I’ve been really enjoying my new job at Time Service in Toledo. I’m about to finish my third month here, and I expect I’ll be staying with this job for quite a while. I find that working in business gives me a variety of interesting problems to solve, and although they’re not deep and abstract in the same way as math research problems, they still require a lot of creative thinking and give me challenges to work on over time and puzzles to chew on as I drift off to sleep, in my morning shower, etc., just like math research did. The whole operation of helping to run a business feels like a big optimization problem — how do I figure out the best way to use all of our company’s resources to the greatest effect?
I hope all my friends in the New York Logic community are doing well. Please keep in touch!
In June, I attended a two-week workshop in Northern California, combining technical research and personal growth. The workshop was run by the Machine Intelligence Research Institute (MIRI) and the Center For Applied Rationality (CFAR) in Northern California. The goal of MIRI is to lay the multidisciplinary theoretical foundations (in math, philosophy, computer science, and decision theory, among other fields) to try to insure friendly artificial intelligence, that is to say, to make it so that when artificial intelligence becomes smarter than humans, its interests are aligned with ours.
Their research has a fair amount of overlap with mathematical logic. I’d encourage any logicians who are interested in these sort of things to get involved. It’s a very good and important cause; the future of humanity is at stake. Unaligned artificial intelligence could destroy us all in a way that makes nuclear war and global warming seem tame in comparison.
Their technical research agenda is a good place to start for a technical perspective. The book Superintelligence by Nick Bostrom is a good starting point for a less technical introduction and to help understand why MIRI’s agenda is important and nontrivial.
One area of MIRI research that I find particularly interesting has to do with a version of Prisoner’s Dilemma played by computer programs that are allowed to read each others’ source code. This work makes use of a bounded version of Löb’s theorem. Actually, a fair bit of MIRI research relates to Löb’s theorem. Here is a good introduction.
Feel free to contact me if you’d like to know more about how to get involved with MIRI research. Or you can contact MIRI directly.
We submitted the infinite chess paper for publication a while back, but I forgot to post it.
The link below connects to a page that Joel wrote summarizing the key ideas, which also contains a link to the ArXiv for the full paper.
I recently started working with Joel Hamkins on a new project on infinite chess. We think that we will be able to improve on some results from his previous paper on transfinite game values in infinite chess to demonstrate a position with game value $\omega^4$. We made a lot of progress during January and February, as I was not teaching during that time. Teaching starts again for me next week. I hope that I will be able to find time to continue working on this project while I’m teaching during the spring semester. If not, then I will work on it more in the summer. Stay tuned to see a really cool infinite chess position 🙂
My paper, “The large cardinals between supercompact and almost-huge,” has been accepted into the Archive for Mathematical Logic, subject to minor revisions. The referee was very generous with his time, going over the paper carefully to make many corrections and improvements. This is my first solely-authored paper to be accepted into a peer-reviewed journal. You can read more details about it under the publications tab.
I am planning to attend the MAMLS conference at Rutgers next weekend. I’ll look forward to seeing many of my friends and colleagues there.
This post is being cross-posted on both my teaching and research blogs, since it lies somewhere in between. Katie Brodhead and I will be teaching a logic course/seminar this semester at FAU. The seminar will be meeting Mondays, Wednesdays, and Thursdays from 3-4PM in the math lounge, room SE 215, beginning on Wednesday, September 4. I will generally be presenting on Mondays and Wednesdays, teaching an introductory course on large cardinals. The suggested prerequisite for my course is a graduate course or an advanced undergraduate course on logic. Katie will generally be presenting on Thursdays, teaching an introductory course on algorithmic randomness. The two courses are independent in terms of the content, but the participants will heavily overlap. Everybody reading this blog is welcome to attend my course. I would assume that Katie would say the same for hers, although you could contact her to be certain.
A year a half ago, I wrote a research statement as part of an application for the Dissertation Year Fellowship at the Graduate Center. The application materials asked me to make my research accessible to a nonspecialist, so I attempted to do that. I later changed the application drastically, upon receiving advice from an insider that even though I was supposedly supposed to make the research accessible, that was not what they were actually looking for. Now, I present an essay adapted from that research statement on my research blog. It shows how my current research interest in big numbers stems from ideas that interested me even as a young child. It’s a few pages long, so I am posting it as a pdf file in order not to hide earlier blog posts with its length. Click here to read it.
Here is a chart showing the consistency strength and implicational relationships among the large cardinals between supercompact and almost-huge. This is a summary of many of the ideas from chapter two of my dissertation, and it is adapted from a chart appearing in that chapter.
UPDATED June 2014 to reflect my work with Lubarsky on extendible, hypercompact, and enhanced supercompact cardinals.
As of April 23, 2013, I have completed all requirements for the Ph.D.
The new header photo shows me with my committee immediately after my defense. The defense was on April 12; after that, I had to make final corrections to my dissertation, submit an official hard copy and electronic copy, fill out some surveys and paperwork.
And now . . . I finally have time to work on this Web site, which I haven’t updated since last fall.