Dracula
We had to download a new app to watch the Superbowl back in February, Tubi. For some reason I was thinking about vampires back then, so I decided to watch the Hammer trilogy, The Vampire Lovers, Lust for a Vampire and Twins of Evil, which were all available on there, and then it recommended me another one, Vampyres, but I wouldn’t follow the IMDB link on that one if you’re at work. Somewhere in the middle I also watched Blood from the Mummy’s Tomb. These flicks are somewhere between horror and pornography. I’m not sure what happened, I think my brother had loved Hammer films when he was young, so they were kind of always on my to-watch list and I finally got around to a few, although I don’t think these are the ones he was endorsing exactly. Anyway, it was a vampire kick, these things happen. The movies are neither so great nor so bad that they deserve many words. But not ultimately satisfied, I decided I would watch a great vampire movie from my youth: Bram Stoker’s Dracula.
This should be a watershed movie. It has great effects, many great actors, great sets and was shot right around the time in my life when I feel like movies were really getting good. A certain scene near the beginning also activated certain neurons in your teenage author, the first movie that really imprinted on me for having done so. I had fond memories of this movie, so when I rewatched it with my wife, I was kind of awestruck at how bad it is. Not to dump on anyone in particular, but Keanu is surrounded by people speaking with accents yet his attempts are dismal, as are Winona’s. Lucy’s character is way oversexed. There’s a love plot device involving Dracula which seemed a little hackneyed. On the other hand, Gary Oldman and Anthony Hopkins are really great, but there’s too much happening for them to fix everything wrong here.
Now I started to wonder, is there something inherently not great about vampires? And just how accurate is this movie to the novel? Is the love story between Dracula and pants and/or Mina real? I had heard the novel was difficult to follow because it is told as a series of diary entries.
It took me over a month to get through this in audiobook but this book is great and it deserves its place as a classic. There is some sexiness but it is far from the principal element. There is a whole spooky ship scene which is rather great and doesn’t seem to be adapted often. Renfield is much more interesting in the novel.
The diary structure is not hard to follow at all, but it adds something wonderful to the atmosphere and the entire narrative structure. First, you get to see each character discover the horror in turn. When Jonathan first brushes off the supernatural, the foreboding is quite intense; later, each of the other characters have his same rationality at first and we get to see it stripped away one by one, a real horror moment. Second, it’s a useful device when in the middle of the novel, instead of narrating each character coming up to speed, we just have this exchange of diaries and then everyone is up to speed. Saves Bram from writing a lot of tedious dialogue about so-and-so telling so-and-so things we already know. Third, it allows him to play with our expectations. When we are getting diary entries from Mina in the final act and then we get one from Van Helsing instead, he creates doubt and tension about Mina right before the last entry. And finally, you get a bit of voyeuristic pleasure from the sensation that you’re rifling through a big pile of diaries containing something not quite believable. Indeed, the final words of the novel state this.
As an armchair language aficionado, I can also tell that Bram Stoker was one as well. He spends a great deal of time discussing the languages and accents of different characters. I don’t find his accents, particularly Van Helsing’s, especially believable, but I appreciate the attempt.
So that was great. I recommend reading or listening to the original. The films are pretty much trash. The Audible version with Alan Cumming and Tim Curry is very nice.
Gratitude
I’m trying to migrate my IT infrastructure to places where it won’t cost much but will be my problem, at least partly so that I don’t feel as much guilt when I see my friend Bill, and perhaps partly just to clean things up. The first of these was this blog, which I moved to Blot because it’s just ridiculous how easy it is to post here. I realized even having to commit and push to a repo is a barrier to writing for me. Which is, on the one hand, silly, but on the other hand, I don’t exactly revise blog posts over and over again trying to make them pass unit tests cleanly.
The second thing I started moving was my mail, which meant I had to go through ~45,000 emails going back to 2003ish. Yeah, 22 years of email. Let me tell you what I have learned.
My hobbies are pretty cyclical. I guess I always knew that, but would you believe my first exchange with Aaron Hsu was in 2008, on the topic of how to write Scheme on Plan 9? Then we were reintroduced in 2017 when I wrote APL Symbol Fetishism, and then I re-reintroduced myself to him a few weeks ago after hearing him talk on Episode 100 of the Array Cast. Funny to me! I doubt he remembered me from before, at least I hope not, because he found that essay pretty irritating and sent me quite a few corrections for it, which have not (as yet) been implemented.
