How to Draw an Elephant Using Trigonometry

Alex Tabarrok points to a new paper this morning that should thrill data nerds and chart enthusiasts everywhere. Steven Piantadosi of the University of Rochester has produced a simple equation with one variable that is “not novel mathematically” but can perfectly fit any set of scatterplot points. Here it is:

As long as you pick your value of θ with extreme precision, this equation will provide a fit of any data, no matter how complex. Piantadosi demonstrates how this works by fitting a scatterplot of an elephant:

How about that? Give me any set of points, and I can describe them precisely with a universal, single-valued equation. All I have to do is choose θ really, really carefully.

As it happens, this is more a novelty than anything else, but Piantadosi says it contains a warning for artificial intelligence:

The existence of this model has implications for statistical model comparison, and shows that great care must be taken in machine learning efforts to discover equations from data since some simple models can fit any data set arbitrarily well.

A human mathematician is unlikely to be fooled by this, but a machine-learning algorithm could easily decide that the best fit for a bunch of data is an equation like the one above. After all, it works, doesn’t it?

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WHO DOESN’T LOVE A POSITIVE STORY—OR TWO?

“Great journalism really does make a difference in this world: it can even save kids.”

That’s what a civil rights lawyer wrote to Julia Lurie, the day after her major investigation into a psychiatric hospital chain that uses foster children as “cash cows” published, letting her know he was using her findings that same day in a hearing to keep a child out of one of the facilities we investigated.

That’s awesome. As is the fact that Julia, who spent a full year reporting this challenging story, promptly heard from a Senate committee that will use her work in their own investigation of Universal Health Services. There’s no doubt her revelations will continue to have a big impact in the months and years to come.

Like another story about Mother Jones’ real-world impact.

This one, a multiyear investigation, published in 2021, exposed conditions in sugar work camps in the Dominican Republic owned by Central Romana—the conglomerate behind brands like C&H and Domino, whose product ends up in our Hershey bars and other sweets. A year ago, the Biden administration banned sugar imports from Central Romana. And just recently, we learned of a previously undisclosed investigation from the Department of Homeland Security, looking into working conditions at Central Romana. How big of a deal is this?

“This could be the first time a corporation would be held criminally liable for forced labor in their own supply chains,” according to a retired special agent we talked to.

Wow.

And it is only because Mother Jones is funded primarily by donations from readers that we can mount ambitious, yearlong—or more—investigations like these two stories that are making waves.

About that: It’s unfathomably hard in the news business right now, and we came up about $28,000 short during our recent fall fundraising campaign. We simply have to make that up soon to avoid falling further behind than can be made up for, or needing to somehow trim $1 million from our budget, like happened last year.

If you can, please support the reporting you get from Mother Jones—that exists to make a difference, not a profit—with a donation of any amount today. We need more donations than normal to come in from this specific blurb to help close our funding gap before it gets any bigger.

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