The Cube Root: A New Short Cut?

In the first week February (2012), Nirbhay Singh Nahar, an Agra-based retired chemical engineer , who is also an amateur mathematician, claimed that he has figured out a formula to work out cube roots of any number using a simple calculator within a minute and a half by just addition and subtraction. Nahar has yet to disclose the algorithm that the scientific community needs to approve and incorporate. The development if proved is interesting, although not a path-breaking discovery.  However, for the student community, especially those planning to take competitive examinations it could prove to be a wonderful short-cut even using a calculator.

In a sense, Nahar has started to follow in the footsteps of the great Indian Mathematicians who made seminal discoveries that aided the development of architecture and engineering in a big way. Cubes have always fascinated mathematicians. Our beloved number theorist Ramanajuan, while admitted to hospital, on hearing that his mentor Hardy had arrived in a taxi with the number 1729, instantly replied that it was the smallest number that could be expressed as the sum of two distinct cubes (1³+12³=1729=9³+10³).

Deriving the cube root was an interesting cerebral challenge among all ancient mathematical traditions. Although the Chinese, Indian, Greek and Arabic mathematicians formulated several algorithms to find the cube root of any given number, an easy algorithm is still elusive. Chapters 35 and 36 of Vedic Mathematics (Motilal Banarsidas Publications) are dedicated only for methods to find cube roots. The Crest of the Peacock by George Gheverghese Joseph codifies all the ancient works towards this. Wikipedia provides a very simple method (refer article Cube Root) to compute cube roots using a non-scientific calculator, using only the multiplication and square root buttons.

Our world is a multi-dimensional one with most objects where, either animate or inanimate, possess a length, breadth and height/depth. Measurement each of these dimensions enables one to calculate the space or volume it occupies. What happens if the length, breadth and height/depth of some objects are similar? Then that object is called a cube. Historically, solids of similar kind are of great interest to man. The cube is also known as regular hexahedron, only because it has six equal faces. Considering ancient Greek philosopher Plato had extensively discussed cubes among others which are known as Platonic solids.

Therefore, depending on the total volume of the objects, architects and engineers seek to optimize the usage of space. Therefore, finding the cubic root proves relevant. Moreover with the availability of advanced computers it will not be a mind boggling exercise. But imagine a student getting a question in a test to solve the equation n³-k=0, where k is any given number, integer or non-integer. Owing to limited time in an examination environment, the best algorithm needs to be used to solve the problem.

Finding the cube root, without the help of a machine, of perfect cubes such as 8, 27, 64, etc itself is a complex problem in mathematics. Now, finding the cube roots of other integers which are not perfect cubes such as 2, 3, 4, 5, 6, etc becomes a harder problem. This is not the end. What about the non-integers? Suppose the volume of an object is something like 2.53, how does not figure out its length?

In day-to-day life one often gets these types of the numbers only. For instance, if a farmer wants to store his grains so that not a small space of his store house is to be wasted. Because a cube has the largest volume among all the cuboids, finding the cube root will solve the problem. In cities where space is limited and costly, cubical structures are the best to store things. Hopefully, Nirbhay Singh Nahar’s discovery should simplify life for those who choose to confront mathematics on a day-to-day basis, either as students tackling examinations or hi-tech engineers involved in design and development works.
(This was published as Equate and Apply in Deccan Herald on March 1, 2012)

Two Symbols in the Syro Malabar Marriage - Tali and Manthrakodi

Tali – Minnu

Talikettu or Minnukettu is supposed to be the most important public ritual by the bride and the groom in a marriage ceremony in the Syro Malabar Rite. There is great importance for Kettikkunna Priest. Marriage itself is called Kettukalyanam. Bridegroom is known as Kettiyavan or Tali kettiyavan (one who tied the Tali).

Tali is the foremost symbol of the Covenant of Marriage in India. Bride wears it forever to signify the permanent commitment and loyalty in the marriage. It is removed only just before the burial. After that it is given to the Church.

