Saturday, September 6, 2008

Change of Address

This site has moved here.

Monday, September 1, 2008

My Contribution to the Mathematical Arts

Many, many years ago, sometime in high school, I learned that the formula for computing

Figure1.png

is

Figure2.png

I'm pretty sure we were shown the geometrical derivation of this formula. In college, in late 1975 or early '76, in a Math Lab one problem asked to guess the formula for

Figure3.png

In my handwritten lab notebook I used induction to solve the specific case k=2:

Figure4.png

However, I wanted to solve the problem once and for all for all values of k so that I would never have to do it again. I conjectured that the general solution would be of this form:

Figure5.png

The derivation used induction on the general formula and found that the coefficients to the solution are:


Figure6.png

Perhaps of interest are these three properties of the coefficients:

Figure7.png

Figure8.png

Figure9.png

Tuesday, July 15, 2008

Good and Evil, Part 1a

In Good and Evil, Part 1 I proposed the definition that good is the distance between "is" and "ought", for some ill-defined, yet intuitive, distance metric.

This has an interesting property from the Christian viewpoint about which I only recently became aware. In Luke 18:19, Jesus said, "No one is good but God alone." With this definition of "good" this statement is equivalent to: "No one is what they ought to be but God alone" or, more succinctly, "Only God is what He ought to be."

This certainly agrees with St. Paul in Romans where he writes, "there is no one who is righteous, not even one" [3:10] and "... for the creation was subjected to futility..." [8:20]. "We are not what we ought to be" is part of the Reform doctrine of "Total Depravity", the other part being, "not only are we not what we ought to be, we cannot get ourselves to where we ought to be." It may also tie into the doctrine of "Unconditional Election". Since we are not what we ought to be there is no basis within us for God to choose one over another. It also shows why union with Christ is the means by which we are made whole and this can be linked to the "Perseverance of the Saints."

Sunday, March 23, 2008

He is Risen!

He is risen, indeed!

Saturday, March 22, 2008

Good Friday, Expensive Friday

When driving home from work Thursday evening, as I was merging onto the interstate, I felt a bump and heard a loud bang. I hadn't seen anything and had no idea what I hit, but I did see my hubcap spinning to the side of the road. I pulled over onto the shoulder, got out, and saw that my rear driver side tire was flat. Walked south along the roadside until I found my hubcap. I returned to my car and popped the trunk. Before removing the spare and jack, I called my wife to have her make an appointment in the morning to get my car fixed. Changed the tire with no incident and drove home.

Friday morning found me at the car dealership. The tire was salvageable, but the wheel was not, and the car needed to be realigned. Two hours and $350.00 later, I went to work.

I decided to leave the office a little early and meet my trainer at 3:30. The plan was to work out until 4:30, shower, then take my wife to dinner before the Friday night crowds arrived. But that plan was not to be. My clothes were soaked with sweat and I decided to rest a minute before showering. Since I was so drenched I decided to sit in the water closet. There, I could cool down in peace, surf the web a bit with my laptop, and not worry about what got wet. I must have taken too long because my wife came in to ask "Are we going?" I got up and found that my left leg had gone to sleep. I was standing but didn't stay that way long. I think I sat back down, pitched slightly forward, and then slumped sitting up on the floor.

I was mostly out of it, but realized that my wife had called 911. I eventually managed to get up, made it into the bedroom, put on a dry shirt, and lay down in bed. The paramedics soon arrived and started their routine. I note that I am not a good patient when I don't think anything serious is wrong, and I detest having a fuss made over me. Vitals were fine but they apparently didn't like my diaphoresis and thought it best to take me to the hospital. Stubborn cuss that I am, I got up and walked through the garage to the ambulance as two of them were trying to bring the stretcher in the front door.

En route to the hospital, the EMT worked on filling out 12 pages of paperwork, although it was all data entry on a laptop. He said that, worst case, I had had an asymptomatic MI but he didn't think it anything more than syncope brought on by dehydration and the pooling of blood in my legs. He was right. EKG, chest X-ray, and blood work were all normal. The problem, though, is that the blood work requires two tests, one and a half hours apart. And the remote control on the TV didn't work. Finally made it home around 10pm, ate some dinner, and dealt with most of the 25 e-mails that had come in from work. Went to bed.

I wonder how many thousands of dollars this little incident cost?

Saturday, March 15, 2008

Synchronicity and Harlan Ellison

The article on Long Forgotten Computer Technology was posted on 3/15 but most of it was written over a week ago. It mentioned Harlan Ellison's story I Have No Mouth, and I Must Scream, the tie in with computer technology being the stories' use of paper tape.

Yesterday I started re-reading Ellison's story The Deathbird. It contains an essay test on the story in Genesis 3 and some of the questions deal with the nature of good and evil, a topic I began here and will continue to develop in the coming weeks (months?). I plan to blog my answers to his test.

Today on Fark.com was a link to an interview with Harlan. In the audio of the interview Ellison talks about how the works of his generation in general, and his work in particular, are increasingly not known now. It's a writer's lot in life. Like technology I've used and forgotten, very little of the software I've written in the past 30+ years is in use now, even though one product once won Macworld's "5 mice" award (twice) and MacWeek's "5 diamond" award (also twice).

If this trend continues, maybe he'll come to my house next week and we can go out to dinner together.

Long Forgotten Computer Technology

I wrote my first computer program in BASIC in 1972. I thought it might be interesting to reflect back on some of the different technology I've used, most (if not all) of which are obsolete today.
  • EasyCoder, assembly language for a Honeywell computer. It was used in my twelfth-grade data processing class. The only program I remember writing was one that had to sort three numbers.

  • Patch panels, for some long forgotten IBM machine. Also part of the curriculum for the previously mentioned class.

  • Keypunch machines, IBM 026 and 029 models. I used to know how to punch the cards that controlled the keypunch.

  • Punch tape, both paper and mylar. H-P would send the system software for the HP-2100 Time-shared Basic system on mylar tape. I have a friend who learned to read paper tape. He is why I know what the punch tape says in Harlan Ellison's story I Have No Mouth, and I Must Scream.

  • Punch cards. I once thought it awesome to have a collection of different punch cards which were custom-printed with company names and logos. I'm now embarrassed to admit that.

  • Dedicated word processing terminals, such as the Lanier "No Problem" machine. A company I worked for developed a sort package for it.

  • Idris, a Unix-like operating system written by P. J. Plauger. I used it in the early 80's. It could have been Linux. Fortunately, Unix is still alive and well and living in my MacBook Pro. And Plauger's book, The Elements of Programming Style, remains a favorite.

  • Weitek math coprocessor ASICs. A friend developed the hardware for a Weitek chip on a PS/2 board and I wrote the software. We managed to sell a few. Weitek chips were later used in a graphics terminal that used floating-point numbers in its display list.

  • CGA, EGA, and VGA graphics.

  • Apple's "Slot Manager" for NuBus-based cards.


  • Yet not everything evaporates that quickly. FORTRAN and LISP are the oldest high-level languages still in use today. I learned FORTRAN in high school and used it in college. I had a brief exposure to Lisp in the late '70s. I still have my copy of Weissman's LISP 1.5 Primer. Having revisited the language in the last three years I find I'd rather write code in it than most anything else. What languages will we program in a thousand years from now? Will we even develop software anymore, or will our machines do it for us?