What's your IQ? ... Aptitude test results?

[Ganoncrotch]

ebw said:

Teeqoz said:

I actually knew the answer to that haha. And also, Mensa can eat shit, because true Klein bottles can only exist in 4D.

When's the last time you tried embedding a Möbius strip in two-dimensional (Euclidean) space?  True Möbius strips can only exist in 3D, or higher.

It is a terrible, terrible question relying on popular misconceptions, but it's not terrible for the reason you claim.  The Klein bottle has the same dimension as the Möbius strip: they're both two-dimensional surfaces, so the analogy is very poor.  One of them has a boundary (an exposed edge), while the other is closed.  One can be realized in R^3 while the other can only be immersed in R^3 and embedded in R^4.  That doesn't imbue the Klein bottle with higher dimensionality.

A better answer might have been the solid Klein bottle, which is a 3-dimensional manifold with boundary, just as the Möbius strip is a 2-dimensional manifold with boundary.  But that is a distinct object — it's as different from a Klein bottle as the Möbius strip is different from a circle (1-sphere).

The main issue isn't with the question though, flawed as it might be, the issue is if you know that information or not does that mean you have a more capable brain than someone who happens to have gone through life without encountering this object or information about it? This to me makes IQ tests less a true measure of persons capabilities mentally but more of a pub quiz level of knowledge, fantastic if you happen to know some of the things which happen to come up in your exam, but most certainly not something to be thought of having any indication of someones ability to learn or figure things out in the future or during their lives.

I don't mean to diss your knowledge of the Klein bottle though, I have been educated today! but like it was mentioned by Einstein, if you learn off the contents of a dictionary, does that mean you are more likely to be able to put those contents into use with a problem than someone who happens to have a dictionary with them but knows not what it contains, but how best to use the dictionary to find information that he needs to deal with what he encounters.