From: "Jeffrey E." <[email protected]> To: Joscha Bach <, Subject: Re: Date: Mon, 19 Feb 2018 11:49:52 +0000 Energy? Unlimited? Equal per computation ? Non local ? Two places at once? Distribution s. Field effects time to compute / all the same time ? Synchronized On Mon, Feb 19, 2018 at 6:24 AM Joscha Bach > wrote: As you may have noticed, my whole train of thought on computationalism is based on the rediscovery of intutionist mathematics under the name "computation". ftp://math.andrej.comAvp-content/uploads/2014/03/real-world-realizability.pdf The difference between classical math and computation is that classically, a function has a value as soon as it is defined, but in the computational paradigm, it has to be actually computed, using some generator. This also applies for functions that designate truth. For something to be true in intuitionist mathematics, you will always have to show the money: you have to demonstrate that you know how to make a process that can actually perform the necessary steps. This has some interesting implication: computation cannot be paradoxical. In the computational framework, there can be no set of all sets that does not contain itself. Instead, you'd have to define functions that add and remove sets from each other, and as a result, you might up with some periodic fluctuation, but not with an illegal state. Intuitionist math fits together with automata theory. It turns out that there is a universal computer, i.e. a function that can itself compute all computable functions (Turing completeness). All functions that implement the universal computer can effectively compute the same set of functions, but they may differ in how efficiently they can do it. Efficiency relates to computational complexity classes. The simplest universal computers known are some cellular automata, with Minsky and Wolfram arguing about who found the shortest one. Boolean algebra is Turing complete, too, as is the NAND gate, the lambd