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
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A dimension is just a direction in which you can measure something. When we work with equations or shapes, we often use coordinates to describe a point’s location.
1. In one dimension, we might have a number line, where each point is described by just one number. Like 5 or -3.
2. In two dimensions, like on a flat piece of paper, you need two numbers (like x and y coordinates) to describe where you are. That’s how we plot points on a graph.
3. In three dimensions, you’re adding depth. Now you need three numbers to describe a point’s location. Think about a box, where you can move lengthwise, widthwise, and heightwise.
We don’t stop at three dimensions. You can have equations or systems that need four, five, or even a hundred numbers to describe something. Each extra number is like adding another dimension.
For example, in physics, we sometimes talk about spacetime, where time is like a fourth dimension. So if you want to meet someone, you don’t just tell them where (3 dimensions: x, y, z), but also when (1 dimension: time).
Theoretical physicists also explore theories like string theory, which suggest there might be even more hidden dimensions curled up so small we can’t see them.
So while our human experience is rooted in three dimensions, math allows us to explore and describe systems and realities that go beyond our everyday perception.
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