By Nick Kasprak on May 10, 2015 6:30 PM

I recently had some of my work featured in the New York Times - very exciting. A couple of years ago, towards the end of my stint at the Tax Foundation, I adapted my code for the online tax calculator to produce a chart showing marriage penalties and bonuses for a range of household incomes and circumstances (later adapted into a series of three charts - my last post for them before leaving for CBPP.)

Fast forward to a month ago, when I simultaneously and (as far as I know, completely independently) received similar inquiries from both FiveThirtyEight and the New York Times Upshot blog asking me if these charts would ever be updated. I worked it out with CBPP and TF and was able to reproduce the charts for tax year 2015 and sent the raw data to both reporters.

This resulted in a couple of cool stories: here's the NYT version and here's 538's take. I'm particularly proud of the fact that, at least for a fleeting couple of hours, my work on the front page of the online New York Times: 

A few days later, TF released their own report with the same new charts - at significantly higher resolution (Kyle had a lot more patience than me and let the code run a lot longer.)

By Nick Kasprak on May 26, 2014 1:30 PM

Kerbal Space Program is a fantastic video game. It combines a reasonably accurate simulation of orbital mechanics and Newtonian physics with a spaceship-building interface in which the player puts together a spaceship from a large number of available parts (such as fuel tanks, engines, stage separators, etc.) The game takes place in the fictional solar system of Kerbol, and not our own Solar System - and this is, I think, primarily a game-balancing mechanic that makes most tasks a bit easier for non-rocket scientists. The planets are significantly more compact and dense than in the real Solar System, and this makes it easier to get into orbit.

Your astronauts are little green aliens called "Kerbals." They come from the planet Kerbin (the Earth analogue of the game) and they're hardy little creatures - for one thing, they can't die unless their spaceship crashes. The game doesn't (yet) bother with things like life support, food, or other consumables, so it's possible for your Kerbals to survive indefinitely in deep space or on the surface of another planet.

Much of the appeal of this game lies in the creative freedom it offers the player - there's a huge variety in the types of spaceships that can be built, and gameplay itself is relatively open-ended in that the game doesn't tell you where to go or what missions to do; you set your own goals. It's relatively easy to get into orbit, a bit harder to orbit and then land on the moon, relatively difficult to land on the Mars-analogue planet, and so on.

The most effective way to communicate the appeal of this game is to tell the story of what (to me, at least) was a fairly difficult mission - a successful return trip from Laythe (one of the moons of Jool, the Jupiter analogue.) Laythe has no real-world equivalent - it's sort of like Saturn's moon Titan in that it has an atmosphere, but it's much more Earth-like, with blue skies, water oceans, but still too cold to support life. My first attempt at getting here ended in disaster - I realized too late (after saving my game) that my lander didn't have enough fuel to make it back into orbit - my star Kerbalnaut, Jebediah Kerman, was stranded, with no way to get back to Kerbin. (Some people, who play this game much more seriously than I do, go through the trouble of calculating the total delta-V of their spaceships from the mass and engine thrust; I don't yet have the energy for that and tend to take a more trial-and-error approach.)

Here's Jeb standing by the lander he came down on.

He's not very happy, because he knows he's going to be here for a very long time.

In order to rescue him, I needed to send him a significantly larger ship. The challenge, of course, is that the larger the lander, the larger the ship to get it there in the first place, which means you need more fuel to get into orbit from Kerbin, which adds weight, so you need bigger engines, and so on and son on - even a relatively small change to a late-stage piece of the ship can dramatically increase the amount of fuel needed in the earlier stages to get the thing off the ground. I knew I was going to need to build a very large ship if this was going to work.

Meet the Laythe Express (version 2.0):

It's huge and obviously completely unaerodynamic, but that tends to not be much of a problem for the relatively simple atmospheric flight model in this game. It also has a probe core attached, so it can be flown remotely - no astronaut required. (This is good because the lander only has space for one, and Jeb needs that spot to come back.) Craft file here if you have the game and want to give it a shot.

Getting into Orbit

If your ship is up to the task, getting into orbit is relatively simple:

Leaving Kerbin

The next stage of the journey is to leave Kerbin's sphere of influence and get into a direct orbit around the Sun. I used a slingshot around the Mun (Kerbin's moon) to save fuel.

