Monsters, Moonshine and Black Sheep
DC I/O 2020 keynote by ABEL MACIEL
Abstract
Think about a number, any number. What structures lie within this number and what symmetries can it represent? Symmetry, an agreement in dimensions of due proportion, can be conceived of as a sense of harmony and beauty, appearing as balanced compositions. In mathematics, symmetry has a more precise definition and usually refers to an object that is invariant under some particular actions of transformation, including translation, reflection, rotation, or scaling. These two definitions are very different, but they are also fundamentally connected. They can be observed in the passage of time, spatial relationships, all objects (including abstract objects like theoretical models), language and music, to name a few.
Although varied, descriptions of symmetry from the perspective of mathematics, natural sciences and the arts are all anchored to the fundamental properties of invariance in response to a transformational action. This underlying fundamental truth of symmetry - the sense of some implicit structure being preserved - has proven to be one of the most powerful devices in the development of theoretical physics [Anderson 1972]. If we were to ask some ‘advanced AI’ or supreme alien civilization to create their own mathematics, what would they come up with? Would it be like human mathematics? Could they out-perform human intelligence? To explore this thought experiment, we have to touch on symmetry and group theory.
Keywords
DC I/O 2020, Symmetry, Architecture, Group Theory, Monster.
