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?

OUR NEW CORRUPTION PROJECT

The more we thought about how MoJo's journalism can have the most impact heading into the 2020 election, the more we realized that so many of today's stories come down to corruption: democracy and the rule of law being undermined by the wealthy and powerful for their own gain.

So we're launching a new Mother Jones Corruption Project to do deep, time-intensive reporting on systemic corruption. We aim to hire, build a team, and give them the time and space needed to understand how we got here and how we might get out. We'll publish what we find as a major series in the summer of 2020, including a special issue of our magazine, a dedicated online portal, and video and podcast series so it doesn't get lost in the daily deluge of breaking news.

It's unlike anything we've done before and we've got seed funding to get started, but we're asking readers to help crowdfund this new beat with an additional $500,000 so we can go even bigger. You can read why we're taking this approach and what we want to accomplish in "Corruption Isn't Just Another Scandal. It's the Rot Beneath All of Them," and if you like how it sounds, please help fund it with a tax-deductible donation today.

We Recommend

Latest

Sign up for our newsletters

Subscribe and we'll send Mother Jones straight to your inbox.

Get our award-winning magazine

Save big on a full year of investigations, ideas, and insights.

Subscribe

Support our journalism

Help Mother Jones' reporters dig deep with a tax-deductible donation.

Donate