Why Does Mathematics Need Imagination?

                      By Vic Odarve

Math is seen as a tough course by many students, and only a few are interested. That is why using your imagination may assist you in comprehending, appreciating, and challenging how this course operates. Many people are unaware that our imagination keeps various mathematical equations and formulas in our heads, allowing us to understand how they work in real-world scenarios and, of course, their limitations. As Mother Nature expresses her beauty through mathematics, from Newton's law of motion to Kepler's laws of revolving planets, our imagination keeps us appreciating the beauty and grandeur of our planet and the universe we live in. And much more; our imagination would keep us challenged to investigate math secrets and their role in the universe's mysteries. Understanding math is more like doing imaginative play than anything else!

Math consists of interwoven equations and formulas, and imagination would keep the students’ interested considering how math works intangible worlds. Imagination also adds our knowledge in quantum and cosmic worlds because variables or quantities involved in the math equations are developed only in modern science labs and scientific experiments which are often out in our real senses. In quantum mechanics, for instance, particles behave differently from classical mechanics. In cosmic science, some mathematical formulas and equations developed from years of observation in various astronomical phenomena like an event horizon, a quantum singularity, the expanding universe, the uncertainty principle, and many others. But Einstein’s equations, where time is not constant, and his conversion ratio between matter and energy, are clearly a result of imagination. Prediction formulas, too, which are the product of probability and statistics, also come from imagination. Hence, imagination helps us going to get deep into equations with mathematical relationships between different things.

Math is beautiful

There is no ugly mathematics. Math is always beautiful. The beauty of math can be further appreciated by imagination. Mother Nature teaches us math, from plant leaves to cloud formations and the intricate webs of celestial bodies stretching into the cosmic ocean. Beautiful and intricate applications of mathematics are illustrated in the complexities of our natural world, such as the golden ratio, the Fibonacci sequence, fractals, and the honeycomb conjecture. The simple twig of a tree is a fragmented geometric shape that looks like the branches that they grow on, which look like the tree itself—a beautiful mathematic expression! Another one is a hexagonal-shaped honeycomb created by the bee. It is geometry in action. And these are all around us. Mathematical equations give us an understanding of Mother Nature’s mind and how the laws of physics are working. The existence of these laws keeps us appreciating the beauty of understanding mathematics.

Engineering class

 And much more. Imagination would keep us challenged to investigate math further, unlocking some of the secrets and discovering things we don’t yet understand. Some mathematical laws discovered are so strange that they keep us mind-boggling and expanding. Through imagination, we are just like playing equations in our minds and thinking about how they work in different circumstances and challenges to solve some of the mathematical problems. Newton and Leibnitz, for example, imagined how to solve areas of figures bounded by several curves and developed integral calculus; Laplace developed the method for solving differential equations; and probability and statistics for gambling or games of chance.

For a math-intensive career like engineering, it is through imagination that students can play around various math equations and formulas. Imagination is a driving force that leads to many inventions and innovations and what brought us to our present state of civilization. Math is not math until it is understood, appreciated, and challenged. And it needs imagination!

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Elect the Best Candidates: The Choice is Ours

         By Vic Odarve

Since several candidates with various intentions want to hold public office in a democratic society, elections have been the usual mechanism by which a population chooses representatives. Elections give people an opportunity to have their say, invoke the symbols of nationalism or patriotism, and more. Elections break the monotony of our daily life with government officials running our economy with a downward trend from which the country suffers. As it always is, the choice to elect public officials to hold public offices is yours and is irrevocable.

 Participating in the election process really invokes the symbols of nationalism or patriotism. It gives us satisfaction in our need to feel a sense of belonging to our country, the place of our birth. Hence, the events during election time that include rallies, banners, posters, and television coverage suggest the importance of our participation. Sharing a post like the one shown below edifies fellow voters. The Philippines is an electoral democracy, but sometimes corruption and a lack of transparency continue to undermine democratic development. Elections have historically been marred by fraud, intimidation, and political violence. Vote-buying and vote-selling obstruct the democratic process, yet they remain pervasive in some parts of our country. Taking part in monitoring a clean and honest election is one of our nationalistic roles.

