MOO Oh, how boring it must / be to be a cow. (__) (__) \ (__) (oo) (oo) _______ (oo) /-------\/ \/-------\ // ||\ \ \/------- / | || || | \ _____//___||_\ \___ || | * ||----|| ||----|| * ) _ _ \ ||----|| * ^^ ^^ ^^ ^^ |_/ \________/ \___| ^^ ^^ ______________________________________\_/________\_/__________________________
Beginner's mind is a concept in Zen Buddhism, often referred to by its Japanese name shoshin (初心) or (much less commonly) nyuanshin. As the name suggests, it refers to having an attitude of openness, eagerness, and lack of preconceptions when studying a subject, even when studying at an advanced level, just as a beginner in that subject would.
Imagine you can see the whole Number Line and every one of the infinite individual points it comprises. Imagine you want a quick and easy way to distinguish those points corresponding to rational numbers from the ones corresponding to irrationals. What you're going to do is ID the rational points by draping a bright-red hankie over each one; that way they'll stand out. Since geometric points are technically dimensionless, we don't know what they look like, but we know that it's not going to take a very big red hankie to cover one. The red hankie can in truth be arbitrarily small, like say .00000001 units, or half that size, or half that half, etc. Actually, even the smallest hankie is going to be unnecessarily large ...I hope you enjoyed imagining an infinite number of infinitely small red hankies as much as I did.
In modern medical terms, it's fairly clear that G.P.L.F. Cantor suffered from manic-depressive illness at a time [1800s] when nobody knew what this was, and that his polar cycles were aggravated by professional stresses and disappointments, of which Cantor had more than his share. Of course, this makes for less interesting flap copy than Genius Driven Mad By Attempts To Grapple With ∞. The truth, though, is that Cantor's work and it's context are so totally interesting and beautiful that there's no need for breathless Promethiusizing of the poor guy's life. The real irony is that the view of ∞ as some forbidden zone or road to insanity—which view was very old and powerful and haunted math for 2000+ years—is precisely what Cantor's work overturned. Saying that ∞ drove Cantor mad is like mourning St. George's loss to the dragon; it's not only wrong but insulting.
The standard way [of dealing with the Paradox of Galileo] is to declare infinite sets the math equivalent of unicorns ... The other—which is revolutionary, both intellectually and psychologically—is to treat Galileo's paradoxical equivalence not as a contradiction but as a description of a certain new kind of mathematical entity [as G. Cantor did]... Except on the other hand such an attitude could not be revolutionary but merely insane. Rather like taking the fact that nobody's ever once seen a unicorn as claiming ... that unicorns constitute a whole new kind of animal with the property of invisibility. Here of course we get The Fine Line Between Brilliance and Madness that modern writers/filmmakers dine out on. The truth is that all manner of strange [concepts] originally entered math under the same sort of insanity/incoherence cloud but are now totally accepted, even essential.
