Blog Profile / Good Math, Bad Math
| URL : | http://scientopia.org/blogs/goodmath/ | |
|---|---|---|
| Filed Under: | Academics / Mathematics | |
| Posts on Regator: | 279 | |
| Posts / Week: | 1.2 | |
| Archived Since: | December 12, 2008 | |
Blog Post Archive
Probability and Interpretations
I'm going to do some writing about discrete probability theory. Probability is an extremely important area of math. We encounter aspects of it every day. It's also a very poorly understood area - it's one that we see abused or just fouled up every day. I'm going to focus on discrete probability theory. What that [...]
Speed-Crankery
A fun game to play with cranks is: how long does it take for the crank to contradict themselves? When you're looking at a good example of crankery, it's full of errors. But for this game, it's not enough to just find an error. What we want is for them to say something so wrong [...]
The Gravitational Force of Rubbish
Imagine, for just a moment, that you were one a group of scientists that had proven the most important, the most profound, the most utterly amazing scientific discovery of all time. Where would you publish it? Maybe Nature? Science? Or maybe you'd prefer to go open-access, and go with PLOS ONE? Or more mainstream, and [...]
What the heck is a DNS amplification DoS attack?
A couple of weeks ago, there was a bunch of news about a major DOS attack on Spamhaus. Spamhaus is an online service that maintains a blacklist of mail servers that are known for propagating spam. I've been getting questions about what a DoS attack is, and more specifically what a "DNS amplification attack" (the [...]
A White Boy's Observations of Sexism and the Adria Richards Fiasco
I've been watching the whole Adria Richards fiasco with a sense of horror and disgust. I'm finally going to say something, but for the most part, it's going to be indirect. See, I'm a white guy, born as a member of an upper middle class white family. That means that I'm awfully lucky. I'm part [...]
Genius Continuum Crackpottery
There's a lot of mathematical crackpottery out there. Most of it is just pointless and dull. People making the same stupid mistakes over and over again, like the endless repetitions of the same-old supposed refutations of Cantor's diagonalization. After you eliminate that, you get reams of insanity - stuff which is simply so incoherent that [...]
Pi-day randomness
One of my twitter friends was complaining about something that's apparently making the rounds of Facebook for ?-day. It annoyed me sufficiently to be worth ranting about a little bit. Why isn't ? rational if ?=circumference/diameter, and both measurements are plainly finite? There's a couple of different ways of interpreting this question. The stupidest way [...]
Finally: Gödel's Proof of Incompleteness!
Finally, we're at the end of our walkthrough of Gödel great incompleteness proof. As a refresher, the basic proof sketch is:
Passwords, Hashing, and Salt
Over on twitter, some folks were chatting about the latest big security botch. A major service, called Evernote, had a security breach where a password file was stolen. Evernote has handled the situation quite well, being open about what happened, and explaining the risks. In their description of the breach, they said that the stolen [...]
New Dimensions of Crackpottery
I have, in the past, ranted about how people abuse the word "dimension", but it's been a long time. One of my followers on twitter sent me a link to a remarkable piece of crackpottery which is a great example of how people simply do not understand what dimensions are. There are several ways of [...]
The Intellectual Gravity of Brilliant Baseball Players
Some of my friends at work are baseball fans. I totally don't get baseball - to me, it's about as interesting as watching paint dry. But thankfully, some of my friends disagree, which is how I found this lovely little bit of crackpottery. You see, there's a (former?) baseball player named Jose Canseco, who's been [...]
Euler's Equation Crackpottery
One of my twitter followers sent me an interesting piece of crackpottery. I debated whether to do anything with it. The thing about crackpottery is that it really needs to have some content. Total incoherence isn't amusing. This bit is, frankly, right on the line. Euler's Equation and the Reality of Nature. a) Euler's Equation [...]
The Meta of Gödel
As you may be figuring out, there's a reason why I resisted walking through Gödel's proof of incompleteness for so long. Incompeteness isn't a simple proof! To refresh your memory, here's a sketch of the proof: Take a simple logic. We've been using a variant of the Principia Mathematica's logic, because that's what Gödel used. [...]
Defining Properties Arithmetically (part 1): Gödel and Primitive Recursion
When I left off, we'd seen how to take statements written in the logic of the Principia Mathematica, and convert them into numerical form. What we need to see now is how to get meta-mathematical. We want to be able to write second-order logical statements. The basic trick to incompleteness is that we're going to [...]
G&oum;del Numbering: Encoding Logic as Numbers
The first step in Gödel's incompleteness proof was finding a way of taking logical statements and encoding them numerically. Looking at this today, it seems sort-of obvious. I mean, I'm writing this stuff down in a text file - that text file is a stream of numbers, and it's trivial to convert that stream of [...]
Gödel's Incompleteness
I've mentioned Gödel's incompleteness theorems many times on this blog, but I've never actually written about them in detail. I was asking, on twitter, for topics that readers would be interested in, and one thing that came up is actually go through the proof of incompleteness. I'm happy to take the time to do that [...]
Least Square Linear Regression
There's one topic I've been asked about multiple times, but which I've never gotten around to writing about. It happens to be one of the first math things that my dad taught me about: linear regression. Here's the problem: you're doing an experiment. You're measuring one quantity as you vary another. You've got a good [...]
Not Really Free Energy from Silicon and Water
A reader sent me a link to an article about a new technique for producing hydrogen. His original request was for me to debunk it, because it looked like another free energy scam. But it isn't, so I'm going to attempt to explain why. BUFFALO, N.Y. — Super-small particles of silicon react with water to [...]
Recipe: Kimchi-Marinated Steak Sandwich
Last weekend, I was watching cooking shows on PBS. One of my favorite chefs, Ming Tsai, came on. Along with a guest, he ad-libbed a dish that looked absolutely phenomenal: a kimchi marinated cheesesteak sandwich. I didn't write down the recipe; I just took the idea, and ran with it. I mean come on, what [...]
Back to an old topic: Bad Vaccine Math
The very first Good Math/Bad Math post ever was about an idiotic bit of antivaccine rubbish. I haven't dealt with antivaccine stuff much since then, because the bulk of the antivaccine idiocy has nothing to do with math. But the other day, a reader sent me a really interesting link from what my friend Orac [...]