Running the numbers on homeopathic dilution

February 13, 2011

Why do we keep saying that homeopathy is not medicine? Why do we keep saying that there is no medicine in it? Surely when you dilute something there is still some of it there. So why do skeptics insist that there is nothing?

Well, I’ll explain.

In a typical homeopathic dilution, a tiny sample of something is dissolved in water, and then 1 mL of solution is transferred to 99 mL of water (making an even 100 mL). It is mixed (well, “succussed”), and then 1 mL is transferred to another 99 mL container, and so on. This may be done 20 or 30 times.

Sure, that’s a lot of dilution, but even if you put a few drops of something in a swimming pool, there are so many atoms in a drop that any sample should contain traces of the substance, and the homeopathic dilution is, after all, only a few litres.

Well, no. Let’s do the math on this, and see what the concentration comes out to be at the end. Let’s choose something like Lithium, as it is light, and it is used as a medication (I have no idea if it is used in homeopathy, but let’s just use it as an example). Lithium has a molar mass of 6.94g, and a density of 0.53 g/mL. Let’s begin with a 1% solution (v/v), and dilute it 20 times:

1 mL of Lithium contains 4.6×10^22 atoms. That’s 4600000000000000000000 atoms. That’s a lot. When dissolved, 1 mL of that solution should contain 1/100 of that, though still 46000000000000000000 atoms. But each time we dilute it, we decrease it by a factor of 100, so with serial dilutions, we have

  1. 460000000000000000 atoms
  2. 4600000000000000 atoms
  3. 46000000000000 atoms
  4. 460000000000 atoms
  5. 4600000000 atoms
  6. 46000000 atoms
  7. 460000 atoms
  8. 4600 atoms
  9. 46 atoms
  10. 0.46 atoms
  11. 0.0046 atoms
  12. 0.000046 atoms
  13. 0.00000046 atoms
  14. 0.0000000046 atoms
  15. 0.000000000046 atoms
  16. 0.00000000000046 atoms
  17. 0.0000000000000046 atoms
  18. 0.000000000000000046 atoms
  19. 0.00000000000000000046 atoms
  20. 0.0000000000000000000046 atoms

What this means is that after only 10 dilutions there is a roughly 50:50 chance of a single atom being present, and after 20, there is a chance of 1 in 217 billion billion that there will even be one atom present. Or, put another way, it would be the same as taking one mL of a substance and dissolving it in a volume of water equivalent to a sphere over two and a half billion kilometres across, or roughly the size of the orbit of Saturn correction: with 20 dilutions the volume would be about the volume of a sphere the size of earth’s orbit. But if you add two more dilutions, that sphere expands to the orbit of Uranus. And if I’m doing my math correctly, 30 dilutions would be equivalent to dilution in a sphere 130 light years across!*

So we know that there is none of the active ingredient in homeopathic medicine, if it is in fact prepared properly. None at all. But then, homeopaths don’t claim the original substance is there – they claim the water is influenced, and retains a “memory” of the substance, and that this memory is what is amplified by the dilution. This, too, is of course utter bullshit.  This idea is born of magical wish-thinking, and is not even remotely related to reality. Water is water, and has the properties of water, not a “memory” of what was once in it.

So that’s why, when we say “there’s nothing in it”, we really mean it.

*check my math:

  • there are 10^15 cm^3 in a cubic km
  • 30 dilutions by 100 is 10^60 mL
  • which is 10^45 km^3
  • which is a sphere with radius 6.2×10^14 km, or 65 light years.

Oh yeah? So there!

January 20, 2011

Oh, what the hell. I really shouldn’t be doing this as I have actual work to do. CL Taylor (@cltaylor463) claimed to have disproven evolution several times. So I called him on it. He says

@BipedalTetrapod I just refuted your ignorant evolution-Athestic ideas in the past seven tweets

Okay then. Let’s have a look-see at the refutation, in reverse chronological order:

I have once again picked apart evolution!

Ya, ya, you said that. Butlet’s have a look

Adaptive radiation is a pipe dream develped by evolutions to justify a faulty assumption of evolution.

Um, no. Adaptive radiation is observable in the fossil record. Sorry, but “I say so” isn’t refutation.

All creatures are not perfect. Imperfections mean nothing evolution is flawed.

No. Evolution never EVER claimed creatures are perfect. Quite the opposite. Creationists do, however, so that’s a point for me.

