Sanjenbam Jugeshwor Singh is a regular contributor of Imphal Times. Presently, he is teaching Mathematics at JCRE Global College. Jugeshwor can be reached at: [email protected] Or WhatsApp’s No: 9612891339.

Wednesday, 19 January 2022 17:29 ### Portents of Imaginary number iota(i)

In 16th century, Venice formulae for solving equations were closely guarded intellectual property. Of particular interest to ballistics and fortifications, expert Niccolo Tartaglia pointed out quadratic and cubic equations which model the behavior of projectiles in flight amongst other things. These may well ring a bell with youto form the school math- quadratic equations having an x2 term in them and Cubic’s an x3 term. Tartaglia and other mathematicians noticed that some solutions required the square root of negative numbers and herein lies a problem. Negative numbers do not have square roots- there is no number that when multiplied by itself gives a negative number. This is because negative numbers when multiplied together yield a positive result like (-2) x (-2) =4 not -4. Tartaglia and his rival, Girolamo Cardano, observed that if they allowed negative square root in their calculations, they could still give valid numerical answers (real number as mathematicians call them). Tartaglia learned this the hard way when he was beaten by one of Cardano’s student in a month –long equation –solving duel in 1530. Mathematicians use ito represent the square root of minus one. This is called imaginary unit-it is not a real number, does not exist in real life. We can use it to find the square root of negative numbers though. This means that the square root of -4 is the square root of 4 multiplied by the square root of -1. In symbol = . The square root of 4 is 2 and square root of -1 is i, giving square root of -4 as 2i and -2i. The arithmetic of i itself initially posed an obstacle for mathematicians. With the imaginary unit, this seems to break down, with two positives multiplying to give a negative number i.e.ixi=i2 =-1. Equally, here two negatives multiply to give a negative i.e.-ix-i =i2=-1. This was a problem for some time and made some people feel that using them in formal mathematics was not rigorous. The work of mathematicians on imaginary numbers allowed the development of what is now called the fundamental Theorem of algebra. In basic terms, the number of solutions to an equation is always equal to the highest power of the unknown in the equation.

According to the University of Toronto, there are a variety of uses for imaginary numbers in the real world, most notably in the field of electrical engineering and measuring natural phenomena. An electromagnetic field, for example, requires imaginary numbers to measure because the strength of the field is determined by both electrical and magnetic components that must be combined into a single complex imaginary number to get an accurate measurement. According to Drexel University, imaginary numbers are further used when measuring phenomena that occurs in nature such as disruption created when water flows around an object. Imaginary numbers are quite useful in many situations where more than one force is acting simultaneously and the combined output of these forces needs to be measured. These forces can be measured using imaginary number makes getting an accurate measurement much easier.

Imaginary numbers have long been used in the most important equation of quantum mechanics. A field of physics that describes a very small world. When you add an imaginary number to a real number, the two together form complex number allowing physics to write out quantum equations in simple terms. But whether quantum theory requires these mathematical chimeras or simply uses them as a convenient shortcut has long been controversial. In fact, even the founders of quantum mechanics thought the implications of including complex numbers in equations were disturbing. In a letter to his friend Hendrik Lorentz, physicist Erwin Schrodinger was the first person to introduce complex number into quantum theory using the quantum wave function (sigh). Schrodinger found a way to represent an equation with real numbers only, along with a set of additional rules about how to use equation. Later physicists did the same in other parts of quantum field theory. However the question remains if there is no solid experimental evidences governing the prediction of these ‘’all real’’ equations. Is imaginary a simplification of option or does trying to work without imaginary losing the quantum theory of the ability to describe reality?

Another popular idea of imaginary number is the Fourier Transform, which states that any function can be made up of a lot of sine and cosine functions added up. This is particularly used in messy signals since they could be broken up into the frequencies that they are composed of, which can then be analyzed and manipulated. In the real world, this is helpful for audio processing, speech recognition, radar etc. The equation for Fourier Transform involved calculus but it is based on imaginary numbers. Imaginary numbers have prevalence in other areas as well. One of the ideas is in quantum mechanics as discussed above. When studying this alongside, other ideas you can see the prevalence of imaginary number in math. Additionally when dealing with control theory in engineering, graphs are used to portray the stability of system and how certain parameters change with respect to individual components of the control system. These types of systems are found in rockets, fighter jets, robots, autonomous vehicle and more. It is important to understand that you can not necessarilyrespect imaginary number in the real world. For instance you cannot just have5i pounds of cheese or 3i grams of sugar. Overall imaginary number helps simply the math for dealing with real world and has a variety of useful applications.

