For a long time I’ve been unsatisfied with natural language. At first, in my naïvety, I thought it was just English that was unsuitable, but it seems there’s a deeper problem that even engineered languages like esperanto don’t help with. People talk past each other, perpetually missunderstanding, driven apart by nitpicking correct phrasing.
When people asked me if I thought in words or pictures I blinked at them, “I think in thoughts, doesn’t everyone?”. I’m still not sure, but it seems that many do not notice the inadequacy of words. Maybe I’m exceptionally bad at phrasing, or maybe most people subconsciously restrict their thoughts to mirror their words so that translating isn’t a great big mess.
It remains to clarify: what makes up a thought, how does it differ from speech? First, what is similar? They’re both ways to pick out points in thingspace, (which you should understand as an injective map from thoughtspace/wordspace resp. to thingspace. Almost technically, there’s actually maps wordspace -> thoughtspace -> thingspace, and the map wordspace -> thingspace is the unique composition, so this suggests that thoughts are at least as powerful as words. Thoughts are anonymous, but words are named. Effectively this means that you can pull a word out of the aether by its name, but you can only pull up a thought by association; imagine words as organized like a dictionary, and thoughts organized by a graph, with edges as metaphors/links in associative memory etc. (this gives us some indication towards their structure as categories). The most apparent difference is that thoughts can refer directly to internal perception, whereas words are completely incapable of serializing sensory perception unless the receiver shares certain experience with you. Words can refer to the thought of sensation (which you assume they share), but not the sensation itself (which they almost certainly do share, being human).
While Wordspace and Thingspace are straightforward at least in concept, Thoughtspace deserves further explanation, as the mediation between the two. The objects of interest in Thoughtspace can be thought of as spatiotemporal firing patterns in the brain. Choosing the correct formalization for these firing patterns is a hard scientific problem (where should we delimit the boundary of one pattern to the next?) so we’ll sidestep the problem for now by invoking the Mind/Space hypothesis, instead considering the subjective experience of firing patterns as ‘formations’ relative to a fixed observer. Oddly enough, the boundary problem disappears in this perspective: each thought obviously feels distinct, but they are connected by a similarity metric. The hypothesis is that these formations have some scientific characterization in the brain, which seems like a reasonable assumption. I suspect that thoughts only have a clean representation as formations relative to their originator, and that comparing the “objective” representation of thoughts as firing patterns is intractable in general, because of the encryption problem. So “formations” really are the more natural setting.
Thoughtspace is the world we really “live” in – it’s the only world we can actually experience, but through it we can know both Wordspace and Thingspace. The structure of Wordspace is logical. The objects of interest are strings of symbols (interpreted as logical propositions), and their connectives are algebraic manipulation. We can think of it as the union of all symbolic logics. This includes not just traditional logic, but also all constructive objects, arrangements of particles, etc. Since thoughts are “just” arrangements of discrete particles in the brain (but maybe not, if continuous quantum interactions turn out to be important for cognition), we could represent thoughts directly in Wordspace. However it makes more sense to think of it as a sort of completion of Wordspace, where the thoughts are distinct objects, that can be represented as potentially infinite arrangements of particles. The dynamics of thoughts-in-the-world, then, are inherited via projection (Thoughtspace -> Wordspace) into a finite brain. Going in the other direction, Wordspace can be embedded in Thoughtspace as those thoughts that can be written down (or otherwise serialized). This embedding is not natural though: the association between words and thoughts is learned (in a non-unique way) through experience – it includes many extensional elements such as feelings, objects (tigers, etc.), and temporal patterns. (A lot of communication errors can be cleared up by remembering that words don’t have independent meaning, trying to determine what thought the other party has in mind, rather than assuming they use the same mapping).
Thoughtspace inherits the logic of Wordspace but it also has it’s own fuzzy logic. Internally, these fuzzy arrows are the “feels like” connectives. For example: a bench is like a rocking chair; a bench is more like a rocking chair than it is like a snake. We can justify the statement that a rocking chair is like a bench, but it is not a logical statement. Rather, the “sameness” is a summery of how many contexts they are equivalent in. Ex: For “most purposes” a rocking chair is indistinguishable from a bench. This acts like a sort of probability space, with 1 being equivalent in all contexts and 0 being never equivalent, so we can start with the category Stoch as a rough approximation. We can also talk about the properties of contexts where they are similar, so the arrows have computational content in addition to weight. For example, rather than considering all contexts, a rocking chair is even more similar to a bench when restricted to contexts of sitting – they’re still a bit different in that sitting in a rocking chair feels a bit different – on the other hand, benches are often made of stone while rocking chairs almost never are, detracting from general similarity but not affecting sitting much at all. It’s all a bit handwavy but I hope the intention is clear – enumerating contexts and quantifying “sameness” is the key.
Careful though! This similarity space is in general NOT a consistent logic in the way you’d expect. My favorite illustration of this principle is the “numerologist’s folly”, exemplified by crackpot sites like this. What’s going on here? At the risk of sounding silly, I’ll point out the general flaw: While each step has high similarity, the contexts they consider are different, so care has to be taken when composing them. “New York City”, “Afghanistan”, and “The Pentagon” are all similar in their number of letters, and it’s true that New York was the 11th state of the union, but these two contexts are different! If we want to compose them as connectives, we have to conflate the contexts, so “New York City”, “Afghanistan”, “The Pentagon”, and “The state of New York” are all similar in the context “number of letters OR state order of joining the USA” which doesn’t seem like a very useful connection now does it? It’s a silly and obvious example, but this kind of conflated reasoning happens quite frequently in more subtle cases. Understanding the true structure of Thoughtspace will let you wield it’s power while avoiding such pitfalls.
The relation between wordspace and thoughtspace can be made sucinct by considering the quote:
When you draw a boundary around a group of extensional points empirically clustered in thingspace, you may find at least one exception to every simple intensional rule you can invent.
Then the embedding of wordspace into thoughtspace/thingspace are exactly the ones that can be described by intensional rules.
The major task now is to translate these subjective dynamics into something that can be quantified mathematically, measured externally, and communicated clearly between people.