波你尼Panini

波你尼出生在Shalatula，这是今巴基斯坦印度河畔阿托克附近的一个城镇。给出的波你尼日期纯属猜测。专家们给出的日期在公元前4、5、6和7世纪，历史学家对他所承担工作的范围也没有一致意见。几乎毫无疑问的是，考虑到他工作的时期，他是整个知识发展中最具创新性的人之一。我们将在下面稍微多谈历史学家如何试图确定波你尼生活的日期。

波你尼是一位梵语语法学家，他给出了语音学、音系学和形态学的全面而科学的理论。梵语是印度印度教徒的古典文学语言，波你尼被认为是该语言和文学的创始人。有趣的是，“梵语”一词意为“完整”或“完美”，它被视为神圣语言，或众神的语言。

一部名为Astadhyayi（或Astaka）的论著是波你尼的主要作品。它由八章组成，每章又细分为四分之一章。在这部作品中，波你尼区分了神圣文本的语言与通常的交流语言。波你尼给出了形式化的产生规则和定义来描述梵语语法。他从大约1700个基本元素（如名词、动词、元音、辅音）开始，将它们归入各类。句子的构造、复合名词等被解释为作用于底层结构的有序规则，其方式类似于现代理论。在许多方面，波你尼的构造类似于今天定义数学函数的方式。Joseph在[2]中写道：-

[梵语]在科学上的应用潜力，由于波你尼对其语法的彻底系统化而大大增强。……仅凭不到4000条经句[以格言形式表达的规则]，他几乎构建了梵语的全部结构，其总体“形态”在此后两千年中几乎没有改变。……波你尼为提高梵语的语言便利性所作努力的间接后果，很快就在科学和数学文献的特征中显现出来。这可以通过将梵语语法与欧几里得的几何学相比较来阐明——这是一个特别贴切的比较，因为在古希腊数学是从哲学中发展出来的，而在印度它……部分是语言发展的产物。

Joseph接着提出了一个令人信服的论点，即印度数学的代数性质是梵语语言结构的结果。他特别指出，代数推理、印度用词语表示数字的方式，以及最终现代数系在印度的发展，都通过语言结构联系在一起。

波你尼应被视为用于规定计算机语言的现代形式语言理论的先驱。约翰·巴科斯范式由约翰·巴科斯于1959年独立发现，但波你尼的记法在能力上与约翰·巴科斯的记法等价，并具有许多相似的性质。想到对当今理论计算机科学至关重要的概念竟起源于约2500年前的一位印度天才，这令人惊叹。

在本文开头，我们提到某些历史学家将某些概念归于波你尼，而其他人对此提出异议。其中一个理论由B Indraji于1876年提出。他声称婆罗米数字是从使用字母或音节作为数字发展而来的。然后他为该理论画上句号，提出公元前八世纪的波你尼（比大多数历史学家所定的波你尼年代更早）是第一个想到用字母表中的字母来表示数字的人。

有许多证据支持Indraji的理论，即婆罗米数字是从字母或音节发展而来的。然而这并不完全令人信服，因为仅举一例，1、2和3的符号显然并非来自字母，而是分别来自一、二、三条线。即使人们接受数字与字母之间的联系，将波你尼视为这一思想的创始者，似乎除了知道波你尼是世界所知最具创新精神的天才之一，因而相信他也可能迈出这一步并非不合理之外，并无更多依据。

还有其他与Astadhyayi密切相关的著作，一些历史学家将其归于波你尼，另一些归于波你尼之前的作者，还有一些归于波你尼之后的作者。这是一个有许多理论但几乎没有（如果有的话）确凿事实的领域。

我们还承诺回到对波你尼年代的讨论。关于这一主题的研究并不缺乏，因此存在跨越数百年的理论并非努力不足的结果，而是这一主题困难程度的体现。为这类文本断代的通常方法是考察其中提到了哪些作者，以及哪些作者提到了该著作。人们可以使用这一方法，看看波你尼提到了谁。

波你尼提到了十位学者，我们必须根据上下文假定这十位都对梵语语法的研究有所贡献。当然，这本身就表明波你尼并非孤独的天才，而是像艾萨克·牛顿一样，“站在巨人的肩膀上”。波你尼必定生活在这些人之后，但这对于确定年代毫无帮助，因为我们完全不知道这十位中任何一位生活在何时。

还有哪些内部证据可用呢？当然，波你尼用了许多短语来例证他的语法，这些短语已被仔细检查，看其中是否含有任何能指示年代的线索。举个例子说明我们的意思：如果我们拿起一个文本，其中作为例子包含“我每天乘火车上班”，我们就会知道它必定是在铁路普及之后写成的。让我们用Astadhyayi中两个经过大量研究的实际例子来说明。第一个是试图看是否有希腊影响的证据。是否可能找到证据，意味着该文本必定写于亚历山大大帝征服之后？有少量希腊影响的证据，但在亚历山大时代之前，希腊影响就已到达印度次大陆的东北部。尚未确认任何决定性的证据。

另一个角度是考察波你尼对尼姑的提及。有人认为这些必定是佛教尼姑，因此该著作必定写于佛陀之后。这是一个不错的论点，但有一个反论指出，在佛陀时代之前就有耆那教尼姑，波你尼的提及同样可能指她们。证据再次不具决定性。

其他人也提到过波你尼。然而，大多数人所指的波你尼似乎是一位诗人，尽管有人认为他们是同一个人，但大多数历史学家同意语言学家和诗人是两个人。这同样是不具决定性的证据。

让我们以Cardona在[1]中对波你尼贡献的评价作为结束：-

波你尼的语法已从各种角度得到评价。在所有这些不同的评价之后，我认为该语法值得断言……它是人类智慧最伟大的丰碑之一。

Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan. The dates given for Panini are pure guesses. Experts give dates in the 4th , 5th , 6th and 7th century BC and there is also no agreement among historians about the extent of the work which he undertook. What is in little doubt is that, given the period in which he worked, he is one of the most innovative people in the whole development of knowledge. We will say a little more below about how historians have gone about trying to pinpoint the date when Panini lived.