The Journey to Jool

Interplanetary transfer is done through a Hohmann transfer orbit. KSP makes it relatively easy to find a transfer using maneuver nodes.

Getting into Orbit Around Laythe

Three years later, I entered Jool's sphere of influence. The earlier approximation that said I was on course for Laythe didn't hold up, so after making some small course corrections, I set up a course to skim across the upper part of Laythe's atmosphere. This maneuver (aerobraking) saves a ton of fuel, but it's hard to get exactly right - too low and you'll end up on a suborbital trajectory and need to land; too high and you'll speed past without getting captured into orbit.

Landing on Laythe

Landing close enough for a rescue was challenging. It's hard to target the landing spot precisely - the atmospheric braking and entry makes it hard to calculate exactly where you'll end up. Jeb's landing site was on a relatively small island, so just a little bit off and I'd splash down into the ocean; furthermore, the island was very hilly - most of it too steep for the lander to stand up. Fortunately, I could save and reload as necessary, and after four or five tries managed to land around 18km from Jeb.

Jeb's Journey to the Lander

Despite my best efforts, the closest I managed to get to Jeb's base was still around 20km away. In theory, I could have just had Jeb walk across the island - but that would have taken a few hours of just holding down the "walk forward" button, which isn't much fun - there's no way to speed up time during EVAs.

Fortunately, the lander Jeb came down on was still functional. It may not have had enough fuel to get into orbit, but it sure had enough to fly halfway across a small island.

Back to the Mothership

The next step was to take off and rendezvous with the interplanetary stage. This requires matching its orbit and velocity, which is somewhat challenging.

Leaving the Jool System

Just as with Kerbin, it was possible to save on fuel by flinging my ship around another one of Jool's moons.

Returning to Kerbin

To get back to Kerbin, I used another Hohmann transfer orbit - basically the reverse of how I got out to Jool.

Re-entry and Landing

After another three in-game years, the rescue mission was almost over. Once I got near Kerbin, I made a few minor course corrections to set up a smooth re-entry, filled the lander back up with fuel, sent the mothership to crash down near Kerbin's north pole, and landed Jeb on an equatorial plain.

Jeb was quite happy to be home. Here he is, safe and sound, waiting by his ship for recovery and debriefing.

I think he deserves a good long rest, so I'll send another Kerbal on my next mission. Not sure where it will be - I want to try landing on Eve (the Venus equivalent planet) - it's easy to get to but very difficult to take off from due to its high gravity and think atmosphere, so I'll need a very large lander.

Anyway, the point is that this game is great and you should buy it.

By Nick Kasprak on August 25, 2013 12:15 PM

Update 12/2/2013: System76 has acknowledged that the original keyboard was terrible and has sent every Galago owner a replacement keyboard for free (actually the second time they've done this - the original keyboard was apparently extremely flimsy, so they put a metal plate behind it - that was the revision that came with mine - and now they've redesigned the keyboard a third time.) This new keyboard is thousands of times better than the old one - I feel like a normal person and don't need to pound the keys to get all my keystrokes to register.

Furthermore, my comments below about the Killer wifi no longer apply - while my fix worked, it no longer appears to be necessary as of the Ubuntu 13.10 system upgrade.

The other outstanding issues are also all more or less fixed - the black screen on boot was fixed by a driver update, graphics performance is vastly improved as of 13.10 (and I've also realized that my previous test was on battery power and not plugged in) - and the battery life is a bit better as well (not dramatically so, but there's a noticeable increase.) So, I'm prepared to say all my gripes below are fixed. This is now a great laptop and I'm quite pleased with my purchase.

I do most of my work on desktop computers, and I haven't really had a decent laptop in a while. But I stumbled across an ad for System76's Galago UltraPro a little while ago and was intrigued - quad core Haswell processor, integrated graphics that are actually decent, lots of build-to-order configuration options, Ubuntu pre-installed, and a high resolution screen. I had tried using Ubuntu on my previous laptop (a truly awful HP machine purchased at a time when my only goal was to get a functional laptop for as cheap as possible) and it didn't play well with the hardware - the battery lasted about an hour at most and the thing got so hot it would nearly melt through my thighs whenever I used it, despite my many attempts to mess around with power-saving tweaks. So a custom-built Ubuntu laptop was appealing, because the OS and the hardware should work reasonably well together.

