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The Nature of Physical Reality by Subhash Kak
This book is a study of the paradoxes that underlie our understanding of the physical world. It is shown that many of these paradoxes are actually variants of classical paradoxes known to the ancient Indians and Greeks. The book presents a historical perspective on the development of key scientific ideas, and discusses the significance of our understanding the nature of consciousness in further advance. The book also examines several philosophical issues at the basis of modern physics.
- GenresPhilosophy
Paperback
First published December 31, 1986
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62 people want to read
About the author
Subhash Kak
45 books62 followersSubhash Kak is an Indian American computer scientist. He is Regents Professor and a previous Head of Computer Science Department at Oklahoma State University–Stillwater who has made contributions to cryptography, artificial neural networks, and quantum information.
Kak is also notable for his Indological publications on the history of science, the philosophy of science, ancient astronomy, and the history of mathematics. Alan Sokal labeled Kak "one of the leading intellectual luminaries of the Hindu-nationalist diaspora."
Kak is also notable for his Indological publications on the history of science, the philosophy of science, ancient astronomy, and the history of mathematics. Alan Sokal labeled Kak "one of the leading intellectual luminaries of the Hindu-nationalist diaspora."
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Displaying 1 - 2 of 2 reviews
December 30, 2019
4/5
This book is dense!
I found Mr Kak via my Facebook feed, and I was immediately intrigued with his detailed analysis of various subjects related to Indology. At the same time, if you read his Wikipedia page it would appear to be written by a rancorous leftist ideologue. I recommend to ignore the tone of that page, but keep it in mind to have a more balanced opinion, unlike the vitriolic leftist historians who have attacked him en-masse.
This book alludes to multiple instances where a number of laws from mathematics/physics have been propounded in earlier works of Indian Rishis. They come close to Newtons laws, are accurate in calculating details like distance to sun/moon, pie ratio, definition of irrational numbers etc. These were at the time when rest of the world, particularly West was struggling with simple basics.
Of course, all this goes completely in the face of Western view of history, which basically says that anything of value was discovered/invented in the West, despite the evidence to the contrary. For instance there is overwhelming evidence of massive interaction between Indian and Arabic world which ultimately became a conduit to the age of Western Age of Renaissance. Decimal number system, Algebra and elementary Astronomy are just some of the examples.
Now one wonder why the vitriol from all the historians who have been bred on western Bromide!
This book is dense!
I found Mr Kak via my Facebook feed, and I was immediately intrigued with his detailed analysis of various subjects related to Indology. At the same time, if you read his Wikipedia page it would appear to be written by a rancorous leftist ideologue. I recommend to ignore the tone of that page, but keep it in mind to have a more balanced opinion, unlike the vitriolic leftist historians who have attacked him en-masse.
This book alludes to multiple instances where a number of laws from mathematics/physics have been propounded in earlier works of Indian Rishis. They come close to Newtons laws, are accurate in calculating details like distance to sun/moon, pie ratio, definition of irrational numbers etc. These were at the time when rest of the world, particularly West was struggling with simple basics.
Of course, all this goes completely in the face of Western view of history, which basically says that anything of value was discovered/invented in the West, despite the evidence to the contrary. For instance there is overwhelming evidence of massive interaction between Indian and Arabic world which ultimately became a conduit to the age of Western Age of Renaissance. Decimal number system, Algebra and elementary Astronomy are just some of the examples.
Now one wonder why the vitriol from all the historians who have been bred on western Bromide!
October 5, 2022
Very worth a read.
****
"The principle of evolution forms the basis of the system of Sāṅkhya but that did not lead to the development of a scientific theory. The Mahābhārata (pre-400 BC) and the Purāṇas have a chapter on creation and the rise of mankind. It is said that man arose at the end of a chain where the beginning was with plants and various kind of animals and giant animals (asuras). ... "
That's incorrect interpretation of the word 'asuras'.
