Burn .. Fill .. Go !!!

We all believe that electric vehicles are non- polluting and environmentally friendly. Yes, they compromise on top speed, have a slower acceleration and take a long time to get charged up, unlike gasoline or diesel engine run automobiles which take less than a couple of minutes for refuelling, but considering the traffic which is building up every day in our cities how often do you get an opportunity to drive fast accelerate?

The rate of re-charging your batteries is still a problem. Better battery re-chargers are being built but none is comparable with the time taken to fill your tanks with that of petroleum fuels. One more major claim by the electric vehicle manufacturers is “Environmental Friendliness”. They claim their vehicles don’t pollute. Does not emit any harmful gases. No engine – No fuel – No harmful gases. 

That's what they say. But is it so?

Let’s dig in deep.

India generates 59% of all its electricity through coal. 17% through Hydro Electricity. 10% through fossil fuels (Gas and Diesel). 2% through Nuclear and the remaining through renewables.

Most of the fossil fuel power is dedicated to the industries. The renewables are seasonal, we get winds only in the months of Feb – March and June to August. The rest of the times the wind mills spin, but do not generate. There is something called a minimum wind velocity, only beyond which a wind mill can generate electricity, although solar is on throughout the year. Hydro power is again seasonal and rarely runs on full capacity even during the monsoon seasons or post winter.

The cities mostly get power from the coal fired power plants and Nuclear. As we see, nuclear contributes very little (only 2%), so for the sake of an argument, we shall consider that the city gets its electricity from coal fired power plants.

Now, how much coal do we need to burn? Before answering that, I’d like you to know something.

The electricity meter in front of your house in which you see a disc spinning inside, that disc when it spins one full circle, it means that you have consumed 1 kilo Watt Hour of electrical energy. It is equivalent to any electrical device/devices consuming 1000 Watts or 1 kilo Watt of power for one hour. Your average fan is about 150 Watts and a tube light 40 Watts, your refrigerator 500 Watts.

So if you turn on your Refrigerator, a couple of fans and 5 tube lights for one hour, you would successfully consume 1 kilo watt hour of electrical energy. That my friend is called a “Unit of Electricity”. So check your Electricity bill and find out how many units of electricity you have consumed and count the number of fans and lights to verify the same.

That apart. The coal fired power plants are not in your neighbourhood, they are generally located far away from cities. That is done to save you from the pollution it throws into the atmosphere.

What actually happens in a Coal fired power plant? Coal is burnt. This burning of coal produced heat. This heat is used to convert water into steam. This steam is then sent to a turbine. The steam flows through the turbine and spins the turbine. The turbine is connected to a huge generator and the generator spins along. This process produces electricity which is then transferred through the transmission cables which run a few thousand kilometres to reach the city distribution station. The city distribution then sends an underground cable to your door step from which you get electricity.

Now now now …. There is a lot happening here. Lot in terms of energy.

First, generating the electricity; it is known that the efficiency of electricity generation in a coal fired power plant is close to 40%. It means you have to burn two and a half times the energy equivalent of coal to generate one kWh of electricity. That is roughly about 500 grams of coal for a unit of electricity.

The carbon content of coal is about 70%, or 700 grams of carbon per Kg of coal. Upon complete combustion where this carbon gets converted to CO₂ two Oxygen atoms are required by every atom of Carbon, which is about 1860 grams of oxygen. The sum is then 700 + 1860 = 2560 grams of CO₂/KG of coal. So to produce a unit of electricity, you burn half a kilo of coal which emits 1.28 kilos of Carbon dioxide into the atmosphere.

Now, the electricity to travel from the generating station to your doorstep has to pass through a lot of devices. Most of them are transformers. Whenever the electric current passes through them, there is a loss, either as heat or as sound. That ‘trrrrrrrrrrrr…’ noise that you hear when you go near a transformer, that a loss. The efficiency of a transformer is about between 95– 98%. There are at least seven transformers that are employed between the Generator at the power station and your door step. At these efficiencies through the seven transformers, about 80% of the electricity that is generated reaches your home. Electric vehicles deploy a motor to spin the wheels. This motor operates at around 65% average efficiency. Multiply both efficiciencies and we get 52% as our overall electrical efficiency. So, we basically need to generate 2 units of electricity for every one unit to be consumed. Therefore you emit 2.56 kilos of CO₂ for every unit of electricity you consume at home.

