Do 5W+H commute in Communication of Science?

We have been taught two non-trivial things since primary school: the commutative property of addition in math and the 5W + H rule in telling. The commutative property of addition depends on the meaning we attribute to the noun “addition”. Implicitly, we immediately focus our attention on numbers whose ad- dition is commutative 5 + 3 = 8 = 3 + 5. Yet, moving beyond the implicit reference to numbers, non-commutative relations become frequent. The classic example comes with the use of letters where their addition means arranging the letters one after the other. It immediately pops up that o + n = on is different from n + o = no. This beautiful example is often proposed to primary school students to emphasize the commutative property of the addition between numbers and that nothing must be implicitly assumed. The exam- ple is taken from the book written by Giorgio Parisi to popularize his studies that led him to the Nobel Prize in 2021 [1]. The commutative property is trivial also for the multiplication among numbers, but it is violated by the multiplication among matrices and operators in general. How rich is the non-commutativity of operators in quantum mechanics? The Heisenberg uncertainty principle itself depends on this failure. Here, starting from Pietro Greco's intuition of extending the Heisenberg uncertainty principle to the communication realm [2]. Let r=rigour and c=communicability one has ΔrΔc⩾ k>0. Hence popularization of science cannot reach the maximum of the rigor (Δr = 0) or the maximum of the communicability (Δc = 0) without losing the complementary quality. Greater communicability means less rigor and, conversely, greater rigor leads to loss of communicability. The 5W + H narrative structure is very easy to explain and, nonetheless, very profound. Note that the 5W + H structure also contains the arithmetic operation of addition and, hence, attention should be paid to its commutative property. Every time we use this narrative structure, we should ask ourselves what it is best to start with. Should we begin with What or should Where come first? Or is When? Who? Perhaps Why or How? What comes next? Which one should play the role of the third in the row, and last, even if not the least. This narrative is used also to structure the programs of many teaching courses. In a history teaching course where and when are swapped the result changes from synchronicity to diachronicity. Similarly, the order 126 is relevant in an starting Mathematics course if the set theory (what) is taught ahead of the algebraic inequality (how) or the opposite.