It is made in the form of a cross with 21 golden beads.  21 = 3 x 7. Cross signifies the Risen Lord. 3 stands for the Trinity and 7 for the sacraments.

Marriage is the union of two bodies and two souls. Trinity is the most important symbol of union.

Matrimony being a Sacrament, remembrance of sacraments gives the couple to remember about the Grace they have received through this sacrament.

It is attached to a cord made of 21 strands drawn from the manthrakodi (wedding cloth (sari)) and entwined in seven sets of three each.  Three again signifies the Trinity and Seven, the Sacraments.

The priest who blesses the marriage (mostly a very close relative of the bride) blesses the Tali. The groom ties the tali around the neck of the bride assisted by the groom's eldest sister. 

The word meaning of Tali is key.  Hence, this is also a symbol of the mutual ownership.. It signifies the authority of one over the other. In biblical terms, husband has the authority on the body of his wife and wife has the authority on the body her husband. (1 Cor 7:4)

Manthrakodi

The priest blesses the manthrakodi. Manthrakodi is imposed on the head of the bride by the groom with the assistance of his eldest sister. This symbolizes the protection and care the bridegroom promises to the bride. The protection and care given by the father of the bride is now taken over by the groom.  

Manthrakodi also symbolizes the new life begins with the marriage. Immediately after the Marriage Rites and the Holy Qurbana, bride wears the manthrakodi and thereafter for all receptions and major functions she wears it. She keeps it for ever.

Bride's head is being covered with Manthrakodi

Tali and Manthrakodi are typical Indian cultural symbols associated with marriage. In olden days Talikettu or kettukalyanam  and Marriage (Pudamuri Kalyanam) were done separately. Groom ceremoniously ties the Tali. But the real marriage is Pudamuri kalyanam. Here, the groom gives the bride kodi pudava (new cloth). Once she receives it, they start living together.

Nowadays, Talikettu and Pudava giving are done in the same function.

Pudava kodukkal is the Manthrakodi Aniyikkal. By this the groom assures that he is there to provide everything for the bride. Cloth is more important to woman than it is to man.

Elevator Etiquette

An Elevator is a very small room where you live with others for few seconds.

Are you happy with the life in this tiny room?

To feel comfortable in your elevator experience and to make others feel comfortable, follow these tips:

DO's

• Take the stairs to your destination if it is one or two floors only, up or down. 
• Allow others to exit the elevator before you attempt to enter.
• On entry, stand close to the walls of the lift. Do not block the way for others.
• Wait briefly to accommodate anyone running to take the elevator.
• Give preference to staff and any one elderly.
• Give others their personal space in an uncrowded elevator.

DONT’s

• Do not block the way while entering or exiting.
• Behave responsibly while inside the elevator.
• Press the button for your desired floor only.
• Avoid crowded lift if you are feeling unwell. Minimize coughing or sneezing while in the lift.
• Don’t hold up the lift for long for your friend or colleague to come in.
• Do not draw or scratch on the walls of the elevator.
• Do not litter the lifts.
• Do not eat or drink or carry food in the lift.
• Do not use cellphones, or any electronic gadget while inside the elevator.
• Refrain from talking loudly in the elevator.
• Do not stare at others
• Do not break wind

Finally, the most important thing is 

• Do not panic, in case the lift fails.

Sixth Friday of the Great Fast

Genesis 19:26-30

Joshua 22:10-20

Romans 15:1-13

John 11:1-45

The Divine Plan is revealed from time to time. To be exact, it is understood to the mortals from time to time. Our God is not a dictator who imposes everything on the mortals. At least since the creation of human beings this is true. God is ready to ‘change’ His plans with the request of the just. God is forced to ‘change’ His plans with the wrongdoings of the unjust. The destruction of Sodom is an example to understand the heart of Yahweh. Sodom was not created for destroying. God does not create anything for destroying. Sodomites invited curse and total destruction. Yahweh was forced to change His plans on Sodom and destroyed it completely because of the cry for justice against it! But, even after such a hard decision being taken by Yahweh, He was ready to change it at the request of His beloved, Abraham. He kept on heeding to the bargains of Abraham and decided at the request of him. But Sodom welcomed self-destruction by their actions. Even at this massive destruction, God remembered Abraham and hence saved Lot and his family. Our God is a God with a tender heart.