 This is the time to give people an opportunity to have their say.  For the old politicians, we can confirm if our last vote was worth what we are looking for in public servants. Whatever other reasons voters may have in their minds, participation in the upcoming election serves to reinforce our self-esteem and self-respect. For the neophytes in politics, voters have a chance to dig deeper if the candidates are the best applicants for the government position. He could not be the perfect candidate—but maybe the best among them. At least the voters can choose better candidates for public servants.

Candidates for President

By arousing emotions and working toward a collective objective of improving our country by electing good-performing government officials, it gives us a chance to replace below-par performers in our governance platform. By helping our voters through education, we can select candidates that cannot be bought and fooled by big businesses, crooked government officials, and oligarchs. Graft and corruption, tax evaders, and drug lords have been the perennial problems in this country. These are the main culprits behind why our economy is on a downward trend. One thing is certain: let others also know that they must vote according to their conscience, even if they do accept money.

Choosing the best candidate can be a challenging job, and when none of them seems to be a perfect fit for the public position, always vote for people who will best represent and uphold biblical values. Candidates, who are usually groomed and supported by media giants and rich and powerful oligarchs, must be investigated if they have records of graft and corruption. If they are one of them, crush them out of your list. Do not vote for them, even if they are endorsed by the President. Do not sell your votes to save our country. Believe in God's supernatural touch. The Bible says,

"When we humble ourselves and pray, God will heal our land (2 Chronicles 7:14)!"

The choice to select candidates is ours and is irrevocable when the dust of all our cities incarnadines the sunsets of the world.

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NAKITA KO NA ANG GOLD BARS

           ni  Vic Odarve

“Tinuod gyod diay ning gold bars” nakaingon ko sa akong kaugalingon samtang nagbasa sa tatak UNION BANK OF BURMA, 7.5 KGS AU  nga nakapatik diha sa ibabaw nga bahin sa bar.

Dili gyod ko motuo aning gold bars sa una kay nabasa ra man ni nako nga daghan ug gold bars nga gitagoan ni Presidente Marcos. Pero sa nibisita si Nong Donato nga gikan sa El Papa bukid sa Davao Oriental ug mituyo gyod sa ako nga dunay  gold bars baligya P110,000.00 kada bareta, daw dili ko katoo. Ug isip pagsiguro ug tinuod ba gyod ni o basin fake, ako siyang giingnan nga magdala sya ug sample gikan ana nga bars sa sunod bisita niya.

Gold Bars

Tuod man human sa usa ka bulan, nibalik sya ug may dala nga sample nga pino gikan sa maong bar nga sya mismo ang nagkuskos sa kilid sa bar. Dayon gipatesting ko sa laboratory sa kompanya nga ako gitrabahoan ug ang katunga  gidala ko sa higalang goldsmith. Tuod man tinuod gyod nga 22K ang result!

Sa hilom uban ang kauban ko sa trabaho nagtipon tipon mi ug kwarta nga P55 T kay tunga o putol ra ang among paliton. Gituyo nako nga tunga lang kay magdala ko ug chemical gikan sa laboratory ug ipatulo nako sa putol nga gold bars para klaro nga gold ba ang pinutlan o sulod ninii kay basin fake diay. Kon gold gyod, adto ra pod ang bayad sa balay sa ako ig agaw diin nakatood man ang nagbaligya para sab safety nga way dala kwarta ngadto sa usa ka lumad o native nga nagkubot sa gold bars.

