### Multilingual authoring for the win

I have been working on a French translation for the math book and in the process I stumbled upon some really powerful “authoring hacks” that I would like to describe here in case they might be useful for other bilingual authors and educators.

### Let’s see les maths!

Before we begin with the “How it’s made” episode, let me show you some examples of the final product. I have selected the best four “backports” — explanations that now exist in the English version thanks to the additions in the French version.

1. Reader feedback was consistent at pointing out the algebra sections as boring and TL;DR. Readers are willing to learn algebra (the rules for manipulating math expressions), but then when it comes to algebra “techniques” they are not sold on the concept. One solution to this problem would be to drop the “boring stuff” (lower the expectations of the reader), but I was having none of this. Instead I decided to just improve the explanations and add pictures: Completing the square en Français et in English.
2. Functions (modelling superpowers) are the best thing ever, and probably the most powerful tool readers will develop in the book. This is why proper definitions and examples of functions are essential.
3. Polar coordinates are super important—for both practical reasons and for the “aha” moment (knowledge buzz) that occur when readers understand $(x,y)$ is just one example of the many possible representations of the points in the Cartesian plane and $r\angle \theta$ is an equivalent representation (instructions that specify the position of a particular point int he Cartesian plane based on the distance $r$ and direction $\theta$).
4. Speaking of knowledge buzz through representation theory, the book now finally has a proper motivation why readers need to think about the concept of a basis (a set of direction vectors that is used as the coordinate system for a vector space). On this one I go back to the basics—explain through an example.

Contuinuez à lire si ça a l’air intéressant. Read on if you’re interested.

### Context

The No Bullshit Guide to Mathematics (a.k.a. the green book) is a short summary of all the essential topics from high school math intended for adult learners. Last year, by sheer luck and good fortune, I was introduced to Gerard Barbanson who offered to translate the book to French. Gerard is a professional mathematician, a native French speaker, and has also taught math in English for many years, which makes him the perfect translator. Gerard is leading the translation project and provides lots of useful feedback and improvements for the text.

Look out for a followup blog post and announcement about the release of the French translation (in a few months). This blog post is not about that, but about the benefits of the translation efforts brought to the original English version.

### Translation as a way to highlight problems

While reviewing Gerard’s “first pass” of translation, I kept noticing spots where the explanations didn’t work well. My initial reaction was that this was a bug in the translation, but every time I looked into a passage, I realized the problem existed in the original English text, and the translation only magnified the problem and made it more noticeable. Examples of “weak spots” include paragraphs that are too conversational (i.e. no content), missing definitions, and explanations that are unclear or confusing.

I found this process to be extremely useful. Even though I’ve read and reread the English version many times, I never noticed these weak spots until now. The translation process highlighted the lack of clarity in certain specific parts and forced me to think of ways to fix these explanations. Essentially, if an explanation is good, it will “survive” the process of translation, but if it’s not 100% solid and clear, then it turns into “noise” at the end of the process.

We can think of translating explanations as a communication scenario, where the source language (English) is the transmitter, and the target language (French) is the receiver. The process of translation adds “noise” in the form of ambiguities, so the received signal is a degraded version of the original signal. The French translation will be good only if the original English explanation is really solid and clear. This puts additional pressure on the original English version to be extra clear and precise.

### The language of mathematics

Another benefit that came out of the translation work has been the focus on the consistent use of terminology and notation. For the most part, mathematical concepts translate well between English and French, but sometimes French has more precise terminology available. For example I’ve adopted the precise terminology of source set and target set to refer to the sets that appear in the function “type signature,” which are distinct concepts from the function’s domain and image.

One of the core responsibilities of any math teacher is to use precise and consistent language to describe mathematics, including choosing the simplest terminology when the complicated terminology is unnecessary, but not shying away from the “real math” terms when they help illuminate the concepts. Working with Gerard to explicitly establish our conventions for the French version forced me to also be consistent in the English version as well.

I guess that’s not too surprising—using consistent terminology and notation is just best practices.

### Bilingual writing for better explanations

Perhaps the most surprising thing I noticed from the translation project is the amazing efficiency of developing English and French explanations in parallel, sometimes aided by Google Translate. This was most apparent in writing the new sections on polar coordinates and vectors. Normally writing a new section would take me days, going through several mediocre versions, rereading on paper, and slowly converging to a decent narrative. I noticed the new sections I added over the holidays converged to a “quality product” much faster. Here is the process I followed:

1. Explain the concept in English.
2. Translate explanation to French improving and simplifying it in the process.
3. Take the best parts of the French explanation and incorporate them back into the English version. Go to step 2.

After a few cycles of going between the English and French version, I saw clear improvements from the initial English version and of course the French version was improving in tandem.

