  Inspired from research subjects in sub-riemannian geometry and metric
geometry, we propose uniform idempotent right quasigroups and emergent algebras
as an alternative to differentiable algebras.
  Idempotent right quasigroups (irqs) are related with racks and quandles,
which appear in knot theory (the axioms of a irq correspond to the first two
Reidemeister moves). To any uniform idempotent right quasigroup can be
associated an approximate differential calculus, with Pansu differential
calculus in sub-riemannian geometry as an example.
  An emergent algebra A over a uniform idempotent right quasigroup X is a
collection of operations such that each operation emerges from X, meaning that
it can be realized as a combination of the operations of the uniform irq X,
possibly by taking limits which are uniform with respect to a set of
parameters.
  Two applications are considered: we prove a bijection between contractible
groups and distributive uniform irqs (uniform quandles) and that some symmetric
spaces in the sense of Loos may be seen as uniform quasigroups with a
distributivity property.
