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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SIX TRUTHS

Reclaiming power from those who abuse it often starts with telling the truth. And in "This Is How Authoritarians Get Defeated," MoJo's Monika Bauerlein unpacks six truths to remember during the homestretch of an election where democracy, truth, and decency are on the line.

Truth #1: The chaos is the point.

Truth #2: Team Reality is bigger than it seems.

Truth #3: Facebook owns this.

Truth #4: When we go to work, we're in the fight.

Truth #5: It's about minority rule.

Truth #6: The only thing that can save us is…us.

Please take a moment to see how all these truths add up, because what happens in the weeks and months ahead will reverberate for at least a generation and we better be prepared.

And if you think journalism like Mother Jones'—that calls it like it is, that will never acquiesce to power, that looks where others don't—can help guide us through this historic, high-stakes moment, and you're able to right now, please help us reach our $350,000 goal by October 31 with a donation today. It's all hands on deck for democracy.

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