" ... Here’s the quote from the Yoga Vāsiṣṭha:4
""I remember that once upon a time there was nothing on this earth, neither trees and plants, nor even mountains. For a period of eleven thousand years (four million earth years) the earth was covered by lava. Then demons (asuras) ruled the earth; they were deluded and powerful. The earth was their playground. And then for a very long time the whole earth was covered with forests, except the polar region. Then there arose great mountains, but without any human inhabitants. For a period of ten thousand years (4 million earth years) the earth was covered with the corpses of the asuras."
Well, one can see why Kak interprets the word as giant animals, but that's not what it meant.
"Vedic evolution is unlike Darwinian evolution. The urge to evolve into higher forms is taken to be inherent in nature. A system of an evolution from inanimate to progressively higher life is taken to be a consequence of Nature’s intelligence that responds to the different proportions of the three basic attributes of sattva, rajas, and tamas.
***
"One primitive concept that has been debated considerably is that of infinity. George Cantor (1865-1918) introduced the theory of infinite sets in 1873 which allowed one to distinguish between different kinds of infinite sets. The idea at the basis of Cantor's theory is that of one-to-one correspondence which is quite obvious for finite sets. We say that two sets are of the same size if their elements can be put into one-to-one correspondence. Thus the sets of 5 books and 5 boys are equal in size because each book can be paired off with a different boy. Cantor argued that since one can set up a correspondence between the whole numbers and the even numbers:
"1 2 3 4 5 6 . . .
"2 4 6 8 10 12 . . .
"where each whole number has been paired off with one and only one even number, the two infinite sets are of the same size. This definition was rejected by many on the grounds that it made a part of the set equal to the whole. Cantor countered that infinite sets followed laws that did not apply to finite collections.
"Cantor called infinite sets that can be put in one-to-one correspondence with the whole numbers as countable and represented this size byאo (aleph null). He next showed that the set of all fractions and whole numbers (rationals) is countable. To prove this he represented the numbers in an array as shown:
"1/1 1/2 1/3 1/4 . . . .
"2/1 2/2 3/3 3/4 . . . .
"3/1 3/2 3/3 3/4 . . . .
"4/1 4/2 4/3 4/4 . . . .
"Note that some numbers are repeated as in the main diagonal where each number is 1. Now in a diagonal zigzag path going from 1/1→1/2→2/1→3/1→2/2→1/3→1/4→2/3→3/2→… , each number in the array is crossed just once. If repetitions of numbers are deleted one can pair off each rational in the path with a unique whole number in sequence. This establishes the result.
"Cantor next showed that some infinite sets are not countable. An example of this is the set of all points on the real line, that includes rational and irrational numbers. Given an infinite set one can, by considering all its subsets, construct another set of larger size. Cantor thus arrived at a sequence of aleph numbers,א0,א1,א2.... called transfinite numbers that represent progressively a higher measure of infinity. Cantor believed that no transfinite number existed between those representing the infinites of the whole numbers and the real line. In other words, he took the infinity of the real line to beא1. This is known as the continuum hypothesis.
***
"Cantor's work was severely criticized by his contemporaries. The mapping of the part to the whole had been anticipated by Leibniz who had said that the “set of all numbers contains a contradiction, if one takes it as a totality.” Cantor defended himself by claiming to be a Platonist, for whom ideas have an objective reality of their own. He did recognize, however, that one had the paradoxical situation of not being able to talk of a set of all sets, since the aleph numbers could be constructed recursively without end. Russell, upon reflection on this observation, produced a paradox dealing with classes which had a great influence on the mathematical world. This situation was described earlier in the form of the catalog and the barber paradoxes. Since classes of sets are often invoked in mathematical argument, this pointed to the care that was needed in using this concept. Later in their book, Principia Mathematica, Whitehead and Russell introduced the theory of types to avoid such difficulties. Individual objects, sets, sets of sets, and so on were classified as belonging to different types. Relations were defined for each type separately. They also introduced the axiom of reducibility, according to which any proposition of higher type is equivalent to one of first order. This axiom has received considerable criticism on the grounds that it is not self-evident.
