# The Mind / Space Duallity

WARNING: This is almost certainly wrong, and the “math” is embarrassingly sloppy – it’s meant mainly as a note to myself and to inspire thought. I assume some familiarity with at least the premise of “modern”* meditation/insight theory as from MCTB / The Overground, and some basic category theory, mainly adjunctions/monads.

Here I’ll expose some ideas regarding the seeming conflict between an objective universe and a personal universe of qualia, building on the so-called “science of meditation

First, let me motivate the question. You may scoff, “Of course, external reality exists, this kind of philosophical play is pointless, we’ve gotten over this centuries ago”. I agree, it’s a confused question, and pointless to question external reality, so rather than seeking some non-existent answer, seek to understand how the question arrises. It is true, at the most basic level, that we do not, cannot, observe external reality, but only our raw senses. So it should seem at least a bit mysterious that external reality feels so real, even if the question poses no practical barrier to interacting with external reality. I seek to dissolve that mysterious feeling. Really, this should be no huge marvel, we frequently treat math as if it exists platonically, independent of our knowledge of it, but it is also clearly true that you can’t “find” math anywhere, it is a human invention. The two frames of reference fit snuggly inside each other.

I’ll attempt to roughly frame the problem through category theory – category theory is useful because it lets us distinguish different types of interaction (arrows in different categories) that might otherwise be convoluted.

Let’s start with what we know: one of the greater epistemic fruits of meditation is the realization that sensory experience is composed of individual frames containing a moment of perception “in motion”, commonly called “formations“. While hard to describe, and even harder to measure, one may think of formations as “differential objects”: not just points but infinitesimal segments of perception, in the context of immediate past and future, where our normal perception is the weaving together (integral) of these building blocks.

Assume for a moment that these formations, as the meditative scholars purport,  are the basic building blocks of perceptual reality, that we can never gain any more information, even in theory, than that contained in the continuous sequence of formations we perceive. Then where is there room for objective reality? “Things exist” certainly seems like a reasonable and useful assumption, and moreover, it feels more natural than a universe composed of fleeting thoughtstuff. To answer, let me quickly detour into the distinction between knowledge and belief.

This is where category theory starts to come in handy: both “everything is a belief” and “things can be known for certain” can be true if we’re careful about our typing. Consider the “belief monad” $B$, where, for a proposition $a$, $B a$ is the belief in $a$. Now, ever proposition can be lifted into a belief (that the proposition is true), and if we believe that we believe something, we really ought to believe it too! (Though humans are quite bad at this kind of reflective consistency). So we have mappings

return :: a -> B a
join :: B (B a) -> B a

And that’s a monad! If we restrict $a$ to have the type of formations, everything still holds, since “I observed formation a” is just a specific kind of proposition.

Now, since formations contain thoughts, our beliefs are encoded in each moment, ie. there is an embedding $B (FORM )\to FORM$. But here again higher-categories are useful – “isomorphisms are not equalities”, formations may encode beliefs, but they are not beliefs, the missing component is time. Computation takes time, thoughts are a particular kind of computation, but formations are timeless. This is where the mystery of belief vs knowledge comes from: You “know” your experience for free, from the monadic return, but there is logical uncertainty regarding what your experience represents. The statement “I think therefor I am” is tantamount to $\exists f. f$ which resolves trivially – this is why it feels more like “knowledge” than “belief”, there is no logical uncertainty, it is proven immediately by the witness of any formation.

If formations are timeless, what links one moment to the next? How can we predict the future from the past? Now we need to deal instead with indexical uncertainty. To proceed, we need to introduce some notion of “possibility”. The most obvious way is to codify a “belief” as a kind of bayesian network, which subsumes both classical and stochastic logic, though the real deal is almost certainly more complicated. Now, for any group of observations pulled from some space, there is a “free” probability distribution on that space generated by maximizing entropy subject to the constraints imposed by data. This free distribution is the “external reality” – the universal property of maximum entropy making it unique and “objective” in the sense that anything that could be known about the universe can be computed from it. Of course, computing maximum entropy distributions is hard, even harder if you have to recompute every instant! So we don’t, we compute our lossy “subjective” views of reality. While we can’t ever know the universe entirely, it is interesting to notice that it’s fundamentally made of the same sort of thing as thoughts leading to a nice interpretation that “learning about the universe is to become increasingly isomorphic to it”.

Of course, if reality were “just” a probability distribution over perception, that wouldn’t be very satisfactory. The universe is cold and uncaring, it doesn’t feel like it’s about you, it feels like there are “things” independent from yourself. How can we reconcile? A probability distribution is an opaque function – but opaque functions are always hiding more structure inside. This is the utility of bayesian networks: to factor our probability distribution, exposing its internal structure. The universe we observe, or rather seek to discover, is then the complete factoring of this “free” distribution, generated by our perception.

Now we come full circle, back to what science has suspected for a long time, that, while the laws of physics may be freely generated from perception, (assuming we know the entire state of the multiverse) physics can entirely explain human perception, by forgetting the rest of the universe and only focussing on the bit responsible for perception. So while reality may emerge from our perception, containing no more information than our experience of it, it can also be viewed as a distinct entity, with a more natural representation, and our perception as simply a view into it.