Good Math, Bad Math

Moving on

Category:

Finally, at long last, I can tell you what I've been up to with finding a new home for this blog. I've created a new, community-based science blogging site, called Scientopia. With the help of many wonderful people, we're ready. We launched this morning. So to continue following GM/BM - along with the work of many other wonderful bloggers, like Scicurious, Grrlscientist, Mike Dunford, Dr. Skyskull, and lots of others, come on over to Scientopia, the new home of Good Math/Bad Math"/a>.

Posted by Mark C. Chu-Carroll at 10:41 AM •

Goodbye, Scienceblogs

Category:

So my decision is made. I'm closing up around here. I'm in the process of working out exactly where I'm going to go. With any luck, Seed will leave this blog here long enough for me to post an update with the new location. But I'm through with Seed and ScienceBlogs.

Posted by Mark C. Chu-Carroll at 10:01 PM • 78 Comments

Seed, Conflicts of Interest, and Sleaze

Category:

As my friend Pal wrote about, Seed Media Group, the corporate overlords of the ScienceBlogs network that this blog belongs to, have apparently decided that blog space in these parts is now up for sale to advertisers.

We've been advertiser supported since I joined up with SB. I've never minded that before. Providing a platform and bandwidth takes money, which has to come from somewhere. The way that ads have been handled before has been no problem: the ads are clearly distinguished from the content. There's no way that you're going to mix up one of my posts with a paid advertisement.

Until now.

Seed has, in its corporate wisdom, decided to let Pepsico buy its way into a blog on ScienceBlogs. Pepsi writes SMG a nice check, and suddenly their content gets mixed in to the ScienceBlog RSS feeds, the ScienceBlog feed to Google News, etc., exactly the way that my blog posts do.

This is not acceptable.

For now, I'm suspending my blog for a few days. If Seed decides to back out of this spectacular stupidity, then I'll start posting here again. If not, then I'll go looking for a new home for GM/BM. The money that I've made from the ads that Seed has sold has been nice - but it's not worth my integrity.

If Blogs here are for sale, then I'm gone.

Posted by Mark C. Chu-Carroll at 8:47 PM • 35 Comments

Searching for Topics

Category: goodmath

As regular readers have no doubt noticed by now, posting on the blog has been slow lately. I've been trying to come back up to speed, but so far, that's been mainly in the form of bad math posts. I'd like to get back to the good stuff. Unfortunately, the chaos theory stuff that I was posting just isn't good for my schedule right now. Once you get past the definitions of chaos, and understanding what it means, actually analyzing chaotic systems is something that doesn't come easily to me - which means that it takes a lot of time to put together a post. And my work schedule right now means that I just don't have that amount of time.

So, dear readers, what mathematical topics would you be particularly interested in reading about? Since I'm a computer scientist, my background obviously runs towards the discrete math side of the world - so, for the most part, the easiest topics for me to write about are from that side. But don't let that limit you: tell me what you want to know about, and I'll take the suggestions into consideration, and figure out which one(s) I have the time to study and write about.

I don't want to limit you by making suggestions. I've tried that in the past, and the requests inevitably end up circling around the things I suggested. But I really want to know just what you want to know more about. So - fire away!

Posted by Mark C. Chu-Carroll at 11:02 AM • 94 Comments

Saturday Recipe: Ginger Scallion Sauce

Category: Recipes

Today's recipe is something I made this week for the first time, and trying it was like a revelation. It's simple to make, it's got an absolutely spectacularly wonderful flavor - light and fresh - and it's incredibly versatile. It's damned near perfect. It's scallion ginger sauce, and once you try it, it will become a staple. To quote David Chang, whose cookbook I learned this from: if you've got ginger scallion sauce in the fridge, you'll never be hungry.

There are two main variations of this: there's a cooked version, and a raw version. Mine is the raw version. I love the freshness of flavor, and while cooking it will intensify some of the flavors, it will also detract from that delightful freshness.