***
"If there are limits to the nature of natural language processing by the computer, what is the nature of these limits? It appears that the best one can do is to devise actual systems -- in other words, use a constructive approach. The greatest success in devising a constructive approach to the description of a natural language is Pāṇini’s grammar for the Sanskrit language, an achievement termed by the famous linguist L. Bloomfield as ‘one of the greatest monuments of human intelligence.’6 The knowledge representation methodology in the grammar of Pāṇini and his successors is, in many ways, equivalent to the more powerful currently researched Al schemes. It includes rules about rules, analogs of which are not known for modern languages. Some elements of the Pāṇinian approach have already been incorporated in the current computer understanding systems. We will review the ‘standard’ approach to natural language processing, so that one may appreciate the commonality between the two as well as main points of difference.
"A discourse may be analyzed in terms of primitives that deal either with being or becoming. In other words, a primitive either describes categories and objects and their relationships, or if the context is clear it describes agents and transformations. These two kinds of primitives are complementary and yet each can serve as a knowledge representation scheme. One may describe transformation implicitly by means of description of the objects at successive times, and categories and objects in a domain can be defined as new objects. At another level, one may name an object from a root related to its most significant function, or one may have separate labels for objects and functions without any apparent relationship between the two. Often, languages have features related to both these ideas.
"Perhaps the earliest example of a debate about the being- becoming dichotomy is the one between the schools of Gārgya and Śākaṭāyana, two ancient Indian philosophers. Śākaṭāyana considered that nouns were derived from verbs or verbal roots, a principle whose universality was challenged by Gārgya on the basis that it often leads to forced etymology. According to Gārgya, if aśva (horse) was derived from aś (to travel) then other beings that travelled would also be called aśva, and states of being would be antecedent to objects. Since objects can be associated with variety of actions, Gārgya's objection was true. However, the significance of Śākatāyana's claim was to consider the object name to be derived from some (arbitrarily) chosen primary action associated with it.
***
"Note that in Pāṇini's system a finite set of rules is enough to generate infinity of sentences. The algebraic character of Pāṇini's rules was not appreciated in the West until very recently when search for similar generative structures was popularized by Chomsky and others. Before this, in the nineteenth century, Pāṇini's analysis of root and suffixes and his recognition of ablaut had led to the founding of the subjects of comparative and historical linguistics.
"Despite similarities between Pāṇinian and modern generative grammars, there exist striking differences as well. Some of these differences are related to the nature of the languages under study: Sanskrit in the case of Pāṇini, and modern European languages in the other case. Furthermore, the contemporary evaluation of Pāṇini is still going on, a process that is slowed down by the fact that the original is inaccessible to most linguists and computer scientists. In any event, one may define an approach to language analysis as being Pāṇinian if it uses:
"1) root and suffix analysis,
"2) linear string of rules and analysis by rule sequence,
"3) analysis by functional structure,
"4) exhaustive description.
***
"Note that in Pāṇini's system a finite set of rules is enough to generate infinity of sentences. The algebraic character of Pāṇini's rules was not appreciated in the West until very recently when search for similar generative structures was popularized by Chomsky and others. Before this, in the nineteenth century, Pāṇini's analysis of root and suffixes and his recognition of ablaut had led to the founding of the subjects of comparative and historical linguistics.
"Despite similarities between Pāṇinian and modern generative grammars, there exist striking differences as well. Some of these differences are related to the nature of the languages under study: Sanskrit in the case of Pāṇini, and modern European languages in the other case. Furthermore, the contemporary evaluation of Pāṇini is still going on, a process that is slowed down by the fact that the original is inaccessible to most linguists and computer scientists. In any event, one may define an approach to language analysis as being Pāṇinian if it uses:
"1) root and suffix analysis,
"2) linear string of rules and analysis by rule sequence,
"3) analysis by functional structure,
"4) exhaustive description."
" ... enumerate some of the ambiguities that make machine translation such a difficult task. These ambiguities need to be resolved, if at all possible, in various steps to obtain a translation. Each kind of ambiguity is addressed separately in a sequence of steps, which constitutes the usual form of a computer based understanding system.
