Our Expert Voices conversation on space.
In mathematics, "space" describes a setting where relations between objects imitate real life phenomena: distances, directions, continuity, convergence. In abstract settings, these relations can be warped or decoupled from one another so we can examine the meaning of each one separately. A space can have infinitely many dimensions, the surface of a ball need not be curved, or we can determine directions without being able to measure distances. The "points" in a space can be complicated objects with structure of their own, such as functions or matrices. Their properties are examined indirectly through the geometry of the space they live in. We build sophisticated and productive theories of mathematical spaces that require no knowledge of what the elements of these spaces truly are, only asking that they conform to certain geometric requirements. This might shed light on why we are able to function so well in the universe, developing science and technology, while there are still fundamental questions about the space we live in that remain unanswered. Bottom line: Mathematics works around the unknown, providing sufficient functionality even while the essence may still be under investigation. Other voices in the conversation:
Sean Carroll, theoretical physicist, California Institute of Technology: Space is overrated Bridget Falck, astrophysicist, University of Oslo: Space is a relation between things, not a thing itself David Albert, philosopher, Columbia University: Maybe there is no space