We might feel content to let science deal with all that since we are all comfortably ensconced in our one particular relevant scale of things—the human scale—and assume that we can ignore all other scales and not even bother with the very concept of scale itself. But we can’t! In truth, scale defines every aspect of our lives in the most fundamental ways—and even more broadly and deeply than in the natural world, as we will see in the rest of this chapter. Becoming aware of exactly how brings to question many of the comfortable beliefs that we take for granted about ourselves, individually and as a species.
The most obvious implication of scale in our lives is the most literal one: We humans exist on a scale defined by our average size. We are so used to it that we never think about it. But just imagine how our lives would be if we were the size of ants; we would exist in a world of unbelievable monsters, we would even be terrorized by spiders and frogs (some of us already are!), and we would have a hard time comprehending an elephant or a blue whale. We can get some idea from the movie, Honey, I Shrunk the Kids! and its sequel. Even small changes in scale can significantly affect our lives; anyone afflicted with dwarfism or gigantism would tell you that being adults who happen to be just a bit smaller or larger than the average makes everyday life a challenge, enough to justify some reality TV shows to document those challenges.
. Imagine that this is just a tiny section of a much larger grid of millions of particles arranged like this. Suppose we have a physical theory that describes the system at a scale where we keep track of each individual particle. We might then want to simplify things a bit and take blocks of four particles as our basic unit, which cuts down the total number of individual entities we need to keep track of in the system by a factor of four, as shown in . We could keep doing this, taking larger and larger blocks as our fundamental entity, and as the blocks get larger, we are essentially increasing the scale at which we are examining the system. Now, it so happens that in some of the most important physical systems, the theories that describe the system at each of those increasingly larger scales are identical in form in all their relevant features and parameters!
), then we lose focus on those smaller irritations as we get occupied by these larger troubles. But, as with renormalization in physical systems, as we get used to this new order of things, our minds eventually settle into treating these new, bigger problems pretty much the same way as we did the smaller ones in the past. Of course, there is a limit to how much we can cope with, and our troubles could reach a certain scale at some point where we cannot renormalize anymore, and our life could just fall apart. Similar “breakdowns” can happen in nature, as well, at certain scales.
This natural rescaling or coping mechanism is not so uniformly present among us all, and for some, there are bouts of nervous breakdowns and hysteria, sometimes even in response to minor problems, like, “Oh my God! My cell phone stopped working! I don’t know what to do anymore!” or “Oh no! I have a pimple on my cheek, my life is over!” A lot of spoiled teenagers and pampered celebrities come to mind. At the other extreme, we have the stoics and folks of heroic nature who seem unfazed by the worst possible personal disasters and take it all in stride. But most of us are somewhere in-between.
In a typical life, we do not even need any serious and sudden disaster to bring us face-to-face with renormalization—aging and the passage of time naturally imposes renormalization on us! The troubles of youth very often seem simple as most people face the realities of later life, yet those youthful troubles are serious enough while going through them, because that is the normal at that point in life. They only seem simpler and easier to deal with relative to the new normal of a more complicated later stage in life.
, with a fast oscillation superimposed on a slower oscillation. Well, depending on what time scales we are interested in, our description of the situation will be totally different. If we are interested in describing what happens over a few seconds, then for all practical purposes we can treat the slow process as static and unchanging, because that is how it will seem on the time scale of seconds over which the fast process happens. But, if we are interested in how the system changes over a time scale of hours, then it makes no sense to keep track of the details of the fast process. We will only see a time-averaged effect of the fast process, and only the longer undulations of the slower process will be relevant. A simple example with a much less dramatic difference in time scales illustrates the point. Consider an oscillating table fan—we can easily observe the side-to-side oscillations, but since the processing time of our eyes is slow compared to the motion of the blades, they all blend together to look like a continuous disc. On the other hand, if we were to take a few pictures with a high-speed camera, we would see the motion of the blades in successive snapshots, but the side-to-side oscillation would seem frozen.
One light-year is the distance light travels in a year in vacuum and is approximately 5.9 trillion miles! It is used as a unit of astronomical distance (not time, despite the confusing presence of the word “year” in it).