I have been studying group structures lately. The loops (and, in general, the quasigroups) seem strange because they are defined and we have studied their properties, but it seems that in reality they are not used at all. In fact, what I find argues that it is very difficult to find any use for loops in physics or science.
I'm looking for any non-exotic application of quasigroups or loops, the less exotic, the better. I am aware that there is an attempt to formulate a Theory of Everything using a loop, but I would say that it is quite exotic. The general question could be formulated with a phrase: "If a person does not want to study quasigroups and loops, why would he want to start that study?" Something similar to how groups capture the concept of symmetry, which is easily applied in many cases, how monoids can be used to parallelize operations such as MapReduce or capture information in strong-type systems, or how inverse semigroups can be used to reason about of partial symmetry.