Rough Around the Edges

The tables have been bumped out of alignment, the whiteboards are covered by a film of dry-erase marker residue, and the floor is more of a a matte burnt ochre than the glossy gray of August.

My classroom at the end of the first quarter mirrors my own physical and mental state–well-worn and a little frayed around the edges. But then again, a classroom is meant to be lived in, and teaching is not supposed to be easy.

Amidst the fun of getting to know a bunch of new faces there were the numinous flashes of wonder and joy that brightened eyes, lit up faces, and make teaching such a magical profession. Some goals were met, and some were not met yet, but I am better for having had the privilege of sharing space with all of the students who have me as their teacher.

Life in the Boundary Layer

In the world of fluid dynamics there is a phenomenon called a boundary layer. This occurs when a fluid of very low viscosity (like air) flows against a solid object (like the wing of an airplane). The velocity of the fluid very rapidly changes over very short spatial scales. Modeling this mathematically involves copious use of epsilons, limits, and Big-O notation.

An observer in the boundary layer near the object would be oblivious to what was happening outside of the boundary layer, and an observer outside of the boundary layer would be similarly ignorant of what was happening in it. Ensuring that the observations of both are properly reconciled requires a technique called asymptotic matching. Limits of things within the boundary layer as spatial scales in the boundary layer get really big must agree with the limits of things outside of the boundary layer as spatial scales outside of the boundary layer get really small.

This, to me, is a perfect metaphor for the interaction between theory and practice. Our own lived experiences and perspectives are unique to ourselves, yet we must reconcile them with those of our workplaces, communities, and indeed the entire mass of humanity, living, dead, and to come.

This space serves as a showcase of not only those things that the wider world deems important, but the thoughts emanating from my own small corner of the world. Welcome, and enjoy!