My dad used WordPerfect 5.1 for DOS to manage our tape library.
The first computer I really had regular access to was my parents’ 486DX 33 MHz with 8 MB of RAM and a 250 MB disk. It came from the shop with various software, I don’t know if that included WordPerfect 5.1 for DOS or not. I don’t know if the shop bundled it—this was common in that era, but my parents friend Jim “Computer Man” Myers (recently deceased) also came and brought shareware over to the house and might have snuck in a copy. It was a widely pirated program.
My parents love poetry, although now that my father has dementia I doubt he appreciates it much. He suffered a traumatic brain injury when he was around 18 that left him with Broca’s aphasia, which meant for him that while he could understand people without much trouble, it was hard to string a complete sentence together. We got used to slipping him a word he was groping around for so he could finish his utterances. He used to write poetry too. One was published in Arizona Highways although I can’t find a link to his poem online.
I think trying to figure out how to use this machine led him to take a community college class on computer literacy. Whoever taught the class must have been a complete maniac because the text was The Secret Guide to Computers, I believe 16th edition or so. If you haven’t seen this book, you are really missing out, because it’s enormous, loaded with tacky clipart, and has the author’s opinion on pretty much everything related to computers over the last decades. The author, Russ Walter, has his phone number on the cover and says you can call him if you ever have troubles.
I did have troubles at one point, I had made the mistake of using Drivespace^3 on another computer and lost all my data. I called Russ and he basically said that program is crap, hope you have backups. I felt let down by this at the time but of course he was right.
I stole this book from my dad and learned an enormous amount from it and I think it led me to my early obsession with programming language diversity.
What did my dad do with this computer? Much less than my mother, who used it to type up all sorts of work-related stuff. She used WordPerfect to write memos and training materials, and she used Print Shop Pro to make certificates and other stuff for work. We used something like Greeting Card Creator to make cards for special occasions. But my dad apparently did two things with it: he wrote up his personal journal and poetry, and he maintained the tape library.
My mother is a bit of a hoarder and my dad was a bit of a financial worrier. My folks did some odd things at the intersection of hoarding and penny pinching. One was the tape library. We must have arrived fairly early on to the whole VCR scene; I have a fairly early memory of trying to watch Zebra in the Kitchen by finding the tape in the list. The list looked something like this:
Buckaroo Banzai......................93, 204
Robin Hood...............................123The movies were alphabetically sorted, and if there was more than one number it meant that the movie had been recorded twice. We had basic cable and sometimes got HBO or Cinemax during a free week or something. Mom would buy extra tapes for when that would happen. The VCR was set to the lowest quality setting so she could cram 6 hours of video onto one tape. She’d pop the tape out, put the label on it and list the movies that were recorded on it and then give it to Dad. He would figure out the last number in the library and write the new number on the tape and go off to the computer room and update the list by hand. I think we topped out around 350 tapes; my brother thinks 400, and they were stored in several bookcases around the house. Most tapes had 2 or 3 movies on them.
I recovered files from this computer some time ago but they’re sitting on another computer right now that I don’t have access to. I started copying the files onto my Dropbox so I could go through them but the upload got stalled out after 6 hours or so. Still I have seen enough other samples of his documents to be fairly sure that he organized this file without using either the built-in sort function or right-aligned tabs or dot leaders. I recorded a session of myself pretending to do this with WordPerfect 5.1 in DOSBox, but using those features:
You can probably tell from this description that what my father really needed was a desktop database. As far as I can tell, he didn’t really survive the transition from DOS to Windows. He eventually became somewhat conversant with the Mac, able to do the same kinds of things he did in DOS, but Windows was I think a bit too much for him at the time. I think the situation with my mom was the opposite; DOS was really befuddling but Windows (and eventually Mac OS X) were pretty easy to get around. Neither one of them ever really became users of desktop databases like Access. I think dBASE would have been way too much for him, although if he’d never had that brain injury I’m sure he would have loved it.
WordPerfect is kind of an amazing program. You can learn the fascinating history by reading this excellent book Almost Perfect but it raised for me the question of “what is a word processor?” The answer, in brief, starts out with the Wang 1200 as “a typewriter with memory.” WordPerfect started here and evolved in many interesting directions. Apart from the somewhat obvious functions you see in the above recording, it has an interesting “math mode” that deserves a longer post of its own, which doesn’t really exist in modern word processors.
Some famous writers still use DOS word processors like WordPerfect and WordStar. A part of me assumed that this was because of the “distraction-free” nature of these programs; another author made similar investigations. Doing my own learning, I can see some truth to that, and that running WordPerfect in an emulator doesn’t quite do it justice because you can just pop over to your browser and get distracted. But another way it doesn’t quite work is that every function key does something in WordPerfect. To get access to everything it can do you would have to eliminate all of DOSBox’s key bindings. WordPerfect came with a “template” you put over your amazing Model M keyboard’s function keys to see at a glance what it could do. You can see it at Xah Lee’s site. I imagine using WordPerfect 5.1 for DOS as an expert user, you would be able to do things extremely quickly. It was a very high-bandwidth conversation between the user and the machine. Not for my parents, of course, but for expert users.
For my parents, it was just a great way to write a professional letter, a personal journal, a poem, or to manage the tape list.
I finished Lockhart’s Lament, the 25-page version, and I have some feedback about it.
On Proof
I regard proof as being the defining activity of math. Really the trio of axiom-theorem-proof. However, proof is the real heart of the matter.
