One of the first steps toward becoming a scientist is discovering the difference between speed and velocity.
To nonscientists, it’s usually a meaningless distinction. Fast is fast, slow is slow. But speed, technically, refers only to rate of motion. Velocity encompasses both speed and direction. In science, you usually want to know more than just how fast something is going; you also want to know where it is going. Hence the need to know direction, and to analyze velocity, not just speed. Numbers like velocity that express both a magnitude and a direction are known as vectors.
Vectors are great for describing the motion of a particle. But now suppose you need to analyze something more complicated, where multiple magnitudes and directions are involved. Perhaps you’re an engineer calculating stresses and strains in an elastic material. Or a neuroscientist tracing the changing forces on water flow near nerve cells. Or a physicist attempting to describe gravity in the cosmos. For all that, you need tensors. And they might even help you unify gravitational theory with quantum physics.
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