Icarus Wing
a novel
Modern Integration
a university mathematics textbook
(under construction)
Free Software
Connected: An Internet Encyclopedia
…other software I’ve worked on…
A New Solution of Hydrogen
About a month ago, I discovered a previously unknown solution to the simplest Schrödinger equation for the hydrogen atom.
It turns out that this wavefunction:
![\[\Psi = J_0(2\sqrt{x+r})\]](https://quicklatex.com/cache3/74/ql_4a719605c50267d160a2c26cf6cfe574_l3.png "Rendered by QuickLaTeX.com")
where J₀ is the ordinary Bessel function J₀, solves this equation:
![\[-\frac{1}{2}\nabla^2\Psi - \frac{1}{r} \Psi = E\Psi\]](https://quicklatex.com/cache3/c2/ql_c88e1d19064771f724a700e207df53c2_l3.png "Rendered by QuickLaTeX.com")
with E=0.
What I find more 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 Solution of Hydrogen”The Soul of Quantum Mechanics
The soul of quantum mechanics, to me, is the complex number system.
When we look around us, we see what mathematicians call “real three-dimensional space”, at least that’s what it looks like. Who knows what it actually is, but that’s what it looks like.
In much the same manner, quantum mechanics looks like complex space, of some kind. The more I study quantum mechanics, the more it looks to me like complex numbers, not real numbers, are the basic kind of number system that it’s made of.
Continue reading “The Soul of Quantum Mechanics”
The Golden Age of Computing
Ah, the Golden Age of Computing!
It isn’t here yet.
Maybe a hundred years in the future.
I’ll be nice.
If you read this then, take joy! You’ve got a wonderful digital assistant that’s an expert draftsman, chessplayer and trivia champion, runs a tight, secure network presence for you, is always letting you know the latest interesting tidbits on the news feed or the personal side, sigh…
For now, I’ve got to deal with nginx configuration files.
When I got this morning the network was down. I had moved a laptop yesterday from wired to wireless and back, it didn’t come back right and its used as a router because the real router doesn’t have a wifi interface. Probably still not right, but I got the power turned on to osito. It took a while.
Jotted some things down in my diary, took a smoke, had something to eat, back to work.
Now I’m trying to re-install collaborate. Remove the development version. Install the distributed version. Why is it so slow? Dig through Google pages because I can’t remember the name of the debugging program – that’s it! iftop! Why is it connecting secure? Why is my website so slow?
Oh, crap, my website is down (again). D—. Dig through the docs and keys to figure how to get into the aws console. Oh, it looks fine. Wait a minute, that was just a typo on my part, logging in to the wrong machine. False alarm.
Finished the install, but it’s broken. Stare at its logs. bbb-html5 didn’t install right. nginx couldn’t start. Check the nginx logs. Why didn’t that file delete? It was part of the removed package. Check the package versions. Yup, we got the right package, but that file shouldn’t be there. Who knows why it wasn’t removed. Remove it by hand. Complete the install.
OK, now I can connect, but no audio. Seen this plenty, just down and up the videoconferencing server. OK, now it works with audio!
It’s 3:30 in the afternoon. I just finished my first task for the day: install the currently distributed version of collaborate on osito.
To those of you reading this in the Golden Age of Computing, take joy!
We in the early twenty first century see their potential, but waste so many hours dealing with all these bugs, the lack of natural language recognition, and the bugs, the bugs, the bugs!
In the Golden Age of Computing, you’ll be able to get some work done.
Afghanistan
The recent collapse of the Afghani government and the Taliban takeover of Kabul offers a fascinating lesson in political science.
We normally associate a nation’s presidency with pomp and privilege, but one of its stark realities is the occasional need to fight for the defense of the established political order. The single person most responsible for the Afghani debacle seems to be Ashraf Ghani, who decided not to stage a defense of Kabul, and left the country instead.
The Biden administration repeated assured the American public that the Afghan government and army would fight when their backs were against the wall. The flaw in this logic, apparent now in hindsight, is that nobody with a five million dollar personal net worth really has his back against a wall.
Contrast this with the situation in Sarajevo after the Serbian invasion of Bosnia in 1993. The Bosnian government decided to fight, and Sarajevo endured a four year siege before international pressure finally brought an end to the war.
Would the outcome of the 2019 Afghani presidential election been different if Ghani had told the nation that he would abandon Kabul without a fight if surrounded by the Taliban?
Resolution of Singularities
Brent’s math lecture for Catholic University’s weekly seminar.
An Abelian Integral
Brent shows how to simplify a basic Abelian integral using Sage 9.
Elevator Speech
I deliver an “Elevator Speech” on Capitol Hill – a three-and-a-half minute summary of my spiritual and political position.
Sage 9: Function Fields
A twenty minute overview of some of the new features in Sage 9.
Christmas Message
I quote from Pope Francis’ Christmas Message to the Roman Curia and emphasize sacrificial charity as the basis for a new evangelism.
The Facebook Integral
Facebook has developed a neural network that can solve some integrals that Mathematica can not. In the first video, I explain how to use free software products (Axiom and Sage) to solve this integral. In the second video, I go into more detail about Robert Risch’s theorem and how it applies to the Facebook integral.