Paingon sa Bukid

Sa tambag sab ni Nong Donato, dili magdala ug celpon ug kwarta ug mga mahalon nga butang kay bukid ang adtoan ug magmotor ra mi tulo uban ang driver. Ug nagbakos pa mi ug anting-anting nga garapa nga ang sulod haplas nga mobukaw kon may dautang tawo nga mahimamat sa dalan. Gikan sa Trento ug El Papa miabot mi sa maong lugar nga boundary na sa Bukidnon ug Davao Oriental human sa 6 ka oras biyahe.

Tuod man pag-abot sa bukid, naglakad pa mi ug 300 meters gikan sa dalan ug diha gyod nakita ang gold bars dala sa usa ka lumad o native duol sa iya payag. Mga tunga oras namong gihuptan  ang maong gold bars ug nakita ko ang gikulit nga tatak “UNION BANK OF BURMA AU 7.5 kgs”. Parang usa ka loaf bread ang porma ug brownish ang ibabaw nga color.

Among gihangyo nga katunga ra ang paliton kay kulang kwarta ug ang bayad didto lang sa balay sa ako ig-agaw. Gituyo pod ni namo kay pahiran pod sa kemikal ang gigabsan para makita ba tinuod o fake.

Marcos Gold Bars

Bisan unsaon ug hangyo, wala gyod sya musogot kon putlon o tunga ra ang paliton. Kay kulang pod amo kwarta ug duda pod basin ang ilawom dili gold, miuli na lang mi nga way nadala.

Paglabay sa usa ka bulan, nabalitaan namo nga nahalin na ang gold bars. Ang usa napalit sa driver sa habalhabal sa isda ug ang uban napalit na sab sa usa ka pari nga naassign sa maong lugar.

Karon kon madungog na pod ang pangalan ni Bongbong Marcos, ako dayon madumduman ang gold bars nga gitagoan sa iyang amahan ug ang akong nakitang gold bars. Ug basin kauban ra na sila sa Yamashita treasures nga gibiyaan sa mga Hapones sa hapit na nahuman ang World War ll.

Nakita na gyod nako ang gold bars!

 

Positive Thinking and Contentment; Keys to Happiness 

     By Vic Odarve 

Although life is made up of ups and downs, thinking positively, coupled with contentment about what we have, may lead to a happier life. When life takes unexpected turns and brings along traumatic pain, evaluate events with an open mind; convince us that life must move on regardless. Think positively. Contentment is necessary for attaining a positive state of mind, accepting the situation, and moving ahead. 

PICOP Technical Services 1986

Sometimes life takes unexpected turns of events. It goes up and down. Think positively. If our failure is awry, inflicting pain and self-pity, positive thinking draws us to accept it as a learning experience and then move on. In statistics, it is impossible to have all failures; there must be success. My engineering classmate, who has passed and failed some math courses, spent about eight years in school before becoming an engineer, a profession he is proud of. He really thought he could finish it, and he did it! Positive thinking can create a realistic plan for goals in life, allow us to move ahead after some failures, and recover from our feelings of loss. This leads us to a better and happier life. 

On the other hand, contentment is necessary for attaining a positive state of mind; accepting the situation; and allowing us to move ahead. By appreciating the great things we currently have in life and changing our mood to focus on things positively may feel a happier life. Do not compare ourselves with others because we live differently. Be content with our achievements for it is our real accomplishment. Be ourselves. Do not imagine things that are beyond our reach. Do not feel jealous and insecure. Be contented with what we have. Do not match our neighbor’s new tennis rackets, shoes, iPads, I-pods, etc., feeling we are behind. Do not feel devastated that somebody overtakes us in some areas of our life. 

Mayana Fiesta Celebration

Be contented and live well on what we have. Take the case of Jose Mujica, the world poorest president who lives on a ramshackle farm and donates most of his pay; do laundry by himself outside the house with water comes from a well in a yard, overgrown with weeds; keep watch outside of only two police officers and a three-legged dog. "I may appear to be an eccentric old man… But this is a free choice. I’ve lived like this most of my life and I can live well with what I have", he said. "I’m called ‘the poorest president, but I don’t feel poor. Poor people are those who only work to try to keep an expensive lifestyle, and always want more and more," he says. 

