On 03/03/2015 01:26, Warren D Smith wrote: [me:]
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.
--what hogwash. "harder to say." My heart bleeds for you.
I wasn't asking for sympathy.
First of all, lg occurs in number theory and computer science, so the idea only ln occurs in pure math is hogwash.
It's a good thing, then, that I (1) didn't say that and (2) already said in so many words that lg occurs more now than it used to.
My personal convention, which is you will note is superior to Halmos (of whose opinions, I have a low opinion),
(This distinguishes Halmos from everyone else in the world how? It must be frustrating for you, living in a world where everyone else is an idiot.)
is: always use ln, except if you are trying, intentionally, to convey the idea that some formula enjoys validity REGARDLESS of the base of the logarithm, in which case use log.
A very reasonable convention, indeed.
Second, where do these pure mathematicians get off proclaiming there should be pure math books divorced from the rest of reality?
The same place as chess players get off proclaiming that there should be books about chess divorced from the rest of reality, I suppose. Seriously, who said anything about "divorced from the rest of reality"? If you are writing a book about (say) complex analysis, then you may need a lot of natural logs and will have little use for logs to other bases. This is equally true whether or not your book mentions applications of complex analysis in fluid dynamics, electrical circuit design, analytic number theory, etc.
And what's wrong with striving in every way possible to make work more accessible to Joe Schmoe?
The same thing that's wrong with striving in every way possible to do any other single thing: you may end up making bad tradeoffs. Accessibility-to-Joe-Schmoe is good; so is conciseness, so is not confusing expert readers by using notation that Schmoe expects and they don't, etc. (Don't misunderstand me; I am *very much in favour* of making mathematical writing accessible to less-expert readers and I would love the balance to shift in that direction relative to where it is now. But accessibility doesn't always come for free and I'm not sure *anything* is so super-important that it should be striven for *in every way possible*.)
Rather than striving to make it less accessible?
I know of no reason to think that anyone does this (though for all X one can find occasional people who do X).
And even the pure mathematicians, you will notice, write their numbers in base 10. (Proving their total hypocrisy.)
Are you just trolling here? Because I find it very, very difficult to believe that someone as intelligent as you seriously thinks that writing numbers in base 10 but finding that natural logs occur vastly more often than base-10 logs in their work is evidence (still less proof) of "total hypocrisy".
Every time I make a log-plot, I use base-10 logs to do it, and I dunno, I guess pure mathematicians never need to plot anything because that would be too applied?
When you make log-plots, how often do they have actual logs in them? (In my case: never. The axes are labelled with the numbers themselves, not their logs; the only mention of logs is in an annotation saying "Scales are logarithmic" or something of the kind.)
And finally, re "l" looking like "1" and "|", you know what? THIS WAS A MASSIVE MISTAKE by typographers.
Yeah. But much of the fault belongs with the design of the Roman alphabet, which it's hard to blame any particular people for. Any typeface that looks the way readers expect is going to make l,I,1,| all look rather alike. (And any typeface that doesn't look the way readers expect is going to be distracting.) Whoever's fault it is, it is the way it is, and it's hardly reasonable to blame pure mathematicians (or anyone else who wants to work with natural logarithms) for preferring notation that works despite this deficiency in our writing system. -- g