I recently read the article Pipe Dreams about treating wastewater. I’m not an engineer and make no claims of expertise about the accuracy of the article. What did catch my attention, as a mathematician, is how the author chose to express small proportions. For example, the opening sentence:
Wastewater is 99.9 percent water, but boy, that last little bit.
Later in the article:
Orange County’s is an example of indirect potable reuse, where wastewater is cleansed to 99.9999999999 percent free of pathogens before it goes to an environmental buffer like a reservoir or an aquifer for further natural filtering and then to homes.
And later:
After treating the water to even higher standards—demonstrating a 99.999999999999999999 percent removal rate of viruses and similarly high removal rates of protozoa—they may send the cleansed water directly into the water distribution system.
I was struck about the psychology of communicating all those consecutive 9s when expressing these proportions. For example, if the proportion of impurities instead of the proportion of water was given, the previous sentences could be rewritten as:
Only one part per thousand of wastewater is impurities.
Orange County’s is an example of indirect potable reuse, where impurities are reduced to one part per trillion before it goes to an environmental buffer like a reservoir or an aquifer for further natural filtering and then to homes.
After treating the water to even higher standards, reducing impurities to one part per 100 million trillion, they may send the cleansed water directly into the water distribution system.
Of these two different ways of expressing the same information, it seems to me that the author’s original prose is perhaps most psychologically comforting. “One part per trillion” seems a little abstract, as most people don’t have an intuitive notion of just how big a trillion is. The phrase “99.9999999999 percent,” on the other hand, seems at first reading to be ridiculously close to 100 percent (which, of course, it is).
Mean Green Math 