– Basudeba Mishra
सा यस्मिन् वर्त्तते तत् साङ्ख्य । विशिष्टरूप से किसी तत्त्व का (अन्य तत्त्वों से भेद प्रदर्शन पूर्वक) स्वरूप प्रकथन को संख्या कहते हैं (भेदाभेद विभागोहि लोके संख्या निबन्धन) । जो सर्वत्र अभेदरूप से प्रतीत होता है, वह एक है (एक इता संख्या । इता अनुगता सर्वत्र या संख्या सा एक । अन्वयव्यतिरेकाभ्यां संख्याभ्युपगमेसति) । वह संख्या (स्वरूप प्रकथन) जिसमें है, वह साङ्ख्य है । इसलिए मूल प्रकृति तथा विकृतियों का स्वरूपदर्शन करनेवाले शास्त्र को साङ्ख्यदर्शन कहते हैं । आत्मसंयमन पूर्वक तत्त्व का सम् (अच्छी प्रकार, एक साथ) ओर अधि (सबसे उपर) चिन्तन रूप समाधि के बल पर आत्मज्ञान के साथ बुद्धि का युक्त हो जाना ही साङ्ख्ययोग है । यह बुद्धिपूर्वक मानस क्रिया है । कर्म बुद्धिपूर्वक शारीर क्रिया है । अतः क्रिया रूपसे साङ्ख्य और योग पृथक नहीं है । इन दोनों में से एक साधनमें भी अच्छीप्रकार से स्थित मनुष्य दोनों के फल प्राप्त कर लेता है (एकमप्यास्थितः सम्यगुभयोर्विन्दते फलम् – गीता 5-4) ।
सङ्ख्यावान् सत्वभूतोर्थः सर्व एवाभिधीयते ।
भेदाभेद विभागोहि लोके सङ्ख्या निबन्धन ।
स धर्मो व्यतिरिक्तोवा तेषामात्मैव वा तथा ।
भेदहेतुत्वमाश्रित्य सङ्ख्येति व्यपदिश्यते ।
समवेता परिच्छेद्ये क्वचिदन्यत्र सा स्थिता ।
प्रकल्पयति भावानां सङ्ख्याभेदं तथात्मनः ।
परत्वे चापरत्वे च भेदे तुल्या श्रुतिर्यथा ।
सङ्ख्याशब्दाभिधेयत्वं भेदहेतोस्तथा गुणे ।
अतो द्रव्याश्रितां सङ्ख्यामाहु संसर्गवादिनः ।
भेदाभेद व्यतितेषु भेदाभेद विधायिनीम् ।
The Western mathematicians claim that they have lifted mathematics to great heights and boast of a long succession of mathematicians. Yet, none of the Western mathematicians defines scientifically what a number is or what mathematics is. The test of validity of a mathematical statement is its logical consistency. While Vaidic mathematics was based on fundamental natural principles, which are logically consistent, modern mathematics is not mathematics in the strict sense as it is logically not consistent. The various branches of Vaidic mathematics were developed to meet the requirements of explaining various physical phenomena from the mathematical angle. However, mathematicians in Europe did not confine their numerical system only to real objects. Some say that mathematics allows statements to be made unambiguously, in a manner that is value-free and culturally independent. Only when hypotheses can be stated precisely in this way can they be compared and tested experimentally or observationally. Yet, now-a-days there is rarely a mathematical statement of physical phenomena, which is value-free or culturally independent. These aspects are given fancy names to camouflage their values or the culture of incomprehensibility that are associated with most modern mathematical statements. In modern science, the technical terms are said to be defined mathematically and the words (terms) are used subsequently as a shorthand representation of the mathematical concept. Yet, such descriptions lack the unambiguous precession while retaining clarity of expression that is associated with mathematical statements.
Thus, while no mathematician defines number scientifically, different mathematicians interpret mathematics variously. Some divide the modern views on mathematics into four categories. According to Platonism, mathematicians discover the concepts such as number, dimension, groups, sets, etc., and not invent it. The π is in the sky – they say. According to Conceptualism, popular among Sociologists, mathematics is a product of the human mind. We create an array of mathematical structures, symmetries, patterns and force the world into this mould as we find it compelling. According to Formalism, mathematics is the manipulations of Symbols according to specified rules. Here the focus is on the relation between entities and the rules governing them rather than the question of whether the object being manipulated has any intrinsic meaning. According to Intuitionism only the simplest intuitive ideas could be used. Anything outside our experience must be constructed from the simplest ingredients by a sequence of intuitively familiar steps. Here the attention is restricted to measurable quantities in order to avoid introducing “obvious” concepts like simultaneity, which may turn out to be experimentally meaningless.
According to the Vaidic theory, number is a property of all substances that differentiates between similars (द्रव्येषु भिन्नत्वव्यवहारः पृथक्तातिरिक्तभेदवशात् संख्यावशाच्च). An object can be perceived only through the differentiation of its inherent structure and its position from other similar objects (आन्तरालिकावयव संस्थानगतभेद). Number is the cause for the perception of differentiation among objects (भेदगणनाकत्मकत्वम्) just like distance variable (परत्व) and proximity variable (अपरत्व) are causes for differentiation of time and space. When we cannot distinguish the substance from other similar substances, we call the substance as one (एक). If we can distinguish, we call them many (बहु). Many can be 2,3,4, ….n (not infinity) depending upon the quantum of sequential differentiation. Mathematics is the quantitative aspect of reality, which is the process of conversion of one to many and vice-versa as well as many to other many through linear or non-linear accumulation and reduction. Linear accumulation and reduction are called addition and subtraction. Non-linear accumulation and reduction are called multiplication and division. Before we proceed further, it is necessary to define “matter” and “properties” as number has been defined as a property of substances, i.e., matter.
(मेरे लिखे हुए पुस्तक वैदिक सङ्ख्याविज्ञानम् से)