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The analysis of reality produces reality


The encounter of the mathematical formula of triangulation with a vegetable.

The process starts with the formation of a triangulated hexagon on the surface of the potato. This hexagon is surrounded by new triangles, following given rules, until the entire surface of the vegetable is triangulated.

The division of the surface into triangles expressed through a slight engraving on the outer part changes the way each potato interacts with its environment, as time passes. The incisions gradually begin to deepen and acquire a darker hue, while at the same time the overall exterior part begins to soften.

Although the triangulation engraving applied to each vegetable is the factor that rapidly accelerates the rotting, at the same time it can assign to each potato a number, capable of describing it regardless of its deformity.

Chemical changes that occur in the decomposing potatoes are in sympathy with the continuous transformations of the topological spaces, and the idea of change through time is paired with the broader idea of change as a way to distinguish something from something else.

The analysis of reality produces reality, 2022
Engraved potatoes (from the land of Italy).

Polo del ‘900, Turin, Italy.

The triangulation method applied to the potatoes' skin leads to the formation of Verices, Edges and Faces on the surfaces of the vegetables. This enables the definition of the Euler characteristic (χ) of each potato, given by the formula χ=V-E+F.

The Euler characteristic of a surface is a property of the surface itself, so it gives the same number χ independent of the choice of subdivision.

In our case, this means that any proper triangulation of any potato give always the same result,
V-E+F =2 for any vegetable.

Additionally, the Euler characteristic constitutes a topological invariant of a shape, which means that this number χ, characterizes this shape regardless of the way it may be stretched or bent and therefore transformed into a new shape.

Due to the engraving and under the influence of the environment, the potatoes start to shrink and the triangles on their outer part are slightly deformed as well.

This occurs in a one-to-one way, so the vertices, the edges, and the faces that the well-formed vegetable originally had are assigned to the corresponding vertices, edges, and faces of the now decomposed vegetable.

In this way, the process of rotting that its vegetable faces, can be seen as a map that matches the initial engraved triangles of the potato when it was still fresh, onto the deformed triangles of the same potato while is getting rotted.

It follows that the value of V-E+F, which is equal to 2 for every potato remains unchanged and therefore, the Euler characteristic is preserved.

The analysis of reality produces reality, 2021
Engraved potatoes (from the land of Franch ).