MY YEAR

MY YEAR

Donald A. Windsor

A calendar year is analogous to life itself. It starts out rough, but full of hope, and it ends in a crescendo of gloom, worry, and despair. Along the way it celebrates the exciting joys of youth in spring, the smug satisfactions of adulthood in summer, and the apprehensive exhilaration of maturity in fall.

As I advance in age (83) and approach my own reluctant demise, I currently see myself dwelling in the waning days of November. Almost all flowers have quit blooming; darkness is triumphing over daylight; the headwinds seem to blow ever harder and colder, and I become weaker and weaker.

Here is my personal year, the calendar superimposed atop pivotal points in my autobiography. I travel through this cycle every year and find it to be very therapeutic.

At sunrise on the day after the winter solstice, I am conceived.

On Epiphany I am born.

On Groundhog Day I start grade school.

On the vernal equinox I start high school.

On May Day I become a soldier.

On the summer solstice I become a research biologist.

On the autumnal equinox I become an employed family man, fathering four children.

On Labor Day I retire from employment.

On Halloween I become a grandfather.

On Thanksgiving I have a heart attack and undergo life-extending surgery.

At sunset on the winter solstice, I die.

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BENFORD'S LAW HAS ITS ORIGIN IN THE PARTITION OF INTEGERS

BENFORD’S LAW HAS ITS ORIGIN IN THE PARTITION OF INTEGERS

Donald A. Windsor

Benford’s Law states that 1 tends to be the most frequent number in compilations of measured data (1).

In the partition of any integer, 1 is the most frequent number. The partitioning of integers is a basic property of our system of numbers and could be the origin of Benford’s Law.

An integer is partitioned by assembling all of the possible ways that add up to it. For example, the partition of 5 consists of 7 partition sets.

5

4+1

3+2

3+1+1

2+2+1

2+1+1+1

1+1+1+1+1

The frequency distribution of the 20 numbers in the partition sets is:

5

4

3 3

2 2 2 2

1 1 1 1 1 1 1 1 1 1 1 1

This highest frequency of 1s holds true for all integers, because the lowest partition state of any integer is all 1s. Therefore, 1 is the most frequent number; 2 is second, and so forth.

I have been using the partitioning of integers as a non-probabilistic standard for modeling phylogenetic, bibliometric, ecological, and economic distributions (2). The reason is that partitions provide a standard, immutable, frequency distribution for comparing against the wavering frequency distributions found in nature and based on randomness and probabilities.

I can simulate many natural frequency distributions by using a simple urn model driven by a random number generator. Some of these Monte Carlo simulations resemble the partition distributions. The biggest departure is at the top with the highest value numbers. The highest value in the partition of 5 has to be 5. In a simulation the highest value could be several times 5. this work continues, albeit at a slow pace because of my advancing age and my obligations as caregiver for my disabled wife.

I did not appreciate the importance of relating partitions to Benford’s Law until I read the article by Brooks (3) in which he asks, “Why on earth should Benford’s law exist?” That was when I realized that the partition of integers could be the origin of Benford’s law, not just another example, because partitions are a basic property of our system of numbers.

I suspect that if Benford had known about my partition model, he may have based his Law upon it.

References cited:

1. Benford, Frank. The law of anomalous numbers. Proceedings of the American Philosophical Society 1938 March 31; 78(4): 551-572.

2. Windsor, Donald A. Integer partitions result in skewed rank-frequency distributions. Journal of the American Society for Information Science and Technology 2002 December; 53(14): 1276.

3. Brooks, Michael. Benford’s law. New Scientist 2017 August 26; 235(3140):38-39.

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ANCIENT ALIENS AND RELIGION

ANCIENT ALIENS AND RELIGION

Donald A. Windsor

I was raised a Catholic and I still am. Catholicism is based on faith – belief independent of evidence.

Ancient Aliens, a television series, offers a different interpretation to some of the scriptural underpinnings of Catholicism and of its precursor, Judaism.

The evidence provided by Ancient Aliens is more compelling because any evidence, no matter how paltry, is more cogent than faith.

Ancient Aliens apparently wants to replace God by attributing divine apparitions and interventions to astronauts from outer space.

Adam and Eve were not created by God, but by ancient aliens. God did not breathe upon clay to create Adam. Aliens genetically modified an ape to produce Adam. I speculate that Eve was a clone of Adam, but with an added X chromosome, perhaps Adam’s rib bone marrow might have been involved.

However bizarre, I do not regard the Ancient Aliens explanations to rule out God. If humanity was indeed produced by aliens, then this was just God working through these aliens.

Angels have traditionally been called the messengers of God. Perhaps what Judeo-Christians have been calling angels are really God’s astronauts. Perhaps prophets were too.

What is more far-fetched, human bodies with feathered wings? Or aliens in flying saucers?

And what about the Devil? What is more believable, a diabolical red miscreant sporting horns, cloven hooves, and a tail, wielding a pitchfork? Or an evil invader from outer space organizing terrorist groups like ISIS to destroy civilization?

The battle between good and evil seems to have been plaguing humanity since its gitgo, through all sorts of technologies and religions. Now we seem to be pulling more cooks into our stew.

If we were made by ancient aliens, where did the ancient aliens come from? God only knows! 

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