Monstrous Moles: Happy Mole Day!

Happy Mole Day! It’s the 23rd of October and, at least where I am right now, it’s still between 6:02 am and 6:02 pm, so that means it’s time for chemists to celebrate! Of course, I’m in the U.K., so the date thing doesn’t quite work — for me this is 23/10, not 10/23 — but since there are only 12 months in a year (even in 2020) the British system is a bit unsatisfactory, so I’ll go with the American date format for the day.

There are literally loads of atoms in everything

What’s a mole? Well, to paraphrase Douglas Adams: atoms are small. You just won’t believe how vastly, hugely, mind-bogglingly small they are. I mean, you may think the latest incarnation of the walnut whip is small, but that’s just peanuts to atoms. Or even walnuts.

There are literally loads and loads of atoms in everything. There are so many of the blasted things that the numbers are a real pain to deal with. A teaspoon of table sugar, for example, has about 7,400,000,000,000,000,000,000 sucrose molecules in it, and since each sucrose molecule contains 45 atoms, that’s a whopping 330,000,000,000,000,000,000,000 atoms. And that’s not even a heaped teaspoon.

Even if we used standard form and wrote that last number as, for example, 3.3 x 1023 it’s a bit of a pain. And chemists are far too busy to write things out in full — why do you think they came up with all these symbols in the first place? — so what we do is we pick a convenient amount, which turns out to be 6.022 x 1023, and call that a “mole”. It’s just like calling twelve eggs “a dozen” only, you know, bigger.

I’m not going to explain the origin of the actual number further than this. There’s an awesome graphic here from Compound Interest and, if you want to know more, just click through.

What I am going to do are some… interesting mole calculations. People usually do grains of sand or coins or something. But those are so boooorrring. It’s nearly Halloween, right? I say we go gruesome.

Let’s start with blood!

A healthy adult has about 35 trillion red blood cells in their body at any given moment. (Vampires, presumably, have even more… although… do vampires make their own blood supply? Interesting question…).

35 trillion is a big number, right? A trillion is a million million (on the short scale, which everyone uses, don’t start), 1,000,000,000,000, or 1012, so 35 trillion is 3.5 x 1013.

But that’s only 0.000000000058 of a mole! Even if we count everyone on the planet, we only get to 0.45 of a mole. Yes, that’s right. Even if we drained the blood out of every, single human on the planet, we’d only about half a mole of red blood cells.

Ooh, how about bacteria? We have a lot of those on us, right? In fact, we have more microbes in and on our bodies than human cells! (Well, we can argue about the definition of “human” here, I suppose, but… let’s not.) Apparently there are around 3.8 x 1013 bacteria in our colons which means… damn. This is the blood cells thing all over again, isn’t it? If we took all the humans on the planet, sucked out their gut bacteria (don’t ask) and collected it all together (really, don’t) we’d have, yes, a little under half a mole of microbes.

Don’t tell the tooth fairy’s boss. She really IS scary.

Okay, this is all very well, but it’s not helping us get an idea of scale, is it? All right. Let’s try human teeth. Why not? I mugged the tooth fairy for this one (she’s much tougher than she looks), and it’s about 8 mm long. Adult teeth are a bit larger, of course, but the fairy has less of those. Let’s assume 1 cm to make things easier. That’s 0.01 m. If we had a mole of human teeth they would stack up to… 6.02 x 1021 metres, or 6.02 x 1018 km, or (we need to ramp this up a bit) about 640,000 light years. That would reach a little dwarf galaxy in the constellation of Canes Venatici, somewhere in the general neighbourhood of the Milky Way. Or, alternatively, to Neptune and back…. some 670 million times. Gosh.

What about… hair? A fine human hair is about 0.05 mm across, which means a mole of (fine) hair would be 3.01 x 1019 metres thick. The diameter of the Earth is 12,700,000 metres so that’s about… 2,400,000,000,000 times wider than the Earth. Even Rapunzel might struggle with that much hair.

There are about half a mole of red blood cells in all the humans on the planet.

