Enire system unresponsive at regular intervals

Question

This problem is similar to others I've found, but none of those suggestions/answers have solved my problem.
While I'm using my computer--which usually 6 or more hours each day--every 10 or 15 minutes everything stops. Quite literally stops, as though the system has crashed. The mouse still moves the cursor, but clicking on any open window simply puts the associated application into a "not responding" state in the Activity Monitor, and the little beach ball just spins and spins. It changes to a pointer if it goes over a window from an application that is not yet identified as "not responding", but click and that changes as well.
The system stays in this state for 30 - 90 seconds, and then, as though by magic, or perhaps an act of God, everything proceeds as though nothing had happened.
Things seem to get worse over the course of that 30 - 90 second absence and even the Activity Monitor stops. The trace at the bottom simply stops, and none of the activity values in the table change, and the AM is unresponsive to any mouse click.
Some observations:
1. The system does not respond to the keyboard when having such a seizure.
2. The time of day clock in the top menu bar stops ticking and does not advance.
3. CPU usage is NOT anywhere near 100% in the AM, or at least it is not reported as such. In fact, it seems to be no different than it was when the seizure started.
4. Nor is the network busy or the disk hyperactive. All critical indicators seem normal. System memory (2 gig) may be full, but no swapping is being done during a seizure.
5. When the seizure ends, I have seen a burst of network activity and at the same time a burst of CPU activity by a task called "spindump". Occasionally there has been more than one such burst at the resumption of activity. I cannot say that this happens every time.
6. I have repaired permissions using the Disk Utility.
7. I removed my real-time virus scanning software (which I run to prevent accidentally sending a virus to a PC based client)
8. I stopped using Safari after reading something that suggested these types of problems might be associated with Safari.
9. I have 135 Gbytes free on my 500 Gbyte Macintosh HD drive. I also have an external 750 Gbyte LaCie USB 2 drive that I use strictly for backup. The external drive may or may not be active when a seizure occurs.
10. I have 2 Gbytes of RAM which was preinstalled when I bought my system.
11. I use a bluetooth keyboard and mouse, but as I said, during a seizure, the mouse at least seems to communicate just fine, and the keyboard input is obviously received, since the system got my login correctly while seeming to be unconscious. See the next paragraph.
12. I do have about 1,500,000 files on my system, but as I mentioned there is no exceptional disk activity associated with this issue.
Now, for the kicker. Yesterday, in another of my frustrating attempts to get this behavior to stop, I was rebooting my computer, and IT SUFFERED A SEIZURE WHILE ON THE LOGIN SCREEN, with no users logged in. I clicked in the user name field and the ol' beachball started spinning away and continued to do so for 45 seconds (which seemed much longer under the circumstances), then accepted all of the characters of my login which I had typed while waiting and logged me in just fine.
Anyone who can provide any help or useful insight will be highly regarded by me forever. I use my computer to earn a living and <great irony, while I was typing this message, my computer stopped right here for over a minute> stopping several times an hour to watch nothing happen, is getting on my nerves.

Answer 1

Since I needed to be out all morning, last night I left my machine running with Sleep turned off and all applications except for the Console shut off. I turned off Time Machine, because I had noticed that the seizures were occurring about 4 minutes after Time Machine finished its hourly backup.
The Time Machine connection turned out to be only a coincidence. From midnight until noon, the seizure problem re-occurred every hour on the hour, and with no activity on the computer at all, it lasted longer, at least five minutes in each case. It's easy to tell how long they last because the console messages conveniently appear every ten seconds.
Time Machine just happened to be running backups at 8 minutes before the hour which made it look as though they were connected.
Other than the hourly recurrence, I have seen the problem only when I open a mailbox in Mail. (Dang, it's 2 PM so I just got to sit here for 4 minutes,)
Tomorrow, I will take printouts of the logs over to the Apple store and talk to a genius as suggested. I'll report what I learn.
In the meantime, my theory is that this is related to the Spotlight indexing activity done, I believe, by the system routine "mds". I installed the 750 gig backup drive just two weeks ago, and now back up all of my non-OS files (~250 gig) instead of just the most critical 30 gig I was putting on a smaller external drive. I have seen other comments here and elsewhere on the Internet suggesting that the indexing can periodically gobble up your processor, especially when there are large piles of new files to play with. But that's just my theory. I'll report facts when I have them.