Today is All Souls Day, known as the Day of the Dead, which begins on this date of November at the initiative of St. Odilon, abbot of a monastery in France, in 980. Today, as more than a thousand years, praying for the souls of the faithful who have died. Both Catholics and Orthodox Christians and Protestants, each with variations in the rites, we pay tribute to those who have left their earthly life. For Catholics, with special emphasis on those who are in a state of purification in Purgatory , unlike the Orthodox and Protestants who deny the existence of this place.
In most countries, especially America and Mexico, the conclusion is different from the other Christian countries, as this celebration was combined with many of the rituals of our history pre-Columbian Indians. I have been fortunate to witness some of these rites in several countries in America and Europe and I have no doubt that in our way of life directly influences how we perceive death.
Paradoxically when talking about death, we celebrate life and not think about the past, but we care about the future, because if one thing is certain, is the departure from this world. History tells us that all peoples have their own version of Judgement and step beyond the call . Let me tell you about three ancient peoples from three continents.
The ancient Egyptians believed that the spirit of the deceased was conducted by Anubis into the room the two truths, the place Judgement, which was presided over by Osiris, god of the resurrection. The Ib , or heart of the dead and a symbol of morality, was weighed in the balance against a feather representing Maat , the concept of truth, harmony and universal order. Depending on the answers to the questions put to him the deceased in this trial, the heart weight increased or decreased. If the end result was favorable, your heart would weigh more than the pen and then the spirit was moved to Paradise Aaru ─ ─ in this mythology, and if the opposite was true, if the heart was lighter than the feather, amniotic , the devourer of the dead ─ a creature with crocodile head, mane, torso and arms of a lion and hippopotamus legs ─, destroyed his heart and prevented the immortality of the court.
The ancient Greeks should bring a coin to pay for the services of Charon, the ferryman of the Acheron River to reach the World Below in Hades reigns. Once you arrive there souls, judge their actions in life. The honorees drink the waters of Lethe to forget unpleasant experiences as well, and are then driven the Champs Elysees where you will find peace. The souls without honor is unfair and leads them into Tartarus, a place of the underworld, where they must serve their sentences. Finally, those who dared to offend the gods, they fall under cruel punishments, like Sisyphus, forced to push a rock to the top of a hill, and once it did, the rock rolled down must repeat This movement for all eternity.
For ancient Mexicans, there were different ways that they would take the dead no matter how they lived, rather, depending on how they died: in The Tlalocan were those who died by disease, in The Omeyocan because of the war in The Mictlán those who died of natural causes, to tour the way to the latter, the deceased was buried with a dog, that would help him cross a river and come to Mictlantecuhtli, who had to give some offerings to continue. The interesting thing is that the dead children lived in the Chichihuacuauhco, where he was a tree that gave them milk as food. These children would return to earth when the human race was destroyed and so the death reborn life. In This is a clear analogy with the teaching of most Christian churches as there will be a general resurrection at the "end times."
Some time ago I read a story, want to share with you today on two mathematical friends, talking about their families, one asks the other if have children and what ages are, of course to have a good time and as is typical for fans of numbers and equations, the simple answer is disguised riddle and the dialogue between them was:
-The product of the ages of my three children is currently 36 and the sum is just the number of the house where you live. I right there ages?
"Actually, I can not yet because I need a fact," he replied after a few minutes.
"You're right answers. I forgot to tell that the greatest plays piano.
Interestingly, this last fact, even if at first seems irrelevant, it is sufficient to give the answer correct (the solution given at the end if you want to try to solve it).
This problem highlights us and reminds us that on many occasions to get answers to the big questions of life we \u200b\u200bneed some information or data that are in principle contradictory, paradoxical and implausible and people are not discarded a priori that make history and take over the time and as they did centuries: Archimedes, Hypatia, Gauss, Newton, Einstein, Curie, Hawking.
Many of the keys needed for the solution of certain problems are in front of our eyes, in the everyday and the same nature. The study of birds, their structure and movement or shape of the leaves of some trees, helped solve many problems in aeronautics. In designing the costumes for swimming, has been imitated shark skin to speed underwater and in the design of the cars is looking for some forms of nature that encourage fuel efficiency. The structure of the cells in the honeycombs of bees or the distribution of trees to optimize the use of light and nutrients are studied in biology. The ancient art of paper folding known as origami o papiroflexia , se empieza a utilizar en el diseño de naves espaciales para extender paneles solares una vez que estén en órbita.