The result of study by researchers on imaginary number suggest that the possible ways we can explain the universe in mathematics are actually much more controversial than we thought. By just observing what comes out of some experiments, we can rule out many potential explanations without making any assumptions on the reliability of the physical device used in the experiment. In the future, physicists may need a small number of experiments built from first principles to reach complete quantum theory. In addition to this, researchers also said that their experimental set up, a rudimentary quantum network, may help outline the principles at which future quantum internets may work. Thank goodness that mathematicians fromm500 years ago to the present day, decided that imaginary numbers were worth investigating after all.

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Wednesday, 12 January 2022 16:55 ### Skill development for Sustainable Livelihood

As Mahatma Gandhi said ‘’If Indian Villages is developed the nation is developed’’ is true even today. India is an agrarian society where more than 70% of the population is living in rural area. The rural population mainly depends on agriculture and associated sectors of agriculture for their livelihood. The ability of the individuals in any society is necessity to vest them for social alteration, economic growth, contribution in development process. Therefore a nation progressing towards development requires institutions, entrepreneurship and skill development to initiate and achieve the course of change and changing societal structure and livelihood profiles. India is rich in human resource. What is needed now is a long term policy for development of human resources through education, training, skill development, empowerment and creation of congenial socio-economic, institutional and political environment for the fullest possible utilization of the vast untapped reservoir of human power and ingenuity.

In order to promote self-employment among the rural youth, Government of India has taken a two-pronged approach viz: enabling skill development and implementation of direct employment programs for lower skilled individuals. To create an institutional base for skill development in India, in 2009 government launched the National Skill development Policy (NSDP) with a target for skilling 500 million people by 2020. With the creation of National Skill Development agency (NSDA) in June 2013, the NCSD, NSDCB and Office of Advisor to Prime Minister on skill development have now been subsumed in NSDA. Ministry of Labour and Employment has taken a number of initiatives in the field of skill development and employment. In earlier days, most of the rural youths are comfortable with seasonal plantation jobs, no specified skill and education was needed; besides parents do not want to send youth to far-off urban and semi-urban areas for livelihood. But recent trends showed youth were attracted on skill development for their livelihood. Public-Private partnership (PPP) model for skill development of unemployed rural youth is very much needed. Based on this PPP model skill development for rural youth in various skill developments will improve self-employment, then more employment opportunity will enhance sustainable livelihood among the rural youth in Manipur too.

National Rural Livelihood Mission (NRLM) was launched by the Ministry of Rural development (MoRD), Government of India in June 2011. The mandate of the Ministry is rural poverty alleviation through programs directly targeted poor household. The major programs of this ministry that directly targeted for creation of assets, skill development and self-employment started with Integrated Rural Development Programs (IRDP) in the year 1980 and induced several other programs like the Training of Rural Youth for Self Employment (TRYSEM), Development of Women and Children in Rural Area (DWCRA), Supply of improve Tools to Rural Artisans (SITRA), Ganga Kalyan Yojana (GKY). On account of the multiplicity of programs, which were viewed as separate programs in themselves, the desire linkage among these were not established effectively. These were more concern with achieving individual program targets rather than focusing on the substantive issue of sustainable income generation. Based on the recommendation of planning Commission, the schemes of TRYSEM, SITRA, GKY and DWCRA were merged into a single self-employment program called Swamjayanti Gram Swarozgar Yojana (SGSY), implemented by the state Government.These self-employment programs aimed at work opportunity for rural special focus on poverty alleviation.

In case of Manipur, implementation of National Rural Livelihood Mission is very complicated. More than 90% of Manipur is the rural hilly areas while out of 9% valley area,majority are taken as urban area. The hilly area covers 20,082 sq.km and centrally located valley covers about 2,238 sq.km, accounting for only one-tenth of the total area of the state. The tribal groups are distributed in all the ten hill districts of Manipur. Scattered pockets are also found in the valley and urban areas. The oval shape small valley area is the targeted place for all section of the people in the state for any purpose. Thus for effective implementation of rural livelihood Mission, youth centered skill training was one of the options. Manipur Society for Skill development (MSSD) is an initiative of the Government of Manipur under National Skill development Corporation and State Skill Development Mission (SSDM) to enable youths to be skilled and to get employment opportunities in a holistic manner. The mission aims that the youths would be trained in skill as per their capabilities and merit to make employable. About 40% of populations in Manipur are in the age group of 15-29 years. They can act as agent of transformation, by being empowered with various employable skills which will enable them to make impact not only on their lives but also on the lives of other individuals.

