Go ahead, I did know nothing about bitcoin a year ago.
Like I said, I'm not an econometric expert (though you seem to be an expert on Bitcoin).
At one extreme: free mining is available anywhere on earth (phase 5)
At the other: all miners are switched off (phase 0).
In the middle somewhere, we range from:
phase 1: just a few miners are functioning (the big value/important transactions get mined, the small transactions aren't worth it)
phase 2: a good few miners are functioning (the system is only good for big and medium transactions)
phase 3: lots of miners functioning (everyone can send BTC about, but the small guys are beginning to feel it)
phase 4: a plentiful supply of miners (pretty much everyone gets to transact with hardly any restriction)
- The days of 4 are over
- We're in 3 and will be moving into 2. Silicon has stalled and electricity isn't getting any cheaper.
To calculate the timing on the transition from 5-> 4 -> 3 -> 2 -> 1 -> 0 would require much more detailed analysis.
You're still getting it wrong. The number of miners has no effect on how many transactions can be processed. Whether it's 1 miner or 1 million miners, it's all the same.
The only real limit to the number of transactions that's currently in place is the maximum size of each block, but there are plans to increase this and so far there's not enough activity yet to hit this maximum other than in exceptional spikes.
edit:
I think this side-discussion is irrelevant to the original question. It's obvious the answer is "No" - you cannot get below 10 seconds. This has very serious practical implications for the deployment of Bitcoin at a global scale.
You can get below 10 seconds when you accept 0-confirmation transactions. For everyday purchases, this is perfectly fine as it is impractical and uneconomic for an attacker to try and profit from double spending those. Payment processors such as BitPay and Coinbase already accept 0-conf transactions and most merchants that accept Bitcoin-payments use one of those two processors.
For very large payments, you will have to wait for one or more confirmations, but these payments are almost always for things that are not delivered instantly (cars, houses, etc...).