Math Has Prepared Me Poorly for This Pandemic

Here are two representations of the horror of this pandemic.

First, a graph of coronavirus deaths in Italy.

Graph of Coronavirus deaths in Italy.

Second, the obituary page of a newspaper in the Italian city of Bergamo, first from February 9 and later from March 13.

Both of these are only representations of this pandemic. They point at its horror, but they aren’t the horror itself. They reveal and conceal different aspects of the horror.

For example, I can take the second derivative of the graph of deaths and notice that while the deaths are increasing every day, the rate of increase is decreasing. The situation is getting worse, but the getting worse-ness is slowing down.

I cannot take the second derivative of an obituary page.

But the graph anesthetizes me to the horror of this pandemic in a way that the obituaries do not. The graph takes individual people and turns them into groups of people and turns those groups of people and their suffering into columns on a screen or page.

Meanwhile, the obituaries put in the foreground the people, their suffering, and their bereaved.

Math has prepared me poorly for this pandemic—or at least a particular kind of math, the kind that sees mass death as an opportunity to work with graphs and derivatives.

For students, it has never been more necessary to move flexibly and quickly between concrete and abstract representations—to acquire the power of the graph without becoming anesthetized to the horror that’s represented much more poignantly by the obituaries.

For teachers, there has never been a more important time to look at points, graphs, tables, equations, and numbers, and to ask students, “What does this mean?” and particularly now, “Who is this?”

BTW

Two relevant quotes here.

  • “A single death is a tragedy; a million deaths is a statistic.” Commonly attributed to Joseph Stalin.
  • “Statistics are human beings with the tears wiped off.” Paul Brodeur, quoted in Mukherjee’s Emperor of all Maladies.

2020 Apr 10

Another example. It’s one thing to see a graph of unemployment, and another to see the lines for the food bank.

2020 May 25

About 
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

9 Comments

  1. Ka Rene grimes

    April 6, 2020 - 7:38 pm -
    Reply

    Dear Dan,

    This is exactly my feeling towards NAEP, TIMMS, or any state mandate graph of scores. EVERY. SINGLE. DATA. POINT. IS. A. HUMAN. SOUL.

    You show me a low score and I’m going to tell you that that low score is a real-life kid that came to school crying because his favorite chicken died. That chicken was one of the only positive things in this young boy’s life.

    Schools do it, policymakers do it. Truth be told, we all do it IF we don’t guard our selves. Whenever we remove the human from statistics, we’ve given up a part of our own soul.

    • Paul Brodeur, cited in Mukherjee’s Emperor of all Maladies: “Statistics are human beings with the tears wiped off.”

  2. Reply

    A lot of math is about abstraction to expose hidden patterns.

    The things hardest to put numbers to are also generally the first lost in that process of abstraction.

  3. Reply

    There is an excellent section in the book “The Girl Who Smiled Beads” where she talks about the need for a word like “genocide” though how that takes away from the individual stories. Poignant.

  4. Reply

    I had an interesting conversation similar to this with a neighbor of mine who was out for a walk and stopped by to visit/check up on me. He asked if I “believe all that stuff”–referring to the mathematics of epidemiology. I told him of course, to an extent. After all, models are meant to represent a situation in a useful way, not capture it completely in all its messy nuance.

    I don’t think I convinced him of its validity. He was clearly concerned about the economic repercussions of social distancing. Rather than Obituaries, he was pointing out the human suffering he was seeing that isn’t reported in newspapers–they don’t put out an “I’m *literally* starving” page. I’m sure there is some mathematical model for that scenario, too, though it doesn’t get much press. We began to discuss in a very frank manner the ‘cost’ analysis of the stay-at-home order. What a great thing it is to have a true friend who has different views than me and can genuinely get me to question my position.

