Discrete here means "non-continuous" - i.e. there is no smooth transition function between ideas/thoughts/rationalizations. For example, a formal proof is a di

Discrete here means "non-continuous" - i.e. there is no smooth transition function between ideas/thoughts/rationalizations. For example, a formal proof is a discrete process: it follows step-wise rules that you can assign natural numbers to (this is the first step, this is the second step, this is the third step). A non-discrete process, a continuous one, would have a smooth transition between these steps, which is hard to even imagine. While I am not convinced it is correct to say that "human reasoning is discrete", human language is definitely discrete. Words don't blend smoothly into each other. If you don't believe me, try to define a function f:[0,1] -> Words, such that f(0) = "red" and f(1) = "blue" and tell me what is f(sqrt(2)/2), or what is df/dx.