Existen relaciones maravillosas entre la teoría de juegos y la economía, entre el crecimiento de las plantas y el diseño publicitario, entre la geometría fractal y la distribución de las poblaciones, entre la teoría de números y la seguridad bancaria, entre la teoría del caos y la contaminación ambiental.
In any situation we find ourselves where we should take decisions, we must analyze each of the data and do not discard a priori assumptions that seem superfluous, and the remedies that seem unlikely.
When you have eliminated the impossible, whatever remains, however improbable, must be the truth. Sherlock Holmes
SOLUTION
For A, B, C ages, it has 8 possible cases where the product is 36
1-2 ABC 01/01/1936 01/03/1912 -18
1-4-9 1-6-6 2-2-9
2-3-6 3-3-4
only 5 cases and 6 you get an equal amount, so that if a missing data, the friend lives at house number 13. In both cases there are twins, but only if 6 can speak of "the greatest", so ages are 2, 2, 9.
remember, forty years ago today, my whole family gathered together waiting for television transmission ─ course in black and white, no remote control ─ the man on the moon. I was a child of three and a half years, despite my young age, felt the thrill levitating around the room, some holding hands and other prayers, the joy that was experienced at the time ─ with man a white robe and funny helmet ─ gave those first steps with slow movements, was extremely contagious. I have my parents who, for several weeks, my favorite game was to simulate the walk of Armstrong and his movements in zero gravity, accompanied a scale model of the Apollo 11 that we set ourselves. As
humanity progresses we see how it ceases to be impossible, and gradually becomes a reality. To be aware of it enough to read or remember what some science fiction writers wrote, at the time, so futuristic cloning, artificial organs , organ transplants, space travel, nanotechnology, wireless communication, hologram, satellites, etc.. Thus, the thought of utopia and its likelihood of reaching the mark just beyond the threshold as possible, will become an attainable goal, a dream of possible implementation.
Jules Verne describes his future in " From the Earth to the Moon " and it has many similarities to the trip which took place in 1969, so what was fiction ceased. Except for Apollo 13, f hey were successful missions from Apollo 7 to Apollo 17, in 1972, was the last walk on the moon. The Apollo Program began in July 1960 and was terminated after the Apollo missions 18, 19 and 20 were canceled due to budgetary problems, it should be mentioned that the Apollo missions 2 to 6 were unmanned, after the crew Apollo 1 died in a fire in a preflight test. In total there were six landings and 12 astronauts set foot on lunar soil.
Armstrong's courage , Collins and Aldrin, astronauts embarked on this adventure, is truly remarkable because there was no certainty of success, even after landing on the moon, there were doubts and there were problems to take off from the Moon and what about the arrival back to Earth where heat friction when entering the ship. One of the greatest achievements of this trip is the realization of a dream and critics who wonder if it was worth so much effort and expense should be reminded that human nature and thirst for knowledge will cry if we pass from arms thinking that borders are finite, and reach all, we would be back in the search for answers to our existence and it is definitely something that we can not afford.
In the coming decades, dreams of treading the soil of Mars, beyond planting a flag the powers that they do, is important to visualize our natural satellite and the other planets as large testing facilities, sources of new resources and new materials . Recommended links trips to the moon were NOT false Forty years later ...
On a day like today, when in Costa Rica is celebrated on Father's Day , like in fifty-two countries, I remember the day my firstborn was born Hector and I officially graduated as , and when the life I RAGALA the arrival of my second son Philip, who revived the same thrill of first two years earlier. At that time, my priorities changed and increasingly appreciate the great effort that my mother and my father did, to form.
While the memories with me, I hear on the radio the song the Colombian singer Juanes where it says " What I miss my mother and my father remember, and we analyze I have a point. In a changing society, still remains in force the demon of machismo and, yes, our mother we do not lack is an illusion, but also our parents did not forget us, even if not us, it is our hope.
remembered the ritual of the Cherokee Indians in the United States, as is proof initiation of men, with some variations, is practiced elsewhere. Parents bring their children to the forest, blindfolded, leave them there alone. These young people should sit on a log all night and, without removing the blindfold from his eyes, face their own fears until the sun shine. It is forbidden to call for help and once you survive the dark, are recognized as men. They can chat with other boys about their experience, because each one must enter the masculinity on their own merits. Young people feel fear and anxiety, then listening to all sorts of noises, and they know that the wild beasts lurking around and they could do harm. Hear the wind whispering in their ears and the grass rustling, they sit in the trunk, without taking off the bandage, it is the only way they say ─ ─ to become men.