The recently approved Pradhan Mantri Kaushal Vikash Yojana (PMKVY), a flagship scheme for imparting skill training to youths, focusing on improved curricula, better pedagogy and trained instructors. The training includes soft skills, personal grooming, and behavioral change at all. Prime Minister Narendra Modi launched Skill India Mission on 15th July 2015, on World skill Day. It is aimed at providing vocational training to youth across the country to over 40.02 crore people in the country by 2022. The formation of the National Skill development Mission (NSDM) has necessitated the need to re-examine the need for skill development in relation to rural livelihood in Manipur. This is felt more in a state like Manipur where the challenge emanating from the demographic dividend, rural and urban set up. As of 2016-17 youth unemployment (for the age group 15-35 years) in Manipur stood nearly 40%. Skill development can therefore be seen as the need of the hour for promoting rural livelihood in Manipur. Manipur is one of the highest unemployment in India which mostly belongs to youth in the age group of 15-29 years. Though youth have the zeal to do something new and innovative but due to lack of training opportunity, lack of skill, financial support they become frustrated and therefore sometimes indulged in consumption of drug or join insurgent groups. Nearly 7 lakhs are seeking for jobs in Manipur of which mostly belong to youth in the age group of 15-29 years. Higher number of unemployed is found in matriculate with 33.36%, closely followed by under matric with 31.08%. Intermediate or class XII account 18.82%, graduate 2.96%, post graduate 2.28, diploma or Engineering graduate with 1.5%. The highest number of unemployment (matric and under matric) show that youths belongs to the highest number of unemployment. Absence of professional training Institution is one of the hindrances to accessing skill training in rural Manipur. The success of skill entrepreneurship and vocational training depends on hard and soft skills and content of the course. Thus improving self-employment opportunities through skill development is the need of the hour. To promote sustainable livelihood through skill development, the rural youth need practicable updated knowledge rather than some traditional training with dull lectures or thick manuals.

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Wednesday, 05 January 2022 17:42 ### Oil Palm: An Apple of Discord

On 18 December 1591, a seven-month sea voyage from Africa to England ended when a ship anchored at Limehouse docks in London. Along with 150 elephants tusks and 589 sacks of pepper the ship carried 32 barrels of palm oil. It is thought to have been the first arrived into Europe of what would become perhaps the most controversial plant product that is not a drug. To say that palm oil is divisive is an understatement. To its advocates, it is a cornerstone of economic development, making efficient use of land and supporting millions of smallholders through profitable international trade. To its detractors, it’s a cause of deforestation and social conflict, a direct threat to endangered species and a contributor to climate change. With demand for palm oil rising rapidly there is growing concern about its sustainability and awareness that some palm oil is ‘’good and some is bad’’. The term covers various things we get from a species of tropical palm called’’Elaeis guineensis’’. Crude palm oil is squeezed from the palm’s fleshy red fruit; palm Kernel oil is extracted by crushing the fruit’s hard stone. Finally many palm oil derivatives are acquired through industrial process which together for about 60% of global palm oil use.

Oil palm trees are native to West Africa but were introduced to tropical regions of South-east Asia and Latin America in the late 19thcentury. Oil extracted from the fruit was traditionally used in Africa for cooking but has now found a wider range of uses: as a substitute for animals fat such as butter in backed products, soaps and cosmetics or as a basis for biodiesel. Around half of the packaged products in supermarkets contain palm oil. Although palm oil is not particularly healthy (it contains higher levels of saturated fat than most other vegetable oils), it has many advantages: compared to soybean(the world’s second most widely consumed vegetable oil after palm oil), and oil palm cultivationrequires only one-tenth as much land, one-seventh as much fertilizers, one-fourteenth as much pesticides and on-sixth of energy to produce the same quantities of oil and is therefore very cheap. In addition, palm oil is highly resistant to oxidation, making it suitable for frying and giving it a large shelf life. As a result, consumption of palm oil has doubled over the past 15 years to nearly 8 kg per inhabitant of the global and shows no sign of slowing down. Until the 1960s, oil palm was mainly grown in Africa but since then production has shifted to south-east Asia. According to FAO statistics, Indonesia (53% of global output) and Malaysia (29%) are the leading producers followed by Thailand (4%), Nigeria (2.6%), Colombia (2.3%) and Ecuador (1%). The top importers of palm oil are India (17.5% of the global total) and China (10.8%). Overall, Asia imports 53.5% of all internationally traded palm oil, while Europe takes 24.7% and Africa imports 14.1%, other countries account for the remaining 7.7%.

