> This is immediately self-evident if you've ever tried to teach anything complex to anyone who wasn't already a domain expert in an immediately adjacent area.
I am a practising computational scientist, and I work in an interdisciplinary field. I work with the sort of folks you mentioned above daily.
And while I often do not start with an equation, that does not mean they are not useful. I don't think anyone is suggesting that to a non-specialist they are. Typically, I start with thought experiments or plots. People are often visual learners.
However, that does not mean that mathematical notation is a problem. Mathematics is a language, and like any language one must spend years (or in my case, decades) learning how to 'speak' it. While I would not suggest it is inherently a global maximum, I'm skeptical it is not at least a pretty good local max.
Could this be because as you go, you introduce more dimensions, degrees of freedom into your mental model. To accommodate for this, the brain needs to make room, and time and time again needs to reshuffle to make space for more connections or to eventually collapse them into multiple different models of a lesser degree.
I just read that second order logic can represent all higher order logics. The degree of the logic means the degree of nesting of sets into sets, that are quantified over by the logic expression. If sets of sets of values are all it takes, a two dimensional spatial representation should be enough. So far so good?
The problem with text is that it is largely sequential, i.e. one dimension, left to right.
I am a practising computational scientist, and I work in an interdisciplinary field. I work with the sort of folks you mentioned above daily.
And while I often do not start with an equation, that does not mean they are not useful. I don't think anyone is suggesting that to a non-specialist they are. Typically, I start with thought experiments or plots. People are often visual learners.
However, that does not mean that mathematical notation is a problem. Mathematics is a language, and like any language one must spend years (or in my case, decades) learning how to 'speak' it. While I would not suggest it is inherently a global maximum, I'm skeptical it is not at least a pretty good local max.