March 2015 - mathfun@mailman.xmission.com

[math-fun] ln
by Warren D Smith 03 Mar '15

03 Mar '15

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. You know, where groups like to create pointless initiation rites, like hazing fraternity brothers and creating secret handshakes. Because otherwise they sadly wouldn't be able to feel like Real Men. There is nothing wrong with being less ambiguous and saving a letter at the same time. What's wrong is doing the opposite. And further, I like Knuth's (?) idea of lg(x)=log(x)/log(2) as well. And nobody ever seems to do it, but if anybody wanted to have a special one for log(x)/log(10), such as lt(x), I would have been ok with that too.

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[math-fun] ln, ζ, and j
by Bill Gosper 02 Mar '15

02 Mar '15

On 2015-03-01 20:39, Dan Asimov wrote: >> On Mar 1, 2015, at 7:51 PM, Adam P. Goucher <apgoucher(a)gmx.com> wrote: >> >> John Napier was Scottish, rather than French. > > Yes, and for that matter I can't even find any suggestion that Napier > worked in base e. > > And natural logarithm in French appears to actually be "logarithme naturel" > instead of what I wrote. While googling about this, I came across > some comments by Europeans who said they learned that ln is an > abbreviation for the Latin phrase (approximately) logarithmum > naturalis. > > Maybe the origin of ln notation is in doubt, but I'm pretty sure how > it became widespread in the U.S. and maybe the world: The calculus > book by George B. Thomas was the number one calculus book used in > college and high school courses for many years*. It is used all over > the world. That book probably helped popularize the ln notation more > than any other. > > --Dan > _________________________ > * The first edition came out in 1952, it's now in its 13th edition. Of > course it has been overshadowed by other books in recent years, > especially those by James Stewart. > >>> Sent: Monday, March 02, 2015 at 3:16 AM >>> From: "Dan Asimov <dasimov(a)earthlink.net> >>> >>> I thought "ln" was invented by the French, maybe even Napier, standing for logarithme naturale. > >>>> On Mar 1, 2015, at 4:33 PM, Victor S. Miller <victorsmiller(a)gmail.com> wrote: >>>> . . . >>>> Some mathematicians disapprove of this notation [ln for log_e]. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish ln notation," which he said no mathematician had ever used.[13] The notation was invented by Irving Stringham, a mathematician.[14][15] > Pippinger, Nicholas (1976). "Formula nova pro numero cujus logarithmus hyperbolicus unitas est". *IBM Research Report RC 6217* JPropp> A somewhat similar issue comes up with the way Mazur uses the term "imaginary part" in his book "Imagining Numbers". The discrepancy between his use of the term and the way many high school students are taught to use the term led one reviewer to proclaim on Amazon as follows: "I regret that I cannot recommend this book for general enlightenment. Neither can I see how anyone reviewing this book can honestly call it lucid and well-written. <Major flamage> Many books explain both imaginary and complex numbers better than this one. Try Churchill's text, for one. I could say more, but need I? Caveat Emptor!!" I've highlighted the relevant passage from the guy's review (I say "guy" because, although the reviewer doesn't give a first name from which gender could be deduced, more men than women write this sort of bombastic prose). And, much as I resent the guy's tone and general ignorance, I have to admit that on this point, Some would say that there'll always be bozos, and that you can't anticipate every way in which you'll be misunderstood by bozos. <JPropp This sounds sounds suspiciously like Martin Gardner pseudonomously reviewing one of his own books. Gene, j is for imajinary. --rwg

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[math-fun] Fwd: New book: Prime Numbers and the Riemann Hypothesis
by meekerdb 02 Mar '15

02 Mar '15

Might be of interest: The link is to draft version which can be downloaded now. William Stein <https://plus.google.com/u/0/115360165819500279592> Shared publicly - 9:04 AM <https://plus.google.com/u/0/115360165819500279592/posts/ZPjKQzqYju9> Barry Mazur and I can't seem to find any more typos or mistakes in our book "Prime Numbers and the Riemann Hypothesis": http://wstein.org/rh/ Can anybody good at spotting typos see anything critical that needs to be done before this goes into production at Cambridge University Press? David Mumford has written the following very nice endorsement for the book: "This book is a soaring ride, starting from the simplest ideas and ending with one of the deepest unsolved problems of mathematics. Unlike so many popular math books puffed up with anecdotal material, the authors here treat the reader as seriously interested in prime numbers and build up the real math in four stages with compelling graphical demonstrations revealing in deeper and deeper ways the hidden music of the primes. If you have ever wondered why so many mathematicians are obsessed with primes, here’s the real deal.” It goes without saying, but all illustrations and calculations in the book were done using Sage.

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Re: [math-fun] Fwd: New book: Prime Numbers and the Riemann Hypothesis
by Henry Baker 01 Mar '15

01 Mar '15

Many computer scientists use lg(x)=log(x)/log(2). Most simple calculators use "ln" for the natural log function, and mostly use log(x) for ln(x)/ln(10). At 05:25 PM 2/28/2015, Adam P. Goucher wrote: >I use log(x) for the natural logarithm, log(x)/log(2) for the binary logarithm >and log(x)/log(10) for that decimal logarithm that's only ever used for >calculating pH values and decibels.

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[math-fun] Variant of Ulam's spiral
by James Propp 01 Mar '15

01 Mar '15

I recently saw an article that mentioned a variant of Ulam's spiral in which the primes magically form parabolas rather than lines. Can anyone provide a source? Thanks, Jim Propp

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