We would all love an argument to end with “wow, you’re right, you have convinced me!” Why then do they so seldom end that way?—if you’re like me, most arguments (especially online) seem to end by giving up in frustration, together with a reinforced idea that the person you were arguing with (and usually, their whole kind of person) is an asshole. So the ultimate effect of arguing is that we all despise each other a little bit more.
Somehow the resolution to stop engaging in arguments is not satisfying. I’ve tried this one. My experience of the internet devolves into a bland echo chamber of likes and positive affirmations. I do not feel intellectually stimulated; interacting with the internet begins to feel like vegging to daytime TV. My ideas are not refined, my critical intellect is not challenged. Restricting the sphere of my interactions, I become so accustomed to the culture of affirmation, eventually the fact that anyone could disagree becomes upsetting and confusing, and when arguments do occur, they are more horrible than ever since I have not been exercising my ability to critically engage.
I have a solution. My solution is superior to many other solutions you will see about discourse, because it is local — it only requires that I change my own behavior; everybody else can carry on as they were. No grand cultural transformation needs to take place; if you read this and engage in arguments this way, even if nobody else reads this article, you will be more intellectually stimulated and have more fun arguing.
I claim that we are all arguing backwards. Let’s ask, what does it mean to win an argument? Conventionally, it means that the position you held going into it ended up being the one that both parties hold at the end. Vindicated! However, if you win an argument in this sense, you have not learned anything new, besides the boring affirmation that you were right. It would have been just as useful to spend your time sitting in your room alone, repeating to yourself the mantra “I’m right, I’m right, I’m right.” The idea has won, but you have lost. Whereas the conventional “loser” of the argument has got a whole new perspective on this issue; their lens has been upgraded, their mundane life has come alive with new patterns, their world has been enriched. Beyond the ten seconds immediately after the argument concludes, feeling the sting of my deflating pride, I would much rather be the loser. The winner has provided a service to the loser at the cost of her own time.
The results we experience in arguments thus make perfect sense. We are all trying to “win”; we are all trying hard to be the one who is not enriched. And we all succeed; nobody is enriched. If we were all a little more selfish, maybe we would start to get something out of arguing. Try to lose! Focus your energy into guiding the argument toward your own utterance of the words “wow, you’re right, you have convinced me!” Win in life by losing the argument.
I’m not claiming you should just lay down and let people walk all over you. To reap the benefits of the loser above, you must authentically lose, you must be earnestly convinced. Never surrender your honesty. Engage in the argument by finding your own objections, discovering those things that are preventing you from being convinced, and asking for the data and logic that will sway them. Assume that your adversary possesses an argument that would convince you, and try to find it. Sometimes this strategy may fail and your adversary will discover they are unable to provide the necessary information; oh well, not every interaction goes your way. Better luck next time!
In conclusion: Don’t go around life helping others by convincing them. Be selfish and make them convince you!
As I mentioned in the last post, I have been feeling a lack of meaning in my life, as though where I am putting my energy doesn’t matter. However, when I try to find a project to invest my energy in, I am overcome with a feeling of confusion. We all want to change the world, but I don’t know what I want to change the world into, nor do I feel I can even see clearly the world I ostensibly want to change. I am growing ever more tired of the political rhetoric I’m exposed to, which seems more and more a tribalistic war; people are not interested in finding real solutions and compromises to the problems we face as a people, rather they care only about whether I am expressing that I am one of the good guys or one of the bad guys. Not only do I find this pattern unhelpful for the advancement of humanity, I find it boring, and so my instinct is to disengage with politics and cultural criticism altogether.
Lately I have been reading and writing a lot in an attempt to see more clearly. However I have an aversion to publishing my thoughts, because I feel they are naïve or incomplete. In this post I wish to criticize this aversion and defend the social value of publishing these intermediate writings. My claim is that publishing my incomplete and imperfect thoughts is a meaningful and positive use of my time.