Like the sparrows and water lilies, we have the right to live and be happy in this universe. No matter what troubles the world brings to our lives, we must be at peace with our parents, brothers and sisters, and friends and deal with them in a gentle manner. 

There is always a void that cannot be filled with material things. This is a wicked world—a troubled place full of uncertainties that bring us nothing but broken dreams. But no matter how wicked and corrupt, it is still a beautiful world. We must strive to be happy, to be at peace with God, and to be at peace within our souls. Be positive and contented; this is the gateway to happiness.

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GILAPARO SA ENGKANTO

        Ni Vic Odarve

“Wala gyod nako tagai ug bili ang tingog sa karatila nga nabati diha sa akong likod. Ug pila lang ka minutos nga diha nako daplin sa karsada naglakaw, gilaparo ang akong ulo dayon kong natumba”, matod pa ni Julian.

Village of Mayana

Mikaylap gyod ang estorya niining lugar nga ginganlan sa usa ka barangay ug Insek, sa sitio Ilaud, Mayana. Lugar kini nga may karsada diin ang tuo nga bahin ani dunay pipila ka punong kahoy nga mga dakit ug may buho sa punoan diin ang tubig sa sapa misulod subay sa iyang dalid ug wala nay agusan. Sa walang bahin na man pod sa karsada usa ka pangpang diin may nitubo nga dakong kahoy nga gitawag nila ug dita ug dakit nga mitungtong sa dakong pangpang o bato. Walay mga kabayanan duol ani nga lugar ug haduol kini  sa usa ka tulay sa pinakadako nga suba sa barangay. Ug adunay gikatingad-an ang mga lumulupyo nga matag takdol sa bulan makadungog sila ug magkantakanta nga mora'g ininsek ang pagkalitok o mensahe.

Labaw pa sa tanan, kon ikaw ra usa ang molakaw bation ka ug kahadlok kay ngitngit ang lugar tungod sa dagkong kahoy nga dakit ug taloto o dita sa kilid sa karsada. Gani ang mga katigulangan nagmaymay sa mga bata sa among kabatan onan sa pagbantay sa paglakaw kon mag-inusara.

Mao ni ang nahitabo ni Julian.

Sabado sa kadlawon pas-an ang usa ka sako nga sibuyas moadto na sa lungsod para ibaligya ug pagbalik dala na ug bugas  ug isda para sa pamilya. Kay 6pm na sa hapon nahalin ang tanan niya nga baligya ug wala nay pasahero nga trak nga motungas sa bukid, hinayhinay siya ug baklay dala ang balon ug 2 ka botelya nga bino. Kon bation na sya ug kakapoy pahuway siya ug ibutang ang bugas niyang gilokdo dayon ug inom ginagmay.

Engkanto

Hayag ang kagabhion sa buwan ug medyo ngitgngit lang usahay sa dapit nga may dagkong kahoy daplin sa karsada. Mga tulo na ka oras niyang baktas ug medyo lipay na sya kay abot na man sa ila baryo ug media oras na lang abot na sa ilang balay. Pero pag abot niya sa awaaw nga lugar tawag ug Insek human gyod sa tulay, may nabati siya ug karatila ug kabayo nga tingog nga nagsunod kaniya. Iyang gitan-aw iya likod pero wa man siyay nakita. Ug daw may naghunghong sa iyang  dalunggan nga may moagi. Kay nagparagparag man lagi ang nilakwan kay medyo hurot na pod ang bino, wa nya tagai ug bili ang paglikay sa dalan. Pagkataudtaod  tungod gyod sa pangpang nga may dakong kahoy, mihaguros ang karatilya sa iyang kiliran ug gilaparo ang iyang ulo. Natumba sya maayo gani kay wa mabuslot ang gisudllan sa bugas nga nahulog. Nahuwasan sya ug kalit ug nagkurogkurog. Nanglimbawot iya balahibo. Mitindog ang buhok dapit sa tingkoy. Wa nya nakita kon kinsa ang naglaparo kay medyo ngitngit man sa mga kahoy ang lugar. Nahuwasan sya ug dayon nikaratil sya ug lakaw nga way lingilingi.”Unsa man to uy!”, nakaingon si Julian nga grabeng kulbaa.