I added some custom options to the default configuration – an SSD for the system plus a 1TB storage drive – my music library is large – an extra 4GB of RAM, and a faster WiFi upgrade. (It seems to me that offering custom configurations is something that not that many vendors even offer any more, and I appreciate it as someone who likes to have significantly more storage space than would be typical relative to the other specs.) The machine arrived a week ago and I've been using it since then.

The Galago packs a full HD display with lots of desktop space and also apparently smells intriguing enough that my cat Boris feels the need to rub his face on it.

The Good

  • The Display: better than I could have imagined – bright, high-contrast, beautiful colors, and the machine packs a full 1920x1080 pixels into a 14” screen for an extremely high pixel density. It's wonderful to look at, though I'll note that it approaches the threshold where small text gets a bit hard to read. I love the screen and all the space, but it's possible that it might give farsighted people headaches.
  • Speed: I don't really do much that's super CPU-intensive, but that aside, the machine has felt quick and responsive for all the tasks I've given it. It boots up in about ten seconds (thanks to the SSD) and applications open immediately.

Needs Improvement

  • Graphics Performance: I wasn't expecting anything amazing here given the lack of a discrete card, but System76's marketing materials led me to believe that the integrated Iris Pro graphics are a reasonable substitute. Maybe my expectations were set a bit too high, but I'm just frankly not that impressed – I downloaded Steam for Linux and tested out Double Fine's The Cave – not exactly Crysis – and even with a reduced resolution and medium settings things were still a bit jumpy and erratic at times. That said, I haven't done much gaming testing beyond that, so maybe it's just an issue with this particular game.
  • Wifi: When I ordered the machine I opted for the upgraded Killer wifi. I got it working fine eventually, but it was misconfigured out of the box and it took a fair amount of frustration and googling to fix. (And I'm not the only one with this issue.) At first, it was highly unstable – the connection would drop every five minutes or so – and even when it was connected, the average speed was abysmal. If you're reading this and have the same problem, the solution is to create a file here:
    - with the text “options ath9k nohwcrypt=1 blink=1 btcoex_enable=1 enable_diversity=1”.
    (I don't actually know which of the above options is actually the one that makes it work, but it's definitely one of them.) This kind of thing isn't that big a deal, since it does work now, but part of the reason consumers go to a company like System76 is that the machine is supposed to just work – you're not supposed to need to screw around with this stuff. I'm sure they'll fix it for future machines, but it was a bit frustrating.
  • Battery: lasts about as long as advertised (3.5 to 4 hours.) For a Haswell processor, it really ought to be better, but at least System76 doesn't inflate their statistics like so many others do. They say 3.5 to 4 hours and that seems to be what you get. Still, this is much longer than I'm used to (having not yet been spoiled by a 12-hour netbook) so I can't complain that much.
  • Startup: while the thing does boot up very fast, it's a bit unreliable. Frequently (maybe 40-50% of the time) I don't actually get to the login screen and just see a black screen with a blinking cursor and a mouse pointer. I can ctrl-alt-f1 to a text terminal and try to manually start the display manager, but I just get error messages. So far, I haven't figured out a solution other than to just reboot until it works, and I don't know what's causing the problem. I'm sure it's just something misconfigured somewhere and that I'll find a fix eventually, but (again) it's the kind of thing that I shouldn't have to worry about in the first place.

The Bad

  • The Keyboard: Oh dear. Just typing out this blog post is torture – I would say roughly 5% of the keys I hit don't actually register (despite typing REALLY REALLY HARD!), and I'm constantly looking back and seeing misspelled words and missing letters. Absolutely unacceptable. Fortunately, it seems that plenty of other people have complained about the same issue, and System76 is sending out replacement keyboards to anyone who asks (I put in a support request on Friday and haven't heard back yet but the Ubuntu Forums and Twitter tell me I should be fine.) I'm glad they've acknowledged the problem, but I'm a bit surprised they didn't notice this issue with the first batch.

