How does a vector work in the fourth dimension?
In: Physics
same as they do in 2D and 28D. Dimensions with vectors aren’t really what we think of them in day to day, they are significantly more abstracted and don’t need to be location in space. You can have a vector of prices, or voltages, or even both of those things.
But the math works the same way. As an example, let’s look at a basic operation called the dot product. Let’s start with 2 2D vectors [x1 x2] and [y1 y2]. The dot product is x1y1+x2y2. Pretty simple right each of the elements are multiplied by the corresponding one in the other vector and then everything is added. Now lets look at 2 4D vectors [x1 x2 x3 x4] and [y1 y2 y3 y4]. The dot product is x1y1+x2y2+x3y3+x4y4. Same pattern. The only issue is that you can’t graph them or really even look at them, you just have to rely on what the math says.
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