I hate to disappoint, DSeid, but since I’m not a string theorist, I’m probably no more qualified to answer that question than anyone else. It also doesn’t help that I’m not remotely convinced that string theory is even right. All I can really say is that there ARE equations which are supposed to describe the shape of any curled up dimensions in string theory (it postulates that there are more that 3 spatial dimensions, and the extras are all curled up and really small so you can’t ordinarily detect them). These shapes are called Calabi-Yau manifolds, and they’re quite complex. But really, we’d need a string theorist here to explain that.
A book titled “Hyperspace” gives some layman details of superstring theory. As it is a very recent field it doesn’t seem to be ubiquitous enough to warrent many layman books on the subject.
However, I am very fond of superstring theory from what I have read of it. There’s a mathematician hidden in me somewhere. If i can just quit playing video games and wake him up… 
firstly,g8rguy, I am also a UF grad and will hopefully attend grad school next fall.
Now, if the infinitely simple it is also infintiely complex. Now, do both levels, complexity and simplicity, extend infinitely? and if so, what implications does this have?
or, ignore me…
Well, the complexity obviously extends a very very long way. Consider a cell. It’s composed of gajillions of molecules, each of which is composed of many many atoms, each of which is in turn made up of a bunch of electrons and a whole bunch of neutrons and protons, each of which is in turn made up of quarks, plus all the various particles that are being exchanged to hold the entire thing together. To accurately model even a molecule is a difficult task, even ignoring the complexities of its various consitutents. I can’t foresee us having the ability to model a cell from first principles in my lifetime. And of course, modelling a complex organism is as far from modelling a cell as modelling a cell is from modelling a molecule.
But I actually am strongly inclined to believe that things are, at the most fundamental level, incredibly simple (the math is hard, yes, but the fundamentals are few). I can’t prove this; it’s mostly an aesthetic statement. I leave the implications of such a thing to the philosophers, but I basically feel that it would be perverse were Nature to get as staggeringly simple as it is but no further. As it is, there are only four fundamental forces, two of which can be unified already; if we couldn’t unite them all in some framework or another, I’d be terribly disappointed in whatever set up natural laws.
Oh, and Lolo, to clarify: I did my undergraduate work at a small school in California, and prior to showing up here as a grad student, I’d never been associated with Florida in any way. Full disclosure, and all that.
"There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.
There is another theory which states that this has already happened. "
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- Douglas Adams
On a related matter:
Is time quantisized? Is there a limit to how many times you can split a second?
It seems to me that if space is grainy, time ought to be, as well.
[tracer]
“Waiter, my Universe is all stringy.”
“Just a moment, sir, we’ll have another one ready for you in a split eon.”
[/tracer]
Yes, there’s a Planck time which is analogous to the Planck length.
If you look at the Universe and all it’s vastness you are bound to think “Wow…that’s complex, man!” But most things in the universe can be reduced to patterns. Most prevalent being the Fibonacci sequence. You see it in the way cappilaries grow in animals, the way trees grow, and you see it all over the universe. It is the natural path many things take.
It has been seen that what once seems chaotic and random is indeed patterned. Chaos theory and all that.
I would say the universe is not so very complex…because there is a pattern to it all. Not matter how small the particles get, there will always be a pattern.
Thank you, ultrafilter.
I don’t want to be a pain, but can you elaborate a little?
Specifically, why is it meaningless to talk about a fraction of a second which is shorter than the Planck Time?
I hope that g8rguy’s explanation was sufficient, but if it isn’t, here’s another: how far can you see with you naked eye? If something were 1 meter in front of you, you’d be able to see, right? But if it were 100 trillion meters away, you wouldn’t be able to see it. So somewhere in between 1 and 100 trillion is some distance at which it ceases to be visible. But it’s not like an object moving away from you would suddenly disappear at the exact moment that it reached that distance. It would slowly get harder and harder to see. Moreoever, different objects would take different amounts of distance to disappear.
No, I really can’t. I don’t understand this stuff very well myself. You might want to do a search in GQ.
Patterns can be very complex, though. String theorists treat particles as 10-dimensional polytopes, and there’s no need for those to be at all simple.
I see your point, though–it’s not as bad as it looks at first.
Oh, and welcome to the boards.
Well, it’s no more meaningless than talking about a fraction of length which is shorter than the Planck Length. Approximately, the Planck Time is the time scale on which quantum fluctuations in the “shape” of time might be expected to be significant. Somewhere in the general range of this time scale, time would thus be expected to behave in ways which seem a little unintuitive to the classical thinker, even one who understands relativity. What precisely happens isn’t something we can answer, but many physicists think that that it’s SOMETHING weird, anyway. So it’s not meaningless, per se, it’s just that we’re not sure what goes on there.
Oh, and The Ryan, I’ll have to remember that explanation! I’m horrible at coming up with helpful analogies, and I need to keep track of all the useful ones I come across!
Ignoring for a moment what g8rguy has posted (which isn’t to say he is wrong) here’s a more layman’s definition.
Planck Time is defined as the amount of time it takes light to travel across the Planck Length. Planck length is generally defined as 4x10[sup]-33[/sup] cm. Light can travel that distance in 10[sup]-43[/sup] seconds. Again, g8rguy’s assertion that these times and distances are vague is worth listening to…I’m just giving the values most often given for the Planck limits.
I guess it depends on what I’m looking at. Unless I was having my leg pulled I once saw the Andromeda Galaxy while star gazing one night. IIRC the Andromeda Galaxy is the most distant object visible to an unaided human eye. At
20,813,540,000,000,000,000,000 meters (if I did my math right) it is quite a lot further away than 100 trillion meters.
[sub]NOTE: Just giving you a hard time. I take your meaning and it is a good analogy.[/sub]
g8rguy:
If I take your meaning then the Planck limits are nothing more than the point at which ‘normal’ physics break apart leading to thoroughly unpredictable results when trying to guess what is happening down there. Does that mean that matter and time and mass can be infinitely divided even if us, as humans, can’t do it? Is there no point where the universe says, “That’s it…there is no ‘smaller’ to be had here…give it up.”?
Well, the way I’d put it is that Planck limits are places where ‘normal’ physics breaks down in such a way as to make our traditional understandings of space and time essentially irrelevant. Mathematically, though, I think one could still describe such regions without resorting to saying that space itself is indivisible on those length scales. “Size” might be ill defined, of course, and it might SEEM meaningless until we learn to think about it properly, but I don’t think it actually WILL be meaningless to talk about sizes smaller than the Planck scales.
Mass is a little different. Of course, everything has one and only one mass. Energy, though, is a different story. I’m not really sure what to think happens to energies. I would guess that you can have an energy as small as you want, so long as it’s not zero, but I don’t know that you could define that sort of thing either.