Naghalhal sya pag abot sa ila balay diin naghulat iya asawa ug duha ka anak. Ug dayon niyang gisaysay ang nahitabo niya diha sa lugar nga Insek duol sa tulay sa ilang barangay samtang nag andam iyang asawa sa panihapon. “Wala man ka mingon nga moagi ka. Nakahibalo na baya ka anang lugara”, sumpay sa iyang asawa nga nalooy nagtan-aw niya nga grabeng luspara ang nawong.

Rice Farming

Pero sap ag-uli nako sa pista saw a pay covid, daw nawala na ang kahadlok sa lugar kay aduna na may mga balay duol niini ug sementado na ang karsada ug konkreto na ang tulay. Wala na pod ang dakit ug dagkong kahoy daplin sa karsada. Pero sa paglabay nako  niining Insek nga lugar, manglibawot pa gihapon akong balhibo kay madumduman ko pa man ang paglaparo sa ulo ni Julian sa panahon sa among kabatan-onan.

Duna gyoy mga hitabo sa unang panahon nga dili gyod nimo hikalimtan hilabi na sa espiritong bahin sama sa lugar nga gitawag namo ug “INTSEK”, sitio Ilaud sa barangay Mayana. Hangtod karon kini nga estorya dili pa mahanaw sa hunahuna sa mga lumulupyo.

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A Quarrel Between Two People

            by Vic Odarve.

We were constantly troubled by their frequent quarrels as one of their long-time neighbors. Even minor conflicts are routinely addressed with insults, mocking, and yelling. The engaged couple revealed that they had fought for 30 years. They remained together for the sake of their children. The woman eventually decided to deliberately leave her husband for good now that they were all adults with their own families. She chose to live alone because divorce was illegal in her country. "I love him, but my patience has already reached the point that I had to leave him”, the wife told the barangay captain before signing the paperwork. I am sorry. "It's just okay," the husband said, "I can understand what she wanted. “The couple decided to sign a mutual agreement to live separately.

Couple in quarrel

Ten years had passed. Their eldest son and youngest daughter decided to go on a wedding vow. Both were invited. The ceremony was performed in one of the city's luxurious hotels. Sitting at the first table together with the newlyweds, the couple, now an old man and a lady, sat near to each other during dinner time. Both were quiet. As the dinner started, the old man immediately gave a piece of lechon manok to the lady and said, "Take this, it’s your favorite." The wife said, "This is the problem; you think so highly of yourself and have never thought of how I feel. Don’t you know that I hate lechon manok? " The old man’s temper was raised, but he managed to control it. Keeping silent for a while, he just behaved as if he had not heard anything, knowing that mumbling something would end in a quarrel.

After the social affair, they returned eagerly to where they lived. That night, both could not sleep. The old man got a bottle of local wine and got drunk. He phoned his old lady and sincerely wanted to tell her he was sorry for the lechon manok and to inform her that he still loved her. He never stopped calling her. He was deeply depressed.

Teach the child the meaning of life

On the other hand, the wife was still angry and could not understand how, after all these years, he still did not understand her that she hated lechon manok. But she still loved him. At that point, she decided not to answer no matter how the phone rang, knowing it was him.

The next day, a neighbor informed her that a man had died from a heart attack. And that was the time he had tried in vain to contact her. It was then she remembered he had previously had a heart problem. The last text she received that night said, "My dearest wife, I want you to know I will always be at your side, even to the ends of the world." I love you. "

Sometimes we think marriage life is a bed of roses. But it is not! For a couple, both must learn how to love each other.

