## 17 June 2011

### A question for linguists and mathematicians

Yesterday I concluded my blogging day with a report I entitled "The decimation of Atlantic food fish."  The scientific study described a decline in biomass of the fish "by a factor of nine over the [twentiety] century."

Sue Dunham quite correctly pointed out that by definition, decimation is a reduction by 1/10th, not a reduction to one-tenth, based on the Roman military discipline:
A unit selected for punishment by decimation was divided into groups of ten; each group drew lots (Sortition), and the soldier on whom the lot fell was executed by his nine comrades, often by stoning or clubbing. The remaining soldiers were given rations of barley instead of wheat and forced to sleep outside the Roman encampment...

The Italian General Luigi Cadorna applied decimation to under-performing units during the First World War. In his book Stalingrad, Antony Beevor recounts how, during the Second World War, a Soviet Corps commander of a division practised decimation on retreating soldiers by walking down the line of soldiers at attention, and shooting every tenth soldier in the face until his TT-33 pistol ran out of ammunition...
She and Wikipedia both note that by modern convention, the term can be used in a less precise way to indicate massive reduction -
In Wonderful Life: The Burgess Shale and the Nature of History, Stephen Jay Gould uses "decimate" to indicate the taking of nine in ten, noting that the Oxford English Dictionary supports the "pedigree" of this "rare" meaning.
So, this morning I wondered - is there a better term I could have used?  The Latin equivalent of a 90% reduction would apparently require a neologism like ? nonagintication.

But an even more interesting question is mathematical.  How many times must humans (and nature) have decimated the Atlantic food fishes (at 10% per decimation) to reduce the population to 10% of its original level?  Probably about twenty true decimations.  That makes the results of the study even more impressive.

1. Interesting corollary between the cited military examples and Jack Welch's management practices. :)

http://en.wikipedia.org/wiki/Jack_Welch#Tenure_as_CEO_of_GE

2. As for the math, yes, its 21.85, because you need to raise .9 to the 21.85 power to yield .1.

Regarding the linguisitcs, the story of language is one of constant change and repurposing, so getting caught up with the literal source for a word's origin is interesting, but not critical to understanding its meaning. I think you used "decimate" correctly and/or appropriately, and the test of that (IMHO) is that most people understood clearly what you meant.

Steve

3. The meaning of "decimate" might have drifted from "destroy a minority" to "destroy a majority" through a process of understatement (also called litotes). If a word is constantly used to indicate something greater than its normal meaning, it'll take on the greater meaning-- I recall seeing "kill" used to mean "hurt" in Shakespeare.

4. The math works like this:

Let's say we started with an original population of 100 (this is an arbitrary choice the original population can be anything). One decimation is:

100*0.9 = 90

Decimating again we get:
90*0.9 = 81

Decimating a third time is:
81*0.9 = 72.9

Each time we multiply by 0.9 again so we could rewrite the second decimation as:
100*0.9*0.9

And the third as:
100*0.9*0.9*0.9

0.9 multiplied by itself three times is 0.9^3 (0.9 raised to the third power). So the number of decimations is just the exponent on 0.9.

The question you are asking is: how many decimations to get to 10%?

10 is 10% of 100 and the number of decimations is the unknown:

100*0.9^x = 10

dividing both sides by 100 yields:
0.9^x = 0.1

This is where our friend logarithm comes into the picture. Remember that logarithm is a function that returns the exponent. So you can rewrite the expression:
10^3 = 1000

as:
log(1000) = 3

Unfortunately log (which is really log base ten) only works for powers of 10 and we are working with powers of 0.9.

Fortunately there is a way to convert between them. It can be shown that:
a^b = c

can always be rewritten as:
log(c)/log(a) = b

no matter what the "base" (a in this case) is.

so now we can rewrite our problem as:
log(0.1)/log(0.9) = x

log(0.1) is -1 (ten to the -1 power)
log(0.9) requires a logarithm table or a calculator (actually you can compute them by hand for as many digits as you care to, but it is very tedious). Mine shows: -0.04575749056

-1/-0.04575749056 = x

A negative divided by a negative is positive and a number divided by a number with absolute value less than 1 gets bigger. Therefore:

x = 21.8543453

5. Perhaps "obliterate" would be a good word, though I believe any study that models based on the biomass of fish in the oceans in 1900 might as well carry the label "silly."

6. Your usage is correct. The modern usage of the word decimate is to describe the process of reducing or destroying something almost completely.

The original meaning of the word was used by the Romans to denote the punishment process applied to a mutinous Legion, where one man in ten was executed. So, the classic—now deprecated—meaning of the word was to reduce something in an unpleasant way. However, modern usage of the word, as pointed out above, focused on the methodology and the word decimate came to mean something far more.

Another word that underwent a similar transformation is the word awful, which was originally used to describe something that inspired reverence. ("Full of awe").

7. I'd vote for "devastate" as an alternative, although I agree with Steve that "decimate" isn't wrong in this context. I suspect most people who use "decimate" aren't even aware it refers to tenths; in fact, I'll bet many of them just think it's a slightly fancier word for "devastate." Nastier, too; you can put a lot of stress on the "s" sound.

--Swift Loris

8. Strange. I'd always equated "decimate" with "reduce to a tenth of what was." When the West Nile Virus first appeared in Richmond, Va., the crow population was decimated, using this definition, not once but twice that year. For every 100 crows you used to see, you now saw about 1. In the intervening years, the population has rebounded, with the survivors (I suppose--citation needed!) providing the genetic pool.

Also, it's interesting to note the inversion of meaning of the Romans' "decimate" from one-in-ten to nine-in-ten. This is akin to "thumbs down" changing from "spare him" to "kill him."

Lurker111

9. Engineers would say 10dB attenuation. Or 1 bel attenuation. Which is the same as reduce to 10%.

10. I have always understood decimate to be to reduce by one in every ten, i.e., as in the Roman punishment. Any other usage is simply wrong.

To say the usage has changed is nonsense, what's happened is that the word is used by people not knowing its meaning.
Compare it with "Unique": you'll often see things described as almost unique, or the most unique.
yet unique has no degrees. Something either IS or is NOT unique. The word's misused all the time. I see that as no reason to redefine it to merely mean "not common".

11. Hm. I wasn't aware that 'destruction of a majority' is now considered a valid meaning for decimate. I and most of the people I know are aware of the historical meaning, and tend to giggle at people who use it as a synonym for 'devastate'. Just because a lot of people are saying it doesn't make it correct English, in my mind. Oh well. Nu-cle-ar, Nuke-you-lar.

12. Sometimes it's good to remind ourselves that words mean what people use them to mean; they don't have meanings that are independent of how we use them.

If we want to communicate, we'd best use words the way most other people are using them. But meanings do change; and while we can try to resist a change that diminishes the richness and nuance of the language, often all that can be done once it starts to change is to slow it down a little. Fortunately, it's likely that there will be other changes that will do the opposite.

"Decimate" in the sense of reduce by one-tenth isn't really all that useful; we don't lose much if it stops being used that way. And I think we may have gained a useful term--I can't think offhand of another word that means "to greatly reduce in quantity," and there are surely plenty of opportunities to use such a word these days.

To lose the "unlike any other" sense of "unique," on the other hand, would be very sad. We have no other word with that meaning. It's, er, unique.

--Swift Loris

13. Eliminating the cod leads to a trophic cascade (the cod eats littler fish) so on a moral basis, it isn't clear what people have done is a problem.

What I find interesting about the comments is the level of discourse between the "language evolving" and "language is what it is and people who use it incorrectly are barbarians" crowds. It bore out everything I had ever thought about the position I disagreed with.