File:BlackSheep.png

Figure 15.6 from page 218 of book «Суперфункции» ^[1], 2014.

The same picture us used as Figure 15.6 at page 215 of book «Superfunctions» ^[2]

Russian

Два математика едут на конференцию по суперфункциям и обсуждают чёрную овцу, которую они увидели из окна поезда:
Ваше допущение, уважаемый коллега, представляется мне не только не очевидным, но и совершенно не обоснованным. Всё, что мы можем заключить из этого наблюдения - что в этой стране существует по крайней мере одна овца или по крайней мере один барашек, и что по крайней мере правая сторона этого существа - черная.

English

Two mathematicians take train to the conference on superfunctions. Through the window, they see a black ship on a green hill.

- Very interesting! In this country, the ships are black!

- Your generalization seems to me not supported. All, that we can deduce from this observation, is, that in this country, there exist at least one sheep; and at least the right-hand side of this sheep is black.

Spoiler

For a mathematician, many "coommon-sense" things are not obvious - unless they are proven or declared as postulates of some formalism.

In the figure, it is not obvious, that the left side of the ship is also black.

In the case of tetration, it is not obvious, that the visually-smooth transition through base \(b=\exp(1/\mathrm e)\) means, that \(\mathrm{tet}_b(z)\) is holomorphiphic with respect to \(b\) at this point.

Actually, there is branch point there, and the choice of the cut lines in the complex \(b\) plane is not obvious and not trivial.

References

Keywords

Base e1e, Mathematics, Superfunctions, Tetration,

Суперфункции