### Kaizen for textbooks

I guess the thing that makes me excited about these “authoring hacks” is the fact that they allow me to go one step deeper in the process of continuous improvement of the books. I’ve read and reread the text at least a dozen times, worked closely with my editor Sandy Gordon to iron out all the major flaws and acted on feedback from readers to fix confusing passages, but at some point I get tired and start to let things go. I say to myself things like “yeah this is not the clearest explanation, but it’s kind of OK as is.” This is partially out of laziness, but also because of the law of diminishing returns: sometimes rewriting makes things worse!

There is a famous quote that says:

#### “There is no great writing, only great rewriting.”

― Louis D. Brandeis

I know this is good advice, but it’s hard to adhere to it. After five editions of the math book, I find it difficult to motivate myself to rewrite things, even if I know there is still room for improvement. That’s why I’m always looking for hacks that can help with the process (see for example the text-to-speech proofreading hack). The translation work of the past few months gave me the impetus to do more productive rewriting without it feeling like a chore. Look out for the updated No Bullshit Guide to Mathematics v5.4 coming soon in both English and French. Sign up for the mailing list if you want to be notified.

### Impression from NYC and the RC

Two months ago I was on a train going from Montreal to New York City. It’s a long ride, but I used the time on the train to triage all the coding project ideas I could work on while at the Recurse Center (RC). So many projects; so many ideas.

Today I’m on the same train heading back to Montreal and have another 10 hours to triage the thoughts, experiences, and observations about the big city and the social experiment that is RC. Here is my best shot at it—stream-of-consciousness-style—before I forget it all.

## New York City

The past two months have all been a blur. From the day of arrival when I tried to enter the wrong apartment, to the first contact with NYC street noise insanity outside of my window, to the snow storm, and all sorts of good foods. I’m very impressed with the city, but I’m not in love. Here are my observations.

New York is a big city. Compared to Montreal, it’s as if someone copy-pasted 10x the city. Or perhaps the better computer analogy is someone filling a map with the “bucket-fill” tool and completely forgetting to stop. Seriously, it seems like there is waaaay too much shopping areas with high-fashion and luxury brands. Do people really need to do so much shopping? I don’t mean to be judgmental, but as someone who is ideologically against consumerism, I felt like I was totally in the wrong place.

The energy of the city is amazing. It seems everyone is getting things done, shipping products, or otherwise being creatively on top of their game. Now I realize it is impossible for everyone to be successful, but people certainly carry themselves as if they’re crushing it. Most people I talked to made a good impression on me. They’re proud of what they do, confident, but not overly full of themselves. New Yorkers are actually interested in hearing you out, and seeing what you have to say. I felt very little closed-mindedness and little-mindedness from the locals, which is great.

I really like the demographics of the city. Everywhere I went, there are young people: from school kids who talk like adults, to the well-represented university crowd, through the numerous artists, to the middle-aged professionals contingent, and also older people who still keep in shape. Everyone is well dressed and good looking. At times I felt as if there is some sort of giant “face control” department at NYC ports and train stations that does not allow non-good-looking people to come to the city (How did I get in?).

I’m used to “measuring my words” when meeting new people in order not to alienate my interlocutors by mentioning math, quantum physics, or computer topics. When touching on such topics, I use an interactive approach to “feel out” the level of comfort of the person I’m talking with and judge how far I can go with this topic of conversation. The last thing you want is to jabber endlessly about a technical topic to someone not interested in tech, or to talk about math with a person who has a math phobia. Talking with people in NYC, I was pleasantly surprised to realize I don’t need to measure my words all that much. I would hit people with the full geekfest, computer jargon, and even quantum topics and they would handle it just fine. People are more knowledgeable than you think, and those that don’t know anything about the subject matter are willing to go into it and still had interesting things to say. That’s really nice. It’s great to be around people who can handle the tech talk and the science talk. All the New Yorkers I spoke with are smart, open minded, and generally well aware of the world.

### Okay, so where is the OER in all of this?

By now, my dear readers, you might be wondering if there is no case of “bate and switch” going on here. We started with the promise/mission to make open educational resources more accessible to students and adult learners around the world, and somehow we ended-up with a reaffirmation of a business plan to make money from selling books. Perhaps there is some of this going on, but you must agree that building stable organizations with individuals who earn a living by teaching is a step in the right direction.

The approach that I imagine for getting achieving the “OER dream” is to encourage authors to sell their university-level books, but contribute primary and high school material as OER. I think the “university for money, but high schools stuff for free” approach will work for two reasons. Some authors might start from an altruistic point of view, and want to do something good for society by releasing some introductory lessons for free. Other authors might be motivated by purely capitalistic incentives, since releasing the high school material for free is an excellent way to promote their work.

### Focus, focus, focus

There’s only a limited things one person can do in their lifetime so it’s important to focus on the things that make sense, and which have potential for growth and high impact. I’ve invested the past 5+ years of my life in the math textbook business so I think it’s important to continue that project instead of changing priorities or working on other projects.

