How I Practice Piano

This is my usual method of practicing, gleaned from my teacher, old posts on the Piano Street forums, Graham Fitch’s Practising the Piano, and various other books and resources. It’s rare that I follow these steps exactly, but they are an ideal to aim for.

  1. Choose one section of the piece to practice, which is short enough that you can memorize it in a few tries. If you can’t, break it down into even smaller pieces. If it’s too easy to memorize, choose a bigger section. Include the first notes of the following section to make joining sections easier later on. For example, if your section is the first two bars of the piece, include the first note from bar three.
  2. Practice the section slowly enough, at first, to avoid making mistakes. If you keep making mistakes when practicing then you are just going to get good at making them, so it’s best to avoid them in the first place. Use the correct fingering, dynamics, articulation, etc. from the very beginning; you are never going to get around to “fixing” it later. Do not work on this section for more than twenty minutes.
    1. Start hands separately at a slow tempo using the metronome. If you can play the section five times in a row without hesitating or making a mistake, increase the tempo and practice again, until you can play at that tempo five times in a row. When one hand is in danger of getting tired, switch to practicing the other one. Aim to increase the speed to above the target performance tempo, so that playing at performance tempo is easier by comparison.
    2. Once you can play each hand individually above the target tempo, practice hands together. Start with a tempo even slower than you think you need—if you are having trouble coordinating, reduce the speed. Once you can play it flawlessly and without hesitation at least five times in a row, start increasing the speed in increments. Aim to get to a speed above the target performance tempo.
    3. Once you can play the section hands together above the target performance tempo, continue practicing it until you can’t get it wrong—but no longer than the twenty-minute limit. Some sections will take much less than twenty minutes to master. Others will take more, which is a sign that the section you’ve chosen is too big and should be broken down further.
  3. Start working on a different section, either of the same piece or a different piece, and don’t touch this section again until the next day. The next day, if you can play the section perfectly in only a few tries, move on to learning a different section. If not, repeat the steps above again. It will take less time the second time around.
  4. Once two consecutive sections have been mastered, work on joining them together as a new section. By adding the first note of the next section during practice, it is much easier to join sections together at this step.
  5. Continue in this way, working on small sections and joining them together, until the entire piece is learned.

While increasing the tempo, you may reach a point where you can’t play any faster, no matter how hard you try. What is likely happening is that the hand motions you are using—which come naturally at the slower tempo you started with—simply will not work at such high speeds. You are basically trying to run by speed-walking faster and faster. One way to get around this is to try playing the section at full speed first, ignoring mistakes, just to figure out what the necessary motions feel like. Then, you can try to practice those motions at a slow speed, not the motions that are intuitive at a slow speed.

It is a good idea to occasionally play a piece very slowly, even after you’ve mastered it. If you only play the piece fast, the piece will deteriorate as mistakes inevitably get introduced and never get fixed. Finally, it’s a good idea to occasionally play hands separately, especially for counterpoint, even after you’ve mastered the piece. In fact, for counterpoint it’s a good idea to learn each voice individually with the correct fingering (even if that means passing the voice back and forth between the hands) and occasionally play each voice separately.

Visualizing Sixty Years of Books

Assume that you will live for 60 more years. This means you have 3,169 weeks left. If you read one book every week, you will have time to read 3,169 more books. Let’s say that each book is, on average, one inch thick. Then, these books take up 264 feet of linear shelf space. How big of a room would you need to store that many books? Let’s assume the room has 8-foot ceilings, so a floor-to-ceiling bookcase would have at most seven shelves. The books would therefore cover 38 feet of the room’s perimeter. If we account for the fact that the bookcases are about a foot deep, then you will actually need a room with a 46-foot perimeter to accommodate them without overlapping at the corners. That is exactly the perimeter of an 11×12 foot room, or a standard American bedroom. Actually, even that would be too small, since you have to account for a door somewhere, and perhaps windows. So if you want to visualize the amount of books you could read in sixty years, picture your bedroom with floor-to-ceiling bookcases covering all four walls and then some.

Are Viruses Alive?

I would like to argue that the question “Are viruses alive?” is a question about language, not about any objective fact about external reality, and that there is no correct answer. I’m sure there’s a standard name for this argument and I’d bet Wittgenstein has already talked about it, but I haven’t read any Wittgenstein so this is my personal attempt to articulate it. The impetus for writing this came from reading this article in Quanta Magazine and from a conversation about it on Twitter.

The distinction between living and nonliving was originally defined ostensively—that is, the meaning was conveyed by pointing out examples of living or nonliving things and hoping the distinction got across to the listener. Cows are alive, rocks aren’t; trees are, dirt isn’t. Do you see the pattern? We do not define life by enumerating every possible phenomenon and stating whether it is alive or not—we are only given a finite number of samples from which to build our intuitions. In other words, the definition is not extensive.

Because the definition is not extensive, when we are confronted with something that wasn’t one of the examples given to us, we have to make a decision. Is this thing more like the examples of living things I’ve been given, or more like the nonliving things? Usually this is easy; a dog moves, eats, and breathes, just like cows and cats, so it must be alive. But when we move further from the central examples, everything becomes murky. Is fire alive? Are snowflakes? Computers? Artificial intelligences? What about viruses?

