The number of miners has absolutely no effect on transactions. You can have 1M times the number of miners we have today, or 1M times the hashing power, and transactions will still be limited to 10 minutes per block, and ~500KB of transactions in every block. I believe the hard limit on block size is 5MB. So, if Bitcoin gets popular and hits that limit, we'll have only two options:
1) Increase the block size. This sin't something the developers do. This is something, like with all proposed changes currently happening with Bitcoin, someone (anyone) can propose on the developer's site, other people can discuss and argue about until they figure something out to settle on, and then developers, or anyone, really, can write code to increase the block size, and submit it to the same site. After the actual code itself is discussed and argued about, and no bugs are found, THEN the developers can include it in their next release of Bitcoin-QT, as can everyone else who makes Bitcoin wallets, and typically they pic some date way in the future to make the switch. Basically, everybody will be running Bitcoin clients that have code embeded in it that will do nothing until X date, and as soon as X hits, will start to run the code, causing a "hard fork" (older clients will not be compatible with the new fork). last few times it was a few months to a year that X was set in advance.
2) Bypass the block chain completely when making transactions. This is essentially what all the exchanges to when people trade money. No bitcoin transfer actually hits the blockchain when it's traded - it's all done on their own local software. The only time something is written to the blockchain is when someone deposits or withdraws bitcoin. Similar services will likely pop up that let you deposit bitcoin, and then use the online wallet or a credit card of sorts to spend it, with all transactions being recorded only on the service provider's accounting books. Then, at the end of every day, they will just make one big transaction, sending the coins everywhere they need to go.
Great post very informative. Thank you!
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