Ingredients

• Fresh ginger - roughly one inch, peeled.
• A bunch of fresh scallions.
• A teaspoon, give or take, of coarse salt.
• 1 tablespoon of soy sauce.
• 1 tablespoon rice vinegar.
• 1/4 cup oil - peanut oil, canola oil, or something other neutral oil.
• A dash of sesame oil.

Instructions

• Mince the ginger. Toss the minced ginger into a food processor.
• Cut the roots off of the scallions, cut them coarsely, and add them to the food processor.
• Add the rest of the ingredients to the food processor.
• Run the food processor until everything is finely ground into a smooth sauce.

That's it. Ginger scallion sauce. Taste it - make sure it's got enough salt. Don't add any soy sauce - just use plain salt if it needs any.

So what can you do with it? Just about anything. A few great ideas:

1. Ramen noodles. Just cook up a batch of ramen, and toss it with a tablespoon of the sauce. You can also add some stir fried meat and veggies to make it a bit more filling.
2. Grilled meats. Use a bit of the sauce as a marinade, then grill it, and dress it with a bit of the sauce when it's done.
3. Use it instead of mayo on a sandwich.
4. Add a bit more vinegar, and use it as a vinaigrette over a salad.
5. Sautee some shrimp, and toss some ginger-scallion sauce in just before they're done.
6. Get a nice whole fish, steam it cantonese style with just a bit of salt, soy, and sake. Spoon a bit of the sauce over it when it's done.

If you wanted to try to cooked version, you take the ginger, scallions, and salt, and puree them in the food processor. Then put them into a large pot. In a different pot, heat the oil up until it just starts to smoke, and then pour it over the ginger/scallion/salt mixture. When it cools, whisk in the rest of the ingredients.

But like I said - I think it's best to just stick with it raw.

Posted by Mark C. Chu-Carroll at 5:19 PM • 5 Comments

The Surprises Never Eend: The Ulam Spiral of Primes

Category: Numbers • goodmath

One of the things that's endlessly fascinating to me about math and science is the way that, no matter how much we know, we're constantly discovering more things that we don't know. Even in simple, fundamental areas, there's always a surprise waiting just around the corner.

A great example of this is something called the Ulam spiral, named after Stanislaw Ulam, who first noticed it. Take a sheet of graph paper. Put "1" in some square. Then, spiral out from there, putting one number in each square. Then circle each of the prime numbers. Like the following:

If you do that for a while - and zoom out, so that you can't see the numbers, but just dots for each circled number, what you'll get will look something like this:

That's the Ulam spiral filling a 200x200 grid. Look at how many diagonal line segments you get! And look how many diagonal line segments occur along the same lines! Why do the prime numbers tend to occur in clusters along the diagonals of this spiral? I don't have a clue. Nor, to my knowledge, does anyone else!

And it gets even a bit more surprising: you don't need to start the spiral with one. You can start it with one hundred, or seventeen thousand. If you draw the spiral, you'll find primes along diagonals.

Intuitions about it are almost certainly wrong. For example, when I first thought about it, I tried to find a numerical pattern around the diagonals. There are lots of patterns. For example, one of the simplest ones is that an awful lot of primes occur along the set of lines f(n) = 4n²+n+c, for a variety of values of b and c. But what does that tell you? Alas, not much. Why do so many primes occur along those families of lines?

You can make the effect even more prominent by making the spiral a bit more regular. Instead of graph paper, draw an archimedean spiral - that is, the classic circular spiral path. Each revolution around the circle, evenly distribute the numbers up to the next perfect square. So the first spiral will have 2, 3, 4; the next will have 5, 6, 7, 8, 9. And so on. What you'll wind up with is called the Sack's spiral, which looks like this:

This has been cited by some religious folks as being a proof of the existence of God. Personally, I think that that's silly; my personal belief is that even a deity can't change the way the numbers work: the nature of the numbers and how they behave in inescapable. Even a deity who could create the universe couldn't make 4 a prime number.

Even just working with simple integers, and as simple a concept of the prime numbers, there are still surprises waiting for us.

Posted by Mark C. Chu-Carroll at 11:58 AM • 68 Comments

Metaphorical Crankery: a bad metaphor is like a steaming pile of ...

