Abandoned Ideas File
Posted May 2023 by Bryan Daniels
Moving along in academia can feel like a gradual transition from the (undergraduate / graduate) hunger for important questions to tackle, to the (graduate / postdoc) satiation of producing good questions and tackling them, to the (postdoc / professor) overabundance of producing more questions than you know what to do with. Even offloading questions to students leaves a path littered with unfollowed leads. As I enter a busier phase of my career, I want to open my dusty file of abandoned ideas and release them into the wild...
Abandoned idea #130715
Cultural evolution of popular colors. Preliminary analysis: Over-represented colors on the covers of yearly top 10 music albums across decades. What is the rate of change in color space?
Abandoned idea #131101
Is the fact that Newton's laws are described in terms of positions and their derivatives connected to the fact that there is a minimum embedding dimension, implying there could be equivalent descriptions in terms of other variables? Inspired by Packard, Crutchfield, Farmer, Shaw (1980).
Abandoned idea #160406
Is the 2nd Law of Thermodynamics equivalent to the Data Processing Inequality?
Abandoned idea #170421
If I'm counting the number of memories that can be stored in a Hopfield network, how does that correspond to human memories? Experiencing a memory tends to be more associative, flowing from one idea to another. It's not as if I fall into one discrete holistic memory state and that's that. How would I count the number of memories I have?
Abandoned idea #201022
Auto-correct could be making communication less reliable. When it works, it makes communication perhaps faster (the receiver doesn't have to make the correction themselves), but no more precise (the receiver can correct errors just as well as the computer). But when it doesn't work, it hinders precision because it's harder for the receiver to decode.
Abandoned idea #121210
Galois theory seems to be providing the conditions under which there are no "shortcuts" to solving a polynomial equation (so you have to resort to doing it numerically—guess and check) in terms of group theory (non-decomposable groups and such). Related to NP hard problems?