I used to have a sort of mystical admiration for the idea of proof. Then Tyler taught me a little bit about Coq, the theorem prover, using Software Foundations. I learned that proof is always intended for an audience, and that the most objective audience would obviously be a computer, a program that is going to make the same determinations every time, thus formal proof is the best kind of proof. Tyler didn’t say this, but it was one of my takeaways anyway.
Now taking Basic Concepts of Mathematics, I’m seeing proof as a story. The audience may vary—I’m a weaker audience than my professor, so I need more hand-holding. But an informal proof can still be rigorous. And I think this is the point that Lockhart is making about teaching kids to prove: we should not hold them to the same standards of rigor, but we should nonetheless expect them to make a mathematical argument.
This reminds me of the “black box game” which I learned about, as a way to teach your kids something about functions. The way you play the game is they give you a number and you give them another number, and they have to figure out how you came up with it. For instance, if you give me 3, I might give you 3, and if you give me 4, I might give you 5. If they know about odd numbers, they may say, “oh you’re giving me an odd number, either my number or the next odd number.” This is a way of helping kids think about functions without being too limiting about how they are constructed. (Another key takeaway for me from this class was that a function is not a bunch of algebra, it is defined if there is a way to find the unique value associated with the argument, whether that is a bunch of algebra or not.)
On Math and Science
Tyler provides an interesting definition here: math is about deduction and science is about induction. In science, we chip away at irrelevant details of reality to try and generalize to everywhere. In math, we can never depart the realm of pure reasoning and make contact with actual reality. I find this thought quite beautiful. It’s almost like a limit, defined from the left and the right, but there’s no reaching the limit other than by assuming it. A beautiful thought, I guess, to me, apropos of nothing in particular.
On Education
Lockhart returns repeatedly to a metaphor of a music teacher who is unable to play an instrument or has never heard music but is simply able to manipulate the notation. There’s an allure to this metaphor so I can’t completely begrudge him but I do have some feedback here.
First, school can and often does have negative effects in every subject. I actually think you can point to music as an example of this: Benn Jordan recently did a video about why there are so few women in the music industry and one (of many) reasons is that we typically make girls learn symphonic instruments like violin and cello, whereas we allow boys to learn instruments like guitar and drums—which are actually used in the modern music industry. The folks with bumper stickers bemoaning funding for band class in school are of course not imagining that we’re going to fill the room with 808 clones and electric guitars with distortion pedals and allowing real noise to be made. They’re picturing 30 kids playing a chamber music piece written sometime between the invention of the printing press and the electric lightbulb to a room full of well-dressed parents calmly golf-clapping. Every subject is ruined by school, not just math. Hence the joke about those who can and those who teach. My apologies to a certain reader who absolutely can is about to start to teach.
That said, I think the curriculum is changing, albeit not to the extent that Lockhart would like. But this essay is 20 years old now—some sympathizers have had time to get power. My kids love their math classes—they’re in 4th and 1st grade—and one of them said her entire class asked for more math homework. They’re worksheets, sure, but they like now to show you a half-dozen ways of solving similar problems. My son clearly has multiplication tables memorized, but at no point did the school send him home with flash cards and tables to fill out. I don’t know exactly how he learned it, but he knows the material. Things are not the same as when I was a kid.
You can actually see the effect of this in places like National Review. We have here a great example of people demanding that things be different, and then being upset when they are not the same (which is exactly what you expect from National Review). But in fact, I recognize some of these problems and several of them are great—if you’ve been taught the material. But many of these problems are using new approaches and if you weren’t taught them and aren’t inventive enough to figure them out, well, you see what happens.
In Conclusion
I had a powerful experience taking this class, and reading “A Mathematician’s Lament” while taking it helped me acknowledge that it is a powerful experience. Lockhart wants my kids to have that experience too. This isn’t a coherent vision of how to restructure math education. It’s a plea for people to experience math the way they experience art. I’m sad that I was 39 before this happened to me.
I want my kids to experience this too. Preferably before they turn 39.
I recently became aware of continued fractions, because my friend Randy mentioned that they are a representation of some insane thing in topology that he mentioned offhandedly and which sort of made sense while he was talking but I really could not reconstruct. However, continued fractions are interesting in their own right, and I started working on this post before I saw the Mathologer video on this topic.
A continued fraction is a nightmare scenario where the denominator of a fraction contains another fraction, whose denominator contains another fraction, and so on, perhaps forever. We can calculate a continued fraction by repeatedly taking the inverse of a value and adding a constant. This may seem counterintuitive at first, but since the denominator of a denominator is in the numerator, it makes a weird kind of sense that you can just keep on inverting. For instance, the Golden Ratio can be calculated by starting with 1 and then in a loop, adding 1 and inverting. Such an expression will eventually converge to the best floating point approximation, and that calculation looks quite trivial in J and APL:
((1+%)^:_) 1
1.61803Similarly in APL:
(1+÷)⍣=1
1.618033989Tyler did mention that I would of course resort to these languages as some kind of humble brag. Which is true and fair. Expect it to get worse if I ever learn linear algebra.