Coming back to electric vehicles. The general mileage which all the electric bike manufacturers promise is something close to 40 kilo metre for one full re-charge of the battery. A full recharge consumes close to one unit of electricity. So 40 km/kWh is what it gives you. That is 2.56 KG of CO₂ emitted for 40 kilometres.

A bike running on petrol also gives you a mileage of 40 km per litre. One litre of petrol weighs 750 grams. The carbon content of petrol is about 87%, or 652 grams of carbon per litre of petrol. In order to combust this carbon to CO₂, 1740 grams of oxygen is needed. The sum is then 652 + 1740 = 2392 grams of CO₂/litre of petrol. That is something close to 2.4 kilos of carbon dioxide emitted.

Assumptions and numbers here and there might vary a little. But long story short, both emit the same amount of Carbon Dioxide into the atmosphere. Although an electric vehicle will not irritate the cyclist on the road, just behind you pedalling his lungs out, by giving him a fresh dose of poisonous gases to inhale.

So you do release a lot of harmful gases but the locations are different. Unless, you charge your electric vehicles using a renewable source of energy like a solar panel dedicated to charge your electric vehicle.

So, the environmentally conscious citizen can choose between the two depending on his needs. On the contrary, the budget conscious citizen can pick an electric vehicle as he gets to drive 40 Kilometres for just Rs. 5/-, that is 13 Paisa per kilometre, whereas petrol prices are soaring through the roof. Choose wisely!!!  

Refinery Economics for non engineering and non financial background.

I'd like to take this opportunity to educate you on some basic concepts, practices and market scenarios that dictate and control the entire Refinery Business all over the world. Be it Ambani's Reliance or TIPER refinery in Tanzania, whatever I have tried to convey to you is applicable for all refineries.

Lets go stage by stage.

First, understand the "haunting" jargon used in the Oil and Gas Sector.

"Stream" refers to a region where crude or its derived products (petrol, diesel etc) flows in a pipe. "Upstream" is the region where crude is brought out of the ground. Upstream is devided into 2 zones, Off shore and On shore. Off shore (Gulf of Mixico) is where oil is dug out from the middle of the sea and On shore is from land (CAIRN Energy in Rajasthan, unless you though Rajasthan had a sea). Off shore and On shore has nothing to do with beaches.

"Mid Stream", the pipeline through which crude oil is brought from Upstream (yes, both off shore and on shore) to a terminal (where it is mixed with other crude oils to meet required specifications) and then to the refinery gate.

"Downstream" is the refinery, where the required products are derived out of the Crude oil.

Now, a refinery is supposed to derive the various different products out of the crude. It does so by employing complex technological machines/instruments and devices. They all come at a cost.
Crude oil flow is generally measured with two units of measurement namely, Barrels per Day and Metric Tonne per annum, the former is a volumetric measure and the latter is mass based. The general thumb rule which i'd like you to remember is that 1 Million Metric Tonnes per annum of Crude is equal to 20,000 Barrels of crude processed. A Barrel is 160 liters.

1 MMTPA = 20,000 BPD.

A 400,000 BPD refinery can process 20 MMTPA of crude.

Now, just because a refinery has a 20 MMTPA it doesn't mean that it is going to help extinguish the fuel demand in the market to which it supplies. It all depends on the nature of crude it handles.

Classification of Crude Oils: Heavy, Light, Sweet and Sour.
Plainly put Heavy is heavy, its got a density of about 900 Kg/m3. Light is a less heavy 750 - 900 Kg/m3. Sweet and Sour are measures of the Sulphur levels in the crude oil. More the sulphur, its sour. History says that a few morons in Pennsylvania actually tasted the crude oil as it came out and apparently crude with high sulfur content tasted 'sour', hence the name. The same story goes for Sweet crude. Crudes are labelled in combination of the 2 categories, Example : Heavy Sour crude, Light Sweet crude etc.

