Did you like the movie “The Matrix”? We are considering it here and if you want to join the discussion, please respect our Ground Rule #1: We don’t say “believe”. The things that emerge from “what if” questions should be put through a progression that starts with “Hypothesis” and then moves to “Theory” and then sits there a long time before moving to “Law”.
One perspective considers the possibility that the real reality exists over a continuous number system, and that we, in our simulation, live in a pixelated reality. In the pixelated reality, various things can be taken down to a smallest unit, such as a smallest unit of length. You might recognize this idea if you’ve done some reading in Quantum Mechanics.
We’re covering that idea here. The ideas behind it fit in a section of Arithmetic called Discrete Mathematics. This concerns math relating to integers. Try thinking of this in terms of our money where the penny is the smallest possible coin. If you buy things with coins and dollar bills, think of that soda from the machine as costing 60, because your frame of reference is pennies, rather than dollars. That gets rid of decimal numbers.
Or think of it as moves forward on a chessboard, with a move from one square to an adjacent square being a distance of one. You can’t move forward half a square length. Think of our reality (in a simulation) as being built on these tiny pieces. Caution, we don’t mean for this to imply that a simulation has to be pixelated (or quantized), or that a real reality must be continuous. These restrictions are put in place so we may consider the results of such restrictions.
Next, contrast that with the ideas we learn in Algebra. Algebra teaches us that between any two values, there exists a value that is a midpoint. For example, the midpoint between 1 and 2 is 1.5 and we can generalize this to a formula for the midpoint, ‘m’, between any values ‘a’ and ‘b’:
For math classes, you take Algebra and Algebra II before you take Discrete Mathematics. The idea of a continuous number system probably seems more “real” to you. After all, numerical values correspond to length and it makes sense that between any two lengths that is a midpoint length. If so, then our quantized reality, for you, is a bit of a cage, and you may soon start feeling a desire to escape, and get out there to the real reality where things are continuous…
Rob Sterling 