The beauty of this idea is that it doesn’t require any miracles, breakthroughs, or external funding. All it takes is an evolution of the project I have currently going on, so I can work with more authors. Life always tends to make things more complicated over time, so starting with a simple plan, and keeping the focus is generally a good way forward. Vamolos; ándale!

### Improving the math chapter

The goal for the NO BULLSHIT guide to MATH & PHYSICS was to make a concise textbook that teaches university-level calculus and mechanics in a nice “combined package.” The math fundamentals chapter grew out of the need to introduce the prerequisite material that many students often lack. I didn’t want to be like “y’all should remember this math from high school,” because if you don’t remember the material such comments would not be very helpful. A review of high school math would be more helpful.

Over time, I kept adding and improving the introductory math material in Chapter 1 until it reached the point that it’s a pretty solid little intro to high school math. I was very proud of the fast paced flow of explanations which manages to cover a lot of material (70% of high school math topics) in less than one hundred pages. Many readers also praised this chapter, saying how useful they found it as a review of high school math topics.

Recently I’ve been hearing from several readers who say the intro chapter sucks, and the book sucks, and by extension I suck. If it was one or two reviewers I could have dismissed this feedback, but now I realize there is a clear and consistent message in the readers’ feedback: Chapter 1 sucks as a first contact with math. My effort to “cover” all the high school topics in a fast-paced narrative like in the free mechanics and linear algebra tutorials is probably the worst thing to do for absolute beginners. I can totally understand why a reader who is not familiar at all with sets, algebra, and functions will have a rough time in the opening pages of the book. In the words of a reader, the book “goes from 0 to 60 in the blink of an eye,” which might be a good thing for a sports car, but not for a math book. It doesn’t help that I say “anyone can learn math from this book, regardless of their mathematical background” in the marketing copy. I need to do something to fix Chapter 1, and soon.

So what am I going to do about it, then? Write, of course—what else can a writer do? I’m going to prioritize the basicmath project and write the best sequence of introductory math lessons that ever existed! I’ll then use these explanations to beef up  Chapter 1 to make it a solid foundation. I think adding 20–40 more pages will be enough, so the book won’t get that much thicker. It’s not just about adding though, I think Chapter 1 could use better organization, flow, and clarity of explanations.

Interestingly, the basicmath project overlaps well with my planned social media campaigns that will push the message “learn math; math is useful,” as well as the math lessons by email. February is gonna be very mathematical!

### Math for lawyers

A reader recently suggested I should write more articles that introduce math specifically for different audiences. Math for doctors (although I’d hope they already know math!), math for artists, math for musicians, etc. I like this idea.

In the spirit of procrastination and given the three other tasks I have to do in currently open tabs, I’m going to now dedicate the next hour to writing a sample post that introduces math to people with a “legal mind.” Don’t worry, dear readers—it just takes an hour to write a blog post. Reading it will only take three minutes.

## MATH

Yes. I’ve said the dirty word. Everyone’s dreaded topic. So factual and unforgiving—you’re either good at math or you’re not. Okay. No, no, no. We’re not going with the usual narrative today. Let’s deconstruct this thing that is math, and see what it’s made of. Perhaps it’s not so bad.

### Axioms and rules

Math is very ordered. It’s a bit like the French system (civil-law). All of math can be summarized as basic axioms on which everything else is built. Think of math as a set of rules that people have found to be generally useful in the past two thousand years. Like, send a spacecraft-to-mars useful. Once you know the dozen or so rules for working with numbers and expressions, and the dozen definitions and observations about geometry, you’ll have access to some of the “best stuff” that human intellect has to offer. I guess what I’m trying to say is that A) math is not that hard to learn because there is a finite set of basic rules to learn, and B) once a reader learns the basics, the reader is granted a nonexclusive, royalty-free, perpetual, irrevocable, transferable, worldwide license, to make, use, enjoy, benefit from, teach, share, offer for sale, sell, reproduce, include in, distribute, modify, adapt, prepare derivative works of, display, perform, and otherwise exploit math.

### Cases

Math has a lot of common-law aspects to it too. Theorems (big results) and lemmas (little results) are like cases that mathematicians have proved. A proof is a bit like a trial, where the mathematician tries to convince the jury (usually consisting of fellow mathematicians) that some new mathematical fact is true. Unlike a real-world courthouse that depends on a judge’s judgment at some point $t$ in time, a mathematical proof is always on trial. If the mathematician’s proof is solid and can be followed to the basic axioms, it’s very unlikely it will ever turn out to be wrong, so it’s common for mathematicians to simply cite theorems as if they were “ruled upon” case law.

### The pitch

So here we are talking about math as if it’s some cool new thing, but we all know that math is difficult to learn and probably not that useful in every day life. Yes, perhaps it is so, but the point remains that certain math—let’s call it the useful part—has been around for thousands of years and hasn’t been proven wrong. Basic math is well understood, highly useful, and totally empowering.

Do you want to be part of this math thing? If so, check out the books.