The Absurdity of Genius
I seem to have a belief something along the lines that you have to be a “genius” in order to have valuable thoughts: the only philosophical perspectives worth reading are those of the approved Great Thinkers, and that mere mortals cannot have any true insight. I think this comes from my schooling, in which the people we study have large names and are exalted and praised. Of course it is ridiculous. How else could someone become a great thinker than by working with and refining what they have? Furthermore, the concept of “great thinker” itself is subject to the same laws of popularity that put Maroon 5 on the Top 40. Furtherurthermore, all theories are amalgams (at least in as much as words themselves are socially constructed, and clearly much more), so it not out of the question that a world-changing theory could be influenced by my ideas.
I am reading Michel Foucault’s “The Order of Things” (which is awesome, by the way). In the introduction he says that the book was inspired by a passage by Jorge Luis Borges, which in turn was written as a critical response to a proposal for a “universal language” by John Wilkins. Here we can see the flow of ideas. Wilkins writes something which Borges thinks is stupid; Borges’s response makes Foucault laugh and then write an insightful book essentially about what is funny about the response; Luke reads the book and decides to start publishing his writing. Perhaps a future Borges will read my naïve theories and make a joke about them which will be the seed of another insightful work.
Refinement by the Risk of Criticism
The lens of publishing helps me refine and add nuance to my thoughts. Insofar as my journal is a log of my thought process, I might write some absurd nonsense that would not hold up to criticism in my journal, and never give it a second thought. That thought-structure is allowed to continue existing in my mind, unexamined. If I publish, even to my meager blog following, I am forced to consider my opinions more deeply, so that I don’t embarrass myself. There is added incentive for me to re-read what I have written, thus to organize it, considering more distant combinations and interactions between my ideas and my knowledge. As a result, a more refined and well-examined knowledge base will, in principle, help provide a stronger theoretical foundation to my future actions, so I don’t get lost in the well of meaninglessness so easily.
Encouraging Nuanced Reflection
One of the problems I identified in the introduction is that I feel that thought is losing nuance and converging toward a few tribalistic echo chambers. I feel that the world would benefit if people would philosophize a bit more. It is certainly possible to navel-gaze too much, but I feel like we are in a period of over-activism and under-reflection. We are in a time of huge protests with tiny results––this indicates that we do not have a clear foundation for our activism. We’ve got the pathos but not the logos. This is not helped by the popular social media platforms, which seem as though they are designed to promote simplistic, echo-chamber discourse. Ideas are communicated in tag-line form, and sealed with a blue checkmark––an idea is good if a popular person said it and we like how it sounds. I believe people are monkeys who imitate each other, so by raising my own standard of discourse, even if my ideas are silly, I am helping to promote a culture of reflection and nuance. I am demonstrating that I value trying to figure it out, rather than having it all figured out, which is doubtless a message I can get behind.
It could be argued that I should keep my ideas to myself until I feel like I have something important to say, otherwise I’m just adding noise. Indeed, it’s something I’ve struggled with in my artistic pursuits, of publishing things that I don’t feel proud of. When I have had a corpus of material available online that I am not proud of, it makes me shy about promoting myself, for fear that I will be discovered as incompetent. But I am not afraid of that here––I don’t care about being a popular writer, I care about refining my own ideas, I care about building a strong theoretical foundation for positive action. So the argument breaks down, it doesn’t matter whether I am proud of my work in this case.
It could be argued that I should be more informed before writing, that I should not claim things which I don’t know for sure. Since I do not have a large reader base I don’t think this is a problem; if I did, I might take this more seriously. I think it is important to plan for your own success––it’s a good question to ask whether, if you did somehow become successful, it would even be a good thing. But just I don’t think it’s important at this stage; the other benefits of publishing outweigh this risk.
Seal Of Permission
In light of the aforementioned arguments, I hereby grant you, Luke Palmer, permission to publish silly sounding ideas in your blog, even if you believe in them.
