19 July 2014

Sunrise, Sunset...Dawn to Dusk

Not long ago I became interested in the schedule of the rising and setting sun at various times of the year and in different places. What I didn't realize is that there are two other periods associated with the rising and setting sun that are equally or even more important than the actual sunrise and sunset. These are the periods before sunrise and after sunset which we usually refer to as "dawn" and "dusk" but are technically grouped under a category called morning and evening twilight.

The twilight hours are further characterized by the amount of degrees that the center of the sun is below the horizon. The first of these, Civil Twilight, is the one that most people are familiar with. One important feature of Civil Twilight is that it defines our laws that govern illumination such as street lights and automotive headlights.

Civil Twilight is the time at which the the geometric center of the sun is between zero and six degrees below the horizon. At this point, there is enough light for objects to be clearly distinguishable and that outdoor activities can commence or end without artificial illumination. Civil twilight is the definition of twilight used by the general public.

Nautical Twilight is the time when the center of the sun is twelve degrees below the horizon, and only general or vague outlines of objects are visible. During the evening this is when it becomes too difficult to perceive the horizon, and in the morning this is the point when the horizon becomes distinguishable. This term goes back to the days when sailing ships still navigated by using the stars.

During Astronomical Twilight the center of the sun is between twelve and eighteen degrees below the horizon. Before the beginning of astronomical twilight in the morning and after the end of astronomical twilight in the evening the sun does not contribute to sky illumination. In fact, for a considerable interval after the beginning of morning twilight and before the end of evening twilight, sky illumination is so faint that it is practically imperceptible. However, this period is very important to more than two billion people around the world for it announces the arrival time for a fasting to begin. It is even mentioned in the Qur'an:

"Eat and drink until the white thread becomes distinct to you from the black thread of dawn"
The Holy Qur'an, Surah al-Baqara, verse 187.

In Spanish there are several vocabulary words used for dawn and dusk:

dawn - amanecer
very early in the morning - de madrugada
daybreak - al alba
twilight - crepúsculo,  las horas del crepúsculo
atardecer - dusk
tardecer - to grow dark
anochecer - nightfall
oscurecerse - to become dark
penumbra - semi-darkness

My favorite Spanish word for daybreak is "al alba". The word "alba" comes from the Latin word "albus" meaning white. Words in Spanish that end in "a" are generally feminine gender but "alba" is actually masculine gender and thus "a el alba" becomes "al alba". It describes the longing of lovers who, having passed a night together, must separate for fear of being discovered by their respective spouses. It is related to the Old English "aubade" which is a morning love song or poem about lovers separating at dawn. An aubade is the early morning equivalent to the evening serenade.

In English Literature the sunrise and sunset are described in countless ways. For sunrise one of my favorite poems is "The Road to Mandalay" by Rudyard Kipling. Here is the first stanza where the sun rises abruptly:

By the old Moulmein Pagoda, lookin' eastward to the sea,
There's a Burma girl a-setting, and I know she thinks of me;
For the wind is in the palm trees, and the temple bells they say:
'Come you back, you British soldier; come you back to Mandalay!'
Come you back to Mandalay,
Where the old Flotilla lay:
Can't you hear their paddles chunkin' from Rangoon to Mandalay?
On the road to Mandalay,
Where the flying fishes play,
And the dawn comes up like thunder
Over China cross the Bay!"

My favorite poem about sunset, that I memorized in High School and can still recite from memory over four decades later, is "Elegy Written in a Country Churchyard" by Thomas Gray. Here are the first two stanzas where the light just fades away:

"The curfew tolls the knell of parting day,
The lowing herd wind slowly o'er the lea,
The ploughman homeward plods his weary way,
And leaves the world to darkness and to me.

Now fades the glimmering landscape on the sight,
And all the air a solemn stillness holds,
Save where the beetle wheels his droning flight,
And drowsy tinklings lull the distant folds;"


22 June 2014

Between Today and Yesterday

Between today and yesterday we experienced the Summer Solstice. It was at 7:51 am Central Daylight Saving Time on Saturday, June 21st. I say it was "between today and yesterday" because the daylight hours for both days are the same length. The thing that I never really realized, however, is that here in Irapuato, Guanajuato we only experienced fourteen hours and thirteen minutes of total daylight while the lucky gee whiz folks in Chicago, Illinois received a whopping sixteen hours and twenty-two minutes. Hey guys...that ain't fair!

