There are a lot of hidden enigmas and misteries in the modern buildings of Barcelona and some of these details are unknown by almost everyone. For example, on the facade at 11 Portaferrissa Street in the Old Town (Barri Gòtic), we can see the sculpture of two little boys above the main door on the top of a pile of bricks between them and the boy on the right holds some kind of square, whereas the one on the left holds a compass and a paddle. At first sight, it may seem another figure of the architectural style of the 19th Century. Nevertheless, it is a masonic sign indeed. The square and the compass were some of the most remarkable symbols of Freemasonry since both appear in the Masonry emblem.

In ancient times, the compass symbolized the Heavens inasmuch as it was used to study the starry Heavens, while the square represented the Earth because it was used to measure it. Nowadays both might have some philosophical and ethic connotations such as boundaries, so as to keep the equilibrium, and morality respectively. So, according to the Barcelona Historical Archive, the construction was made in the late 19th Century since there is a file with a works license of 1867, projected by Domingo Sitjas. It is interesting to notice that, in the original plans of the project, there is no sign of this sculpture. Due to Masonry persecution, everything related to it had to be kept secret. So, logically, the sculpture doesn’t appear in the plans!

Freemasonry describes itself as a beautiful system of morality, veiled in allegory and illustrated by symbols. Traditionally, masons are fond of architecture and are dedicated to the seven Liberal Arts: Grammar, Rhetoric, Arithmetic, Logic, Music, Geometry and Astronomy. Therefore, since Arithmetic, Geometry and Logic belong to mathematics, there is a link between Masonry and mathematics somehow. For instance, number 1 is represented by a point, which has no dimensions and turns to be the generator of any imaginable figure. According to the Masons, one is the arithmetic symbol of the Unity as well as the point is the geometric image of the Being. On top of that, if there are two points, they can be joined with a compass considering the straight segment connecting them like the one-dimensional projection of the geometrical link. It is important to note that the symbol of the Unit is the generator of duality, ternary, etc. using the compass. In addition to that, Geometry is the basis on which the Masonic superstructure stands and is considered by them as the mother of Science. However, Arithmetic has an important role in Masonry philosophybecause under Freemasons’ point of view, each of the four fundamental operations corresponds to a present value in their lives. For example, the sum is related to adding knowledge to our cognizance. In regard to such importance of the Unity as the genesis of the rest, it should be noted that the quaternary arises just like the ternary does. The last one would be represented in the form of a square. Mathematically, this generating method from the Unit would be considered as *N* = 1 + *n* (0<*n<*9 integer number), where *N* is associated with geometric figures representing values or facts of their daily life. It must be kept in mind that this is a cycle whose culmination is the following expression: 9+1=10=1+0=1. Let’s look at some examples of the corresponding symbolism to certain geometrical figures identified, as we have seen, with numbers. Remember that the “construction” of these is given by using a compass and a square like the ones in the image:

- The triangle, which represents number 3, is the geometric figure par excellence. The rest of figures can be represented as a set of triangles. It is known among Masons as Radiant Delta and each of its vertices represents space, time and energy. The union of these vertices turns out to be the force that gives structure to the universe, which is the Great Architect of the Universe (G), i.e., God.
- The square, which represents number 4, symbolizes at the same time two squares or the union of two triangles, that is, harmony and balance. If these two squares are within a circle, then they represent the harmony between the Earth and the Sacred World.
- The 5-pointed star (or pentagrammon) represents number 5 and symbolizes the man and life, what is masculine and what is feminine, and the union represents androgyny.

It’s imperative to comment that, although there may be no direct link between Pythagoras and Freemasonry, the teachings of Pythagoras have greatly influenced its structure and its teachings: numbers (especially numbers from 1 to 10) are symbols representing the philosophical universal organization and the only way to reach God. Furthermore, every degree of the Masonic initiation corresponds to one number.

Finally, it is necessary to remark that this is just a selection of the whole mathematics they studied, since the 47th Euclid problem and the golden proportion should be also mentioned.

In conclusion, the sculpture emblems a fraternal community full of mysteries which has always been passionate about mathematics. One last mathematical fact: if you come in the building, you will see 7 steps followed by 7 steps and 14 steps more!

*This post has been written by Paula Arrebola and Abel Hernandez in the subject Història de les Matemàtiques (History of Mathematics, 2014-15).*

**Location** Casa Domingo Sitjas (map)