In physics, atoms and particles are complex objects with diverse properties. Digital Philosophy deals with just two kinds of objects and they are the very simplest kind of things possible. While we call them “bits”, it doesn’t matter what we call them. We choose to call the bits of Digital Mechanics 1 and –1. All bits are the same in every way except every one is either 1 or it is –1. A bit is 2 state and has no other intrinsic state. The only properties that a bit (such as 1) has are that it is absolutely identical to all other 1 bits, and different than all –1 bits. Similarly, –1 bits are the same as all other –1 bits and different than all 1 bits. Of course, every bit is located by 4 integers which are its space-time coordinates. Properties of physics such as charge, energy, momentum and spin are all made up of space-time configurations of bits. There is space, there is time, there are bits, there is a simple digital process and there is nothing else in Digital Philosophy. In creating the DM model described in this paper, we have had to define a large number of very simple digital constructs, digital processes, geometrical arrangements and ad hoc concepts. However, every one of the things defined is extraordinarily simple. We think that the totality of a final and correct DM model (if one is ever found) will be even simpler than what we present here. It’s like Emerson’s comment when he apologized to a friend for writing such a long letter; he didn’t have time to write a short one!
The bits of DP differ from the bits in an ordinary digital computer in that the bits of DP cannot be changed, created or destroyed. While bits in a computer are normally thought of as either 1 or 0, they are sometimes thought of as True and False. In DM we are often interested in a symmetrical binary system, so we have chosen a bit that is 1 or –1. Arithmetically, our ( 1, –1) binary system has an obvious multiplication table, but the addition table is not so obvious. We assume that we must always add an odd number of addends. Note, 1 1 1 = –1, and –1–1–1 = 1. Sometimes we use an alternative label where the bits are named i and –i. The reason has to do with Bits that operate in the opposite phase to the ( 1, –1) bits. Within the ( i, –i) binary system, both sums and products must both always involve an odd number of arguments. If we make a rule that arithmetic operations always involve an odd number of arguments, then sums in the ( i, –i) system are the same as products, but sums in the ( 1, –1) system are the negative of products. The details of the kinds of bits we propose for our DM models impose no hindrance on the computational generality of these models. The arithmetic properties of the bits only matter when we want to analytically derive standard equations of physics from digital state information.
