But I do know what an algorithm is.

Do you? I find the unexamined use of this particular concept possibly the most problematic component of what you call "LW-style thinking." (Another term that commonly raises my red flags here is "pattern.")

(I know the exchange isn't primarily about Kant, but...)

Kant certainly isn't a "distrusting logical reasoning" kind of guy. He takes for granted that "analytic" (i.e. purely deductive) reasoning is possible and truth-preserving. His mission is to explain (in light of Hume's problem) how "synthetic a priori knowledge" is possible (with a secondary mission of exposing all previous work on metaphysics as nonsense). "Synthetic a priori knowledge" includes mathematics (which he doesn't regard as just a variety or application of deductive logic), our knowledge of space and time, and Newtonian science.

His solution is essentially to argue that having our sensory presentations structured in space and time, and perceiving causal relations among them, is universally necessary in order for consciousness to exist at all. Since we are conscious, we can know a priori that the necessary conditions for consciousness obtain. [Disclaimer: This quick thumbnail sketch doesn't pretend to be adequate. Neither am I convinced that the theory even makes sense.]

What Kant says we cannot know is how things ("really") are, considered independently of the universal and necessary conditions for the possibility of experience. As far as I can tell, this boils down to "it's not possible to know the answers to questions that transcend the limits of possible experience". For instance, according to Kant we cannot know whether the universe is finite or infinite, whether it has a beginning in time, whether we have free will, or whether God exists.

It's important to understand that Kant is an "empirical realist", which means that the objects of experience - the coffee cups, rocks and stars around us - really do exist and we can acquire knowledge of them and their spatiotemporal and causal relations. However, if the universe could be considered 'as it is in itself' - independently of our minds - those spatiotemporal and causal relations would disappear (rather like how co-ordinates disappear when you consider a sphere objectively).

(It's similar to the dust theory.)

The nature of logical reasoning is actually a deep philosophical question...

You know what an algorithm is, but do you know if you are an algorithm? I am not sure to understand why you need algorithm at all. Maybe your point is "If you are a human being X that receive an input Y, this allows you to know a nontrivial fact about reality (...)". I tend to agree with that formulation, but again, this supposes some concepts that do not go without saying, and in particular, it supposes a realist approach. Idealist philosophers would disagree.

I can understand that your idea is to build models of reality, then use a Bayesian approach to validate them. There is a lot to say about this (more than I could say in a few lines). For example : are you able to gather all your "inputs"? What about the qualitative aspects: can you measure them? If not, how can you ever be sure that your model is complete? Are the ideas you have about the world part of your "inputs'? How do you disentangle them from what comes from outside, how do you disentangle your feelings, memory and actual inputs? Is there a direct correspondance between your inputs and scientific data, or do you have presupositions on how to interpret the data? For example, don't you need to have an idea of what space/time is in order to measure distances and durations? Where does this idea comes from? Your brain? Reality? A bit of both? Don't we interpret any scientific data at the light of the theory itself, and isn't there a kind of circularity? etc.

I suppose it's a virtue of that interpretation that 'information that cannot be coded in any particular scheme' is a conceptual impossibility (assuming that's what you meant).