Out of Light crude, comes a lot of Distillates. Distillates are the useful fuels that come out of the crude. The major Distillates produced are LPG, Naphtha, Gasoline, Kerosene, Diesel and Fuel Oil. Now remember that order, my boss throws whatever he gets at me if make a mistake in the sequence, it is in the order of their boiling point. Heavy crudes have less distillate yield, they give a lot of Fuel Oil and not Petrol/Diesel.

Now there are a lotta useless streams also, like Heavy Naphtha, Off-Gases, Cracked gas, VGO etc. The refinery has special equipment to convert these useless streams into useful ones, just like how you pack your sandwich with left over veggies from yesterday, pretty much the same logic.

This ability of the refinery is attributed with a terminology called "Complexity" and it was invented by a genius called Nelson, I still refer to his book printed in 1954, that guy is just amazing. Reliance Refinery at Jamnagar is the Asia's most complex refinery. Its got a Nelson Complexity Index of 14.6.
It just means that no matter what you throw into those machines, you get gasoline or diesel.

Now, given a green chilli in your hand, you can eat it, you can sell it for Re.1 or you can chop it up and add it to normal fried rice and make chilli fried rice and sell it for Rs 10/- more, the difference is the chilli . I know this is the worst  possible example one can give, this was just to emphasize the need to make more money.

Refineries did not open up for charity. They need to make their money too. They can only do it by selling the products and producing products that sell at a higher price (Gasoline and Diesel in today's global scenario) and as I have mentioned earlier, they do so by employing special equipments.

Now, the actual economics. The yield pattern in a refinery is as follows.
Gas and LPG = 5 %
Naphtha = 30 % (Gasoline is part of Naphtha)
Kerosene = 10% (Depends on Crude) its also called ATF - Aircraft Turbine Fuel.
Diesel = 30 %
Fuel Oil = 20%

Yeah I know it did not total up to a 100. The remaining is considered as F & L . Fuel and Losses.
Fuel ? why ? All processes in the refinery requires a lotta heat, so fuel is required to heat em up. Why would you buy fuel from somewhere else, when you yourself are producing it.
Losses? yup. Everything in the refinery was invented and manufactured by men, so its not all that great. there are losses.

GRM - Gross Refinery Margin.
I am giving you a scenario here. DO NOT QUESTION THE ASSUMPTIONS. This is just to help you understand.
A Refinery makes money by selling its products. Rewind 40 days in time and read along.
The price of crude is 100$ a Barrel.
Gasoline and  Diesel at 125$,  Kerosene at 115$ and Fuel Oil at 100$. LPG varies with respect to geography. Now multiply these prices with their yields specified above.

Gasoline and Diesel has together fetched you $75/Barrel , kerosene $11.5 /Barrel and FO another $20/Barrel and some $3/Barrel from LPG. Total them and you get $109.5/Barrel. This additional $9.5/Barrel is what is called as the GRM or Gross Refinery Margin.

The average processing cost is about $2 a Barrel. Processing cost includes the cost of energy, maintenance, labour, repairs, catalysts and other consumables required. Then there are other deductions like depreciation, financial expenses (debt and equity) which totals to about $1.5/ Barrel. Now deduct 30% taxes. So, a refinery hardly makes hardly $5/Barrel of Crude it processes.

It costs about $6 Billion for a 10 MMTPA refinery which can process 200,000 BPD. So it makes a million dollars per day.  That is 365 Million a year profits annually. To break even, it takes 17 years.
Will you invest in something that gives you a ROI in 17 years??????? Not unless you were in the 19th century. Then why do people build refineries? Figure it yourself.

Lets move over, what do you think determines the Refineries economics now ??? Or how much of engineering skills is affecting the refinery. Only that $2 a Barrel of processing cost. It cant become zero, you need to spend some energy. It is crude and product prices that determine 98% of the refinery economics.

Now, there is something called RTP - Refiney Transfer Price. The product prices discussed above were Refinery Transfer Prices. The price you pay for your fuel on the road is the retail price. Refineries have no control over these. It is the fuel marketing companies that sell the fuel on the road at the bunks. To the RTP, taxes and duties are added. Then transportation/distribution cost and the Oil Marketing company's margin.