Category: 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 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 metaphor isn't the thing you describe - it's just a tool that you use. But someone takes the metaphor, and runs with it, making arguments that are built entirely on metaphor, but which bear no relation to the real underlying concept. And they believe that whatever conclusions they draw from the metaphor must, therefore, apply to the original concept.

In the context of Cantor, I've seen this a lot of times. The post that inspired me to write this isn't, I think, really making this mistake. I think that the author is actually trying to argue that this is a lousy metaphor to use for Cantor, and proposing an alternative. But I've seen exactly this reasoning used, many times, by Cantor cranks as a purported disproof. The cranky claim is: Cantor's proof is wrong, because it cheats.

Of course, if you look at Cantor's proof as a mathematical construct, it's a perfectly valid, logical, and even beautiful proof by contradiction. There's no cheating. So where do the "cheat" claims come from?

Read on »

Posted by Mark C. Chu-Carroll at 1:45 PM • 50 Comments

The Unfalsifiable Theory Of Everything from viXra

Category: bad physics

Today is another bit of rubbish from viXra! In the comment thread from the last post, someone (I presume the author of this paper) challenged me to address this. And it's such a perfect example of one of my mantras that I can't resist.

What's the first rule of GM/BM? The worst math is no math.

And what a whopping example of that we have here. It's titled "Spacetime Deformation Theory", by one Jacek Safuta. I'll quote the abstract in its entirety, to give you the flavor.

The spacetime deformations theory unifies general relativity with quantum mechanics i.e. unifies all interactions, answers the questions: why particles have mass and what they are, answers the question: what is energy, unifies force fields and matter, implies new theories like spacetime deformations evolution.

This is a theory of principle (universal theory delivering description of nature) and not constructive theory (describing particular phenomenon using specific equations).

The theory is falsifiable, background independent (space has no fixed geometry), not generating singularities or boundaries.

This is hard to believe but a belief has nothing to with it. The real intellectual challenge is to falsify the theory.

Read on »

Posted by Mark C. Chu-Carroll at 2:29 PM • 63 Comments

Gravity, Shmavity. It's the heat, dammit!

Category: bad physics

Sorry for the ridiculously slow pace around here lately; I've been ridiculously busy. I'm changing projects at work; it's the end of the school year for my kids; and I'm getting close to the end-game for my book. Between all of those, I just haven't had much time for blogging lately.

Anyway... I came across this lovely gem, and I couldn't resist commenting on it. (Before I get to it, I have to point out that it's on "viXra.org". viXra is "ViXra.org is an e-print archive set up as an alternative to the popular arXiv.org service owned by Cornell University. It has been founded by scientists who find they are unable to submit their articles to arXiv.org because of Cornell University's policy of endorsements and moderation designed to filter out e-prints that they consider inappropriate.". In other words, it's a site for cranks who can't even post their stuff on arXiv. Considering some of the dreck that's been posted an arXiv, that's pretty damned sad.)

In my experience, when crackpots look at physics, they go after one of two things. Either they pick some piece of modern physics that makes them uncomfortable - like relativity or quantum mechanics - and they try to force some argument that their discomfort with it must mean that it's wrong. The other big one is free energy - whether it's perpetual motion, or vacuum energy, or browns gas - the crackpots claim that they've found some wonderful magical process that defies the laws of thermodynamics in order to make limitless free energy. The cranks rarely (not never, but rarely) go after the kinds of physics that we experience every day.

Well, this is something different. This guy basically wants to claim that gravity doesn't really exist. And along the way, he claims to have solved the problems of dark matter and dark energy. See, we've all got it totally wrong about gravity! Gravity isn't a force where matter attracts other matter. It's a force where warm things attract other warm things! Gravity is actually a force created when things radiate heat.

Read on »

Posted by Mark C. Chu-Carroll at 11:47 AM • 100 Comments

Big Number Bogosity from a Christian College Kid

Category: Bad Probability • Big Numbers

I know that I just posted a link to a stupid religious argument, but I was sent a link to another one, which I can't resist mocking.

