New Hampshire has issued new proposed guidelines about allowable levels of a type of pollution in drinking water, which gives me an excuse to run this edited version of a 2016 column I wrote when the subject first came up:

This has brought into regular discourse a word that we don’t use much and don’t understand at all: trillion.

The pollutants known collectively as PFAS are being found in New Hampshire well water not in parts per million or parts per billion, but in parts per trillion – a mind-blowingly minuscule measurement.

How to grasp such numbers? I like to parse it by thinking about time, thusly:

A million seconds is nearly a fortnight (11 days). A billion seconds is a human generation (31 years). A trillion seconds is five times the length of all recorded history (31,000 years).

“Billion” and “trillion” seem pretty similar – they’re goofy words that mean “a whole lot” – but when you compare the length of a human generation with the length of all recorded history, it helps you grasp the magnitude of the difference.

So detecting a toxin down to one part per trillion is like spotting a single important second in the midst of 31,000 years. Which leads to another question: How do you do that?

It’s all technology, said Stephen Knollmeyer, vice president of technical sales at Alpha Analytical in Portsmouth. “A combination of the way you extract the sample and the way you run the test has gotten us into the parts-per-trillion area,” he said, walking me through the details.

The first step, he said, is solid phase extraction to concentrate the pollutant and make it more accessible.

“It uses a solid material that is porous, like little grains of sand, if you will, made out of a chemical that’s absorbent to the chemical we’re looking for. We run water, maybe a liter, through a little tube that might have a couple teaspoons of this solid material in it, then you put in a chemical that extracts everything off that solid,” Knollmeyer said.

This extraction is then analyzed by lab techniques such as liquid chromatography, in which molecules of different compounds move differently through columns of material depending on a lot of complicated chemistry stuff, and mass spectrometry, which sorts molecules based on the ratio of their mass to their charge (more complicated chemistry stuff). Sometimes, Knollmeyer said, back-to-back mass spectrometry is used to increase the specificity.

As you might expect, all of this isn’t cheap. “It uses a quarter-million-dollar instrument,” Knollmeyer said. “In the last 20 years, this has come to fruition in the environmental market.”

As mind-boggling as this is, it gets mind-boggling-er when dealing with dioxin, a group of persistent organic pollutants caused by various industrial applications that are very, very carcinogenic. Dioxin, Knollmeyer said, is measured down to parts per quadrillion.

Quadrillion! That’s a thousand times a trillion! A quadrillion seconds is about 12 times longer than the last Ice Age.

Once my mind stopped boggling, I had a secondary thought: Maybe homeopathy isn’t as ridiculous as I figured.

The key action in homeopathy is to greatly dilute substances in a way that they are somehow supposed to maintain all of their positive characteristics. I assumed this was baloney because the dilution was so extreme, but if one part per quadrillion of dioxin can potentially cause cancer, maybe a homeopathic dilution really can have medical action?


Homeopathy uses its own terms for dilution, such as C, which designates a 100 times dilution. So a substance labeled 2C has been diluted 100 times 100 times, or 10,000 times; 4C is 100 times 100 times 100 times 100 times, or 100 million times, and so on.

The least diluted homeopathic remedy you’ll see on the shelves is 6C, which has been diluted one trillion times. That’s at the edge of possibility, but most of them are labeled 12C or 20C or even 30C. Those have been diluted to the point that I can’t even find a good name for the number. More importantly they have been diluted to the point that the bottle you’re holding is guaranteed to contain zero molecules of the original substance.

So while dioxin and PFCs and other pollutants can increase the rate of cancer at tiny percentages, the percentage of ingredients in homeopathic remedies are so much tinier that the medicine is just sugar water. But it is sugar water that the manufacturers claim has mysteriously absorbed the properties of some other substances.

By the way, there’s one other point to make: I am using what is known as “short scale” terminology, in which each “-illion” is 1,000 times more than the last one. There is also a “long scale” in which each “-illion” is 1,000,000 times more than the last one; it was used in Great Britain for a long time but has almost entirely disappeared. If you want to learn more you can go to Wikipedia, where the article “Long and short scales” will tell you more than you really want to know.

See you next week – that is, in about 0.00006 trillion seconds.

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