After a long and terrible night, the sun appears and removed the blindfold, they realize that their father has been sitting next to them and ensured, slope protection your child all day. His parents have not forgotten them, never left them alone and even thought they were absent, the only thing on their minds were their own children.
Most parents try , with great dedication and each in its own way, that their children break the barrier of fear of the unknown, never abandon us, but some do not talk and do not express their feelings, they are there, present in body and soul.
Let me share with you, dear readers, an unpublished poem that I wrote my father in 1997, when I got my degree, and of course means a lot to me.
MicrosoftInternetExplorer4
Manuel Humberto A mathematician
1
Morning me dreams revealed two
and then I could discern
the infinite length vanishing sea
on the square root of the raging waves.
From the white sands of my bones
watched the third dimension geometry Euclidean
blue as Murano glass,
with spaces filled with velvety dolphins
and the breeze warm, sweet,
tenderly bathing the lawn of my hair.
On the perimeter of silence
look like dawn is
yellow arc of the full moon.
2
tropical Fall,
that he passes out naked in the laziness of the fingers,
is obtuse, and in it I discovered something wonderful:
when the zenith point of the universe
is gray Cota Mayor,
π the sign becomes a galaxy pendulum
sliding happy in the splendid bell curve
which calls us to rattle Midnight Mass
in honor of the third millennium.
3
Since those bygone days,
forgotten by the memory of man,
Jan when squared plus one not yet born,
travels to derive the infinite sky,
floating within black holes,
drawing parallel lines on the smile a child.
So
hippocampus a dance in the tangent of the Cartesian profile
and at right angles to the pride of the sun.
4
The cosmos is an orange alien and eternal
with millions of celestial cosines.
distress is supported by stars isosceles
splendid in the reverberation of significant ways,
few weeks ago I got my hands, not by chance but as a direct product of fate, a book that made me reflect on the changes that happen in our lives, often almost without realizing it. I had the honor of presenting this work to a large and distinguished audience. Let me share with you a summary of words that I prepared for this occasion, even if they had not read the book, I'm sure appreciate to get to the final reading.
Zarcero, January 2009 Juan Ramon, who, like himself tells us, was born on last day of January in Zarcero in a night full of fireflies phosphorescent lit peaches, both wrinkled old, gives us a new book, with a very suggestive title " peach flowers." Without being literary critic, try to tell you a few thoughts, memories and feelings that led to his reading.
memories, symbolizing the past, and hope that encourages us to the future, these stories were amalgamated into finely extra tacked on causality. Zarcero is a magical city and in every breath you breathe, you feel peace and harmony that can only be felt in places that have been blessed by nature: the green mountains, blue sky and rivers crystal clear, are remembered in this beautiful book that gives us Juan Ramon, but it is intertwined national and global history, we talk about migration and wars, coups and educational reforms of love, betrayal, jealousy and death, geography, cuisine and literature of Jews and missionaries and weaves, magically, with the particular history of our grandparents, who, as mythological heroes, crossed rivers, crossed valleys, climbed mountains, tamed defoliated margaritas and volcanoes.
Yanuaria Cubillo, Francisco Feliciano Otoya and Acuña, mentioned in this book are just some of the early settlers is ta city. They managed to cheat death that comes from oblivion, and seized time and the centuries, no civilization, society, or simply a generation of men can boast and say with pride that came alone. We need to be more respectful and grateful to the generations that preceded us, more generous and vigilant to the generations to come.
