I think we aren’t being very clear with the description of what the blockchain can and cannot do. Here’s a start, but please feel free to suggest changes … I’m sure I’m oversimplifying or just plain wrong in some cases (although not as egregiously as three word marketing slogans), but it’s a start…
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A blockchain gives independent nodes an efficient way to determine if their local version of history agrees with another node’s version of history. If they are identical, the block hashes will match. If they aren’t, they won’t, and the two nodes will know that there is some discrepancy.
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Anyone is free to make any change they want, anytime time they want, without anyone’s permission. However, the change will be detected and rejected by other nodes unless they also make the same change. A single person can split the chain – the extent to which is matters to everyone else is dependent on how many other people use that version of the chain.
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The history of the blockchain is immutable only for a given block hash. In theory, there are actually many versions of history that could produce a given block hash, although we assume only one such sequence of blocks will ever be known, and it will only be known if the hash is computed from history (not the other way around).
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The ledger, as an ongoing concern, is not immutable. It mutates with every transaction that is included in a block. If it were immutable, everyone’s balance would be zero (and that multisig library contract if somehow it were able to appear on a truly immutable system could not have been deleted, right?). Claiming that a change cannot be injected into the blockchain in the future because “the blockchain is immutable” doesn’t make any sense.
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Changes to the blockchain are automatically permitted when a submitted transaction follows a pre-defined set of rules. i.e. if I hold the private key for account X, and I submit a transaction that will send ETH from account X to account Y. Note, in this case, the rules permit me to mutate Y’s account balance without Y’s consent. You could imagine a blockchain in which the rules do not permit this.
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The rules of the blockchain system are not necessarily fixed. This is especially true in the case of Ethereum, where plans to regularly hard fork to upgrade the chain were expected from the very beginning. That is, part of the rules were that you could change the rules.
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There are rules about changing the rules, but we probably can’t fully describe them.