Mental exercises for a better brain

There’s this discussion going on over at Respectful Insolence between an anti-vaccine activist and an epidemiologist, like me. The anti-vaccine activist — whom I thought was banned from there (oops) — is known to be quite “dense” when it comes to epidemiology and biostatistics. I don’t blame him, much. His highest degree in science is in Fire Science. I don’t know where this guy when to school, but most programs I’ve found, like this one, don’t have biostatistics or statistical reasoning in their curricula. This would explain the activist’s misunderstanding of a case-control study. Like the PhD in Biochemistry being discussed by Orac in that post, the activist thinks that matching cases and controls in a study somehow disallows for the examination of their vaccine status and its relationship to autism. They think that cases (autistic children) should have a different vaccine status than controls (neurotypical children), and then we can see if they have a difference in vaccine exposures.

Can you see the logical fallacy in that? Continue reading

Fun with homeopathy and math, again

After the last discussion on homeopathy, someone asked me to give a description of what a 200C homeopathic remedy would have to start out with in order to have at least one molecule at the end of the dilution. So let’s use the example of sugar (glucose) and see how much sugar we would need to get at least one molecule of sugar in a liter (1,000 mL) 200C remedy. We will use math for this, so hold on to your butts.

Remember that Avogadro’s constant states that there are 6.02×10^23 molecules of glucose in 180 grams of the stuff. So, if we add 180 grams of sugar to a liter of water, we will be adding 6.02×10^23 molecules of glucose into that liter. Remember that diluting that initial solution 1C (by one hundred) will leave us with 1.8 grams per liter or 6.02×10^21 molecules of glucose per liter. Finally, remember that we have to do this 200 times (to get to 200C), and that doign this makes us run out of molecules at around the 8th or 9th C dilution. After that, we are diluting water with water.

But what if we want to make sure there is at least one molecule of sugar at the end, at the 200th C dilution?

In that case, we work backwards with the assertion that there is one molecule per liter at 200C. To go to 199C, we would have to concentrate (the opposite of dilute) the solution by a factor of 100, leaving us with 100 molecules in the 199C dilution. Moving up to 198C, we have 10,000 molecules (100 multiplied by 100). Not quite Avogadro’s constant yet. Let’s go to 197C, and see that we have 1,000,000 molecules (10,000 multiplied by 100). Have you noticed the trend?

For every C concentration, we are adding two zeroes to the right of the 1 that we started with at 200C. So, after 200 concentrations, we will have 400 zeroes to the right of the 1. That’s an enormous number of molecules.

How enormous? Taking into consideration that Avogadro’s constant is 6.02 followed by 21 zeroes to make up just one mole, 1×10^400 molecules make up… well… a lot of moles.

Seriously, I don’t have a calculator with me with a display big enough for all those zeroes. I plugged in 1×10^400 into my mac’s calculator and it laughed at me! I tried to divide that number by Avogadro’s constant to get the number of moles, and the damn thing grew legs and walked away, cursing at me.

No, the computer didn’t do that. But if you believe homeopathy then the computer doing that doesn’t seem so far fetched.

If you multiply all those moles times 180 grams, you will have a lot of tons of sugar that you need to somehow cram into one liter of water in order to dilute that liter of water by 100 two-hundred times to get a final 200C homeopathic remedy that has at least one molecule per liter.

Did you catch that?

One molecule per liter. One. You have a 1 in 1,000 chance of catching that molecule if you only take one milliliter of the final solution – the remedy – at a time.

Even if you go from 30C to an original solution, you add 60 zeroes to the right of the 1, which is still a huge number, you will have 1.66×10^36 moles of sugar at your beginning solution. At 180 grams per mole, you’re looking at about 3×10^38 grams of sugar that will need to be put in one liter of water.

You’re going to need a lot of sugar. So…

Now do you see why homeopathy is more about magical thinking than any sort of science or medicine?

