It is generally assumed, and usually taken for granted, that reality is fully contained in space. However, when taking a closer look at the strange behavior of the entities of the micro-world, we are forced to abandon such a prejudice and recognize that space is just a temporary crystallization of a small theatre for reality, where the material entities can take a place and meet with each other. More precisely, phenomena like quantum entanglement, quantum interference effects and quantum indistinguishability, when analyzed attentively, tell us that there is much more in our physical reality than what meets our three-dimensional human eyes. But if the building blocks of our physical reality are non-spatial, what does it mean? Can we understand what the nature of a non-spatial entity is? And if so, what are the consequences for our view of the world in which we live and evolve as a species? This article was written having in mind one of the objectives of the Center Leo Apostel for Interdisciplinary Studies, that of a broad dissemination of scientific knowledge. Hence, it addresses a transversal audience of readers, both academic and nonacademic, hoping to stimulate in this way the interdisciplinary dialogue about foundational issues in science.