October 10, 2008
Category: Recipes
This is a recipe I created just a couple of weeks ago. I saw a beautiful Angus beef flank steak on sale, and wanted to find something to do with it. I came up with this idea of stuffing it. Amusingly, the day after it, a recipe appeared in the New York Times food section for a stuffed flank steak. But there's really nothing common between the two except the name.
The basic idea behind this is that flank steak has a terrific flavor, but it can be a bit tough. So I wanted to do something to it that would
make it tender, while taking advantage of that terrific flavor. The idea I came up with was to flatten it out by butterflying and pounding with a tenderizer, and to marinate it with some wine. After doing that, I had a very large, very thin piece of steak. So I wanted to roll it up - and if you're rolling, you've got a great chance to put something between the layers of the roll. I used a bit of bacon in the recipe - it's important not to give in to temptation and use more. Bacon has a very strong flavor, and you want to complement the flavor of the flank steak, not overwhelm it.
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Posted by Mark C. Chu-Carroll at 3:03 PM • 2 Comments
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October 7, 2008
Category: goodmath
Today the 2008 Nobel Prize winners were announced for physics. It was given to three physicists who described something called symmetry breaking. Since most people don't know what symmetry breaking is, but people remember me writing about group theory and symmetry, I've been getting questions about what it means.
I don't pretend to completely understand it; or even to mostly understand it. But I mostly understand the very basic idea behind it, and I'll try to pass that understanding on to you.
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Posted by Mark C. Chu-Carroll at 8:36 PM • 10 Comments
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October 6, 2008
Category:
I don't have a lot of time to write; I'm having my fifth (I think) upper endoscopy done tomorrow, which means that the day's going to be a wash; and Yom Kippur is thursday, and I need to cook, so between the personal crap and work, I'm not going to have much time for blogging. So I'm trying to make use of the time I have to write one short but (hopefully) interesting post.
One thing that I've mentioned in passing is the distinction between message confidentiality, and message integrity.
Confidentiality is most of what we've been talking about
so far. Confidentially provides a guarantee that when you send an encrypted message, no one but your intended recipient is able
to read the plaintext.
Integrity is something very different. Integrity guarantees
that if you send an encrypted message, there's no way that the encrypted message could have been tampered with after you encrypted it, without the recipient knowing it.
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Posted by Mark C. Chu-Carroll at 9:39 AM • 12 Comments
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October 3, 2008
Category: Music
Don't forget to go and donate some money to schools through
our DonorsChoose challenge. Seriously - throw them a couple of bucks. It doesn't need to be much. There are around three thousand people per day who read this blog; if you each contribute $5, it would more than pay to fully fund every project I chose for the challenge!
And don't forget: if you donate more than $100, you get to pick a topic for a post! (Just email me to let me know you donated that much, and tell me what you want your post to be about.)
- Metaphor, "The Sparrow": An excellent track
from a great neo-progressive band. They've got a very distinctive sound, and this is an excellent example of it.
- Marillion, "A Collection": a track off Marillion's
worst-ever album. It's not a bad song; probably the best
on that profoundly mediocre album. But that's not saying much.
- Sonic Youth, "Fauxhemians": very good, very strange, very noisy stuff.
- Porcupine Tree, "The Creator Has a Mastertape": I love Porcupine Tree. This is an excellent track, very typical of them. Great stuff built around highly distorted vocals and guitar, backed by great bass work. Amazingly great stuff.
- A Silver Mount Zion, "Sow Some Lonesome Corners So Many Flowers Bloom": Post-rock from a subset of Godspeed You! Block Emperor. They're nowhere close to as good as the full-blown
Godspeed collective, but they're pretty good. This is off of my favorite Mt. Zion recording, "This is Our Punk Rock, THee Rusted Satellites Gather + Sing". It's very good, with a nice minimalist structure of building up layers.
