## Archive for February, 2009

### president’s day

it is what it is

The Quantum Leap synthesizer sounds are commendable, but take a Herculean effort to program well.

### Wired on the Gaussian copula

For five years, Li’s formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

And anyway, here is the paper referenced in the article.

### halo orbit, Lagrange points, ITN

Great stuff, this comet. I only recall seeing one comet in person, back in the 1990′s. Must have been Hale-Bopp. Now that was a rare one.

Comet Lulin is arriving from the far reaches of the solar system on a nearly parabolic orbit—”it’s almost as if it comes from infinity and goes back out to infinity,” he said.

This must have been one of these initially stationary objects then. Speaking of orbits, unrelated to comets, these so-called halo orbits are pretty amazing. They are orbits around stationary points in the gravitational field of three bodies called Lagrange points. L1, L2, and L3 are pretty obvious and therefore not that cool, but L4 and L5 surprised me and they are even stable… The application of going to an unstable Lagrange point and redirecting routing with low energy is even nicer.

### continuous chord progression

Following up on a side note from this post, it is possible to construct continuous changes from one chord to the other by linear interpolation of their frequency envelopes (i.e., chord interpolation).

Here is an example in Mathematica.

A[f_] := Sin[2*Pi*t*f*220];

For example, one of the major triads is 4:5:6, and the harmonic minor triad is 6:7:9.

First, the two chords:

Play[{A[1260/1260] + A[1575/1260] + A[1890/1260]}, {t, 0, 1}]

Play[{A[1260/1260] + A[1470/1260] + A[1890/1260]}, {t, 0, 1}]

I came across a story today of somebody who avoided a head on collision by moving to the next lane at the last moment, almost by involuntary reaction and without realizing what was going on. The full gravity of the situation always dawns on the survivor slowly, because everything happens so quickly.

This reminds me of my own near death experience. It was in the Bay Area near an airport in the middle of the night, I can’t remember where now. There was a very confusing road division where there were two left turn lanes, and one of them is somehow on top of some kind of surface rail (trolley) track running parallel to the lanes. I couldn’t see clearly at all. The traffic lights were not normal traffic lights, but some kind of symbol for each lane. Anyway, there were no dividers, fences, or barriers of any kind and I somehow ended up half on the tracks waiting for the light to turn green. Then in my rear view mirror, I see the bright lights of a train coming straight behind me. As the train comes ever closer, I get a feeling just like in a dream when something unreal is happening, a feeling of … “wait, this doesn’t make any sense”. So just like you might violently snap out of a dream in cold sweat, I stepped on the gas, ran the red, and moved into the next lane on autopilot, as the train whizzes by not more than a few feet beside me.

No horns, no noise, just a quiet train in the middle of the night. The whole thing still feels like sleepwalking to me and still doesn’t make any sense, but that would have been a terrible way to die.

### random thoughts on classifying chords

I’m going to attempt to classify chords from first principles, forgetting about the restrictions imposed by existing terminology. Chords are essentially a partial harmonic series. Therefore, they can be indicated as a series of ascending integers indicating ratios of frequencies of elements in the chord, such as 1:2 (octave), 2:3 (fifth), 4:5:6 (major triad), and so on. This is for pure tone combinations. Real instruments contain overtones in each note, so the total effect is more complicated (or collapsed, depending on the view). We will just deal with pure tones for now.

### minimax vs. maximin

An elementary, nice lemma relating to the optimization of multivariable functions says that the smallest “big thing” is still bigger than the biggest “small thing”, in other words,

$$\min_x \max_y f(x,y) \ge \max_y \min_x f(x,y)$$.

### Lang Lang getting tutored

It’s not like I play piano (I don’t), but I’ve never been convinced by most of Lang Lang’s performances. Too raw. Sure, one can argue it’s his own interpretation but it really is a bad one if it doesn’t make sense… I mean Beethoven is not video game music, which seems to be Lang Lang’s self professed straightjacket… Barenboim explains it well and I must say I agree with most of his criticisms:

### Microsoft Songsmith

fakalin pointed me to this product from MSR. I was actually sort of aware of this during my stint at MSR, via overheard hallway conversations, but didn’t know it was going to be released as a product.

http://research.microsoft.com/en-us/um/redmond/projects/songsmith/

So I downloaded it to see what’s up. It has been called the reverse Karaoke program. It has only been released a month and it appears there are already a handful of parodies of well known songs. There is one that turned a rap by Eminem into bluegrass (stupid vulgar song, but anyway):

Next Page »