Hope it helped.

What is true and what is not.

              Information today is available at the snap of your fingers. So many search engines, forums, social networks and blogs to help you get what you want. But the biggest question is, “Is that the information you want?” or is it just convincing enough to satisfy your needs. Everyone, to some extent, agrees that not all information available online is true but still continue to be satisfied with what they read. This has actually caught on elsewhere other than just the internet. Today you have popular newspapers quoting opinions and assertions I the place of facts. One thing everyone should be aware is that, you should never be afraid of facts. Facts are the truth, they are the exact interpretation of the present condition of something worthy. Say stocks or GDP or your own savings in the bank. All problem arises when you modify or manipulate facts.

             Top consultancies like McKinsey, KPMG etc. never manipulate facts. In fact, that is the only difference that separates them form the others. They work their solution around the facts. They do not manipulate nor modify nor selectively opt for those facts that prove to be consistent or enough to convincing to frame solutions. This is hard work, no wonder they charge you a bomb. Not what I intended to write on, but this is all just the beginning.

              Today’s news and information on website has hardly any fact contained in it. This blog will help you understand the difference between fact, assertion, argument, opinion and a theory (or) hypothesis.

Let me define them with relevant examples.

Fact: something which is always true.    

Ex : “Sun rises in the East.”

Simple, isn't it ?

Assertion : This is tricky. It is held to be true, but not a fact, because, it cannot be proved (or) can be disproved.

Now, A recent survey by XYZ firm (assumed to be trustworthy) reports that 1 million citizens of Delhi are over 60 years old. Is this a fact or an assertion?

An assertion, Why? A fact would look like this. A recent survey by XYZ firm, reports that 1,054,308 citizens of Delhi are over 60 years old.

All what you get in your newspapers or news channels are full of assertions unless the numbers are less than a hundred. No one actually cares nowadays. Everyone is satisfied with a rough estimate.

Argument: An argument is a bit complex. Difficult to explain in one sentence. An argument is a conclusion which is supported by reasons. It’s like winning case in the court, though not in the literal sense. An argument needs a “premise” which are basically assumptions. The premise has to be supported by reasons. Then we do some logical deductions to make it sound convincing.

Well then what is a “Sound Argument”? If these premises are facts, the argument becomes sound. It simply cannot be disproved. You come across so many funny mathematical proofs that prove 0 =1, all these have arguments as their premises and not facts. How do you disprove them? Their logical deductions are flawless. The only way to disprove them is to question their premise.

            Now we come to theory. A theory is an attempt at an explanation based on current knowledge and experience. Theories are meant to change. We knew once, there existed a theory which stated that, the earth is the centre of the earth. And how different is a hypothesis? You can say that a hypothesis is either made into a theory or is an idea that is generated which helps to govern the behavioural pattern of a group in any sense.

             Assuming all of us back then had the same intellect as we did today, everyone believed this and it sounded very convincing with whatever observation and experience they had. Until Copernicus came in and created a commotion. He basically disprove a theory. Yes, it is possibly for a theory to be disproved. Theories constantly keep changing and upgrading. Let us take Darwin’s theory of evolution into consideration. Darwin was not the first one to suggest that men evolved from apes. He is popular because he validated his premise for his argument in support of evolution based on evidence that he created from all around the world and sat down created a hypothesis on the basis of his observations. When his hypothesis was widely accepted it transformed itself into a theory. Nobody publishes theories in real life. If anyone says so, it actually means they put forth a hypothesis.

            Now let us get to the last part, an opinion. It comprises of 95% of all the articles posted on the web. It is one’s own observation and mostly uses baseless assumptions and the logical deductions can also be flawed. Any sentence starting with “I think” or “The world feels” or “The Nation thinks” or just simply uses the words “think” “feel” “presumes” and many more with a personal touch, is an opinion. As a caution, never believe opinions.