Hang on, let’s go back to those red blood cells for a minute… okay, if there’s about half a mole of red blood cells in all the humans on the planet, and we assume a single red blood cell is 7.8 μm (0.0000078 m) if we put all those red blood cells in a line it would be…2.3 x 1015 kilometres long. The circumference of the sun is about 4,400,000 kilometres so…

… with all the people on the planet, we could make half a billion rings of blood around the sun, one cell thick.

There’s a thought.

In summary, the mole is a flipping big number. Too big, really, to count anything other than atoms (or molecules, or ions). But it is useful for that.

Happy Mole Day!


Look, these numbers are big, right. I’m going to be amazed if there isn’t some sort of order of magnitude mistake. Just… let me know.


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Hazardous homeopathy: ‘ingredients’ that ought to make you think twice

Would you take a medicine made with arsenic? Or deadly nightshade? Lead? Poison ivy?

You’d ask some serious questions first, at least, wouldn’t you? Is it definitely safe? Or, more accurately, are the odds better than even that it will make me better without causing horrible side-effects? Or, you know, killing me?

There ARE medicines that are legitimately made from highly toxic compounds. For example, the poison beloved of crime writers such as Agatha Christie, arsenic trioxide, is used to treat acute promyelocytic leukemia in patients who haven’t responded to other treatments. Unsurprisingly, it’s not without risks. Side-effects are unpleasant and common, affecting about a third of patients who take it. On the other hand, acute promyelocytic leukemia is fatal if untreated. A good doctor would talk this through with a patient, explain both sides, and leave the final choice in his or her properly-informed hands. As always in medicine, it’s a question of balancing risks and benefits.

Would you trust something with no proven benefit and a lot of potential risk? There are, it turns out, a swathe of entirely unregulated mixtures currently being sold in shops and online which clearly feature the substances I listed at the beginning. And more. Because they are all, supposedly, the starting materials in certain homeopathic remedies.

Homeopaths like to use unfamiliar, usually Latin-based, names which somewhat disguise the true nature of their ingredients. Here’s a short, but by no means comprehensive, list. (You might find remedies labelled differently but these are, as far as I can tell, the most common names given to these substances.)

If you haven’t heard of some of these, I do urge you to follow the links above, which will largely take you pages detailing their toxicology. Spoiler: the words “poison”, “deadly” and “fatal” feature heavily. These are nasty substances.

There are some big ironies here, and I’m not referring to the metal. For example, a common cry of anti-vaccinationists is that vaccines contain animal tissues – anything and everything from monkey DNA to dog livers. But many also seem to be keen to recommend homeopaths and courses of homeoprophylaxis – so-called “homeopathic vaccines” – which use bodily fluids such as pus and blood as starting materials.

Now, at this point I’m sure some of you are thinking, hang on a minute: aren’t you always telling us that “the dose makes the poison“? And aren’t homeopathic remedies diluted so much that none of the original substance remains, so they’re just placebos?

Yes, I am, and yes, they are.

Does anyone test homeopathic remedies to make sure there’s nothing in them….?

In THEORY. But here’s the problem: who’s testing these mixtures to make sure that the dilutions are done properly? And how exactly are they doing that (if they are)?

One technique that chemists use to identify tiny quantities of substance is gas chromatography (GC). This is essentially a high-tech version of that experiment you did at school, where you put some dots of different coloured ink on a piece of filter paper and watched them spread up the paper when you put it in some water.

GC analysis is brilliant at identifying tiny quantities of stuff. 10 parts per million is no problem for most detectors, and the most sensitive equipment can detect substances in the parts per billion range. Homeopathy dilutions are many orders of magnitude higher than this (30c, for example, means a dilution factor of 1060), but this doesn’t matter – once you get past 12c (a factor of 1024) you pass the Avogadro limit.

This is because Avogadro’s number, which describes the number of molecules in what chemists call a “mole” of a substance, is 6×1023. For example, if you had 18 ml of water in a glass, you’d have 6×1023 molecules of H2O. So you can see, if you’ve diluted a small sample by a factor of 1024 – more than the total number of molecules of water you had in the first place – the chances are very good that all you have is water. There will be none of the original substance left. (This, by the way, is of no concern to most homeopaths, who believe that larger dilutions magically produce a stronger healing effect.)

What if the sample ISN’T pure water after it’s been diluted?