Both of these expressions essentially construct an “add one and invert” function, which they then locate the fixed point of, given an input of one. The choice of input doesn’t really matter much:
(1+÷)⍣=100
1.618033989
(1+÷)⍣=0.1
1.618033989This turns out to be a stock example in the Dyalog documentation:
1 +∘÷⍣= 1 ⍝ fixpoint: golden mean
1.618033989Furthermore, it turns out every square root can be expressed in a similar way too, either by a finite or an infinite repeating continued fraction. The trick is discovering what the base number is and what the repeating number is. For instance, for 2, the base is 1 and the repeating digit is 2:
1+÷((2+÷)⍣=2)
1.414213562
(1+÷((2+÷)⍣=2))*2
2Similarly, for 5, the base number is 2 and the repeating digit is 4:
2+÷((4+÷)⍣=1)
2.236067977
(2+÷((4+÷)⍣=1))*2
5These same calculations can be made in Haskell if we develop our own fixpoint. We can generate this with iterate but we need to determine when to quit with something like this:
untilEqual :: (Eq a) -> [a] -> a
untilEqual (x:y:xs) | x == y = x
untilEqual (x:y:xs) | otherwise = untilEqual (y:xs)Now we can create somewhat more readable versions of these things:
*Main> untilEqual $ iterate (\x -> 1 + 1 / x) 1
1.618033988749895
*Main> 1 + 1 / (untilEqual $ iterate (\x -> 2 + 1 / x) 1)
1.4142135623730951Let’s make this a helper function.
squareRootCf :: (Fractional a, Eq a) => a -> a -> a
squareRootCf a b = a + 1 / (untilEqual $ iterate (\x -> b + 1 / x) a)Now we can compute these more easily if we know the basis and repeating digits:
*Main> squareRootCf 1 2 -- sqrt 2
1.4142135623730951
*Main> (squareRootCf 2 4) -- sqrt 5
2.23606797749979
*Main> *(squareRootCf 3 6) -- sqrt 10
3.1622776601683795It turns out Haskell has a rational type we can use, in Data.Ratio:
infiniteCf :: (Integral a) => a -> a -> [Ratio a]
infiniteCf a b = map ((a % 1) +) partials
where
partials = (1 % b) : [recip ((b % 1) + prev) | prev <- partials]We can then generate rational approximations:
*CFrac> take 10 $ infiniteCf 1 1
[2 % 1,3 % 2,5 % 3,8 % 5,13 % 8,21 % 13,34 % 21,55 % 34,89 % 55,144 % 89]As you can see that’s producing 2, 3/2, 5/3, 8/5, 13/8, etc. which is the Fibonacci-like sequence of ratios you get for approximating the Golden Ratio. This is kind of explained by the above Mathologer video, so to spoil it for you he calls this is the “most irrational number” because it has the slowest-to-converge repeating continued fraction.
We can also produce some pretty compelling root-2 approximations the same way:
*CFrac> take 10 $ infiniteCf 1 2
[3 % 2,7 % 5,17 % 12,41 % 29,99 % 70,239 % 169,577 % 408,1393 % 985,3363 % 2378,8119 % 5741]What’s interesting about this you ask? One thing I find interesting is that you aren’t really bound by what floating point happens to represent. You could of course resort to using some arbitrary precision library, but then you might want to know what’s (one way) of doing whatever it does under the hood. How do you get arbitrary precision? One way that you could build a system like that would be on continued fractions. But you don’t really get perfection out of a continued fraction representation of a square root. Instead, you get something back where you can say, I want more precision than that, and it will give you another, better rational approximation. For instance, we can ask Haskell to take the square root of two and tell us what its ratio is:
*CFrac> toRational $ sqrt 2
6369051672525773 % 4503599627370496Seems pretty good, but it doesn’t take us very many iterations to beat it:
*CFrac> length $ show $ denominator $ toRational $ sqrt 2
16
*CFrac> takeWhile (\x -> length (show (numerator x)) < 18) (infiniteCf 1 2)
[3 % 2,7 % 5,... 41 more elided..., 83922003724759193 % 59341817924539925]So we have already discovered that 83,922,003,724,759,193 / 59,341,817,924,539,925 is a better approximation of the square root of 2 than 6,369,051,672,525,773 % 4,503,599,627,370,496, which interestingly, does not appear in the list of rational approximations we generate—which would be very surprising, because the rational approximations generated by the continued fraction are proven to be the best rational approximations at their information content, except for a couple problems: namely, that floating point numbers are literally the worst, and we’re probably using some kind of hardware root approximation that is very fast and, you know, tolerably accurate (note that (sqrt 2)^2 = 2.0000000000000004, for instance).
Another fascinating property of continued fractional representations of these numbers is that they bounce back-and-forth above and below the value they’re approximating. So you could easily specify a precision you want, and just take from the representation until the difference between the last two approximations you generated is less than that precision. This is starting to sound suspiciously like a Dedekind cut (infinitely many better and better rational approximations of a real number), or maybe like the epsilon-delta concept of a limit (find me an approximation that’s closer than epsilon to the number).
It turns out this information isn’t very new; in fact Bill Gosper of Lisp/Macsyma fame developed a procedure for doing arbitrary sums and products with continued fractions. If you find that appendix hard to read, perhaps you’ll enjoy Mark Jason Dominus’s discussion of the same topic a little more, including a reference implementation of continued fractions in C.
I live in Socorro, New Mexico, which is near to the Alamo Navajo chapter. The Navajo are the largest Native American tribe by membership in the United States, and their combined lands are the largest of any tribe in the United States. Their reservation includes much of their historical homeland. Their language is the most widely spoken Native American language in the US—I often hear Navajo spoken at Walmart. Navajo culture is an important part of what makes New Mexico the special multicultural melting pot that it is.
I developed an interest in the Navajo language a couple years ago. The Navajo language seems practically engineered to differ from English on as many levels as possible:
- Tone and length distinctions
- A wealth of consonant sounds we either do not have or do not distinguish
- Zero noun morphology
- Verb morphology that makes linguists blush
- Animacy distinctions
- Productive dual number
It is rightly held in high esteem by linguists and is thoroughly different from any language a random American like me might be familiar with. Unlike many other Native American languages, there is also a huge amount of quality resources for the Navajo learner.
