Mathematics and the Russian Doll Structure of, Like, the Whole Universe
The Blind Brain Hypothesis implies that the best way to make sense of apparently inexplicable explainers is to see them as fragmentary kluges, as ways the thalamocortical system makes due without any access to the cognitive ‘heavy lifters,’ the unconscious processes that do the bulk of the work. When it comes to comparing intentional and functional accounts, the former always lacks the resolution of the former, even though its synoptic nature enables cognition at levels of complexity that overwhelm our ability to produce the latter. So wherever philosophy stalls, the BBH sees a possible information horizon, a point where the neural correlates of consciousness can only access a mere fraction of the neural correlates of some brain activity.
The great debate in mathematics, for instance, is between the constructivists (formalists) and the Platonists, those who see mathematics as an artifact of the human brain, and those who think it’s a kind of conceptual perception, a way of grasping things that exist independently of the mind.
The question boils down into whether there’s any mathematics absent our experience of it. The prior question should be whether there’s any such thing as mathematics as we experience it at all. What if mathematics as we experience it is neither constructed nor discovered, but imposed by the severe structural and developmental constraints faced by the thalamocortical system?
This is what the BBH suggests.
From a metaphysical standpoint, the idea would be that the universe possesses a Russian Doll structure, that what we perceive as ‘structures’ are conserved and recapitulated across vast differences in scale.
A neurostructural recapitulation is simply a neural circuit, distributed or not, that is capable of interacting with intermediary systems so as to enable systematic interaction with some other structure. You could just as easily say that the recapitulation is distributed across the entire system, and that each recapitulation harnesses circuits shared with all other recapitulations. In this sense, the brain could be seen as a recapitulation machine, one capable of morphing into innumerable, behaviour-to-environment calibrating keys. In this sense, there need be no ‘one’ representation: differentiating fragments could be condensed, waiting to be ‘unzipped’ in a time of need. There need be no isomorphism between recapitulation and recapitulated, simply because of the role of process. In all likelihood, recapitulations are amoebic, dynamically forming and reforming themselves as needed.
We tend to call these recapitulations representations, but this is a mistake from the perspective of the BBH. Representations beg normativity, insofar as they can be either right or wrong, and normativity stands high on the list of inexplicable explainers mentioned above. (The problem of hidden kluges).
There is no simultaneous testing: According to the BBH the sense of ‘actions’ happening in a ‘moral space’ is likely a consequence of the thalamocortical system’s fractional access to all the relevant processes. The absence of access to processing precursors renders the event available for experiential processing as action, something ‘willed.’ The absence of access to processing precursors renders testing as something phenomenologically ‘detached.’ The collapse of lived time into the Now renders testing ‘flat,’ which is to say, without discrimination. The result provides the amorphous experiential conditions for what we typical thematize as ‘rules.’ Unique, but structurally isomorphic instances of testing become instances of the ‘same’ rule.
So the idea would be that mathematics is the experience of our brain’s ability to recapitulate structure across a vast array of scales at the multicellular scale.
The sense of differential systematicity and timeless necessity which inclines some to think they’re experiencing some kind of distinct and privileged alternate reality when doing mathematics is simply the result of encapsulation, how consciousness elides whatever empirical wiggle-room our neural networks possess. (This is the difficult turn…)
Combined with the Now, the way the experience of time seems to hang outside time, the utter absence of processing histories means that its operations are ‘flattened’ into apparently perfect sameness. In reflection, they seem to become timeless objects, or at least an autonomous system riding the same lines of identity as you.
The process of chasing out mathematical consequences seems like the very form of cognition because, in a strange sense, it is. Lacking any comprehensive access to the actual neural processes, what we are stranded with becomes everything. There is, quite simply, nothing else for the experience of mathematical cognition to be.
The experience of mathematics is an artifact of the way the thalamocortical system accesses the neural processing involved. The big questions are How? and How much? Given the metabolic expense of the brain, one would assume ‘Only as much as necessary’ would be the answer. Of course, this begs the question, How much is necessary? Given the boggling contrast between the phenomenology of mathematical cognition and the correlated neural complexity, one could safely assume, ‘Not much.’
Arguing What Math Is on the basis of our experience of it is like arguing the layout of Ceasar’s Palace from the lobby. Why should we assume that we’re somehow acquainted with the essence of math? The simplicity of what we see could very well be the shadow and not the kernel. The shadow is every bit as systematically ‘faithful.’ It betrays only the intuitive conceit that we make mathematics happen, that we will it, a conceit that is presently in a credibility free fall. On every front we are realizing that we are not what we think we are: Why should mathematics be an exception?
So then, what are ‘recapitulations’? Just an alternative possessing an alternative implicature, one that seems to shed a different kind of low resolution light. Another cartoon. Why should the universe possess a Russian Doll structure, one that allows the microscopic to recapitulate the cosmic? I have no idea. How does this approach do anything more than shift the burden of inexplicability from one set of terms to another? I’m not sure it does.
But the BBH makes pretty clear that committing to ontological speculations about mathematics on the basis of mathematical experience is far from warranted.
I can’t help but think of Chaos Theory, and those stunning 2-D representations of Mandelbrot sets, the endless repetition of structure, like pimples on pimples, unto infinity. Move over Big Bang – here comes the Big Squeeze…