I’ve been kind of quiet here lately, partly due to my job and partly due to writing blog posts and essays for other venues. Happily, one of these blog posts is now available to read over at American Scientist, on the manifestation of weird infinite mathematics in optical systems. A sample:
This specter of unattainability has changed over the past year, as two papers—including one I wrote—demonstrated that infinite mathematics can be realized in optical systems possessing swirling vortices of light. In particular, both demonstrations showed how particular systems mimic exactly a paradoxical thought experiment known as Hilbert’s Hotel, in which the occupancy of a hotel consisting of an infinite number of rooms shows very strange behavior. These examples seem to be the first ever showing that infinite mathematics not only manifests in some real world systems, but is essential in explaining them.
In it, I not only talk about some of my own recent bizarre theoretical discoveries, but related work by other researchers. This is a consolidation, update, and improvement on blog posts I’ve written previously on curious relationships between optics and infinity.
Please go and read the whole thing! Hopefully, I’ve written it well enough to explain how the extremely colorful figure below relates to mind-boggling and paradoxical mathematics.
Loved it! Though I still wonder about the manifestation of the infinite vortices… just as a point particle is but an abstraction of a non-point mass or the infinite paths taken by electrons in the double slit experiment, are the infinities you describe really only exist as an explanatory device for a messy discrete system or are the infinities only an expectation of an underlying stochastic process? [end ramble].