# QI philosophy

I think about the blog Quantifying Information as an expression of my curiosity about complexity and uncertainty occurring in the world. When trying to make sense of real world phenomena under uncertainty, I think we often do not get new information about some quantity of interest directly. Instead, we only get new information on quantities that are related to it. Hence, it is on us, to take this related information and draw the right conclusions from it. This process is what I call quantifying information, since I thereby try to stick to the following five pillars:

## 1 quantification

In my opinion, the best way to eliminate subjectivity as far as possible is by translating information into quantified expressions. Loosely speaking, it is much easier and more precise to compare two given days with respect to their measured temperature, than by whether the days’ temperatures have been described as “nice” or “hot” respectively.

## 2 data

It is a very natural thing for human beings to learn from past actions and experiences. Each experience will give us additional knowledge and additional insights into the interrelations of the world. However, in some situations individual people will only be able to gather a very limited number of experiences and observations. And these small “samples” in turn can cause imperfect views about the world. For example, take a look at the diagnosis of a very rarely appearing tropical disease. Let’s say doctor A never had any patient suffering from this disease. Therefore, he will usually tend to underestimate its probability of occurrence, or – worst case – will even not be aware of the existence of the disease at all. Assuming that doctor B, however, has already encountered two patients suffering from the disease, he will usually end up testing future patients for the disease disproportionately often. Only sharing and interchanging their data about historic disease occurrences will reduce these biases. Well, forestalling the outcry of your inner data privacy activist: of course, “with great power comes great responsibility” (to use the words of Uncle Ben). Nevertheless: with large data comes great power!

## 3 models

The more data, the better. So far, so good. But what to do in situations with only limited data to our hands? Well, there is a basic substitution that we can always engage in: replacing data with assumptions. This is a dangerous step that we basically will have to face in every situation – although to varying extent. For example, assuming that each side of a fair die will occur with probability 1/6 seems to be a much more innocent assumption than claiming that people are always rational and interested in their own well-being exclusively. And relying on wrong assumptions in turn will – to some degree – always result in misinterpretations of your data. That being said, in many situations it still will be the best – or only – way to draw conclusions about the real world. There is a simple logic for that: the further the probability of occurrence of an event deviates from the “fair” case of 50%, the more data we will need to estimate this probability with precision. Hence, for very unlikely events, it will be much more efficient to derive the probability from a more easily estimated event through the help of assumptions, instead of estimating it directly. For example, assume that we want to determine the probability of observing a “6” for all of 100 throws of a die. This could be easily derived from the probability of getting a “6” for just one die, through incorporation of the additional assumption of independence for die rolls: $\left( \frac{1}{6} \right)^{100}\approx 1.5\cdot 10^{-78}$. It would require a lot of sampling from a dice to be able to directly pin down such a small probability! Concluding, you can think of models as abstraction of the real world, trying to find the right balance between data and assumptions.