A recruiter for DFinity, a nonprofit cryptocurrency company working in Haskell, reached out to me the other day. I did some research, read their whitepaper. The tech is pretty clever and interesting, in particular providing solutions to my main two misgivings about cryptocurrency: (1) proof of work, which always seemed like a huge waste of computational resources, and (2) immutability (which some cherish about the technology, but I don’t personally think “pure capitalism” has humanity’s best interests in mind). The alternative to proof-of-work in particular is quite appealing, instead delegating block generation to a series of randomly-chosen “committees”. The immutability solution, “algorithmic governance”, has some clever premises and ideas, though it gets a bit abstract for me, that I remain unconvinced that it would actually work as intended (but it’s possible, I just need more time and information to digest).
Some context in my life: I left Google for “mini-retirement” in early 2016 after I had earned four years worth of savings––I wanted to find out what I would do when there was nothing I had to do. Not really to my surprise, I ended up spending most of my time on music, and have improved vastly as a musician in that time. I still spend some time coding as a hobby, since I still enjoy it. It’s a great life, and I have learned a lot about myself. But one thing I notice that is missing in this life is a sense of purpose––when I try to justify that my music helps people, it always feels like I’m talking out my ass. So, while dedicating myself to my art, I’ve also had a radar out for things to do that will tangibly help humanity. But I’m still in limbo––am I just avoiding my True Purpose as a musician because it’s scary?; am I wanting to help people just for the status?; is believing that my music doesn’t help people actually some self-devaluing belief that I need to let go of?, etc. etc. And I wonder if such questions are just what being alive is like and they never really go away.
ANYWAY thanks for reading my little journal entry there. I’ve been asking myself, if I did take a job with them, how might that be of service in ways that matter to me? And I can think of ways, and it’s getting me excited. I’m not really very deep in the cryptocurrency world, so these ideas are probably either naive or old news. Nonetheless I’m an invent-first, research-later kind of person.
The idea of financial contracts being written precisely and formally is a great idea to me, replacing pseudo-precise legalese with actually-precise math. But smart contracts don’t actually improve anything if they are so complicated that humans, who they ultimately serve, can’t understand them (and we know how quickly code can get unbearably complex). It’s also possible to write misleading code, and in a world based on smart contracts, there is a great incentive to do so. We need excellent tools for understanding and verifying contracts: assurances that they actually express the intent on the label.
Indeed, in a world of public contracts, there are new possibilities for “integration tests” that could detect instabilities, possible market crashes, and the like (though it is difficult to comprehend the magnitude of such an undertaking). There is a story about Simon Peyton-Jones formalizing the Enron scandal, which was allegedly built on an series of impenetrably complex contracts, and finding its error. The story might even be true, since he and others published a functional pearl about financial contracts.
Imagine a continuous integration system of our global financial system, monitoring it for health, automatically rolling back unhealthy contracts, protecting people from shit like Enron and the subprime mortgage crisis before it happened. Imagine also moving to New Orleans and getting deep in the music scene. Imagine doing both at once. Does that sound like a good life, Luke?
I’ve been vaguely wanting to write again––ideas pop up now and again, say, in the car––”I should write about that!”––but then I get home, my habits take over, and the idea is lost. So I guess I am following some wisdom I learned from who-knows-where and dipping my toe in the water, just to see how it feels, and maybe it will become a habit, or maybe not.
I have enough experience with myself to know that when I set out to create some Great Opus––usually a series of blog posts or videos, or anything ending in “number 1”, or anything where I give too much service to imagining the great and important impact that this thing will have––I do the first bit and then literally never work on it again. Commitmentphobe. So this is not that. I am not Starting Blogging Again, I’m just blogging again.
Which is weird, isn’t it? You’d think feeling like something is going to make a splash on the world would be motivating, not demotivating. The only thing I am consistently motivated to do is practice piano (ironically, I didn’t practice at all today, but that does not make me the least bit skeptical of my statement since it has been so consistent for so many years). I suppose that’s not true––I have successfully made short-term commitments to meditate, exercise, what have you, and kept them. I guess my reading of this is that I am deeply process-oriented, not results-oriented. Even in practice––I will happily practice my scales for an hour, but I have tried to make a commitment to master some piece of music by a certain date, or finish a book of sightreading exercises, and those, too, fall through.
