Reverse engineering the brain is proving difficult, perhaps impossible. While many believe that this is just a matter of time and effort, a different approach might help... Here, we describe a very simple idea which explains the power of the brain as well as its structure, exploiting complex dynamics rather than abstracting it away. Just as a Turing Machine is a Universal Digital Computer operating in a world of symbols, we propose that the brain is a Universal Dynamical Systems Modeller, evolved bottom-up (itself using nested networks of interconnected, self-organised dynamical systems) to prosper in a world of dynamical systems. Recent progress in Applied Mathematics has produced startling evidence of what happens when abstract Dynamical Systems interact. Key latent information describing system A can be extracted by system B from very simple signals, and signals can be used by one system to control and manipulate others. Using these facts, we show how a region of the neocortex uses its dynamics to intrinsically "compute" about the external and internal world. Building on an existing "static" model of cortical computation (Hawkins' Hierarchical Temporal Memory - HTM), we describe how a region of neocortex can be viewed as a network of components which together form a Dynamical Systems modelling module, connected via sensory and motor pathways to the external world, and forming part of a larger dynamical network in the brain. Empirical modelling and simulations of Dynamical HTM are possible with simple extensions and combinations of currently existing open source software. We list a number of relevant projects. (read more)