***
"Lexical ambiguity. This arises from a single word having two or more different meanings, all of which are potentially valid. Consider ‘Stay away from the range’ which could be advice to a child to keep away from either the kitchen stove or the meadow. ‘The court was packed’ is a more complex example as the court may refer to a judicial court or a rectangular space and packed might mean a deceitful composition or a crowding by people.
"Structural ambiguity. The source of this ambiguity is the many ways words in a sentence may be combined into phrases and then interpreted. Thus in ‘He saw the crane fly outside’ one might be referring to the crane fly, a long-legged two-winged fly. Other examples of this ambiguity are: ‘My friend came home late last night’ and ‘Flying kites can be tricky.’ Another kind of structural ambiguity is where the sentence has a unique grammatical structure but it still allows different meanings owing to different underlying ‘deep structure.’ For example, ‘The policeman's arrest was illegal’ does not tell us who was arrested. Another example is ‘That leopard was spotted.’
"Pragmatic ambiguity. This is related to the context of the sentence. Thus in ‘She put the brick in the dryer and spoilt it’ the meaning would be different depending on whether the brick was made of metal or wax. Likewise the meaning of ‘John loves his wife and so does Bill’ would be unambiguous only if it were known that Bill was a bachelor.
"These difficulties are inherent in English but are not fundamental to all natural languages. Śāstric (scientific) Sanskrit is one natural language that appears to be particularly precise.
***
"To consider the meaning of the mathematical structure of a theory, note that the problem of divisibility is taken care of mathematically by the fact that the sum of its infinite series is finite. Apparently, without resolving the question of whether time and space are discrete or continuous, we resolve the paradox mathematically. Likewise, renormalization in quantum mechanics is a mathematical procedure that is not well understood -- it involves cancellation of infinities -- that works.
"The uncanny effectiveness of mathematics has filled the hearts of high school students as well as accomplished scientists with wonder. Eugene Wigner terms it the unreasonable effectiveness of mathematics in the natural sciences. According to Einstein, “Here arises a puzzle that has disturbed scientists of all periods. How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality? Can human reason without experience discover by pure thinking properties of real things?”"
Non-professionals would declare it was done by thinking. Mathematics professionals know better. Thought is the subject of mathematics, and logic a tool used for proofs. But the real work, the magic, is discovery of underlying structures, pure and abstract and yet manifest everywhere, seen easily by those that have comprehended them in the abstract purity.
And this discovery, grasp, comprehension of the beautiful structures, is not by thinking or logic. It's as magical as a gentle descent of a fairy, a manifestation of a heavenly bring with lights and fanfare.
Not on the physical plane, of course. Not visible below the world of mathematics.
***
"Some say that once machines become sufficiently complex they would be conscious. But machines only follow instructions and it is not credible that they should suddenly, just on account of the increase in the number of connections between computing units, become endowed with self-awareness. To speak of consciousness in the machine paradigm is a contradiction in terms. If a machine could make true choices (that are not governed by a random picking between different alternatives), then it has transcended the paradigm because its behavior cannot be described by any mathematical function.
"Some ascribe awareness of the brain to the fact that the brain is a self-organizing system which responds to the nature and quality of its interaction with the environment, whereas computers can’t do that. But other ecological systems, which are biological communities that have complex interrelationship amongst their parts, are self-organizing, without being self-aware. This suggests that while self-organization is a necessary pre-requisite for consciousness, it is not sufficient."
Author assumes the Western thinking, that's ascribing thought and much else including self-awareness to only humans. This is incorrect. At a minimal level, elephants coming across their own images in a mirror set up in forest surrounding have been known to be seen acting in a way that could only mean that they knew they were looking at their own image. We recall, for that matter, bears posing en famille for photographs, and lions too although not showing a friendly attitude like bears but a royal disdain instead, for humans, in a zoo where each species were kept in an environment consisting, not of a cage, but an open hillock surrounded by a moat.
***
"Some individuals, who have serious developmental disability or major mental illness, perform spectacularly at tasks in the areas of mathematical and calendar calculations, music, art, memory, and unusual sensory discrimination and perception.12 Such cognitive ability cannot be viewed simply as processing of sensory information by a central intelligence extraction system.
