Research
From Dakota
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Research
Most of the time what I call "research" does not lead to any sort of scholarly publication, but I have been told I look at things differently than most people. This page is intended to be a resource for my own sake as well as for those who might find my observations helpful. I don't make any claim to be the first to notice these things, only that I have noticed them.
Mathematics
Published
Conway's Game of Life
- Lightspeed wire patterns
- I found a basic way to make lightspeed signals arbitrarily wide.
Langton's Ant
- Mutli-ant glider
- Four adjacent ants in a square all facing the same direction yields a period 32 (0, 2) space ship. This seems to hold in almost every reasonable extension to account for multiple ants.
- Impossible Paths
- I also tried to publish a paper entitled Impossible Paths in Langton's Ant.
- Primary impossible paths are of length 4n+1.
Insolvability of the Quintic
- I wrote a paper for The History of Mathematics that I think provides a nice historical introduction to the topic.
Minesweeper
- Same Difference Lemma
- The difference in the values of two adjacent Minesweeper spaces is the difference in the number of mines in the disjoint neighborhoods of those spaces.
Zeno's Paradoxes
Here are my interpretations (and possible resolutions) of Zeno's Paradoxes.
- Zeno's Paradox
- Zeno's paradox (also called the dichotomy or race course paradox) derives a contradiction from having dense space and discrete time.
- Zeno's Arrow Paradox
- In a sense, the arrow paradox foreshadows the Uncertainty Principle.
Physics
- Classical Newtonian Two-Fixed Centers
- I found many examples of numerical solutions to this problem. My hope is that these shapes will give insight into possible analytic solutions.
