Dispatches from writing a new fractal book

I spent a lot of the weekend making figures. If a picture is worth 1000 words, then my book would be 500,000 words long. There are a lot of things to consider when making an image for a book:

  • Since this will be a B&W book, what’s the best gray-scale values to look two-tone without looking faded?
  • What resolution will work best for the print size, but still work for an eBook (so I don’t have to make two of every picture, hopefully)?
  • How does the image flow with the text? Does it make it hard to read, or does it illuminate a point the text is making?

This last is the primary goal of pictures. Pictures serve two purposes in my book: to show people pretty images, and to show people how to make pretty images. A lot of the heavier math texts I read can still be very informative if they have good illustrations that make it clear what the writer is trying to say. Still, you don’t want to lean on the pictures too heavily, the text still has to make sense.

My early drafting process has been to write the chapter without illustrations. I insert an [ILLUSTRATE] tag into my text where I think an image would/should go, and then I move on. So far this seems to be working okay. I’m remembering from writing the first fractal book that what I think is a clear explanation and image isn’t always what people actually understand, so I may have to try a few different images, and change the text accordingly.

It probably doesn’t make sense to talk this long about pictures without showing you one, so here is a Minkowski sausage:

kochQuadMinkowskiSausageL3

Neat, huh?

One other weird quirk of the early going is the feeling that I’ve written this all before. In some ways, this fractal book is the culmination of 5-10 years of thinking about fractals, as well as an intense period of six months research. I have run through the progression of thoughts that make up the first chapters dozens of times in my head, and even though this one of the first times I’m committing them to paper in this particular order, it still feels like something I’ve been doing all along. Probably some of that comes from blogging about fractals, that’s really where this recent and previous interest started.

Last thought of the day is a nice little moment at the library. I was checking out yet another fractal reference, and got to talking with the librarian about the new book, and how I got interested in fractals back in the 6th grade EPP program at school (more than 18 years ago now). Turns out, her son had just recently been part of the same program, and had loved fractals and all of the ways you could use them to make math beautiful. It’s for these kinds of kids and curious adults that I’m writing this book, and it was a nice little encouragement to know that they’re still out there.

Have a good week. I’ll check in when I can.

kochTriCurveSingleLineOneTenthL5

Leave a comment

Filed under Writing

Squirrel Rant: Mathematical Notation

foamy_by_foamy_the_squirrel

Since this post veers into very inside baseball territory, let’s start with how we got here.

Have you ever had that book that you had to take with you everywhere? It could be the latest exciting story you were reading, or a really handy reference guide, or something with deep sentimental value. Maybe this book has been a passenger in your car; you take it out to lunch even though you know you’re not going to read it while you eat because you might get sauce on the pages. You just want to pick this book up and hold it, flip through the pages, feel the weight of it as you toss it from hand to hand. Maybe you even… smell the pages. That sort of book.

My latest book of this type is “A Perspective in Theoretical Computer Science: Commemorative Volume for Gift Siromoney“:

GiftSiromoney

I know, it’s cliché. Everyone loves this book and has a copy next to their nightstand.

No? Just me, then? Okay.

Why this book is important is that it is the end of a long trail of looking through references in papers, from a stray mention of Kolam patterns in a L-System book by Przemyslaw Prusinkiewicz to the work of Darrah Chavey, Paulus Gerdes, Marcia Ascher and countless others. This book has some of the best grounding in the computer science behind drawing curved line patterns using context-free and array grammars, and contains images from work in the field. It is perfect because it is obscure and exactly the right book at the right time, even though it was written almost 30 years ago.

Which brings me to mathematical notation.

As a fledging programmer one of the first things they teach you is to use meaningful variable names. A variable is an object that holds a value. So if I’m counting oranges, I might have a variable called numOranges. What I wouldn’t have is a variable called ‘o’. ‘o’ could be anything: orangutans, oscilloscopes, Timothy Olyphants, etc.

Math on the other hand tends to use one letter symbols all the time. You’d think this was okay, because the symbols only ever have one meaning. A ‘+’ symbol is a plus symbol. ‘π’ is pi the number.

Except when π is an iteration symbol, or a time stage symbol. And ‘x’ means multiplication, until you graduate to Algebra where a dot is now multiply and x is a variable. And ‘+’ could mean turn right if we’re talking L-systems.

