4th Dimension... what are you?

[DeltaSpectre]

Is it a measurement of time? Or a spatial measurement like the existing three known dimensions?
Or is it perhaps some connection where a measurement of it is equal to a measurement of time and vice versa.... but I think that is more likely to be in the 12th dimension... oh well,it's late and my mind is thinking abstract..

[jinydu]

Mathematically, the fourth dimension is formed by 4 mutually perpendicular lines intersecting at a single point. Thus, in that sense, you can say that the 4th dimension is spatial. However, the word "is" can be considered misleading, because it implies that the 4th dimension actually exists, a claim for which there is no proof.

In some areas of physics, time is often represented using such a 4th axis. However, this is merely a useful representation. In economics, the price of gold can be represented by a 4th dimension (assuming that the previous three have already been filled in by other quantities).

[houserichichi]

Jinydu, in your description of the fourth dimension, the word "exists" is also misleading. It exists mathematically - anything you can define from logic exists in its own right. However, can we experience something in four spatial (I'm assuming you're refering to Euclidean) dimensions? This is where I draw my lines, as do most physicists, though the string theorists perport that 6 dimensions are curled into tiny "balls" at all points of the universe which is why we don't feel or experience their effects directly.

Time is the fourth dimension of spacetime (made famous by Einstein's relativity papers), not of space (which is mathematical in its own right). F-theory (something else) requires 2 "orthogonal" time dimensions...oh the fun!

Your reference to the price of gold being a fourth dimension is ANOTHER kind of definition - the number of degrees of freedom when describing something. Frankly, you could run that same bout of logic for just about anything, so long as the four things you're refering to are mutually independent.

[jinydu]

Jinydu, in your description of the fourth dimension, the word "exists" is also misleading. It exists mathematically - anything you can define from logic exists in its own right. However, can we experience something in four spatial (I'm assuming you're refering to Euclidean) dimensions? This is where I draw my lines, as do most physicists, though the string theorists perport that 6 dimensions are curled into tiny "balls" at all points of the universe which is why we don't feel or experience their effects directly.

Time is the fourth dimension of spacetime (made famous by Einstein's relativity papers), not of space (which is mathematical in its own right). F-theory (something else) requires 2 "orthogonal" time dimensions...oh the fun!

Your reference to the price of gold being a fourth dimension is ANOTHER kind of definition - the number of degrees of freedom when describing something. Frankly, you could run that same bout of logic for just about anything, so long as the four things you're refering to are mutually independent.

Thanks for clarifying things. I wouldn't disagree with anything in your post.

The main point is that we shouldn't confuse the pure mathematical theory of four dimensions (which can begin along the lines of "Assume its possible for four mutually perpendicular lines to intersect at one point") with physics/economics/etc. theories that use 4 dimensions (such as Einstein's Theory of Relativity).

[RQ]

From what I know, the 4th mathematical dimension describes the fourth extended spatial dimension. Whether it exists in actuality is a matter of personal opinion, in my personal opinion, but in math, the 4th spatial dimension has its equations, whether it exists in actuality or not. The joy of pure mathematics.

[jinydu]

From what I know, the 4th mathematical dimension describes the fourth extended spatial dimension. Whether it exists in actuality is a matter of personal opinion, in my personal opinion, but in math, the 4th spatial dimension has its equations, whether it exists in actuality or not. The joy of pure mathematics.

Exactly. Pure mathematics (at least by itself) cannot prove whether a fourth spatial dimension exists in actuality. All it can do is give information about what it would be like if it did exist.