for asking it.
We often take shortcuts in evaluating evidence. So there will be a time when we encounter a fresh H and E, but before we actually do the full calculation to decide on H. Often times, we just use a guesstimate, and that’s fine - as I said, approximations have their place. But they shouldn’t be mistaken for the truth. And I think it’s in this space that it’s helpful to remember that “everything is evidence”, to not completely ignore whole areas of reality based on approximations and rules of thumb.
For example, one useful approximation is to ignore certain kinds of evidence. Let’s use the example of astrology again. It’s widely known that astrology is bunk. Now, I once ran into a claim that said that solar cycles can affect my mental health. I immediately dismissed it, as just another nonsense from astrology. After all, how could any movements due to celestial mechanics affect anything here on Earth? But that was a mistake - because solar cycles really may affect people’s mental health. So I used an approximation, and that turned out to be wrong.
Now, here’s the key part: if you do not recognize that “everything is evidence”, you will confuse your approximation for truth, and never take into account some key pieces of evidence, and never learn some important truths. In my example, if I simply ignored the “solar cycles can affect my mental health”, and persisted in my belief that this was just astrological nonsense, then I would been one of those fools who will remain forever ignorant of entire realms of reality.
Other examples abound. You may think that some numbers are just too small to care about - and that may be a very good approximation in a vast majority of applications. But current experiments in particle physics rely on finding tiny deviations from the theoretically calculated values - deviations which can be ignored for all practical purposes except for in that experiment. Or some people may have the belief that only “science” is evidence, and ignore everything else. They would not be able to understand why we took such care to explore the evidence from the Bible in the original article that started this thread.
Basically, it’s important to remember that evidence can come from anywhere. It’s a simplistic view of evidence to classify the world into things that are “really evidence” and “not evidence”.