Somehow I remembered it as being an actual story where a Rabbi showed a heretic a poem that he claimed had formed when he accidentally knocked over his inkwell - perhaps a different section/author?

@loewian that's all you're going to find in the chovos halevavos

@loewian see this by Aryeh Kaplan ou.org.s3.amazonaws.com/publications/kaplan/infinitelight/1.htm ("A philosopher once came to Rabbi Meir...") though the footnore there points to this

Have you ever played the "chaos game"? webserv.jcu.edu/math//vignettes/chaosgame.htm Obviously this is a really simplistic example, but Chaos Theory does allow for "complex structures arising from unguided natural processes". Understanding the full complexity of the argument is a bit over my pay grade, but I do think your last comment is a little too sure of itself.

@Nic you can find in nature nice symetrical or asymetrical patterns like snowflakes, but as the chovos halevavos writes complex things displaying "wisdom", you wont find.

@Nic I think that probably has a lot to do with the double meaning that is used for the word "complex" in these discussions. What Chaos Theory is describing is more of a psychological phenomenon that when you translate a simple mathematical formula into a statistical realization it can produce a repeating, symmetric, aesthetic figure. There is no deviation from probability to signal purpose from structure, however. As opposed to the "complexity" described in the proof I'm discussing which is really just inferring intention from intentional structure selected from all possible arrangements.

@ray For some definitions of the 'wisdom' that is trivially true and for some it is false. Why an argument like that is wise is beyond me.

@Nic aesthetic yes but not complex. they are no more complex than the original triangle. you can encode the whole thing in a simple triangle repeat algorithm

@ray: As I mentioned, the specific example is rather simple, but I believe the point remains that random events do create complex structures that to a simple approximation show "design". In fact, I consider snowflakes to be another good example of this. How about stars? They are made up of huge amounts of atoms all bouncing around randomly, and yet they have "purpose" -- they heat things up. They shine. As for "displaying wisdom", I consider that to be slightly facetious, since you can essentially redefine your set of acceptable answers to exclude any counter-example.

@loewian The statistical argument is really hard to make, because you don't have a Prior. The only reason we're asking the question in the first place is because we happen to be in the (small as it is) probability where humans have capacity for existential questions. It's like a guy claiming he's moshiach because he was born on Feb 26th, 3:24:01, and the chance him being born on that exact second of the year is 1 in 31,536,000. The fallacy is that you could make the same claim for any second. Thus, making a statistical statement about humanity is something I would be very leery of.

BTW there's no reason to expect anyone would have observed such a thing, which to any noticeable degree would take a very long time.

@Nic That's not a rejection specifically of the proof from design. It's a rejection of all statistics and hypothesis testing in general (and, en route, all of science and rational inquiry as well.) How now do you ever prove any model as plausible? Why now would you avoid poisons and eat food and not vice versa?

@lowian Not at all. There are very rational methods of doing statistical analysis. The simplest way would be to simply exclude any data that was collected before stating the problem and the experiment designed to test that hypothesis. Any data collected after stating the specific experiment/measurements are stated are valid. E.g. "Wow, I rolled a random number between 1 and 1000,000,000 and got exactly 209,256,222. What are the chances? Ok -- let's see you do it again."

@loewian There are statistical methods of incorporating existing knowledge, but you have to be very careful when implementing them. There are so many pitfalls (esp. which such a complex problem), I would balk at applying these methods without a gaggle of statistics experts checking every assumption.

@Nic So you don't believe there is, in normal day-to-day cognitive behavior at the layman's level, the usage of reliable probabilistic reasoning such as that described by Ibn Paqud?

@Nic (And you believe that those western "philosophers", who rejected the proof from design in favor of a very broad accidentalism, employed a gaggle of expert statisticians before doing so?

@loewian As mention above, I believe you can make "layman level" probabilistic reasoning when you only use results obtained after stating the experiment. I believe that Ibn Paqud's argument is interesting, but by no means provides definitive proof because of all the statistical complications. I do not know what the "philosophers" claim as I don't have a direct quote, but if they merely rejected Paqud's proof I would say they were being reasonable. If they tried to prove the opposite (i.e. deny the existance of g-d) using statistics, then yes, I would require real statistical integrity.

@nic your snowflakes are obviously not complex. if they were complex, they would be rare. the fact that they appear so frequently is strong proof that they are quite simple. stop saying nonsense

@ray If your definition of complex is limited to things which are rare, then don't be surprised you haven't found any naturally occurring examples as they are so few and far between. Moreover, is the world rare or common that you can know it's 'complex'? How can you tell if you have nothing to compare it too?

@DoubleAA for random processes yes, rarity is an indication of complexity. for chance and complexity are counter-prevailing forces. the more complex, the rarer.

@ray Snowflakes are complex. If I showed you a specific snowflake and asked you to duplicate it in a lab, I don't believe we have the capability yet. Certainly not to a microscopic level. And yet, you are calling it "obviously not complex" because there are so many of them, each of them mostly unique. Consider then the continuum of universes. Our little corner contains life in the form of humanity and duplicating it exactly is hard in the same way duplicating a snowflake is hard. That's not to say there are countless other solutions out there.

@ray The problem is that you are starting from a universe in which humanity already exists. Did you ever hear the one about the guy who always brought a bomb to a plane because "what is the chance of two people bringing a bomb to the same plane?". The same thing applies here. It's like shooting at a wall and then drawing the bullseye around the place you hit the target.

@nic if there were only one type of intelligent design on earth, then you are right. but there is a huge diversity. many structures even arose independently many times even according to evolutionists.

@nic that's one problem. huge diversity of intelligent designs. another problem is that random processes converge and get stuck on local optima. this makes them unable to construct even a mere bridge, as explained here dafyomireview.com/article.php?docid=427&d=9

@user813801 Honestly, it seems to me this makes intelligent design look more like snowflakes. There are millions of different kinds of snowflakes, each completely unique and it is currently impossible for a lab to duplicate any single one of them. In the same way, there are many species intelligently designed that are each unique that we cannot duplicate. Sure, there's a matter of scale here (a species is a lot harder to build than a snowflake), but I don't see a fundamental difference.

@ray First of all, one could argue that the human body is a local optima. The fact that a person can choke happens because the breathing and eating apparatus are combined implies a not-so-intelligent design. Ditto for things like our backs getting bent because of walking on two feet and hernias, etc. Secondly, even if the Theory of Evolution really is total bunk and we find out that there really is intelligent-design, I submit that it is not the statistical argument that will make the case, but some sort of "maker's mark".

@ray Finally, I think that arguments pro/against evolution are beyond the scope of this question. The initial argument is about the statistical nature of humanity, not about the validity of alternate methods of explaining how we got here. Honestly, I don't care one way or the other about evolution. It's only that last paragraph of your original answer that I feel is problematic.

@nic there's a heck of a difference between humans and snowflakes. for one the engineering wisdom it takes to build a human being is in my opinion infinite. Gd may have introduced certain flaws to maintain free will. but you have to look at the total picture.