# Is the derivative a rhetorical intensifier?

A mathematician named Stephen Pollock once pointed me towards a strange turn of phrase. In a *New York Times Sunday Review* piece on August 23, 2013, two authors penned this clause: “As the rate of acceleration of innovation increases…”

Listen to that again, and count the derivatives.

Stephen broke down the mathematics like this:

Level of technology in society = **T**

Innovation = change in technological level = **T’**

Acceleration of innovation = second derivative of innovation = **T ’ ’ ’**

*Rate of* acceleration of innovation = **T ’ ’ ’ ’**

Rate of acceleration of innovation is *increasing *means **T ’ ’ ’ ’ ’ > 0**.

In short: this is a claim about *fifth *derivative! Stephen wrote to the authors (two economists) and received the following gracious reply:

I am thrilled at the care you put into unpacking ‘the rate of acceleration of innovation increases’ – clearly, we used the terms as intensifiers in this context, and I am glad to have my attention returned to the implications of phrase in a technical context. Thank you.

Stephen’s interpretation is literally, technically correct, but (and I say this with full admiration) quite silly. It’s pretty clear they meant these derivatives neither literally, nor technically. Still I’m fascinated by the idea that the derivatives can be used in such a way.

Can a derivative really work as an intensifier?

I’m forced to conclude it can. Even ignoring their mathematical meanings, *high acceleration* feels somehow grander than *high velocity* (and the meek *high position* is scarcely worth mentioning).

I’m reminded of *exponential*. For mathematicians, it means “possessing infinite positive derivatives.” For laypeople, it means “really fast.”

Thus, the colloquial “exponential” is just a disguised version of the derivative as intensifier.

So, hold on: does this mean that *integrals *can work as *mitigators*? After all, in math, integrating *does* soften a function; it is an averaging process, and even a discontinuous function may have a continuous integral. Is the same true in English? To soften a claim (“eek, don’t drive so fast!”) do I simply take an antiderivative (“eek, don’t drive so far!”)?

No dice. If anything, an integral is sometimes an intensifier: not “X,” but “the sum total of all X.”

Further evidence that the languages of mathematics and English are not isomorphic: mathematical inverses become English synonyms.