His book is dedicated to those who have come for love, this evocative inscription is no coincidence, since the end of reading, we realize that love is the theme of the book. About love will continue writing and defining the era as, for example, Pastor Martin Luther King perceived as the only force capable of transforming an enemy into a friend. Or the perception of eternal love and need to survive, they exuded by each of its pores Florentino Ariza endearing character in the novel " Love in the Time of Cholera " García Márquez when you think " had to teach him to think love as a state of grace that would do nothing at all, but a source and end in itself "in a letter he sent to Fermina Daza, his eternal love. I think very successful and we, too, the vision ng my grandfather: "Only coffee man lives not because there is another healthy aromatic essence: love, the tastiest of all vices "Mentioned therein.
boundaries become smaller. Globalization despersonifica absorbs us and we to be convinced of this, simply observe how our language has changed, now the redskins old are sold antiques and American clothes instead of the junk, replace the supermarket grocery stores, the moles to malls, pharmacies and drugstores to gas stations to pump even live in an age where we invaded euphemisms: wrinkles of oldies, such as peaches, now are the fine lines of people seniors . The problem is not that we visit the modern malls, but yes it is he who despises small artisans and producers to domestic markets will not attend. The problem is not qu and we like the tango or the zarzuela or attending a concert of rock and roll , but yes it is the disregard, or reject, our beautiful folk music, forget the marimba and stop feel like our Tambito pace. The problem is not that we like hamburgers, pizza or soda , but yes it is he who despises the tortillas, tamales, gallopinto, the minced vegetables, the natural fresh and Aguadulce. The problem is not the incorporation of new features and benefits CIOs our culture, but yes it is the elimination of parameters characteristic of our character and, above all, we leave to transmit to future generations is part of the cultural identity of being in Costa Rica. Thus, in " peach flowers " it recounts many of the traditions that give us the national identity, including language and use our very own words. We must guard against the transculturation inherent in globalization, lest one day, at dawn and mo ment that we looking in the mirror, look, with macabre surprise that we have become mutants, as happened to own Gregor Samsa in Kafka's The Metamorphosis .
When I read and enjoyed " peach flowers, our ancestors thought that, with few material things and sometimes not to eat, but with large families that did not leave empty spaces, were happy were very happy. Meditated, on the contrary, and paradoxically, we are now better prepared academically and more spiritually ignorant. Travel faster and arrive later. We spend more money and give less charity. Lie less and love more. Expect too much from life, sometimes more than we deserve and always, life gives us more than we require. We live in bigger houses for convenience but we separated more by vanity. Visited less than those closer. When we walk, run and when to run, walk. See more TV and have no time to pray, pray or just to say thanks. We went to fast food to save time, but time is never enough. Survived more but we live less. We have fewer children and more divorces. Read less well, the little that we read, we do more damage. The more we know the environment, the less we know; some know what happens in the Middle East or in the stock market on Wall Street, but not what happens in their neighborhood. Anyway, we got used to do the urgent before the important and society is not fully happy.
At some point in my reading began to surface memories of my childhood, my grandmother America Vargas, mother of Juan Ramon, who, as is written there, before the proposed marriage of John Murillo and within a month's time I think so, replied: "Better than three months," said the bride, without asking anyone's permission, "I'll have time to meditate and to my mind. But should you know one little thing to understand as God intended: I like to shave his mustache. There
magnifies the importance of reading in recent history, which tells Juan Ramón Murillo, and impels us to rethink the direction of our lives, we remember the struggles our ancestors undertook to achieve their dreams, reminds us to write stories about us and the life cycle is repeated endlessly reminds us of the importance that the family in the construction of what Costa Rica is today, and inevitably, many of you, many of us and our descendants, will migrate out of love.
In the previous post The magic of numbers , we refer to some interesting considerations about the numbers and their relationship to magic and superstition. Always related to this subject, talk about today of magic squares. The first known, in ancient China in the third century BC, is:
is so called, magic square, they were used to build the numbers 1 to 9 and by adding the elements found in its columns, rows or diagonals will always get the same result 15, which is called the magic sum .
Now consider the square of order 4 which is obtained by placing the numbers 1 to 16 as follows:
Se puede comprobar, para verificar que es un cuadrado mágico, que la suma de los elemento de las filas, columnas o las dos diagonales es el mismo valor de 34, su suma mágica. Este cuadrado fue incorporado por el pintor Alberto Durero en su ob ra M elancolía , en la parte superior derecha de la obra y cumple algunas propiedades adicionales, como por ejemplo, incluye la fecha de la pintura en la parte inferior al centro, año 1514, la suma de las cuatro celdas centrales (10,11,6,7), las cuatro esquinas (16,13,4,1) y otras combinaciones simétricas, also added 34, among many other properties, which give a more than magic in this square.
