The basic idea is to have a sequence of layers of nerve cells—much as one knows exist in the brain—with each cell in each successive layer responding only if the inputs it gets from some fixed random set of cells in the layer above form some definite pattern. … The response of a single layer of idealized nerve cells to a sequence of progressively different inputs is shown. Each nerve cell fires and yields black output only if the inputs it gets from certain fixed positions match a particular template.

The basic idea is to have m outputs as well as m inputs—with every one of the 2 m possible sets of inputs mapping to a unique set of outputs. … With gates that in effect implement {p, q}  {p ⊼ q} and {p}  {p, p} (with other inputs constant, and other outputs ignored) one can set up a direct translation of Boolean functions given in the form shown on page 619 . Of the 24 possible reversible s = 2 gates, none can yield anything other than additive Boolean functions (as formed from Xor and Not ).

The basic answer seems to be that there are nerve cells in our eyes and brains which are set up to respond to particular local patterns in the image formed on the retina of our eye. … The connections between these cells are set up so that a given cell in the visual cortex will typically receive inputs only from cells in a fairly small area on our retina. Some of these inputs will be positive if the Patches generated by a variety of one-dimensional cellular automaton rules.

more input. And often the actual form of this train of thought is influenced by memory we have developed from inputs in the past—making it not necessarily repeatable even with exactly the same input.

Physics versus mathematics Theoretical physics can be viewed as taking physical input in the form of models and then using mathematics to work out the consequences. If I am correct that there is a simple underlying program for the universe, then this means that theoretical physics must at some level have only a very small amount of true physical input—and the rest must in a sense all just be mathematics.

It is common for uniform behavior to be quite independent of initial conditions or other input to a system. But sometimes different uniform behavior can be obtained with different input. … Beyond uniformity, repetition can be considered the next-simplest form of behavior.

From knowing explicit algorithms many problems can be assigned to such classes as: • NC: can be solved in a number of steps that increases like a polynomial in the logarithm of the input size if processing is done in parallel on a number of arbitrarily connected processors that increases like a polynomial in the input size. (Examples include addition and multiplication.) • P (polynomial time): can be solved (with one processor) in a number of steps that increases like a polynomial in the input size. … Central to computational complexity theory are a collection of hypotheses that imply that NC, P, NP and PSPACE form a strict hierarchy.

Nerve cells In the retina and the brain, nerve cells typically have an irregular tree-like structure, with between a few and a few thousand dendrites carrying input signals, and one or more axons carrying output signals. Nerve cells can respond on timescales of order milliseconds to changes in their inputs by changing their rate of generating output electrical spikes. … Their values can presumably change to reflect certain aspects of the activity of the cell, thus forming a basis for memory (see page 1102 ).

And the cell in the visual cortex will then respond only if enough of its inputs are positive, corresponding to a specific pattern being present in the image. … And one can then assume that in the visual cortex there is a corresponding array of cells, with each cell receiving input from, say, a 2×2 block of squares, and following the rule that it responds whenever the colors of these squares form some particular pattern.

In the past the most common belief has been that there must be some form of external influence from fate—associated perhaps with the intervention of a supernatural being or perhaps with configurations of celestial bodies. … And the crucial point is that this happens just through the intrinsic evolution of the system—without the need for any additional input from outside or from any sort of explicit source of randomness. … Indeed, as a practical matter what usually seems to happen is that we receive external input that leads to some train of thought which continues for a while, but then dies out until we get