Oil palm is something of a wonder crop. It yields 4-10 times more oil per hectare than other source of vegetable oil such as soybean or coconut palms. This makes it an efficient and profitable use of land. The economic value of palm translates into jobs, infrastructures and tax revenues. In Indonesia and Malaysia, some 4.5 million people earn a living from the palm oil industry. In Indonesia alone, another 25 million people depends indirectly on palm oil production for their livelihoods. This all means, palm oil could play a big role in reducing poverty-if done right. The palm oil rush of recent decades has come at considerable cost to forest and people who depend on them, so it has become so controversial. Palm oil production has been associated with corruption, forced eviction and land grabbing. It has sparked conflict with local communities, including indigenous people. There have also been serious concern about forced labor and child labor and violations of workers right on some plantations. Oil palm now covers a combined area about the size of Syria and an estimated 60% of this land was previously covered with forest. Much of the deforestation has been in Indonesia and Malaysia destroying the habitat of rare creatures such as Orangutans, tigers, rhino and elephants. Greenpeace estimates that in Indonesia alone, rainforest cover corresponding to the size of around five football fields disappears every single minute. A study reports that a booming small palm oil production is largely to blame for it. Group such as Greenpeace; have documented how rainforest are being eroded at a rapid pace to make way for oil palm plantations. That makes oil palm a major climate killer. Peat land believes to be reservoir for huge amounts of carbon, is also being burned and cleared for oil palm plantations. That makes the carbon foot-print of a liter of biodiesel up to 2000 times worse than a liter of conventional fossil –based fuels.According to a recent study, replacing rain forest with oil palm plantations release 61% of the carbon stored in the forest mostly into the atmosphere. Each hectare of rain forest converted release 174 tons of carbon. The ubiquity of palm oil and the growing demand for it highlight the scale of the challenge. Between 2000 and 2015, the global average amount of palm oil consumed per person each year doubled to 7.7 kg. Demand for palm oil is set to triple from 2015 levels by 2050, with much of the growth coming from market with low sustainability requirements.

A steadily growing oil palm monoculture is also destroying biodiversity and contaminating the Earth with large amount of pesticides and manure. Environmental experts say that certifying oil palm amounts to nothing more than ‘’green washing’ ’because large agriculture companies and local corruption have an easy time dodging the sustainable standard laid down by the certification. They point out that oil palm plantation aren’t just causing environmental problems but also social upheaval. They documented hundreds of conflict between local communities and palm oil producers in the Island of Sumatra in Indonesia. In Colombia, tens of thousands of people are said to have been forcibly removed from their land to make way for large scale oil palm plantations. International human rights groups as well as organizations in Colombia say the palm oil industry is closely linked with paramilitary and drug baron in Colombia. They say that drug money is laundered by-investing in the plantations. On one hand PM Modi said that agriculture scientists and agro economist have pointed out the potential of N.E farmers to take up oil palm plantations. He further said, oil palm cultivation in N.E would be a big help to the country and farmers community of N.E. He even mentioned about the policy of oil palm cultivation in his speech at Hapta Kangjeibung yesterday ( 4/01/2022). Accordingly Government of Manipur constituted the oil palm Mission Manipur on 20th August 2021 to start cultivation of oil palm in the hilly regions of Manipur to control jhum cultivation and eradicate poppy plantation. However, according to experts, oil palm cultivation is not suitable in high altitudes like hilly regions of Manipur. They opined that it is not advisable to practice oil palm cultivation in far flung areas. Oil palm cultivation in a bio-diversity hotspot area like Manipur will be more damaging to the environment than poppy plantation. Besides the disadvantages of monoculture, chemicals used in oil palm cultivation will have a bearing on the ecosystem of Manipur.

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Wednesday, 29 December 2021 17:36 ### Quantum Vs Classical Computers

The world of quantum physics is bizarre and most difficult to understand. Think of the formulation like ‘’Heisenberg’s Uncertainty Principle’’ where you cannot simultaneously measures the momentum and position of any particle or thought experiments like ‘’Schrodinger’s cat’’, where a cat is kept inside a sealed box with radioactive substance and the cat is simultaneously both alive and death or phenomena like quantum entanglement where two quantum particles can remain somehow entangled irrespective of the distance between them. All these properties/phenomena sound absurd but since quantum mechanics is a science of probabilities, it makes the absurd look possible. There are many ways to understand why quantum mechanics is hard to simulate. Perhaps the simplest is to see that quantum theory can be interpreted as saying that matter; at a quantum level is in a multitude of possible configurations (known as states). Unlike classical probability theory, these many configurations of the quantum state, which can be potentially observed, may interfere with each other like waves in a tide pool. This interference prevents the use of statistical sampling to obtain the quantum state configurations. Rather we have to track every possible configurations, a quantum system could be in if we want to understand the quantum evolution.

