Undeserved Respect

This day is a celebration of free speech. As such, let's have a quotation from Richard Dawkins!

The God of the Old Testament is arguably the most unpleasant character in all fiction: jealous and proud of it; a petty, unjust, unforgiving control-freak; a vindictive, bloodthirsty ethnic cleanser; a misogynistic, homophobic, racist, infanticidal, genocidal, filicidal, pestilential, megalomaniacal, sadomasochistic, capriciously malevolent bully.

Not only is Dawkins a scholarly gentleman with a fantastic sense of humour, he is also a master of understatement.

Blasphemy Day Thoughts

Nothing is to be held sacred. No stone is to be left unturned. Civil discourse is never inappropriate. No subject is taboo.

Question everything.

The Law of Infinitesimals

I was recently involved in a discussion of homeopathy, and I brought up Avagadro's constant in passing, noting that Hahnemann proposed ludicrous serial dilutions before the value of the constant was known. I was then asked how the value of this number related to homeopathic dilutions. I replied vaguely that it was mostly an order of magnitude thing. My companion pressed me for details, so I sat down and walked her through it, because I like math and also because I think that such inquiry is important. Samuel Hahnemann's principle of serial dilution (the idea that the further a substance is diluted, the more potent is its effect) is a ludicrous one, and actually doing the calculations can be very enlightening.

Let's begin with the assumption that our homeopathic medium is water. What we need to begin is the molecular mass of water; this is easy to calculate, if you have a periodic table handy. Water (H₂0) contains two hydrogen atoms (one proton each) and one oxygen atom (eight protons and eight neutrons, usually), making for atomic masses of 1 u and 16 u, respectively. This makes the molecular mass of water 1 + 1 + 16 = 18 u.

Now, if you remember high school chemistry (I won't blame you if you don't), 1 unified atomic mass unit (I just found out that chemical and physical amu were deprecated!) is equal to 1 gram/mole. This means that water, at an atomic mass of 18 u, has a mass of 18 grams per mole of particles. And here's where we come to the importance of Avagadro's constant: one mole is approximately 6.02 x 10²³ (this number was arrived at by calculating the number of atoms in 12 grams of carbon-12, in case you're interested).

If we want to take a hard look at our dilution, we need the number of molecules in our dilution medium before we begin. So if we have 18 grams per mole (which, for water, is 18 millilitres per mole—thank you, metric system!) and one mole is 6.02 x 10²³... Well, let's do the math!

18 g/mol = 0.0556 mol/g
0.0556 mol/g = 0.0556 x 6.02 x 10²³/g
0.0556 x 6.02 x 10²³/g = 3.34 x 10²²/g

Or you could just have WolframAlpha calculate it for you. But that wouldn't be nearly as fun!

How about alcohol? Ethanol being more popular (and less deadly) than methanol, we'll use that:

46 g/mol = 0.0217 mol/g
0.0217 mol/g = 0.0217 x 6.02 x 10²³/g
0.0217 x 6.02 x 10²³/g = 1.03 x 10²²/g

So what does this tell us? Well, a standard homeopathic dilution is 30C (or 60X), which means one part "active" ingredient in 100³⁰ (or 10⁶⁰) parts water or alcohol. But here's the kicker: we just calculated the maximum number of "parts" into which it is possible to divide water! Unless you go splitting the atom, you can't divide 1 cc of water into more than 3.34 x 10²² parts. Let's say we're dealing with a full litre of the stuff (approximately two pints, for you Americans): we're still only dealing with 3.34 x 10²⁵ molecules—we're still off by a whopping thirty-five orders of magnitude!

So what's the maximum dilution at which you're more likely than not to have at least one molecule of the original substance? You use logarithms! Assuming one litre of water (1 kg):

log₁₀ 3.34 x 10²⁵ = 25.5

Alternatively, assuming 1.27 litres of ethanol (1 kg):

log₁₀ 1.03 x 10²⁵ = 25.0

That would be a dilution of 25X (approximately 13C). At dilutions above 13C, you are unlikely to have a single molecule of the original substance left!

The solution? (Pun unintentional, but appreciated!) Water has memory! For an erudite discussion of this subject matter, may I suggest Storm, by Tim Minchin?

Leprechauns

I quite like this.

Biblical Unity

I recently sent the following email to the folks over at Reasonable Doubts, and I figured that I might as well share it:

Good morning, gentlemen!

I listened with interest to (the first part of) your dissection of the unity argument. I was, as always, impressed, but I noted that you focused primarily on the first (and meatier, if you'll excuse the implicit omnivorous bias) part of the argument, the premise that the Bible is a marvelous union of ideas, and paid only passing mind to the supposed consequent, that it must have been crafted by God.

Although taking out the premises is an easy (and in this case, fascinating) way to show an argument to be unsound, I was disappointed that there was little or no mention of the argument's invalidity. It is an obvious non sequitur, as there are countless ways to force unity into an anthology such as this.

