The significance of Mach numbers

This article is for time-pass.

Supersonic and trans-sonic flights are those that are greater than or around the speed of sound. They are an interesting and difficult region of flight because the assumed characteristics of the atmosphere no longer hold water.

When a body moves through the atmosphere, a kind of pressure wave is generated and sends an advance warning to the air ahead that a body is 'coming'. These pressure waves travel at the speed of sound. As long as the body is moving at low speeds through the air, the air ahead adjusts itself accordingly and makes way for the body.

But when the aircraft moves at speeds close to the speed of sound, the air ahead gets no 'advance' warning about the incoming body. Instead, the airflow comes up against the object all of a sudden. This is responsible for the changed behaviour of the airflow at transsonic and supersonic speeds.

At this juncture, we have to discard all our traditional assumptions about airflow. Air at low speeds prefers smooth surfaces; air at high speeds prefers sharp and pointed corners. This is one of the reasons behind the 'Delta' configuration for supersonic aircrafts.

The absolute speed of the aircraft or the absolute speed of sound doesn't matter; what matters is the ratio between the two. Again, the speed of sound is not constant, it decreases with increasing altitude. Thus the relative speed of aircraft (as a fraction of the Mach number) increases with increasing altitude.

On the other side of the sound barrier, we face an entirely new world: the supersonic and hypersonic zones. Aircraft are specially designed for flying in these regions of speed. Our knowledge of these regions is better than our knowledge of the transsonic speed zone. Therefore, the pilot's aim is to get through the sound barrier as soon as possible.

In the olden days, when a speed record had to be set, the pilot waited for a warm day, because the speed of sound would be highest on those days. High-speed flying required the speed of sound to be as high as possible. But today, we soar for new heights and new speeds, and can no longer be bound by the speed of sound.

Hindustan and Balkanization

The spat between Bal Thackeray and Sachin Tendulkar is too recent in memory. Also recent is the behaviour of the MNS MLAs against another member for taking the oath of office in a different language. But though the state of Maharashtra may be unduly in the focus due to these incidents, they are by no means confined to one part of the country, nor are they going to disappear unless we confront the problem.

Ever since the agitations of the 1950s produced linguistic governing entities, the nation has always been divided along regional lines. But it is only in the recent times that claims of exclusivity have reached epidemic proportions. Every special interest group seems to think that the concept of region belongs only to the natives of that region.

This phenomenon reflects a deeper problem: the failure of the state (as opposed to the centre) as a viable governing entity in India’s federal system. No longer are state governments able to manage their finances. Doling out of freebies has all but emptied their treasuries and they are dependent on the central government’s handouts and national-level projects for their well-being.

The above-mentioned feature of the Centre-State relations should act as an effective barrier against the disintegration of the country, for the resulting splinter-states would be unviable entities. But that is not the problem facing the country now. Special interest groups now desire that the jobs in that particular region be given only to the natives. This militates against one of the fundamental rights of the Indian citizen enshrined in our Constitution: the right to settle down and earn a living in any part of the country.

Institutions like the Indian Railways and the State Bank of India belong to the whole country, not just to a particular state. These companies have the right to choose the best employees and generate the maximum revenue for the country. Of course, social justice is also a mandate for these companies, but the concept is being stretched out a bit too far.

There is another thing that is intriguing: Why are these Senas so concerned about Mumbai and not about their rural areas? The same philosophy holds good for other regions.

Perhaps, the answer can be found in the fact that much of Maharashtra’s revenue is generated by Mumbai. A separation of Mumbai from Maharashtra (envisaged by some as an autonomous Union Territory) would entail a serious loss of income and political suicide. Again, as I have pointed out in one of my earlier blogs, cities are the magic pot from which money and jobs flow out, and which can be easily milked. This is true for the larger, dynamic and more cosmopolitan metro areas.

Another reason for these agitations is that they offer a convenient distraction from the real and pressing issues. No longer do we get food at affordable rates. Nor is employment generation keeping up with economic growth. Any serious debate on these issues will provoke a backlash against the entire polity.

This brings forth another point: the discrimination of regions within a particular state. As it turns out, Andhra Pradesh, which was the first state of India created on a linguistic basis, is now divided between its Telengana region on one side and the Rayalaseema and coastal Andhra regions on the other. This is proof enough that linguistic division, though well-intended, was a flawed exercise, and fifty years later, has only reopened old wounds. The division between western Maharashtra and Vidarbha have also been documented. A political party (which fortunately did not win any seats this time) have also talked of dividing Tamil Nadu into northern and southern parts.

