What Mathematics Teaches Us in Life

Recently while we were enjoying the holidays in the beautiful village of Chindhi (Tehsil Karsog District Mandi in Himachal Pradesh), I was forced to teach mathematics to my elder daughter. Usually Suman, my Wife, takes care of this stuff, but firstly because I was free and secondly because I love mathematics the work was handed over to me. While helping my daughter with the problems I found that she is not much interested in calculating the age of a person on given evidences. So I taught here why we are learning these smaller problems, that these will help her in future with the bigger problems in mathematics. And to the question what is its utility in the world outside mathematics I told here few points about the Utilisation of mathematics in problem solving. I thought to share the same points with you also.

Every Problem has a Solution: This is the first step to solve any problem. Every problem which we face has a solution. Sometime in the course of life every one is faced with such problems which shake one from top to bottom. Then he suddenly realises that he is the most depressed most helpless person in the world. Then this self defeating thought comes to mind that there is no solution to my problem. The moment this thought enters the mind the self destruction starts… which leads to end of the life either through suicide or some illness. But if we think in terms of the mathematics every problem has a solution … whether a small problem or a bigger problem. Once in the time of depression if a person tells himself strongly that this problem has a solution that this problem must have a solution, this becomes journey of self building. Not only does the person get out of the problem but he becomes a light house for the others. The Human History is enlightened by these Light Houses who believed that there is a solution to every problem. When Sidhartha and Mulshankar (in different eras) came up face to face to the problem known as death… their reaction was the same… ‘The Death Has a Solution’. They Bothe searched for the Solution and today we know them by the name of Gautam Budha and Mahrishi Dyananda. If they had believe like many of the persons in their times that Death has no solution then they might have also ended up like them. So whenever you are surrounded by a problem or problems believe that there is solution to all of them. How to find a solution let us go ahead to the second step.

Solution lies in The Problem Itself: The solution to any problem lies in the problem itself. After realisation that the problem has a solution the second realisation we get from mathematical experience is that the solution lies in the problem. Many times we have seen people to search for the solution to their problems in all direction, except the problem. They go from one Guru to another, one expert to other to find the solutions and forget to analyse their problem. They search for some quick fix to solve the problem, but in life quick fix don’ work for a longer time and problem re occurs. Of course there are certain problems (like Health related problems) we have to go to expert for the solutions. The decision to go to an expert should also come from the understanding of the problem. I f u understand the problem and find out that solution is to go to the expert then definitely one should go to the expert. But first analyse the problem because the solution as I have said lies in the problem. Once that is final we should go through the problem and reach that solution. For going through the problem we should write down the problem in the form of the statement (as in Mathematics). Then we need to dissect the problem in smaller parts and that takes us to step three.

For Solution divide problem into Equations: The problem statement gives us many equations. Every problem big or small can be divided into smaller ones. These smaller problems which I refer to as equations here combined give us a way to reach to the solution. For example a parent is faced with a problem of his child not getting enough scores in studies. The problem when seen casually seems one problem and one solution is seen as to find out the ways to motivate or force the child to study properly and increase scores. But when we look deeply into the problem and see under lying smaller equations we may find some other and proper solutions. Let us try to bring out some equation out of the statement of this problem. These equations are general and may vary from situation to situation.
a. The child wakes up in the morning at 6
b. He then roams around for some time and then starts getting ready for the school.
c. At about 7:30 the child is ready for the school. (1.5 hours for getting ready?)
d. The mother due to some other obligations in the morning is not ready with the tiffin, so the chilled takes some time to watch his favourite cartoon serial. (??)
e. By the time tiffin is ready the child is so much involved in the cartoon that it takes another five minutes to force him to the school.
f. He reaches just in time at school and is searching for a seat in the class. Since he is late he is forced to sit on some last benches.
g. He sits with the most talkative child in the class or his partner is not much interested in the study and instead is drawing some thing on the copy.
h. One way the other the child is distracted from the teachers lecture and is not able to learn much.
i. He reaches home and is not sure what the home work is.
j. He then tries to shy away from the problem of home work by telling a lie. (??)
… k…l …m
And so on. There can be these or some other equations to this type of problem with such parents. Now as we have written down the equations we can get some concrete and long lasting solution to the problem. This is just an example we can do the same for every problem in our life. We have to look for each equation which that problem offers us and write down those equations. Then we can go for the most appropriate solution. (Not the one which suits us). The permanent solution is not in getting what we should get by hook or crook, but the problem equation point towards. The long lasting solution is the one which balances all the problem equations.