Not having thought about things this way before, and tired of arguing about it, we decide we need to update the definition of life to cover these new cases. The ultimate goal is to create an intensional definition—a list of defining characteristics that one can use to categorize any object as alive or not, even if you’ve never seen it before. If it has those characteristics it’s alive; if it doesn’t, then it’s not. Sometimes it is easy to see what a group of objects have in common and to construct an intensional definition. Other times, like in the case of life, it’s very difficult.

Consider the following plot. Each point represents a different kind of object; cats, dogs, cows, rocks, trees, viruses, et cetera. Their location is determined by their properties. Maybe the horizontal axis represents a measure of metabolism, and the vertical axis represents a measure of self-replication. It doesn’t really matter. What matters is that we can see two clusters. Let’s say the top-right one contains what we’d call living things, and the bottom-left one represents nonliving things. Animals, plants, bacteria, etc. are all in the top-right cluster, and rocks, dirt, stuffed animals, etc. are all in the bottom-left. The reason we came up with the life/non-life distinction in the first place is because these dense clusters exist. But there are more things in heaven and earth than are dreamt of in your philosophy; what do we do about the dots that don’t obviously belong in either cluster? Where do we draw the line that divides this plot into two groups?

Well, we can choose to divide it however we want! There are many possible intensive definitions that agree with our intuitions, but they disagree with each other about the edge cases. In other words, there are many curves one could draw on the above graph that would separate the two major clusters from each other, but which would disagree about which side the other dots fall on. This is fine—there’s no right answer. Whether to call viruses or artificial intelligences “life” is a subjective choice, based more on convenience and utility than any objective fact about the world.

But this is where the problem occurs. Some people think that our old, intuitive, ostensively-defined concept of life must have secretly been referring to an intensional definition the whole time. They believe there must be a “true” way to define life, the one we really mean when we talk about life, and that there really is a fact of the matter about whether viruses are alive, independent of human definitions. As if there are little tags on every object in the universe that say “living” and “nonliving” that we could see if only we had more powerful microscopes and cleverer philosophers working on the issue. As if there’s one true, obviously correct curve to draw between the two clusters and all other lines are wrong.

But “life” is not a natural category. It’s a convenient way of categorizing phenomena that has proven especially useful to humans. There were two distinct clusters in that plot, after all, so “living” and “nonliving” was a very good concept to have. But that doesn’t mean the universe cares about the exact line where we draw the boundary. The universe doesn’t care if we choose an intensional definition of life that includes or excludes viruses. A good argument could be made for either case.

If you have a definition of life that excludes viruses and I have a definition that includes them, we are not actually arguing over any fact about the material world—we’re not arguing about whether the dot that represents viruses in the above plot is drawn in the wrong place. Rather, we’re arguing over how to draw an imaginary line to categorize things. We’re playing a language game. I think this sort of problem shows up all the time in philosophy. Consider the endless arguments about the true meaning of justice, love, good, evil, etc. I guarantee if you internalize this pattern you will see it everywhere.

Thoughts on Hallucinations and the Supernatural

When I stay up too late—say, past two in the morning—I tend to have auditory hallucinations. Sometimes I’ll hear muffled conversation that stops abruptly when I get out of bed to investigate. Other times I’ll hear music coming up through the floor. Occasionally I’ll hear a voice harshly whisper my name from right behind my head. These are pretty benign as far as hallucinations go, and I usually just ignore them.

One night, I also experienced some visual hallucinations. It was during a summer during undergrad when I had nothing to do, and I had let my sleep schedule drift really far from normal; I was going to bed at 5 a.m. and waking up around noon. That night, I saw dark shapes crawling up the walls in my peripheral vision. I decided to go to bed. A few hours later, I was abruptly woken up by what I thought was a man with his face inches from my own, shouting as loudly as he could while pounding his fists into the mattress near my head. I shot upright and realized I was alone. That’s when I decided I would never again stay up past 2 a.m., and I’ve stuck to this promise.

Aside from hallucinations, I also occasionally have sleep paralysis. I wake up and realize I can’t move, aside from some weak vocalizations and muscle twitches in my arms. I generally find this annoying but not scary, and either continue to twitch until I regain the ability to move, or decide to go back to sleep. I’ve never had hallucinations during sleep paralysis, but one time a relative of mine saw a stereotypical grey alien slowly walking toward them from the corner of their room during an instance of sleep paralysis. Their response was “Oh, that’s neat!” Then they fell back asleep.

This makes me wonder if most ghost sightings are simply attributable to hallucinations. It would explain why most “supernatural” events happen at night. It would explain why they happen most often when you’re alone and tired. It explains why people who claim to have seen or heard a ghost insist that they’re not lying or mistaking a bag for a ghost or whatever—they really did experience it, but they don’t realize it was a hallucination.

Hallucinations are more common than you’d think, and people who don’t know this would probably assume their hallucinations have external causes. “Hallucinations only happen to crazy people, right? I’m not crazy. It was a ghost!” This is a much simpler explanation than some of the other explanations that have been proposed, like the resonances of certain rooms causing people to feel fear and vibrating their eyeballs in just the right way to cause them to see shadows, or that all the people who claim to have seen or heard ghosts are mistaken or lying.