I was always wondering how many people who search on google, actually visit the second page of their search results. I tried 'Googling' about that and I found this article

 http://www.searchenginejournal.com/57-of-consumers-will-go-to-the-third-page-to-look-for-reviews/51841/

Try to distinguish between facts, arguments and opinions in this article. It’ll be a good exercise for you. If possible frame a hypothesis from your reading too. Do this and you would have finished one course in critical thinking. And yes, the previous statement was an "opinion". Good day !! 

Anti"Karma" : What goes around, continues to go round and round ..

Gravity … well, we all know it is the tendency of objects to fall towards the ground. Even before Columbus sailed, people knew that the earth was round. The only dispute was how big it was. So we knew that gravity was the tendency for objects to fall towards the centre of the earth and then Newton came along and sat under an apple tree and rest is all history. Hi5 to those who still wonder why he did not find a seat under a coconut tree, it would’ve made our lives a lot better at school.

Jokes apart; we all know that he saw apples falling and locked himself in a room for a couple of years, did some calculations and came out with the Universal Gravitational Constant. But what was Einstein wondering about when he saw the apple fall? He saw an apple fall, he saw another apple fall, then he saw some leaves fall as he kept looking above, but the moon stayed right there. The moon never fell. Well as we discussed above if gravity is the tendency of objects to fall towards the centre, then why isn’t the moon falling? Consider it analogous to a bird flying. The bird stays in air successfully by pushing air downwards. Or you could refine it by saying that it gives a forces equal and opposite to the gravitational force and hence does not fall. The moon does the same. Just that it pushes in a different way. 

Let’s break for a while and analyze some missiles. You know what a projectile means, don’t you?.  The picture below helps u understand what a projectile is. It is basically the path adopted by something launched in air or dropped from air. All missiles launched take the shape of a projectile. Now I’d like to visualize something.  

 

Let’s think about a situation. There is a war and country A wants to bomb the other country B. How would the projectile of the bomb look? Something like what is shown below.

 Okay now what if the countries are pretty far apart? It’s simple; you just throw your bomb with more force. But you got to calculate the missiles' path and destination precisely. Any miscalculation would put you in a very bad position.

Okay what happens if someone fires a missile and miscalculates its projectile? Say he gave it some extra force that is misses the earth on the other side. Something that looks like this.

What happens to the bomb? Where does it go? Say you’ve programmed it to go "KABOOM" once it touches the ground. Now when does this bomb blast?  Think ..

The inertia (or the tendency for something to keep moving unless stopped by an external agent) keeps it going. Going on and on. But till where ???

What would eventually happen would look like this. The missile would carry on along its path and continue to miss he earth on the other side as well. This would happen for a couple of cycles and would eventually stabilize at a particular distance. Let us not get into too much physics as to why the distance would stop growing. The distance at which it would stop is dependent on the velocity with which it travels. The faster it travels, the further is the distance of stabilization. As simple as that ! Now you would know what the title of this blog really means.

This distance at which the missile stabilizes, my friend, is called the “orbital”. Yes even I wish physics was taught to me with such simplicity.  

Now take the missile out of the picture and put a satellite in it. This stupid mistake of giving extra force to the missile by some war chief suddenly looks like an accomplished feat by a NASA Scientist. 

And now, going back to the moon. The moon is just a projectile which travels around the earth missing the earth every time it goes around. Fortunately there is no air resistance in outer space so it would continue with to spin around the earth forever without crashing in.  

This post is dedicated to educate my fellow Indian citizens on the basics of space technology as my country launches its Mars Mission today. I hope it helped. Vande Mataram !!! 

Do share your valuable thoughts in the comments section .. Thank you.

Zig, Zog and the fair priced Indian economy...!!!

               What is price? It is not the reflection of any intrinsic value something may have, nor is it the sum of what is cost to produce it and profits fetched. It is instead what the owner will demand in order to part with it. I hope you get this straight into your head as this happens to be the main reason as to why prices rise during scarcity and do not drop to the same levels when demand meets supply. The term “Inflation” is merely a cover up to justify this act. Of course I am not ridiculing inflation here, I’m just pointing out misconceptions.