The Verdict

This is a really nice machine marred by a handful of frustrating problems. In retrospect, I probably shouldn't have pre-ordered a machine with no reviews anywhere, and I suppose it's to be expected that a brand-new model might have some launch issues. The two most frustrating are the Wifi and the keyboard – and since I was able to fix the Wifi and have every reason to believe the replacement keyboard will be better, I'm still mostly satisfied with my purchase. However, for now I'd recommend that anyone eying this machine hold off for a couple of weeks until it's clear that the replacement keyboards are functional.

By Nick Kasprak on June 24, 2013 9:30 PM

I recently decided to take advantage of Finale's advanced MIDI features (and my new blazingly fast PC) to re-do some of the sequencing on this. Not perfect (some parts are weirdly soft) but I was able to make it do things that I couldn't before and I'm pretty pleased with the results. Also, YouTube no longer has a length limit, so I can put the whole thing in one video. (This composition was my senior project at Bowdoin - give it a listen if you haven't heard it before!) 

By Nick Kasprak on May 27, 2013 11:00 AM

So this is a pretty silly post, but whatever - I had lots of fun doing it. Basically, I had "The Final Countdown" stuck in my head because I was excited about the new Arrested Development, and then it occurred to me "that guitar riff would make a really great fugue subject." So I went ahead and tried to do a fugue. It's been a while, so it it's a bit sloppy, there are probably a few voice-leading errors and parallel fifths, but it still sounds pretty good. So here you go - the FUGAL COUNTDOWN!

Sheet music here. Differs slightly from the video above - I'm fixing voice-leading errors as I find them.

By Nick Kasprak on December 05, 2012 1:00 PM

I haven't updated this thing in a while what with buying a condo and moving and all that but I'm going to make a real effort to start blogging regularly again. I also am going to try and add blog comments in the near future, partly because the programming aspect of doing that from scratch will be a good exercise. But for now I'm going to just link a few recent highlights:

First off, I was recently quoted in the New York Times here, as well as a few other online newspapers, mostly talking about my state-by-state fiscal cliff paper

Secondly, I've recently done a few radio interviews here and there: Montana's The Flint Report, and also Maryland talk radio as well, though I can't find audio for that one. I was also recently on local TV for about three seconds, which was fun. This morning I did another TV interview for South Korean state TV - a reminder that U.S. fiscal policy affects the whole world. If I can find a video link for that I'll post it here, though I'm not sure when it will actually air.

By Nick Kasprak on July 11, 2012 1:00 PM

President Obama's proposal to let the Bush tax cuts expire for married taxpayers making over $250,000 and single taxpayers making over $200,000 sounds simple enough. If you make under those amounts, nothing changes, and if you make more, you pay the old Clinton-era tax rates. Right?

As with anything related to the federal income tax code, things are much more complicated than they seem. For one thing, the Bush tax cuts included much more than just marginal rate reductions – they also changed the way dividend income is taxed, reduced capital gains tax rates, and phased out various limitations on exemptions and deductions for upper income taxpayers.  Additionally, marginal tax rates apply to taxable income, while Obama's thresholds apply to adjusted gross income (AGI). Finally, Obama first proposed those $200,000/$250,000 thresholds back in 2009; using the same numbers four years later in 2013 would cause this tax increase to affect significantly more taxpayers than initially intended because of inflation, and the official proposal in his 2013 budget indexes those thresholds using a 2009 base year. So when Obama talks about letting the Bush tax cuts expire for families earning over $250,000 and single filers earning over $200,000, he really means $267,000 and $213,600.

The marginal rate increases are relatively simple to understand, but it requires knowing the difference between taxable income and AGI. Taxable income is simply AGI minus personal exemptions ($3,900 per dependent in 2013 plus an additional $3,900 for the head of the household) and deductions (in 2013, a minimum of $6,100 for single filers and $12,200 for married filers, plus more if the taxpayer itemizes.) So for an AGI of $267,000 (remember, that's the $250,000 threshold adjusted for inflation to 2013), the applicable taxable income threshold is $267,000 - $12,200 – (2 x $3,900): that's subtracting the standard deduction for married filers and two personal exemptions (one for each spouse.) That comes out to $247,000.

