A Wonderful Mentorship Experience with a Chinese High School Student

Blog, Information Theory (Winter 2021)

By Qingxi Meng (qingxi@stanford.edu)

I am very lucky to have a great opportunity to mentor a wonderful Chinese high school senior, Yuting. I got connected to Yuting through my mother’s friend. Yuting and I met regularly on Sunday 8pm PT (12pm Beijing time). Yuting has taken many high school math and physics classes, but she only knows a little bit about probability and nothing about calculus. Therefore, my goal is to help her have a high-level understanding in information theory. Both Yuting and I are very interested in science fictions and I used many examples in science fictions for her to understand information theory.

Since Yuting knew nothing about information theory before, I was very nervous in the first session. Before our first meeting, I made a short video and gave a brief introduction of information theory as a story.  During our first session, I showed Yuting one real-life application of information theory: data compression. I showed her that many of the large files we used in daily life (e.g. movies) are stored in a compressed way. In the first session, I also introduced the basic concepts of probability in a very general way. Originally, I prepared a slide of 20 pages to introduce the mathematical backgrounds for information theory. However, I found that Yuting got lost very quickly. Thus, that part of the first session did not go as smoothly as I expected. In the last thirty minutes of the first session, we have a very interesting discussion about what will happen if there is no compression in our world. We also quickly discussed about Shannon. Surprisingly, Yuting heard of Shannon in her history class. It turned out that the contribution of Shannon was mentioned very briefly in the modern technology section of Chinese history book. Also, as a homework, I asked Yuting to estimate the sizes of all compressed files she had in her computer.

After the first session, I did not use slides to introduce mathematical ideas that much because I realized that Yuting was very easy to get lost in that manner. Instead, I usually played an interesting video related to the topic I wanted to cover. Then, I would only give a brief introduction and then Yuting and I had an interesting conversation over it. After each session, I encouraged Yuting to talk to her parents and cousins about what she learned in our session. Since her relatives had nearly no background at all in the science or technology, she also sometimes drew a picture or told a story.

The video I made in Chinese for a quick introductory to information theory for Yuting

In the next a couple sessions, I taught Yuting about the entropy. I first played an interesting video about why we would we use bits in computer. Yuting was very surprised in the beginning about the fact that the computer only consists of 0 and 1 at its core. We also had a great philosophical discussion about whether or not the world is made of 0 and 1. Yuting did not believe that the world is made of 0 and 1 because she thought it was just a human-made convention. Then, I raised a question about what a universal scale for information could be. Yuting first thought that it is not possible to do that because the language is ambiguous and thus it is not possible to use a mathematical measure for that ambiguity. Then, I played a game with Yuting. Specifically, I let Yuting think about an animal in her mind, and then I asked her 10 questions to guess what it was. Then, I explained to her that the information entropy is a measure of randomness of information. For example, as I asked more and more questions to guess which animal she had in mind, the entropy was lower because I had more certainty.

Over the next a couple sessions, I introduced the high-level ideas of lossless compression to Yuting. First, I wrote down a DNA sequence and let Yuting translated it into bits. Then, I explained very briefly why we could save space by utilizing the different frequency of each symbol. Yuting was not sure if this is the case in real life. Thus, I encouraged her to count the frequency of each letters in one paragraph of her favorite novel “Lord of Ring”.  In one session, we also discussed a very interesting topic about “The Golden Disk” and how information theory is related to it. Since both of us are passionate about science fictions, we had a great time discussing it!

The slide I made to discuss the information theory and the “Golden Disk”

Over the last a couple session, Yuting and I quickly went over the concepts of channel capacity. Yuting heard about the bandwidth a lot in the science fiction movies. However, it is her first time to hear about the channel capacity. Thus, we spent a lot of time discussing the difference between the channel capacity and bandwidth. In my understanding, the channel capacity is the maximum amount of data that can move over a specific channel while the bandwidth is the frequency range of a channel. Although Yuting still could not fully understand the difference between channel capacity and bandwidth, she learned about the connection between the two.

I faced some challenges when I was mentoring Yuting. One of the biggest challenges was that it was difficult for me to convey the ideas of information theory in an interesting and straightforward way. Since many concepts in information theory involve lots of mathematical expressions, I need to build up intuitions for Yuting. Also, I found that it was very easy for Yuting to forget what she learned after a week. Therefore, I encouraged her to also teach her parents and cousins about information theory. In addition, sometimes I also left some fun homework for her to apply what she learned from information theory.

Another biggest challenge I had was to clearly express the ideas of information theory in Chinese. Although Yuting learned about English in her English classes, she preferred to use Chinese for communication. Since I learned Information theory in English, it was challenging to express the ideas well in Chinese. I resolved this challenge by translating all terminologies into Chinese and did lots of practice. I also tried to speak the ideas of information theory in Chinese to myself to get used to it before each session.

Yuting was an awesome mentee! She had many great ideas and perspectives about information theory that I never thought about. Also, I learnt a lot about how to express information theory in a non-technical and fun way! Yuting mentioned that she wanted to take more related classes in the future to learn more about information theory. Both Yuting and I are looking forward to meeting in the future again to continue our discussion about information theory!