"There also exist accounts in the literature speaking of spontaneous discovery in a variety of creative fields. But as unique events that happened in the past, they cannot be verified. In the scientific field, Jacques Hadamard surveyed 100 leading mathematicians of his time, concluding many of them appeared to have obtained entire solutions spontaneously. This list included the claim by the French mathematician Henri Poincaré that he arrived at the solution to a subtle mathematical problem as he was boarding a bus, and the discovery of the structure of benzene by Kekulé in a dream.13 More recently, the physicist Roger Penrose claims to have found the solution to a mathematical problem while crossing a street.14
***
"Intuitive discovery must be common, and the reason why we don’t hear of more such stories is because some people are unprepared to appreciate their intuition or translate it into a meaningful narrative, and others feel uncomfortable speaking of their personal experience. The preparation of the scientist comes in the amplification of his intuition. It is also true that the creative intuition is not always correct, and the scientist’s judgment is essential in separating the false solution from the true one.
"Anomalous abilities and first person accounts of discovery that appear to be spontaneous could either indicate that consciousness is more than a phenomenon based solely on matter or that these accounts are just coincidences. Conversely, there is no way to prove the veracity of the scientist’s account of discovery. It is possible that the account is one that the scientist has come to believe over time and it does not correspond to fact."
Those negative judgements simply amount to Kak never having experienced it.
***
"Another coincidence is that of the novel, Futility (1898), by Morgan Robertson about the unsinkable ship Titan that is shipwrecked with much loss of life when it strikes an iceberg on its maiden voyage. In 1912, the Titanic struck an iceberg at midnight on her maiden voyage and sank on 15 April with great loss of life. There are several correspondences between the two boats but these may be due to the fact that both the novel and the design of the actual ship were based on proposals that were being written about in the 1890s. The coincidence may not be as remarkable as appears on first sight."
Author is quite wrong, and unless Titanic were deliberately scuttled and falsely claimed to have hit an iceberg, the coincidence IS striking.
Unless, of ....
****
"The principle of evolution forms the basis of the system of Sāṅkhya but that did not lead to the development of a scientific theory. The Mahābhārata (pre-400 BC) and the Purāṇas have a chapter on creation and the rise of mankind. It is said that man arose at the end of a chain where the beginning was with plants and various kind of animals and giant animals (asuras). ... "
That's incorrect interpretation of the word 'asuras'.
" ... Here’s the quote from the Yoga Vāsiṣṭha:4
""I remember that once upon a time there was nothing on this earth, neither trees and plants, nor even mountains. For a period of eleven thousand years (four million earth years) the earth was covered by lava. Then demons (asuras) ruled the earth; they were deluded and powerful. The earth was their playground. And then for a very long time the whole earth was covered with forests, except the polar region. Then there arose great mountains, but without any human inhabitants. For a period of ten thousand years (4 million earth years) the earth was covered with the corpses of the asuras."
Well, one can see why Kak interprets the word as giant animals, but that's not what it meant.
"Vedic evolution is unlike Darwinian evolution. The urge to evolve into higher forms is taken to be inherent in nature. A system of an evolution from inanimate to progressively higher life is taken to be a consequence of Nature’s intelligence that responds to the different proportions of the three basic attributes of sattva, rajas, and tamas.
***
"One primitive concept that has been debated considerably is that of infinity. George Cantor (1865-1918) introduced the theory of infinite sets in 1873 which allowed one to distinguish between different kinds of infinite sets. The idea at the basis of Cantor's theory is that of one-to-one correspondence which is quite obvious for finite sets. We say that two sets are of the same size if their elements can be put into one-to-one correspondence. Thus the sets of 5 books and 5 boys are equal in size because each book can be paired off with a different boy. Cantor argued that since one can set up a correspondence between the whole numbers and the even numbers:
"1 2 3 4 5 6 . . .
"2 4 6 8 10 12 . . .