 

MOUNT HERMON, A MYSTERIOUS MOUNTAIN

               by Vic Odarve.

Let's look at Mount Hermon. This mountain is 2,814 feet above sea level and is known for its spectacular splendor. It shares land boundaries with Israel, Syria, and Lebanon. It is the Jordan River's main source. Mount Hermon is a massive triple-peaked peak. One of its three summits is the highest point on the Mediterranean Sea's east shore. The transfiguration of Jesus Christ is said to have occurred on this mountain. This mountain is also where the 200 fallen angels descended from heaven, according to Enoch's account. The religious faithful, including Christians, Muslims, and Jews, have been profoundly affected by these occurrences.

Mount Hermon

JESUS' TRANSFIGURATION

Transfiguration is a dramatic change in appearance. In mathematical language, this is like transformations! A change of form in expressions or formulas makes our mathematical calculations simpler and easier! That’s why we have logarithms, Laplace, Fourier, Mellin, and Z transformations in engineering courses!

Jesus also does transformation. A dramatic change of appearance or transfiguration! It was witnessed by the apostles. He transforms into other dimensions – from earthly appearance to the spiritual or heavenly dimension of existence. Among the twelve disciples, only Peter, James, and John had witnessed their Master dramatically transfigured. This transfiguration reveals his glory as of the son of God. The true nature of his divine existence!

Fallen Angels

By transfiguration, Jesus gives his disciples a glimpse of what he looks like when he will be in his kingdom with his Father. Just a glimpse! See what happened! Jesus’ face shone like the sun, and his garments became white as light! The following are verses from Matthew 17: 1-2;

1 Six days later, Jesus took with him Peter and James and his brother John and led them up a high mountain where they were alone. 2 Jesus’ appearance was changed before them: his face shone like the sun and his clothes became bright as light.

This thing happened at Mount Hermon…. a mysterious mountain!

THE FALLEN ANGELS

There were two hundred fallen angels who descended to Earth at the summit of Mount Hermon. These watchers, as they are called in the book of Enoch, mated with humans. This class of spiritual beings oversaw the observance and study of creation. And what happened? They transgressed by intermarrying with humanity and introducing forbidden technologies to Earth.

Engineering Mathematics By Odarve

They saw that the daughters of Adam were beautiful and good-looking. All of them took wives. This was against God’s law as angels did not need to procreate like humans. As a punishment, they could not go back to heaven anymore. These angels violated both their own nature and their office. God will not forgive their sins. Having families, these angels taught their human wives’ charms, enchantments, astrology, cutting of roots, and acquainted with plants, sorcery, and others.

Since then, these fallen angels have been living in and around the area of Mount Hermon. Their hybrid children were monstrous giants called Nephilim. The aftermath of these giants was awful. Upon their death, they would release evil or demonic spirits that would remain bound to the earth. Since then, mankind won’t have any peace. That’s why we have demons and evil spirits.

It was believed that the tribe of Dan, from which the Antichrist would come, moved to this area during the days of the Judges. They adopted the Canaanite worship of these angels. The Caanites Gods, Baal and Ashtaroth, have their origins on Mount Hermon! The following are taken from the book of Enoch 6:1-3;

And the angels, the children of heaven, saw and lusted after them, and said to one another: "Come, let us choose our wives from among the children of men, and beget us children." And they were in all two hundred, who descended in the days of Jared on the summit of Mount Hermon, and they called it Mount Hermon because they had sworn and bound themselves by mutual imprecations upon it.

Again, this happened at Mount Hermon…. A mysterious mountain!

Today, this mysterious mountain is one of the hot spots in the Middle East. Christians, Muslims, and Jews have contested this mountain for thousands of years. After the 1967 Six-Day war, both Syria and Israel administered military posts on Mount Hermon’s slopes.

Today, thousands of visitors come and visit this mysterious mountain! Some folks believe that this mysterious mountain is one of the Earth’s portals to other universes. A gateway to another world! Nobody knows!

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