We can’t physically see or understand how complex numbers exist or work in our world in a nice way, but we know they do exist. Because we’ve made massive advancements in science and technology off the assumption that they exist and work, and our understanding of many things in the world including stuff as basic as the solutions to quadratic equations would fall apart. By the same token, there are many problems for which vectors and problem spaces of nth degree are used, where n>3, and there’s that whole adage where time is considered a 4th dimension. In that way, we often solve many problems, even rudimentary linear algebra ones, using sets in R⁴, R⁵, etc, and there are many, many invisible forces at work in our world such as gravity. We know how easily our brain can trick us, we still are easily fooled by optical illusions even when we know they’re there and what they are/how they work, despite our visual cortex being the one of the most powerful and most used part of our brain. So the idea of forces and things which we don’t have the capacity to perceive existing in the world is not anything new or foreign. There are frequencies we can’t hear, colors we can’t see, etc which other animals can and do. So why is the concept of n dimensions in the world so widely rejected? There must be a simple reason, I have heard that it has to do with the volume of a gas in a container being proportionate to its dimensionality or something
In: 2497
Couple ways to answer this. The simplest is, because we see three dimensions. If there were more spatial dimensions, we would expect to see a lot of weird things that we just don’t see. For example, objects would sometimes just disappear, as they move along another dimension (as an analogy, imagine an ant on a piece of paper: it can see a crumb on the paper with it, but if you pick up that crumb then to the ant, it just disappeared). We don’t see objects randomly disappear, so we can be pretty confident there are only three spatial dimensions.
You mention time as a fourth dimension, and that is 100% true. However, it isn’t a spatial dimension, in the sense that you can’t freely move through time like you can move up/down, forward/backward, and left/right. Getting into the nitty-gritty of how time is a dimension and all the implications that go along with that is complicated, but the important point is that unless you’re a physicist, it’s not a dimension in the same sense that space is three dimensional.
Final point is that yes, there could theoretically be more spatial dimensions that we can’t see. In fact, string theory in physics predicts at least 11 spatial dimensions, with some theories predicting 26 or more. However, we have never detected any sign of these dimensions existing, so if they do exist or not, we will still only experience a 3D world, so there’s not much point in saying otherwise (unless you’re a physicist doing calculations that require them, but that is not most people).
Latest Answers