In general, I think spending money on Navajo language resources does more good than harm. Demand for Navajo language materials makes it more profitable to produce them. The Duolingo course is OK. If you have the money I have heard that the Rosetta course is very good. I bought several books, I particularly liked Conversational Navajo because it came with a CD. Navajo orthography and pronunciation is very regular, although it is difficult for adult second-language learners. I can’t roll my r’s very well, but that doesn’t matter in Navajo because there’s no rs. If you can imitate beatboxing you can make ejective consonants and you will be able to make the sounds. Unfortunately English treats aspiration as allophonic variation so there are some phonemic sounds in Navajo that you’ll have some trouble distinguishing. But you will be able to produce them.
If you want to know more about the grammar, The Navajo Language is pretty complete and goes into huge detail, but will be hard to learn from. The Navajo Verb is just amazing (I have skimmed it via ILL) but way beyond my level. The language is just about as far from English as you can get, and pretty irregular. At the moment I’m fairly content that I can say hello, what’s up, and distinguish it from other languages that are spoken nearby.
There are a lot of massive and wonderful Navajo books. If you want to learn Navajo and live outside New Mexico and Arizona, I would strongly recommend figuring out a way to get interlibrary loan going through your school or a local academic library, and start pulling stuff in from libraries here.
There’s also a lot of apps. You can listen to Navajo radio, you can get Clayton Long’s videos on Youtube if you have patience for it. There’s another guy, Daybreak Warrior who goes over words and you can listen to his stuff and really improve your pronunciation.
Navajo culture is really interesting and beautiful. I enjoyed what I got from Diné Bahane’ and there are lots of other booksto read as well, like Sharing the Skies and Food Sovereignty the Navajo Way. I would strongly recommend getting familiar with Navajo Taboos. There are a lot of things it really isn’t OK to ask about. You should expect to get a somewhat aloof treatment, at least until you make a friend. People love to tell you their story and you’ll be really surprised by what you hear, but don’t press anyone about superstitions or supernatural stuff.
When I started I had big dreams about becoming fluent. Contact with reality kind of disabused me of that notion. I’m content to be a friendly neighbor. But there’s a ton of resources out there, many of them free or inexpensive, and I don’t think you’re harming anyone by loving something enough to study it.
Originally posted on reddit but the original context is now gone.
I am just finishing up the book Math Without Numbers by Milo Beckman. This is a good book for a layperson like me, in that in introduces lots of interesting stuff and provides a kind of a map to mathematics.
I have a hunger for more knowledge about math, and I found the book a bit like an amuse-bouche before a meal that isn’t coming. I’m not entirely sure what to do about that, since I’m not prepared to return to school for math, yet I’m not satiated by superficial treatments of math from YouTube videos and the like. I think if I had taken an extra year or two of math in college, it would be easier for me to make progress on my own.
Real Numbers
I got interested in the real numbers a few years ago and read Essays on the Theory of Numbers by Dedekind, who has this amazing quote at the beginning of the book:
The present memoir soon after its appearance met with both favorable and unfavorable criticisms; indeed serious faults were charged against it. I have been unable to convince myself of the justice of these charges, and I now issue a new edition of the memoir, which for some time has been out of print, without change, adding only the following notes to the first preface.
The real numbers present a sort of confounding problem. We need real numbers to handle irrational numbers such as √2 and the like, which can be approximated. But the uncountability of the real numbers, their absolute continuity, is a property that is needed for calculus. Yet we’re unable to construct a single real number that doesn’t also belong to the set of algebraic numbers, which are countable. This is sometimes called the “hay in the haystack” problem. Neither one of us has ever seen a real number and probably never will.
Topology
Measure is an elementary topic of topology, and I’m an expert because I’m on page 35 of a book about it, Introduction to Topology. The book is great. On page 35, though, I got the answer to a question I sort of posed a number of years ago in A Heretical Calculus, why don’t we use a number system with an actual infinity and actual infinitessimals, since that’s what Newton did and for a few hundred years it seemed to be fine?
Figuring out a way to solve our problems with these “hyperreal” numbers occupied math for quite some time but the solution, the epsilon-delta definition of closeness, is not just a nice solution. It happens to open up the possibility of doing calculus to many other situations than just real numbered functions. Exercise 2.4 in Introduction to Topology has you prove that integration of functions over a fixed domain form, themselves, a metric space. This means you could in principle do anything you do with calculus over that space, like integrate.
Talking to my friend Mike Tamburro about it, I get the sense that topology is not so much about donuts and spheres and whatever as it is about questions like, what does it mean for points to be close? What is a neighborhood? What do does “connected” mean? All of these questions seem to spring forth from the idea of continuity. In our first-year calculus classes we get a very pragmatic sense of what continuity is about, but what does it really mean?
Proof
Solving the first three assignments on page 35 of the topology book, I found myself wrestling with the same old questions I have always had about proof. How do I know if a proof is complete? How do I know if a proof is good?
Many years ago my friend Tyler taught a class about theorem proving using the book Software Foundations. I wrote about this before briefly, but that class raised some other questions: if you’re not able to convince a computer of the proof, does it count as proof? What if you’re able to convince a computer but you don’t understand it yourself?
I still don’t really have the answers, but I decided the following for this attempt:
- I should understand that something I’m supposed to prove is true. I should understand why before attempting a proof.
- I should try to write a proof that would convince me, sometime in the future, when I have forgotten about this.
- I should not worry too much about convincing a real mathematician.
