Tau and full ciricles

Today is Tau Day, June 28th or 6/28. It is little celebration of Tau (τ), the circle constant that begins 6.28 and equals exactly two times Pi (π).

Tau is just 2π, but it represents something cleaner: one full turn around a circle.

Pi gets most of the glory. Recently, a team pushed π out to 314 trillion digits on a single server, a computation that ran for months on end. One of the great records before that landed on June 28th, 2024 (Tau Day itself) which feels like the sort of private joke the universe enjoys.

Here’s the odd part. For all that effort, NASA only needs about 15 digits of π to navigate a spacecraft across the solar system. Using on the order of forty digits is enough to describe a circle as large as the observable universe with accuracy at about the scale of a single atom.

We chase trillions of digits not because we need them, but because π is an exquisitely pure benchmark for testing how far we can push our machines.

Back to Tau (τ) and why I love it.

A full circle is one tau. A quarter turn is τ/4. Half a turn is τ/2. The number matches the motion. Pi, by contrast, describes a half circle: it’s the angle that carries you across, from one side of the circle to the other. Tau describes the entire journey.

Tau is the constant of things that come around. Waves, orbits, seasons, heartbeats, the swing of a pendulum, the vibration of a string. Anything in nature that truly repeats is, underneath, tracing a circle in some abstract space.

The size of that full circle, the measure of one complete cycle, is τ.

And this turns out to be surprisingly close to how the AI in your pocket thinks.

I often say that with modern AI we have a 1,000 PhDs in our pockets. But when one of those models reads a sentence, it has to figure out the order of the words. For example, the difference between “dog bites man” and “man bites dog.”

Many state-of-the-art models do this by effectively spinning each word’s internal representation around a circle, rotating it by an angle that depends on its position in the sequence. Word order is encoded as rotation. The 1,000 PhDs in your pocket are, quite literally, thinking in circles.

And there is one last thing about τ worth sitting with.

There is a famous equation (Euler’s formula) that says if you travel one full circle in the complex plane, multiplying by e^(iτ), you arrive back at the number 1. A full turn brings you home. You end up exactly where you started, except you are not quite the same, because you had to go all the way around to get there.

We like to imagine progress as a straight line: further, faster, forward.

BUT the most fundamental motions in nature are not straight lines. They are returns, orbits, cycles that come back to their own beginnings.

So maybe the point is not always to push forward in a straight line.

Sometimes it is to come full circle and to notice how much has changed by the time you do.

Happy Tau Day!

Until next time, Ram

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Ram Srinivasan

MIT Alum | Author, The Conscious Machine | Global Future of Work and AI Adoption Leader published in Business Insider, Fortune, Harvard Business Review, MIT Executive Viewpoints and more.

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Ram Srinivasan currently serves as an Innovation Strategist and Transformation Leader, authoring groundbreaking works including "The Conscious Machine" and the upcoming "The Substrate Shift."

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