On 01/03/2015 06:27, Warren D Smith wrote:
I happen to think ln(x) is a damn fine idea, and log(x) without defining it but nevertheless secretly agreeing it is ln(x), is just obnoxious insistence on some sort of "you know what it means if you are part of the 'in' crowd" status symbol psychological bullshit.
"ln" is no more immediately obvious than "log"; in either case you need to know what the notation means to do anything useful with it. The same goes for every other bit of mathematical notation there is. What's "secret" about it? Only the fact that in some other communities other than that of pure mathematicians it happens that "log" is used to mean something else. That isn't the result of any kind of in-crowd status-symbol psychological bullshit. It's just that if you happen to need one kind of logarithm much more often than others it's natural (ha!) to use "log" to denote that; and it happens that for pure mathematicians that happened with the natural log, while for engineers and schoolteachers it happened with the base-10 log. Natural logs are still much the most, er, natural kind in pure mathematics (though maybe base-2 logs are more important now than they were 50 years ago). There's less excuse for the dominance of base-10 logs in engineering and school teaching, now that slide rules and log tables have been so thoroughly supplanted by other means of computation. But of course the real reason why the notation persists in both cases is simply tradition: changing would require lots of people to abandon the notation they're used to for very little benefit, and invalidate lots of existing textbooks, journal articles, etc. It might be no bad thing if pure mathematicians and engineers and schoolteachers all got together and agreed never again to use unqualified "log" to denote any particular base, and to use (say) "lg" for base 2, "ln" for base e, and "ld" for base 10. Realistically, though, it's not going to happen. (Also, "ln" is distractingly hard to read because lowercase-l looks like capital-I and digit-1 and so forth and needs all the extra context it can get, and "ln" is harder to say than "log"; that agreement would be pretty much a pure loss for the pure mathematicians.) Among people who aren't pure mathematicians it is common to write angles in degrees, and common -- albeit sloppy -- to leave off the degree signs. Is it in-crowd status-symbol psychological bullshit for mathematicians to define the sine function so that its period is 2pi rather than 360? Among people who aren't pure mathematicians it is common to use terms like "compact", "real", "manifold", "similar", etc., with meanings very different from those pure mathematicians give them. Is it in-crowd status symbol psychological bullshit for pure mathematicians to use their meanings for these words? Of course not. Same for "log". -- g