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Topic: Which Polynomial?
Replies: 28   Last Post: Jul 27, 2006 3:13 PM

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Victor Steinbok

Posts: 1,580
Registered: 12/3/04
Re: Which Polynomial?
Posted: Jul 31, 2005 10:36 PM
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At 09:07 PM 7/31/2005, luciepoirier wrote:

>The convergence is quite easily derived. With Phi = (1+SQRT5)/2, as n goes
>to infinity, |(1-SQRT5)/2|^n (<1) goes to zero so lim[f(n+1)/f(n)] for n ->
>inf is Phi.
>It's indeed a very rich topic (multiple points of entry -> connections)

Thank you for doing the derivation. It's been long enough that I did not
have the full recall and I have been swamped this week so didn't have the
opportunity to redo the detailed analysis.

I want to point out that my objection to Kirby had nothing to do with the
richness of the problem or the context. My concern is the same as in the
case of any prescriptive curriculum. The fact that something is rich and
interesting is not a justification for mandating, but merely a strong
indication that it can be a recommended approach. I have noted in the past
that neither the reform nor anti-reform crowd seems to get this. I know
that this exactly what got Wayne & Co to arbitrarily place me deeply in the
ultra-fuzzy camp. Of course, they chant the Bush mantra everyday: "Either
you are with us or you are with the terrorists." So it's pointless to argue
with them about relative merits of anything. Of course, left to their own
devices, they will eventually encounter parts of curricula on which they
disagree. At the point, they'll either resort to another (un)civil war or
will lose interest in the subject. My concern is not with their eventual
demise but the damage they would do in the meantime.

Many would-be reformers suffer from a similar Napoleonic complex.
Sometimes, well-intentioned attempts to improve the standards also run into
absolutists bureaucrats who don't get the difference between mandates and
recommendations. This is how examples of good ideas (as I think Kirby's is)
end up as required elements of state curricula. Unfortunately, both sides
recognize only the extremes. The fact that the majority of practitioners is
and should be in the middle, does not stop them from pulling the standards
to the extremes. Although there is a reason to be concerned that being
"centrist" is a wishy-washy, spineless position (just take a look at
Lincoln Chafee), this need not be the default state for a "centrist". Being
in the middle means carefully navigating the issues and making independent
decisions--something that the zealots on either sides could never accept.


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