बस एक गुज़ारिश है - थोड़ा सा रो देना ...

जब माँ का "कलेजा" कटकर अलग हो जाए, थोड़ा-सा रो देना !
जब मातृभूमि-रक्षण विफल हो जाए, थोड़ा-सा रो देना !

जब "कश्यप-तपोभूमि" पर तिरंगा-भस्म हो जाए, थोड़ा-सा रो देना !
जब "स्व-धरा" पर विदेशी ध्वज-लग्न हो जाए, थोड़ा-सा रो देना !

जब भारत-भूमि का "मुकुट"-पतन हो जाए, थोड़ा-सा रो देना !
जब सन संतालिस (1947) कल हो जाए, थोड़ा-सा रो देना !

जब देह से "प्राणों" का "प्रथक्करण" हो जाए, थोड़ा-सा रो देना !
जब पौरुष पर नपुंसकता स्थानापन्न हो जाए, थोड़ा-सा रो देना !

थोड़ा-सा रो देना के ना हम बचा सके, न तुम बचा पाओगे........
थोड़ा-सा रो देना के हम लिखते रह गए, तुम पढ़ते रह जाओगे.........
थोड़ा-सा रो देना के कल को संसार ये न कहे कि कश्मीर हमारा था ही नहीं !

(written in 20111)

Axiomatizing Natural Numbers

One can not prove theorems by assuming nothing. But what is more fascinating is that a large number of concepts can be explained by a fixed number of elementary notions, known as axioms.
Axioms are assumed to be self-evident truths. One such set of axioms about Natural Numbers was proposed by Peano:

Peano’s Axioms

Let $\mathbb{N}$ denote a set. Suppose we are not permitted to see its contents. Instead, we are given the following information about $\mathbb{N}$:

1. $0 \in \mathbb{N}$
2. A mapping $s: \mathbb{N} -> \mathbb{N}$, different from indentity map, such that $\mathbb{N}$ is invariant under $s$, i.e., $a \in \mathbb{N} \implies s(a) \in \mathbb{N}$
3. Pre-image of $0$ does not exist under $s$,
   i.e., there does not exist an $a \in \mathbb{N}$ such that $s(a) = 0$
4. The mapping $s$ is injective, i.e., $s(a)=s(b)\implies a=b$
5. If $S \subseteq \mathbb{N}$ with $0 \in S$ and $a \in S \implies s(a) \in S$, then $S=\mathbb{N}$

With these axioms alone, we can describe/generate the entire set $N$, without actually seeing its elements. Let us see how.
Let us start by analyzing what are we provided with. We are sure that there exists an element denoted by $0$ in $\mathbb{N}$. So $\mathbb{N}$ is non-empty. Additionally there also exists a map $s$ from $\mathbb{N}$ to itself, which is different from identity map.
This map is defined in such a way that when fed with an element of $\mathbb{N}$, it gives us another element from $\mathbb{N}$. Notice here, that had the map been identity map, it would be useless to us, since it would return the same element. So $s$ must be a non-identity map, so that we can get new information about $\mathbb{N}$.

Written with StackEdit.

राष्ट्र को समर्पित जो तरुणाई है ...

मंदिर के भगवान भी पूजे हैं मैंने, हर सुबह मैंने ज्योत जगाई है,
पर सजदा करता हूँ आज उसका, राष्ट्र को समर्पित जो तरुणाई है !

मेरी पूजा की थाली तुम्हारे लिए है, आज वतन पर तुम फ़ना हो गए,
मेरी श्रद्धा के अश्रु तुम्हारे लिए हैं, मेरी नज़रों में तुम खुदा हो गए !

वो माँ के दुलारे तुम भी थे, बहना के प्यारे तुम भी थे,
किसी के सुहाग तुम भी थे, बच्चों के ख़्वाब तुम भी थे,
एक माँ को माँ का दान था ये, क्षत्रिय का बलिदान था ये,
जी सकें हम सब भारतवासी, इस वचन का सम्मान था ये,

इन शहादतों का मान रखो, खुद से पहले हिन्दुस्तान रखो,
थोड़ी गैरत रखो उन वीरों की, वतनपरस्ती के इन हीरों की,
नहीं कहता मैं भर्ती हो जाओ फ़ौज में, करो सीमा पर लड़ाई,
जहाँ भी हो जैसे भी हो, कुछ करो जिससे हो देश की भलाई,

कुछ बनाओ हिन्दुस्तान ऐसा, हर दिल में हिंदुस्तान हो,
फिर से बनें हम विश्व गुरु, दुनिया में हमारी पहचान हो,
माटी है ये बलिदान की, इसका न अब अपमान हो,
जागो, पुकार रहा है वतन, जागो अगर इंसान हो !

