Re: Illusion and Forthrightness in Wikipedia

[Vaughan Pratt <pratt@cs.stanford.edu>]

On 9/17/2010 11:58 PM, Fred E.J. Linton wrote:
> Is it really informative to hide the fact that the color illustration
> (at top) for the (3,7)-torus knot*is*  using the parametrization that
> the text displays, while the b/w (2,3)-torus knot (displayed next) is
> using rather a*different*  style of parametrization, whose details are
> ... well, you see what I'm after? And if I change it, who next will
> change it away again?

At first I thought there must have been some race condition here, until 
I transformed all times including those on Fred's email header into UTC 
(Universal Coordinated Time).  The relevant events in chronological 
order are then

01:52, 14 September: User Selinger "clarified that images don't agree 
with formula," by pointing out in the Wikipedia article that "Other 
parametrizations are also possible, because knots are defined up to 
continuous deformation. The illustrations on this page are derived from 
various different parametrizations."

20:29, 17 September: User Vaughan Pratt "illustrated point about 
different parametrizations" by appending to Peter's second sentence
": for example (leaving z unchanged) the (3,8)-torus knot uses r = 
cos(qφ) + 4 for a smoother effect while the (2,3)-torus knot avoids 
inflexion points altogether by taking x + iy = r e^{pφi} −  3 e^{−φi} 
where r = cos(qφ) − 4."

06:58, 18 September: Fred posted to the categories list as above, namely 
that the 14 September edit was insufficient and that the (2,3)-torus 
knot is using a different *style* of parametrization.

Now Wikipedia edits are seen essentially instantaneously by all users. 
Hence Fred must have based his complaint on the state of the article 
10.5 hours before his post to this list, without checking whether the 
current version still had that defect (e.g. by refreshing the page).

Since x + iy = re^{pφi} − 3e^{−φi} is merely the Euler-De Moivre 
abbreviation for x = r cos(pφi) - 3 cos(−φi), y = r  sin(pφi) - 3 
sin(−φi), I wouldn't call this a change in *style* from the original 
parametrization of x = r cos(pφi), y = r sin(pφi).  (Now that I think of 
it, the abbreviation is not short enough to offset the loss of clarity 
so I unabbreviated it just now.  All these changes can be tracked with 
the article's history page, accessed via the History tab at the top.)

Fred's variable-ellipse representation of the "aflective" 
(inflexion-point-free) trefoil that he posted to this list the other day 
is certainly a change in style, regardless of whether it's equivalent to 
some version of the original style.  But his claim that his is *the* 
representation is called into question by the above parametrization, 
which can be seen at http://boole.stanford.edu/Trefoil.jpg (actually I 
changed it very slightly by decreasing "- 4" to "- 4.3", increasing "- 
3" to "- 2.93", and rotating the figure 90 degrees clockwise, for a 
closer match to the figure, but perhaps the figure should be changed 
instead).

But whether the Wikipedia figure is a better match to my parametrization 
or to Fred's is I would say moot given that there is no need to change 
parametrization *style* to get an aflective trefoil, as should be clear 
from http://boole.stanford.edu/Trefoil.jpg .

Even more puzzling to me is that prior to Fred's posting to this list on 
this topic he had sent me 32 emails regarding his problem of drawing a 
trefoil-shaped logo in Postscript, and I'd answered him 25 times, to his 
complete satisfaction I thought.  That he then turned to the categories 
list for further help with trefoils would seem to indicate that I'd been 
less helpful than I thought.  I guess I can justify whatever he found 
unhelpful with the observation that with free consulting you get what 
you pay for.

Vaughan Pratt


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