- Peter Schickele, "Allegro Ma Non Troposphere": If you don't know about PDQ Bach, you're sadly deprived. PDQ is the invention of Professor Peter Schickele; he is allegedly the 13th illegitimate grandson of J. S. Bach; the last and least of the
musical descendants of Bach. Schickele writes music allegedly by PDQ. It's amazingly funny stuff, ranging from slapstick (this
one starts off with the musicians playing off of the wrong sheetmusic), to the very deep (musical tricks making fun of the typical gimmicks used by various composers; for example, this
one contains a climbing melody in the beginning that's similar to something commonly used by Vivaldi; but instead of rising up twice or three times the way Vivaldi would, it does it something like twelve times. It's also got a few digs at Mozart, John McLachlan, and a few others.) I happen to have been lucky enough to be in the audience of the performance this recording was made from.)
- Zoe Keating, "Legions": This is brilliant and strange. It's a classically trained cellist who performs solo with tape-loop. She starts by laying a basic loop, and then building layers on top of it, until she's got a texture, and then playing the main composition on top of the loop. It's amazing.
- Anekdoten, "The Great Unknown": a neo-progressive group that sounds a lot like "Red"-era King Crimson. They're very good, but they sound a bit too much like KC. In general, I think that there aren't enough groups that try to follow in the footsteps of Fripp and Friends, but I'd like to hear something a bit more original. If you listen to one track by Anekdoten, it sounds fantastic. But by the time you've listened to an entire album, you're very bored; it's all so derivative.
- The Redneck Manifesto, "Good With Tempos": a post-rock band that's very much in the style of Mogwai, but with their own distinctive style. The Rednecks are fantastic.
- Magma, "Ork Alarm": I've mentioned Magma before. They're one of the strangest groups I listen to. They're sort of a cross between classical music and progressive rock. The leader of the band actually invented his own language to sing in, and the singing is more in the style of a choir singing in a symphony. This sounds a lot like a 20th century classical opera. Fortunately, I like
20th century opera. I'm not a fan of the older, traditional Italian opera like Verdi, but a lot of the 20th century stuff by folks like John Adams, Phillip Glass, and Igor Stravisky have, while not necessarily being traditional opera, been utterly brilliant.
Posted by Mark C. Chu-Carroll at 3:27 PM • 4 Comments
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October 2, 2008
Category: Encryption
Now, we're finally reaching the point where the block-cipher stuff gets really fun: block cryptanalysis.
As I've explained before, the key properties of a really good
encryption system are:
- It's easy to compute the ciphertext given the plaintext and the key;
- It's easy to compute the plaintext given the ciphertext and the key;
- It's hard to compute the plaintext given the ciphertext
but not the key;
- It's hard to compute the key.
That last property is actually a bit of a weasel. There are really a wide variety of attacks that try to crack an encryption
system - meaning, basically, to discover the key. What makes that
statement of the property so weasely is that it omits the information available to the person trying to crack it. In the first three properties, I clearly stated what information you had available to produce a result. In the last, I didn't.
There's a reason that I weaseled that. Partly, it's because a correct statement of it would be ridiculously long and incomprehensible; and partly because it's often deliberately set up differently for different encryption systems. You can design systems that are extremely strong against certain attacks, but not so good against others. There's no universally ideal encryption system: it's always a matter of tradeoffs, where you can handle some scenarios better than others.
Today we're going to look at one particularly fascinating attack that's used against block ciphers. It's called differential cryptanalysis.
Read on »
Posted by Mark C. Chu-Carroll at 3:07 PM • 8 Comments
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October 1, 2008
Category: goodmath
Every year at ScienceBlogs, we do a charity drive for
DonorsChoose.org. If you haven't heard of them, DonorsChoose is a charity that takes proposals from schoolteachers, and lets people pick specific proposals to donate money to. We run our charity challenge through the month of October.
For personal reasons, I couldn't participate last year. The year before that, Good Math/Bad Math readers donated just over two thousand dollars to support math education in impoverished New York area schools.
This year, I'm still focusing on the NYC area, because with where I live and work, I get to directly see how these schools and students are treated, and how desperately they need help. I've selected a number of projects that fit into two main categories:
- Basic Supplies: These are proposals to buy very
basic classroom essentials, like pencils and paper. It's
pathetic that teachers need to come to a charity asking for this
kind of stuff. But the unfortunate fact is, there are schools in
NYC where the school can't even provide paper and pencils for their
students. How can you possibly expect a student to learn math, when
they don't even have blank paper to work problems on?
