1d, 2d, 4d, and other strange things in the cosmos

Sometimes I come across a science article where physicists or maybe astrophysicists talk about things that are not 3-dimensional. Are they really talking about something physical or something else like some characteristics of a specific area of space? I mean, everything physical has a length, width and a height so I’m confused. I am hoping for a very dumbed down explanation if you will.

Thanks

It depends, obviously, on the “thing” that is being discussed. IINAAstrophysicist, but my layman’s understanding is that the idea of a four (or more) dimensional universe is at least being kicked around as a genuine description of the actual universe, not just a hypothetical model.

For an example of “it depends on what you’re talking about”: 4 dimensional spacetime is the fabric of our universe, consisting of 3 dimensions of space and 1 of time.

Yes. General relativity requires time be a “physical” dimension, but that doesn’t necessarily make it so. Julian Barbour, a physicist who is actually pretty well respected within that community, has shown that all of the predictions of GR can be replicated using a purely relational (Machian dynamic) framework. IIRC, the only stipulation is that the topology of space itself has to be curved - and no, don’t ask me what that means. :frowning:

Our common sense perceptions seem to be the worst way of understanding the universe, which is stranger in every way than our daily life on earth leads us to believe. For example, we always, under any circumstance, perceive time to flow at one second per second forward. Yet Einstein showed that two clocks moving at one second per second inside their separate reference frames can disagree if brought together. There are zillions of examples like this, and they all make for good GQ threads. :slight_smile:

So just because we think only in terms of height, length, and width doesn’t necessary cut it with the actual universe. We can’t imagine a fourth perpendicular line* but so what? The math behind extending three dimensions to four has been understood for centuries. You can extend that to any number of dimensions. Mathematicians play around with dimensions in the millions, even an infinite number of dimensions.

Do any of these have physical meaning? Maybe. String theory requires 10 or 11 dimensions to make everything work. Here’s a fairly straightforward article on that. No evidence of this has yet been discovered, though. Scientists continue to play around with larger numbers of dimensions in order to get the universe to make sense. Heck, some are working with two time dimensions. I understand that even less.
*Some people claim they’ve taught themselves how to do it. Who knows?

Scientists talking about dimensions may be talking about length, width, height and/or time but they could also be talking about independent parameters of a system that completely describe it.

I’ve always wondered if it’s possible to live in ONE dimension. Would we be able to only move in one direction? Or just be like a photograph and completely still?

Life as we know it would not be possible to exist in 1 dimension. Any features would be breaks between points and lines. I suppose it could be possible for some sort of replicating memetic theme to populate such a universe, but it certainly be anything like we would recognize as life.

Mandatory that anybody asking the question read *Flatland *by Edwin Abbot.

I thought this was going to be a thread about the old British money system, where pennies were indicated by a lowercase d. It was known as the Lsd system, because whoever devised it was obviously tripping out of their head.

and here I opened this thread thinking it would be about pre-decimal British coinage (one pence, tuppence, four pence), which some might argue was a strange thing in the cosmos.

Is it still called a ‘ninja’ if you haven’t posted something yet?
Nevertheless, **aNewLeaf **just stole my thunder with Flatland by Edwin Abbot.

The concept of “dimension” is often misunderstood. It’s better explained as how many numbers are needed to indicate the location of one point in relation to another.

In a one-dimensional universe (a line), just one number is used. Point B is 3 inches from Point A. A negative number changes the direction.

In a two-dimensional universe (a plane), two numbers are needed: -3 inches at a 45 degree angle. Note that the dimensions are not necessarily height and length; there can be more than one way to describe them.

We live in a four-dimensional universe because four dimensions are necessary to cover all cases. However, very often, you don’t need all four. “How far is it to the next McDonald’s.” “Go three miles along this road.” This requires only one number, since the curves and height differences are not necessary, but it doesn’t change the dimensionality. Time isn’t required, either, since the destination will remain in the same location the entire trip.