"where each whole number has been paired off with one and only one even number, the two infinite sets are of the same size. This definition was rejected by many on the grounds that it made a part of the set equal to the whole. Cantor countered that infinite sets followed laws that did not apply to finite collections.
"Cantor called infinite sets that can be put in one-to-one correspondence with the whole numbers as countable and represented this size byאo (aleph null). He next showed that the set of all fractions and whole numbers (rationals) is countable. To prove this he represented the numbers in an array as shown:
"1/1 1/2 1/3 1/4 . . . .
"2/1 2/2 3/3 3/4 . . . .
"3/1 3/2 3/3 3/4 . . . .
"4/1 4/2 4/3 4/4 . . . .
"Note that some numbers are repeated as in the main diagonal where each number is 1. Now in a diagonal zigzag path going from 1/1→1/2→2/1→3/1→2/2→1/3→1/4→2/3→3/2→… , each number in the array is crossed just once. If repetitions of numbers are deleted one can pair off each rational in the path with a unique whole number in sequence. This establishes the result.
"Cantor next showed that some infinite sets are not countable. An example of this is the set of all points on the real line, that includes rational and irrational numbers. Given an infinite set one can, by considering all its subsets, construct another set of larger size. Cantor thus arrived at a sequence of aleph numbers,א0,א1,א2.... called transfinite numbers that represent progressively a higher measure of infinity. Cantor believed that no transfinite number existed between those representing the infinites of the whole numbers and the real line. In other words, he took the infinity of the real line to beא1. This is known as the continuum hypothesis.
***
"Cantor's work was severely criticized by his contemporaries. The mapping of the part to the whole had been anticipated by Leibniz who had said that the “set of all numbers contains a contradiction, if one takes it as a totality.” Cantor defended himself by claiming to be a Platonist, for whom ideas have an objective reality of their own. He did recognize, however, that one had the paradoxical situation of not being able to talk of a set of all sets, since the aleph numbers could be constructed recursively without end. Russell, upon reflection on this observation, produced a paradox dealing with classes which had a great influence on the mathematical world. This situation was described earlier in the form of the catalog and the barber paradoxes. Since classes of sets are often invoked in mathematical argument, this pointed to the care that was needed in using this concept. Later in their book, Principia Mathematica, Whitehead and Russell introduced the theory of types to avoid such difficulties. Individual objects, sets, sets of sets, and so on were classified as belonging to different types. Relations were defined for each type separately. They also introduced the axiom of reducibility, according to which any proposition of higher type is equivalent to one of first order. This axiom has received considerable criticism on the grounds that it is not self-evident.
***
"If there are limits to the nature of natural language processing by the computer, what is the nature of these limits? It appears that the best one can do is to devise actual systems -- in other words, use a constructive approach. The greatest success in devising a constructive approach to the description of a natural language is Pāṇini’s grammar for the Sanskrit language, an achievement termed by the famous linguist L. Bloomfield as ‘one of the greatest monuments of human intelligence.’6 The knowledge representation methodology in the grammar of Pāṇini and his successors is, in many ways, equivalent to the more powerful currently researched Al schemes. It includes rules about rules, analogs of which are not known for modern languages. Some elements of the Pāṇinian approach have already been incorporated in the current computer understanding systems. We will review the ‘standard’ approach to natural language processing, so that one may appreciate the commonality between the two as well as main points of difference.
"A discourse may be analyzed in terms of primitives that deal either with being or becoming. In other words, a primitive either describes categories and objects and their relationships, or if the context is clear it describes agents and transformations. These two kinds of primitives are complementary and yet each can serve as a knowledge representation scheme. One may describe transformation implicitly by means of description of the objects at successive times, and categories and objects in a domain can be defined as new objects. At another level, one may name an object from a root related to its most significant function, or one may have separate labels for objects and functions without any apparent relationship between the two. Often, languages have features related to both these ideas.