This comes down to the problem that I didn’t have to do any real proofs in college, so I never wrote proofs or had them scrutinized. Writing real proofs is probably at least half or more about having experience reading real proofs, and that isn’t something I spent much time on in college either. This is a bit like trying to write programs without reading programs.
I would say about half of my skill at programming comes from be able to read code and reading other people’s code and stealing their ideas. So to get better at writing proofs, I need to spend time reading proofs, struggling with writing proofs, and then stealing other people’s ideas when I finish them. This is all going to take time.
I would have hoped that formal proof, i.e. software proof using things like Coq and Lean would help with writing informal proofs, the kind that mathematicians like. In practice though, it doesn’t seem to be the case, because A) you might know something is true and not really be able to convince a theorem prover, because you don’t understand enough about the system or how to write the tactics or whatever, and B) it often does seem to be possible to convince the machine that something is true without really knowing what steps it took, thanks to automated tactics.
I spent some time this last week playing The Natural Number Game which is a pretty cool introduction to the Lean theorem prover. I still came away with the feeling that the game of building the proof didn’t necessarily come with a lot of understanding of what I was trying to prove. And I absolutely do not see how to take a book like Introduction to Topology and do my homework with Lean. I just have no clue how you would get started. So that remains an open question: would it be useful to learn Coq or Lean enough to be able to use it to assist with one’s homework in some other advanced class? Or is that just a bridge too far?
Lattices
I learned a little casual abstract algebra from Haskell, but one area I had never heard anything about was lattices, until I read this excellent article from Christopher Alexander called A City is Not a Tree.
Lattices are interesting for a number of reasons, but one that might surprise you is that you often do not have a total ordering between some apparently orderable items. We often want a total ordering, so that we can sort a set, but often we only have a partial ordering—some of the elements come before some of the other elements, but not every pair of elements can be compared.
Lattices turn out to be everywhere once you know about them. I was having a conversation last week about my preferences for a version control system. I’ve used (briefly) CVS, subversion, mercurial, git, Tom Lord’s arch, fossil, and darcs. I have trouble comparing some of these to each other but I have definite preferences between some of them. Because I have a favorite and a least favorite (not using version control at all), my preferences form a lattice. What makes lattices interesting is the notions of infimum (meet) and supremum (join), the idea that no matter which pair of elements you present to me, I can give you another element from the same set which is either below or above the pair you presented. When the items are directly comparable, it’s one of those two items, but if they aren’t, I can still find something else from the set to give you.
Considering my version control preferences, the join of nothing and CVS is CVS, because I would prefer you use something (anything) over nothing. The join of Tom Lord’s arch and CVS is probably git though, because I really didn’t enjoy arch when I used it and CVS has lots of well-known issues.
The book I’m reading, Introduction to Lattice Theory with Computer Science Applications uses lattice theory to solve distributed computing problems. I’m sure there are lots of other interesting applications for it. But even having a name for something causes you to search for it and notice when you have it, creating opportunities to leverage your knowledge.
Another area of abstract algebra I wish I knew more about is group theory, which apparently comes up a lot in particle physics.
Final thoughts
I think probably I will try to take a class this fall with an emphasis on proof. My feeling is that getting better at proof will make it much easier for me to explore these areas of math on my own. And being forced to do it with time constraints will probably make it flow more easily. I guess we’ll see.
Computer music at New Mexico Tech
Around this time last year, my friend Eric Sewell said he was going to teach a computer music class at New Mexico Tech. I had been thinking about taking a class, probably a math class like linear algebra, but on a lark I decided this would probably be interesting. I’ve always loved music, but never really learned an instrument, and I thought, maybe if I involve the computer I can get further than if it’s about dexterity and years of tedious practice.
I started the class with no real expectations. We’d be using Csound. The lectures were a mixture of technical stuff about using Csound, basic concepts of synthesis, and listening to works by pioneering composers and musicians in the realm of computer music and synthesis. I didn’t enjoy many of those works except on an intellectual level, but they were all fascinating, and a few I have listened to a couple times since, like The Bull by Morton Subotnik.
I had a “haha embarassing” moment when I realized I could probably replicate the sound from the opening of Regular Show with Csound, and talked to my friend the professor about it. With a hardware synth, this is just opening and closing the filter on a simple saw wave.
Hardware synthesis - Uno Synth
I think I was in class for 3-5 weeks before I realized we were actually talking about synthesizers. I started to think it would be much easier to make music if I had a hardware synthesizer and thus could turn knobs rather than having to create envelopes in Csound, run Csound, listen to the output, and then go back and try to guess what settings had been interesting. So mid-February I bought an Uno synth. If you want to know how it sounds, here’s Jade Wii playing it.
I choose this synth mainly because it had a nice analog sound, was inexpensive, did not have a real keyboard, and wasn’t a Korg. At the time, I was doing a lot of synth hardware comparisons and very nearly got a Korg Monologue, but decided the sound was too clean and cold. I was also intimidated by real keyboards because I had no formal music training, wasn’t planning on getting any formal music training and just wanted to make interesting sound. My friend Drew Medlin came over with his synths and I found myself quite unable to do anything interesting with him, partly because I just had no familiarity with the keyboard.
I found that I did greatly prefer interacting with the synth via the knobs, so much so that I found it very hard to be excited about using Csound again. When Covid hit, I had a nice excuse to drop the class, which was going to culminate in making some kind of 2-minute composition I was also terrified of. I also felt like Csound was so wide-open in terms of what it would let you do that it was impossible to figure out how to do rhythm effectively, and so there was no way to structure a song. I had to basically draw out on paper what I thought I wanted, program it in, compile/run, then tweak it and try again. It was reminding me too much of programming. I decided I wanted to escape from the computer altogether, and get deeper into an instrument.