Wait a minute...this just in! At Christmas time we get eleven hours and 41 minutes of total daylight and you only get ten hours and eleven minutes but that is only if your sun is shining and not frowning. In Chicago during the Winter Solstice just before Christmas it will probably be cloudy or snowing and only ten degrees above zero while I will still be picking tomatoes in my shorts and flip-flops...so there!

15 June 2014

Three Little Pigs

The other day I read a blog post on "Ripples, Very Small Waves in R"
It is about a game of dice called "The Three Little Pigs" where only
one die is used. The rules are:

"Each turn, a player repeatedly rolls a die until either a 1 is rolled or the player decides to hold. If the player rolls a 1, they score nothing and it becomes the next player’s turn. If the player rolls any other number, it is added to their turn total and the player’s turn continues. If a player chooses to hold, their turn total is added to their score, and it becomes the next player’s turn. The first player who reach at least 100 points is the winner."

I showed this game to my eight year old grandson and he was delighted. He calls the game "Cochinito" (little piggy) because in this game you are penalized by chance if you get too greedy. He is playing it with anyone and everyone he can talk into it. He kept talking about good luck and bad luck so much that I decided to teach him a little bit about probability. I showed him that with one die each number has an equal chance to land face up and since there are six numbers on the die the probability of throwing any particular number is 1/6 or in other words about 16.7 percent. I made some simulations and graphs in "R" programming with the help of "R Workshop for Beginners" (Barry Rowlingson,Lancaster University, UK http://www.maths.lancs.ac.uk/~rowlings/Teaching/Stafford2013-Sept/dice.html

The simulations let you make multiple rolls of the dice and let you see the distrbution of the multiple roll results. Here are the results for four sets of 100 roll trials with a single die:

 1  2  3  4  5  6
18 18 15 15 22 12

 1  2  3  4  5  6
15 17 15 19 13 21

 1  2  3  4  5  6
19 18 14 18 20 11

 1  2  3  4  5  6
19 16 19 18 14 14

Here is the result of a 10,000 roll trial:
   1    2    3    4    5    6
1664 1639 1695 1651 1680 1671

You can see that as the number of multiple rolls increases the average gets closer to 16.7.

Here is the result order for the roll of one set of 100 rolls with a single die:
6 5 4 5 6 3 5 5 4 4 1 1 3 4 5 6 4 4 4 4 6 5 1 4 1 3 1 3 3 2 6 4 3 2 1 5 3 3 1 3 2 5 1 2 6 6 6 3 2 3 1 3 2 6 5 1 2 5 6 4 1 6 2 5 4 4 4 4 2 1 5 4 5 6 6 5 5 6 5 1 4 3 1 6 1 5 3 6 1 3 5 6 2 6 4 2 2 1 2 3

Each 100 rolls of a single die will result in a new random number. You can see that you never know when the number "1" will jump up and grab you or leave you alone for awhile.

This is the R code that I used:

table(as.integer(runif(10000, 1, 7)))  # method with one die

table(sample(1:6, 10000, replace = TRUE))  # Alternate  with one die

# Wrapped in a function and plotted - one die
die = function(n) {
  return(sample(1:6, n, replace = TRUE))

# Wrapped in a function and plotted - two dice
die = function(n) {
  return(sample(1:6, n, replace = TRUE))
plot(table(die(10000) + die(10000)))

# A dice function to throw one die 100 times and return the result.
die = function(n) {
  return(sample(1:6, n, replace = TRUE))
dice = function(T = 100, N = 1) {
  m = matrix(die(N * T), N, T)

# A function to throw two dice 100 times and return the sum.
die = function(n) {
  return(sample(1:6, n, replace = TRUE))
dice = function(T = 100, N = 2) {
  m = matrix(die(N * T), N, T)

This video by Eric Cai is very helpful in explaining the probability of rolling dice:

05 June 2014

I can see clearly now...

I can see clearly now the rain is gone.
I can see all obstacles in my way.
Gone are the dark clouds that had me blind.
It's gonna be a bright (bright) bright (bright) sunshinin' day.
(Jimmy Cliff - I Can See Clearly Now)

A couple of years ago I felt like I needed my vision checked because things were getting a little fuzzy. The doctor changed my prescription and warned me that I had the onset of cataracts and that I should return in about six months to see if the situation was deteriorating. Well, one thing lead to the other like they always seem to do and I procrastinated until finally I knew that I had to do something. My vision, which was never very good anyway, had deteriorated to the point where I couldn't even drive at night because of the blurriness caused by the headlights of the oncoming cars and the street lights.