For Solution Look for Balance: All of us who has solved problems in mathematics might be aware of the term LHS=RHS. That means Left Hand Side is equal to Right Hand Side. Once we reach at this point the problem is declared solved. That is where most of our conflicts should also end. By undermining or exaggerating one side of equation we can never reach a solution. Like in the parent child example above, if parents believe that the whole problem is due to the friends of the child, or whole problem is due to the child and friends have nothing to do with it, then in both cases they are wrong. The problem and solutions are most of the times in between and not at the extremes. The balance is the key to happy and peaceful living. Balance is the key to success in any field. Once when Sachin Tendulkar was not performing so well (in the years 2006-2007), some body asked Donald (the fast bowler from South Africa) – ‘Do you reckon Sachin is still the best Batsman in the World’. His answer was- ‘Yes, because it is not the runs which he scores or does not score, it is about his balance when he plays the ball. He still has such a good balance, that he is a threat to every bowler. Soon you will see him back in form.’ And the time has proved Donald right. If the balance in life has been lost peace will be lost at once. The solution to the peace will to regain the balance. Every person will have to search for the balance (the solution) from his own expertise. Because there is not a single method to every problem.

For Solution choose your Own Method: Though every problem has a solution and solution lies in the problem, but every problem can have more than one method to reach the solution. In mathematics single problem can be solved in many ways. Once in an Interview I was asked the question which term is greater 2/3 or 3/5. Now for solving this you have different methods, I cross multiplied the values thereby getting 10 and 9. So the one with the value ten that is 2/3 is greater was my answer. The interviewer refused to accept the answer because my method was wrong (I still cleared the interview and was selected). But this prompted me to say to the interviewer that methods are not as important in Mathematics as are solutions or results. For the problem I was given you can have many different methods, you can convert them to decimals (0.67, 0.60) or you can make the denominators equal (10/15, 9/15) so on. My point here is we all have different capabilities and different limitations so if a method in a problem works for Mr. X it is not necessary that Mr. Y should also work on the same method. He can have his own choice depending on his own capabilities. Once you choose a method and if it does work then store the procedure in your mind. If does not work reassess the equations and plan a different method. It should also be remembered that the whole process is not waste, trying different methods and succeeding to solve the problem is only one part the other part is that it enables you to solve many more future problems.

Remember all Methods from Smaller Problems: The problem today will become an equation tomorrow. This is a fact in mathematics and in life. The problems which we faced in the childhood, looks like small problems now, but at that time those were the biggest problems for us. How we faced those small problems has prepared us to face the bigger problems now. Usually we listen and often say the life is continuous learning process, with every step we are learning new methods new possibilities. That is very much true. So while solving a problem it is very necessary that we learn the lesson the problem gave us. Learning the lesson from the methods which did not work for us is as important as from the method we used to solve the problem.

Keep Learning to Handle Future Problems: While solving the problem and dividing it into smaller equations we find the reason why the problem has occurred. This is the first lesson, we have learned the reason the problem occurred and if in future we are able to avoid this very reason the problem will never crop up. Second while solving the problem we have understood how to solve the problem. So two lessons with one problem.

Unlike mathematics the problems in life does not have a single fixed solution. Like we have to deploy different methods in different situations, we might get different solutions in those conditions. But the common solution to all problems should be peace and harmony. The solutions should bring the peace and harmony not only to the involved parties but also to the society in general. If this is not the case reassess the equations and find a new method.

