"but I think throwing out math as a tool for understanding computing is very premature given its success as a tool for building and understanding abstraction"

"but I think throwing out math as a tool for understanding computing is very premature given its success as a tool for building and understanding abstraction" But the problem with mathematics is that it doesn't deal with time. This may (in a sapir-whorf fashion) be limiting our understanding of the universe (see Lee Smolin's Time Reborn). But even if the universe is actually timeless in many circumstances it still does not suit us to model it like that. We can have some timeless physical law expressed mathematically (say F=ma) and if we know all the initial conditions in a fairly pure environment we can predict the state of the system at any time. But this kind of system is useless in many real world situations. For example we don't build a control system for a robot or a car based on this kind of thinking. We don't try and predict the state of the world. We just treat it as a stateful system that changes and we keep reading those changes and then try and behave accordingly - Its all I/O and state. Similarly our brains in order to be efficient do hardly any calculation, instead its a massive cache against which we pattern match (see "On Intelligence"). As Leslie Lamport's state:. "Computer scientists collectively suffer from what I call the Whorfian syndrome the confusion of language with reality. Since these devices are described in different languages, they must all be different. In fact, they are all naturally described as state machines. "