Under current policy, there are six taxable income brackets – 10%, 15%, 25%, 28%, 33%, and 35%. Obama's proposal would let part of the 33% tax bracket and all of the 35% tax bracket rise to Clinton-era tax rates: 36% and 39.6%[1][2]. The split in the 33% tax bracket (where the upper part goes up to 36%) is set to be the number calculated above: $247,000. (The same calculation for single filers comes out to $203,600). So the marginal tax rates on taxable income under each scenario are as follows:

Filing Status

Tax Cuts Expire (2013 projected parameters)

Current Policy (2013 projected parameters)

Obama Proposal (2013 projected parameters)


$0 to $36,250:15%
$36,250 to $87,850: 28%
$87,850 to $183,200: 31%
$183,200 to $398,350: 36%
$398,350+: 39.6%


$0 to $8,950: 10%
$8,950 to $36,250: 15%
$36,250 to $87,850: 25%
$87,850 to $183,200: 28%
$183,200 to $398,350: 33%
$398,350+: 35%

$0 to $8,950: 10%
$8,950 to $36,250: 15%
$36,250 to $87,850: 25%
$87,850 to $183,200: 28%
$183,200 to $203,600: 33%
$203,600 to $398,350: 36%
$398,350+: 39.6%


$0 to $60,550: 15%
$60,550 to $146,350: 28%
$146,350 to $223,050: 31%
$223,050 to $398,350: 36%
$398,350+: 39.6%

$0 to $17,900: 10%
$17,900 to $72,500: 15%
$72,500 to $146,350: 25%
$146,350 to $223,050: 28%
$223,050 to $398,350: 33%
$398,350+: 35%

$0 to $17,900: 10%
$17,900 to $72,500: 15%
$72,500 to $146,350: 25%
$146,350 to $223,050: 28%
$223,050 to $247,000: 33%
$247,000 to $398,350: 36%
$398,350+: 39.6%

Things get more complicated when you look at other aspects of the Bush tax cuts – capital gains and dividends, for example. Currently, capital gains are taxed at a top rate of 15%, whereas under Clinton they had been taxed at 20%. Obama proposes to tax capital gains at 20%, but only for taxpayers whose income is above his threshold. The way that works in practice is this: take the lesser of your taxable income over the applicable taxable income threshold and your total capital gains income, and that's the amount that is taxed at the higher rate. A family that has $257,000 in taxable income and $80,000 in capital gains is $10,000 over the $247,000 taxable income threshold. So $70,000 of those capital gains are taxed at 15%, and the remaining $10,000 are taxed at 20%.

It's similar for dividends. The Bush tax cuts created a new category of dividends referred to as "qualified" – so named because the qualify to be taxed as if they were capital gains rather than ordinary income. In order to qualify, a dividend needs to be paid by a US corporation and the stock needs to have been held for at least 60 days. Roughly three quarters of dividend income is qualified[3]. Obama proposes to let qualified dividends revert to being taxed at the ordinary rates – but only for taxpayers earning over the threshold. So qualified dividends are taxed at capital gains rates until the taxpayer's taxable income exceeds the threshold, and beyond that are taxed at ordinary rates. The exact amount that is taxed at the higher rate is, as with capital gains, the lesser of the taxpayer's taxable income over the threshold and his or her qualified dividend income.

One other change made by the Bush tax cuts was the gradual phase out of two provisions aimed at limiting the benefit of tax deductions for high income taxpayers. These are known as PEP, the Personal Exemption Phaseout, and Pease, named for Representative Don Pease, who proposed it. (For more on PEP and Pease and how they work, see Tax Foundation Special Report No. 178 – "PEP and Pease: Repealed for 2010 But Preparing a Comeback.") These provisions came with their own income thresholds because they were also targeted at upper-income taxpayers: if PEP were reinstated next year with no changes, it would affect single taxpayers with an AGI over $178,150 and married filers with an AGI over $267,200. Obama therefore proposes to bring back Pease, but to raise the threshold for single filers to $213,600 so as not to violate his pledge (again, that's $200,000 in 2009 dollars). He'd also leave the married threshold where it is (being ever so slightly above his magic number of $267,000.) PEP, too, is similar: if reinstated next year with no changes it would apply to filers with incomes over $178,150 regardless of filing status, so Obama would bring it back but raise the applicable thresholds to $213,600 for single filers and $267,000 for married filers.

