It would be much more helpful if there was a separate page, titled for example, `Smale's Eversion of the 2-sphere' (or some such) which discussed 2-sphere eversion, pointing to this page on why or why not this is a paradox, rather than around the other way: historically, all existing books and videos refer almost exclusively to `eversion'/ `turning inside out', and not to `Smale's Paradox', which the article wording suggests. While certainly emphasising the inherent visualization difficulties of eversion, they do not become preoccupied with the nature of the word `paradox' in this context, which seems to be the initial focus of this article. Moreover, Smale is not known to have used the word paradox in the courses on immersion theory he taught at Berkeley (such as the one I attended). It would be more positive to concentrate on how to understand an eversion, rather than to create potential barriers by dwelling on the nature of a `paradox', which is the subordinate theme.
It would be more helpful and informative for someone new to Smale's conception and proof of 2-sphere eversion if they were not distracted by issues of what is intuitive or not, or what is or is not a `paradox' of whatever kind, before they were introduced to the concept of sphere eversion: They are then in a better position to decide whether this is or is not counter-intuitive, and to debate whether or not this is a paradox of a particular kind. There is a danger that this page misleads a reader into believing that there is something called `Smale's Paradox' which is in the same conceptual context as `Russell's Paradox': they are not, as the early discussion describes.
My edit of `Smale's Paradox' to include the creation date of the page is directly related to the addition of the reference to Etnyre's review paper of 2004 -- which post-dates the creation of the wiki entry on February 20 2004. One reason for adding the Etnyre reference was presumably to find a paper that references the term `Smale's Paradox', for reasons of historical legitimacy -- an issue I had raised in a previously deleted edit -- and it does no such thing if its date post-dates the date of creation of this page. It is a good pointer to the h-principle, of course. A better reference point, in terms of understanding the chronology of terminology, would be to consider ALL of the videos which had been created beforehand, and observe that NONE of them refer to `Smale's Paradox' as a concept.
There should be no objection to the advertizing of the concept of `Smale's Paradox' per se, but for historical accuracy and cultural integrity, it makes more sense to see this concept as derived from his original work, and not to present things as if always perceived in that way.
As it stands, there is a danger that, for experts in the field, this page may have the flavour of someone's personal desire to have created a `name' for a pre-existing concept, as their own contribution.
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