Abstraction

Dear Princess ‘Ishka,

Try to pick the intruder among the following group of things: glass, bottle, stock cube, vase. I don’t really want you to solve this elementary puzzle of abstraction. Instead, I would like to tell you about the original solution my sister gave to it, when she still was at the beginning of secondary school.

The faculty to abstract the general from the particular is an amazing capacity of the human mind. Its discovery goes back at least to Aristotle, and had enormous impact on the way we think about the functioning of our mind.

Abstraction enables us to categorize things in the world and give them an order. It is the fundamental ability underlying the very possibility of scientific research, which aims at giving general laws of nature (if not universal). You couldn’t say anything informative about movement, molecules or cells if all you could talk about were single movements, single molecules and single cells. Abstraction makes it possible to say how every single movement works according to the laws of physics, and how all molecules and cells behave according respectively to chemistry and biology.

The merits of abstraction are countless. One could even claim that there would be no human intellectual progress without the capacity of finding the common property among many individual things. The world would look like a chaotic ensemble of particular entities, precluding any possibility of orientation.

Luckily, all humans share abstraction. Or so I thought, until my sister ruthlessly smashed my convictions.

A questionnaire was given to all schoolchildren of her year. Its purpose was to test their logical abilities with respect to public education, I guess. When confronted with the “intruder’s puzzle”, they were expected to abstract the common property of most of the items presented and pick the exception. Of course, there is one evident property shared by glass, bottle and vase, which stock cube doesn’t present, namely the property of being a container. Apparently, that was not evident enough, since my sister answered “vase”.

Should we worry about my sister’s intelligence back then? Where on earth did she find the property common to glass, bottle and stock cube, vase doesn’t present? The best way to counter my apprehension was to ask her directly. Her response was along these lines: “you don’t necessarily find a vase in the kitchen, do you?”

What she did when confronted with the puzzle, wasn’t to abstract the shared property. She rather asked herself if there were contextual similarities among those objects of common usage. And the first thing that came to her mind was that you never find a kitchen devoid of glasses, bottles and, when available, stock cubes. Vases, on the contrary, are not necessarily part of the kitchen’s furniture.

My sister’s thought was contextual rather than abstractive. And, to a certain extent, that was more appropriate, insofar as the term “intruder” comes with a feeling  of disappointment rather than logical rigour. In a certain sense, you would have good reasons to be disappointed if you weren’t to find glasses, bottles and stock cubes in someone’s kitchen (when available). On the contrary, you just don’t go to someone’s place asking “why aren’t your vases in the kitchen?”

Of course, my sister’s way of thinking was not as rigorous and general as abstraction would have been. But instead of wondering how contextual thought is less reliable than abstractive thought, we should ask ourselves if the intruder’s puzzle was rigorous enough in the first place! Indeed, it seems that the puzzle was already expecting a certain kind of answer there was no precise criterion to expect. And my sister involuntarily showed the flaw in the formulation: one needn’t necessarily use abstraction to give a pondered answer to certain questions.

It was very stupid of me to have fun of her when I first heard that answer. I share part of the blame with those who formulated the intruder’s puzzle first, presuming that people who think, need thinking in a certain way. But my sister proved us wrong.

Indeed, she taught me a very important lesson: don’t expect people to act and think always upon the best theoretical principles because, in practice, abstraction might be of no use in everyday activities, like having dinner or the like. A stock cube might help instead.

Forever yours,

‘Miasha

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