A Thousand Brains: A New Theory of Intelligence

by Jeff Hawkins

To a mathematician, equations are familiar objects, similar to how you and I see a smartphone or a bicycle. When mathematicians see a new equation, they recognize it as similar to previous equations they have worked with, and this immediately suggests how they can manipulate the new equation to achieve certain results. It is the same process we go through if we see a new smartphone. We recognize the phone is similar to other phones we have used and that suggests how we could manipulate the new phone to achieve a desired outcome. However, if you are not trained in mathematics, then equations and other mathematical notations will appear as meaningless scribbles. You may even recognize an equation as one you have seen before, but without a reference frame, you will have no idea how to manipulate it to solve a problem. You can be lost in math space, in the same way you can be lost in the woods without a map. Mathematicians manipulating equations, explorers traveling through a forest, and fingers touching coffee cups all need maplike reference frames to know where they are and what movements they need to perform to get where they want to be. The same basic algorithm underlies these and countless other activities we perform.