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Comment by roundsquare | Hacker News Reader

I really hate this video. It makes things more complicated than needed.

You can't "visualize" the fourth dimension (or I haven't met anyone who could... and the kind of math/physics where this comes up was a common topic for me for a while).

However, you can understand it pretty easily. Its really just another coordinate. You can do algebra with it. If I say someone is at (3, 2, 5, 6) and moves (1, 2, 3, 4) they are now at (4, 4, 8, 10)...

Want a 5th dimension? Add another comma/number.

People who "visualize" the higher dimensions actually visualize 2 or 3 dimensions and know how to generalize (from practice/experience/theorems).

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I think the question that most often comes up is how many dimensions are we living in? And, are all of them equal?

Sure, on paper you can have as many dimensions as you like, just add coordinates, but that won't help us come up with the grand unified theory, or find other new laws of our universe, which might have pretty useful practical applications.

Unfortunately we are limited in seeing beyond our primary senses.

Its a fair point... sadly I don't know the answer in any great details. What little I know says there are 26 dimensions and they are not all equal. 3 of space, 1 of time, and 22... others...

Actually, I wonder, when people usually ask this question, are they just using the word dimension as a buzz word or do they know what it means?

You can visualize the 4th dimension. Just imagine 3d space moving through time. 5 is where is starts to be problematic.

BTW the video is ok until 4:30. Then it quickly degrades into nonsense, not just more complicated than needed.

Okay... no.

This is the problem. The 4th dimension is not time. We can represent time as the 4th dimension in a system if we want to, but you can have systems where the 4th dimension is not time.

A good example is when people create a matrix representing links in webpages. If you limit your universe to online 100 webpages and their interconnections, you can get a vector for each webpage. The vector is a point in 100 dimension space. The 4th dimension is not "time" but "if the 4th website on the list links to me."

OK, then I should have worded it like this: I can visualize a 4 dimensional vector space over the reals. Even if the 4th dimension in your particular setting is not time, I can still visualize it as such.

Also, visualizing an n dimensional vector is not very interesting. A vector indicates a point, and a point looks the same in any number of dimensions.

Sure, I suppose visualizing a point is not very interesting. I'm talking about visualizing 4 dimensional space. Can you close your eyes and imagine 4 mutually orthogonal lines?

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