Comment by hpoe | Hacker News Reader

Comment by hpoe | Hacker News Reader

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It is very possible that I just don't understand but when I was studying ML and learning a little bit about the math behind it I suddenly realized that in one sense the word "dimension" simply means a value required to identify the location of a point. The number of dimensions requires indicates the number of values required to distinctly identify a point. For example in 2 dimensions it requires only 2 values or data, x and y, to uniquely identify a point. In 3 dimensions x, y and z, etc.

Now visualizing them can become much more tricky but mathematically we can still describe them.

Thus to bring it to your point about time as the fourth dimension if you want to ask your friend to meet you for lunch in the empire state building, you would have to give him the longtotude and latitude of the Empire State building (x and y) the floor to meet you on (third dimension z) but you would also have to give him the time to meet you, time being the 4th data point and ergo the 4th dimension.

Honestly what confuses me is what special distinction does time get to make it not considered a dimension like the others?

One weird thing about time is that it’s sign is “flipped” in the spacetime distance equation. So, while in some sense it’s “just another dimension”, it behaves somewhat differently from the spatial dimensions when measuring distance.

(I’m not an expert, just remembering something I found interesting in Einstein’s book _Relativity_)

For what happens if the sign is NOT flipped, see https://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html#CC

This is a really cool sort of science fiction: attempting to build a story around a world where some fundamental scientific law has been adjusted.

> Honestly what confuses me is what special distinction does time get to make it not considered a dimension like the others?

My less-than-a-layman understanding is that it really is just a physical point/plane - but as 3-dimensional creatures it will appear to us as time.

Sagan's flatland video shows the 3-d apple moving through 2-dimensional as transitory slices; the 2-d creatures don't see the entire apple because they are fine tuned for 2-d existence.

Interesting, but this seems to contradict(?) the fact that there are 4+ spatial dimensions.

This reminds me of passage in a book or movie (can't remember which one) which talked about the idea of human beings in 4D as worms, with the tail of the worm being the baby, and the face being our current state. As we go through life we keep elongating the work and overlap ourselves in space.

There’s a Heinlein short story with a similar passage. It’s in a compendium of stories called The Man Who Sold The Moon.

Mr. Nobody?

One thing is that we can only move forward in time. I have always heard the second law of thermodynamics (entropy always increases) defines the "arrow of time": you cannot go back to a previous ordered state unless you add work, thus you are forced to march forward in time.

Is entropy The Langoliers?

My hunch which is that the term "dimension" is an example of overloading a word which originally simply meant the three coordinates required to describe a point in traditional Euclidian space. With the introduction of the fourth 'dimension' (time) the floodgates broke open and with mathematics in the lead any attribute can now be said to be a dimension. For people still holding on to (and valuing) the original meaning it becomes confusing.

Case in point is the star schema of traditional data warehouses: there is no end to the number of 'dimensions' that a fact may have. But they are really just attributes. Same could be said of dimensions in mathematic; they simply denote attributes, albeit in somewhat 'spatial-like' domains.

You are entirely correct about how time should be thought of as just another point of reference. The reason I think it is viewed as the "4th dimension" is because it's something we can naturally observe without any tools.

Time is the only dimension we can’t control travel on - we’re stuck at 60 minutes an hour. So it doesn’t exactly map the same way the others do (though arguably all the first three are only analogous to the real world, as points and lines and planes don’t exist as non-3D objects we can interact with).

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