Math papers in general make an assumption about mathematicians that isn’t always correct. It assumes they can write in a way that can be understood. They understand their field technically, but not in common language, or even readable technical language. Now I’m not picking on the Siromoney book too much. The text is very readable. Some of the paper’s problems come from problems in reproduction. Older books like this one had papers submitted physically and then photocopied into a full book. This was done a typewriter or an early word-processor (courier font is kind of a tip off that we’re looking at a typewriter), so some subscripts and superscripts are incorrect, and some symbols have to be hand-drawn after the paper is typed.

The bigger offenders are the ones who use a symbol without any explanation. I remember after staring at it for a few seconds that ∪ means union, but it might be nice to have some handy definitions at the back or in the text. Defining your terms is often a necessary part of making any proof, or explaining any new concept. It never hurts to make sure your audience is on the same page you are. Especially if you plan to have terms mean something other than their common meaning, like ∪ meaning recursive level, or some such.

For a while now, my goal with this new book has been to take complicated concepts and explain them in ways that make sense to everyone. These papers often do the opposite, take something simple and explain it in a complicated way. Fractals actually aren’t that hard to understand. More and more after reading these papers it feels like I’m translating from some arcane and obscure language, with symbols that change in meaning from one place to another.

It’s confusing, and it doesn’t have to be this way. We can be rigorous AND we can be clear. If you can explain a concept to a 6th grader, then you really understand it.

2 Comments

Filed under Uncategorized

Whatever it is, it can’t be that bad…

Long-time readers of the blog will know that I and the esteemed Brian Buckley are pretty big fans of Babylon 5. Babylon 5 is full of great characters and great character actors, and sadly over the years we’ve lost a number of them all far too soon. This week another member of the cast has “passed beyond the veil,” Jerry Doyle, who portrayed Security Chief Michael Garibaldi.

Garibaldi, like all the characters, could be funny, noble, and a pain in the ass, sometimes in the same scene. He makes mistakes, deals with real addictions and loss, and comes out on the other side a better person. In small tribute I thought I’d compile some of the best clips of Garibaldi over the years, most of which I’ve been seeing on Facebook over the last two days.

Jerry Doyle was actually briefly married to the woman who portrayed Talia Winters, though only after she’d left the show (something I didn’t know till my Wikipedia research today).

Probably one of the best known scenes in the first season, and still one of my favorites.

You wanna talk socks?

More Londo’s moment, but still a great scene.

Alright, my second favorite thing…

Funny the Doctor could never prescribe anything for Garibaldi’s hair loss.

Garibaldi kicking some corporate butt.

And taking down evil regimes even as a hologram.

This was how I imagine installing Windows 10 must have gone for some people.

Do not thump the book of G’Kwan!

And this one was being posted around yesterday. Never seen it before.

And lastly, our favorite God of Frustration…

So long Jerry. We will see you again in the place where no shadows fall.

PS. Couldn’t find the clip, but Scott Adams (of Dilbert) plays opposite Doyle in the Season 4 episode “Moments of Transition” (starting around 23:39).

Leave a comment

Filed under Round-Ups

Review: Star Trek Beyond meets expectations

Jaylah_and_scott

SPOILER POLICY FOR THIS REVIEW: Most of the plot details I mention in this review are things we knew from the trailers (casting, fate of Enterprise, name of villain, etc.) I plan to talk a bit about the specifics of the Enterprise sequence, but I’ll avoid some details about the villain. The basics of Jaylah are discussed, as well as some of the cast pairings that happen in the middle section of the movie. If you’re spoiler sensitive, avoid this post until you’ve seen the movie. If you want a sense of what’s cool, what could have been done better, and whether you should go see this movie (you should), then read on.

Right from the first trailer and the announcement of this film’s director a lot of fans were worried that we were getting Star Trek: The Fast and the Furious, a generic action movie instead of true trek spirit we’ve come to know and love. Simon Pegg’s script and a lot of sly references do what they can to challenge that expectation and there are bits and pieces of something greater, but most of the middle section is exactly what we expected from Justin Lin. But the movie is still eminently watchable.

