CHAPTER 5 A Model of Reality and Time  Incrementing Time in Simulations. (77)



To understand reality one must understand time. During the next six chapters, we will use the notations “deltat” and “DELTAt” extensively. Because this notation is borrowed from the field of mathematics, it may seem strange to some, but do not be put off by that. This chapter provides an explanation of incrementing time in simulations to the mathematically challenged and introduces a unique perspective on the nature of time to the Big Picture reality challenged. The words “delta” and “DELTA” represent the lower and upper case Greek letter of the same name. They are spelled out to avoid using abstract symbols that might inadvertently trigger mathephobia or other related mental technoblocks. This is easy – you’ll see.



CR  Traditional mathematical notation places the Greek letter delta next to a variable (some quantity that changes) to represent an increment (small change) in that variable. I use it here because many people are familiar with this notation. If you are not, don’t worry, the concept is simple and explained in detail below. “DELTAt” and “deltat” are simply names for two different increments (small chunks) of time.



CR  In an iterative dynamic simulation, such as the calculation of the position of a fired artillery round (or a thrown ball) as a function of time, one starts with the equations of motion (equations giving position as a function of time) and the initial conditions at time t=0. The first time through the computational process loop, one lets t = (deltat) and then calculates position – next time through t = 2•(deltat), next time through t = 3•(deltat), next time through t = 4•(deltat), and so on. You calculate a new position of the object (artillery round or ball) for each time t, which is one deltat larger than the previous value of t. Consequently, time, in your calculation of position, progresses forward by increments (small discontinuous jumps) of deltat.



CR  Your simulation can approximate continuous time, and thus continuous motion, by making the size of deltat very small. The cumulative sum over the deltat is called "simulation time" because it drives the dynamic simulation, (as opposed to "realtime" which is what is measured by the clock on the computer room wall).