- साहिल

रोज़ थोडा-सा

थोडा-सा खुद को रोज़ खोया तुझमें,
तुझमें ही रोज़ खुद को तलाश किया,
कुछ इस तरह मैंने तुझसे प्यार किया ...
- साहिल

बस यही बात कहनी थी तुमसे

Bharat - A journey striving for Perfection

Recently I have realized something very subtle. Something which is not realized by many in day-to-day life. I may be wrong, but it is a very self-evident observation:

Noun does NOT exist, everything is just a collection of adjectives (attributes).

 Each person can be taken as the sum-total of some qualities, that he/she possesses. So one of the ways to see a person/entity is to look at the kind of features/traits that are present in him/her/it. In this perspective, noun becomes an abstract concept (illusion), which requires real attributes to express itself in a real world.
Look at it this way, whenever we meet someone, we usually remember some aspect of him/her. We may remember him/her by multiple roles he plays: father, mother, clerk, teacher etc. We always need some kind of description for him/her. This description is not our own fantasy, rather it is the set of terms/traits through which we perceived him/her.

A person has multiple qualities. But when one quality dominates all other qualities, he/she becomes famous for that single quality. Public remembers him/her for that single quality. That quality becomes associated to his/her name, rather becomes her name. For example, Arjun in Mahabharat had many qualities, but when we say "धनुर्धर" (archer), the face of Arjun quickly comes to our mind. Arjun might be having many qualities, but this art of archery that he had mastered, got associated to his name.

When you refine your one attribute, then you will get that attribute as your name. In deeper sense, you will become the attribute itself. On microscopic scale, it can be said that your one attribute will dominate so largely over others, that that attribute will be identified by you. You will become a "symbol" of that particular attribute. This is pictorially represented in the adjoining figure.

Specialization is the key to glory. History of Indian civilization is full of people who were specialized in special art and science. For example, look at the intricate yet beautiful architecture of temples all over India. This specialization is not only important for an individual, but also for a nation. These specializations when followed over multiple generations in a family, become the कुलीनता (Kuleenta). Kuleenta is the civilizational asset (resource) of a nation. A nation full of multiple specializations is destined to progress and prosperity.

So now the question arises, what should an individual look to specialize in ?
This is a question, difficult to answer. Earlier a single Guru used to monitor the behavioural, mental, physical and psychological aspect of the student. So he could visualize what the personal traits of a student are and he would initiate him/her into that field from very early in life, so that he/she could learn to the maximum.
This is not possible in today's education system, because today's education system is not bothered about holistic development of a child by polishing his/her traits. Today, many teachers teach but none of them is concerned about polishing the inherent abilities of the student.

So today, an individual must do self-evaluation. He/she should reflect on one's own inherent abilities. So coming back to the topic, we were discussing that what is the advantage of having specialization and not having little little knowledge of all fields. Let me take you on another tour...

Suppose a group of people are shown a very very large-sized scenery of Nature having a mermaid in it....just for 2 min. Now all of them are told to redraw the entire scenery. How will they re-draw it ?

Simple and easy way is to distribute the work. The entire scenery is divided into several portions and each portion is assigned to a particular person of the group. But sadly more than 80% of the people were more interested in analyzing the mermaid. So they didn't notice the remaining part of the scenery. Those who were assigned the mermaid portion were able to redraw it but all other portions (the land, the sky, the trees, the birds, the clouds.....) couldn't be drawn.

So what is the moral ?

The nation neither needs little knowledge in all fields nor does she need specialization in only few fields. India needs specializations in multiple fields. Thus, as an individual, we must strive to fill out the complete scenery. To achieve this, one must align his/her personal abilities into the path which makes him/her stand out. 

In the first fig. we saw graph of one person. What will happen if we combine specialization graphs of all persons ?

Then we will get the complete scenery (the perfection) !

- Sahil Kakkar

कलम सरिता

सम्वेदनाओं की बाढ़ में जब गला रुंधता है,
जब भावों की लहरों को कोई छोर नहीं मिलता,

कलम-सरिता का बाँध तब खुलता है,
जब रुधिर-कण्ठ को साधन, कोई और नहीं मिलता !

- साहिल