I watched this neat TV program. Let me tell you what it said:
Imagine a membrane where each point is located by giving 10 numbers ... a 10-dimensional space.

>Huh?
To locate, say, an airplane we could give its longitude, latitude and elevation. That's 3 numbers.
But if we went to that location the plane may or may not be there, so we also give a time. That makes a total of 4 numbers.

>Yeah, Einstein's four-dimensional space-time, right?
Yes, but Einstein's theories couldn't explain the relationship between electromagnetism and gravity and the physics of the day couldn't explain the details of the Big Bang and ...

>Big Bang?
Yes. It's postulated that the universe began, billions of years ago, as a single point ... then it expanded from there, the stars and galaxies moving away from each other and ...

>That's the Big Bang?
Yes. The universe began with this Bang ... as a point. When astronomers look at the galaxies now, they notice that they're moving away from each other. They imagine how it was a billion years ago, two billion, ten ...

>Until the galaxies were all located at one point, right?
Yes, but the laws of physics couldn't explain how this happens, how all matter in the universe could expand from that point, how electrons and photons and the myriad of other particles could have formed, how they coagulated to form stars and how black holes were formed, and, in particular, what (if anything) was there before the Big Bang.

>You were talking about a 10-dimensional membrane, remember?
Ah, yes ... the membrane.

So here's another theory:

Strings

We suppose that matter isn't composed of particles that exist at a point. (Einstein's space-time model). Instead, we imagine that electrons, photons, etc. are really microscopic, vibrating strings. These strings can be closed, like loops, or open, like a hair. They can vibrate in various ways and each different mode of oscillation results in a different particle. If a string vibrates this way, it's an electron. That way, it's a gluon. Another way, it's a photon ... etc. etc.

>What about gravitons?
Yes, that's the neat part. For one mode of vibration, it's a graviton. The photon string describes electromagnetic forces, the gluon carries the strong nuclear forces and gravitons ...

>Gravitons account for gravity.
Yes. Neat, eh? Einstein would be happy. Although he tried, he never could find a Theory of Everything that would describe both electromagnetic and gravitational forces. This so-called string theory did explain many of the ...

>So String Theory is the latest-and-greatest theory, right?
Uh ... no. String theory began about 1970, but the basic ideas were enunciated in the 1920s and are known as the Kaluza-Klein theory.

In that theory we begin with one time dimension and 3 space dimensions (described by 3 numbers: x, y and z) and add one more space dimension. Unlike the first 3 space dimensions, where one can presumably travel forever in the x-direction without returning to where you began, this 4th space dimension is curled up into a tiny circle.

>So if I travel in that 4th space dimension, I'll get back to where I started, right?
Yes, that's the theory. This extra space dimension is very small (about 10^-35 metres), smaller than the smallest particle.
If you travel in that direction you'll arrive where you began almost immediately.

>And that curled up dimension ... that 4th space dimension, that's a curled up string, right?
Well, years after the Kaluza-Klein theory, String Theory was born ... except it had not just 4 space dimensions, but 9 !

>And "time" makes 10.
Yes. I can imagine that, for each value of x, y or z (the three "standard" space dimensions), we associate a tiny ...

>A tiny curled up string!
No, I was going to say a tiny sphere, each sphere having its own dimensions (like latitude, longitude).

>A 2-dimensional sphere for each of x, y and z? That makes 6 space dimensions in total, right?
No, that makes 6 extra dimensions. Add the 3 "standard" dimensions and we have 9 space dimensions.
Now add the single time dimension and we've got our 10-dimensional universe.

>Those spherical regions associated with each of x, y and z ... that's why there's 9 space dimensions?
I have no idea. I'm just providing a simple-minded explanation why we might anticipate 9 space dimensions.

>The "standard" three are right-left, up-down, forward-backward ... but what do you call them other spacial dimensions?
Well, they do have names, I think. Maybe there's spin and color and ...

>But 3 of those space dimensions are ... uh, large.
Yes, and 6 are small, unobserved ... called compact dimensions.
Indeed, the wee strings exist in the 3 "standard" dimensions, but they also vibrate in the 6 "compact" dimensions.

>You were talking about a 10-dimensional membrane, remember?
Oh, yes ... the membrane.
Although String Theory apparently explained a lot of things, it didn't explain everything.
Further, there were mathematical problems in the theory ... so five string theories evolved over the years as theorists attempted to tweak the theory to accommodate the various inconsistencies and ...

>Five theories? I'd say that hardly makes for a Theory of Everything.

Membranes

Right. So here's the latest-and-greatest so-called Membrane Theory:

We retain the idea that matter is made up of strings, either closed or open.
They vibrate in different ways, appearing to us as different particles.
The various string-particles describe the various forces we observe in nature.
Now we imagine that all the elemental strings in our universe live on some 10-dimensional membrane.
The vibrations of the strings are the matter (and consequent forces) we oberve in our universe.
BUT (and here's the clincher!), there are other such membranes very close to ours

>You mean other universes?
Yes, that's the theory. Indeed, there are an infinite number of parallel universes, each a 10-dimensional membrane with (perhaps) stars and galaxies and electromagnetic and gravitational forces and ...

>That's not new! I read about that years ago in ... uh, I can't remember which science fiction novel.
Yes, it's been the stuff of science fiction for many years. Can't you just imagine cosmologists of the past laughing at the parallel universes of science fiction ... and now, adopting that notion to explain observed phenomenon. Can't you imagine them sitting in front of the TV, watching Star Trek? Can't you see them, with notebook in hand, jotting down ...

>Okay, how do we get to one of these parallel universes?
That's easy. We just move perpendicular to our own universe membrane ... in the direction of an 11th dimension.

>You're kidding, right?
It's not my theory! If you move in our 10-dimensional space you'd still be in our universe.
To get to another universe you'd have to move in another spatial direction.

>So now we have 10 space dimensions!
Add time and we have an 11-dimensional ... an 11-dimensional ... uh ...

>Universe?
No, it'd be an 11-dimensional collection of universes.
They're very close to each other. They can vibrate. They can touch.

>Then what?
I guess if a vibrating membrane-universe A collided with membrane-universe B, then B would start to vibrate.
The vibrations would start at the point of contact between A and B.
The vibrations would radiate outward in the B membrane.
But what is doing the vibrating?
The elemental strings in the B-universe!
And what are vibrating strings?
Matter. Stars. Galaxies
... and forces: electromagnetic, gravitational and nuclear.

>Hey! that's a Big Bang!
Yeah, looks that way, don't it?

>And you really understand all this stuff?
Well, not exactly. I still have several episodes of Star Trek to watch.

for Part II