# Cantor Crankery

So, another bit of Cantor stuff. This time, it really isn't Cantor
crankery, so much as it is just Cantor muddling. The
href="http://rjlipton.wordpress.com/2010/06/11/does-cantors-diagonalization-proof-cheat/">post
that provoked this is not, I think, crankery of any kind - but it
demonstrates a common problem that drives me crazy; to steal a nifty phrase
from youaredumb.net, people who can't count to meta-three really shouldn't try
to use metaphors.
The problem is: You use a metaphor to describe some concept. The metaphorisn't the thing you describe - it's just a tool that you use. But…

A bunch of people have been asking me to take a look at
href="http://arxiv.org/abs/1002.4433">yet another piece of Cantor crankery
recently posted to Arxiv. In general, I'm sick and tired of Cantor crankery -
it's been occupying much too much space on this blog lately. But this one is a
real prize. It's an approach that I've never seen before: instead of the usual
weaseling around, this one goes straight for Cantor's proof.
But it does much, much more than that. In terms of ambition, this thing
really takes the cake. According to the author, one J. A. Perez, he doesn't
just refute…

So, remember back in December, I wrote a post about a Cantor crank
who had a Knol page supposedly refuting Cantor's diagonalization?
This week, I foolishly let myself get drawn into an extended conversation
with him in comments. Since it's a comment thread on an old post that had been inactive for close to two months before this started, I assume most people haven't followed it. In
an attempt to salvage something from the time I wasted with him, I'm going to
share the discussion with you in this new post. It's entertaining, in a pathetic sort of way; and it's enlightening, in that it's one…

Poor Georg Cantor.
During his life, he suffered from dreadful depression. He was mocked by
his mathematical colleagues, who didn't understand his work. And after his
death, he's become the number one target of mathematical crackpots.
As I've mentioned before, I get a lot of messages either from or
about Cantor cranks. I could easily fill this blog with nothing but
Cantor-crankery. (In fact, I just created a new category for Cantor-crankery.) I generally try to ignore it, except for that rare once-in-a-while that there's something novel.
A few days ago, via Twitter, a reader sent me a…

I've been getting lots of mail from readers about a
href="http://knol.google.com/k/are-real-numbers-uncountable#">new article on Google's Knol about
Cantor's diagonalization. I actually wrote about the authors argument
href="http://scienceblogs.com/goodmath/2009/01/the_continuum_hypothesis_solve.php">once
before about a year ago.
But the Knol article gives it a sort of new prominence, and since
we've recently had one long argument about Cantor cranks, I think it's
worth another glance.
It's pretty much another one of those cranky arguments where they say "Look! I found a 1:1…

Another chaos theory post is in progress. But while I was working on it, a couple of
comments arrived on some old posts. In general, I'd reply on those posts if I thought
it was worth it. But the two comments are interesting not because they actually lend
anything to the discussion to which they are attached, but because they are perfect
demonstrations of two of the most common forms of crackpottery - what I call the
"Education? I don't need no stinkin' education" school, and the "I'm so smart that I don't
even need to read your arguments" school.
Let's start with the willful ignorance.…

Of all of the work in the history of mathematics, nothing seems to attract
so much controversy, or even outright hatred as Cantor's diagonalization. The idea of comparing the sizes of different infinities - and worse, of
actually concluding that there are different infinities, where some infinities are larger than others - drives some people absolutely crazy. As a result,
countless people bothered by this have tried to come up with all sorts
of arguments about why Cantor was wrong, and there's only one infinity.
Today's post is another example of that. This one is sort of special. Unless I'…

Now, it's time for the final chapter in my "visits with old friends" series, which brings us
back to the Good Math/Bad Math all-time reader favorite crackpot: Mr. George Shollenberger.
Last time I mentioned George, a number of readers commented on the fact that it's cruel to pick on poor George, because the guy is clearly not all there: he's suffered from a number of medical problems which can cause impaired reasoning, etc. I don't like to be pointlessly cruel, and in general, I think it's inappropriate to be harsh with someone who is suffering from medical problems - particularly medical…