In the previous post in this series, I gave the rationale for undertaking this extended (re-)examination of the geometry of the semi-symmetric metric connection (SSMC): essentially, it represents (to my mind) the most ultra-minimalist extension to General Relativity (GR) at all possible – or so I thought back in the early 1990s – given that it introduces precisely one new object – a vector field – as part of the connection.
In gauge field theories the “connection” carries the gauge field, while the “curvature” corresponds to the field strength, a view that was argued in a book by Göckeler and Schücker (1989), which I had also been reading at that time. Since electromagnetism is often introduced as the archetypal gauge field in mathematical treatments of differential geometry (such as that by Göckeler & Schücker), it seemed to make intuitive sense to me that introducing electromagnetism into an extension of GR intended to model electromagnetism by way of a geometrical object might require it to enter by way of the connection, rather than as an additional field just lying around in spacetime, as it is in Einstein-Maxwell Theory (EMT). Hence, in this view, the SSMC is an obvious candidate.
Many years ago (getting close to 30 now), while doing my PhD (Voros 1996) in theoretical physics on mathematical extensions to General Relativity – and in particular, on Einstein’s own “unified field theory” – I happened across a book by Jan Schouten (1954) called Ricci-Calculus, which was an introduction (by a mathematician) to tensors and their applications, especially to geometrical thinking and analysis.
The question asked in the title of this post is one I have been pondering for the most part of a decade now, ever since I saw the image, shown in Figure 1, of the galaxy PGC54559 (popularly known as Hoag’s Object) in 2010, following several months of thinking about what Kardashev Type III civilisations might look like.
Last year a colleague at the International Big History Association (www.ibhanet.org) asked me how futurists work/think. This was for a book she was writing for high school students on Big History. The final chapters of these types of books tend to focus on the future, hence the request for some ideas from someone who does this for a living. I tapped out a quick, off-the-top-of-my-head answer and sent it off. In thinking about how long since I’ve posted here, I thought I’d better get back into gear, especially as there are some ideas to share coming soon… Here is the essence of what I wrote: Continue reading “How Futurists Work/Think”
I’ve returned from the Christmas (and, here in the Southern Hemisphere, summer) holidays and, after settling back in to my office, I began the daunting task of dealing with the torrent of emails that came in over the 3 or so weeks I was away (hence a need to let off some nervous energy in a blog post… 😉