एक आवश्यक क्रिया

एक आवश्यक क्रिया सा हो गया है
हर रात गुस्से में आग बबूला होना

क्योंकि हमारे आस पास जो हो रहा है
अंग बन गया है दिनचर्या का

कानों ने चौंकना बंद कर दिया है
आंखों ने छोड़ दिया है फैलना सिकुड़ना
वातावरण में भर गई सड़ांध की
आदी हो गई है नाक भी
करोड़ों रुपए अब आम बात लगते हैं
घोटाला यूं जैसे परिचित का नाम हो

हर रात समाचार सुनकर
नपुंसक गुस्से को चीख चिल्लाकर निकाल
विस्तर में घुस जाते हैं
सुबह दफ़्तर भी तो जाना है

ग़ज़ल - 2

फ़क़त हम ही को न सज़ाएं मिलीं
ग़म की और भी कथाएं मिलीं

गले लग जी भर के रोया
तेरे वतन की जो हवाएं मिलीं

जो भी चाहा वो कहां मिला
मौत मांगी थी दुआएं मिलीं

तुझे भूलना कहां आसान था
हर गाम तेरी सदाएं मिलीं

‘अश्क’ ने बरसना ही हुआ
क्या ताज्जुब कि घटाएं मिलीं

ग़ज़ल - 1

चलो फिर ग़ज़ल कहें उदासी दूर करें
पूरी तरह न ही सही ज़रा सी दूर करें

आओ फिर हाथ जोड़ें आंखें बन्द करें
दिल में उठती शैतानी बला सी दूर करें

कब तक उम्मीद रखें कोई मसीहा आएगा
आओ ख़ुद ही मुस्कराएं खला सी दूर करें

राहें सुनसान इंतज़ार करें कब तलक
ताज़े मोड़ दे के सिलसिला बासी दूर करें

क्यों न दिल ही के आईने में तलाशें उसे
दैर-ओ-हरम भूल जाएं काबा कासी दूर करें

खिड़कियां दिमाग की खोल दें अपनी ‘अश्क’
सड़े फ़िक्रों की उमस भरी हवा सी दूर करें

तुम्हारी प्रशंसा के गीत

कई बार सोचा रुकूं
तुम्हारी प्रशंसा में गीत कहूं
फिर चलूं

कहूं वह सब कुछ जो तुम्हें खुश कर दे
पर रोका है स्वयं को
अगर सब कह दिया –
तो मेरे पास मेरे मन में क्या रह जाएगा

तो प्रिय रहने दो
मुझे संजो कर रखने दो
तुम्हारी हर ज़ुल्फ़ के गीत को
होंठों की ग़ज़ल को
ता जो तन्हाई में
मेरे पास कुछ तो हथियार हो...

तारे तोड़ लाने के सपने

तारे तोड़ लाने के सपने/
मेरी आंखों तक भी पहुंचे
पर पैरों के नीचे ज़मीन ही नहीं थी
ख़ुद को ज़मीन खोजने में लगा दिया
ताकि ज़मीन पर पाँव रखूं
उछलूं
और भर लूं तारों से झोली
पर काफ़ी खोजने के बाद भी
ज़मीन नहीं मिली
अब मेरी आंखों में ज़मीन ही का सपना है –
तारों को मैं भूल चुका हूं

एक किताब की मानिन्द

एक किताब की मानिन्द
खोल दिया ज़िन्दगी को हर किसी के सामने
ता जो दोस्त न सही
ग़ल़तफ़हमी में कोई मिलने वाला दुश्मन न बन जाए
पर हर आदमी सलीके से नहीं पढ़ता किताब
कुछ उसके वरक मोड़ कर निशान लगाने की साजिश करते हैं
कुछ उसकी अहमियत न समझ –
उसे इस्तेमाल करते हैं चाय या पानी का गिलास रखने के लिए
वाज़ इन्सान –
खुली किताब की फ़िक्र न कर - करने लगते हैं कुछ और काम
ऐसे में उसके खू़बसूरत या बदसूरत पर अहम वरकों पर
स्याही या कुछ और गिर जाए
उसे दाग़ी कर दे
इतना कि हर्फ़ दिखने बंद हो जाएं
उन्हें इससे कुछ लेना देना नहीं है
मैं सोचता हूं
बल्कि यकीनन यह चाहता हूं
कि किताब बन्द कर दूं
कि फिर कभी न खोलूं
पर यारब़ !
जिनके सामने खुल चुकी है बन्द करने भी देंगे।