Homology means that we have common traits with other animals but nothing more evolution is flawed

You share the same number of arms and legs and hands and feet with your siblings and cousins, yes? Are these genetic? Did you inherit those traits from a common grandparent? Or is it just chance that your whole family has the same number of fingers and toes? If these characteristics are genetic traits that are inherited from a common ancestor, then ALL organisms that share those traits inherited them from a common ancestor.

98% is not 100%.A chimp is not a human.Our DNA is so complex that we do not share a common ancestor.

Duh. If a chimp were human it wouldn’t be a chimp. DNA isn’t actually complex. It is very simple. Paired nucleotides strung together. It’s just that there are a shitload of pairs.

Life does not have a family tree evolutionist.We did not come from bacteria.

“because I say so” isn’t an argument. So, wrong.

It is impossible both mathematically&observingly for evolution to exist.

Whatever that means. Evolution is observable and has been observed (see, and mathematics is used all the time in evolution.

Since radioactive dating is inaccurate,Evolution is based on unscientific&undocumented assumptions.

Radioactive dating is quite accurate. Evolution is based on science, and always has been, whether you like it or not.

Evolutionist,still believe in the principle of superposition?

That recent strata are deposited on older strata? Duh.

Evolutionist-Calculations based on invalid assumptions always=invalid results

But calculations made repeatedly on assumptions that have been validated by umpteen different analyses from all walks of science tend to be valid. I would say, however, that Intelligent Design calculations, which are based on invalid assumptions, do lead to invalid results. So thanks for pointing that out.

There is no way for scientist to know the original amount of radioactivity in rocks when made.

Yes, there is, by looking at the quantity of the products of radioactive decay.

The earth’s rotation was stopped twice in Joshua10:13-14;II Kings20:9-11.

Gee, you got me there. Why, I must give up my atheistic evolutionist ways! No. Just kidding. Sorry, but it really wasn’t.

Only God could have designed cell differentiation so well. Random chance could not have done such.

Evolution is NOT about random chance. It is about iteration under selective pressure.

Evolution flaws-the uniqueness of DNA is so complex that it proves complex organism were made seperate&along side simple living things.

See the Chimp comment earlier. To which I will add that “It’s too complicated for me to understand so it must be false” is not a valid argument. I count 14, not 7 tweets. But anyway, let’s take a couple more:

@kaimatai It is not observable to believe in Evolution, b/c it denies the existance of God. God is the law and order in life.

So, what you are saying is, your faith is so shaky that it is threatened by actual observations of real events?

@kaimatai I find it very hypocritical that your lack of stable morality is lecturing me on your Postmodernism. Really? You are a fraud also

You want lack of stable morality? Research shows that the faithful have a wandering moral compass.

The Disingenuous “Thermodynamics” Argument

January 20, 2011

You know, I still keep seeing the second law of thermodynamics being used as an argument against evolution, despite multiple thorough rebuttals. So let me add a few words of my own in an effort to stem the flow of stupid.

The argument, loosely summarized, goes like this:

  1. The Second Law of Thermodynamics says that entropy must increase in any closed system.
  2. Since life from non-life requires complex molecules to form from simple molecules, life could not arise by chance, because this would violate the 2nd Law.
  3. Since mammals and birds and fish are all more complex than single-cell organisms, they could not have evolved, as a system cannot become more complex over time.

The rebuttals for this are, quite simply:

  1. The Earth is not a closed system. We receive about 1.3 kJ of solar energy per square metre per second, every second, always.  The second law of thermodynamics does not apply.
  2. Life from non-life is abiogenesis, not evolution. But abiogenesis is thought to have been driven by heat and chemosynthesis, so again there is an input of energy.
  3. Lastly, and most ironically, the very people who claim that single celled organisms couldn’t possibly become complex, multicellular organisms, themselves grew from a single cell. So it’s good enough for them, but not any other organism. And secondly, the argument using thermodynamics against evolution proposes, instead, the sudden appearance of all living things. Like that doesn’t violate the laws of thermodynamics. Sheesh.

But wait, there’s more. You see, the argument that evolution is impossible because of the second law was widely promoted by the likes of Drs. Henry Morris and Duane Gish of the Institute for Creation Research. Please note that these gentlemen, at the time they made these claims, had doctorates in Engineering and Biochemistry respectively. Which means they understood the laws of thermodynamics, and would have known that the argument was wrong. Which means they were blatantly lying.

