> Bitcoin is already very untraceable. Yes, there's a public ledger of all transactions, but it has no identifying information. There are some public addresses whose owners are known, because they volunteered that information. Exchanges also know the owners of certain addresses. But that's about it.
That isn't true. Bitcoin transactions can be traced like almost all other transaction types (even more so because it's a public leger), the only difference is that the end points are pseudonymous (sure, they might not have your names, but they do have unique identifiers, like account numbers). It's a mistake to consider the above as being "untraceable" or anonymous.
> Bitcoin's address space is huge, something like 10^48. I can make a thousand of them in a few seconds, along with the private keys. I can send the money to any of them, and you will never know who owns it. I can send my money between these 1000 addresses as much as I want, and all you will see in the leger is money going from A to B to C, just like the rest of it.
This principle is all about mixing to "clean" bitcoins, but it doesn't provide strong anonymity properties (if all of the addresses you use for mixing are only used for mixing your bitcoins, you haven't improved your anonymity).
> Bitcoin network doesn't know any difference between me buying something on Overstock, or me sending the money to my brother across the globe, or to myself.
Other than the globally unique addresses, which can be used to tie together groups of transactions or owners of accounts.