One could discard the parts that don't fit (the obvious New Testament example being the Council of Nicea [edit: this should be "Nicaea"], although, as I'm certain you'll mention in your next episode, it didn't really do the trick as intended). One could choose to harmonize, rewriting portions, as many scribes did, either intentionally or unintentionally.

But what seems most obvious to me is self selection. The apologist suggests collecting ten friends with similar backgrounds and educations, and asking them their thoughts on Life, the Universe, and Everything, and he suggests that they would have answers wildly at variance. But this is obviously not how it happened. Give those same people a lifelong education in the religious texts that preceded them, and tell them to write the next chapter, and you'll have much more interesting results. We're still not finished, though, because this is where the selection bias comes along. Surely most would take the scriptures as written, either agreeing or disagreeing in their own minds, and that would be that. Most clerics would refrain from tacking on new bits; only those interested in continuing the story would do so.

There are so many things wrong with this argument that it truly becomes absurd. Thank you folks for your excellent work. I look forward to each new installment.

Jonathan Archer, Complete Asshat

I was listening to the most recent episode of The Non-Prophets, this morning, and discovered to my surprise and delight that they were discussing an ethical dilemma in an episode of Star Trek: Voyager. The various incarnations of Star Trek (certainly one of my favourite franchises ever) are generally excellent (Deep Space Nine being, of course, the best of the five-and-a-half), but frequently contain blatant Broken Æsops, where a writer is obviously trying to give a moral to an interesting story, but the moral is clearly freakishly misguided. The most egregious example of this, in my opinion, is found in an episode of Star Trek: Enterprise.

In this episode, the Enterprise NX-01 encounters a planet inhabited by two distinct humanoid species, one more cognitively and technologically advanced than the other (the suggestion is that the distinction is analogous to Homo sapiens and Homo neanderthalensis). In this case, the more advanced of the two species is suffering from a pandemic genetic disease that will eventually wipe them out, while the more primitive of the two is completely unaffected.

Eventually a cure is found. Dr. Phlox administers it to the populace, and saves billions of lives. The end.

Oh, wait: that's not quite what happened. To quote the episode recap from TV.com:

Phlox meets with Archer and says that he doesn't think that it would be ethical to give the Valakians a cure because it would interfere with an evolutionary process that has been going on for thousands of years. Based on his genome studies, Phlox sees increasing skills and intelligence in the Menk that quite possibly would leave them the dominant species -- provided the Valakians died off. He suggests that Archer simply let nature take its course.

What?

So rather than save billions of lives, the doctor (yes, we're talking about a real medical doctor, here; not some quack homeopath or nutritionist) suggests that they allow the total extinction of an entire sentient species on the grounds that it might clear the way for some other species to take over. The best part is, Captain Archer is persuaded by this argument. He even goes so far as to suggest that to provide the cure would be playing God.

As an interested layperson, I have a bone or two to pick with this.

First of all, let's face it: if you have a cure for a disease that you could dispense at effectively no expense, and you fail to do so, you are responsible for any deaths that result. We can quibble about whether situations might arise where this would be the more ethical thing to do, but if you you push the fat guy in front of the bus to prevent it from running over a kindergarten class, you're still responsible for the fat guy's death.

Secondly, we have a glaring logical fallacy: we ought to let nature take its course. This is the naturalistic fallacy [edit: actually, the appeal to nature] (in most cases [edit: a] subset of Hume's is-ought problem), which conflates "natural" with "good" (modern examples include statements such as: "Vegetarianism is wrong because humans evolved to be omnivorous" and "Organic food is better for you because it's all natural"). The fact that noninterference would lead to the extinction of a sentient species take a backseat to the idea that "nature has a plan".

Speaking of nature's plan, the writer of this episode (and therefore his mouthpiece, the doctor) seems to be terribly misinformed about how evolution works. He's not alone, of course. I'm no evolutionary biologist (if you want one of those, look here), but even I understand that there is no "natural plan". We're not evolving toward anything (intelligence, for example), nor are we higher on some form of scala natura (which seems to be the implication in this episode): we are adapting to our environment (although this may be a thing of the past, as we have long since been adapting our environment—and, more recently, ourselves—to our every whim). If intelligence is advantageous for procreation, then that will be the general trend. If sharp eyes or sharper talons were advantageous, then the organism in question would be steered in that direction, instead. For Dr. Phlox to suggest that he could predict the evolution of this species, especially given the complete environmental upheaval that would result from the death of the dominant species on the planet, is nothing short of ludicrous.

And where does "playing God" come from? Is this simply a statement of scale? Archer presumably has no problem with the good doctor curing one patient, or two... But an entire species? That, apparently, is beyond the pale! I've had problems with the Prime Directive before (and I'm not alone: defying the Prime Directive has been a pastime of starship captains since the beginning), but to apply it so poorly before it's even invented? That's simply insane.

I know that there is much more to this issue than what I've discussed here, but I'm tired, so I'll end with this. As Perry DeAngelis might have said: "He's a dick."