Slightly idle thought. I believe that algebra (as in "algebra 101") "calls on the linguistic part of your brain". For example, the linguistic part of your brain can apply the rules of grammar to the sentence "the gostak distims the doshes" to get other sentences like "doshes are things that the gostak can distim". Just as it can rearrange "a * b / c" into "a / c * b"
First, I really doubt that "algebra calls on the linguistic part of your brain" based for instance on https://elifesciences.org/articles/59340
Second, I personally have very "syntactic" (as in "apply formal rules or equations until you rewrite formula into the required form") approach to math (algebra included), but I learned that "real mathematicians" (and in general most of the people doing math) follow "semantic" approach, basing their reasoning on actual objects (or models) formulae describe and their (objects'/models') properties, and not purely formal rewriting. That feels even more distant from "linguistic processing".
We may mean different things by this. I would describe your "syntactic approach" as calling on the purely linguistic part of your brain.
I am on board with the distinction between that and reasoning about the "actual objects". In the case of code, the arrays and variables, in the case of algebra, maybe a set or a point moving through a space.
Once you're in the "I know the objects to which these symbols refer" phase, you apply logic, and that study isn't a huge surprise to me. But the rearrangement part (which isn't done by programmers as much as mathematicians) still seems linguistic to me.
the rearrangement part still seems linguistic to me
It doesn't seem linguistic to me. 😁
Few linguists I know have nothing to do with "syntactic rewriting" like in math. logic, that's completely alien thing to them, that's not how they work. 🤷♀️
your brain can apply the rules of grammar to the sentence "the gostak distims the doshes" to get other sentences like "doshes are things that the gostak can distim". Just as it can rearrange "a * b / c" into "a / c * b"
I don't think the above analogy is direct - at least not how I think. In the first case I do not use rules of grammar to do the transform. I parse and "understand" the meaning. There is in an internal model in my brain and a schema. So the symbols become objects in this compact model. Now this model can be used to generate other sentences that are related in some way - I can even subtract or add information E.g. "did the gostak distims the doshes yesterday?" or "The gostaks distim some things"
This is quite different from 'grammar only' transforms which are basically identification of patterns and application of rules to those patterns, without any "understanding". I suppose in smaller cases I could understand it, e.g. (a + b) * c is a*c + b*c - that is something that makes sense. But in more complex algebra, I'm just 'looking for patterns' and matching against a 'rule database' I've memorized.
@Alexander Chichigin I may be misunderstanding your reply but rewrite rules are not alien to linguistics. Phrase structure rules were one of the fundamental parts of generative grammar and are a subset of rewrite rules https://en.wikipedia.org/wiki/Phrase_structure_rules
"in more complex algebra, I'm just 'looking for patterns' and matching against a 'rule database' I've memorized" - also sounds like language to me
Since the words "gostak", "distim" and "doshes" are nonsense words, your only information on them (the only information you can ever get on them) is what you can infer based on how English works. I.e. there is no semantics / "understanding to be had", only syntax. There's the illusion of reasoning logically about objects, but I claim that all you can hope to do with the sentence is to apply rewrite rules (that then FEEL logical)
Hamish Todd I wrote that several people I knew who were doing linguistics had nothing to do with formal rules as in mat. logic. Still they were studying the language professionally. And yep, they knew about Structural Linguistics and other stuff, but were not interested in it and were not using it.
Ah ok!
Do we still disagree about algebra calling on the linguistic part of our brains though?
I.e. there is no semantics / "understanding to be had", only syntax.
The understanding is more abstract than in 'the kid eats breakfast' - but then how much of this sentence do you 'understand' too? Do you know what the kid ate? Eggs or bread? Or how - using their hands or utensils? Or did they eat it in a reasonable time? No - all that is detail that is left out. So its still a 'partial understanding' of the idea- there are many concrete possibilities of the sentence. The distims sentence is even more general. All we know there is an agent (gostak) and there is something that can be done (distim) and something that it can be done to (doshes).
I think the general pattern of 'the agent does something to some object' is a schema that we deeply understand and in our mind it can hold many similar instances with varying degrees of detail. Your original sentence immediately got parsed in my mind into this schema.
I agree that there is some kind of illusion - which is what I'm calling the internal schema and think all understanding is a kind of illusion - but isn't that the useful part of it? If you parse a sentence structure into the wrong schema, you will make the wrong internal model. This is where the language related jokes come from. E.g. the structures look similar but the schema is different for 'fruit flies like a banana' and 'time flies like an arrow'.
Your original sentence immediately got parsed in my mind into this schema
I agree it's hard not to do this*. My point is that you can do certain things with the sentence regardless of what the schema is.
My claim is that algebra calls on the linguistic part of your brain, and that this is a part that can do sentence-rearrangement. Maybe the schema-inference also happens in the linguistic part of your brain. But the schema isn't required for sentence rearrangement.
Do you agree with me that we are doing productive/useful "work" in algebra with just rearrangement? You can then infer a schema, perhaps a visualization or physical interpretation, but that's optional and probably not unique.
*And I don't think you do know there is an agent. The gostak could mean something like "the general high temperature of this time of year" and distimming could be a reaction it causes. I don't know whether that qualifies as having agency.