# Matera in Many Dimensions

## Abstract

**:**

## 1. Introduction

## 2. Going for a Walk in Euclidean Dimensions

**fourth dimension**. Some interesting installations can be seen by mathematicians as three-dimensional projections of four-dimensional objects. On the other hand, speaking to a curious tourist who likes scientific language, the guides must point out that this museum exhibits space–time. Not just space. Nor only time. Indeed, though Palazzo Pomarici was built in the 16th Century, today it houses a collection of modern works which concern the future. The proximity of the Sassi zone, with houses dug into limestone rock hundreds of years ago and contemporary sculpture, tell us about the ancient world. The stone itself gives this space–time shock, and one piece of evidence is Alberto Viani’s sculpture, see Figure 1, and the way in which it collects rays of light and shadows as a physical universe. Indeed, it was inspired by a collection of mathematical surfaces used by scientists at the beginning of the 20th Century when a new cosmological vision appeared. See Reference [9]. From our point of view, MUSMA is the place in Matera where space and time are intertwined.

**three dimensions**. Sculpure mainly plays with depth. We can see this, for example, in the facial expressions of the small Birichino by Menardo Rosso (see Figure 2). Without depth, we cannot see the core of the work. The same artist said that “Nothing is material in space, we are nothing but plays of light”. From a mathematical point of view, this statement refers to the theories on light paths (therefore shorter ones) in curved space. In this museum, there are also installations that realize the games of light deviated from more or less curved obstacles.

**two dimensions**are sufficient for an image. Lucania 61, a large mural by Carlo Levi in Palazzo Lanfranchi shows the inhabitants of Basilicata in 1961. In this mural, the artist neglects depth, leaving to the viewer the task of finding it. See a detail in Figure 3.

**complex multi-dimensional**world. As in the Gauss-2D complex space, we have four multi-quadrants. The origin of this complex system is in Piazza Vittorio Veneto where we can cross the horizontal and real plane of the city level. In addition, we can also think of an imaginary vertical plane between the populated city and the natural landscape (see Figure 7). The canyon, here called “gravina”, is a thin line between rocks without humans and populated rocks. In all the other parts of the vision, human building and natural scenery are intertwined.

**one dimensional concept**is always present in Matera here, since an apparently chaotic city increases relations. A convex set is a set in which any two points are connected by a line which remains in the set. It is important to notice that any square is convex since it is the place of relations. In the Sassi zone, the houses were distributed in small groups of almost 10 which had a courtyard in common in which the life of everyone was controlled. This yard has a local name of “vicinato”. Like a theatre, it is convex. Any convex set is a connected set. This is a very important mathematical inclusion that is translated in any human agorà!

**zero dimension**. However, very complicated sets of “separated” points are also zero-dimensional: The set of lights in Matera nights is one of these.

**negative dimension**as that of the empty set. It would be nice to give to the tourist this explanation on the balcony of Ortega’s house that overlooks two vacuums: the canyon, the void dug by water and the stone gardens, the void dug by the wind. See Reference [11].

**infinite dimension**by opening the windows of Ortegas’s house and mentioning that spaces with infinite coordinates are the right ones to study the motion of the flight of the nibbio.

## 3. Taking a Photo of a Fractal City

## 4. Applications

## 5. A Living Lab Experience

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Palombaro Lungo, aqueduct graph from Reference [2].

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**MDPI and ACS Style**

Lucente, S.
Matera in Many Dimensions. *Heritage* **2019**, *2*, 380-389.
https://doi.org/10.3390/heritage2010026

**AMA Style**

Lucente S.
Matera in Many Dimensions. *Heritage*. 2019; 2(1):380-389.
https://doi.org/10.3390/heritage2010026

**Chicago/Turabian Style**

Lucente, Sandra.
2019. "Matera in Many Dimensions" *Heritage* 2, no. 1: 380-389.
https://doi.org/10.3390/heritage2010026