## Why Does a Tiger Have Stripes and a Lion Doesn’t?

I’ve encountered a pretty nice insult on reductionism in the “Categories for the Practising Physicist”. I’ll just cite the whole Example 17 from it:

Why does a tiger have stripes and a lion doesn’t?

One might expect that the explanation is written within the fundamental building
blocks which these animals are made up from, so one could take a big knife and open the lion’s and the tiger’s bellies. One finds intestines, but these are the same for both animals. So maybe the answer is hidden in even smaller constituents. With a tiny knife we keep cutting and identify a smaller kind of building block, namely the cell. Again, there is no obvious difference between tigers and lions at this level. So we need to go even smaller. After a century of advancing `small knife technology’ we discover DNA and this constituent truly reveals the difference. So yes, now we know why tigers have stripes and lions don’t! Do we really? No, of course not. Following in the footsteps of Charles Darwin, your favorite nature channel would tell you that the explanation is given by a process of type

$\displaystyle{prey \otimes predator \otimes environment \to dead \; prey \otimes eating \; predator}$

which represents the successful challenge of a predator, operating within some environment, on some prey. Key to the success of such a challenge is the predator’s camouflage. Sandy savanna is the lion’s habitat while forests constitute the tiger’s habitat, so their respective coat blends them within their natural habitat. Any (neo-)Darwinist biologist will tell you that the fact that this is encoded in the animal’s DNA is not a cause, but rather a consequence, via the process of natural selection.

This example illustrates how monoidal categories enable to shift the focus from an atomistic or reductionist attitude to one where systems are studied in terms of their interactions with other systems, rather than in terms of their constituents. Clearly, in recent history, physics has solely focused on chopping down things into smaller things. Focussing on interactions might provide us with a complementary understanding of the fundamental theories of nature.

In my opinion the reasoning above is brilliant. However note that by no means it implies the reductionist approach should be abandoned. The fact that objects can be dissected into their constituents is as true as the fact that the whole is more than the sum of its parts. The cited passage just demonstrates that many people (like me) are really not in favor of dominating role of reductionism in our worldview.