"Perhaps the earliest example of a debate about the being- becoming dichotomy is the one between the schools of Gārgya and Śākaṭāyana, two ancient Indian philosophers. Śākaṭāyana considered that nouns were derived from verbs or verbal roots, a principle whose universality was challenged by Gārgya on the basis that it often leads to forced etymology. According to Gārgya, if aśva (horse) was derived from aś (to travel) then other beings that travelled would also be called aśva, and states of being would be antecedent to objects. Since objects can be associated with variety of actions, Gārgya's objection was true. However, the significance of Śākatāyana's claim was to consider the object name to be derived from some (arbitrarily) chosen primary action associated with it.
***
"Note that in Pāṇini's system a finite set of rules is enough to generate infinity of sentences. The algebraic character of Pāṇini's rules was not appreciated in the West until very recently when search for similar generative structures was popularized by Chomsky and others. Before this, in the nineteenth century, Pāṇini's analysis of root and suffixes and his recognition of ablaut had led to the founding of the subjects of comparative and historical linguistics.
"Despite similarities between Pāṇinian and modern generative grammars, there exist striking differences as well. Some of these differences are related to the nature of the languages under study: Sanskrit in the case of Pāṇini, and modern European languages in the other case. Furthermore, the contemporary evaluation of Pāṇini is still going on, a process that is slowed down by the fact that the original is inaccessible to most linguists and computer scientists. In any event, one may define an approach to language analysis as being Pāṇinian if it uses:
"1) root and suffix analysis,
"2) linear string of rules and analysis by rule sequence,
"3) analysis by functional structure,
"4) exhaustive description.
***
"Note that in Pāṇini's system a finite set of rules is enough to generate infinity of sentences. The algebraic character of Pāṇini's rules was not appreciated in the West until very recently when search for similar generative structures was popularized by Chomsky and others. Before this, in the nineteenth century, Pāṇini's analysis of root and suffixes and his recognition of ablaut had led to the founding of the subjects of comparative and historical linguistics.
"Despite similarities between Pāṇinian and modern generative grammars, there exist striking differences as well. Some of these differences are related to the nature of the languages under study: Sanskrit in the case of Pāṇini, and modern European languages in the other case. Furthermore, the contemporary evaluation of Pāṇini is still going on, a process that is slowed down by the fact that the original is inaccessible to most linguists and computer scientists. In any event, one may define an approach to language analysis as being Pāṇinian if it uses:
"1) root and suffix analysis,
"2) linear string of rules and analysis by rule sequence,
"3) analysis by functional structure,
"4) exhaustive description."
" ... enumerate some of the ambiguities that make machine translation such a difficult task. These ambiguities need to be resolved, if at all possible, in various steps to obtain a translation. Each kind of ambiguity is addressed separately in a sequence of steps, which constitutes the usual form of a computer based understanding system.
***
"Lexical ambiguity. This arises from a single word having two or more different meanings, all of which are potentially valid. Consider ‘Stay away from the range’ which could be advice to a child to keep away from either the kitchen stove or the meadow. ‘The court was packed’ is a more complex example as the court may refer to a judicial court or a rectangular space and packed might mean a deceitful composition or a crowding by people.
"Structural ambiguity. The source of this ambiguity is the many ways words in a sentence may be combined into phrases and then interpreted. Thus in ‘He saw the crane fly outside’ one might be referring to the crane fly, a long-legged two-winged fly. Other examples of this ambiguity are: ‘My friend came home late last night’ and ‘Flying kites can be tricky.’ Another kind of structural ambiguity is where the sentence has a unique grammatical structure but it still allows different meanings owing to different underlying ‘deep structure.’ For example, ‘The policeman's arrest was illegal’ does not tell us who was arrested. Another example is ‘That leopard was spotted.’
"Pragmatic ambiguity. This is related to the context of the sentence. Thus in ‘She put the brick in the dryer and spoilt it’ the meaning would be different depending on whether the brick was made of metal or wax. Likewise the meaning of ‘John loves his wife and so does Bill’ would be unambiguous only if it were known that Bill was a bachelor.
"These difficulties are inherent in English but are not fundamental to all natural languages. Śāstric (scientific) Sanskrit is one natural language that appears to be particularly precise.
