Crankiness!

[sniffnoy]

Eventually I remembered how this guy wanted to create a theory of "arbitrarily large sets" to replace the current understanding of cardinality ("transfinite theory", as he always refers to it), and a Google on that turned it up. Behold: A Critique (*snicker*) of the Diagonal Method. I'm not going to even begin to point out the problems with this, there are so many. OK, I'll point out one: a paradox is when you derive a contradiction. How does "Galileo's Paradox" meet that criterion?! OK, one more: everyone knows that the diagonal proof is closely related to Russell's Paradox. The fact that it's closely related to a paradox does not make it a paradox! Anyway. I misremembered, he does not actually compare set theory - er, sorry, "transfinite theory" - to Naziism; rather he says that it gave laid the foundations for both Naziism and Communism. Amazing.

Now that I've found this again, I'm going to sumbit it to crank.net.

(Not to mention he also claims that .9999...≠1)

Comments

[jonpin.livejournal.com]

.9999... != 1 is nothing new for internet idiots. I remember flipping through some Usenet threads on google groups about that topic. They just invent a concept of infinity and expect others to obey it.

[dreyonlegacy.livejournal.com]

I'd say that was the stupidest, most misguided thing I've seen in a while, except for the fact that I stumbled across "The Evolution Crusher" a couple days ago while making fun of Intelligent Design proponents on a science forum. It comes close, though, although hampered in this quest by being significantly shorter than The Evolution Crusher.

[mathnerdguy.livejournal.com]

Well I got bored with the Diagonal thing, but his thing about .9999... isn't actually all that bad. He basically just talks about things like the hyperreals, I think. I don't think he realizes that mathematicians have been doing stuff like the things he's talking about for ages. It's kind of amusing. And also sad.

[mathnerdguy.livejournal.com]

Oh, man, I'm really tempted to write him a letter that explains the basics of real analysis, but he would probably just bitch about infinite sequences or some such shit, if he read it at all.

Plus, there are just too many cranks in the world to explain to each of them the basics of real analysis.

Still, this one seems like he's actually thought about that .999...=1 stuff. Besides, there are a lot of people who know real analysis. If every one of them explained it to one crank, maybe the world would be a better place.

[jonpin.livejournal.com]

Upon actual reading, my favorite part is the critique of Hibbert's Hotel. The first link I clicked to it said only Room 404 was open, but eventually I got there.

Surely, if there is an example involving an intellectual cripple, like a bellhop, then the proof must be true.
If the teacher moves quickly to the next example, the infinite hotel is a convincing argument; However, if the teacher drops an eraser and the students accidentally start to think, the example can take a turn for the worst. As we all know, students who think often turn into intuitionalists.

Realizing that he had a big problem, Al did as most great men do. He put the guest's money in the safe, then murdered the guest and hid the body where no one could find it...Al had, after all, a transfinite consciousness that should not be sullied with reality.

Also, the "Infinite hotels are overrated. Book a room at a finite hotel by clicking here."

[sniffnoy.livejournal.com]

The other thing I noticed was that, while I didn't read his whole "rich theory" thing in too much detail, it seemed to me that what it was basically saying was that cardinality is often not the best way to measure the size of a set, which is, of course, absolutely true. He just doesn't seem to realize that mathematicians *have* other ways of measuring sizes of sets, and that the fact that it's often not appropriate doesn't make the notion of cardinality defined by bijections and injections invalid.