The fact that this argument is still being presented as evidence against evolution is appalling, and shows just how ill-informed the anti-evolution movement really is.  Feel free to send anyone you find using this argument to this page, or for a more torough thrashing, to the Talk Origins Thermodynamics FAQ.

What does this say about intertube users?

October 25, 2010

Every once and a while I check my stats. Not every day, I’m not quite that narcissistic, but every few days. And one thing that I noticed was that almost every day there are one or two hits to this blog using the search “guinea pig funny”. Presumably linking to the one and only guinea pig related post. But then I got to thinking – how far down on the list must this post be when doing a search for “guinea pig funny”. So I went on to four different search engines, and entered that search term, and scanned through the first 20 pages. And guess what? No Bipedalia. That’s really not surprising – but it does mean that there are a couple people each day searching through more than 20 pages of search engine hits for funny pictures of guinea pigs. Somehow that lowers my estimation of mankind.

Economic argument against the woo

October 20, 2010

XKCD for the WIN:

Quality, not quantity, leads to speciation

October 7, 2010

In 1859, Charles Darwin published a book that changed how biologists understand the living world. Although his book was titled “On the Origin of Species by Means of Natural Selection”, it never actually explained the process of speciation. Although an elegant and thorough explanation of the mechanisms underlying evolution, he extrapolates this to say “species have changed, and are still slowly changing by the preservation and accumulation of successive slight favorable variations”. In other words, natural selection produces change, and the accumulation of enough changes produces a new species. A century and a half later, this is still accepted wisdom.

For most Biologists (and scientists in general), accepted wisdom is not enough. Ernst Mayr put forth the notion of allopatric speciation – that physical isolation can allow genetic change to occur separately in two populations, eventually leading to reproductive isolation and thus to speciation. Steven Gould and Niles Eldridge produced the idea of punctuated equilibrium – that the history of life consists of long periods of stasis (ie species remain relatively unchanged) punctuated by rapid bursts of species diversification.

Although many viewed speciation and macroevolution as the rapid accumulation of many individual variations, effectively speeding up the process, others (Goldschmidt, Gould) proposed that these events occurred through single (or a small number of) events that produced significant morphological or physiological change. The technical term for this is saltation (meaning a jump), though Goldschmidt’s term “hopeful monster” is also used – not always kindly.

In the early 80’s, Homeobox genes were discovered. These are genes that regulate body pattern, and it was discovered that the duplication, relocation, and modification of these genes is responsible for significant changes in body plan. Suddenly there were genes that could produce “hopeful monsters” without significant genetic change. And yet, the gradualistic model of speciation through accumulation of many small changes has persisted, primarily because there has been no evidence that a single or small number of changes can produce enough change to create a new species.

Recently, Dr. Mark Pagel at the University of Reading decided to put to the test. He reasoned that if speciation is dependent on the accumulation of a number of genetic changes, that would show up statistically as a normal distribution in a survey of the number of genetic differences between species in the family trees of different groups.

What he found was that the distribution did not follow a normal curve, but an exponential (poisson) distribution instead. This is the distribution one finds with truly random distributions, such as the frequency of lightning strikes. The differences between these two random distributions are subtle but significant. The most important difference is that a normal distribution has a mode – a peak value around which the values are distributed. A poisson (exponential) distribution does not – any value is equally likely.

The implication for evolution is that there is no typical, usual, or expected number of mutations required for a population to become a separate species from its parent population. In other words, We can’t say that a new species arises after about 20 (or 60 or 2000) mutations. It may take any number of mutations to form a new species – 50, 100, 1000. Or just one.

At first this seems to fly in the face of the “accepted wisdom” that there is some sort of threshold for speciation. But given that mutation is random, any number of mutations could occur that produce little or no effect, or that do produce an effect but in genes that are unimportant. For speciation to occur, a change must arise that leads to a reproductive barrier. What this study tells us is that a sufficiently significant change is as likely to occur from a single mutation as from 10, 30, or 100.

So while the accepted wisdom – or at least the default assumption – is that speciation arises as the result of an accumulation of minor changes, it now looks more like a single significant change is responsible for a speciation event. The implication being that the quality of mutation, not quantity, is the deciding factor for speciation.

Although in retrospect this makes perfect sense, it does provide additional context for models of evolutionary change – such as punctuated equilibrium and Goldschmidt’s “hopeful monsters” – that were ridiculed when first proposed. Which just goes to show that Hamlet was right: There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.

