I strongly recommend that you read the two papers (here, here) that Arild noted in the previous post. They appear to demonstrate that unicellular organisms can “compute.” Of the two I found the first more directly relevant to Randy’s conjecture as it shows that memory and recall of acquired information is possible in a single cell organism. Thus neural nets, whatever their function in higher organisms, are not necessary for writing to and retrieving from memory (i.e. the rudiments of mental computation). It seems that unicellular organisms can “learn” and use the learned information to modify their responses. In other words, they can write information to memory and retrieve it.
Moreover, like Randy’s discussion (here) what slime molds can memorize is interval information, something that is not something that one can glean from the nature of the conditioned stimulus alone. As Saigusa, Tero, Nagaki and Kuramoto (STNK) out it, the slime mold “can anticipate the timing of periodic events” (p. 1). To do this, the slime mold “needs the ability to memorize the periodicity. Moreover, the organism memorizes not only the periodicity, but also the specific phase of the period” (p. 4). And, in one of the experiments, STNK made sure that single stimulations provide “no information about periodicity.” Thus, as STNK notes, “[t]his means that the previous periodicity must not only be stored but also evoked by the trigger stimulation” (p. 4). This sounds very similar to what the Hesslow experiment that Randy discussed shows. Indeed, just as Randy argued for, STNK cautiously entertain the conclusion that their experiment “indicates that the organism has a generalized capacity for learning, independent of the details of the periodicity.”
The second paper is also interesting, and as it is only a page, I would recommend taking a look. That paper demonstrates that slime molds “maximize” their foraging efficiency via “a remarkable process of cellular computation.”
These are fascinating results. Look, no nets!! Thanks Arild.
 STNK appears to be worried by ecological validity concerns. From the little I understand, these seem misplaced here. They worry that the kind of learning they induce in the slime mold is not “common.” Big deal. The slime mold learned it which means that it can code for the information. I suspect that this is what STNK actually believe, but they have they display some methodological scruples, most likely in response to some knee jerk reviewer reaction.