4 ms·

Something I think makes mathematics both incredibly powerful but difficult to break into is the notation

beagle3 6y ago
I don't think notation is what's making things hard. The concepts behind are the hard thing. If you can't figure out the concept, the notation doesn't make much sense - and it is the notation that you meet first, so it seems to be the culprit. Which is not to say that all notation is equally good - some is exceptionally bad, and other just confusing. The article mentions [x] which was i use for almost 200 years despite being confusing - but was then fixed into something non-confusing. Similarly, for most uses, Leibniz's differential notation (dy/dx) is superior to Newton's (y with a dot on top) - and is now universally used in those uses - but for a long time Newton's dominated, mostly for political reasons (yes, over 250 years later). But these are the exceptions: Usually, like in the floor/ceil case, when a better notation comes along, it is quicky (30-40 years...) adopted.
- ncmncm 6y ago
  Concepts can be explained and demonstrated. You can read the demonstration, and eventually understand. If you can find it. But there is no way to look up any given dumb-ass notation, or even to know how to pronounce it. Most notations are used to mean a dozen different things, so you can't even be sure, if you read about it, you are reading about the right one, if you do find it. And if you find the right one, it still won't say how to pronounce it, so you can't even ask without sounding like a dummy. It is all very insular. Or, maybe, was, before Youtube.
  - casselc 6y ago
    It doesn't help with stuff found in the wild, but if you're working from a text most math books will either list all symbols at the beginning of the index with references to where the notation is introduced and defined, or they have a separate symbol index or glossary of notation.

I don't think notation is what's making things hard. The concepts behind are the hard thing. If you can't figure out the concept, the notation doesn't make much sense - and it is the notation that you meet first, so it seems to be the culprit. Which is not to say that all notation is equally good - some is exceptionally bad, and other just confusing. The article mentions [x] which was i use for almost 200 years despite being confusing - but was then fixed into something non-confusing. Similarly, for most uses, Leibniz's differential notation (dy/dx) is superior to Newton's (y with a dot on top) - and is now universally used in those uses - but for a long time Newton's dominated, mostly for political reasons (yes, over 250 years later). But these are the exceptions: Usually, like in the floor/ceil case, when a better notation comes along, it is quicky (30-40 years...) adopted.

ncmncm 6y ago
Concepts can be explained and demonstrated. You can read the demonstration, and eventually understand. If you can find it. But there is no way to look up any given dumb-ass notation, or even to know how to pronounce it. Most notations are used to mean a dozen different things, so you can't even be sure, if you read about it, you are reading about the right one, if you do find it. And if you find the right one, it still won't say how to pronounce it, so you can't even ask without sounding like a dummy. It is all very insular. Or, maybe, was, before Youtube.
- casselc 6y ago
  It doesn't help with stuff found in the wild, but if you're working from a text most math books will either list all symbols at the beginning of the index with references to where the notation is introduced and defined, or they have a separate symbol index or glossary of notation.