Contributing Writer Discusses The Math of ‘Bad Apples’ in Regards to Police

By Matt Turetsky || Contributing Writer

Our elementary school math teachers were right: remembering the units is the most important part of solving a problem. Adding one more bad “apple” might not seem like much, but every addition should be enough to send alarming signals about how America grows its apples. Many people are not willing to accept established facts about apples like we do with numbers. Clearly we need to accept the consistent history of good and bad apples in America the way we accept numbers—as objective facts.

Let’s start by adding up some numbers: 1+1/2 +1/3+1/4. We get 2.0833. If we keep going with that same pattern, 1+1/2+1/3+1/4+1/5+… surprisingly, we keep increasing up to infinity, even though the numbers we are adding get smaller and smaller. Honestly, it’s sobering every time I see that result of how each small increment leads to big changes. It is the scope that trips me up. At any one step, the next addition seems trivial, yet it amounts to a massive result.

Apples, despite their prevalence, can be more complicated than they look. The long, legendary history of apples has been effective propaganda. How can you not smile when you hear the story of Johnny Appleseed traipsing about the country, planting lovely little apple trees with a metal pot on his head? Well, Johnny’s apples were all bad apples; they were never grown to be eaten. They were planted to be plucked from the tree to be pressed into an intoxicating cider. I like to believe that they were designed to be good apples and that Johnny later realized he was better served by degrading the apple to fill his own pocket. It would give me hope that we can undo gross misconduct.


Every time I take a bite of a bad apple, I am reminded of the importance of choosing the right one. My friend went apple picking one summer, and at the end of roaming one quadrant, he had found a few bad apples. He was concerned, he alerted the manager, and she told him—an apple picker herself—that she would find the root cause and thwart it. Maybe a fungus grew that made it bitter. Maybe her pesticides didn’t eliminate all the disease-carrying ants that rummage around her forest. She told him these hypotheses and more. She told him she would look into it.

The surprising thing about that sum of numbers 1+1/2+1/3+1/4+… is that it is not too hard to prevent its unabated growth. If we strategically remove some entries, we can manage it quite easily. Let’s take out 1/2 and 1/3. Oh, and definitely 1/5. Better yet, let’s make a strict requirement that if you don’t follow a simple rule, you’re off the list. That way, there is some barrier to entry. Not too high to leave us with nothing, but just enough to get what we ask for. So let’s only accept numbers with square denominators, like 1/4, 1/9, 1/16, 1/25…. Instead of existential questions of infinity that come with including all the fractions in our first list, we have 1+1/4+1/9+1/16+1/25+…. These fractions get smaller and smaller like before, but this time, adding them up ends at approximately 1.64 because the fractions get smaller much more quickly after restricting which numbers we include. Adding them up always ends at about 1.64 (unlike the other series which has no such limit). It turns out it’s a complicated number, but at least we fixed the problem.

My friend went back next apple-picking season, this time with other experienced apple-pickers. He wanted to really get a good sample of what goes on in some of the nooks and crannies of the field; in trees he never looked at; in patches that seemed barren. And what did he find? Unsurprisingly, his quadrant wasn’t the only one with a few bad apples. They scanned the man-made forest and found every patch—small and large—had at least one bad apple. The trend was clear. There simply was not a very high bar of entry for an apple in this apple-picking place. Sometimes, after a bad apple is identified, the crew lets it hang there, instead of throwing it out. Sometimes they spread fertilizer on the ground and make the problem worse. Occasionally, they might spray some pesticide to try to rid the bad apple of its disease, but more often than not they let it fester until winter comes and the bad apple withers away, infecting the entire tree. Months later, the offspring will germinate, plump itself up, harden, disregard well-intentioned pesticides, and welcome—maybe unknowingly—that bad-apple-causing disease, wriggling its way up from the trunk of the tree.

If only there were a way to strategically remove the bad apples and regrow the tree, like we did when adding up infinite fractions.

I don’t have the full answer, but it starts by talking to others who have experience. It starts by reading about good apples and bad apples, new types of apples on new types of trees, and basic knowledge of biology about how the inner workings of a tree allow for a bad apple to thrive. Or, maybe it starts by reading Martin Luther King Jr. and Toni Morrison, or Ta-Nehisi Coates and Nana Kwame Adjei-Brenyah, or W.E.B Du Bois and Maya Angelou. It starts by listening to the stories of those who are subjugated by the system, those who consistently pick bad apples of all shapes and sizes, even if we ourselves have never taken a bite from one. It starts by trusting that our friends’ experiences are not the exceptions to the rule, knowing that everyone at some point will have first-hand experience with bad apples if we stand idle while the forest grows. 

We cannot be fooled when we see 1+1/2+1/3+1/4 equal 2.0833; that is the beginning to an ever increasing, more imposing infinity. Nor can we be fooled when we see a bad apple on a tree and think it’s the only one in the patch. We should realize the long history of apples and  focus on changing the forest because throwing out bad apples,uprooting diseased trees, and believing the problem is dealt with will not change the likelihood that the next one picked is a very bad apple.

Matthew Turetsky is a Contributing Writer. His email is


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