I mean, it depends on your definition of "stable"? The yearly deltas in the price of gold between 2009 and 2015 are +31%, +8%, +9%, -28%, 0%, -12%. It's stable relative to, say, BitCoin, but if my salary changed that much I'd hardly call it "a stable income", and if my weight changed that much I'd definitely not call it "a stable weight".
If there is a fool born every minute, and we have 10 minute blocks, then this can continue ad infinitum and therefore produce a great medium of exchange and store of value. It is like a better version of Hawala. If this is the case, then it would appear to be that the greater fools are the ones holding onto a depreciating currency.
To some extent though it illustrates that after 200 years the value of $1 of gold was something like $1 in real terms while the value of a paper dollar became 6 cents. Even if that only kicked in after the 1970.