can you run any software on a computer with 0 bytes of RAM, I.e. only using the CPU cache?

like maybe with some kinda dummy RAM that was actually ROM to bootstrap it

@jk The answer is actually "yes", because that's how x86 CPUs actually boot up!

The CPU boots in a mode where the BIOS ROM is mapped into memory space, and the BIOS code configures the CPU to allow (temporarily) using the cache memory as RAM.

Pretty much the only thing the BIOS code does while running in this mode is initialize the memory controller so you can get real RAM, though.

@jk you can't initialize much hardware fully until you have RAM (especially not video cards), so code running in this mode is a bit limited in IO capabilities. The PC speaker is accessible though, so the BIOS writers helpfully make it beep at you if it failed to initialize the RAM.