My first year at university was spent formally proving things that have been known for many centuries. The very narrow definition of a mathematical proof makes it that once you prove something, it is undoubtedly true. However all it takes to disprove something is one counter example. Note that an example is not a proof; after all you never know how the example generalizes (if you would, you can build a proof out of that). Three years later I find myself looking outside of my discipline and enroll for the honours course "Leiden Revisited: Social Control and Social Cohesion in Insecure Times". Imagine my surprise when I was assigned to read a scientific article consisting of only examples.

I had dabbled in social science. A discipline that is among the hard sciences 'joked' about as "not *real* science" and it is now crystal clear why. It is the difference in culture and lack of awareness of positionality by the hard sciences. The social sciences have the unfortunate property of being relevant, this causes everyone and their dog to have an opinion on it. It is therefore seen as an easy subject when in reality people don't know what they're really talking about; very much like the Dunning-Kruger effect. Contrast this to for example mathematics. Many people ignore the subject and write it off as 'too difficult' because they aren't consciously confronted by it on a daily basis. Then there is the lack of positional awareness: the hard sciences don't realize they are conditioned to want to prove everything with mathematical rigor while examples are left as an exercise. Combine the two and it is understandable that the situation is as it is.

Sometimes its not about proving generalities. For example the work by Entzinger taking Rotterdam as an example of a superdiverse city. For one it illustrates the point of superdiversity. A hard beta scientist would argue that a hard and fast definition is more useful. The fact is that things are hardly ever binary; the grey area is largest. Subtleties and the dynamics of a concept can't be captured easily and multiple examples can be justified for this. In this respect the point of the example is to get a more complex idea across. Another aspect is that examples are an entry to unexplored territory for generalizations. By noticing Rotterdam is a superdiversity one might ponder if other cities are a superdiversity. What distinguishes them? What is the overlap? And, what is in between?

There is no well defined border between qualitative and quantitative science. Consider most models used in solid state physics, the energy landscapes used in calculations almost never reflect the true energetic potential. The power is in the qualitative predictive power: periodicity leads to band structure, no matter how difficult the details of the interactions. The energies might be off by orders of magnitude and the shape of the band structure might change, yet there is still qualitative value in the model. In this sense it is only a qualitative model though it is rooted in mathematics. These 'toy models' occupy a liminal space between qualitative and quantitative research, it is the intermediate regime of two limiting cases. It is no accident that this is often the regime where understanding can be expanded and true insight lies.

However, true insight is not always found. In a class about academic and professional skills the professor explained the concept of intersectionality to a class of physicist using the collapse of a quantum state as an analogy. The key point being that a person is projected onto some lower dimensional basis determined by the social environment at 'the time of measurement'. Everyone understood exactly what he meant by this. A friend and I ran with the concept and tried to make a qualitative model of the gingerbread person. Being used to thinking in terms linear spaces we conjured that a basic model of sexuality could be captured in two dimensions. On one axis would represent heterosexuality and the other would homosexuality. We got stuck when we tried to think deeper about a rotated basis. We figured that heterosexuality + homosexuality = bisexuality, but what would be heterosexuality - homosexuality? You could say that we failed to realize that homo- and heterosexuality are not orthogonal, but you have truly understood this blog post if you realize that the idea of capturing such concepts in a rigid manner was a hopeless idea in the first place. For completeness: we tried mapping sexuality onto the surface of a sphere before we realized the futility.

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