The next thing I learned is that most of my email comes from my mom. Yeah! My mother is my most frequent email correspondent, and it’s not even close. After her it’s my brother. The frequency has tailed off in recent years, but there are months in my old mail that are just one after another from him, with no one else intervening.
I also have a lot of mail from my friends. And I have found quite a few emails apologizing for setting me off, or replying to my apologies for setting them off. I regret that my depression caused a lot of people to be on eggshells around me, that many people were sliced by shrapnel for the crime of trying to be my friend. I became pretty intolerant, and pretty intolerable, and lost a few dear friends to this. I blanket apology is probably insufficient. But in the compressed timeline, I can really see how much of an asshole I have been, to many, many people.
I was reminded of all the major moments of my life since college. Meeting my wife, having my kids, buying and selling houses, moving, deaths of friends and dear ones. Weird to think that email is this important. But it is.
Anyway, I’m grateful to you for reading this, and if you have emailed me in the past, I am even more grateful. Thank you!
Hey, remember this one? It turns out we can do it a little more simply:
({.;#)/.~ 'Mississippi'
┌─┬─┐
│M│1│
├─┼─┤
│i│4│
├─┼─┤
│s│4│
├─┼─┤
│p│2│
└─┴─┘Some notes about J from today
Charting
chart =. {{ l {~ >. (<: #l =. u: 16b20, 16b2581 + i.8) * y % >./ y }}
] dat =. 10 ? 20
13 18 9 0 1 4 16 19 3 7
chart dat
▆█▄ ▁▂▇█▂▃tsvector in J
A tsvector in Postgres is the tokens of the input and their locations. We can compute this in J by cutting the input and associating it with the number of words of the input. Here is the Postgres example:
SELECT to_tsvector('english', 'a fat cat sat on a mat - it ate a fat rats');
to_tsvector
-----------------------------------------------------
'ate':9 'cat':3 'fat':2,11 'mat':7 'rat':12 'sat':4In J:
txt =. 'a fat cat sat on a mat - it ate a fat rats'
w ([,<@])/.. i. #(w =. ;: txt)
┌────┬──────┐
│a │0 5 10│
├────┼──────┤
│fat │1 11 │
├────┼──────┤
│cat │2 │
├────┼──────┤
│sat │3 │
├────┼──────┤
│on │4 │
├────┼──────┤
│mat │6 │
├────┼──────┤
│- │7 │
├────┼──────┤
│it │8 │
├────┼──────┤
│ate │9 │
├────┼──────┤
│rats│12 │
└────┴──────┘There are some differences due to cleanup that Postgres does on the input which I’m not doing. But the idea is pretty much the same.
Collecting Data using /..
Considering the following:
]data =: _2 ]\ 'Fred';90;'John';75;'Fred';95;'John';85;'Susan';100;'John';86
┌─────┬───┐
│Fred │90 │
├─────┼───┤
│John │75 │
├─────┼───┤
│Fred │95 │
├─────┼───┤
│John │85 │
├─────┼───┤
│Susan│100│
├─────┼───┤
│John │86 │
└─────┴───┘The documentation provides the following solution:
]s =: ({."1 data) <@;/. ({:"1 data) NB. Use first column as keys; collect second-column values
┌─────┬────────┬───┐
│90 95│75 85 86│100│
└─────┴────────┴───┘
(~. {."1 data) ,. s NB. Reinstall the name
┌─────┬────────┐
│Fred │90 95 │
├─────┼────────┤
│John │75 85 86│
├─────┼────────┤
│Susan│100 │
└─────┴────────┘I found my own solution:
(}:"1 data) ([,<@;@])/.. ({:"1 data)
┌─────┬────────┐
│Fred │90 95 │
├─────┼────────┤
│John │75 85 86│
├─────┼────────┤
│Susan│100 │
└─────┴────────┘The channel found this:
(,<@;)/../|:data
┌─────┬────────┐
│Fred │90 95 │
├─────┼────────┤
│John │75 85 86│
├─────┼────────┤
│Susan│100 │
└─────┴────────┘This notices that we have one column on the left and one on the right and inserts the calculation between them, reducing the amount of tearing apart we have to do by hand.
(}:"1 (,<@;)/.. {:"1)This is a tacit definition from someone else on the channel, which reduces parens by using a tacit definition.
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.