How many cats to catch 100 rats? Not what you think.

Anthony Doerr's World War II novel All the Light We Cannot See poses the following question in the notebook of Werner Pfennig, a mathematically gifted German boy. Take a couple of minutes to answer the riddle, then expand to read my take.

If five cats catch five rats in five minutes, how many cats are required to catch 100 rats in 100 minutes?

My intuition initially jumped to an answer of "one hundred cats." It feels like a simple scaling: 5 x 5 x 5 to 100 x 100 x 100.

My next instinct was that the answer couldn't be that easy, or there'd be no reason to pose the question. So I applied logical analysis and mathematics to yield an answer of "five cats." Most answers to similar questions on internet sites take the same approach.

However, this conjecture is only accurate if the cats are killing machines, malevolent cousins of the Energizer Bunny, methodically catching rat after rat until their batteries run down. But real cats are individuals with motivations and needs and desires.

So, why do these hypothetical cats want to catch rats?

Cats often stalk and play with mice for practice or for fun, but rats are significantly larger than mice, relatively dangerous prey armed with sharp teeth and claws. Cats usually only take risks with rats in hopes of a substantial meal. In my experience with a sample size of one rat hunter (hi Pookie!), a hungry cat can eat an entire rat in one sitting, then might catch a second rat in the same night, to partially eat or stash for later. I'd guess it rare for a cat to risk catching more than two rats in one hundred minutes.

If five cats catch five rats in five minutes, how many cats with wills of their own are required to catch 100 rats in 100 minutes?

Taking into account what I think I know about cats and their motivations, my answer is "about seventy or eighty cats."

* * *

Our culture turns everyone into numbers, manipulated as variables in equations to maximize profit. Trees older than any human, soaring skyward and spreading a vast canopy sheltering countless individuals of hundreds of species, become board feet. Hens, evolved to scratch and eat seeds and insects while gossiping and squabbling and teaching their chicks to forage, become "layers," their worth measured in eggs deposited from battery cages.

Humans evolved to be nurtured by and in turn contribute back to an intimate community. Human communities evolved to be nurtured by and in turn contribute back to their land bases. In such environments, people fully express their personalities, develop their interests and strengths, and build lives of purpose and responsibility and meaning. In contrast, our culture reduces us to taxpayer IDs, statistics and quotas, interchangeable employees of global systems of extraction and exploitation.

In Nazi Germany, the Jewish men, women, and children in cattle cars were the quintessential abstraction of living beings into numbers, forcibly computed into a final solution. In Doerr's book, even Aryan Germans are valued not as individuals, but because "what the führer really requires is boys. Great rows of them walking to the conveyor belt" as war fodder, "this final harvest of the nation's youth rushing out in a last spasm of futility."

Werner Pfennig, trapped within the Nazi war machine, is repeatedly told "It's only numbers, cadet. Pure math. You have to accustom yourself to thinking that way." But as the story unfolds, abstract numbers wielded in the real world impact real people in devastating, even deadly ways.

Our minds are evolved to form and maintain relationships with a few thousand humans and nonhumans, lifelong family and friends and acquaintances. We can only conceive in abstractions of the 7.6 billion humans and trillions of nonhumans with whom we share the earth. We can't possibly feel the reality of 40.3 million human slaves, 6 million annual deaths from fossil fuel pollution and climate change, 2.4 million children dead from malnutrition, half an acre of natural forest lost every second. In a world globally linked by technology, abstractions are often necessary to grapple with the ethical choices of our time.

But we must never forget that there are lives behind the abstractions. It's not only numbers.