(Cross posted from the Tax Foundation's Tax Policy Blog)

[1] Office of Management and Budget. The President's Budget for Fiscal Year 2013: Analytical Perspectives, p. 201., accessed 7/11/2012

[2] Department of the Treasury. General Explanations of the Administration's Fiscal Year 2013 Revenue Proposals, p. 70., accessed 7/11/2012

[3] IRS SOI Tax Stats – Individual Statistical Tables by Size of Adjusted Gross Income, Table 1.4, accessed 7/11/2012


By Nick Kasprak on June 29, 2012 5:45 PM

I was pleased yesterday that the Supreme Court decided to uphold health care reform. For what it's worth, I think it's pretty clear that the dissent was originally the majority opinion and that Roberts switched his vote late in the process. This is all just speculation on my part, but I think what probably happened is that Scalia, Thomas, Alito, and Kennedy didn't think there was a good solution to the severability problem and wanted to strike down the whole law. Roberts wanted to strike down the mandate because it would have been an opportunity to establish a reasonably clear limit to the Commerce Clause - something that originalists and federalists have been trying to do (more or less unsuccessfully) since the 1930s. But he also was worried about the Court's image and didn't want to strike down the whole law - it would have looked nakedly political if he struck down the signature piece of legislation of the guy who voted against his confirmation in 2005 - so he looked for a way to establish Commerce Clause limits while still using an excuse to uphold the mandate for some other reason: Congress's taxing power.

Upholding the law is the right decision, but the tax argument is the wrong reason. Health care affects interstate commerce, PPACA's purpose is to regulate health care, and the mandate is necessary and proper to make the rest of the bill work - and I think that's a good enough reason to uphold the law. The tax argument doesn't make a whole lot of sense, because it seems to say that the government can penalize a whole lot of things it otherwise couldn't. Congress can't pass a law banning criticism of John Boehner, for instance, but can it levy a $10 tax on every unfavorable mention of his name? Obviously not, but it's not clear where or how you draw that line.

In any event, the mandate might actually be more toothless than people realize. From the bill, Section 5000A(g), cited by Roberts as part of his argument that the mandate is not a penalty:

Administration and Procedure.--

  1. In general.--The penalty provided by this section shall be paid upon notice and demand by the Secretary, and except as provided in paragraph (2), shall be assessed and collected in the same manner as an assessable penalty under subchapter B of chapter 68.
  2. Special rules.--Notwithstanding any other provision of law--
    1. Waiver of criminal penalties.--In the case of any failure by a taxpayer to timely pay any penalty imposed by this section, such taxpayer shall not be subject to any criminal prosecution or penalty with respect to such failure.
    2. Limitations on liens and levies.--The Secretary shall not--
      1. file notice of lien with respect to any property of a taxpayer by reason of any failure to pay the penalty imposed by this section, or
      2. levy on any such property with respect to such failure.

I hadn't heard of this before, but my colleagues at the Tax Foundation seem to think that this means I can just go without insurance and refuse to pay the mandate anyway, and the IRS is powerless to stop me. In practice, it's a bit more complicated. If my wages are overwithheld throughout the year, then I get a tax refund after I file. Legally, everything on my tax form has to be truthful, so I can't just write that I have health insurance when I don't - I could be prosecuted notwithstanding the exemptions above. So my refund would get reduced by the amount of the mandate, and everything would work the way it's supposed to. On the other hand, suppose I change my withholding so that not enough tax is being taken out each pay period, and I owe lots more when I file. I write that I don't have health insurance, and and end up owing an additional $1000 in individual mandate tax.  As far as anyone I work with can tell, I could just write the IRS a check for $1000 less than I owe and there's nothing they could do about it.

The IRS may be able to get around this by changing its withholding rules so that pretty much everyone gets a refund, but I don't know how much authority they actually have to make these decisions independently.