Quantum mechanics was developed between 1900 and 1925 and it remains the cornerstone on which chemistry, condensed matter physics and technologies ranging from computer chip to LED lighting ultimately rest. The conventional method of computing is the most popular method for solving the desired problems with the estimated time complexities. Algorithms of searching, sorting and many other are there to tackle daily life problems and are efficiently controlled over time and space with respect to different approaches. Certainly we use bits (either 0 or 1) for storing the information and with the help of these 2 bits; we calculate Giga to Tera to Petabytes of data and even more with quite unparalleled efficiency. Our CPU calculates at average 2.4 GHz apparently, it looks like that all combinations are calculated simultaneously but of course they are distinct from each other and CPU calculates one at a time. The fact is that our CPU calculates each combination one at a time. Here arises a big and advanced research question- can all of them be simultaneously calculated at once without having any multiprocessors? To answer this crazy question, Quantum Computing came into the picture. Quantum Computers were proposed in the 1980s by Richard Feynman and Yuri Manin. The intuition behind quantum computing stemmed from what was often seen as one of the greatest embarrassment of Physics: remarkable scientific progress faced with inability to model even simple system. In 1976, Roman Stanislaw ingarden of Nicolas Copernicus University in Torun, Poland published one of the first attempts at creating a quantum information theory. In 1980, Paul Benioff of the Argonne National Laboratory published a paper describing a quantum mechanical model of Turing machine or classical computer, the first to demonstrate the possibility of quantum computing. In 1981, in a keynote speech titled ‘’ Simulating Physics with Computer’’Richard Feynman of the California Institute of Technology’’,argued that a quantum computer had the potential to simulate physical phenomena that a classical computer could not simulate. That was the first time, the term Quantum Computer was arguably introduced. Following that, in 1994, Peter Shor of Bell Laboratories, developed a quantum algorithm for factoring integers that has the potential to decrypt RSA-encrypted communications, a widely used method for securing data transmission.

Quantum computing is the branch of computer science that is based on the principle of the superposition of matter and quantum entanglement and uses a different computation method from the classical one. Quantum computers look very different from anything we’ve associated with computers for decades. The technology is centered on the use of quantum bits or qubits, units of information, which represent zeros or ones, qubits, can represent both at the same time. At a very basic level, a high voltage, on a transistor or a state represented a 1 and a low voltage represented by a 0. And that is how bits are constructed. Quantum Bits or Qubits on the other hand are constructed by the superposition or entanglement of quantum particles and hence making quantum computing fundamentally different from classical computing. Qubits store 2 raised to power N numbers, which means that if a Qubit is added (N becomes N +1), the storage doubles, thereby making the growth exponentially. This translates into significant computing power thereby making Quantum computing much more powerful than classical computing. There are logic gates, as there are in a classical computer but they have a fundamental different. Quantum logic must be non-dissipative. Therefore you cannot have the classical three-port logic gates such as AND, OR etc. Instead you need a non-dissipative gate-type such as the four-port controlled NOT (CNOT) gate. It only takes a minimal set of quantum logic gates to build a universal quantum computer which is similar to classical logic needed for a universal Turing machine. Just as a quantum computer can store multiple numbers at once, so it can process them simultaneously. Instead of working in serial, it can work in parallel. Only when you try to find out what state it’s actually in at any given moment does it collapse into one of its possible states and that gives you the answer to your problem. A quantum logic gate acts on a quantum state to transform it according to some conditions. The condition could be a local setting or it could depend on the state of another qubit. Such a conditional logic is very important because quantum information can interact and consequently affects the evolution of the entire quantum system.

There is couple of reasons for this. Unlike classical computer, quantum computers are not easy to construct. Building a quantum computer simply means building complex networks of logic elements. Quantum mechanics is deterministic if we exclude measurement. That means only future quantum state can be predicted based on the present state. The design of a quantum algorithm needs to take into account what you can do such that measurement will correspond to what you want. This is the domain of quantum algorithm design. Computer scientists believe the technology needed to create a practical quantum computer is years away. Quantum computers must have at least several dozen qubits to be able to solve real –world problems.

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