In this talk, I will show the representation power of sphere embedding: (1) a variety of basic geometric objects can be defined as spheres; (2) Spheres are perfect for neuro-symbolic unification – sphere centre hosting latent feature embedding for associative thinking (System 1), sphere boundary explicitly embodies part-whole or category relations for logical reasoning (System 2); (3) Spheres and the connection relation can define commonsense spatial relations, including orientation and distance; (4) Cartesian product of sphere configurations can formulate event structure. Putting all these together, we can use sphere configurations to define the knowledge structure of humour, which is not far away from the knowledge structure of syllogism. This talk ends with the conclusion: spheres are natural representations of syllogistic reasoning (the microcosm of human rationality) and humour reasoning (the highest level of human rationality). They are the two end-poles that span the continuum of human intelligent behaviours.