About writing… I wonder if I could make a commitment to––shut up. The result doesn’t matter to me, so why make a commitment!? I think this gets at the truth of it. I don’t actually care whether I finish that series of videos, or master that piece of music. Sometimes I spend a lot of time telling myself what I ought to care about, and
Just wanted to let y’all know that I’m making videos sharing the life tools I’ve learned, which have been so valuable and supported me over the years. I think it’s fun to watch, it’s got my piano music in it, and you might even get something out of it.
I have a natural curiosity for mathematical things, but I’ve made the decision to put as much focus as I can on music. So, naturally, I’ve been studying the math of music.
From the perspective of a musician, it may seem frivolous to study music mathematically. After all, does all this left-brain stuff really help you express yourself? I think it does. By investigating musical structures systematically, we can build our intuition, our understanding of how the pieces fit together, and then more ideas are available to us. It also allows us to hear others music in a more detailed way, with more language available for our minds to describe, and thus understand, patterns.
Today I wanted to share some of the investigations I’ve been making into modes and scales, from a mathematical perspective rather than a sonic perspective. Some of this stuff is well-known to musicians, and other bits of it are rather novel, as far as I know.
Here I’ll quickly review modes. Play a C major scale, all the white keys starting on C. Now play another scale starting on A with all the white keys. This, as you may know, is the minor scale. It has all the same notes as C major, but because it starts in a different place it sounds different. This is how modes are generated — we use the same notes but start in a different place.
We always refer to the key of a mode by the note it starts on. So the two scales we just played are “C major” and “A minor” — they have the same notes, but they started in different places, and we refer to them by their starting position. In “C major”, C is the key, and “major” is the mode.
The modes that have the same notes as a major scale are called “natural modes” (I’m defining this right now, I don’t think this is standard jargon). There are 7 of them (because there are 7 different places to start!). Play all the white keys starting on each of these notes and you will get the different modes:
Start on C: major (aka “ionian” if you want to be pretentious)
Start on D: dorian
Start on E: phrygian
Start on F: lydian
Start on G: mixolydian
Start on A: minor (aka “aeolian” for the grandiloquent)
Start on B: locrian
It is a bit hard to hear how these sound when you play them next to each other — our mind aligns to the key of C major and it just sounds like we are playing runs in C major. To hear how these sound, and also to exercise your music math skills, transpose all these modes so they start on C. So look at the pattern of whole and half steps, e.g. minor goes whole-half-whole-whole-half-whole-whole, and then do that same pattern starting on C. It looks like this:
Do this for all the modes above, starting on C. Doing it this way you will get a feel for how each of the modes sounds.
(Another way to think of this if you know your major scales already, is that for dorian you play a Bb major scale starting on C, for phrygian you play a Ab major scale starting on C, and so on.)
For expert mode, do it starting on all the keys (I do this as part of my daily practice). Obviously don’t burn yourself out though, learn a little at a time.
It turns out there’s a best order to do this in: it goes lydian, major, mixolydian, dorian, minor, phrygian, locrian. Doing it in this order will show you something about the relationship between the different modes (I’m not going to give it away!).
After we get going here, we’ll see that there are actually 21 different 7-note modes. It took me a long time just to learn the names of the 7 natural modes, and the other modes we will study often don’t even have agreed-upon names. So first I’m going to give a scheme for naming modes, which also helps you think about them.
We will focus our attention on “4 note scales”. In the natural modes, there are only four of these that ever appear. Their names come from the most common natural mode that they are the first four notes of.
It’s of course about the pattern of whole and half steps, not about the specific key we’re starting on. Every natural mode can be made by putting two of these guys together, with an appropriate step in between. For example, the minor mode:
Thus I might refer to the minor mode as “minor phrygian” or “min-phr“.