Do I recommend the Uno Synth?
I realize some people reading this may be looking for reinforcement on the idea that maybe they should get the Uno synth. It is, after all, the one of the most affordable analog synthesizers out there.
I do not recommend the Uno synth. I say that without hate. There are aspects of the design of the Uno that make it hard to enjoy. One is that you want to power it with batteries, because if you use USB you get noise. But there are parameters in the patches that can only be reached by the companion applications, which must connect to it over USB. Ironically, the noise setting does not appear to “stick” unless you reach it from the companion application.
The USB connection, on the other hand, draws a large amount of power—this is an analog synthesizer, after all. Well, I found that the power draw was enough to damage my cheap Aukey USB-C port dongle thing. Maybe you could just power it over batteries? Yes, except the thing has a runtime of 1-2 hours on 4 AA batteries, and they strongly recommend against rechargable batteries. That makes sense, the power draw on this thing is enormous, and it starts acting funny in all sorts of surprising ways when the batteries start going low.
You can get around the USB noise problem by buying a USB isolator (?) for $40. Thanks.
My kids dropped it once, and that was enough to dislodge something in the battery case, so that now it can no longer really take AA batteries. I have worked around that by stuffing a wad of aluminum foil in there, but guess what, I now have noise issues in AA battery power mode.
I think it has a good sound, on the filthy side which I like, but I found these little frustrations depleting, and even getting around these, I started to see that it wasn’t really for me, although I made other mistakes first.
I think you were me, just starting out, and your budget is $200, you should probably allocate your funds elsewhere for your synthesis journey.
Elektron Model:Cycles
In April, I became aware of the Elektron Model:Cycles. I was very intrigued by FM synthesis from the class, and really felt like the complete absense of anything like a rhythm primitive in Csound was driving me away. This device appeared and was built around both FM synthesis and a very powerful rhythm concept, capable of doing polymeter or polyrhythms easily. Online, people talk about “the Elektron workflow” a lot and it was intriguing to me. Plus, it would keep me away from the computer. And then I saw this video, which basically sold me on the sound of it.
I made quite a few songs (or at least songish performances) with the Cycles, which you can find on Soundcloud if you really want to suffer. I didn’t realize it at the time, but it has a feature that novices greatly appreciate: it appears as a USB audio device when you plug it into a computer, and no hardware audio interface is needed for you to record it! This is a significant benefit for sharing what you do without having to throw out another $100–200.
I dove into the Cycles pretty hard for a month or so. I became a little disillusioned that I couldn’t make anything as nice as Jeremy from Red Means Recording, as if a guy playing music for a month on one device really had a chance to catch up to a professional with decades of experience. I didn’t realize it until months later, but a blank pattern on the cycles has one of each “machine,” which kind of implicitly guided me towards trying to make songs with one kick, one snare, one cymbal, one tom, one chord progression, and one melody line. In fact, I ran into the same obstacle as with the Uno pretty quickly, that it does not really have a keyboard and I didn’t really know how to play a keyboard even if it had one, so the beautiful melodic lines that Jeremy and others are able to make on these devices were just out of reach for me unless I bumbled into one on accident, which mostly I did not. I expected that I could make a decent drum line (there was a Pocket Operator PO-12 “Rhythm” purchase that I forgot to mention somewhere between the January and May), and I could, so most of the frustration came from the melody/chord side of the house. And the keyboard problem was getting untenable.
Do I recommend the Model:Cycles?
I have mixed feelings about the Model:Cycles today. I do use it from time to time, but although the presets show you a really wide variety of sounds, I mostly feel like the stuff I am making is all sounding about the same. I find FM synthesis fascinating and thought the kiddie pool version of it in the Cycles would be both powerful and easy to use. That thesis is wrong, but whether it’s because I’m too immature or it’s not that powerful, I don’t know.
I assumed because I enjoyed using the PO-12 that the “Elektron workflow” would be a natural fit for me. I did not find that to be the case. At the time I was trying to avoid using the computer as much as possible and my assumption was that by being marooned away from the computer would force me to get better at playing the instrument. I think considerable effort must go into programming a track on the Model:Cycles. I’m quite open to the possibility that it just requires more work from me than I have been willing to put in.
If you are curious about the Elektron workflow, both the Model:Cycles and the Model:Samples are affordable ways to find out if it’s for you. The instrument is sort of a curiosity for me now. I think of it more as a drum machine, but I don’t enjoy using it as much as the PO-12.
Syntorial
Subtractive synthesis is just one type of synthesis, but it’s widely used in hardware, especially analog synthesizers and analog-modelling digital synthesizers. The “four part” subtractive synth is a classic design, and something that I eagerly tried to replicate in Csound for the class. The idea that presets could create so many distinct and amazingly different sounds from just a few parameters fascinated to me. I discovered Syntorial, which is basically ear training for subtractive synthesis, and became enamored with the concept of hearing a patch and being able to recreate it just by knowing which knobs to twist.
I emailed Joe shortly after the pandemic started asking if he was offering discounts, and indeed, he gave me a discount immediately and then did a big public offer. I got Syntorial, and am about halfway through it now. A major lesson of this year has been that there just isn’t enough time for my hobbies, and I have a burgeoning pile of tutorial material I still need to get through, and Syntorial is in that pile.
