Nihal Uppugunduri's WebsiteI’ve been recently thinking about the potential of newer technology to accelerate a phenomenon that I call “source consolidation.” It seems to me that this will only speed up even further as technology progresses, for example as generative AI becomes more powerful and prominent. In this post, I talk about what I mean by source consolidation, how it relates to tech and generative AI, and what its implications can be.
In this post, I argue that, in the grand scheme of the description of the physics of all reality (all objects in reality), the designation of which scientific assertions are “the laws” and which assertions are “the initial conditions” is relative and informal. A similar statement can probably be made about other branches of science too, especially “hard” science like chemistry.
In the United States and many other countries, media such as movies and television are assigned intensity ratings that are meant to give audiences expectations around potentially objectionable content. Today, these ratings are age-based; for example, for movies, we have the ratings G, PG, PG-13, and R (for movies that are traditionally allowed to be exhibited in theaters), and each of these ratings corresponds to an age that someone should be in order to watch content with that rating. However, I argue that this rating system based on age is actually not effective, and I argue instead that an alternative approach based on just content descriptors (like TV ratings in the US but without the age identifier) is better.
People who discuss programming often talk about the distinction between declarative and imperative programming as two different paradigms. However, in this post, I argue that these terms are really only relative and informal, and in fact that we don’t lose much if we de-emphasize the distinction.
What language features are (minimally) necessary in order to implement full refactorability of symbols? (Think “Rename Symbol” in your favorite IDE.) For example, when I used Python instead of Java, I had discovered that refactoring interfaces was much harder. Is there a deeper explanation for this?
Consider the following thought experiment: we setup an experiment consisting initially of objects and known forces, and we run Newton’s laws to predict the motion of the objects. We then run the experiment, and the observed results do not match the predicted calculations. Can we just attribute the discrepancy to a new force that we haven’t yet studied, and still satisfy Newton’s laws with this just-defined unknown force? Can we explain all discrepancies with Newton’s laws in this way? Then, are the laws really saying anything materially? Can we think of forces as convenient mathematical devices to represent “contributions of mass times acceleration”?
In other words, taken away from the specific laws of gravity and the other forces, are Newton’s laws themselves falsifiable?
In this post, we investigate a curious question: say we are given 
I first learned about (and actually re-discovered) semilinear maps through one of my mathematical explorations. In this article, we introduce them and prove some basic results about them. We assume some knowledge of abstract algebra and related subjects (vector spaces, modules, universal algebra, category theory, etc.)
(I was still learning more about the concept alongside writing this article, so if there are any inaccuracies here, please let me know!)
I have been realizing recently that many of my math ideas in their “ultimate” forms seem highly suited for formulations in model theory. However, when first trying to study some of the resources I found online for model theory, I didn’t even understand that well what the subject was about or why certain definitions were made, let alone appreciate the overall power of the subject. I think there should be a different approach to teaching model theory, incorporating better motivation and more fully reflecting the incredible power and scope of the subject.
We continue the discussion from this post.