Faith in God is primarily an individual responsibility. But it has a community aspect also. Every faith community has a role in keeping the members together. The response of Israelites to the action of the Reubenites, the Gadites and the half-tribe of Manasseh is a justified one. Community as a whole must make sure that everyone is waking in the Way. In this era of increasing migrations in many forms, the Mar Toma Nasranis should take initiatives like the Israelites to bring back their brethren who deflected from true faith.

Paul wants us to be strong and liberated and hence to help the weak. When each one is strong and liberated, the community is strong and liberated. Once each community is strong and liberated, the whole world is strong and liberated. A world which is strong in praising in one voice God, Father of Christ Jesus by the power of the Holy Spirit is the liberated world.

Jesus did what his Father wanted to do. Jesus did how his Father wanted to do. Jesus did how his Father did things. With a tender heart, Jesus restores Lazarus back to life. Jesus as a man was risking His life in doing so. By giving life He surrendered His life. Yahweh was there to help Lot because of His attachment to Abraham. A true believer can truly ‘change’ the heart of God. He can truly experience the tender heart of God. Jesus did the impossible because of His attachment to Lazarus and his family.

Great Fast is a season to experience the tenderness of Yahweh’s heart !

Sixth Sunday of the Great Fast

Genesis 19:1-7,9-26

Joshua 21:43-22:9

Romans 14:13-23

John 9:39-10:21

Quite often, we find it difficult to understand the message and meaning of natural calamities. Disasters and Catastrophes are always eye-openers for the human beings. These days we have first hand experience of tsunami, Flood, Volcano, Earthquake etc. God is not in favour of those are completely going against a divine order. Sexual aberrations are always against divine plan.

Condemnation and destruction of Sodom is described in the first reading. In the modern world, one of the greatest aftereffect of Sexual Aberrations is AIDS. Even a non-believer can understand the effect of AIDS and keep away from the misuse of sexual power.  Lot was dear to Yahweh. Hence He protects him in the midst of a massive destruction. God is mindful of His faithful always. Hence being faithful to Him is the only vow we need to have and the rest is assured. He will prepare a Zoar for His beloved ones.

The sum total of all a believer need to do is there in the words of Joshua: “love Yahweh your God, follow His paths always, keep His commandments, be faithful to Him and serve Him with all your heart and all your soul.” To believers who stick to the above advice of Joshua, Yahweh gives them peace throughout their land and not one of their enemies would be able to stand against them. Faithfulness to God is highly rewarded.

A true believer is a person with convictions. Faith itself is the greatest conviction. The convictions should lead one in one’s life. It is not in what others do that convictions and actions of one are to be based but in one’s own belief. Food habits, Languages, Complexion, Family, Culture etc. are always matters of dispute in people’s life. A true Christian should be able to celebrate the differences because Paul says:”nothing is unclean in itself, it is only unclean for those who consider it unclean.” Celebrating the differences also leads to understanding the other as an individual and hence avoiding unnecessary conflicts.

Jesus declares in no uncertain terms that He is the Way. Jesus is the Way through which everyone needs to reach God. The sight of a person is judged by his seeing of this Way. If somebody fails to see the Way, he is blind. Jesus gives us the gift of sight to see the Way and to enter through the Way. If one has found this true Way, he would abstain from Sexual Aberrations, he would keep the commandments of Yahweh and love Him above everythingelse and do not cause scandals to his brethren. The Great Fast is a time for introspection to check whether we are in the Way.

