Right, that's why the focus is on introductory classes. As I noted, yes a sufficiently motivated individual will get used to the notation in time but that doesn't mean things are okay.
These things that seem minor to the expert actually make a big difference before chunking is achieved and can hinder all but the most motivated. If you are taxing short term memory by using unhygenicly bounded variables then no, it is not just a matter of who is interested. If you are not pointing out the difference between higher order functions and regular functions nor separating the notion of function from application then you are causing unnecessary representational couplings that create a lot of friction. These things have real cognitive and physiological costs. The design should streamline thought for expert and novice alike, it should not be arbitrary. And in the absence of anything better we cannot say that the issue of notation is not a problem at high levels. Sure learning is no longer the problem but what of adroit mental manipulations? I tend to agree with Alfred Whitehead who said
"By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.".
We can't lament the lack of scientists and engineers on one hand and not try to do reduce uptake friction on the other. There's a real problem with math education if the experts are not trying to relate to the ones who are struggling.
btw braket is a wonderful notation in my book and I'm not a physicist, it is an elegant way of writing sparse vectors.
These things that seem minor to the expert actually make a big difference before chunking is achieved and can hinder all but the most motivated. If you are taxing short term memory by using unhygenicly bounded variables then no, it is not just a matter of who is interested. If you are not pointing out the difference between higher order functions and regular functions nor separating the notion of function from application then you are causing unnecessary representational couplings that create a lot of friction. These things have real cognitive and physiological costs. The design should streamline thought for expert and novice alike, it should not be arbitrary. And in the absence of anything better we cannot say that the issue of notation is not a problem at high levels. Sure learning is no longer the problem but what of adroit mental manipulations? I tend to agree with Alfred Whitehead who said
"By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.".
We can't lament the lack of scientists and engineers on one hand and not try to do reduce uptake friction on the other. There's a real problem with math education if the experts are not trying to relate to the ones who are struggling.
btw braket is a wonderful notation in my book and I'm not a physicist, it is an elegant way of writing sparse vectors.