Warbo
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Warbo has not written any posts yet.
I think you're placing too much emphasis on the von Neumann architecture. It's
not essential to anything, and AFAIK was only intended as a short-term engineering
decision, pending redesign once we have more experience and understanding. This
separation of CPU and memory is now our biggest performance bottleneck; hence
why we shift so much on to GPUs, DSPs, etc. which aren't von Neumann.
Boole's big contribution was turning logic into an algebra: "and", "or", "not", etc. became mathematical operations for combining values ("true"/"false"), which we can quantify over, prove theorems about, etc. in a more abstract way than the sort of 'sentence templates' studied by the Greeks.
Important contributions were made by Shannon as well: in particular, his Masters thesis showed the equivalence of Boolean algebra, binary arithmetic, and digital circuits. Hence arithmetic and logic can be carried out by circuitry.
Regarding Turing machines: their definition is due to a philosophical argument, rather than mathematical (hence Church-Turing "thesis" rather than "theorem"). Essentially, Turing argues that any finite region of space can only have a finite set of distinguishable states; that any finite set can be enumerated and indexed; and therefore any physical system can be described by a (vast) transition table between these indexes. For input/output, a similar argument is made that only finitely-many possibilities can be distinguished between, that we can equivalently operate on their indexes instead, and that they can be written along one unbounded "tape". Hence we can describe the behaviour of any physical system (including any procedure that a... (read 361 more words →)