From: "jeffrey E." <[email protected]> To: Joscha Bach Subject: Re: Date: Sun, 14 Aug 2016 12:00:00 +0000 Thx perfect On Sunday, 14 August 2016, Joscha Bach < > wrote: Jeffrey, there are several sides to this: 1. Computers that are technically different from our current digital computer architectures, but can do the same things, because they can mathematically be proven to be equivalent, and we can build a digital equivalent. Examples are computers with ternary logic, neural networks, factor graphs etc. 2. Probabilistic computers: instead of deterministic state transitions, they change state with a certain probability. We can get them to approximate determinism with arbitrary precision by stacking the probabilistic gates. Many cognitive scientists and AI researchers believe that brains are in that category. (We can also reproduce their behavior on a digital computer by adding random noise.) 3. Computers that are technically different from our current digital computers, but are still mathematically equivalent, yet it may not be practical to build a digital equivalent, because it would be too large or too slow. Examples are DNA computers, chaotic computers etc. Digital physicists (Steven Wolfram, Ed Fredkin) believe that even the universe is in this category. Chris Eliasmith thinks the brain is in this category (we need to build electronic simulations of spiking neurons). 4. Quantum computers: they still cannot do anything but manipulate information, but they can (hopefully one day) do a few things efficiently, like factoring large numbers, so they are in principle more powerful than conventional computers. Seth Lloyd thinks the universe is in this category, and Penrose thinks the brain is in this category. 5. Hypercomputers with true continuum dynamics. Such computers can solve the 3 body problem with infinite precision in finite time etc. (Most of) traditional physics believed that the universe must be continuous, and even contemporary