There is a shadow world flowing through all that surrounds us. It is a world of numbers and symbols, possibility and computation. Every touch, every perception, every word is an atom in the landscape beneath our shared hallucination that is reality.
When we engage mathematics and computation we directly address this shadow world, reaching beneath the surface to control the world at large. It is indirect, wrong and effective. It our only means of projecting ourselves beyond ourselves.
Even the self is a collection of statistical models, competing for the floating point of attention. Everything we know is a temporal projection of data, the result of past computation. Every thought is the application of a function to transform ourselves into a new state. We are more analog that the digital computers we create. But they reflect our underlying nature; they are part of the same shadow world as our natural perceptions.
Studying computer languages reveals aspects of the natural world. The computation models we create reflect our nature as concious beings. The study of lambda calculus or turing machines is the study movement in the shadow world that encompases all human minds. Whether we study the wings of bees or the domain of continuations, we learn something about ourselves and world around us.