The fate of the Enterprise: There’s a real “oh sh-t!” moment early on in the sequence that my wife actually caught a few seconds before the rest of the audience. The design of the Enterprise throughout the decades has often been criticized for putting the nacelles on long delicate arms. And in Beyond we see the consequences of that choice. It actually takes a good ten or so minutes from initial battle till everything comes crashing down as the Enterprise is picked apart by a swarm of ships unlike anything they’ve ever encountered. Most Trek battles are naval engagements, two heavy cruisers duking it out until one is victorious. The swarm of enemy ships in this movie is a force of nature, one that will be next to impossible to defeat. Everyone gets a good moment, from Scotty’s clever escape, to Uhura’s battle with the baddie, to Kirk saying a last goodbye to the bridge. Everything up through this moment is the Trek we love.

Let’s wander around on a planet for a while: There was a lot of potential in the middle act of this movie, and we get glimpses of it through some character beats. Most of the crew is picked off by Krall and huddled together in cells pretty early, but a few are able to escape on their own or with a buddy. We see some traditional and unexpected pairings here: Kirk and Chekov, Spock and McCoy, Scotty and Jaylah. There’s some real potential for interaction and character development in these sequences, but the best we get (as expected) is Spock and McCoy. Their grudging respect for each other is explored, as well as Spock dealing with a big loss. I’ve been a fan of Urban’s McCoy and feel like he’s been underused until this movie. The Kirk and Chekov stuff is all action, and Scotty and Jaylah are mostly played for laughs. Uhura, Sulu, and rest of crew in Krall’s camp is less compelling, though Uhura’s one-on-one’s against the villain aren’t bad.

New life-forms: Jaylah’s a nice character. She’s got a cool character design. Her outfit’s not exploitative. She’s shown as being a capable engineering novice and a fighter. She calls Kirk “James T.” Overall, not a bad effort. Simon Pegg mentioned on Late Night with Seth Meyers that her name comes from her script designation (Jennifer Lawrence from Winter’s Bone) and I don’t know if we would have made more of a connection with this character if it was actually Jay Law. Her development is a little lacking, but I look forward to seeing how potential future movies use her (or at least the comic books).

Ordering off the menu: Idris Elba on the other hand, is buried in the makeup and that voice he put on for this movie. Whatever you think of Cumberbatch’s Khan, you were getting everything that actor had to offer as a sympathetic villain. There’s so much we could have gotten from Idris, even just from his voice, that his slow, spittle-spewing performance didn’t give us. On Fallon, Idris remarked that you didn’t really have to act when you looked like his character, which makes me wonder why they used someone as talented as him for the role. If you hadn’t told me it was Idris, I wouldn’t have known for much of the movie.

Callbacks: The trek references in this movie were largely from one of the least popular series: Star Trek: Enterprise. There were a lot of good TOS refs as well. The Enterprise callbacks make sense, since technically the prime and Abrams (Kelvin) timelines share that common ancestry. There was one choice of music in a sequence toward the end of the movie that came off as very hokey, especially considering what it was being used to do. That was probably the most Fast and Furious the movie got. Yes, I know that First Contact used “Magic Carpet Ride” in a sequence, but it made way more sense in context than the moment in Beyond. The best moments are the movie’s tribute to Leonard Nimoy, which is handled with more than just a title card. There’s a moment at the end that really connects with Trek’s 50 year legacy.

Raise the stakes: Star Trek (2009) destroyed Vulcan mid-movie. It’d be hard for any movie to rise to that level without repeating itself. Into Darkness did it with a personal character death, Pike being killed by Khan early on. Beyond does shock us early on with the Enterprise attack, but the actual threat of the movie seems relatively minor. Most of our villain’s violence, and the devastating power of his weapon, is implied not shown. The thing to protect is largely significant because it looks cool and has a lot of people on it (oh and Sulu’s husband and daughter who we’ve never seen before, and never talk to). I’m not sure how you correct this point, but since there was less connection with earlier movies or Trek lore, it seemed more generic in a building-smashy way than the previous films.

Bottom-line: The movie is fun. There’s a lot of laugh lines. The space action sequences are superb. The planet stuff is more generic, but still fun. We’re back to the curse of the odd numbers, but if you think about it, only 1 and 5 are real stinkers. 3, 7 and 9 are all very watchable. I think Beyond actually most resembles 9 though without the romantical time-freezing bits. It’s definitely still in the top third of Trek movies. I doubt you’ll hate it, and you definitely will want to see it in the theater.

Just maybe go for the matinée.

2 Comments

Filed under Uncategorized