युद्ध का सत्य

मैं मानता हूं मित्र
कि जिस ओर खड़े हो तुम
वहीं है सत्य
वहीं है धर्म
वहीं है जगदीश्वर भी
मगर जब तक महाभारत की घोषणा न हो जाए
कृष्ण का कर्त्वय होता है युद्ध टालना

तीर तलवार विध्वंस की भाषा जानते हैं
गोली का सत्य केवल मृत्यु देना है
और युद्ध का परिणाम नहीं होता जय या पराजय
होता है परिणाम
अवशेष
टूटे हुए मकान
डरे हुए मन
सिमटे हुए मनुष्य
अभिमन्यु हो – द्रोण हो – या हो भीष्म
सबको होना होता है अन्याय का शिकार
धृतराष्ट्र को भी कोसना पड़ता है अपने अन्धेपन को
युधिष्ठर को भी भोगना पड़ता है नरक
जब कभी भी किया जाता है सत्य के लिए युद्ध
सत्य भी हो जाता है दफ़न शवों के ढेर के नीचे
फिर कोई नहीं बचता जो कह सके कि
सत्य की हुई है विजय

कोई भी महाभारत निर्णय नहीं कर पाता सत्य का
मगर जब कभी भी होता है सत्य की द्रौपदी का अनादर
महाभारत निश्चित हो ही जाता है
द्रौपदी का शील स्वयं प्रमाण है सत्य का
उसका दांव पर लगना ही उसका अनादर है

इसीलिए कहता हूं मित्र सत्य को दांव पर मत लगाओ
सत्य का अनादर जन्म देगा महाभारत को
और महाभारत होना सत्य की मृत्यु है

नपुंसक पीढ़ी

काफी हाऊसों में
काफी में घुलते मिलते नाराज़गी के शब्द
थोड़ी गर्म बहसें
ऊपर उठा कर हाथ ज़ोरदार आवाज़ में विरोध प्रकटन
और फिर आंखों में उतर आए गुस्से को
दो चार भद्दी गालियों के साथ थूक देना पूरी व्यवस्था के माथे पर
फिर
काफी पी कर सड़क तक आते आते
वो गालियां
वो विरोध
वो बहसें
वो नाराज़गी
जाने कहां खो जातीं हैं
और यहीं समाप्त हो जाता है
मेरी पीढ़ी की युवाशक्ति का विद्रोह

आईए कुछ बात करें

आईए कुछ बात करें

जलते मौसम की, बरसते बादल की
ठिठुरती सर्दी की, सरकते दलदल की
हवा की, ठण्डक की, घटा के काजल की
फूलों का खुश्बू की, सबा के आंचल की

आईए कुछ बात करें
दूर अंधेरों की फैलती रोशनी की
गमों के जमघट की खेलती खुशी की
सियासी चालों की लुभाती कुर्सी की
बिरोधी भाषणों की सरकारी चुप्पी की

आईए कुछ बात करें
चोरी के गानों की, फिल्मी नंगेपन की
दरकते रिश्तों की, टूटते आंगन की
तड़पती जवानी की, बिलखते बचपन की
मुट्ठी भर खुशी को तरसते जनगन की

आईए कुछ बात करें
बीते आज़ादी के इतने सालों की
हमने जो झेले उन सब तूफानों की
चिकने से खुरदरे होते हुए गालों की
बापू की आंखो में उभरते सवालों की

आईए कुछ बात करें
आईए कि हम कर सकते हैं बस यही
बतियाएं और सो जाएं चैन से सभी
जुल्मों को देखें सहें न करें कुछ भी
आज़ादी है हमें बस बातें ही करने की

आईए कुछ बात करें