A Drop in the Digital Ocean

Change of Address

2008-09-06T20:25:00.001-04:00

This site has moved here.

My Contribution to the Mathematical Arts

2008-09-01T19:36:00.001-04:00

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

is

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

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

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:

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

Perhaps of interest are these three properties of the coefficients:

Good and Evil, Part 1a

2008-07-15T20:44:00.001-04:00

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."

He is Risen!

2008-03-23T08:04:00.001-04:00

He is risen, indeed!

Good Friday, Expensive Friday

2008-03-22T21:49:00.001-04:00

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?

Synchronicity and Harlan Ellison

2008-03-15T15:53:00.001-04:00

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

2008-03-15T15:15:00.001-04:00

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?

Good and Evil, Part I

2008-03-02T22:46:00.001-05:00

I am a frequent reader of The Evangelical Outpost, Vox Popoli and even Fark. A frequent topic is that of morality, which is the study of good and evil and the practical application thereof.

What I find interesting is a certain lack of rigor. While not surprising for Fark, it isn't quite expected of the other two blogs. What I mean by this is that in any debate it is crucial to first define one's terms. If we can't agree on what we're discussing then we won't effectively communicate. Too, reason cannot turn a sow's ear into a silk purse. Sloppy definitions beget sloppy reasoning.

Defining "good" turns out to be a surprisingly difficult problem. The Oxford English Dictionary provides one definition as "to be desired or approved of." This begs the question of why is something desired or approved of? The obvious answer is "because it's good", but this is just a circular definition: good is good. Another definition from the same source is "possessing or displaying moral virtue." Since "moral virtues" are those which are good, this is yet another circular definition.

"Good is the absence of evil" is also proffered. If evil is defined as "not good", then this definition is equivalent to "good is not (i.e. the absence of) not good (evil)". Using the transformation that the negation of the negation of "something" is "something", this definition just says "good is good". Once again, it's circular and therefore meaningless. Sometimes "good" is treated as if were analogous to something material like light or heat: "evil is the absence of good like darkness is the absence of light, or cold is the absence of heat." In these cases, we know what light is (a collection of photons) and what heat is (energy in transit). But this brings us no closer to knowing what is measured by "good".

Another definition is one that is often used by Christians: "God is good". This is certainly in accord with Christian doctrine; the Psalmist said, "Taste and see that the LORD is good." [Ps 34:8] But Scripture also says that "God is love" [1 John 4:8 & 16] and that "God is holy"[Ps 99:9, Isa 6:3, Rev 4:8]. Just as without a definition of "love" and "holy", these statements don't tell us what these attributes mean, the same is true of "good". "God is good" is a true statement but it isn't a definition.

Another problem with saying "God is good" is that it only applies to theists. One might argue that an atheist is simply a theist who stubbornly refuses to acknowledge what he or she instinctively knows to be true, so that this definition is universal, but that presupposes the truth of (mono)theism and the falsity of atheism. The topic of morality is difficult enough without deliberately provoking either side. Too, the polytheist would object to being left out and could deliver a crippling blow by simply responding, "yes, but which god?" If at all possible the goal should be to find a definition that is worldview invariant. We know that all humans have an intuitive notion of "good" even if the definition is ill-formed and this gives some basis for hoping to find a definition on which theists, atheists, and agnostics can agree.

Fark user jaedreth offered this definition, "Good is a lack of corruption. Evil is the presence of corruption. Corruption is the damaging and twisting of something natural from its natural state. So Good is being in one's natural state, and Evil is being twisted out of one's natural state." Like the definition "God is good", this suffers from the imprecision of the term "natural state." What is the "natural state" of a weapon? Is an atomic bomb good or evil? A polarizing question, to be sure. Someone might argue that weapons aren't "natural", being the product of man. But one could equally argue that humans are natural and so the products of humanity are also natural. Any number of other contentious examples could be given. This, too, is a dead end; but it contains the hint of a clue.

The Christian apologist Ravi Zacharias offered a similar definition that evil is the misuse of design. Unfortunately, the reference escapes me. Nevertheless, "design" is more well-defined than "natural state." Zacharias used the example of an airplane to illustrate his point: an airplane is good if it is used according to it's design, which is to transport people and freight from one place to another. It is bad if it is used some other way, such as being deliberately flown into a building. The problem with this definition is that is assumes that everything has a purpose. The theist may think that there is a divine purpose for an earthquake but the naturalist will not. We still seek a definition that doesn't favor one worldview over another.

But, we're almost there. Design implies purpose. In the article Can Michael Martin Be a Moral Realist?: Sic et Non, Paul Copan wrote that "evil is a departure from the way things ought to be". Unfortunately, Copan says this in a parenthetical note and so misses the power and significance of his words. Good and evil are "distance" measurements between "is" and "ought". The closer something is to the way it ought to be the more good it is and the father something is from the way it ought to be the more evil it is.

Is this, finally, the right definition of "good" and "evil"? The distance between "is" and "ought"? I think so. First, it is measurable. Granted, the notion of distance used here is poorly defined. But this intuitive notion is at the heart of the words "good", "better" and "best". Second, this definition doesn't depend on worldview. The theist may argue that the mental machinery necessary for a mind to understand "oughtness" can only come from God while the atheist can argue that "oughtness" is an emergent property of evolutionary processes. But both agree that it exists regardless of its origin. This property is hugely important and the implications will be explored in later sections. Third, this definition can be obtained from other, independent, lines of reasoning. I submitted this definition to the evangelical outpost (post #31) approximately three months before finding the article by Copan. Going back to 2004, I find that I wrote: "For both the Christian theist as well as the atheist, morality is no more than subjective personal opinion. In other words, for both God and man, there is no external moral 'ruler'." I was close, but I didn't have a metric. Perhaps I'll recount this development in my thinking in another post. Nostalgia aside, multiple independent ways to arrive at the same result provide a warrant for thinking the result correct.

Definition: good and evil are distance measurements between "is" and "ought". The closer something is to what it ought to be the more good it is. The farther something is from what it ought to be the more evil it is.

Speech Codes

2008-03-02T01:00:00.001-05:00

Asserting a right that you do not have (to not be offended) over a right that someone has (free speech) is to deny the US Constitution.
--wrf3, 2 Feb 2008

Hello

2008-03-02T00:30:00.001-05:00

In early January (1/8/2008, to be exact) I started working on a poem. The general theme was that the internet will outlive me and that what I write today will remain archived, but forgotten, somewhere in some cache. One of the lines goes "A forgotten drop below, the digital ocean above."

The poem remains unfinished but I used this idea as the title for this blog. A Google search for "a drop in the digital ocean" turns up exactly five matches. I hope Bay Street SEO doesn't mind that we came up with this description of the vastness of information space independently. We certainly have different approaches to the problem. Bay Street specializes in search engine optimization while the poem ends on the hopeful note: "Yet God remembers me. I am ever before Him."

I'll incorporate the poem in the layout of this blog if I can get it to scan the way I want it to.

I also hope that I have more success with writing this blog than I do with poetry.