I enjoyed taking what I was learning from Syntorial and applying it on the Uno synth, but the Uno synth was showing its limits. I started thinking about a larger synthesizer, one with a real keyboard that would enable me to actually learn how to play a little bit, or at least understand some music theory. I waffled between wanting something small that I could use on the couch, like the Yamaha Reface CS, and something larger, like the Arturia MatrixBrute. But then something awful happened.
I fell in love with the Moog sound.
If it isn’t a Moog, is it really a synthesizer? — Tyler Cecil
Moog Matriarch
I saw two ways forward: I could buy one synth and be done buying synths for my life, or I could screw around with a small one, and keep getting larger ones and spending more and more until eventually I just couldn’t postpone it any more. Thankfully Liz understood and there was a big sale, so in June I got the Matriarch. Here’s Lisa Bella Donna playing it, and here’s another excellent 15 minute demo if you want a sense of the sound.
Syntorial had taught me enough that I knew my way around the synth immediately, as far as sound design. I still did not know how to play the keyboard. And I began to feel an intense guilt that I had this miraculous instrument that I couldn’t really play.
I contacted Eric and he agreed to give me some lessons, not oriented towards piano performance, but more towards music theory, basic chords, scales and dexterity for playing the synth. We did this for a few months. I got to where I can do the scales in various keys, play a major chord in various keys, and improvise in a way that sounds good to me. I am a lot less embarassed now than I was, although I should of course pour more time into this.
Following this, I realized it was pretty dumb to avoid the keyboard just because I did not know how to play it. Even if you can’t play it, music theory is written on the keyboard, and it will make more tactile sense than having capacitive pads, and more musical sense than a totally linear arrangement of keys as on the Model:Cycles.
Do I recommend the Moog Matriarch?
Yes, unquestionably. The sound is just unbelievable. At the time I got it I was also thinking about modular synthesis, and the idea of being able to safely and freely rewire things physically was really alluring to me. I liked the idea of doing extensive modulation through patch cables. Since then, I am mostly satisfied with the built-in routing and I don’t really see much need for manual cable patching, at least so far. The sound is just great, and it looks fucking awesome.
I’m no longer significantly interested in modular synths. I see the appeal. But I just don’t see myself spending $400 on a boutique oscillator or filter or delay module. That said, I don’t think Moog has a model of synth I would rather have at a similar price point. I could see the value of being able to store presets, but I kind of like that I have to turn the knobs to get the sound I want, and “debug” the patch when it doesn’t sound right. The “init patch” doesn’t scare me at all. More than presets, I think I would like having an internal mod matrix. The Sequential Pro 3 has a fun mod matrix routing mechanism that is appealing to me, but the sound isn’t as good to my ears. Moog One has something cool for this too, but it’s $6500 for the 8-voice model. I don’t think I could ever drop that kind of money on a synth. So around this price point, there just isn’t anything comparable in my opinion, and if you think you might want it, you probably do.
ORCΛ
When I was in my early-mid teens, before MP3 really became a thing, I discovered these MIDI files on my computer. You could open one of them and the computer would play a song; no lyrics, but it was pretty fun anyway. So you see why until this year I thought MIDI was a file format for music notes. This is a big misunderstanding. MIDI is actually a protocol for high-level music communication, at the abstract level of notes and parameter changes, and it has a central role in synthesis because it wires everything together.
I became aware of the fact that Csound had MIDI support during the in-person portion of the class, but this didn’t turn into any sort of useful information. It started to dawn on me that to make use of MIDI one needed a controller—a physical keyboard—and since I developing a shine for hardware synths, it seemed irrelevant.
Once I got the Model:Cycles, I noticed that in the manual there was information about both sending MIDI to the Cycles and receiving MIDI on the Cycles. So the Cycles could control other synths, like a keyboard, but it could also be controlled by a MIDI controller. This was a bit of a noodle baker for me. I also began to notice that there were, broadly speaking, two groups of people doing YouTube videos about synthesizers: the larger category of people like Andrew Huang who talked about “music production” and, while they maybe had and used hardware synthesizers, they tended to bring everything back into their digital audio workstation (DAW). I had no idea what a DAW was, other than some kind of software, and that meant it was going to be like Csound and therefore garbage and bad. If I was going to use a computer to make music, it would be like programming, and it would be precise and therefore good, but I didn’t want it to be like programming, at least not yet. So I tended to focus on the second group, the so-called “DAWless producers.” But even they were using MIDI and talking about how useful it was, so clearly something was missing.
The first piece of software I used that gave me the feeling I could actually make songs was ORCΛ. It was this program that finally drove home for me what MIDI was about. I could wire up ORCΛ to Pilot, the companion synth, or I could wire it up to GarageBand, or, I discovered, I could wire it up to the Model:Cycles and record the output in GarageBand. So I did this and made a few little demonstrations.
ORCΛ is really fun, but kind of a terrible environment for composition. An interesting idea. Not quite right for me though.
Bitwig Studio
At some point this year I started chatting with Drew Medlin about synths and synth stuff, and he has exerted a small but unyielding amount of pressure on me, to produce bits fit for sharing with him, and to keep the conversation going about music and synthesis. Early on, we were both using GarageBand to record. He invested in different things than me, so he wound up with a flagship OB-6 synthesizer and a couple Roland desktop recreations, a KeyStep Pro and was willing to play software instruments. So to him the DAW was something that existed mainly to crop the performance, which was mostly a one-shot affair with one instrument. I was ardently avoiding the computer because I wanted to allow myself some time to develop depth with the keyboard and synthesis, in fear that it if I involved the computer it would turn into another kind of programming for me.
