The Hive Again

A reader has a fascinating comment about the hive discussion in Buzz Blogyear:

I love this concept that you guys are playing with. I think each layer of life believes the other layers, not its own, have the hive minds.

I'm a retired pathologist and I will never forget the first time I looked through a dark field microscope: there were all the pus cells--the polys and macrophages--glittering in the fluid from the specimen from the urethra (I was looking for spirochetes to diagnose syphilis.) Their cytoplasm was filled with dancing mitochondria, ribosomes and phagosomes, and it overall is like a soap bubble, sluggishly moving and creaking away. Sometimes it extends a foot process--a pseudopod-- and then retreats when it runs into a particle of dirt or a talc or fiber. The cells appear to be alien mucous spheres filled with festive lights zig-zagging around at a hundred miles per hour. Beautiful.

Here was a separate cell without structural connections to the body except for chemistry--cytokines and hormones and a zillion soluble molecules-- and it was indifferent to all that was going on in the next larger layer up in the macro world and probably in the next smaller layer down at the molecular level. It could not possibly know what the pathologist was doing or the significance of anything in the lab, nothing beyond a few microns from its plasma membrane. Yet it was obviously happily and boistrously living it up. Nothing could be more alive. It was not aware of us, although it was an ingredient of us, and we were not aware of it... except for the few seconds we peeked in astonishment.

If the individual cell ever thought about hive minds, it would have to believe that the human being had the hive mind and that only 'it' had the legitimate mind. Or, it might look the other way, down deeper, and think that its own proteins and electrolytes and the ribosomes, etc., had the hive minds, else they could not have gotten together to create 'him'.

Fun topic.

Let's consider the downward and upward aspects of the problem separately at any given level. There is clearly a recursive element in the downward aspect. A "hive" can devolve a problem downward to its components. And the subsystem, now a hive in relative terms, can kick parts down in turn to a lower level. But for the recursion to be successful, at some point it has to return a definite result, maybe at the cellular or molecular level in the reader's example, or at the level of the human investigator in the case of the Buzz Blogyear case. At some point the recursion stops, then reascends the ladder of systems, each time it is reentrant with an evaluated result, till at last, the function returns.

One interesting question is whether a metasystem can in principle always "know" what has happened because it has all the function call returns to hand. If it does, then it must know more, in some sense, than its components. But what of the other direction? What can a subsystem know looking upward? A subsystem has no idea what is going on in the level above, because it is too primitive, and is even logically walled off by necessity from other processes so that a metasystemic catastrophe doesn't occur. In the reader's example above, the individual cell can never understand Shakespeare, for which the input of optic nerves, memory cells and other sensory apparatus are probably necessary and which is not available to the cell itself. But the hive can understand it, or think it can. Extending this idea, it has been claimed that there are ideas beyond the ken of individual human beings which are within the grasp of humanity.

If mathematics is the total of what all mathematicians understand, then the "hive mind" is capable of far more than any individual brain. This leads to a bizarre possibility that there are mathematical objects or concepts which are only understood in the collective unconscious of the mathematical community, but which are too complex for any individual mathematician to comprehend.

In some trivial sense, this must be true, although I have not yet seen a formalism (my mathematical education isn't that good) that describes this problem adequately. Consider the ordinary lead pencil. It has been reasonably claimed that no single individual knows enough to make one: to mine the lead, refine it, clinch it, make the eraser, which would in turn require knowing where to find lead, how to develop the mining machinery, etc. Yet it is obviously true that the hive knows how to make a pencil easily.

No more on hives. Zayed, see what you've done!

P.S. Many thanks to a reader for pointing out that lead pencils are actually made from graphite, not the element lead. He graciously assumes that I knew that already, which I did, but had forgotten. Hence the fault is entirely my own and I stand corrected.