Increasingly, it is observed that the results of the General Elections are an aggregate of the results of the individual elections of the states. This reflects that, even though the states are dysfunctional entities, the people are increasingly voting based on local issues (which should ideally be confined to state assembly elections).

I am not being optimistic or pessimistic on the above issues. What I want to say is, that, as a nation, we are facing some problems, and these problems are not going to go away unless they are urgently addressed and tackled by the polity, the civil society, the intelligentsia and the media. Instead of uniting behind Sachin Tendulkar’s remarks and against Bal Thackeray’s, (even though that may be the right thing to do in the immediate present) we must do some soul-searching into why we have ceased to function truly as a federal republic.

Jawaharlal Nehru: An Enigma

Today is Children’s Day. It is so celebrated because it commemorates the 120th birth anniversary of Pandit Jawaharlal Nehru, India’s first and longest-serving Prime Minister.

Unlike Mahatma Gandhi, Nehru has been subject to far greater criticism during his period and also in recent times. It is often pointed out that he was responsible for India’s partition at the time of independence. It is possible, although a number of his contemporary personalities were collectively responsible for the tragedy of partition.

Nehru’s legacy has been more widely debated than that of any other leader in India’s history. It was Nehru, who advocated complete independence and sovereignty from the British Empire, unlike others, who were content with the dominion status, in which the monarch of England would be India’s head of state. Again, it was Nehru, who stressed that the princely states had no place in an independent India.

Nehru’s contribution as the Prime Minister of India was as important as his contribution to the freedom struggle. He advocated an active role for the State in economic activity, and was responsible for setting up of a number of public sector undertakings. As the economic crises of today’s times have shown, the market cannot be allowed to have a free run. He was responsible for setting up of AIIMS, IITs and IIMs. He also set up the National Book Trust and the Literary Academy to promote national integrity.

In the international sphere, Nehru promoted the Non-Aligned Movement, which advocated a stand independent of the two major Cold War blocs. Though the relevance of the non-aligned movement has been questioned in recent times, it is important for every nation to articulate an independent stance in international affairs.

On the Kashmir issue, Nehru originally promised to hold a plebiscite as per the resolution of the United Nations, but backed off from it as the other resolution of the U.N. was not fulfilled, namely the withdrawal of Pakistani troops from Kashmir. But he was also responsible for the division of the Indus river basin’s waters between the two countries, which has stood the test of time.

Probably, Nehru’s greatest error of judgement was in not anticipating a Chinese invasion of India in 1962. Nehru thought that, as both countries were former victims of imperialism, they would not aggress on each other’s territories. But this proved to be a great miscalculation, as even today China lays claims on Arunachal Pradesh.

Much has been talked about Nehru’s relationship with Edwina Mountbatten and how it influenced his decision-making. In my opinion, any examination of others’ personal lives will always bring skeletons out of their cupboards, and it is in the best interests of etiquette not to scandalise people.

Nehru is remembered as ‘Chacha’ or Uncle for working for children all through his life. But he remains controversial due to various decisions of his which have had an impact on our polity. Probably the two sides of his legacy will forever remain an enigma.

Beautiful Fractals

The dictionary defines fractals as “a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry.” Indeed, fractals are some of the most beautiful forms produced by dry mathematics. A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.

[The following are extracts from the Wikipedia entry for fractal.]

A fractal has the following features:

• It has a fine structure at arbitrarily small scales.
• It is too irregular to be easily described in traditional Euclidean geometric language.
• It is self-similar.
• It has a simple and recursive definition.

Fractals are considered to be infinitely complex.

One way of classifying fractals is according to the way they are generated.

• Escape-time fractals: They are defined by a formula or recurrence relation at each point in a space.
• Iterated function systems: They have a fixed geometric replacement rule
• Random fractals: They are determined by probabilistic processes.
• Strange attractors.

Fractals can also be classified according to their self-similarity.

In nature, fractals can be found in clouds, snowflakes, rivers and lightning.

Applications of fractals include

• Fractal landscape or Coastline complexity
• Generation of new music
• Generation of various art forms
• Signal and image compression
• Creation of digital photographic enlargements
• Seismology
• Soil Mechanics
• Computer and video game design
• Fracture mechanics
• Fractal antennas – Small size antennas using fractal shapes
• Small angle scattering theory of fractally rough systems
• Generation of patterns for camouflage
• Digital sundial

Addiction: Impact on the Social Animal

The dictionary defines addiction as “being abnormally tolerant to and dependent on something that is psychologically or physically habit-forming”. Normally, the word is used to denote a person’s craving for narcotic drugs, but sometimes people use phrases like ‘I am addicted to my work.’

