[Cryptography] LUKS on ATA versus on SSD

[Ron Garret]

> On Jan 1, 2026, at 4:36 PM, Jon Callas <jon at callas.org> wrote:
> 
> content-addressed storage is pretty close to Godel numbering.

Um, no.  Gödel numbering is a one-to-one mapping from strings of symbols to numbers.  Hashes are not a Gödel-numbering scheme because they are not one-to-one.

Gödel-numbering nowadays is obsolete.  Gödel's original scheme used prime factorization, and would be considered horribly byzantine by today's standards.  But Gödel was a mathematician working decades before the first digital computers, and years before Turing even laid the theoretical foundations for such machines, so it was not an unreasonable approach given the historical context and what he was trying to do.  Nowadays we are used to thinking of everything simply being represented in binary, and converting from symbols to numbers is just a change in perspective, not actually a computation.

Also, going back to the original question:

> Is that -- block device can be anything that implements a block device -- because of how Turing machines / Godel numbering work, basically?

No.  This is conflating two completely different things.  A block device is an abstraction layer that hides the details of the actual hardware.  Some hardware behaves "natively" like a block device, but all mass storage nowadays have additional hardware that make it behave *as if* it were a block device even if it looks very different under the hood.  Gödel-numbering is, as I said, just a mathematical construction that converts strings of symbols into numbers.  Comparing these two things is a category error.

rg