Can We Model Generosity With Mathematics?

four celebrities and their donations – hemsworth $1000000, mariam (hs student) - 75, British Petroleum - $700000, Jeff Bezos – $700000

I posted that image on Twitter last week, asking:

Which of these bushfire relief donors was the most generous? What’s your ranking? What information matters here? What would your students say?

Some teachers quickly identified a connection to ratios.

Meanwhile, Lee Melvin Peralta critiqued ratios as too limited to fully model generosity.

I tend to side with George Box here, who wrote:

All models are wrong, but some are useful.

Anyone who thinks that proportional functions fully describe runners in a race, or that linear functions fully describe the height of a stack of cups, or that quadratic functions fully describe the height of objects under gravity, or that ratios fully describe generosity is, of course, kidding themselves.

But those models are all useful. Ratios are a useful way to think about generosity.

Emily Atkin originally stirred this question up for me in her fantastic climate change newsletter:

Chevron’s donation is paltry, however, given its earnings and relative contribution to the climate crisis. Not only is Chevron the second-largest historical emitter of all the 90 companies, it also earned about $15 billion in 2018. So a $1 million donation amounts to about .00667 of its yearly earnings. To the average American, that donation would amount to about $3.96.

So Atkin is evaluating generosity as ratio of net worth/earnings to donation size. But then she also considers the donor’s contribution to climate change.

The model is complex and grows more complex!

One teacher wanted to add fame and notoriety to our model, something Chris Hemsworth donates that Mariam might not. (Maybe she’s a TikTok teen, though. We can only speculate.) I talked with someone who lives in Australia about this question, and she said Hemsworth is less generous than someone from another country donating the same amount because of his identity as an Australian citizen. Robyn V wondered how to evaluate time donations, and even the donation of one’s life.

So ratios aren’t a perfect model for generosity, but they do offer us an important insight that, under some circumstances, someone who donates $75 is more generous than someone who donates one million dollars, which one teacher noted is a quantity that is really hard for students to fathom!

One teacher preparation program asked the question:

If the ambiguity of the original question strikes you as anything other than a feature, then please don’t risk the conversation.

If you go into the conversation presupposing a model for generosity rather than admitting to yourself in advance that all the models are broken, you’re likely to diminish students who suggest variables you had already excluded.

Okay, yes, um, ‘whether or not someone lives in Australia.’ Okay, that’s one idea, but can I get some other ideas, please? Perhaps ones more related to the math we’ve been studying?

All of these models are complex. All of them are certainly broken. And all of them offer you the opportunity to celebrate and build on your students’ curiosity and contextual knowledge, an experience that is all too rare for students in math class.

BTW: Shout out to Christelle Rocha for her observation that individual generosity is no way to solve the climate crisis.

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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.

4 Comments

    • Btw. I think this answers the question that has been stewing about modeling and defining “real world” vs. “non-real world”
      Obviously in the pure world of mathematics all models are perfect! It isn’t until we try and apply them to the “real world” that they become broken.

  1. Reply

    Loved the comment, “interestingly fuzzy or annoyingly vague?” – because in many ways that encapsulates the Dan Meyer style of questions!

    Throw up an annoyingly vague question, then let the room straighten it out and tell you what they “should” be answering

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