                I’d like to take you through a cautionary tale here. Two cities Zig and Zog prevailed long ago. Both had around the same population, same terrain and people who ate the same kind of food, similar cultural practises but different rulers. One was a benevolent king and the other was a good Economist.

In Zig, food produced was always in surplus and every grain reached the palace doors and they were equally distributed to all. The king set fair prices and food reached everyone, and so all praised the king. But when famine hit, the benevolent king under priced the food articles to help his people live at the cost of his reserves diminishing. And as the famine persisted, the dying people continued to praise the dying king. And once the king was dead, so did Zig. There was theft and chaos and the remaining people fled.

In far away Zog, the government never intervened in pricing commodities. It left the responsibility to its merchants, trusted them and supported them. During times of surplus these merchants stealthily built warehouses to store excess food. And when famine hit, they sold the food at double the price stripping people even of their watches n jewels. These traders even gave some of these jewels and watches to the peasants to coax more food. News spread and this attracted people from nearby areas surrounding Zog. The longer the famine, the higher the prices went, until the people restricted themselves to a minimal diet. Or you can say that the markets rationed them to such a a state. This made them more competitive survivors than mere dependant slaves to the government as in the case of Zig. By the time the famine ended, the whole city was indebted to the merchants, but was alive: and each merchant was resentful that competition from his colleagues restricted him to raise his fortune twenty fold, rather than only four fold.

In Zig, when fair prices were paid for food, the supply dried up and people starved and died along with their fair-minded ruler. Farmers were not prepared to supply food at the fixed low prices set by the government. Whereas in Zog, when no fair prices were legislated, there were large price rises, big enough to attract farmers, not only from nearby regions but even as far as Zig (remember the people who fled from Zig). The people of Zog grumbled, but lived and adapted.

                  This is just a tale, but it emphasises the fact that as prices rise, competition increases, quality increases, new techniques evolve and people become more adaptable. Moreover it portraits that prices have an existence and influence people beyond the intentions of the ruler/government.

             Yes, the entire article was referring to subsidies. 27 years ago, Indians unintentionally miscalculated the back firings that the country would face by introducing subsidies. They never had a time frame. Subsidies are generally given at the time of an emergency in order to sustain a dying population and in that particular time frame; the government should empower its people to alleviate themselves from existing misery. Take world history and you’ll find food and fuel subsidies being the most popular form, and all of them came with a well defined time frame. Once the country revives, the subsidies vanish. Unfortunately here in India, subsidy is a way of life. And we did follow the trail left by Zig. We are desperately working towards reviving ourselves to avoid an economic breakdown. The country dies with its dying king. Should we allow it?

           By creating a cheaper country to live in, we create a less competitive environment for us to survive. This is not to be confused with creating 'Security', rather this is merely inculcating 'Stupidity'. On a concluding note, evaluate politicians who help the country and its people grow progressively, rather than the ones who make your life easier.

Arithmetic, Population Energy and Money

Arithmetic, Population Energy and Money

This Is my second blog and I would like to take you through some math and the importance of numbers in life especially percentages and doubling time with some psychology and news reading skills. As many of you know, I’m a math and Science enthusiast but now I’m inclined towards psychology too. First of all, we must understand that math is more than just numbers and it should be rightfully defined as the science of computing. When math is represented with discrete values it is called arithmetic and algebra when we use alphabets or symbols when you represent something broader, say a law or a theorem. We were all taught basic of mathematics in our schools and colleges, but we merely study them as subjects which are a part of our curriculum. We sometimes fail to recognize or acknowledge some simple relations we come across in our daily life that are governed by the same mathematics that we learnt, which if seen from the right perspective, is easier than you thought it was. I would like to inform you that All Global Problems are connected by Arithmetic. The article would also touch upon today’s speculative news market and how to read news article, though not in detail. The way I write will be very direct and I use only simple English, albeit, you may have to read a few sentences twice to understand what I mean to say.

Do not understand what you want to, but, what I want you to. I hope you like it.

