6 ms·

Counterexample: > In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic p

Counterexample: > In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles. [...] The interaction of sub-atomic particles can be complex and difficult to understand intuitively. Feynman diagrams give a simple visualization of what would otherwise be a rather arcane and abstract formula. As David Kaiser writes, "since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations", and as such "Feynman diagrams have revolutionized nearly every aspect of theoretical physics". https://en.wikipedia.org/wiki/Feynman_diagram https://en.wikipedia.org/wiki/Feynman_diagram ---- This is the first example that came to mind, but there are certainly very many others. Because the idea that written flat text is inherently a global maximum for representing/communicating/working with all concepts is absolutely absurd. 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.

arcanus 10y ago
> 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.
- posterboy 10y ago
  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 only practice makes perfect (notice the 2nd C ;-)
posterboy 10y ago
> the idea that written flat text is inherently a global maximum It's quite the opposite, text is a global minimum. Sequential text is best suited to represent some first order logic, a recursive enumeration of nouns. Or better yet a zeroth order logic, a simple enumeration of nouns. That is a desirable logic to work in, because it's complete. But we do need second order logic to ... beats me :)
lisper 10y ago
Diagrams are good for representing and reasoning about physical things, and for mathematical concepts that have straightforward physical models, like numbers. But this is because there's a natural correspondence between these diagrams and the things they represent. There is no natural correspondence between a triangle and logs/exponents/roots beyond that fact that triangles have three sides and three vertices, and the set {log, expt, root} has three members.

arcanus 10y ago

> 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.

posterboy 10y ago
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 only practice makes perfect (notice the 2nd C ;-)

posterboy 10y ago

> the idea that written flat text is inherently a global maximum It's quite the opposite, text is a global minimum. Sequential text is best suited to represent some first order logic, a recursive enumeration of nouns. Or better yet a zeroth order logic, a simple enumeration of nouns. That is a desirable logic to work in, because it's complete. But we do need second order logic to ... beats me :)

lisper 10y ago

Diagrams are good for representing and reasoning about physical things, and for mathematical concepts that have straightforward physical models, like numbers. But this is because there's a natural correspondence between these diagrams and the things they represent. There is no natural correspondence between a triangle and logs/exponents/roots beyond that fact that triangles have three sides and three vertices, and the set {log, expt, root} has three members.