In November I guess I came around the corner on that and decided that it was time to figure out a DAW. I wasn’t so much interested in software instruments, but in the idea of combining several recordings into one. I had used an iPhone app called Koala Sampler to play some simple sample-based stuff. I started to wonder what a DAW does, if it could be more than a way of gluing together recordings, and what else it could do and how. Andrew Huang’s channel, especially the “four-producers, one sample” videos like this one, was starting to convince me that there was something interesting going on.
I dinked around with Ableton Live and immediately saw something greatly more powerful than GarageBand. The clip launcher seemed like such an obvious improvement. I have no desire to play live music but as a way of organizing the composition into phrases, it made a lot of sense. I was starting to enjoy the idea of it, and then my Mac’s battery died and I was without a Mac for two weeks over the week of Thanksgiving. So I took the opportunity to try and see if there was anything out there for Linux.
I discovered several options. The hideous but widely-loved Reaper, the beautiful but incomprehensible Waveform, and Bitwig Studio. I spent a few days “used car shopping” between these alternatives and I tried them all out, and the only one that survived the process was Bitwig. I wound up actually buying the $30 tutorial course for beginners by Thavius Beck before buying the program itself, which is one of the best decisions I made all year. Simply having someone patiently tell you what all the panels do, how the shortcuts work, and the overall approach to using the program, made a huge difference in my comfort and understanding.
Like Live, Bitwig has a clip launcher/timeline dichotomy. It’s also more cross-platform, and it looks very beautiful. It handled the display resolution in Linux perfectly (Waveform did too). But it was when I started to learn more about it that I became convinced it was not only a powerful and useful program, but actually an amazing feat of engineering that would provide a powerful basis for experimentation long into the future for me.
The sense I get from other DAWs is that, most of your work is going to be done by loading various plugins to do the work. Many of the flagship software synthesizers out there have their own internal LFO and modulation system. Bitwig, on the other hand, understands modulation on a very deep level, so the necessity just isn’t there for you to rely on other soft synths to provide it. Bitwig also is highly recursive. Tracks can be groups of tracks, recursively; instruments can be instrument layers; devices can contain other devices or effects, there are note effects that come before audio effects and can be chained. Many devices have internal effects chains as well. I sense the presense of powerful and intuitive data structures underlying the system, and that makes it very natural to me as a programmer.
The coup de grâce is Poly Grid, which is a fully modular synthesis environment. I had tried VCV Rack and Voltage Modular at some point and found them unintuitive and one of them seemed kind of like a money pit. The Bitwig Grid eliminates a great deal of pain thanks to pre-cords, the ability to swap components out by right-clicking on them, and a plethora of excellent built-in components. It’s not trying to imitate a Eurorack modular synthesizer package, so visually it’s much clearer to see what’s going on. Polymer also makes it easy to convert a configured 4-function synth into a grid setup for further tinkering. The community of youtube people who actually use Bitwig are extremely smart and creative, and their video tutorials are just amazing: Tâsche Teaches on Euclidean Rhythms is a great example, along with Polarity Music on creating chords.
Seeing the world with new eyes
I have sort of a twenty year gap in my musical taste. I would characterize my parents taste in music as Woodstock. They loved the Beatles, and from my early childhood they are the first band I really think about liking. I grew up in the 80s, by the way. By high school I had made it into the early 70s and became quite obsessed with Led Zeppelin. By the time I graduated, my favorite band was Blue Öyster Cult, and I was starting to develop a taste for metal. In college, I had a friend who was into metal, so I discovered Death, who are responsible for one of my favorite songs and the eponym of the site, and had gotten in fairly deep with Megadeth, developed a real love for the band Mekong Delta (I was an early member of their internet forum), and was playing Primal Fear for my friends, who hated it but did begrudgingly admit that the musicians were more talented than Metallica. So it would be safe to say that I had a profound love of electric guitar. I made a point of trying to inculcate in my kids an appreciation of how amazing it is, that this instrument works through electromagnetism and not sound, the pickups are not microphones.
Beneath all that rock and metal, there had been a subterranean current of electronica. Before my friend helped me get deeper into metal at college, my big discovery had been Astral Projection, I had loved Juno Reactor. The first CD I bought with my own money was Ace of Base, which is the sort of deeply embarassing thing you don’t admit to your wife until you’ve been married for a year or so. I had owned albums by Aphex Twin. And by the time I did meet my wife, I was warming to pop music. That has become a full-fledged love, to the point I would say to people for the past ten years or so, that I love metal and pop and that was about it. This last year, for instance, I mostly listened to Charli XCX’s how i’m feeling now, which I think summarized the year for me.
So it came as a bit of a shock to discover this year, that many of the pop bands that I loved, I loved because of their use of synthesizers. Devo, CHVRCHES, Charli XCX, The Naked and Famous. It is blindingly obvious, but I didn’t really realize it until this year, that in fact I have loved the synthesizer for most of my life without realizing it, with considerable ignorance. I had often wondered at amazing “sounds” in different songs, but apparently not deeply enough to figure out how they were made. Even probably my favorite all time metal album, Rising by Rainbow, opens with a lengthy Moog synthesizer solo and has duelling solos between synth and guitar in the final act of the final song.
Musically, this year has been a constant moment of awe and discovery for me. The wonder of it all. And I owe this to Eric Sewell in first for opening my eyes, and to Drew Medlin in second for urging me on to keep them open. And to Tyler Cecil, probably the only one to actually read this blog, for providing guidance and counterpoint at various critical moments, and making it so that this actually gets written down. And to my wife Liz, who has supported my interest with patient ears, financial flexibility, and tolerated many YouTube videos on these topics. Whatever pleasing sounds I have learned to make are only in my mind because she delights me.