The greatest short coming of the human race is our inability to understand the arithmetic exponential function. Yes..!!! Logarithmic and Exponential functions, by far the best means available in mathematics used to forecast or predict future trends and values are not understood by most of us. When an information passed from one person to another  the quality of information is maintained only when all the necessary data in the message is understood and interpreted by the listener. Most of our information that we depict today, are in terms of percentages. I hope everyone is well aware of percentages. Percentage merely describes anything that grows with time, increase by a fixed fraction for a fixed period of time. Even though the information travels in a very crisp manner, the listener/reader should still compute as to how much increase or decrease it actually is.

And then there is doubling time. Doubling time is the time taken for a particular quantity to become twice its magnitude.   Lets take 3 examples 

1. “A baby grows to twice its height if 2 – 3 years”.

2. “You will have twice the amount of homework to do if you spend the weekend watching movies and playing video games”.

3. “The world oil consumption doubled in the sixties”.

Now these are just mere examples which depict what a Doubling time is …. Or wait..!! Are they …???

NO. !!!

 Doubling time needs to be specific. It’s a measure of time. You need to quantize the time period for a quantity to double in its magnitude. The first statement somewhat tentatively conveys the message regarding the starting and the ending period. Start when the baby is born and end somewhere between 2-3 years.

The second example however does not talk about time period at all. You have to assume a lot of things to understand this. Firstly, you should be given home work on weekends and you should be given homework after the weekend. Third, you should be given the same amount of homework after the weekend. The third example is even more disastrous. It only has the word doubling time. It does not compare the consumption pattern to a previous time scale. It did not speak about what oil. It did not specify a particular time period as to when it actually doubled.

Now re-consider your thought process if you happened to be convinced with those three examples when you read it for the first time. Most of the news you see on TV or read on the papers today are baseless as the examples stated above. Now why do people fall for these news anyway?

Express it in percent, no one cares. Represent it as doubling time, and everyone is awestruck. Yes ..!!!!!

Invest in BANK A and your money will double in 6 and a half years.
Invest in BANK B and you will get 11.50% interest per annum. 

Which statement catches your eye ??  Well, for all the effort I’ve put in, I hope it is the first one.

However, the truth is that Bank B gives you slightly more than double the amount you invest in the same time period. All said and done, how do  you calculate doubling time ? You do not want to sit with a calculator when you read the news, do you? It is easier than you thought. Just divide 70 by the interest rate.  7% interest takes 10 yrs to double (70/7 =10).

So if you have Rs 100 today growing at 7%, it grows by another Rs 100 in 7 years and you end up having Rs 200 at the end of 10 years. The average world economy for the past 400 years has been steadily growing at something under 7%. I’m pretty much sure about this as I’ve read it somewhere sometime ago. Anyways, let us assume it to be so and let us go back 300 years. The Indian princely states had to pay an amount equivalent to Rs 100 at that time, as a yearly tax to the British.

 Rs 100 at 6.8%, doubles 30 times in 300 yrs,

 2 ^ 30 x 100 . It is something more than 100 Crore Rs or something less than $20 million. Now there was more than one princely state falling under the British rule in 1713 and the British made a lot of money. And $20 million per annum per state is sumptuous. Another piece of information Manhattan was purchased in 1626 fr 24$. Assuming a steady growth of 6.8%, Do the math.

Legend has it that the game of chess was invented by a mathematician who worked for a king. The king was very pleased with the invention of the game that he wanted to reward him. The mathematician said, “Well my king, my needs are modest. If you just take my chess board and on the first square place one grain of wheat. On the next square double the one to make two and on the next, double the two to make four. Just keep doubling till you reach the 64^th square and that would pretty much suffice my needs and my family’s”. The king thought he was a fool and said “You fool, I was going to give you a real reward and you resort to some grains of wheat? “. Well let’s work it out and find whether the mathematician was actually a fool or not.

The table below is pretty simple to understand. The first column numbers the squares, the second column tells you how many grains are in the square and the third column shows the total number of grains in the chess board.

