Why Mythological Golems Serve as a Metaphor for Statistical Models
What we can learn from ancient folklore to use statistical models responsibly.
Golems are a concept of Jewish Folklore. They were creatures made from dust, fire, and water, endowed with life through instructions given to them by their creator. The name comes from the Hebrew word “golem,” which translates to “something incomplete or unfinished, like an embryo”. They do not have knowledge, reason, or free will of their own, but have the power to perform the instructions they are given to their utmost, often better than humans. There are numerous creation stories revolving around Golems and their knowledgeable human counterparts who have bestowed life upon them.
One such story is that of the Rabbi Judah Loew of Prague from the sixteenth century. Prague was the seat of power of the House of Habsburg — a world power that controlled most of Central Europe, the Netherlands, Spain, and its colonies at the time. It was then ruled by Rudolph II — an emperor who truly admired intellect and invested in the arts, sciences, and mathematics. Under his rule, Rabbi Judah Loew had created a golem to defend Jews who were then being prosecuted in Prague. Swaths of people raised concerns over giving the power of life to this golem. Their fears manifested when the power granted upon the golem subsequently led it to take innocent lives while blindly following its creator’s instructions.
This story highlights how well-intended instruction, without the subtleties of environmental context, can result in serious negative consequences.
Statistical models are similar to golems in that, beyond their given directives, they do not ascertain any knowledge or intent of their own. They hold no wisdom or power to understand the context of where they are being applied, and whether their resulting output is appropriate for the given situation. They are only but a set of instructions made to compute and analyze data to challenge beliefs, inspire intuition, or validate hypotheses.
The instructions provided to statistical models can often be myopic and flawed due to limitations in the information available to the scientist. Users of statistical models, akin to mythological Golem creators, must take responsibility for the mandate and assumptions of each model to be able to deploy and interpret its results in a relevant manner. Since models are ubiquitous across scientific disciplines, it is imperative that all models undergo due diligence to avoid misinterpretation of results from their output.
One way to better understand, in-depth, the inner workings of models, is to compute them by hand rather than utilizing statistical software. This can be done for a wide range of computations, such as regression models, confidence interval calculations, or running t-tests. Once familiar with the process by hand, statistical software can then be leveraged for implementation.
Here is an example of an analysis, with details of how its results could be interpreted inappropriately, describing computation of confidence intervals by hand, and by using statistical software.
- We will construct a 95% confidence interval for the mean highest elevation.
- We will evaluate assumptions for being able to run any statistical computation and see its implications.
- We will also run the 95% confidence interval by hand and with the help of statistical software to get experience with both methods.
There are two assumptions we need, to be able to draw t-based confidence intervals:
1. The data points must be identically and independently distributed
2. There is a unique Best Linear Predictor
We will evaluate #1 to see where it fails and what that would mean for our results
They are not identically distributed:
1. The number of expeditions were somewhat increasing till the 2010s and have declined since. It seems that the history of expeditions influences how many are attempted after them.
2. The expeditions in this sample are not identically distributed across seasons with spring and autumn being more popular than others.
These popularities also seem influenced by lessons learned in past - possibly of climbing conditions.
Independence cannot be guaranteed either since the number of concurrent expeditions at a time could affect:
1. Crowding at the summit, as it happened in 2019 at Mount Everest. This derailed anticipated plans causing some to not make it to the top. Thus some expeditions were dependent on others.
2. If multiple expeditions are attempting a climb, they could share knowledge of the route, climate conditions, and resources making it more likely to achieve the summit. Thus defying independence.
Since the assumption for identically and independent distribution is not met, we must be cautious with the conclusions we draw. The inability to satisfy this assumption hampers us from generalizing any conclusion we get from this sample to the general population, even though the confidence interval can still be computed.
Computing the Confidence Intervals (by hand):
Computing the Confidence Intervals (using statistical software):
References:
[1] N. Michaelson, Golem, https://www.myjewishlearning.com/article/golem/
[2] R. McElreath, Statistical Rethinking, https://www.amazon.com/Statistical-Rethinking-Bayesian-Examples-Chapman/dp/1482253445
[3] The Editors of Encyclopaedia Britannica, Golem, https://www.britannica.com/topic/golem-Jewish-folklore
