Mirrored to https://gwern.net/Turing-complete#on-seeing-through-and-unseeing

I analogize 'Nakatomi space' to 'weird machines', and I think what they/OP/security/speedrunning/hacking/social-engineering all have in common is that they show that the much-ballyhooed 'hacker mindset' is, fundamentally, a sort of reductionism run amok, 'seeing through' abstractions to a manipulable reality. ('Thinking outside the box' can be this, but often isn't. This is a very specific pattern of reductionism, and many instances of 'thinking outside the box' are other patterns, like putting on another layer, or eliminating the systems in question entirely.)

In each case, the fundamental principle is that the hacker asks: "here I have a system W, which pretends to be made out of a few Xs; however, it is really made out of many Ys, which form an entirely different system, Z; I will now proceed to ignore the Xs and understand how Z works, so I may change some Ys to thereby change W however I like". The abstractions always leak. This is in some sense the opposite of a mathematician; a mathematician tries to 'see through' a complex system to a simpler more abstract more true version which can be better understood & manipulated, but the hacker is instead trying to unsee the simple abstract system to a more complex less abstract (but more true) version. (A mathematician might try to transform a program up into successively more abstract representations to eventually show it is trivially correct; a hacker would prefer to compile a program down into its most concrete representation to brute force all execution paths & find an exploit trivially proving it incorrect.)

It's all 'atoms and void':

• In hacking, a computer pretends to be made out of things like 'buffers' and 'lists' and 'objects' with rich meaningful semantics, but really, it's just made out of bits which mean nothing and only accidentally can be interpreted as things like 'web browsers' or 'passwords', and if you move some bits around and rewrite these other bits in a particular order and read one string of bits in a different way, now you have bypassed the password.
• In speed running, a video game pretends to be made out of things like 'walls' and 'speed limits' and 'levels which must be completed in a particular order', but it's really again just made out of bits and memory locations, and messing with them in particular ways can give you infinite 'velocity' or send you to the 'end' of the game.
• In robbing a hotel room, people see 'doors' and 'locks' and 'walls', but really, they are just made out of atoms arranged in a particular order, and you can move some atoms around more easily than others, and instead of going through a 'door' you can just cut a hole in the wall (or ceiling) and obtain access to a space. (That example reminds me of the Carr & Adey anatomy of locked room murder mysteries, laying out a taxonomy of all the possible solutions which, like a magician's trick, violate one's assumptions about the locked room: whether it was always locked, locked at the right time, the murder done while in the room, murder rather than suicide, the room having a ceiling etc, which inspired Umineko, although there a lot of them just turn out to involve conspirators/lying.)

• In weird machines, you have a 'protocol' like SSL or X86 machine code which appear to do simple things like 'check a cryptographic signature' or 'add one number in a register to another register', but in reality, it's again processor states and widgets and things like reading other parts of memory and then quickly erasing it, and these can be pasted together to execute operations and reveal secrets without ever running 'code'.

  Similarly, in finding hidden examples of Turing completeness, one says, 'this system appears to be a bunch of dominoes or whatever, but actually, each one is a computational element which has unusual inputs/outputs; I will now proceed to wire a large number of them together to form a Turing machine so I can play Tetris in Conway's Game of Life or use heart muscle cells to implement Boolean logic or run arbitrary computations in a game of Magic The Gathering'.

  Or in side channels, you go below bits and say, 'these bits are only approximations to the actual flow of electricity and heat in a system; I will now proceed to measure the physical system' etc.

• In social engineering/pen testing, people see social norms and imaginary things like 'permission' and 'authority' and 'managers' which 'forbid access to facilities', but in reality, all there is is a piece of laminated plastic or certain magic jargon words spoken with people being elaborate ways of implementing simple rules like 'if laminated plastic, allow in', and if you put on a blue piece of plastic to your shirt and you incant certain words at the right time, you can walk right past the guards or a person will speak back to you more magic jargon words (which are a password or something else).

• and while we're at it, why are puns so irresistible to hackers? Computers are nothing but puns on bits, and languages are nothing but puns on letters. Puns force one to drop down from the abstract semantic level to the raw syntactic level of subwords or characters, and back up again to achieve some semantic twist.

And so on. These sorts of things can seem magical ("how‽'), shocking ('but - but - that's cheating!'), or hilarious (in the 'violation of expectations followed by understanding' theory of humor) because the abstract system W & our verbalizations are so familiar and useful that we quickly get trapped in our dreams of abstractions, and forget that it is merely a map and not the territory, while inevitably the map has made gross simplifications and it fails to document various paths from one point to another point which we don't want to exist. Perversely, the more educated you are, and the more of the map you know, the worse this effect can be, because you have more to unsee. This is why atheoretical optimization processes like animals (eg cats) or SMT solvers or AI can be so good at surprising us and finding 'unreasonable' inputs or hacks: being unable to understand the map, they can't overvalue it, and must explore the territory directly to get what they want.