Square # Number	Grains on Square	Total Grains on the Board
1	1	1
2	2	3
3	4	7
4	8	15  (24 – 1)
5	16	31  (25 – 1)
.	.	.
.	.	.
63	262	263 – 1
64	263	264 – 1

Again I hope you don’t have any difficulties in understanding the table above. Let us identify a pattern here. Every new square has one grain more than the total number of grains on the entire chess board. The 2^nd square has 2 grains which is one more than the total number of grains which were there, which was one. The 5^th square has 16 grains which is one more than 15 which happens to be the sum of all grains till the previous square. And so the relation is obtained where n happens to be the Square# number and “ 2ⁿ – 1 “ is the number of grains n the square. So every time a quantity doubles it takes more than all that you’ve used before

So you have to understand that the whenever something doubles, it means that the production/consumption of that particular item is going to be more than what existed till date. Going back to the news which said, “The world oil consumption doubled in the sixties”, which actually meant crude oil, this statement says that the amount of oil consumed in the 1960s was more than what was consumed in the entire history of the earth till 1959.

The word population today is around over 7 billion. The population was 3.5 billion in 1968. So, in just 45 years, human beings have produced more off springs than the total number of off springs ever produced in the history of mankind which runs to 10s and 1000s of years. The frightening fact is that, we still continue to grow at close to 2% p.a. This means that we have also produce more food than what we have produced in the history of mankind. And also the space available per person on land has shrunken by slightly more than half and all of this has happened in just 45 years.  The picture depicts a rough timeline just for the sake of understanding it is not perfect to scale.

          Consider the black patch to be the timeline from 10000BC to today, it is to be noted that the first billion was achieved only in the starting of the 19^th century and now we have a whopping 7 billion people in our planet. The thin blue line in the end depicts the last 45 years in which our population doubled.

Now, going back to the king and his chess master, exactly how much was the total amount of wheat grains on the chess board. “ 2⁶⁴ – 1” is just a little more than  400 times the 1990 world harvest of wheat. Oooooohhhh yeaahhh … !!!! IT IS .

Well this should feed his family till eternity.

Well, I think, this is precisely the reason why people are AWESTRUCK when something is depicted in terms of doubling time.

I’d like to finish this off with one more explanation. Bacterium multiplies by dividing into two. The two become four and the four become eight, sixteen and so on. Suppose you put them in a jar and the bacteria doubles every minute, the jar gets filled up in one hour.  Say, you place one bacterium inside a jar at 11 a.m in the morning, the jar gets filled at 12 noon. Easy to understand and I hope you are clear. The growth is constant and occurs in a finite environment. 

Now I’d like to ask you 3 questions:

1. When is the jar half full?

          Some of you may be surprised by the answer. It is exactly at 11:59 a.m. Just one minute before 12 noon, because, they double in number every minute and so, if you reduce a minute you’ll arrive at exactly half of what you had.

2. If you were the bacterium in it, at what time would you have realized that you’re running out of space?

           Well coming to think of this, a minute before 12 noon, the bottle is half full. Two minutes before, it’s a quarter full. Three minutes, 12.5% full. Well, jus 5 minutes before 12 noon, there is tremendous scope of growth as there is approximately 97% free space in the jar and how many of you are going to predict that you are going to be choked up in the next five minutes .????

Well then, let us consider that there are a few brainy bacteria inside the jar who predict this short coming and set to launch a search mission for new bottles. They are successful enough to find 3 new bottles. Now question 3.

3. How long do you think the bacteria can sustain after these bottles have been identified?

Well, at 12 noon you will have one bottle filled. At 12:01 p.m. the other bottle gets filled and at 12:02 p.m. all the four are filled. 

Well then Folks..!!! I know you have already figured out the moral behind this article. Keep an eye on percentages. Always look for specific details, just the percentage without time scale is just speculation. Doubling means not only increase in production or extraction, but also depletion. And at the rate in which our population is rising, we are already in the last minutes like those of the bacteria. Looking at the timeline diagram again I wonder whether we are in the last minutes or last seconds...!!!

Keep thinking until I get back to you, hopefully, on something more interesting.

NOTE:

The “easy to understand”, “ I hope you understood” are all psychological impact statements that I have experimented with you. These statements are supposedly used to ease your head and help you convince yourself that the data is easy to comprehend. I hope it worked.