(My brother, who is also a mathematician, figured out a formula for the volume of an n-dimensional sphere during church one day using calculus, so going from 3 dimensions to any dimension you want took less than an hour). Geometry is simpler in many ways than physics is, and the math is easy to apply and find analogies for, once you understand it well enough (4th dimensional calculus isn't much harder than 3rd dimensional calculus), so figuring out math tools to help you measure something in a geometric 4th dimension isn't too hard. So what good is doing geometry in 4 dimensions, if you don't have 4 spatial dimensions?Ī. Any time you use 4 variables to describe something, it's a fourth dimensional problem (spacetime: (x, y, z, t)).
If I want to specifically locate something, I need to say not only where it is, but also when it is there. Time is rather different than a spatial dimension, because we can't go backwards in time, but it is another degree of freedom. Physicists say that spacetime is four dimensional: 3 spatial dimensions+1time dimension. If you'd be satisfied with a less geometric 4th dimension, then the answer is yes. You're not going to find a 4th dimension that you can touch and perceive directly, but someone might be able to figure out if there's one out there even though we can't see it or touch it. There are theoretical physicists who think there is, and others who think there isn't, and so far nobody knows who is right. If you want a 4th spatial dimension, the jury is still out.
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