Notice how there is a whole step between the two components. You put in whatever step between the two fragments that will make the last note the same as the first one. It’s usually a whole step, but it will be a half step when lydian is one of the components, because there’s an extra half step between its first and last notes. For example:
This mode (which is not a natural mode, by the way!) has a half step between its two fragments.
(Theoretically the lydian-lydian mode should have a 0th step between its two components. Instead we just fuse the two identical notes into one, and you get the six-note whole tone scale.)
With this vocabulary, we can refer to the 7 modes in a way that makes them easier to understand:
Play each of these modes, concentrating on their fragment anatomy.
This anatomy suggests more modes than the natural ones, for example the min-lyd mode we saw above, which doesn’t appear as one of the natural modes. What’s up with that?
Melodic Minor Modes
In standard music theory, the min-lyd mode we saw above is one of the modes of the melodic minor scale, and it does not fit into the scheme of natural modes (i.e. it won’t be all the white keys starting from any key). The melodic minor scale is a major scale with a flatted third:
And it sounds really cool (very classical sounding when played as an ascending scale, and becomes much more jazzy when you start building riffs out of it). The melodic minor scale has 7 of its own modes, just like the major scale. You can find these by playing the melodic minor scale above starting on each of its consecutive degrees, just like we did for the natural modes. The colloquial names I’ll give for these are from Mark Levine’s excellent book “The Jazz Piano Book”:
Start on C: min-maj (“melodic minor’)
Start on D: phr-min
Start on Eb: lyd-dim* (“lydian augmented”)
Start on F: lyd-min (“lydian dominant”)
Start on G: maj-phr
Start on A: min-lyd (“half-diminished”)
Start on B: dim*-lyd (“altered”)
Notice that there’s a new fragment that we haven’t seen before in a few of these scales, the diminished (dim) fragment:
Like the lydian fragment, it does not have a perfect fourth between its first and last notes. Whenever there is a diminished fragment as part of a mode, the two components should be separated by an extra half step. Because we’re only looking at scales with whole and half steps right now, and usually fragments are separated by a whole step, that means that the diminished fragment is always paired with a lydian fragment to cancel it out — otherwise we’d end up with a minor 3rd somewhere in our scale (which happens, e.g. in the harmonic minor scale, we’re just not considering that at the moment).
Transpose each of these modes into C (or wherever you like) to get a feel for how they sound.
If you make any mode randomly out of whole and half steps, chances are it’ll be either a natural mode or a melodic minor mode. They account for two-thirds of all the possible modes. There is one more type of mode that we haven’t covered, and is very uncommon in western music (which makes me itch for opportunities to use it!). I’m not sure what to call it, right now I’m calling them “exotic” modes alongside the “natural” and “melodic” modes. It looks like this:
These modes are strange because they have two half steps in a row (separated by an octave in the the above version, but notice it has B,C,and Db). This means many of its chords have major seconds as intervals, and it’s quite weird and foreign sounding.
But I am interested in it because together with natural and melodic modes, we have now covered all the seven note scales. No matter what scale you make, as long as it has seven notes and no interval greater than a whole step, it will be a mode of one of these three families. Why?
Let’s consider what it takes to make 7 intervals cover 12 half steps. If every interval were a whole step, the scale would span 14 half steps, which is 2 too many. So we need to shrink it by two half steps: change exactly two of the whole steps into half steps. The different families come from the different places we can do that.
Put your focus on the two half steps in the scale. They can either be separated by 2 whole steps, 1 whole step, or none. They can’t be separated by 3, e.g.:
Because you can just rotate it around
And now we can see that they’re actually just separated by two.
So when you have your scale, it should just have two half steps in it. If they are separated by two whole steps, it’s a natural mode; if they’re separated by one, it’s a melodic mode; and if they’re separated by none, then it’s an exotic mode.
There you have it, some interesting mathematical music stuff. I have more — there are lots of neat symmetries between all these modes, but I’m tired of writing for today. Remember to follow me if you’re into this kind of thing (lower right). I get a little burst of approval happiness every time I get a new follower, and it makes me want to write more! The same goes for sharing, of course. ;-)