What are dimensions?

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What are dimensions?

In: Other
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It could mean a couple of things. Mostly it refers to the physical representation of some space or object

Here’s a video I found many years ago that I like showing people. https://youtu.be/p4Gotl9vRGs. Hope it helps! 🙂

A dimension is typically a scale of measure that one can travel on that is orthogonal to all others. That is, no matter how far or fast you travel along a given dimension, your travel along other dimensions is unaffected.

At it’s most basic, it’s a unique way to measure how something changes.

Drop something. It falls. We can measure how far it moved, and we can also measure the time since if time didn’t change the thing wouldn’t have moved to fall in the first place. We now have two dimensions: up-down and time.

Now roll something down a hill. Time still changes, up-down still changes, but our up-down ruler didn’t measure the whole change. We need a new ruler, and I’ll skip to the best answer and say our new ruler needs to be at 90 degrees to the first one to make it’s measurement unique where even when the up-down ruler says nothing changed the new sideways ruler is measuring a change.

And since we live in a three dimensional world, we’ll end up needing three rulers to go with our timer to describe how things move. Note that how our rulers are pointing doesn’t matter. It only matters that each one is at 90 degrees to the other two. Someone with their ruler pointing differently than yours (but still 90 degrees apart) will agree with you how something moves, they’ll just have the motion divided among the rulers differently. Space is three dimensional because we only need three rulers; we don’t have to agree at all how they’re pointing.

Moving isn’t everything though. There’s also mass, charge, and other base properties we can measure that are also dimensions. We can also derive dimensions. Before direction and time were separate things, but we can work out how much distance was changing as time changed and call that the dimension of speed. In the same way, we can get force, energy, pressure, etc.