Good Bye

From: couplestraininginstitute.com

So few are the words,
so sweet the voice.
So eccentric the opinions,
so natural the choice.

Digging from the inner core,
Day by day, more and more,
Fill the wholes pore by pore,
Starts now conscious snore.

Mathematics and Motivation with a Compound Case

Have a glimpse:

Many of you might have seen this picture. Whether through internet or magazines, books, etc., it has gained fair amount of popularity. It is really a fascinating picture, an erotic picture for the mathematical guys. James Altucher once termed this picture as weird mathematics in his article. This fascinating picture has some significance too. This picture is often seen in the inspirational articles. While giving motivation people like to use it very much.

Significance:

More often than not it is interpreted as follows:

If you improve yourself everyday by 1% of what you are today you will end up improving by 37.78 times by the end of a year.

Likewise, if you degrade everyday by 1% of what you are today you will end up degrading by 39.21(1/0.0255) times by the end of a year.

[Note: To be precise it is 0.0255, 0.03 is an only approximation. As I am analyzing it mathematically I am taking more precise value than the market value. Taking 0.03 will make error in my calculation and shows result contrary to elementary mathematical laws.]

It is interesting to note here that although your increase and degrade rates are same, final degrading ratio is more than increasing ratio at the end of a year. I will give you a hint on why this happens and you could work out its reason.

Hint: If you increase 4 by 1, you end up increasing by 20% and if you decrease 4 by 1 you will end up decreasing by 25%. Now it is on your hand to find out the reason for the above interesting finding.

Is it true (mathematically)?

In our first case, rate of improvement is 1% and n is 365 days i.e. R=1 and n=365.

Is it practically possible?

What do you think about its practical feasibility? Mathematically we proved it. Increasing by 1% is not a big deal, isn’t it? It is just a percent. We feel we can do it. Then can we increase ourselves by 37.78 times in a year? To be honest we cannot. Really we cannot. Let’s see how the condition can be visualized.

At first let’s see it in a graph.

Though we may feel the rise is like linear but actually the rise is exponential.  The graph shows that. Even we can reduce our equation to exponential equation as shown in equation (1). And it is known fact that improving exponentially is impossible. Therefore the first condition is not practically feasible. Those inspirational speakers were only being philosophical while mentioning first expression ;). They used it to inspire you, to make you optimistic. But what they said is not practically possible. We even can’t go little near to this equation.

Nevertheless the second expression is true. Absolutely true!

Its equation is:

Let’s see it graphically.

You can degrade exponentially. Cost can depreciate exponentially. Radioactive decomposition occurs exponentially. Those speakers and writers have used second equation to suggest you be alert. They are absolutely right in second equation. You never know how you are ripping into. 

You might have remembered this famous quote by Warren Buffet, “It takes 20 years to build a reputation and five minutes to ruin it.”

Other similar cases in Mathematics:

I would like to call it as a compound case. In many places they have their use like compound population, compound interest, compound depreciation, etc. They are all exponential equations.

For an example:

In compound depreciation everything is same except the constant c being <1.

The function becomes increasing or decreasing function depending upon the value of c (whether it is greater than 1 or smaller than 1 respectively). If c = o the function is a constant function as c = 0 comes from rate of increase ‘R’ being zero.

Thank you very much. I will bring more and more mathematics stuffs in coming articles. 

8 Ways to Make Your +2 a Wonderful Journey

Classes of most of the +2 colleges have already started. The students who have passed so called Iron Gate have entered into the new stage of life. The school’s days are no more there and the amazing journey of +2 is waiting for every +2 students. What I have felt during my +2 stage is +2 stage is really puzzling. Many of the students find it academically difficult. Academically difficult because of the vast course content and time you should devote for the subjects. The course content is large and you can’t put it away by rote-learning. There is no way you can excel academically without understanding the key concepts and doing regular labor. That said, +2 stage is also the time for you to grab opportunity and learn and explore the world.

I want to talk here specifically for the research oriented physical group +2 science students who want to pursue their career in academics and research. Many students who are interested in exploring the world, knowing the universe and doing interesting things unfortunately follow the wrong path. This article helps those students by giving some guidelines that 'may' help them to follow correct path.