Why October 23?

If you’ve been paying attention, you may have seen that the countdown clock to “The Poxes” is almost there. It will reach zero time on Sunday, October 23, at one minute past midnight that morning. Why did I pick that date?

I picked that date because it is “10.23” a date in which people in different parts of the world point out the scientific inaccuracies of the homeopathic remedies sold as cures to all sorts of things. Why 10 23? Because Avogadro’s number is a constant which establishes that there can only be 6.022 times 10 raised to the 23rd power (6022 followed by 20 zeroes) atoms or molecules of something in a mole of that something. It’s a pretty big number, but you can see how diluting something by 100 two hundred times can wipe out even that many molecules. An example? Keep reading.

From the periodic table of elements we see that glucose (made up of six carbons, twelve hydrogens, and six oxygens) has a molecular weight of about 180 grams per mole. That is, 6.022×10^23 molecules of glucose weigh 180 grams. So let’s take those 180 grams and put them in a liter of water (1000 milliliters). Now, like any good homeopath, let’s take that initial solution and make a “200C” homeopathic remedy.

The “C” in “200C” stands for a dilution of 1 to 100. So “200C” means that the solution is diluted 1 to 100 two-hundred times. So we start with a 180g per liter solution. Dilute that by 100 the first (of 200) time, and we have a 1.8g per liter solution. Dilute it the second (of 200) time and we have 0.018g per liter. The third time? 0.0018g per liter. But let’s just stop and look at what’s happening at the mole of glucose.

The mole of glucose we started with in one liter was 6.022×10^23 molecules. There were that many molecules of glucose, remember? After the first dilution, there were 6.022×10^21 molecules. Second dilution? 6.022×10^19. After the third, there were 6.022×10^17. Can you see where this is going?

As we continue to dilute our homeopathic remedy, we are adding two zeroes immediately to the right of the decimal point in terms of grams per liter. In terms of moles, we are subtracting two powers of ten from the exponent (ten times ten is one-hundred, get it?). In both cases, if we go through to the 200th dilution of 1 to 100 parts, we’re going to A) have a whole bunch of zeroes to the right of the decimal point (400 zeroes, in fact), and B) run out of exponents of the moles.

It’s B that really brings the message home. Why? Because 0.0…198 zeroes here…018 grams per liter equals less than one molecule per liter left. What’s less than one molecule? No molecules. (You can’t split a glucose molecule and still call it “glucose”.) That’s right. If you dilute a mole of glucose (180 grams) – or anything else in the known universe – to a “200C” solution for homeopathic treatment, you end up with no chance of even one single molecule left in the final dilution.

No chance… Well, okay, there’s a chance, but it’s small. I’m talking really, really small. How small? Let’s say that we have the ability to fill the universe with lottery balls. You can pick one ball. What is the chance that the winning ball will be yours if we have the entire universe to pick from? Yeah, it’s that small.

And what does one goddamn molecule of anything do, anyway?

So how does homeopathy “work”? It doesn’t. But the charlatans that push it will still tell you fantastic stories of how water “remembers” what’s been in it. So, even with no molecules left, the water in the 200C remedy will remember that it once had whatever you dissolved into it. Yes, you guessed it, there is no evidence of this claim. (In fact, if it were true, then water would remember all sorts of nasty things it’s been in contact with… Like feces.)

What if you add more than one mole to the initial solution? Is there an amount of moles you can add to still have at least one molecule left at the end? Yes, there is. But that number is so large (6.022×10^23 multiplied by 180 grams, in our example), that you’re diluting the water in the solution, not the “active ingredient”.

In “The Poxes”, you will meet two very skeptical characters. One is skeptical by nature, because he is always questioning the universe around him, a true scientist. The other is skeptical out of spite. A homeopath did something very, very bad to him earlier in his life. So the second character has an axe to pick with questionable medical practices. You’ll get to meet them on 10-23. I hope you join me.