How Unicode can save math: part 2

It’s widely known that decimal – or “numbers” to most of us – is an inferior system. Decimal doesn’t work well for computers, which prefer base two and it doesn’t work well for humans either, at least not when compared to dozenal.

Dozenal is also called “duodecimal,” or “base 10” (when writing in dozenal) and it is a much more natural system for humans than decimal. The usual example of why is a clock. Look how neat it is with the number 10 right at the top:

Dozenal clock face
From the Dozenal Society of Great Britain

Dozenal has a big problem though, as we can see from the clock. What number does 10 represent, when you see it out of context? You just don’t know.

For decades, we’ve solved this problem in computer programming with funny prefixes. To a programmer, dozenal and decimal might be “base 0xA” and “base 0xC”. Likewise, in a dozenal world, we might write “hexadecimal” as “base 0z14” or something. If we need to start writing all our numbers with warts to indicate the base, however, dozenal seems doomed.

But wait, there’s hope. Unicode already contains the digits for “dek” and “el.” (That’s ten and eleven, if you’re not a cool dozenal kid.) If your browser doesn’t have a suitable font, refer to the clock above. If it does, they look like this:

↊ ↋

Now all we need is nine more Unicode symbols for the rest of the digits. Zero is special: for zero, there need be only one.

How Unicode can save math: part 1

Every casual math enthusiast has by now heard of the raging war between tau and pi.

The what?

Ok, I mean, tau’s gaining a little ground, but really, pi has the weight of history behind it, so “raging” and “war” might be overstating things a little. The point is that 3.14, et cetera, is a bad circle constant and there’s a more intuitive option, “tau.”

Take a 90-degree angle. In radians, it’s half pi, but one quarter tau makes much more sense:

A quarter cut out of a pizza
Half pi!

If we call 2 times pi “tau,” this slice is one quarter, and things just make more sense.

Doesn’t seem to be catching on.

Not really, no. And tau has some problems too: for example τ=2π, but the tau glyph has only one leg and pi has two, so it looks like pi is twice tau. Shouldn’t tau have four legs? Clearly, the problem is this symbol: we need something more familiar. How about we just redefine pi to be twice itself?

Madness. Only confusion and chaos can result.

But not if we change the spelling. We’ll say that pie = 2pi.

Mathematicians will never go for it.

Perhaps, but food-based math has rich history. If you’re worried that it lacks a succinct one-character symbol, well, that’s where Unicode comes into the picture. In 2017, we finally have pie emoji, 🥧.

Where have my emoji gone?

Bob, what were your six biggest challenges in developing pdf?

Dave, that’s easy. Fonts, fonts, fonts, fonts, fonts and fonts. In that order.

The most noticeable limitation of Text Collector is that when it converts your text messages to pdf, it drops emoticons. Instead of smiley faces, it displays diamond-question mark things, “replacement characters.”

As ever, fonts are the problem.

When you need to display something laid out just so, such that it prints on a page and everything fits correctly, text alone isn’t enough.

Text, nowadays, usually means some encoding of Unicode. Technically, it’s a “Unicode transformation format,” which is where we get the “utf” in utf-8. Impress your friends and family with that.

Unicode represents abstract concepts, like the idea of the letter A or a smile. Emoji, just like letters A through Z are Unicode text, but precisely how letter A or winky face actually gets written to the page depends on your font.

A A

If you want to ensure that your text fits on the page, doesn’t run over or under the things around it, or, indeed displays at all, you must also include a font. In pdf terms, this is called “font embedding,” and it is what Android’s built-in pdf library does.

So far so good: just embed the emoji font and smiles or piles of poo come along for free, right? Wrong.

Most fonts specify letter outlines and leave color of the letters up to the user. Thus, I can say that I want letter A in blue or orange and both are the same font:

A A

Not so, Google’s emoji font. It includes cats, dragons and piles of poo in glorious, and heavyweight, color. Including this font makes for a massive pdf: almost 10 megabytes, on Android 6. It only takes two or three such documents to blow past Gmail’s attachment size limit. Typical collections would run into hundreds of megabytes, or gigabytes. They could easily consume all available space on the device.

This isn’t a new problem, and there’s a well-known solution: font subsetting. That is, only include glyphs for the small handful of characters that you actually use. Android’s built-in pdf library can’t do that.

So, to get emoji, I have to bring in an entirely new pdf library… and I’ve been working on this long enough. Version 1 needs to ship. Emoji will have to wait till version 2.