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It isn't holding the paradigm back. I do not have time to repeat the examples I often give, but a short analogy might help: 'I think mathematics is being held

It isn't holding the paradigm back. I do not have time to repeat the examples I often give, but a short analogy might help: 'I think mathematics is being held back because people write cryptic syntax like "xx + 2x + 1 == 0" instead of the easily readable "multiply your unknown by itself, then add twice that very same unknown, and finally add 1 -- the result you get should be zero; that's the constraint satisfied by the very same unknown"; it's a shame' There is very little difference. The reason it seems like the cryptic syntax is the problem is because that's the first thing you see -- but it's just the top of the iceberg. The problem is that most people don't grok the paradigm regardless of the syntax; and the very few which do grok the paradigm but don't grok the syntax are not enough to get rid of the syntax, which has significant symbiosis with the paradigm (much like Leibniz's differential notation is symbiotic with the ideas, much more so that Newton's "simpler to use" one)

nerdponx 9y ago
The "cryptic syntax" of math was an organic outgrowth over hundreds of years by researchers from all over the world. And yes, long and complicated mathematical expressions are cryptic. That's why you often see constants being combined and equations being re-expressed in "simpler" terms, even when those terms are themselves relatively complicated functions. It's partly about conceptual abstraction, but it's also about visual clarity. Math can get very, very hard to read.
- beagle3 9y ago
  > Math can get very, very hard to read. That's exactly my point: Math gets hard to read, but it's because of the math, not because of the notation. When new notation simplifies things, and is quickly adopted by practitioners - e.g. Einstein's tensor notation. I am not aware of a single case in history where a more verbose notation was preferred to a terse notation in mathematics - except perhaps in the case of Leibniz' notation for calculus, which is slightly more verbose than Newton's but it address a significantly larger set of concepts, and does so with regularity and orthogonality.

nerdponx 9y ago

The "cryptic syntax" of math was an organic outgrowth over hundreds of years by researchers from all over the world. And yes, long and complicated mathematical expressions are cryptic. That's why you often see constants being combined and equations being re-expressed in "simpler" terms, even when those terms are themselves relatively complicated functions. It's partly about conceptual abstraction, but it's also about visual clarity. Math can get very, very hard to read.

beagle3 9y ago
> Math can get very, very hard to read. That's exactly my point: Math gets hard to read, but it's because of the math, not because of the notation. When new notation simplifies things, and is quickly adopted by practitioners - e.g. Einstein's tensor notation. I am not aware of a single case in history where a more verbose notation was preferred to a terse notation in mathematics - except perhaps in the case of Leibniz' notation for calculus, which is slightly more verbose than Newton's but it address a significantly larger set of concepts, and does so with regularity and orthogonality.