What is addiction? As the definition says, it implies three things [with respect to the subject of addiction]:

• The addict must have an abnormal tolerance to and dependence on the target subject.
• The subject must have a physical or physiological impact on the addict.
• The removal of the subject must produce ‘withdrawal symptoms’ [physical or psychological disturbances].

Usually, addiction results in two important consequences:

• Increased focus and engagement about the subject.
• The ‘shutting-down’ of the rest of the person’s external aspects.

From this point of view, we can’t be addicted to each and every thing that we do in our life. Most of us know our limitations of our attempts to experience everything. But some of us unfortunately fall victim to drug abuse. What are drugs?

‘Drugs’ in this context fall into two categories: Narcotics and Psychotropic substances. Narcotics are substances that cause a feeling of paralysis or numbness. Psychotropic substances are chemicals that primarily act upon the central nervous system and alter the brain function, resulting in changes of behaviour, consciousness, mood or perception. These substances create a sensation of craving by misguiding the brain’s dopamine system, which is responsible for our sensation of happiness.

Not only drugs, people are more commonly addicted to smoking and drinking. These habits form mostly during the teenage or early adult years. Like drug abuse, they also produce a temporary ‘high’ followed by prolonged depression if the activity is not repeated.

This physical dependency wrecks havoc not only on the concerned person, but also in the person’s immediate neighbourhood and to the society in the long term. Thus there are numerous ways to deal with the problem and treat the affected persons.

A number of models have been proposed to explain addiction. These include the disease model, the pleasure model, the genetic model, the experiential model, the opponent-process model, the allostatic model, the cultural model, the moral model, the habit model and the blended model.

Numerous organisations all around the world are engaged in curing people of their addictions and helping to prevent new cases. We too, have a social responsibility not to get into any form of addiction that can be devastating for us and our loved ones.

The Wonder of Motivation

Few stop to wonder what differentiates man from other forms of life. It cannot be nutrition, because all living beings need it. It cannot be pleasure instinct, for all animals need it. If we look at it deeply, it is the need for self-actualisation.

In Maslow’s hierarchy of needs, self-actualisation is defined as “the desire for self-fulfilment, namely the tendency for him [the individual] to become actualized in what he is potentially. This tendency might be phrased as the desire to become more and more what one is, to become everything that one is capable of becoming”. It is the highest level to which one can motivate oneself to.

Maslow’s hierarchy defines the levels at which different kinds of motivations are effective. They are physiological, safety, belonging, esteem and self-actualisation. Fulfilment at each stage requires appropriate motivational methods.

The dictionary defines motivation as “The psychological feature that arouses an organism to action toward a desired goal; the reason for the action; that which gives purpose and direction to behaviour”. Thus motivation depends upon a goal, a reason, or a purpose. It is of two fundamental types: extrinsic and intrinsic.

Extrinsic motivation is more common in less developed human thought processes. In this, the person is subject to certain external conditions (called ‘motivating factors’). These may be either incentive-providing (money, food, pleasure or something else) or deterring (fear, pain, or humiliation). The trouble with this form of motivation is that when the external factor is gone, the motivation is gone. Some other studies have also shown that extrinsic motivation weakens inherent intrinsic motivation and dampens the human spirit.

Intrinsic motivation is a higher though process. In this, the subject is motivated by the self. Usually this develops if the subject can see that the desired results can be controlled by internal factors (such as effort), or if the subject develops a passionate interest in the achieving. The highest form of intrinsic motivation is self-motivation.

There are several theories of motivation other than Maslow’s hierarchy of needs.

To understand how to motivate people, we must understand the reasons for lack of motivation.

Motivational theories are applied everywhere, from home to business to schooling to national-level decision making.

For instance, I am motivated to write this blog because I get satisfaction in voicing my opinion over the internet. In short, understanding human motivation is very important to understand the success or failure of human societies.

Regardless of the reader, I would tell everyone that self-motivation is what every one of us must aim for, and move higher up Maslow’s hierarchy.

The Pre-paid fiasco

On reading a headline “Pre-paid service in Kashmir to be stopped” I did not understand what exactly the Government of India wants to do. If they think this will curb terrorist activities, I have no definite reply.

