The Free Dictionary states: “The least number of independent coordinates required to specify uniquely the points in a space.”
What the heck does That mean?
What I’m getting at is, why is “Time” considered a dimension? Does “Time” take up space? Or what is, or in, say, the 6th dimension?
Needless to say, I’m not a math person, so if possible can anybody explain to me in non-mathematical terms?
Thanks in advance,
Jake The Ignorant
Suppose that you’re trying to meet someone for lunch in a skyscraper with sixteen unnamed restaurants on every floor laid out in a 4 x 4 grid. In order to successfully make a meeting, you need to say which restaurant, which floor, and when to meet. That’s four coordinates, and that’s why we regard time as a dimension.
By “6th dimension”, I’m guessing you’re thinking of some alternate plane of reality? That’s most often used in a fictional situation.
If so, that’s not part of the mathematical notion of a dimension. If there are 6 dimensions, we’re already in them, even if we can’t perceive them.
Alternate realities are not the same way a mathematician uses the word dimension, just as an “imaginary number” doesn’t mean a made-up number but a type of actual, honest-to-goodness in existence number.
Think of how you’d answer “what are the dimensions of this box?” You might answer “3 inches by 8 inches by 5 inches”. That’s the way a mathematician uses the word dimension. It’s a way of defining the “space”, whether that space is purely a mathematical construct or used to describe the real world (which is also modeled using mathematical constructs, now that I think on it).
The canonical example is an ant walking on the surface of a balloon. From the ants perspective, there is no “up” or “down”. The entire world, to the ant, consists of 2 dimensions. The ant exists in 3 dimensions but can’t perceive the 3rd dimension of the world.
Likewise, the space we live in can have more spatial dimensions than we can perceive.
As for time, that’s why we call it space-time. Time is a dimension of space-time, even if it’s not a traditional spatial dimension.
However, you could have “alternate realities” which are displaced from our own along some dimension or dimensions of which we are currently ignorant.
“String theory” involves 10 or 11 dimensions, but the extra dimensions are so microscopic, that we cannot see them and are unaware of them. I guess this is along the line that Chronos posted.
Correction: The other dimensions might be microscopic. There are other models where they’re as large as several microns, and yet other models where they could be arbitrarily large.
The microscopic models are the simplest, though.
You don’t need string theory to understand the idea of more than 4 dimensions.
Suppose you want to buy a car, and wish to consider
[ul][li] Purchase price[/li][li] Fuel economy[/li][li] Safety[/li][li] Body type[/li][li] Passenger room[/li][/ul]
You are exploring a 5-dimensional space.
You might be able to reduce this to a lower-dimensional search by exploiting correlations among the dimensional values (just as a search in our 3-D space become a 2-D search if you know your target is on the surface of the Earth).
Notice that the definition you quote says “in a space,” not “in space.” The use of the word “space” is potentially misleading if you’re not used to this terminology, since a “space” in this sense doesn’t necessarily refer to physical space/position. septimus gave an example of a “space” that was 5-dimensional, because every “point” in that space requires 5 numbers (“coordinates”) to describe.
Explained by HG Wells.
There are at least 10 dimensions we can visualize - this video does a good job of describing them.
It’s easy.
Dimensions define an event. It has four coordinates - length, width, height, and time. These are the four dimensions of timespace, the arena in which we humans operate every day. We use those four dimensions intuitively.
You meet me 400 miles west of here, 200 miles north, 300 feet above here, in 12 hours (or “on the roof of that building in Chicago at 11pm”, as we might paraphrase it).
The gun went off 200 yards east, 50 yards north, 20 feet below us, 45 seconds ago.
You need all four to define an event. You can’t, for example, meet someone without knowing all four dimensions (fortunately, we have shorthand for the first three, and can say “on the top floor of the Empire State Building” or “in the pub” and we know what those three dimensions are).
Just as another example, this famous chart File:Minard.png - Wikipedia describes Napoleon’s invasion and retreat from Russia. It shows 4 dimensions of that campaign - the thickness of the line indicates the size of Napoleon’s army, the position of the line shows the route (2-dimensional) that they took through Europe, and the associated temperature chart adds one more dimension. The “space” is a 4-dimensional description of the army and its environment, with each aspect (number of men, latitude and longitude, and air temperature) being a dimension in that space.
Great chart. From 140 years ago and discussed here.
Another great chart at gapminder.org/world has been cited many times on this board but is worth yet another link. In addition to the dimensions associated with x- and y-axis (wealth and health in the example) time is represented (as time, a fraction of a second per year) once you click Play to start the motion; and the size of a country’s bubble represents its population. And there are other controls and info beyond these four dimensions.
Yeah - I know about the Minard figure because of Tufte.
The gapminder video is brilliant.
And here’s the 11th dimension: Who lives in the eleventh dimension? - Parallel Universes - BBC science - YouTube
And while time might be “a” fourth dimension, it is not “the” fourth dimension, by which someone might mean the fourth spatial dimension. To be more specific, sometimes people use phrases like “three spatial dimensions and one time dimension”.
To understand what a fourth (spatial) dimensional object would seem like, read the book Flatland, in which a three dimensional object (a sphere) tries interacting with the inhabitants of a two dimensional world.
“dimension” is a trip-up word that confuses laymen. But it shouldn’t.
A “dimension” is simply a coordinate system.
The best example I’ve experienced - in Calc 3 (wherein you do terrible partial derivatives), in college, a fellow confused undergrad asked our calc 3 professor, “Can you give an example of a four dimensional system?”
He chuckled, shrugged, and said “sure.”
“You’ve got your X, Y and Z coordinates as a position in three-dimensional space. Everyone OK with that? Everyone understand?”
“Now add anything. Let’s use temperature. So for every point in space you’ve got X, Y, Z and temp.”
“That’s a 4-dimensional system. Be confused no more.”
Actually, that video does a terrible job of describing them. It’s mostly OK (but only mostly) for the familiar three, but after that it quickly devolves into utter nonsense. Please, don’t continue to use it as an illustrative example.
This is a really bad example, and doesn’t actually refer to a four dimensional system. You can’t go to two different points with the same space coordinates but different temperatures.
[Hey, Chronos started the criticizing]
Sure you can. You travel in space with your feet. You travel in temperature with a flamethrower and maybe a portable air conditioner to go the other direction, but a flamethrower is cooler.
Come to think of it, if I ever get into the flamethrower manufacturing business, I think I’ll market them as “Temperature Travel Devices”.