# A Game of Information

EE376A (Winter 2019)
`Arkira Chantaratananond, Isaac Scheinfeld, Maya Ziv`

Information theory gives us a framework for reasoning about many aspects of communication that are essential to our everyday lives. In light of our advisor Tsachy Weissman’s efforts to bring information theory to the masses, we set ourselves the goal of introducing a central insight of the theory to people independent of any mathematical background. While pop-science explanations of concepts such as entropy exist and can convey some of the intuition behind them, we wanted to address a broader audience than such presentations target. Everyone, from EE graduate students to small children, experiences effects modeled in information theory. Our goal was to have people, young or old, be able to think about such effects without (necessarily) mentioning the theory behind them.

One of the most important concepts we wanted to explore and convey with this project was the idea of compression through encoding – fitting more information into a smaller space. It’s one thing to explain compression as a process , and another thing entirely to create an activity where the idea of compression and its benefits arises organically. That’s the experience we wanted to give our audience – if they were doing the compression and encoding themselves, then they’d have much better access to some of the intuition of why it’s useful.

The way we ended up deciding to do this was through a variety of games with a central compression mechanic. In the most basic version, a number of words, pictures, symbols, etc. are presented. The goal is to encode some subset of these using a word, picture, or symbol. Games of this type allow the players to explore different methods of compressing meaning, whether mechanical or free form.

For our outreach project, we presented a simple form of such a game to young children (mostly between 7 and 12 years old) at a local elementary school. We had 6 tiles out on our table – bear, apple, fish, flower, shirt, and ball. One person would look at them and pick one word which represented some number of the tiles. The other player would then have to guess which tiles the first player meant. After we played a few rounds, we would pull back the curtain and go: “tada! You’ve been doing compression this whole time!”, and we’d explain that they were fitting more words (usually 2 or 3) into the space of just one. Additionally, if players guessed wrong along the way, we’d tie in the idea of lossy compression – that sometimes there are encoding schemes where the information can’t be perfectly reconstructed, and that’s what was happening when they guessed wrong. It was cool to be able to give them an intuition for why compression is useful and valuable, and let them do some of their own encoding.

The game we played with the kids and their families is actually a modified version of another game called Codenames, which also falls into our general game model. The only difference in the game is that you don’t get to choose which set of words you need to encode, they’re determined for you (and there’s some elements of risk in the whole process).

While encoding schemes involving wordplay, rhyme, and other forms of information local to the language and words at hand are possible, we found in playing such games ourselves and with others that by far the most useful information is our common knowledge of the world. Ball and fish become “beach”, fish and flower “smell”, and flower and ball “field”. Such associations, especially when encoding larger word sets, involve specialized knowledge about common situations, places, etc. While this does not necessarily make humans better at this task than computers, it raises interesting questions about how to measure all this implicit information hidden in our minds.

One final variation of our game introduces a new concept while increasing the difficulty of the task. In addition to having to communicate some set of words/pictures/symbols to a fellow player (in this case, your teammate), a third player attempts to guess the set before they can. Thus, the shared information used for encoding is forced to be exclusive to the teammates. Here, we can start to consider smaller, less universal subsets of our experiences shared only with some. In the future, games like these could be studied as one approach to quantifying our shared representable knowledge of the world.