Icarus Wing
a novel
Modern Integration
a university mathematics textbook
(under construction)
Kyle’s Thai Travelogue
Free Software
Connected: An Internet Encyclopedia
…other software I’ve worked on…
a novel
a university mathematics textbook
(under construction)
Connected: An Internet Encyclopedia
…other software I’ve worked on…
An January 2023, I discovered a previously unknown solution to the simplest Schrödinger equation for the hydrogen atom. It’s my only truly new mathematical discovery to date, so I like to keep it pinned at the top of the blog.
It turns out that this wavefunction:
where J₀ is the ordinary Bessel function J₀, solves the Schrödinger equation for hydrogen:
with E=0.
It does not, however, satisfy the global integrability condition required for it to be a valid wavefunction:
Therefore, it is only a pseudo-solution, since it satisfied the differential equation but is not a valid wavefunction.
What I find surprising about the result is that it solves one of the best known equations in mathematical physics, yet has apparently remained undiscovered for over a hundred years!
Continue reading “A New Pseudo-Solution of Hydrogen”Bruce Caslow says I was “running for pope”, and I really was! There was only one voter, but I was hoping He would work some great miracle and elevate me to that high office. As I was walking back to the Vatican from Roma Termini, I was crying, and crying out to God, saying that even if He did, I would have no idea what to do with it. I soon realized that was not true. I knew I’d need to be guided by prayer every step of the way.
Continue reading “Running for Pope”I have often heard the phrase “that’s just the way the world is”.
Here’s the way the world is, as I see it:
I have a hypothesis to explain the excess heat produced in a Fleischmann-Pons reaction, that the heat is produced by a nuclear reaction, and that reaction is triggered by a twistronic effect.
Continue reading “Is cold fusion a twistronic effect?”How would I advise the Roman Catholic Church?
First, end the schism. Admit protestants to full communion, and do so in the following way. Give discretion to local bishops to set their own guidance on who can receive the Eucharist. Many of the bishops already exercise this discretion; they’re just called Methodists or Baptists, etc. Issue guidance from Rome for those bishops who choose to follow it, and that guidance is to administer the Eucharist to all those who accept Jesus Christ as their Lord and Savior. Don’t excommunicate anybody if they won’t do this.
Next, open the religious communities to couples and families. Presumably they were already opened to protestants in the first step. Recognize that the “widows” spoken of in Acts 6:1 were probably admitted to the church in that state – it wasn’t old enough for them to have joined as young women. End the caste division in the church where we have religiosos and laity. Religious community, in some form or another, is the preferred organizational style for the saints.
Communities will probably attract a crowd of homeless followers. They should be accommodated to the greatest extent possible. Provide space for tent cities, and don’t neglect the need for basic hygiene such as toilets and showers. Organize food banks and community feedings.
Preach the authentic Christian gospel. Quit focusing so much on sexuality and teach against the economic immorality of the majority. Our default answer to most requests should be “yes, of course” instead of “here’s how much it will cost”. It’s so hard to believe that God will give us the greatest gift of eternal life for free, when we won’t let people fly on an airplane for free.
I was recently at a performance of the Chester River Chorale that featured an ASL performance of Ain’t No Grave, a traditional gospel song.
I think one of my students will appreciate this!
Last year, I was awarded a U.S. patent for the remote desktop video conferencing system that I developed, collaborate.
Collaborate is, and will remain, open source and free to use. The purpose of the patent is only to claim my legal rights as the inventor; I have no intention of trying to monopolize the use of this technology.
Collaborate is hosted on a github repository.
Last week I filed a lawsuit against the Virginia Employment Commission.
They seem to have developed an illegal administrative procedure called “Vacate” and have used it twice on my claims for unemployment benefits. This goes back to the summer of 2020. I fought them in federal court in 2022 and had them in state court earlier this year (2023). I had a lot of trouble finding a lawyer to take the case and have been representing myself pro se.
Update: I lost the case.
Continue reading “Baccala v. VEC”The recent surge of interest in Large Language Models (LLMs) like GPT-4 has motivated me to set aside my mathematical research for a time and focus instead on A.I. The current LLM revolution does not seem to be a passing fad.
I’m predicting not one, but three A.I. revolutions that I expect to follow in fairly short order: