And yet, perhaps, the reason why the brain works this way is because it could not do otherwise to fulfill its purpose. After all, nervous systems have inherited their objectives from genes. Nervous systems and genes alike process environmental stimuli to lengthen survival, they just do so at different speeds and scales – the brain provides an immediate action-reaction scheme to diagnose imminent threats, while the gene operates across generations and plays the long game, as the discovery of DNA and subsequent mechanical explanations crowned the glorious intellectual achievements of Wallace, Darwin, and Huxley. And, again, genes are nothing more than interacting proteins. It’s interactions all the way down.
This is even more fundamental than physical existence, because it allows for the existence of ideas. At some level, the Pythagorean theorem “doesn’t exist”: there is no physical “thing” embodying it. But it does interact with our minds, as all ideas do, and thus it exists. (Maximilian Schich. Cultural analysis situs. 2019)
The fundamental realization is that you can split geometry in two complementary parts: the part that is all about quantifying relationships – i.e. measuring how long something is –, and the part about qualifying relationships – “the two right triangles in which you can split a square touch” is true regardless of how long the square’s edges are.
Most famously, this insight is what Euler used when solving the famous Königsberg Bridge Problem. The problem asks whether it is possible to cross all bridges of Königsberg (now Kaliningrad) without crossing the same bridge twice. Following Leibniz’s intuition, Euler realized that the problem didn’t require reasoning about any quantities: it didn’t depend on the length of the bridges nor the size of the islands. It was exclusively a problem about the qualitative relationships between islands and bridges: whether you could use the latter to reach the former.
We already have a theory for this compartmentalization of the scientific investigation. This is what Hayek called “division of knowledge”, which is a much more powerful concept than Smith’s classical division of labor. If I specialize as a chemist and hone my skills and tools to that specific task, I can be immensely more productive, because I am outsourcing all other knowledge discovery endeavors to other specialists. This is how societies grow their pool of knowledge efficiently. However, the result is that, now, no individual can really fully grasp a well-rounded picture of reality. The collective society can, but not its individual components. It is all deformed by the lens of their specialization.