Fifth Friday of the Great Fast

Genesis 18:1-19

Joshua 14:6-15

Roman 13:1-14

John 8:30-59

God visits us regularly. How do we recognize Him? It is through our actions that we and others feel the presence of God among us. For Abraham, all his actions testify that he is visited by Yahweh regularly. For a person who acknowledges the regular visit of God, the the bond among them is very thick. Both the parties are in a helpless situation to avoid each other and to hide things from each other. This passage is an obvious example of this. Yahweh-Abraham relationship is one of the greatest Divine-Human encounters in the history of humanity.

Rewards for the ones who obey God are in abundance. Abraham, Isaac, Jacob, Moses, Joshua are examples for this. Caleb son of Jephunneh is another one in the line. He was bold enough to say that he has faithfully obeyed Yahweh his God. He gets the city of Hebron as an inheritance in return to his commitment to Yahweh. His trust in Yahweh is what is more important. He says, “if Yahweh is with me, I shall drive them (a race of giants) out as Yahwheh said.” With God, nothing is impossible.

Duties and responsibilities of a Christian are very categorically specified in Chapter 13 of the letter of St. Paul to the Romans. Christianity is a way of life. It is a life in the path of the Nazarene. When we are in this world, we are expected to accept and respect all the legitimate authorities. Christians live as salt of the earth. Christianity improves the quality of life in any social setup. Paul justifies his arguments by asking us to be in love with everyone. For, love cannot do the neighbour any harm and it fulfills the whole Law.

Are we the children of God? How do we know it? Abraham justified and testified through his actions his relationship with God. He proved that he is a true son of God. Joshua and Caleb through their actions proved their legitimacy. Paul advocated for the true sonship of God by fulfilling the commandment of love. If we are children of God, we will do accordingly as God wanted us to do. Jesus challenges us to prove by our actions our legitimacy. If we are from God, we hear the words of God and we do according to the words of God. This is the surest test to prove what we are.

Fourth Friday of the Great Fast

Genesis 14:18-15:15

Joshua 9:1-14

Romans 11:25-36

John 7:14-36

Divine-Human encounter is most sublime in the Yahweh-Abraham relationship. In the Abraham episode we see the human face of Yahweh and divine transformation of Abraham. His call and response, his subsequent actions and his final atonement are unique. But this is the a blue print for anyone who wishes to have a divine experience. His encounter with Melchizedek, king of Salem and a priest of God Most High, his response to the offers of the king of Sodom, his hope in the hopelessness and his destiny were not accidental. They establish Abraham as the father of faith.

Prudence is a gift of God. In taking decisions in life, this gift has to be efficiently used. Unless one is prudent and vigilant, the distance to trouble in one’s life is much less. Here, Israelites are bluffed by Hivites because of their quick judgement and lack of prudence. On the contrary, Hivites saved themselves from complete destruction by their prudent action.

For Paul, the gifts and the call of God are irrevocable. Jews and now Christians have an upper hand in the process of Revelation. But this irrevocable call and gift from God gives greater responsibility. Gospel and patriarchs give a responsibility that is unavoidable. Paul is a perfect representative of those people who were responsible to their call and grateful to the gift they received. As a Jew and as a Christian, he is in the rank of the patriarchs.

Jesus tells what His origin is and foretells what He would do. He asks us to learn the obvious, the priority of mercy over law. What law intended was love and mercy but what it lacked was them. It is this contradiction that led to the Original Sin and the subsequent sinful nature of human beings. It finally led to the Crucifixion of Jesus. Even now the message is clear, i.e., “Stop judging by appearances, but judge justly.”

Revelation of God was not an exclusive one and hence salvation is not a monopoly of some group. There are parallel ways and diversified means whereby God revealed His plans to all the created beings. Melchizedek is the best example for this. God wants us to look deeply into ourselves and proclaim publicly His plan on each one of us during this Great Fast and subsequent seasons in our lives.