All our access to mathematics... is because we do computation. We can — Joscha Bach

"How does... representation by simulation work? ...If you are a brain and you want to understand sound, you have to model it. ...Neurons do not want to do 20 Khz. Thats way too fast for them. They like something like 20 Hz. So... you need to make a [which] measures the amount of energy at different frequencies. ...This ...in our ears ...transforms energy of sound at different frequency intervals into energy measurements... This is something that the brain can model. ...[A] neurosimulator tries to recreate these patterns. If it can predict the next input from the cochlea, then it understands the sound."

"Mathematics is the kingdom of specification and computation is the kingdom of implementation. Its very important to understand this difference."

"[C]omputation is about doing the work... executing a transition function."

"Computation is different. Computation can exist. It starts with an initial state, and then you have a transition function. You do the work. You apply the transition function [and] you get into the next state. Computation is always finite."

"With this vector space you can do amazing things, [e.g.,] if you take the vector from king to queen, its pretty much the same vector as between man and woman. ...[B]ecause [these concept spaces are] really a high dimension manifold, we can do interesting things like machine translation without understanding what it means, that is, without doing any proper mental representation that predicts the world. ...[T]his is [a] type of mental representation that is somewhat incomplete, but it captures the landscape that we share in a culture."

"[O]ur best bet is not just to have a single classification with filtering. ...[I]nstead... take the low level of input and get a whole universe of features that is interrelated. ...[W]e have different levels of determinations. At the lowest level we have percepts. At a slightly higher level we have simulations, and on an even higher level we have a concept landscape."