# Information Density in Languages July 5, 2020

I remember seeing an interesting article a little while back positing that different languages have roughly the same information density; that is, even though speakers of one language may speak faster than those of another, human languages naturally tend to convey ~39 bits of information per second. I don’t remember where I originally saw that article (more likely than not it was one of Hacker News, Reddit, or the New York Times), but apparently this is the source paper, and here is a writeup in The Atlantic that I was able to find.

Today, PCC had a joint service between the Chinese- and English-speaking congregations. This usually means that the sermon is delivered in one of the two languages and translated line-by-line by an interpreter. I’m not sure if the translation is written in advance or done on the spot; I figure that it depends on the person, because I’ve definitely seen translators pause for a moment to think of a translation (sometimes even with audience suggestions).

I don’t know why it came to mind this morning, but I thought that it’d be funny to do an empirical test of the information density constancy hypothesis. This scenario seemed ideal for such a test, since the pastor and the translator are (theoretically) delivering the exact same content, line-by-line, in two different languages. The nice thing about attending church over Zoom is that you can take such measurements without being very disruptive.

Even though Zoom said that the sermon was being recorded, I’m a little impatient, so I decided not to wait for the recording to come out and just timed a few arbitrarily chosen samples on my phone a few times. I didn’t do it too extensively because I was, you know, also trying to actually pay attention to the sermon. Here are the raw data:

``````# E[i], C[i] are the durations (in seconds) of fragment i spoken
# in English (pastor) and Chinese (interpreter) respectively
E = [4.01, 4.40, 5.15, 7.72, 8.73, 2.26, 4.54, 8.61, 7.94, 5.38,
7.71, 10.33, 9.47, 3.51, 5.06, 9.48, 13.27, 11.60, 8.64]
C = [2.88, 4.19, 4.11, 7.59, 10.78, 2.02, 3.74, 6.46, 7.15, 7.45,
8.22, 8.13, 6.46, 3.29, 4.93, 12.90, 15.94, 8.93, 8.95]``````

I also timed two longer samples: a reading through Ruth 1:15-22, which took 1:25.93 minutes in the English and 1:24.63 in the Chinese, as well as a fragment that took 23.68 seconds in English and 15.54 seconds in Chinese. I did not include them because I’m not a statistician and am a bit spooked by potential outliers.

I don’t remember much of AP Statistics (not that that class was exactly the paragon of scientific rigor…) and haven’t had the pleasure of taking PnC at CMU yet, but I suppose some kind of paired T-test would be relevant here. I will skip checking the preconditions and just assume that they hold:

``````from scipy.stats import ttest_rel
ttest_rel(E, C)  # p = 0.6383``````

Seeing that the p-value is so high, we surely fail to reject the null hypothesis, which is to say that based on these data it would appear that English and Chinese indeed convey information at the same rate.

Of course, this depends a lot on the speaker and interpreter setup. I’ve found that some pastors like to speak slowly, drawing out emphasis in their sermons. On the other hand, if the interpreter is not prepared, he or she may have to think on the fly, which can impair the speed of translation.