$30k challenge to Interpreter’s “Team Bayes”

[Rivendale]

It's maybe worth mentioning that the Laws of Thermodynamics are often like that: they tell you that something won't work, but they often don't tell you why it won't work. There always will be some specific detail that is the reason why,

Exactly. Remember the suggestion that it is very probable that your have breathed the same air molecule as say Jesus? Then never described why?

[Physics Guy]

I don't know that that's really thermodynamics, exactly.

According to some thing I just googled, CO2 diffuses through air at a rate of 16 mm^2/s. Diffusion works with a square root, because it's a random walk, so in 2000 years we've got 6x10^10 seconds or so, making a typical diffusion length of (10^12 mm^2)^(1/2), or 10^6 mm. Which is only about a kilometre, meaning that if we had had 2000 years of dead calm in Palestine then most of the air Jesus ever breathed would still be in Palestine now. That square root really hurts.

In fact there has been wind, of course. I don't know how well anyone can estimate fluid dynamical mixing over thousands of years. It's not stuff that any physicist should be able to estimate on the back of an envelope.

Maybe someone has done a persuasive estimate but I suspect the notion that Jesus and I have breathed the same molecules is probably just based on, "Gee, there are a lot of molecules in even a small bit of air!" It might well not be likely at all.

[malkie]

I don't know that that's really thermodynamics, exactly.

According to some thing I just googled, CO2 diffuses through air at a rate of 16 mm^2/s. Diffusion works with a square root, because it's a random walk, so in 2000 years we've got 6x10^10 seconds or so, making a typical diffusion length of (10^12 mm^2)^(1/2), or 10^6 mm. Which is only about a kilometre, meaning that if we had had 2000 years of dead calm in Palestine then most of the air Jesus ever breathed would still be in Palestine now. That square root really hurts.

In fact there has been wind, of course. I don't know how well anyone can estimate fluid dynamical mixing over thousands of years. It's not stuff that any physicist should be able to estimate on the back of an envelope.

Maybe someone has done a persuasive estimate but I suspect the notion that Jesus and I have breathed the same molecules is probably just based on, "Gee, there are a lot of molecules in even a small bit of air!" It might well not be likely at all.

But hey, why ruin a perfectly good claim by using facts - spoilsport!

That's the problem with you scientists - you won't take stuff purely on faith - always looking for facts and evidence and proofs.

[drumdude]

Kyler's latest screed:

The TLDR
It seems unlikely that Joseph could guess the name Nahom by chance alone, or that he could’ve gotten that location from a map.

What was that Sledge was saying about "we've heard this all before"...

[Physics Guy]

That's the problem with you scientists - you won't take stuff purely on faith - always looking for facts and evidence and proofs.

I'd quibble here depending on exactly what we mean by "take". It's not scientific to conclude by faith that something is true, but it's common to gamble a lot of time and effort on hunches. Some discoveries seem to require bold leaps, and precisely because there's no guarantee that my leap will be the right one, we need a number of people to be leaping. That kind of open-eyed risk-taking is different from blind faith, but I don't think we should exaggerate the difference.

In empirical sciences, at least, scientists are looking for ways to test their hypotheses, not trying to prove them. In a sense they're even trying to disprove the hypotheses, by identifying measurements that could contradict them. Pursuing disproof by contradiction means, though, that for most of the time over many years a scientist is thinking, "If it's true then that would mean that we could maybe see this ...". So most of the scientist's research thinking is going to be assuming the hunch-hypothesis as a premise. And there may be a whole research community, with conferences and journals, dedicated to the same uncertain premise as a working hypothesis. A promising but uncertain hypothesis can remain as the basis for the work of a whole community over decades.

Most occupations involve risks and the stakes can certainly be much higher in other occupations than they are in science, but I think science may be unusual in the length of time over which one may have to sustain the investment before learning whether it will pay off or not. Even if adverse evidence begins to appear, it's not actually unscientific to stick with the hypothesis even though it now seems more doubtful. One should be clear-headed enough to acknowledge the adverse evidence but it's true that experiments can be wrong or misleading. It's not scientifically necessary, or even wise, to abandon a longstanding hypothesis at the first sign of trouble.

From an epistemological viewpoint blind faith may still be quite different from that kind of persistent dedication to an uncertain hypothesis. You can tell the difference by asking bluntly, "Are you sure that it's true?" The believer will typically declare that they are, without hesitation; the scientists should admit that they're not, also without hesitation. Or at least without too much hesitation. After years of starting work by assuming a premise, one may have to switch mental gears to recall that the hunch isn't sure.

From a psychological viewpoint, however, blind faith looks to me like a tactic. It risks over-commitment; a blind believer may keep on throwing good resources after bad when it would be smarter to quit and cut losses. But it also lowers the risk of missing a daring discovery just by getting discouraged. So it can be a useful tactic in spite of its risks. A lot of scientists probably do slip into believing in their hypotheses in a religious-like way, at least for much of the time, just by the force of the mental habit of assuming them.