I returned to the eye doctor, an ophthalmologist named Dr. Alejandro Aldana Fariñas, who has been my eye doctor for quite a few years. After admonishing me for my foolhardy tardiness he announced that I could put it off a little longer if I so chose but that he recommended that I have the cataracts removed from both eyes...and so I did. It turned out to be a good choice.

Once again I am pleased to report that the medical care that I received from Dr. Aldana is better than I had ever experienced in the United States. We are very fortunate here in Irapuato to have the large, state-of-the-art eye care clinic that he runs which I think is at least the best in the whole State of Guanajuato if not the whole of the Central Mexico Region outside of perhaps Mexico City.

I had the left eye done first on Saturday, May 17th and the right eye done on Saturday, May 31st. On both occasions I arrived a little before the appointed time of 8:am and was ushered to a room to change into surgical clothing. Then I was taken to a place adjacent to the operating theater where my eye was prepped with various medications and procedures. From there I was moved to a reclining operating chair where the operation was performed quickly and professionally. It only took about fifteen minutes. After a short time recuperating afterwards I was allowed to return home with a plastic eye shield over the eye. It took about four or five hours for the effects of the anesthetic to wear off. Until then I had some double vision but that gradually faded away.

Right after the first eye was done I knew that I had done the right thing. For one thing I could see out of my left eye much better than I ever could before. The replacement lens that was inserted in place of the cataract had corrected much of my vision problem. I also noticed that everything that I saw with my left eye was very bright and colorful and my right eye which hadn't been done yet made things appear dingy and with a yellowish cast that I had never noticed before.

There was one other aspect of the cataract surgery that I had never even considered. With my new vision it gave me a new vista on life itself. Absolutely everything seems brighter and my spirits have risen to a new level. It is a really blessing from God and I have asked God to bless the doctor and all of his fine assistants and nurses. The service was great, the equipment very modern, the people were all nice, and on top of everything else, the cost was reasonable. That's about as good as it gets.

26 May 2014

Revelations About the Wealthy

This is one of the most amazing documentaries that I have seen in a long time and it provides much food for thought. I think that you will feel the same if you take the time to watch it. It is a documentary on the American rich segment, conventionally called the one percent. Interestingly, the document is the work of one of the heirs of the Johnson & Johnson fortune. Undoubtedly name helped him get to the people who are usually reluctant to speak in public, especially when the questions are about their fortunes. It seems like the rich have some real problems with anxiety about being rich. There are some startling surprises.

11 January 2014

Irapuato Three King's Day Parade

07 January 2014

Chicago People

My daughter Angela posted the item below to her to her Facebook page. She received it from her good friend Ashley. It was captioned "I think Grandma and Grandpa Mrotek would have liked this post. Happy New Year to some of my favorite Chicagoans."

The Grandma and Grandpa that she is writing about are, of course, my parents, George and Armella, who are now in Heaven and to whom I owe so much. They are part of the generation that came of age during the Great Depression, served their their country during the dark days of World War II and the Korean Conflict, built the Interstate Highway System, and put a man on the moon. That generation deserves a great debt of gratitude which will never be paid in full.

One of the hallmarks of the people in those days was their ability to take things in stride. I believe it was called backbone and common sense. The cold and snowy weather may have been a nuisance at times but was never allowed to be an excuse. When I was a lad in the 1950's they just bundled us up well against the cold and sent us to school and the schools never closed for bad weather. The only time that I can remember my school being closed was for the death of President JFK.

God bless you Mom and Dad, and I hope this gives you a chuckle.


03 January 2014

My Word of the Year for 2014

Today I was reading the blog of my friend Pamela Toler called "History in the Margins". She chose the word "boundaries" as a theme to concentrate on in 2014. In December of 2010 I came up with a one word resolution for the year 2011 in a post called "My Word for MMXI". After careful consideration the English word that I chose was "ideate" (pronounced AHY-dee-aet) which is a verb that means "to form an idea of", "to think of", "to imagine" or "to conceive of". It is synonymous with "to dream", "to envision", "to fancy", to "fantasize", "to picture", "to visualize", "to conjure up", or "to see in your mind's eye". When used in the intransitive form (without an object) and in the imperative mood (command) it means: THINK!

The word that I chose for 2012 was "update" in a post appropriately named "2012 Update". The word "update" is, of course, a verb that means to make something that was suitable for times gone by more suitable to the present and the future by adapting it to recent ideas. It is synonymous with "improve", "correct", "renew", "revise", "upgrade", "amend", "overhaul", "streamline", "modernize", "re-brand" and "contemporize".

