# Love in Projective Planes, Chinese Valentine’s Day & Phonotactics

A few days ago China celebrated one of many Chinese Valentine’s days: the 20th of May. Why is this a special day in China? Chinese has around 30 to 36 phonemes which is plenty, but Chinese phonotactics dictate that you can only make around 1200 syllables out of them, for instance, see this video. English has more than 8000 possible syllables. Additionally, Chinese (unlike many other languages) uses one syllables per morpheme. This distinguished from languages such as Japanese which have very few syllables, but usually use two or three syllables for one morpheme. Often Chinese avoids any resulting confusion by various means, for instance, by combining at least two morphemes/syllables. Yet you find around 1500 one syllable words in Mandarin. By the pigeonhole principle, we find at least two words which sound the same!

## 520

Let us come back to the 20th of May. In China you write dates YYYY/MM/DD, so the 20th of May is 520. You say “520” as “wǔ èr líng” (五二零). The phrase “I love you” in Chinese is “wǒ ài nǐ” (我爱你). You can see, it is not precisely the same, but apparently (see my remark about my Chinese below) close enough to count for native speakers. Hence, it is a Valentine’s Day here.

[My Chinese is very rudimentary. Earlier today I successfully asked for the price of a dress in a shop: “Zhège duōshǎo qián?” (“How much is this?”, 这个多少钱, but I mispronounced even this simple phrase). The saleswoman replied with something like “Yī liǎng qiān” (“One or two thousand”, 一两千), but I heard “Yī liǎng qián” (“One or two money”, 一两钱) which does not make any sense for a silk dress. Luckily, she then just typed the numbers. Hopefully, in five years I will read this and be astonished by my inability.]

## Projective Planes & a Video of me

Many readers of this blog will know the definition of a projective plane. You need a set of points, a set of lines, and three axioms:

- Any two distinct lines meet in a unique point.
- Any two distinct points lie on a unique line.
- There are four points, no three of them on the same line.

The first two axioms are the important ones. The third axiom is what I know as a richness condition in German, namely, a requirement that prevents you from getting silly examples. My main interest are finite projective planes. Many interesting conjecture are associated with them, mainly the prime power conjecture and the prime order conjecture.

Now last Friday the PR secretary of my department asked me if I want to contribute to a video that the university was producing for 520. I agreed (even though I dislike this days). So I had to come up with something that expresses my alleged love to mathematics in a romantic way. I saw examples from the last years, but these were mostly math memes which I have seen on the internet countless times. The thing I came up with (and which I did not see before) is based on projective planes. These are **the most romantic geometries**: Imagine you are a line. And another line is your soul-mate. By the **first axiom** you will meet your **soulmate** at some point! And now imagine you are a point. By the **second axiom** you will be connected to any other point in a** unique way**!

[Maybe the third axiom can be also seen in a positive way: It guarantees you at least some choice.]

Hence, this was my one (and, hopefully, only) contribution to any Valentine’s day in the world. Here is the video on Bilibili.