Panini was a Sanskrit grammarian who gave a comprehensive and scientific theory of phonetics, phonology, and morphology. Sanskrit was the classical literary language of the Indian Hindus and Panini is considered the founder of the language and literature. It is interesting to note that the word "Sanskrit" means "complete" or "perfect" and it was thought of as the divine language, or language of the gods.

A treatise called Astadhyayi (or Astaka ) is Panini's major work. It consists of eight chapters, each subdivided into quarter chapters. In this work Panini distinguishes between the language of sacred texts and the usual language of communication. Panini gives formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 basic elements like nouns, verbs, vowels, consonants he put them into classes. The construction of sentences, compound nouns etc. is explained as ordered rules operating on underlying structures in a manner similar to modern theory. In many ways Panini's constructions are similar to the way that a mathematical function is defined today. Joseph writes in [2]:-

[Sanskrit's] potential for scientific use was greatly enhanced as a result of the thorough systemisation of its grammar by Panini. ... On the basis of just under 4000 sutras [rules expressed as aphorisms], he built virtually the whole structure of the Sanskrit language, whose general 'shape' hardly changed for the next two thousand years. ... An indirect consequence of Panini's efforts to increase the linguistic facility of Sanskrit soon became apparent in the character of scientific and mathematical literature. This may be brought out by comparing the grammar of Sanskrit with the geometry of Euclid - a particularly apposite comparison since, whereas mathematics grew out of philosophy in ancient Greece, it was ... partly an outcome of linguistic developments in India.

Joseph goes on to make a convincing argument for the algebraic nature of Indian mathematics arising as a consequence of the structure of the Sanskrit language. In particular he suggests that algebraic reasoning, the Indian way of representing numbers by words, and ultimately the development of modern number systems in India, are linked through the structure of language.

Panini should be thought of as the forerunner of the modern formal language theory used to specify computer languages. The Backus Normal Form was discovered independently by John Backus in 1959, but Panini's notation is equivalent in its power to that of Backus and has many similar properties. It is remarkable to think that concepts which are fundamental to today's theoretical computer science should have their origin with an Indian genius around 2500 years ago.

At the beginning of this article we mentioned that certain concepts had been attributed to Panini by certain historians which others dispute. One such theory was put forward by B Indraji in 1876. He claimed that the Brahmi numerals developed out of using letters or syllables as numerals. Then he put the finishing touches to the theory by suggesting that Panini in the eighth century BC (earlier than most historians place Panini) was the first to come up with the idea of using letters of the alphabet to represent numbers.

There are a number of pieces of evidence to support Indraji's theory that the Brahmi numerals developed from letters or syllables. However it is not totally convincing since, to quote one example, the symbols for 1, 2 and 3 clearly do not come from letters but from one, two and three lines respectively. Even if one accepts the link between the numerals and the letters, making Panini the originator of this idea would seem to have no more behind it than knowing that Panini was one of the most innovative geniuses that world has known so it is not unreasonable to believe that he might have made this step too.

There are other works which are closely associated with the Astadhyayi which some historians attribute to Panini, others attribute to authors before Panini, others attribute to authors after Panini. This is an area where there are many theories but few, if any, hard facts.

We also promised to return to a discussion of Panini's dates. There has been no lack of work on this topic so the fact that there are theories which span several hundreds of years is not the result of lack of effort, rather an indication of the difficulty of the topic. The usual way to date such texts would be to examine which authors are referred to and which authors refer to the work. One can use this technique and see whom Panini mentions.

There are ten scholars mentioned by Panini and we must assume from the context that these ten have all contributed to the study of Sanskrit grammar. This in itself, of course, indicates that Panini was not a solitary genius but, like Newton, had "stood on the shoulders of giants". Panini must have lived later than these ten but this is absolutely no help in providing dates since we have absolutely no knowledge of when any of these ten lived.

What other internal evidence is there to use? Well of course Panini uses many phrases to illustrate his grammar any these have been examined meticulously to see if anything is contained there to indicate a date. To give an example of what we mean: if we were to pick up a text which contained as an example "I take the train to work every day" we would know that it had to have been written after railways became common. Let us illustrate with two actual examples from the Astadhyayi which have been the subject of much study. The first is an attempt to see whether there is evidence of Greek influence. Would it be possible to find evidence which would mean that the text had to have been written after the conquests of Alexander the Great? There is a little evidence of Greek influence, but there was Greek influence on this north east part of the Indian subcontinent before the time of Alexander. Nothing conclusive has been identified.

Another angle is to examine a reference Panini makes to nuns. Some argue that these must be Buddhist nuns and therefore the work must have been written after Buddha. A nice argument but there is a counter argument which says that there were Jaina nuns before the time of Buddha and Panini's reference could equally well be to them. Again the evidence is inconclusive.

There are references by others to Panini. However it would appear that the Panini to whom most refer is a poet and although some argue that these are the same person, most historians agree that the linguist and the poet are two different people. Again this is inconclusive evidence.

Let us end with an evaluation of Panini's contribution by Cardona in [1]:-

Panini's grammar has been evaluated from various points of view. After all these different evaluations, I think that the grammar merits asserting ... that it is one of the greatest monuments of human intelligence.