The word that I chose for 2013 was "motivate" but I didn't write much about it in a post called "What Motivates YOU?".

My word for 2014 is "ataraxia".It is a Greek word meaning a proper attitude characterized by “freedom from worry”. By suspending judgment, by confining oneself to phenomena or objects as they appear, and by asserting nothing definite as to how they really are or should be, one can escape the perplexities of life and attain an imperturbable peace of mind. For example, the current struggles between the different ideologies of the Democrat and Republican parties with the extreme ideologists of both sides firmly entrenched in dogma is causing much angst in the general populace. If we suspend dogma, however, even just for a little while, and just explore possibilities perhaps we can find a path to enlightenment about those things where we can share a consensus. Take the case of Galileo, Copernicus, and Pope Urban VIII. Galileo and Urban VIII were locked in dogmatic controversy over the heliocentric model of the universe. Even though Urban knew that Galileo was probably right, he just couldn't give up church dogma at the drop of a hat. Galileo stubbornly asserted his scientific “dogma” and ended up suffering dearly for it by the loss of his freedom. Copernicus, however took the path of “ataraxia”. He wrote about the heliocentric theory as if it were nothing more than an exercise in thought without claiming it to be dogma and thus furthered the aim of science without strife.

So, how about you? What is your word for the year? Something positive I hope!


30 December 2013

Continuing Resolutions List for 2014 and Beyond

Every year I make New Year's resolutions and most the time I forget what they were by the end of January. What I need is a follow-up  plan and some kind of rating system to measure my progress. Benjamin Franklin at the age of twenty had four resolutions...To become more frugal, to become more honest, to become more industrious, and to avoid slandering. Out of these four resolutions he developed thirteen virtues to concentrate on one at a time. They are:

1.)  Temperance: Eat not to dullness; drink not to elevation.
2.)  Silence: Speak not but what may benefit others or yourself; avoid trifling conversations.
3.)  Order: Let all your things have their places; let each part of your business have its time.
4.)  Resolution: Resolve to perform what you ought; perform without fail what you resolve.
5.)  Frugality: Make no expense but to do good to others or yourself; that is, waste nothing.
6.)  Industry: Lose not time; be always employed in something useful; cut off all unnecessary actions.
7.)  Sincerity: Use no hurtful deceit; think innocently and justly; speak accordingly.
8.)  Justice: Wrong none by doing injuries or omitting the benefits that are your duty.
9.)  Moderation: Avoid extremes; forbear resenting injuries so much as you think you deserve.
10.) Cleanliness: Tolerate no uncleanliness in body, clothes or habitation.
11.) Tranquility: Be not disturbed at trifles or accidents common or unavoidable.
12.) Chastity: Rarely use venery but for health or offspring; never to dullness, weakness, or the injury of your  own or another's peace or reputation.
13.) Humility: Imitate Jesus and Socrates.

Franklin's list seems pretty good if not a bit stodgy but it is a bit incomplete and doesn't match up directly with the Boy Scout  Law that I memorized as a youth but probably didn't obey as well as I should have. You know how it is when you are young and besides, that was back in the 60's. Enough said.

Each country has a slightly different version of the original list of virtues made by Robert Baden-Powell, the founder of the Boy Scout movement. The list was a bit militaristic in its expanded form but that is understandable since he was a British officer of high rank. Nevertheless according to the Boy Scouts of America, a Scout should be:

1.)  Trustworthy,
2.)  Loyal,
3.)  Helpful,
4.)  Friendly,
5.)  Courteous,
6.)  Kind,
7.)  Obedient,
8.)  Cheerful,
9.)  Thrifty,
10.) Brave,
11.) Clean,
12.) Reverent.

Baden-Powell is said to have generated the list after studying various codes of conduct from around the world. He wanted it to be positive and uplifting and not negative and foreboding. He drew inspiration for the Scout Law from the Bushido code of the Japanese Samurai,  laws of honor of the American Indians, the code of chivalry of European knights, and even the traditions of the Zulu warriors that he had fought against in Africa. He chose a positive a set of affirmations, in contrast to Old Testament style, "thou shalt nots". The two lists, even if combined as much as possible, still did not give me exactly what I was looking for. I finally found my answer in the middle of the flag of India. You never know where you are going to find what you are looking for and it seems like persistence and determination are the keys to searching for something just as they are the keys to success in almost everything else.

