Autopoietic Nest

An autopoietic machine is a machine organized (defined as a unity) as a network of process of production (transformation and destruction) of components that produces the components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in the space in which they (the components) exist by specifying the topological domain of its realization as such a network. It follows that an autopoietic machine continuously generates and specifies its own organization through its operation as a system of production of its own components, and does this in an endless turnover of components under conditions of continuous perturbations and compensation of perturbations." (Maturana & Varela 1980; p.79)

At the bottom of the hierarchy are the physical systems that emerge spontaneously, and here we see why an idealistic permanence can be attributed to what are actually emergent patterns.  Peirce points out that mathematics are forms that are always true, in other words, tautologies, but their importance is in semiosis, or reflection, to use a term more common to other philosophers, including Dewey.  When an inquiry results in a model of the world, mathematics gives us reliable pathways of reflection.  This leads to ways to test our models.  The structures of mathematics exist as a possibility that can be realized in the experienced world whether they have already been discovered, are yet to be discovered or even if they are beyond our mental capacity, now or ever.