As I've written about quite often, we humans really stink at understanding big numbers, and how things scale. This is an example of that. We've got a jerk who's about to graduate from a dinky christian college, who believes that there must be something special about the moral atmosphere at his college, because in his four years at the school, there hasn't been a single murder.

Yeah, seriously. He really believes that his school is special, because it's gone four whole years without a murder:

Considering that the USA Today calculated 857 college student deaths from 2000 to 2005, how does one school manage to escape unscathed? It's certainly not chance or luck. For Patrick Henry College, it's in our Christian culture.

Critics mock us for our strict rules - like no dancing or drinking on campus, no members of the opposite sex permitted in your dorm room, nightly curfew hours - and the lack of a social atmosphere it creates. We have been the subject of books (God's Harvard), television shows, op-eds, and countless blogs who rant against our brand of overbearing right-wing Christianity that poisons society's freedom.

Yet, what is the cost of students being able to "express" themselves? Is that freedom worth the cost of drunk driving deaths, drug related violence, and love affairs turned fatal?

There were 857 college student deaths in the five-year period from 2000 to 2005! Therefore, any college where there weren't any murders in that period must be something really special. That christian culture must be making a really big difference, right?

Well, no.

According to Google Answers, the US Census Department reports that there are 2363 four year colleges in the US. So, assuming the widest possible distribution of student deaths, there were 1506 colleges with no student deaths in a five-year period. Or, put another way, more than 60% of colleges in the US went that five-year period without any violent student deaths.

Or, let's try looking at it another way. According to the census, there are 15.9 million people currently enrolled in college. The school that, according to the author, is so remarkable for going without any murders in the last four years? It has 325 students. Not 325 per class - 325 total.

In other words, among a group making up less than 2/1000ths of one percent of the college population, there were no murders. Assuming that the distribution of violent deaths is perfectly uniform (which it obviously isn't; but let's just keep things simple), given that there were 857 violent deaths in the student population as a whole, how many violent deaths would you expect among the student body at his dinky christian college?

That would be a big, fat zero.

The fact that there were no violent deaths at his school isn't remarkable, not at all. But to a twit who's incapable of actually understanding what numbers mean, that's not the conclusion to be drawn. It's also not that the violent death among college students is actually remarkably rare. Nor is it that most college students will go through college without any violent deaths on campus. No - according to a twit, with 857 violent campus deaths over five years, the only reasonable conclusion is that there must be something special about the ridiculous religious rules at his college that prevented the great rampaging plague of violence from touching the students at his school.

I actually spent five years as an undergraduate at Rutgers University in NJ. During that time, there were no violent student deaths. (There was one death by alchohol poisoning; and there was one drunk driving accident that killed four students.) But zero violent deaths. Gosh, Rutgers must have been an absolutely amazingly moral university! And gosh, we had all of those horrible sinful things, like dancing, and co-ed dorms! How did we manage to go all that time with no violence?

It must have been the prayers of the very nice Rabbi at the Chabad house on campus. Yeah, that must be it! Couldn't just be random chance, right?

Ok, now let me stop being quite so pettily snide for a moment.

What's going on here is really simple. We hear a whole lot about violence on campus. And when you hear about eight-hundred and some-odd violent deaths on campus, it sounds like a lot. So, intuitively, it sure seems like there must be a whole lot of violence on campus, and it must be really common. So if you can go through your whole time in college without having any violence occur on campus, it seems like it must be unusual.

That's because, as usual, we really suck at understanding big numbers and scale. 800 sounds like a lot. The idea that there are nearly sixteen million college students is just not something that we understand on an intuitive level. The idea that nearly a thousand deaths could be a tiny drop in the bucket - that it really amounts to just one death per 100,000 students per year - it just doesn't make sense to us. A number like 800 is, just barely, intuitively meaningful to us. One million isn't. Fifteen million isn't. And a ratio with a number that we can't really grasp intuitively on the bottom? That's not going to be meaningful either.

Bozo-boy is making an extremely common mistake. He's just simply failing to comprehend how numbers scale; he's not understanding what big numbers really mean.

Posted by Mark C. Chu-Carroll at 8:34 PM • 68 Comments