[ExI] The tyranny of context free grammars.

Alan Grimes agrimes at speakeasy.net
Tue Dec 7 06:49:58 UTC 2010


While I should be sleeping right now, I was thinking about my extensive
library of books and was inspired to break character and write an
inspirational piece about some transhumanist research that can be done
by anyone with little or no equipment.

Most of my books on computer science present context free grammars as
the one and only way to program computers. It is true that languages
such as Perl do have some context sensitivity but that doesn't disprove
the point. The point is that all of computer programming and compiler
design is nested in the ontology of the Chomsky Heirarchy. The reason
for this is that Chomsky grammars provably solve the problem of
describing and classifying computations so why not simply teach that and
then move on to programming them?

Because it is a difficult problem, there seems to be only one widely
known solution. While it is possible to prove that it solves the problem
of describing computations, I seriously doubt that it is either a unique
or optimal solution.

In my 6-core phenom machine, I have, lets say, four ALUs per core, so if
given an optimal workload, I can compute a maximum of

64 * 4 * 6 * 3.2 = 4.9 trillion bit operations per second, absolute
maximum under optimal conditions. But the more interesting thing is that
I only have 1536 bits of general purpose computing in my late model
machine. (there are some other computational circuits devoted to
managing the instruction stream and accessing memory that are not
general purpose).

When contemplating (om) an optimal computational substrate in what we
believe to be the 3D nature of our real world, we are lead to an
architecture that resembles the human brain in many respects. The gray
mater would be a 3D cellular automata architecture. Then, in order to
maximize bandwidth between distant nodes, a substantial portion of the
available volume would consist of communication channels of some sort so
that distant parts of the network could communicate at low latency. Each
cell would be comparable in size to 3 or 4 cache cells on a processor of
a similar process technology, so my 9 megs of cache would equate to
roughly two or three MILLION computational units ( as opposed to the
number just over 1,500 given above).

What we lack, of course, is a good way to design and program these CAM
cells so that they can be used for high performance computing. Some
basic work has been done with Conway's game of life. Reportedly, there
have been implementations of turing machines in the form of gliders and
other structures in the CAM matrix.

What is really needed is a serious re-evaluation of everything the
textbooks say we know for certain about computer science to achieve the
conceptual breakthrough required to really master this type of programming.

I would consider this important basic research and the tools required to
carry it out are already in front of you.


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