Gliese 581g – Define “Habitable”

October 1, 2010

Much has been made of the announcement about the recently announced discovery of a potentially habitable planet around a nearby sun. The planet, dubbed Gliese 581g is estimated to be around 3 times the Earth’s mass, and about 1.5 x it’s diameter (depending on composition).

The excitment over this particular exoplanet – the 492nd discovered – is that it lies in the “goldilocks zone” where th etemperature is not too hot, not too cold. That is, its distance from the star is such that the surface temperature is likely to be such that liquid water could exist on the surface, something that is key to life as we know it.

However, the announcements touting “Scientists discover habitable planet” and “Earthlike planet discovered around nearby star” are grossly misleading.

It is true that Gliese 581g lies in the goldilocks zone. However, we know nothing of its composition, its amosphere, or its rotation. This latter is important, as the planet lies only 0.15 AU’s from its parent star. In contrast, Mercury 0.39 AU’s from our sun. 581g’s proximity to the star means the planet is likely tidally locked – in other words, one side always faces the star, the other away. One side would be a permanent, hot day, the other a permanent, frozen night. Even with an atmosphere to carry heat back and forth between the two sides, much of the water and other atmospheric gases could freeze out on the night side, leaving a thinner atmosphere, and permanent desert on the day side. The temperature along the terminator (the “twilight zone”) should be intermediate, allowing for liquid water, but not if all the water is frozen on the night side.

On the other hand, the star Gliese 581 is a red dwarf star (which is why the goldilocks zone i sso close), which is very stable and long lived, so if there were conditions suitable to life, it would have a good ling time to evolve.

Until we have the tools available to analyze the spectrum of the atmosphere, we really can’t know any more, as much as we want to speculate.

This doesn’t mean we shouldn’t get excited – far from it. The discovery of Gliese 581g tells us something very important. It tells us that there are two earth(ish) size planets orbiting in the goldilocks zone in a tiny volume of space (relatively speaking) – Gliese 581g and our own. the statistical implication is that goldilocks planets are likely common in the galaxy. And that means that even if 581g is a lifeless, half-frozen wasteland, there are more earthlike planets out there.

The Triceratops that Never Wasn’t

August 11, 2010


I recently returned from a holiday abroad to find headlines proclaiming that Triceratops Never Existed! My first thought was of course, WTF? And my second thought was, just how stupid are they? And then the little pessimistic third thought was that the way this story is being waved about, it will be used as “ammunition” by antievolutionists, one more little item with which to further wrap themselves in ignorance.

So here is the story.

Ceratopsian dinosaurs were (mostly) large, quadrupedal herbivoves with a frill behind the skull, and many bore horns from the nose and/or the top of the skull over the eyes. There is substantial diversity in the group in the shape and size of the frill and horns, leading to the definition of many different genera and species. But there is also variation within each species, blurring the boundaries between the different classifications. Because of this, the group as a whole has undergone taxonomic revision several times. The recent work by John Scanella and Jack Horner continues this trend by further clarifying the taxonomy of this intriguing group.

Scanella and Horner surveyed known specimens of the ceratopsian classified as Torosaurus, and concluded that the developmental and morphological evidence suggests they are not members of a separate genus, but in fact “fully grown” members of Triceratops. This is bolstered by the fact that there are no known juvenile Torosaurus remains – though the discovery of such remains would, of course, reverse this change in classification. Since the name Triceratops was coined first, it remains while Torosaurus becomes obsolete (pending further study and corroboration by other researchers). This sort of thing happens all the time, partly because defining “species” for organisms that have been dead for 70 million years with only a limited dataset is tricky business, and partly because we learn more. Science progresses.

So, in fact, the story headlines should have read “Torosaurus reclassified as adult Triceratops“. But a) that requires understanding what is being written, and b) wouldn’t sell papers. It really ticks me off just how wrong the statement “Triceratops never existed” really is. Animals classified as Triceratops and Torosaurus did exist, which is why we have their fossils. The classification of one of these groups may be in error, but it would be Torosaurus that ceases to be as a genus.

Thought of the day

June 20, 2010

A man can fail many times, but he isn’t a failure until he begins to blame somebody else.
-John Burroughs


April 23, 2010

Two things I love – guinea pigs and Doctor Who. Put them together and…