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Not sure if this is really a worldbuilding question, but here goes.

Could someone put wealth into a bitcoin and then subsequently

1) Remember the bit sequence (however long it is) that represents the bitcoin account?

2) Destroy all references to the "wallet", so the only reference to the funds is in the individual's head?

I guess it depends on how long the sequence would be.

(The notion is that at some later point in time, the individual could recall the sequence and thus (with the help of a computer and the internet) access the funds.)

It seems that the sequence of bits is on the order of 100Kb, so recalling that might be a bit of a chore.

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    $\begingroup$ The Electrum bitcoin wallet generates a sequence of about a dozen words from which the wallet can be restored. However I'm not sure whether that contains all the relevant information, or if something is stored on their server. Note however that the actual bitcoins aren't stored in your wallet anyway, but in the blockchain. The wallet only provides the data you need to access them. $\endgroup$
    – celtschk
    Jul 6, 2016 at 18:09
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    $\begingroup$ Note: in bit coin when you spend some money, you must spoil the entire account, moving the remainder into a new account with a new number that you'd have to memorize. Wallets are a way to store these bitcoin account numbers in a way which is more conveneint for management because they act more like we inutitively think they should $\endgroup$
    – Cort Ammon
    Jul 6, 2016 at 18:32
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    $\begingroup$ This is literally called a "brain wallet". Of course how money is "stored" in a system where there are no tokens is a tricky question, but what you described above is possible and sometimes used already. $\endgroup$
    – Annonymus
    Jul 6, 2016 at 18:48
  • $\begingroup$ @CortAmmon That is wrong. You are not forced to move the remainder of your money to different addresses. Most wallet programs do that for you to promote anonymity, but it is by no means strictly necessary. $\endgroup$
    – Annonymus
    Jul 6, 2016 at 18:50

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Specific to your answer, yes you could recall the bitcoin private key. If you deleted the private key from all devices you owned and removed any reference to it, you could, in theory, have the only copy of the private key stored in your head.

However, that does you zero good, as in order to use it you would need to re-enter that private key into a management tool of some sort to transfer bitcoin to another account.

However, you could also do this with things like swiss bank accounts.

The downside to "hiding" money on the blockchain in bitcoin is that technically anyone can look up any balance of any address at any time. The upside is that your name and information aren't directly associated with the address. Also, the only thing that secures it is your private key, so if someone were to get ahold of it, your funds would not be secure (whereas most banks have some level of fraud prevention that would protect you, and the FDIC insures accounts to a certain level against the bank failing). Theoretically it is an NP-Complete problem to brute force find a particular private key associated with a given public key. However, drastic advancements in computing power or a flaw in the algorithm (unlikely at this point) could render bitcoin addresses vulnerable.

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  • $\begingroup$ No amount of computing power can change an NP-complete problem into a non-NP problem. $\endgroup$
    – celtschk
    Jul 6, 2016 at 18:13
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    $\begingroup$ @celtschk not linear increases to computing power, no. I'm talking about something so drastic and different that it dwarfs with a single machine all computing power in the world today. There is a finite number of bitcoin addresses and bitcoin private keys (its a ludicrous number, but it is a finite number) $\endgroup$
    – Marshall Tigerus
    Jul 6, 2016 at 18:16
  • $\begingroup$ That would make the current bitcoin keys vulnerable, but it would still not change the NP nature of the problem. $\endgroup$
    – celtschk
    Jul 6, 2016 at 18:18
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    $\begingroup$ FWIW, I'm pretty sure quantum computers could crack current bitcode security. $\endgroup$
    – Jiminion
    Jul 6, 2016 at 18:37
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    $\begingroup$ Note that while brute force or a flaw in the bitcoin algorithm are both unlikely to resolve an NP-complete problem, if an algorithm was found that proved P==NP (which is unlikely but has not been ruled out) one would also be able to defeat known encryption. I only bring this up because P != NP hasn't been proven. $\endgroup$
    – Nathaniel Ford
    Jul 6, 2016 at 20:22

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