Quote from: ByteCoin on September 19, 2011, 11:27:40 PM

Quote from: doktor99 on September 19, 2011, 09:11:26 PM

a theoretical series of transactions which move 100% of the existing bitcoin to some previously-unknown wallet address would reduce the BTCDD figure to 0%

You meant "increase the BTCDD to 100%". Your previous post in this thread was correct in this regard.

Quote from: doktor99 on September 19, 2011, 09:11:26 PM

Even if you consider that there are lost coins, the theoretical BTCDD figure approaches zero as the number of days goes to infinity.

If there are lost coins and a finite total number of coins then the BTCDD percentage cannot possibly reach 100% ever.
If there are no more transactions then the BTCDD tends to 0%.
In the long run, if there are any transactions then the BTCDD has a lower bound given by the proportion of the transacted coins out of the total coins.

Quote from: Boussac on September 17, 2011, 08:12:20 PM

Arithmetically it seems to me that the percentage cannot exceed 50%: in fact it should reach 50% asymptotically.

Both statements are incorrect.

ByteCoin

OK, so I reversed 100% and 0%, you're absolutely right. But it seems like you realized that!

Sticking with the substance of the discussion: if the total transactions per day average 50% of the total coins outstanding over some longish period of time, then sure, it's asymptotic to 50%.

Let's do some math on that: assuming the BTC stabilizes at $5, the long term implication of the 50% asymptote is about 22M * $5 = $11M of Bitcoin transacted commerce per day or about $4B / year. That is 1/1000 the size of the VISA network at $4T/year, or about 0.1%. Not great. To reach 10% of the VISA network at a 50% asymtote, the network would require a BTC valuation of $100. It's not a bad goal!