I say there, other than those given above, several squares of order 3 and many others of order 4, and of course the higher we make the order or size of this square, the greater the difficulty of sorting the numbers so as to meet the sum of the elements of each row, column and diagonal is the same. Interestingly, for those of order 4, De Bessy established in 1693 that there are 880 different magic squares. Later it has been shown that there are magic squares of order 275305224 5. For larger orders we only have estimates.
The great American inventor Benjamin Franklin found the magic square of order 8 given by
In each row, column and diagonal add 260, he was passionate about this type of problems that occupied his spare time while doing clerical work in Philadelphia, a curious fact, and evidence of his genius, it is said that in one afternoon, managed to solve the square order 16.
Leonard Euler, the most prolific and great Swiss mathematician found a magic square of order 8, where each row and each column adds 260, but in addition, each row and column of each of the four subquadrate of order 4 obtained, if we start this square into four , numbered 130 and, further, that in this "magic board" of order 8 describes the path of the horse's movement around the board without being twice in any of them known as the " problem of motion horse ".
variations of magic squares, the one that caught my attention is that of order 4 which is incorporated The Passion façade the expiatory church of La Sagrada Familia in Barcelona , monumental and amazing work of Antonio Gaudí , see the kiss of Judas:
The Cryptogram Gaudí, as they call it, is extended:
In this case the magic constant of the square is 33, the age of Jesus Christ for this, two numbers (12 and 16 ) are reduced by two units (10 and 14) with two replicates displayed in this way is achieved the magic constant lower by 1 unit, 34 to 33.
This magical sum is always 33, in 310 different combinations in groups of four, just to name a few: 1,14,11,7 (subquadrate top left) or 8,10,13,2 (subquadrate bottom left) or 7,6,10,10 (subquadrate interior) or 14,11,6,2 (a cross) or 14,7,9,3 (cross) or 14, 6,10,3 (shingles) or 14,14,2,3 11,8,9,5 or , including yourself can try using geometric shapes or paths.
Thus, we can use in our classrooms the magic of these squares to motivate our students and, in turn, demonstrate the close relationship that exists between mathematics and art.
remember that I was a student of mathematics, he had a student once asked a distinguished professor what is infinity? to him, after thinking a few seconds, and without saying a word, took the chalk and started a trace on the board, which spread across the wall and then down the stairs, until it is out of sight. In the next lesson the teacher came again, always with chalk in hand and following the stroke, and asked the student if he had been a clear idea of \u200b\u200binfinity. And as he repeated a thousand times and you park in the collective unconscious of a society, in this case that of the mathematical, starts to become reality, now no doubt that this story was true.
The story of the infinite and the infinite, because although it sounds strange, there are infinitely larger than others, it is exciting and has traveled in many directions, of course, the idea principal, in any case, it is about "something" that never ends, that has no end or continuing or prolonged indefinitely.
The concept of infinite latent in geometry, for example when it comes to straight, in the analysis when constructing the real numbers in the theory of numbers when, for example, we know that there is an infinity of prime numbers, among many other branches of mathematics.
I do not want to dwell on the definition given in the English Royal Academy, or some details in their history, but I wanted to share some examples that have a clear idea Some people, mathematical and non mathematical, in everyday life:
On nights like this I held my arms.
kissed her greatly under the infinite sky !
Later writes
the other. Will be someone else. As before my kisses.
Her voice, her bright body. His eyes infinite.
Del Poema 20 de Pablo Neruda . (In voice Neruda, the voice of Alex Ubago , only the letter )
"Only two things are infinite : the universe and human stupidity. And the first thing I'm not sure" Albert Einstein . Here it is worth adding that by 1927, Edwin Hubble proved that the universe was expanding and gradually slowed, as Einstein had predicted in his theory of relativity, gradually was giving a 180 degrees, and consider the universe of infinite age, came to realize that an expanding universe required a start.
"And do not give me that for sheet of air is only a symbol and symbols do not correspond to reality. If I know there, eh, barbecue, yes? You will hang on a thread and each lobe your new born and young plants true that more and more girls, but do you know that there is a large infinite and infinite small like the tortoise and Achilles, remember? in the Lyceum. "
At the end of the short story air sheet of Joaquín Gutiérrez.