In the center of the flag of India there is a wheel with twenty-four spokes. It is a form of the Dharmachakra which is one of the oldest known Buddhist symbols. In its simplest form, it looks like a ship's wheel with eight spokes and is known as the "Wheel of Dharma". It represents the Buddha's "Path to Enlightenment".  In Buddhism, "dharma" signifies the "cosmic law and order" and "chakra" means "wheel" or "vortex" and signifies that there is life in movement and death in stagnation.

The twenty-four spokes of the chakra on the Indian flag called the "Ashoka Chakra" comes from the base of a statue of four lions facing back to back that sat atop a pillar at Sarna, in the state of Uttar Pradesh. It was put there about the year 250 B.C by the Emperor Ashoka to mark the spot where Buddha first proclaimed his gospel of peace and emancipation to the four quarters of the universe. After Buddha achieved enlightenment at Gaya, he came to Sarnath. There He found five of his disciples who had previously abandoned him. He preached his first sermon to them, explaining the Dharmachakra. This is the motif taken up by Emperor Ashoka and portrayed at the base of the statue of the lions on top of the pillar. A graphic representation of the statue was adopted as the official emblem of India in 1950 and can be found on Indian currency and legal documents.

The 24 spokes on the Ashoka Dharmachakra represent the following qualities or "virtues":

1.)  Love
2.)  Courage
3.)  Patience
4.)  Peacefulness
5.)  Magnanimity
6.)  Goodness
7.)  Faithfulness
8.)  Gentleness
9.)  Selflessness
10.) Self-Control
11.) Self Sacrifice
12.) Truthfulness
13.) Righteousness
14.) Justice
15.) Mercy
16.) Gracefulness
17.) Humility
18.) Empathy
19.) Sympathy
20.) Spiritual Knowledge
21.) Moral Values
22.) Spiritual Wisdom
23.) The Fear of God
24.) Faith or Belief or Hope

In my opinion this is a very nice list and is just what I was looking for. Then I had to come up with a rating system. I didn't know if I should use a simple binary thumbs up or thumbs down or something more sophisticated perhaps, like the five star rating of items on Amazon.com. Then I thought that the scale of one to ten might be better since it would lend itself to numerical comparisons from week to week, month to month, and year to year. I finally decided on a scale of zero to ten with five as the beginning median around which I could plot distributions.

Finally, I had to make some rating criteria for each item in order to be as consistent and as objective as possible. I must also develop a procedure for documenting the pluses and the minuses of the occurrences on a timely basis without making it too complicated. The more I work on this the more interesting it gets. I am happy that I initiated this project. Actually it was the Greek philosopher Plato who got me started. He equated virtue with truth. Benjamin Franklin gave me an example to get me going. Robert Baden-Powell gave me a boost, and Gautama Buddha gave me some great ideas. After all, the official motto of India is: "Satyameva Jayate"..."Truth Alone Triumphs".

Happy New Year wherever you may be and may your New Year be newer than ever before.

15 November 2013

The Mathematician, The Philosopher, and the Camels.

A man who had seventeen camels and three sons died.

When the last will and testament was read, it stated that one half of the camels would be for his oldest son, one third for the second, and one ninth for the third. What to do? There were seventeen camels so how could you give half to the oldest son? One of the animals would have to be cut in half. This wouldn't resolve the problem either because one third still needed to go to the second son and one ninth to the third.

The sons went to look for the smartest man in the city who was also a mathematician. He thought hard about the problem but couldn't come up with a reasonable solution that wouldn't damage the camels. Then someone suggested: "It might be better to look for somebody who knows about camels and not mathematics".  The boys finally found a philosopher who seemed to know a lot about various things and who had some experience in these matters. They explained the problem to him. The philosopher laughed and said, "Don't worry about it. The solution is quite". Now it just so happened that the philosopher had recently been given the gift of a camel so he lent it to the boys to help them even up the account.

Now there were eighteen camels instead of seventeen, thus making the problem much easier to deal with. The philosopher began to divvy up the camels. He gave nine to the oldest son who was very satisfied because this was half of the camels. To the second son he gave six camels which was a third of the camels, and he gave two camels, which represented one ninth, to the third son. Guess what? There was one camel left over which was returned to the philosopher.

Let's see...
17+1= 18
Oldest son gets 18/2= 9 camels
Second son gets 18/3= 6 camels
Third son gets 18/9= 2 camels
Total camels in the father's will 9+6+2= 17 camels
18-17= 1 camel returned to the lender.

So what's wrong with that?

About Me

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I was born and raised in Chicago, Illinois, U.S.A. I have been living in Mexico since January 6th, 1999. I am continually studying to improve my knowledge of the Spanish language and Mexican history and culture. I am also a student of Mandarin Chinese.