It continues to amaze me how many “facts” get out there without even the most cursory checking. (See Wikipedia’s List of Common Misconceptions for an amusing summary.) But how can one defend against a constant stream of misinformation?

There are number of techniques that really ought to be written about more, but an easy one is to become familiar with orders of magnitude, and what they represent. As a general rule, if A is orders of magnitude smaller than B, A can’t have any real effect on B. (There are exceptions, of course, but it’s a good general rule.) If a comet crashes into the Sun, the comet (about ten miles across) can’t have any real impact on the Sun (about a million miles across). It’d be like a fly slamming into a 747. In fact, comets crash into the Sun all the time, and people would never notice without powerful telescopes.

That example might seem obvious, but one sees equally absurd claims all the time. The difference between ten and a million is five orders of magnitude, but for something like astrology to work would require ignoring ten or more orders of magnitude. It’s good to remember that humans are scope insensitive by default.

To take power as an example, a watt will run an electric watch; a kilowatt will power a refrigerator; a megawatt runs a piece of heavy industrial machinery; a gigawatt is about what’s put out by a full-scale power plant; a terawatt might be produced by a major industrial country. Hence, we can easily see that (for example) claims of WiFi causing cancer must be nonsense. A WiFi transmitter is plugged into a standard electrical socket, and produces power output in the milliwatt range; since this is distributed over a wide volume, the power being absorbed by a human body must be in the microwatt to nanowatt range. The body’s own metabolic processes, which generate hundreds of watts, would swamp any effect. (On the other hand, getting near a kilowatt radio transmitter really is bad for you – it’ll give you RF burns from the heat.)

Similarly, for quantities of mass, the human body weighs about seventy kilograms, and contains trillions of cells. In order to kill you, a toxin would have to affect a large number of those cells, enough to cause systems to stop functioning (the body has a lot of redundancy). Hence, a microscopic amount of anything is harmless. One sees claims all the time that “plutonium is toxic in any amount”, but that can’t be true, because for a sufficiently small amount (one atom, say) there isn’t enough to affect all the cells. At worst, a single plutonium atom might kill a single cell, but there are many more cells where that came from. (Indeed, more detailed studies show that the most toxic substances like botulin have doses in the nanogram range, where there are still enough molecules present to shut down each of billions of cells.)

Most recently, I heard a claim that pharmacogenomics, the industry of combining pharmaceuticals with genetic technology, would soon be generating $450 billion a year. $450 billion a year is about the size of the entire GDP of a small country, like Belgium or Sweden; it far outstrips the profits of any private company, which top out in the tens of billions. Hence, for the claim to be true, there would probably have to be many companies as large as Apple or Google or Walmart dedicated exclusively to pharmacogenomics, which sounds unlikely. It would also have to mean that pharmacogenomics was about 3% of US GDP ($14 trillion), and more than 20% of all healthcare spending ($2 trillion). It would also mean that, on average, a person (lifetime spending single-digit millions) would spend tens of thousands on pharmacogenomics, compared to the few hundred dollars an average genetic test might cost. For all these reasons, we can dismiss the claim as unlikely even before looking it up.

Like a foreign language, there’s no quick way to just know the orders of magnitude of everything; a lot has to be memorized. Fortunately, Wikipedia comes to the rescue, with some helpful summaries:

Orders of Magnitude (Currency)

Orders of Magnitude (Speed)

Orders of Magnitude (Energy)

Orders of Magnitude (Length)

Orders of Magnitude (Radiation)

Orders of Magnitude (Time)