[Representations] Talk 1: Form and Function. The Geometry of DHTs.

Whether it be the sweeping eagle in his flight, or the open apple-blossom, the toiling work-horse, the blithe swan, the branching oak, the winding stream at its base, the drifting clouds, over all the coursing sun, form ever follows function, and this is the law. Where function does not change, form does not change. The granite rocks, the ever-brooding hills, remain for ages; the lightning lives, comes into shape, and dies, in a twinkling.

It is the pervading law of all things organic and inorganic, of all things physical and metaphysical, of all things human and all things superhuman, of all true manifestations of the head, of the heart, of the soul, that the life is recognizable in its expression, that form ever follows function. This is the law.

Sullivan, Louis H. (1896). “The Tall Office Building Artistically Considered”

Vitruvius who was a Roman architect and engineer during the 1st century BCE asserted that any structure we build must exhibit three qualities: firmitas (robust), utilitas (useful), and venustas (beautiful). The American architect Louis Sullivan coined the phrase “form ever follows function”, to capture the idea that how something looks (form) is governed by what it is supposed to do.

Both Vitruvius and Sullivan made their observations about the structures of buildings primarily. But it should be obvious that they are true universally — whether they are structures of nature or those created by humans. The amazingly colorful and complex patterns of mollusc shells exemplify the qualities Vitruvius proclaimed. Consider the swarming of locusts, schooling of fish, flocking of starlings; food webs, protein interaction networks, ant colonies, and so on. There’s an interplay between form and function in each of these.

This carries over to virtual structures as well: structures that are used to store, retrieve, and transport information. Designs of data structures and network topologies are a result of optimizing for different objective functions.

In this talk (and the next two), we’ll start our journey towards understanding the interplay of form and function. Let’s look at different geometric representations that are at the core of Distributed Hash Tables (DHTs). Let’s examine what kind of trade offs they lead to in terms of functionality. We’ll look at trees, hypercubes, butterflies, multidimensional tori (torus singular, tori plural), and circular graphs. We’ll understand their graph theoretic properties and limitations.

DHTs form the underpinnings of most real world distributed systems. They enable efficient caching and routing. They are used by distributed data stores as well. Therefore, all of the previous discussion is going to be motivated by real applications in distributed systems.

Prerequisites: Basics of analytical geometry and graph theory will help, but not essential. We’ll develop the necessary math as part of the talk.

You can register yourself for the talk through this event link.

I’ll post the talk slides later.