This blog is the result of this project. I began using the Julia programming language about two years ago and have been using it very extensively for just about all of my personal projects as well as for some of my work projects. As a means of keeping myself sharp with the language and continuing to build and expand my knowledge, I've been documenting various tasks and processes in the language. When I am working on some mathematical research and need to crunch some numbers, working on some problem set for fun, or whatever it is, I've been documenting the work and including a short, bite-sized post.
An abstraction for being able to predict economic and societal instability based on a generalized notion of social or cultural elasticity driven by events which influence society at various levels. My work on this topic takes the concept of the Overton window which to this point was no more than an idea which could not be proven or applied. I developed a rigorous, mathematical system to incorporate data points which has enabled me to be able to prove the core ideas behind the Overton window as well as potentially being able to make predictions based on applying the system to sets of event-data for a given country or population. The main questions at this point are: (the obvious one), a.) do the predictions actually hold in real-life? as well as b.) assuming they do hold, how much data is required to make an accurate prediction, and c.) what is the relationship between the amount of event data and the specific methods of quantifications, and ultimately how do they impact the sensitivity of prediction accuracy?
Another research project in flight is a mathematical model which explores non-linear mappings between how geographically-localized impacts to climate result in events which influence climate at the global-level. More specifically, I am looking at geographic shifts in climate and studying the resulting intensity of the influences. With respect to mitigating the climate impacts of which humanity is responsible, I think a lot of people feel like nothing they do with really make a difference. That can be deeply de-moralizing. I engaged in this project based on wanting to be able to ask and answer the question, how much does a change of arbitrary size at some localized point impact the country or region or globe as a whole? To what degree does one carbon producing factory impact an entire nation? To what degee does one individual's recycling efforts impact the entire globe? While I doubt I will be able to answer such specific questions with my research on this topic, I am hoping to be able to accurately relate how the local impacts the global and potentially this would offer insights regarding where aid resources should be distributed by identifying the sources of the most significant global problems.
The third project I have been working on a significant bit recently is trying to identify potential patterns that could suggest a direct relationship between different modulo residues and the twin primes. I've identified several patterns, but proving them is a challenge and in some cases identifying them is rather round-about. While this has little to no direct application at this time outside of the obvious connections to cryptography, studying the primes is always of immense importance in pure mathematics and we would be lucky to be able to uncover the mysteries of this incredible topic.