Expanding on my “PS” to Wolfram’s community on the "Shortest meta-circular description of a univeral computational structure:
Circa 2006 when I first ran into this “philosophical nuisance” (Hutter’s description of responses like Yann Lecun’s troll-worthy response to me) from the obstructionists at LessWrong, I suggested to Marcus self-simulation of the Turing machine as an approach, to which I alluded in the “PS” where I mentioned “NOR gates” as addressing the question of “minimal instruction set”.
The apparent answer “What is the minimal directed graph of N-input NOR (henceforth NiNOR) gates that outputs the dataset?” is incomplete as it meta-begs the original question since we must have a measure of the NiNOR graph’s complexity. But this seems like the right direction if we’re to define what we mean by “the shortest metacircular description of a universal computational structure” and, indeed it is.
Here’s how to calculate an integer which might be called NiNOR-Complexity:
Write a program, in a given instruction set, that simulates the directed graph of NiNOR gates that provides the given instruction set, including the memory that holds the program. Use that instruction set to write a program that, when fed to the simulation program, outputs the given dataset. The minimum sum of the length of these two programs is the NiNOR-Complexity.
Note that empty RAM can be generated by a simple algorithm parameterized by the amount of RAM required which is an N-bit integer, where N increases only as the log of the size of the RAM.
It’s hard for me to imagine a more principled/operational (less “arbitrary”) measure of Kolmogorov Complexity than NiNOR Complexity.
PS: Look, guys, this is what I mean by obstructionists at LessWrong etc. These guys think they’re being clever by fighting a major advance in the philosophy of science. Little 'ole me shouldn’t have to spell all of the above out for them and then beg them to stop ignoring me. If this were personal then I suppose it would just be impacting “Little 'ole me” and hence qualifies as being a “nuisance”. But given the character played by Jane Curtain’s reaction to Theodoric of York’s “NAHHH…” multiplied by a billions of people, it does seem a crime against humanity of a scale that makes the Holocaust or even the Maoist purges seem like paddy-cakes.