However, try to give directions to find a fly in a glass box. In order to determine its location, you need to include the time: it’s 3 in. down, 6 in. over, 2 in. up – right now. In one second, the directions will be different.

Everything in our universe has four dimensions. It’s just that often fewer are sufficient to describe matters. A sheet of paper may look like it’s only two dimensions, but it does have (very small depth) and duration (Eventually, the paper will be recycled).

Three spatial dimensions are a useful calculation space for quickly solving survival problems on the African veldt, so that’s how we perceive the universe. They’re good for answering questions like “Is that lion able to catch me before I can scramble up that tree?” or “How hard should I throw my spear to kill that gazelle?”

However, the fact that we evolved to use a 3-D calculation space does not mean that the universe is actually 3-D. Maybe it’s 2-D or 4-D or 11-D. As physics has advanced we’ve discovered that sometimes it’s easier to solve problems if we abandon our intuitive 3-D notions of the universe and work with different numbers of dimensions instead.

What does it mean for something to have 11 dimensions? All it means is that eleven degrees of freedom are needed to solve certain physical problems. There’s no point trying to fit that understanding into your intuitive 3-D understanding of space because its intentionally be designed to handle problems that are intractable in 3-D.

Even in a 2D (plus time) world life would probably be impossible certainly intelligent life. There are limited numbers of ways to connect different points with lines when the lines remain on a surface and don’t cross each other. That means it would be very difficult to have circulatory and neural systems that connected to all the body without interfering with each other. There might be some other system, but one might think that connectivity is important for life. I think this also means that it would be very difficult to construct the complex molecules out of which life is made.

Another complication is that no body could have more than a single opening (at any one time). If you have one hole for air to enter and another for food, some parts of the body are not connected to others.

One additional complication is that if gravity falls off like 1/(distance)[sup]D-1[/sup] where D is the number of dimensions (or more accurately the number of macro dimensions if you’ve read some of the links here) then only if D = 3 do stable orbits exist. Stable orbits might not be necessary for life if it can live in space.

I was surprised nobody else mentioned it. I wonder what percentage of Dopers have a physical copy of the book in their possession?

It may take only three dimensions to describe a *location *in space, but if you include *orientation *(where is it pointed?), you need another three dimensions for a total of six. That’s why robotics and computer graphics use a six-dimensional description of the universe, and why a fully-dextrous robot needs six joints.

Think of it this way: imagine two objects that appear to be identical to you or I. We can look at them and measure them and they appear to have the exact same size. But we’re only measuring them in the x, y, and z dimensions - height, width, and length.

Now imagine there’s a q dimension and quidth is the amount an object extends in that dimension. And one of the objects is twice as quide as the other object. So even though they appear identical to us - because we can’t sense quidth - one object is bigger than the other.

How I imagine the quantum mechanical state of a system is a fixed arrow rotating continuously about a point in an infinite-dimensional space, until I perform a measurement when it makes a random and discontinuous ‘jump’ (assuming that the system when measured is in a superposition of states wrt to the measurement).

The fact that quantum mechanics uses an infinite-dimensional space as its mathematical setting isn’t all that shocking when you realize that knowing the exact ‘direction’ the arrow points is the same as knowing the exact quantum state.

Which shows that dimension, primarily and even in physics, is a mathematical concept. The dimensions in a quantum mechanical state space are not the same as the 3 spatial dimensions of Newtonian mechanics.

1-dimensional would be a straight line. If anything could live on a straight line, it would have to be a line segment that could move forward or backward, but not in any other direction.

2-dimensional would be a surface, like a computer monitor. Any “life form” has the capacity of moving, but is limited to the plane. Some people think, for example, that a cursor is “in front of” everything else, but they’re mistaken.

The interesting thing is that for anything to be a “life form,” it has to be capable of motion, which means existing in the 4th dimension. So your 1- and 2-dimensional life forms can exist within the 4th dimension, but not necessarily all 3 of the spacial dimensions.