 The many smart systems that surround us make our lives a lot easier. Cars alone host a whole suite of smart features, such as adaptive cruise control and collision avoidance, that keep us safe and comfortable. Every day, scientists and engineers work to understand how the various components of these systems interact, to make our smart machines even smarter. But one critical element continues to prove unpredictable and hard to define, stunting the evolution of smart systems, the human user. Now, researchers are turning to a branch of mathematics called fractional order calculus to translate our unique behavior into terms machines can easily understand, helping them operate more efficiently and more reliably. Fractional order calculus is a generalized form of the more familiar integral calculus. Instead of computing rates of change, or derivatives, of integral order, such as the velocity or acceleration of a moving car, fractional order calculus asks, what is the half derivative, or the one third derivative, or the one fourth derivative, and so on. The answer is a little harder to interpret than an integral calculus, but turns out to be well suited to modeling real human behavior. That's because fractional order equations, like our brains, have a kind of built-in memory, a way of accounting for past events or errors in a system. Using a small set of variables, fractional order models can also account for other time-dependent features of our physiological response system, such as the lag between seeing an oncoming car and jerking the steering wheel to avoid it. More traditional models, on the other hand, typically involve a large number of parameters that aren't always relatable to real physical responses. To test the performance of this model, researchers set up an extremely simple driving simulator. A human test subject was asked to rotate a steering wheel according to the angle indicated on a computer screen. During the test, the researchers monitored how much the subject over or undershot the target angle and how long it took the subject to respond. They then fit the data with their fractional order model and with other, more traditional models. The fractional order model not only matched the test subject's behavior more closely, but also required fewer parameters. More testing is needed, especially on more complex and more useful systems. But these results suggest that humans are best interpreted as walking, talking, fractional order models, at least by the machines that make our everyday lives easier.