Three-Body Problem: Soluble or Insoluble?

[Frame Dragger]

Depends on the calculation. PDE's are very heavily limited by memory. ODE's are not. In any case the cost of memory has gone down as quickly as the cost of CPU.



Or you can wait for better computers to come out. Also putting together brute force is sometimes non-trivial.

I can only admit to familiarity with the use of H/PDE's in this particular case, but cost aside, it's still a factor given the amount of information produced (as Nabeshin has said). As for waiting... I find the demands placed on computers outpace the development of the computers themselves, thus far at least. EDIT: I should add, as I said, "in the case of the work at the API...", and they ARE using H/PDE's for their current simulations. I don't believe I claimed that this was a universal truth in Numerical GR. Also... waiting doesn't really advance research.

For the brute force... my only familiarity with BF algorithms has been... well... let's say it was in the "information security" region. They are difficult to assemble because you need such a vast library to attempt it... hence the need to pick and choose. Cracking a password or encryption, and breaking down PDEs is similar. That said, trivial or not, sometimes it's the only way given limited information, or if you want to be careful that you don't screen valuble information (say, in the case of medical imaging).

 

[twofish-quant]

I find the demands placed on computers outpace the development of the computers themselves, thus far at least.

That's because you are always trying to use the compute power that you have for something new. In the case of PDE's, more compute power, higher resolution.

Cracking a password or encryption, and breaking down PDEs is similar.

I don't see the connection. The two are very, very different problems.

 

[Frame Dragger]

That's because you are always trying to use the compute power that you have for something new. In the case of PDE's, more compute power, higher resolution.



I don't see the connection. The two are very, very different problems.

I was speaking strictly in the context of brute-force vs. algorithmic attacks on a problem, and the demands they place on the computer. Brute Force uses the CPU heavily, but spares the memory. The other produces a great deal of data, which hogs memory.

 

[twofish-quant]

I was speaking strictly in the context of brute-force vs. algorithmic attacks on a problem, and the demands they place on the computer. Brute Force uses the CPU heavily, but spares the memory. The other produces a great deal of data, which hogs memory.

I still don't see the connection with PDE's. With PDE's, the amount of memory that you need is large, but it's constant over time, since you aren't saving any results in memory. All your results are dumped to disk.

Also with PDE's, "brute force" techniques tend to use a lot more memory.

 

[Frame Dragger]

I still don't see the connection with PDE's. With PDE's, the amount of memory that you need is large, but it's constant over time, since you aren't saving any results in memory. All your results are dumped to disk.

Also with PDE's, "brute force" techniques tend to use a lot more memory.

I'm not sure how to describe this well (for lack of technical knowledge, not a glut of it)...

PDEs take results, feed them back into the original problem, run it again, etc. A good cracking algorithim does much the same thing. I'll take your word for it (you're knowledgeable,) as to the memory demands of PDE's being constant over time... as for CPU demands however, Brute Force vs. Algorithm is still a valid comparison. I didn't realize that memory was constant with PDE's... how is it that you don't need to keep track of the process for error correction? I'm now genuinely confused.

 

[twofish-quant]

PDEs take results, feed them back into the original problem, run it again, etc.

No they don't. If you are doing time stepping, you are just looking at the last set of results. Anything before that you don't need in order to do any calculation, and you can dump all of that to disk.

as for CPU demands however, Brute Force vs. Algorithm is still a valid comparison.

I think we are talking about very different things here.

how is it that you don't need to keep track of the process for error correction?

Because you set up the algorithm in ways so that the errors are bounded. If the errors are not bounded, then what happens is that your calculation becomes unstable and you get garbage very quickly.

I think you are getting confused because you are thinking there is some sort of connection between security algorithms and PDE calculation, and as far as I can tell there isn't.

 

[Frame Dragger]

No they don't. If you are doing time stepping, you are just looking at the last set of results. Anything before that you don't need in order to do any calculation, and you can dump all of that to disk.



I think we are talking about very different things here.



Because you set up the algorithm in ways so that the errors are bounded. If the errors are not bounded, then what happens is that your calculation becomes unstable and you get garbage very quickly.

I think you are getting confused because you are thinking there is some sort of connection between security algorithms and PDE calculation, and as far as I can tell there isn't.

Well, this seems to be a pretty clear case of, "I'm completely wrong." On the bright side, I have another area to research. Thanks for taking the time to lead me by the hand (so to speak) on this one. I appreciate it.