    One thing I *am* thankful for that this exchange highlights in my mind: while the human connection and compassion that comes from thinking about the individuals and the experience is no doubt important and meaningful, I am thankful for the cold hard mathematics that evaluate beyond the susceptible realm of human emotion–if anything to at least inform us of where our emotional bias lies.

    Though both of these representations are imperfect. Neither captures the fullness. Nothing can (though the muses of the humanities might come the close). Some things in the human experience are inexpressible. Even the obituaries fall short of truely expressing fully what they were intended to express. All we can share are the shadows, it is up to each individual to leave the cave–keeping proper social distancing of course.

  5. Chester Draws

    April 7, 2020 - 4:02 pm -
    Reply

    The graph you show doesn’t have to be cumulative. It would be far less frightening if it wasn’t. Media are showing us the cumulative tolls *because* they are more frightening, and it’s done precisely to scare us more.

    One thing this plague has shown is that most people are grossly innumerate. And particularly journalists.

    People ask me aren’t I worried about my 85 year old dad. Of course I’m worried. He had a 10% chance of dying this year *before* CV came along. I’m always worried about him, because I know the base risk. Therefore I’m less concerned about adding to it than someone who thinks 85 year olds hardly ever die. (He, incidentally, isn’t bothered by CV at all — he knows he’s going soon either way.)

    We could also show the death toll this year compared to previous years. In much of the world it is *down* on normal at the moment. That wouldn’t be scary though. And journalists want us to be scared.

    People see “12 people an hour” are dying of CV19 in NYC, and don’t realise the *normal* death toll is 18 an hour. At the peak of flu season 6 people an hour can be dying of flu in NYC in an ordinary winter.

    Rather than Maths preparing you poorly, I think it actually prepares you well. You know what a second derivative is Dan, and therefore can read past the deliberately scary cumulative graph.

    Our leaders and our citizens need to be able to do that too. Ruling by emotion sounds lovely, but it isn’t a great idea — more people will die if innumerate decisions are made. That’s why teaching Maths is important. And yes, there are humans at the end of the numbers — but that’s why the Maths needs to be done well.

    • @ Chester…I agree that using math can help save human lives, and I think that’s exactly what we’re doing. One might look at aggregate death totals for all of civilization on the planet right now and see that deaths might be down compared to usual and thus conclude that the media is sensationalizing the Coronavirus Pandemic. Deaths are down in other areas precisely because of the shutdown and social distancing measures. According to the vast majority of health experts, epidemiologists, and economists, we are doing the right thing by shutting down. If we didn’t, we would have all of the usual deaths that everyday life brings in the way of hazards, pollution, other viruses, etc. PLUS a much more rapidly spreading pandemic virus. I’m not sure that all journalists want to scare everyone. I’m sure that they want people to watch their news feeds and programs to generate income, but they also have a responsibility to inform the public and help them understand why the governments are taking the measures they are.

      I heard an interesting podcast the other day that talks about the economic tradeoff between human life and economic output and vitality. The economists have estimated that each life saved is worth about 8-10 million dollars. If you were to multiply the projected number of lives saved by the shutdown by 10 million dollars, you get about $20 trillion. They concluded that for now, social distancing was not only morally correct, but also economically prudent as well. If putting a price on human life sounds austere, note that we do it all the time as Chester mentions. Decisions are made about the safety of cars, planes, machines, seasonal viruses that cause mortality, etc. where we know death will be inevitable, but society marches on nonetheless. There will always be a delicate balance between safety and freedom.

  6. Reply

    I disagree with the title of the post, although not for reasons the post goes into.

    Featured Comment

    I understand exponential growth. That prepared me to social distancing myself as soon as I heard from the experts that that was the best thing to do. I also started warning everyone I know to social distance well before many many around me and definitely around the country. Also, every day I get frustrated about needing to social distance I think about exponential growth and I stay in my house.

    I do think you raise some good points about statistics here, but I am very glad that I know math (and enough about science to know to *believe* science) as we go through this pandemic.

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