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This is a very important concept to internalize. I don't think Satoshi realized it, and I think if he did Bitcoin Script would be very different from what we have.
In a future ideal world where arbitrary zero-knowledge-proofs are time-tested and have robust implementations, everybody except for the N entities directly involved in a transaction would validate a short, opaque proof that some computation took place authorizing the transaction.
If you're designing a better transaction system, you should design with that ideal in mind.