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…
“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?”
I can see no reason to restrict this speculation to mathematics. If it is true for mathematics then surely it is true of all perceived regularities.
I think mathematics is simply the axe to grind in an overarching theoretical sense. Personally, I think the BBH has immediate implications more closely related to our individual human experiences. But math is primarily responsible for scientific fact and our consensual objectivity. Where better to riddle with cracks than the very foundation of knowledge?
So math is the abstract representation of experiences within the scope of our perceptual limits? I can dig it. It does place limits on our ‘knowing’ an absolute morality, but would still leave morality wide open for discovery within the human experience/system.
“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?”
This is a new one to chew on. Genuinely disturbing implications.
Truth is, I haven’t come close to thinking any of this through. But it strikes me as an interesting departure point for several different reconceptualizations of mathematical cognition. I like the idea of ‘unconscious proofs’ versus conscious ones!
Hey Scott, Could you expand the whole article into another that is easier to grasp?
I only vaguely grasp certain ideas, and some go both ways. In the sense I can’t figure out if you are stating a thing or its contrary.
That quote above: are you saying that “we make mathematics happen” or that this is specifically not “credible” (and so contradicting that idea)? I can’t make head or tails of that paragraph. I need more extended elaboration 😉
I found this essay fascinating. The language is more dense than I’m used to, so I might have lost some of the finer points in translation to more familiar terms.
If mathematics is an example of an illusory mirror we hold up to ourselves to see the cognitive sparks that sometimes escape from under the hood, then is some kind of feedback loop created by which sparks we catch (or don’t)? It seems mathematics is the closest thing we have to a sterile study of complicated patterns, in some form of universal tongue (I’m not a mathematician, so I have no idea how true that appearance is). If humans are, as it boils down to, just really complicated weavings of patterns that can perceive and fashion smaller patterns (mental or physical) into tools to change their own structures or their surrounding environment.. couldn’t this insight be applied to the way that we apprehend all manner of patterns to use in our lives?
For example, let’s say the structure of a man and the structure of his environment interact like flint and steel, and if our thought/mirror/thalamocortical system is positioned in the right way (that is, with a significant mental bastion of past experiences to create a context for the occurrence), we can see fire. Or an illustration of more complicated patterns/restraints that inform our decisions in ways we wouldn’t remotely reason out from any other perspective and whose rules and implications aren’t immediately obvious. Or whatever you want to call it. I’m curious if this makes sense, or if it doesn’t, where the flaws are. I’m not sure I can accurately deliver thoughts this complex yet. Feedback is welcome.
Anyway, this sort of fare is richer than what I’m used to, so I may not entirely be catching on. I’m still lean and hungry. Thanks for posting.
That’s the upshot, I think. Our brains and our environments form supercomplicated informatic wholes, and we find ourselves perched on an informatic sliver–the circuits comprising the thalamocortical system–that necessarily confuses itself for the whole. Given this particular cartoon (which I call the Blind Brain Hypothesis), the question is, what kind of errors will we be inclined to make. What I try to do hear is suggest why we should find mathematical Platonism intuitively compelling.
Ah, gotcha. So, errors like the intuitive faith in what we ‘discover’ or ‘feel’ as truthful and correct when it’s actually just us scraping at the edges of our perceptual limitations and christening the abyss we find as ‘Truth’ would fall under the aegis of that question? Or maybe I’m just waxing poetic.
So the Platonism is compelling because it painlessly aligns with an understandable paradigm that we’ve already got an established context for, but applies to an inverted way of looking at things?
Either way, it’s definitely something that stimulates my thought in new directions.
Poetry makes for the best wax. The notion of form (the BBH) suggests, arises from the brain’s inability to distinguish between unique iterations. Think of the difference between paradox and infinite feedback loops. In the former, opposing truth-values seem to obtain simultaneously, whereas in the latter they alternate back and forth interminably. The BBH suggests that the former is actually a ‘flattening’ of the latter, due to the brain’s inability to track its own processing.
[…] About this and everything below on this blog. I found out that Bakker is miles ahead of me. As I should have expected. Maybe I’ll write about that next. This entry was posted in […]
Could you unpack that flattening process a bit more, Scott? It kind of strike me like the old woman/young woman optical illusion, where you basically see one at a time. Seems more like a process of ‘making a bet’, a focus on one thing being the case and hinging further actions upon that bet. But with the paradox, which thing to bet upon? But I’m not sure what you mean by flattening? And granted, I’m using intent based descriptors (ie, making a bet).
Analogies are hard to come by here: the idea is that our sense of experiencing some ‘timeless realm of internal relations’ is an artifact of the brain’s inability to recursively track its own mathematical processing. So think of cartoons, the way perspectival depth gets ‘flattened’ simply because of the limitations placed on representational resolution. Now imagine the perspectival resolution dialed to zero, so that no perspectival information is provided at all. I’m suggesting (because like I say, the consequences of the BBH are just too dismal for me to embrace) that the ‘feeling of mathematics’ is like this, that no temporal information is fed foward to the thalamocortical system, so that, from the standpoint of experience, mathematical cognition becomes susceptible to the kinds of ontological intuitions the formalists are want to attribute it. The super-complicated, real time, externally related neuromathematical processing is ‘flattened’ into a cartoonish experience we then – with predictable human vanity – declare is the ‘essence’ of mathematics.
I love the prince of nothing – It’s one of the all time greats. I thoroughly enjoyed the philosophical aspects of the book, more so them being a driving force of the plot.
1) I think it’s interesting to note that a lot of what you are saying was expressed by Kant – of course one you discard his (christianity infused) premise about the eternal (form of the) human mind and you add evolution as a premise – e.g., we can only see what we are built to see, so little wonder that reality appears mathematical to us.
2) I’m always appalled by how standard praxis when discussing math/language/thought in the relevant disciplines is to dispense with the fact that it is process – and one that is far from being infallible at that. This goes FAR beyond the fact that the underlying computations are fundamentally opaque. One in a tens of thousands of people is a decent mathematician, yet logic is to date the starting point for pertinent theories (and BTW even gifted logicians don’t do so well with their reasoning if they dissent far enough from their sweet spot in terms of content – e.g. personal stuff)
3) What’s up with the “thalamo-cortical” moniker. Brain seems much less theory skewed (not aware of even a half decent argument as to why wouldn’t any creature with a nervous system have some form of proto consciousness)
The thalamocortical system seems to be the neural arena where consciousness knocks around in. In another decade, it could become the next pineal gland – who knows.
I actually think the Blind Brain Theory explains the intuitive basis of Kant’s approach.
[…] we see in the human brain: what we see and presume to know is only a tiny part. So again the Russian Doll structure. These echoes are just too powerful to be random, but maybe too easy to be solved intuitively. What […]
[…] language of god, but it is interesting to think about this in systemic terms. There’s also this piece from Bakker and the speculation of math as the shadow projected by an unknown […]