I’ve been making pretty solid progress on my next book on symmetry. In writing a passage on the basic structure of matter, I started talking about the vast number of chemical compounds out there, and realizing I was out of my depth, I asked a chemist friend of mine how many were known.
I was way off. I (very wrongly) guessed that there were literally thousands of different molecules known. According to my colleague:
Chemspider is a great site (based out of the Royal Society of Chemistry) for obtaining information about chemical entities… They are
trying to be a clearinghouse for all information chemical- it indicates
there they are now up to >26 million structures.
I was only off by a factor of 10,000 or so! He also pointed me to another database with 61 million organic and inorganic compounds.
But this conversation got us both thinking about typical order of magnitude stuff; the false idea that errors of being off by only factors of 10 or 100 is “good enough.” Think mistaking billions for trillions in the case of the current debate on the deficit.
As my friend said:
I’ve thought lately one of the problems with people understanding science things is the inability of the human mind to understand things non-linear. For instance- people are generally ok with the idea of pH, pH<7 things are acidic, pH>7 things are basic. But what is forgotten is that pH is a LOG scale. It’s kind of like the Richter scale or decibel scale- those factors of 10 are harder to fathom. We all think much more linearly, so when things change logarithmically, we’re toast.
He’s right, of course. We may think linearly, but we almost almost always em>perceive logarithmically. Musical octaves, for example, have a constant ratio of frequencies, which means that they represent a log scale.
The magnitude system in astronomy was originally developed by Hipparchus because 1st magnitude stars appear about as much brighter than 2nd magnitude as 2nd do compared to 3rd and so on. But this system is also logarithmic. 1st magnitude stars are about 2.5 times as bright as 2nd magnitude, and 2nd magnitude are the same ratio brighter than 3rd.
It’s interesting how interrelated are the questions of order of magnitude estimate and logarithmic perception.