- Math Manipulatives: manipulatives are much more
interesting. They're things like shaped pattern blocks blocks,
which can be used to provide a direct, tactile tool for
understanding math. I live in an excellent school district, and my
children's classrooms have enormous supplies of manipulatives of
several different kinds. I've seen very directly how these simple
things make basic mathematical concepts concrete and understandable
for elementary school children. Manipulatives can be used to help
develop the intuitions behind shapes, numbers, addition,
multiplication, patterns, areas, fractions, angles, and basic
geometry. They're an amazing tool for elementary education, and I
think every school should have boxes of manipulatives in every
elementary classroom. They're not terribly expensive, and they're
wonderful.
To me, there's a bit of a personal element to this stuff. The work that I'm most proud of in my life is several summers that I spent working for something called the New Jersey Discovery program. Discovery took children from some of the worst schools in the state of New Jersey, and set out to help them. The kids spent their weekends all year in tutoring. Then during the summer, they came to Rutgers, and spend the summer at the university. Three days a week, they took classes; the other two days, they worked for the university. If the kids did this for the two full years, then they got scholarships to get their bachelors degree at Rutgers.
I got to teach the Discovery kids computers and math. They were great kids: smart, hard-working, and motivated. I got to hear from them what their schools were like: places where they didn't have basic essentials. In 1990, they were using math textbooks from 1960 - books that were falling apart, with missing pages. And that was one of the better equipped classes. They had english classes where they had no books at all. They didn't have paper. They had classrooms where the blackboard were cracked and broken, and couldn't be written on.
Before that experience, I had no idea that poor schools
were anything remotely close to that bad. It astonished me, and
opened my eyes. It's easy to not realize, to not notice
how bad things can be for people who are less fortunate that you.
It's a bad time in the economy, so I understand that a lot of us have a lot less money available to donate to things like this. But at the same time, it's important to realize that inner city
impoverished school systems will generally be hurt much worse by economic troubles than the schools of those of us are better off.
So please: go to Donors Choose, and find some good proposals, and help
fund them!
Of course, I'll throw in some goodies. If you throw in over $100, you can pick a topic for me to write an article about. I'll probably also set up something at Cafepress to make some Good Math/Bad Math goodies for donors. Don't wait though - I'll still send you the goodies even if you donate before I decide what they are.
Posted by Mark C. Chu-Carroll at 8:22 PM • 0 Comments
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September 25, 2008
Category: Bad Economics
Ok, another batch of questions have come in, all variants on
the same theme.
The question is, if mortgages are at the root of the current economic disaster, how can it possibly result in close to a trillion dollars worth of losses?
It definitely seems strange, on two different levels. On an absolute scale, it's hard to see how mortgage losses could add up to a trillion dollars. And on a relative scale, it's hard to see how the foreclosures could really overwhelm the lenders when even an extremely high foreclosure rate represents a fairly modest loss considered as a percentage.
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Posted by Mark C. Chu-Carroll at 7:54 PM • 46 Comments
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September 23, 2008
Category: Bad Economics
There is at least a little bit of interesting bath math
to learn from in the whole financial mess going on now. A couple
of commenters beat me to it, but I'll go ahead and write about
it anyway.
One of the big questions that comes up again and again is: how did they get away with this? How could they find any way of
taking things that were worthless, and turn them into something that could be represented as safe?
The answer is that they cheated in the math.
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Posted by Mark C. Chu-Carroll at 9:41 PM • 56 Comments
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September 22, 2008
Category: Bad Economics
With the insanity that's been going on in the financial world
lately, a bunch of people have asked me to post a followup to my
earlier posts on the whole mortgage disaster, to try to explain
what's going on lately.
As I keep saying when people ask me things like this, I'm not an economist. I don't know much about economics, and what little I do know, I tend to find terribly boring. And in this case, the discussion inevitably gets political, so I'm expecting lots of nasty email.
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Posted by Mark C. Chu-Carroll at 5:39 PM • 64 Comments
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September 15, 2008