If you carried out GC analysis of such a sample, you should find just pure water. Indeed, if you DIDN’T find pure water, it should be cause for concern. Potassium cyanide, for example, is toxic at very low levels. The lethal dose is is only 0.2-0.3 grams, and you’d suffer unpleasant symptoms long before you were exposed to that much.

So what if the dilutions somehow go wrong? What if some sample gets stuck in the bottle? Or on the pipette? Or a few dilution steps get skipped for some reason?

Are these largely unregulated companies rigorously quality-checking their remedies?

Well, maybe. It’s possible some producers are testing their raw materials for purity (ah yes, another question: they CLAIM they’re starting with, say, arsenic, but can we be certain?), and perhaps testing the “stability” of their products after certain periods of time (i.e. checking for bacterial growth), but are they running tests on the final product and checking that, well, there’s nothing in it?

And actually, isn’t this a bit of a conflict? If the water somehow “remembers” the chemical that was added and acquires some sort of “vibrational energy”, shouldn’t that show up somehow in GC analysis or other tests? If your tests prove it’s pure water, indistinguishable from any other sample of pure water, then… (at this point homeopaths will fall back on arguments such as “you can’t test homeopathy” and “it doesn’t work like that”. The name for this is special pleading.)

A warning was issued in the U.S. after several children became ill.

Am I scaremongering? Not really. There’s at least one published case study describing patients who suffered from arsenic poisoning after using homeopathic preparations. In January this year the U.S. Food and Drug Administration issued a warning about elevated levels of belladonna (aka deadly nightshade) in some homeopathic teething products. Yes, teething products. For babies. This warning was issued following several reports of children becoming ill after using the products. The FDA said that its “laboratory analysis found inconsistent amounts of belladonna, a toxic substance, in certain homeopathic teething tablets, sometimes far exceeding the amount claimed on the label.”

Now, admittedly, I’m based in the U.K. and these particular teething remedies were never readily available here. But let’s just type “homeopathy” into the Boots.com (the British high-street pharmacy) website and see what pops up… ah yes. Aconite Pillules, 30c, £6.25 for 84.

What happens if you search for “homeopathy” on the Boots.com website?

Have you been paying attention lovely readers? Aconite is…. yes! Monkshood! One of the most poisonous plants in the garden. Large doses cause instant death. Smaller doses cause nausea and diarrhea, followed by a burning and tingling sensation in the mouth and abdomen, possibly muscle weakness, low blood pressure and irregular heartbeat.

I must stress at this point that there is no suggestion, absolutely none whatsoever, that any of the products for sale at Boots.com has ever caused such symptoms. I’m sure the manufacturers check their preparations extremely carefully to ensure that there’s absolutely NO aconite left and that they really are just very small, very expensive, sugar pills.

Well, fairly sure.

In summary, we seem to be in a situation where people who proclaim that rigorously-tested and quality-controlled pharmaceuticals are “toxic” also seem to be happy to use unregulated homeopathic remedies made with ACTUALLY toxic starting materials.

I wonder if the new “documentary” about homeopathy, Just One Drop, which is being screened in London on the 6th of April will clarify this awkward little issue? Somehow, I doubt it. Having watched the trailer, I think it’s quite clear which way this particular piece of film is going to lean.

One last thing. Some homeopathic mixtures include large quantities of alcohol. For example, the Bach Original Flower Remedies are diluted with brandy and contain approximately 27% alcohol (in the interests of fairness, they do also make alcohol-free versions of some of their products and, as I’ve recently learned, they may not be technically homeopathic). Alcohol is a proven carcinogen. Yes, I know, lots of adults drink moderate quantities of alcohol regularly and are perfectly healthy, and the dose from a flower remedy is minuscule, but still, toxins and hypocrisy and all that.

There are cheaper ways to buy brandy than Bach Flower Remedies.

Amusingly, the alcohol in these remedies is described an “inactive” ingredient. It’s more likely to be the only ACTIVE ingredient. And since Flower Remedies retail for about £7 for 20 ml (a mighty £350 a litre, and they’re not even pure brandy) may I suggest that if you’re looking for that particular “medicine” you might more wisely spend your money on a decent bottle of Rémy Martin?


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