For what does the Government expect to achieve from this, it is not exactly clear. On top of this, the Honourable Home minister has also said that a similar policy might be introduced in the insurgency-hit North-Eastern states. By a logical extension, this might be extended to the Naxal-affected central Indian states, and eventually, to cities like Delhi and Mumbai, which have been periodically rocked by terrorist attacks.

Now, it must be obvious to our authorities that misuse of pre-paid SIMs and lax verification procedures are by no means confined to Kashmir or the North-East or the Naxal-affected hinterland. Indeed, the trouble is prevalent in our very metropolitan areas. For this very reason, our Government plans to cut connections to cellular phones without valid IMEI numbers.

Pre-paid SIMs are far more preferred over post-paid ones, because they enable the user to keep track of how much they have spent and how much they need to conserve and economise. They can be easily used by people on the move. Moreover, pre-paid connections can be discontinued at will. This is the key feature that anti-national groups misuse.

Also, it must be noted that over the years, the people of Jammu and Kashmir have become slowly alienated from the Indian mainstream due to various errors of omission by our polity. At a critical juncture like today, when we have the best chance of getting the people of India’s northernmost state back to India’s soul, we can seldom risk a chance of repeating history. If the government has real and valid reasons against pre-paid connections, I have an advice for them: Ban it throughout India.

For, then only our authorities will see the dent in India’s superpower image. Foreigners, whom we love to sucker up to so much, will say, “Here is an aspiring country which denies technology in part of its country.”

I do not deny that the Government’s decision can be right. But historical milestones are seldom decided by right and wrong intentions. One faulty move made on our part and we may have to regret it for the rest of our existence. We must carefully weigh the consequences of our actions.

Let us hope that we are guided more by our heads and less by our instincts.

Knowledge and Power

“Knowledge is potential power. It becomes power only when it is acted upon.”

For the past few days I was reading Alvin Toffler’s book “Powershift”. Written in 1990, this book talks of how power centres in today’s world are influenced by knowledge. It has not always been so, for in the past, violence, and later wealth, controlled power centres.

But today we live in a knowledge era. What we know matters a lot. The book makes an interesting point that while muscle and money cannot be used simultaneously, knowledge can be, and concurrently used to create further knowledge. The power of knowledge and information is that it can be used to rapidly transform the lives of people, and efficiency can be improved on a rapid scale. In fact, much of our service industry is based on the premise of knowledge and information, and increasingly manufacturing and agriculture are also using knowledge to expand production and profits.

But what exactly do these two terms mean? The dictionary defines knowledge as “The psychological result of perception and learning and reasoning.” It also defines power as “Possession of controlling influence.”

Power has always been the ultimate desire of man. He has always sought to subordinate others around him, but since this is not possible for everyone, there have always been conflicts over power. Power is neutral. There is nothing inherently right or wrong about power; right and wrong occur when the power is suitably or unsuitably applied. In different eras, power has flown from different sources.

Before the 1950s, the world was dominated by manufacturing and agriculture. Work output in these professions required brute force. Workers were interchangeable; it did not matter as to which worker did the job. Thus, power remained in the hands of people who controlled farms and factories.

But then, the growth of the service industry began to change this. The work could now not always be performed by muscle-force, it also needed workers to think and adapt to particular situations. No longer were workers as easily interchangeable as before. Those who learnt to adapt to this change by becoming knowledge centres also obtained the power to shape the mosaic of the world.

Consider for example two industries, one highly respected, and the other most detested (no reason why it should be). The financial sector, which ostensibly seems to be doing nothing productive (looked from a tangible product point of view), controls the levers of all the great powers. Why? They have information. On the other end of the spectrum, we have the espionage services, which are also sought after, for they are useful for obtaining information that is secret, or information that can be obtained only by carefully sifting through the existing open sources. They are also extremely powerful, but that is never obvious owing to their covert ways.

In the past, power flowed from the barrel of a gun, and later, from the chest of the wealthy. But today, power flows from what is there in our cranium. Most importantly, we cannot rest on what we know now. Knowledge, by its very nature, is fluid and changing, and the only way to keep up is to keep learning. Nor can we expect to keep to ourselves what we know today. Knowledge and information have a nasty habit of seeping out into the open.

When this knowledge is put into action, power will come to the actor. So if you want to have power, then accumulate knowledge, one that can be put to immediate use. We should keep learning and not rely on the exclusiveness of our knowledge.

So, as the saying goes, “Knowledge is Power”. If you have power, you may do something good or bad, but if you don’t have power, you can do nothing. So, start accumulating knowledge. Well begun is half-done!