> No, as the article notes, the measurement of magnitude (in
> the Richter scale) is proportional to the base-32 logarithm
> of energy released (its defined as proportional the base-10
> logarithm of seismic wave amplitude.)

Yes, "magnitude" here is a logarithmic rather than linear measure of energy, but the critique is wrong (or underhanded) to suggest that Taleb doesn't realize this. Taleb may have been wrong to assume his audience would know the same, but never suggested that we should be surprised that 6 Magnitude 1 earthquakes do no harm to a coffee cup whereas a single Magnitude 6 might break it. To the contrary, quoting from the appendix that the critique refers to:

There are close to 8,000 micro-earthquakes daily
on planet earth, that is, those below 2 on the Richter
scale —about 3 million a year. These are totally harmless,
and, with 3 million per year, you would need them to
be so. But shocks of intensity 6 and higher on the scale
make the newspapers. Accordingly, we are necessarily
immune to the cumulative effect of small deviations, or
shocks of very small magnitude, which implies that these
affect us disproportionally less (that is, nonlinearly
less) than larger ones.

So when the critique describes adding the numbers together and says "this is what Taleb means", it is either poor reading or actively disingenuous:

Even though the sum of the magnitudes of the smaller
earthquakes is equal to the magnitude of the larger one,
the coffee cup is damaged much more by the big quake than
by the small ones. This is what Taleb means when he
describes the coffee cup as fragile.

No, this is not what Taleb means!

> suggesting that the real relative impact of a magnitude 6
> quake compared to a magnitude 1 quake is disproportionately
> greater than their size because one magnitude six quake
> does more damage than six magnitude one quakes

I'm pretty sure that Taleb never suggests this, and that the "6 times the damage" concept is simply a strawman constructed for the critique. Taleb may have erred by taking for granted that his audience understands that earthquakes are measured by a logarithmic scale, but since it is a scientific paper rather than an Op Ed, this doesn't seem unreasonable.

Now, I will grant you that Taleb may well have mistakenly assumed that the measure of earthquakes went up 10^{1} per number of magnitude rather than 10^{1.5}, as this would explain why he chose to use the specific numbers he did. It would be a fair critique to point out this out to him, and I'd be interested to see his response. As you say, 10^{9} would require hundreds of years of earthquakes, and thus is not a particularly compelling example.

> Taleb makes a comparison that sounds significant because
> most people don't know what the numbers involved mean.

If you take a look in the linked document at that the actual Appendix C that defines Taleb's concept of fragility, I think you'll agree that it is not targeted at people who don't know what the numbers mean. I've only skimmed it, and it may not apply to GMO's, but it seems like a reasonable definition. Rather than trying to confuse people who don't understand logarithmic measures, I don't think he much cares what they think.

(Separately, this is my opportunity to ask: Who are you? What's your background? You consistently impress me with the quality of your comments on HN.)