How about "Bernewli" numbers? Sent from my iPhone On Sep 15, 2013, at 16:57, Eugene Salamin <gene_salamin@yahoo.com> wrote:
It would cause much less confusion if a new name is associated with the new definition, e.g. a "new-Bernoulli" number.
-- Gene
________________________________ From: Gareth McCaughan <gareth.mccaughan@pobox.com> To: math-fun@mailman.xmission.com Sent: Sunday, September 15, 2013 1:50 PM Subject: Re: [math-fun] The Bernoulli Manifesto
On 15/09/2013 17:05, Hans Havermann wrote:
Back in 2004, Peter Luschny wrote an open letter to Donald E. Knuth about his conviction that the proper definition of the Bernoulli number B(1) should be 1/2, not -1/2. Professor Knuth declined to embrace the idea. ... Peter has now put up a detailed response to Knuth, calling it The Bernoulli Manifesto.
As Knuth says (and Luschny agrees), there are lots of little issues of this kind. Perhaps what is called for is a widely agreed upon set of New Conventions, with a website and (if anyone will publish it) a manifesto in a widely read journal, so that mathematicians wanting to break with the mistakes of the past can just begin their papers with something like
In this paper I use the so-called New Conventions of mathematical notation documented at www.newconventions.org and in [1]; in particular, note that the definitions used here for the Bernoulli numbers $B_k$ and the gamma function $\Gamma(z)$ may be unexpected.
(I don't actually think it makes sense to change the definition of the gamma function -- better just to abandon it in favour of the factorial function -- but never mind that. It's just an example.)
For this to have any chance of success, the new conventions would be appealing enough *collectively* to persuade a reasonable number of mathematicians to adopt them wholesale. There would probably need to be a preliminary round of opinion-canvassing.
All of which would doubtless seem like a total waste of time to many mathematicians. But if the end result were half an hour less of wasted head-scratching for each of 20k undergraduates once a year (let's assume, contrary to fact, that by the time a mathematician is properly trained all these poor conventions cease to cause any extra work or annoyance) then it would be worth a substantial one-off effort.
I doubt it'll ever happen. Herding cats, etc.
-- g
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