Measuring Fractal Dimension ?

[Mark Dickinson]

On Jun 23, 3:52 am, Steven D'Aprano
<ste... at REMOVE.THIS.cybersource.com.au> wrote:
> On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote:
> > In my universe the standard definition of "log" is different froim what
> > log means in a calculus class
>
> Now I'm curious what the difference is.

It's just the usual argument about whether 'log' means
log base 10 or log base e (natural log).  At least in the
US, most[*] calculus texts (and also most calculators),
for reasons best known to themselves, use 'ln' to mean
natural log and 'log' to mean log base 10.  But most
mathematicians use 'log' to mean natural log:  pick up a
random pure mathematics research paper that has the word
'log' in it, and unless it's otherwise qualified, it's
safe to assume that it means log base e.  (Except in the
context of algorithmic complexity, where it might well
mean log base 2 instead...)

Python also suffers a bit from this confusion:  the
Decimal class defines methods 'ln' and 'log10', while
the math module and cmath modules define 'log' and
'log10'.  (But the Decimal module has other problems,
like claiming that 0**0 is undefined while
infinity**0 is 1.)

[*] A notable exception is Michael Spivak's 'Calculus', which also
happens to be the book I learnt calculus from many years ago.

Mark