Just because the number of almost-orthogonal vectors in d dimensions scales exponentially with d, doesn’t mean one can choose all those signals independently. We can still only choose d real-valued signals at a time (assuming away the sort of tricks by which one encodes two real numbers in a single real number, which seems unlikely to happen naturally in the body). So “more intended behaviors than input-vector components” just isn’t an option, unless you’re exploiting some kind of low-information-density in the desired behaviors (like e.g. very “sparse activation” of the desired behaviors, or discreteness of the desired behaviors to a limited extent).
The above toy model assumed that we’re picking one signal at a time, and that each such “signal” specifies the intended behavior for all organs simultaneously...
… But you’re right that the underlying assumption there was that the set of possible desired behaviors is discrete (i. e., that X in “kidneys do X” is a discrete variable, not a vector of reals). That might’ve indeed assumed me straight out of the space of reasonable toy models for biological signals, oops.
Just because the number of almost-orthogonal vectors in d dimensions scales exponentially with d, doesn’t mean one can choose all those signals independently. We can still only choose d real-valued signals at a time (assuming away the sort of tricks by which one encodes two real numbers in a single real number, which seems unlikely to happen naturally in the body). So “more intended behaviors than input-vector components” just isn’t an option, unless you’re exploiting some kind of low-information-density in the desired behaviors (like e.g. very “sparse activation” of the desired behaviors, or discreteness of the desired behaviors to a limited extent).
The above toy model assumed that we’re picking one signal at a time, and that each such “signal” specifies the intended behavior for all organs simultaneously...
… But you’re right that the underlying assumption there was that the set of possible desired behaviors is discrete (i. e., that X in “kidneys do X” is a discrete variable, not a vector of reals). That might’ve indeed assumed me straight out of the space of reasonable toy models for biological signals, oops.