Re: Flies in the ointment.

From: Tim Peters (tim.one_at_comcast.net)
Date: 03/17/05 

Date: Wed, 16 Mar 2005 23:28:45 -0500

[Tim Peters]
...
>> I also stumbled into this amazing scam on Wikipedia:
>>
>> "John Gabriel's Nth root algorithm"
>> http://en.wikipedia.org/wiki/John_Gabriel%27s_Nth_root_algorithm
>>
>> Nothing wrong with the algorithm, but it's just a clumsily-stated
>> direct application of Newton's method to finding a zero of f(y) = y^n-x
>> (iterate y <- y - f(y)/f'(y)). This certainly doesn't go under the
>> name of "John Gabriel" in any numerical analysis circles I've run
>> in <heh>.

[r.e.s.]
> Surprisingly, it's cited at
> http://www.cs.princeton.edu/introcs/96optimization/

Brrrrrr.

> which seems not to recognize it as an application of Newton's Method.
> It is somewhat interesting that the recurrence relation has been
> written in the form of an *average* (shades of an "average tangent"?).

Well, it's a weighted averge, and it's not unusual to write it like that;
e.g.,

http://www.gnu.org/software/gmp/manual/html_node/Nth-Root-Algorithm.html

It takes a bit of algebraic manipulation to get it into that form, so I'm
not surprised if a teacher who understands Newton-Raphson but hasn't
actually applied it to n-th roots in anger didn't recognize the
weighted-average form. Still, to give a reference to a web page that can't
do better than characterize its convergence as "much faster" is pretty lame
even for a professor <wink>.

> This post is even more interesting ...
> http://mathforge.net/index.jsp?page=seeReplies&messageNum=635
> "There are infinitely many numbers between 0.999.. and 1
> [...] My name is JOhn Gabriel and I am on a crusade [...]
> Why not call 0.999... what it really is - an irrational
> like 1/3, pi, e or sqrt(2)."

Excellent! That link just took me to the top of a large page, so I started
skimming down. When I got to:

    There are infinitely many numbers between 0.999.. and 1
    Submitted By: Anonymous (Fri, 06 Aug 04 at 00:31:11 PST)

    By definition, 0.999.. is less than 1.

    ... 1000 100 10 Units . 1/10 1/100 1/1000 1 . 0 0 0 0 . 9 9 9 ...

    Look at the above carefully! Now most mathematicians are
    unfortunately fools and will pull out all stops to cover their
    folly.

my first thought was "ah, so Jason Wells posted here too". Giving 1/3 as an
example of an irrational just nailed it. LOL -- maybe they're just
identical twins. I _would_ like to believe this kind of insanity is
confined to rare unfortunate families <wink>.

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