Talk:WikiJournal of Science/A card game for Bell's theorem and its loopholes/Impossible correlations

Moving a bad section to talk page.

 * I don't know what I was thinking when I wrote this lede section:

Here we extend the analogy of Bell's theorem beyond that of a card game to account for the fact that researchers in the field do not typically "keep score" as if they were playing an unfair game of chance against entangled particles. Instead they establish correlations between remote events that are, in a manner of speaking, "impossible". Also, the switching of detection angles for photon polarization usuallly involves only two options, instead of the three suits used to pose the "questions" in the card game. This requires that Bell's original inequality be replaced by the CHSH inequality.

To appreciate the need for mathematical simplicity while teaching this philosophically significant topic, consider this flawed argument:

$$i=\sqrt{-1} \implies$$ $$i^4 = 1 \implies$$ $$(i^4)^{1/4} = 1^{1/4}$$ $$\quad |\underline\overline{\,\therefore i = 1\,} |$$

What went wrong? One might answer this question by reviewing the rules of algebra, perhaps including the fact that f(z)=z1/4 is a multivalued function on the complex plane. But the real problem is that mathematics is so important that educators don't have the time to include rigor without greatly extending the time it takes to become mathematically literate. Neither the teachers nor the students are at fault. But, since there is no reason for students to trust that mathematics is (almost always) rigorous, we should avoid calculus and use only the most transparent algebra. On the other hand, since they are so ubiquitous in everyday life, there is value in using spreadsheets to develop arguments. Guy vandegrift (discuss • contribs) 00:12, 12 February 2024 (UTC)