• Don’t give your life on marks:
  Marks is essential. No one denies that. But trying to attain perfection in marks and grades may make you miss many things as important than marks. It is wide different between getting A’s and 80% and attaining perfect marks. I feel today I missed out many other aspects by over focusing on marks and percentage.
  
  
• Get out of the topper fantasy:
  I think ‘topper’ is (very very) overrated word in Nepal currently. I can’t see any college or school not bragging about their toppers and their marks as if being topper equivalents happiness and future success. Many of the students are deceived by this overrated thing ‘topper’. Not everyone can be toppers and it won’t be so too. Different students have different interests, different routine and different nature. All of the students should not be expected to score 90% and be toppers. The students who prioritize on marks and grades be toppers. Simple as that. There is nothing you should worry about if you don’t get in ‘TOPPER’ world. Understanding in your capabilities and priorities and exploiting them is essential not excusing yourself saying I am not in toppers zone. I also don’t mean being topper is bad or you should not care about your academics.
  
  
• Know yourself and your (possible) career:
  Many students do not get to know themselves. When in the latter stage they look behind they remorse the things they did not do. The first thing you should understand is yourself. You may be introvert. Exercise on that. You may be shy guy. Don’t feel yourself weak. You need not to be extroverted or party guy to succeed. Know who you are, how you are and what you are. After knowing your behavior and personality, explore different subjects, fields. You will know about your interests only after you explore and know about different subjects. What your interests are, what you are passionate about work on that, labor on that.
  
  
• Listen to others; don’t follow what they say, understand only why they are saying that: 
  Parents and society may compel you to pursue medical field, engineering field without you getting to say what your interests are. Just know why they are saying such. Even know why you want to be ... Don’t follow anyone. Everyone has their own life and own way of living. You may choose the field that encompasses these three factors:
  

  1.      The field that you love.

  2.      The field that society recognizes/ that you can earn sufficient money.

  3.      The field that you are good at.
  
  
  
  
  
  This Venn-diagram figuratively shows where you will be headed regarding you choosing different options. You may take help of this Venn diagram to know where you are going.

• Not I should do or I will do, but do:
  Yeah, we plan. We wait for the time to come. But we are always far away from execution. Remember about your hundreds of plans. Have you done any of that? Probably no.
  So do it from today. You are interested in physics, do home experiments. Study (more and more). Make projects in collaboration with like minds. Be ‘doer’ not only thinker and planner. Nonetheless thinking, planning and dreaming are also very much essential. You are interested in computer science, why not try programming? (for basic C, C++)
  
  
  
  

  You are good in literature and writing why not start writing articles, poems and stories from now? Expose and explore yourself. DO. DO. And DO. Even what you do may be of little significance, DO.

   
  
  
• Know about your possible paths and opportunities:
  What you can do after your +2, have you ever thought about that?
  I am not saying you to focus only on future but being aware about your future options is going to help you tons.
  You don't always have to come in ranks in your college terminal exams. Participate on ECAs. Make your reading as well as writing skills of English good. You get to participate in Olympiads where you can show your knowledge and talents. Similarly there are many other opportunities.Going into IOE or Indian Embassy is not mandatory try you should do after your +2. I thought they were compulsory things. I thought there were not any other options. You have tons of options. Know the options and do what is good for you. Many research-oriented students who love physics fall trapped in IOE(who find later IOE not interesting as they expected). I got trapped in Indian Embassy :D . May you not get trapped.
• Make good and like minded circle:
  Be in the good circle who share common interests and passion. If there is no good circle, create one. After you make circle of your people, good people, like people, you can work on many things like projects, researches, etc. You can share ideas and experiences. It will be helpful for all of you. There is no one not getting benefit from it.
  
  
• Focus on knowledge, wisdom and research:
  You are a budding plant. With knowledge you will grow. Knowledge helps you to nurture. Wisdom is another valuable thing. Wisdom leads you. Wisdom chooses your path. Wisdom helps you take actions.
  Acquiring knowledge is not for the sake of acquiring. Use it. Excellent if practically. Play with your knowledge. I use mathematics to amuse myself. I play physics to entertain myself. If it is for entertainment it is all way better. FOCUS ON RESEARCH AND EXPLORATION.
  
  
  
  
  
  

I will add others if I get other things substantially essential in +2 stage.

Don’t follow me.  Really I mean. But make sure you are not cribbing others too. :) 

Thank you.

See you again in next article.