And conversely I think it may be superficial to conclude that all religious believers are really doing something different from the committed scientist just because they may declare that they are. How important is that one-word answer to a seldom-asked question, "Are you sure that it's true?", compared to all the thoughts and feelings and actions over years, in which the religious believer and the scientist may be behaving very similarly? Perhaps the religious believer is just being naïve about epistemology, and not really understanding what it means to be sure something's true. Perhaps mischaracterising their own mental state as one of certainty is their only real error. If that were so, would it be such a big deal?

[Doctor Steuss]

Kyler's latest screed:

The TLDR
It seems unlikely that Joseph could guess the name Nahom by chance alone, or that he could’ve gotten that location from a map.

It also seems unlikely that Joseph and his family would be close acquaintances of a man whose son was named Nahum.

Therefore, Thetans.

[Lem]

Kyler's latest screed:

It also seems unlikely that Joseph and his family would be close acquaintances of a man whose son was named Nahum.

Therefore, Thetans.

well that's probably the best explanation for why Warren Aston alternates between writing about Nahom and the existence of extra-terrestrials.

[Rivendale]

I don't know that that's really thermodynamics, exactly.

According to some thing I just googled, CO2 diffuses through air at a rate of 16 mm^2/s. Diffusion works with a square root, because it's a random walk, so in 2000 years we've got 6x10^10 seconds or so, making a typical diffusion length of (10^12 mm^2)^(1/2), or 10^6 mm. Which is only about a kilometre, meaning that if we had had 2000 years of dead calm in Palestine then most of the air Jesus ever breathed would still be in Palestine now. That square root really hurts.

In fact there has been wind, of course. I don't know how well anyone can estimate fluid dynamical mixing over thousands of years. It's not stuff that any physicist should be able to estimate on the back of an envelope.

Maybe someone has done a persuasive estimate but I suspect the notion that Jesus and I have breathed the same molecules is probably just based on, "Gee, there are a lot of molecules in even a small bit of air!" It might well not be likely at all.

Neil DeGrasse Tyson explains it this way. "More air molecules in breath of air than breaths of air in Earth's atmosphere. Some air you inhale was exhaled by Cleopatra."

[Physics Guy]

That's true, but diffusion still seems like an issue to me even after 2000 years. At 16 mm^2/s, diffusing molecules will only spread a kilometre in all that time, because of the diffusion square-root law.

Diffusion isn't a sharp front that moves in unison, but a smearing-out probability distribution, so the fastest and luckiest molecules may have gotten further—and there are enough molecules for the luckiest few to be very lucky indeed. The hugeness of molecular numbers also means, though, that getting through several kilometres of air well ahead of the pack means getting lucky breaks on an insanely long series of collisions with other molecules. The bell curve of probability density really drops quickly; it can cut down even huge numbers very fast.

So I'm really pretty sure that Jesus- or Cleopatra-breathed air molecules have not yet been mixed throughout the whole atmosphere by diffusion. That would take a diffusion length of a few tens of thousands of km, which would take a few hundred million times longer than the 2000 years it took to spread one kilometre. So we're talking a trillion years for diffusive mixing into the whole atmosphere. The sun will puff up giant and consume the Earth long before that ever happens.

The 16 mm^2/s diffusion rate also implies that it takes over 16 hours for CO2 to diffuse a meter in still air. Smells clearly spread faster than that. So evidently the spread of molecules in air can be dominated by air currents rather than diffusion. That shouldn't really be a surprise. To get things to mix into a teacup it really helps to stir a bit. Do air currents really mix air from Palestine or Egypt through the entire atmosphere, though? Diffusion leads to uniform mixing in all directions but air currents might not, and I have no idea how to assess this. If no wind has ever blown from Palestine or Egypt to within a kilometre of you, then it seems to me that you'll have to rely on diffusion to get Jesus's or Cleopatra's molecules to you, and there hasn't been nearly enough time for that yet.

I have actually walked around Jerusalem a few times in my life, so I have the opposite issue. Did winds blow all Jesus's air molecules away from there before I arrived, or did some manage to stay trapped in sheltered corners until they diffused out into the street just before I arrived?

[drumdude]

Kyler has a new screed up:

The TLDR
It seems unlikely that Nephi could have built and sailed a boat from the Arabian Peninsula to the New World.

Though some critics have labeled Nephi’s voyage as an impossibility, those perceptions are largely based on the assumption that Nephi had to have built a Renaissance-style sailing vessel, as if the Nina, Pinta, or the Santa Maria were Nephi’s only options. That assumption doesn’t hold, given a variety of demonstrated oceanic voyages that rely only on ancient technology. Given the success rate of those voyages, and a conservative estimate of 16,000 man-hours of available labor for Nephi and his family, I put the probability of him being to build a boat at p = .3085 and the probability of him being able to sail it the requisite 17,000 miles at p = .0265. The odds would have been stacked against Nephi, but not enough to drastically alter the Book of Mormon’s authenticity.

Evidence Score = -2 (reducing the probability of an authentic Book of Mormon by two orders of magnitude)

That, ladies and gentlemen, is how you turn a mountain into a mole hill.