Update: SCOTUSBlog has some more on this.

By Nick Kasprak on June 13, 2012 8:00 PM

I've been re-listening to a lot of Mozart piano concertos recently, which are, along with his operas, his best work. I'm always a little bit surprised that stereotypical, "popular" Mozart consists, by and large, of music that is relatively boring and plain in comparison (things like Eine Kleine Nachtmusic and so forth - essentially composed as background music). Even most Mozart symphonies, except for the latest few, are pretty light and unremarkable. His piano concertos, by far, show the greatest depth, yet most of them (except for a handful of popular movements) are essentially unknown to the vast majority of people who aren't classical music nerds, and it's a real shame. When I tell people my favorite composer is Mozart, I can almost understand why they might think "Well, okay, but isn't he kind of boring?" Sure, if you've never actually heard his best work.

I think the main reason his piano concertos stand out is because he composed most of them for himself to play - they're much more personal works. They also gain a lot from their formal and structural requirements - the first movement is always in a modified sonata form specific to instrumental concertos, whereas a symphony or string quartet is usually in standard, unmodified sonata form. The main difference is that in a symphony, you simply hear the expository material played through twice, exactly the same; in a concerto, the orchestra plays an abbreviated exposition by itself, and the soloist doesn't enter until the second run through, in which new material is introduced and there's a sort of dialogue between the soloist and the orchestra - it all gives the piece a more elegant and melancholy character.

In my view, the hardest problem that a composer has to solve when writing music of any appreciable length is how to balance two contradictory goals: one, having enough variety to hold the audience's interest, and two, writing in such a way that all that variety still sounds like it belongs together in the same piece. Mozart's piano concertos are probably the most successful pieces of music ever written in that regard. Every Mozart concerto movement has an astonishing range of emotion and quantity of thematic material, which is true of many 19th century pieces as well, but Mozart's strength is to keep all of that range unified as part of what is clearly the same piece of music throughout. Lots of 19th century music sounds sort of "stitched together" - there's a lot of emotional range covered, but the music is constantly changing speeds and textures and so sounds inelegant. Not so with Mozart.

Here are a few of my favorites:

This is the first movement of No. 24 in C Minor. I think it shows, probably more than any other work could, the degree to which Ludwig van Beethoven didn't just simply burst onto the musical scene at the turn of the century and single-handedly change the course of music - there's a lot of precedent in Mozart for the direction he took. Who knows - if Mozart had lived past the age of 35, maybe he'd have out-Beethovened Beethoven.

Next is No. 25 in C Major:

This one has a sort of martial character to it. The main melodies are musically very simple, and I think the fact that Mozart was able to do so much with them is a testament to both his genius and the strength of the piano concerto as a genre. The "B" theme that is first introduced by the violins at 1:35 is a very simple idea, and it's a real joy to listen to Mozart build on it throughout the movement, particular its final formal statement much later during the recapitulation from 11:00 to 11:15 or so - who would think that such a basic melody could sound that inspiring?

Finally, here's one that you've probably heard before: 

This is probably the most boundlessly optimistic piece ever written. It's the 3rd movement of the 23rd concerto in A Major. To some extent, it's an exception to the idea of balancing variety and thematic unity as the key strength of the concerto, since it's so consistently happy throughout.  However, there's one particularly beautiful passage from 5:30 to around 5:50 which I think is a perfect example of this - listen to how effortlessly Mozart slides from a relatively melancholy section back into the optimistic mood that characterizes the rest of the piece.

By Nick Kasprak on June 11, 2012 5:15 PM

I'm back from the Netroots Nation conference. Today I went to a day long course by Edward Tufte, the famous data visualization guru. He had a lot of cool things to say, particularly about not dumbing down your data and charts. In his view, the best way to give a presentation is to to a huge "data dump" at the very beginning, giving your audience time to look through it, then giving your own take and answering questions. He contrasted this with the typical Power Point approach, where information is organized sequentially and proceeds at the pace of your slowest audience members. He was also very critical of focus groups, and I was struck by a Steve Jobs quote he mentioned - "It's not the job of the consumer to know what they want." I couldn't agree more - if we designed everything by popular vote we'd have no need for designers.