***
"To consider the meaning of the mathematical structure of a theory, note that the problem of divisibility is taken care of mathematically by the fact that the sum of its infinite series is finite. Apparently, without resolving the question of whether time and space are discrete or continuous, we resolve the paradox mathematically. Likewise, renormalization in quantum mechanics is a mathematical procedure that is not well understood -- it involves cancellation of infinities -- that works.
"The uncanny effectiveness of mathematics has filled the hearts of high school students as well as accomplished scientists with wonder. Eugene Wigner terms it the unreasonable effectiveness of mathematics in the natural sciences. According to Einstein, “Here arises a puzzle that has disturbed scientists of all periods. How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality? Can human reason without experience discover by pure thinking properties of real things?”"
Non-professionals would declare it was done by thinking. Mathematics professionals know better. Thought is the subject of mathematics, and logic a tool used for proofs. But the real work, the magic, is discovery of underlying structures, pure and abstract and yet manifest everywhere, seen easily by those that have comprehended them in the abstract purity.
And this discovery, grasp, comprehension of the beautiful structures, is not by thinking or logic. It's as magical as a gentle descent of a fairy, a manifestation of a heavenly bring with lights and fanfare.
Not on the physical plane, of course. Not visible below the world of mathematics.
***
"Some say that once machines become sufficiently complex they would be conscious. But machines only follow instructions and it is not credible that they should suddenly, just on account of the increase in the number of connections between computing units, become endowed with self-awareness. To speak of consciousness in the machine paradigm is a contradiction in terms. If a machine could make true choices (that are not governed by a random picking between different alternatives), then it has transcended the paradigm because its behavior cannot be described by any mathematical function.
"Some ascribe awareness of the brain to the fact that the brain is a self-organizing system which responds to the nature and quality of its interaction with the environment, whereas computers can’t do that. But other ecological systems, which are biological communities that have complex interrelationship amongst their parts, are self-organizing, without being self-aware. This suggests that while self-organization is a necessary pre-requisite for consciousness, it is not sufficient."
Author assumes the Western thinking, that's ascribing thought and much else including self-awareness to only humans. This is incorrect. At a minimal level, elephants coming across their own images in a mirror set up in forest surrounding have been known to be seen acting in a way that could only mean that they knew they were looking at their own image. We recall, for that matter, bears posing en famille for photographs, and lions too although not showing a friendly attitude like bears but a royal disdain instead, for humans, in a zoo where each species were kept in an environment consisting, not of a cage, but an open hillock surrounded by a moat.
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"Some individuals, who have serious developmental disability or major mental illness, perform spectacularly at tasks in the areas of mathematical and calendar calculations, music, art, memory, and unusual sensory discrimination and perception.12 Such cognitive ability cannot be viewed simply as processing of sensory information by a central intelligence extraction system.
"There also exist accounts in the literature speaking of spontaneous discovery in a variety of creative fields. But as unique events that happened in the past, they cannot be verified. In the scientific field, Jacques Hadamard surveyed 100 leading mathematicians of his time, concluding many of them appeared to have obtained entire solutions spontaneously. This list included the claim by the French mathematician Henri Poincaré that he arrived at the solution to a subtle mathematical problem as he was boarding a bus, and the discovery of the structure of benzene by Kekulé in a dream.13 More recently, the physicist Roger Penrose claims to have found the solution to a mathematical problem while crossing a street.14
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"Intuitive discovery must be common, and the reason why we don’t hear of more such stories is because some people are unprepared to appreciate their intuition or translate it into a meaningful narrative, and others feel uncomfortable speaking of their personal experience. The preparation of the scientist comes in the amplification of his intuition. It is also true that the creative intuition is not always correct, and the scientist’s judgment is essential in separating the false solution from the true one.
"Anomalous abilities and first person accounts of discovery that appear to be spontaneous could either indicate that consciousness is more than a phenomenon based solely on matter or that these accounts are just coincidences. Conversely, there is no way to prove the veracity of the scientist’s account of discovery. It is possible that the account is one that the scientist has come to believe over time and it does not correspond to fact."
Those negative judgements simply amount to Kak never having experienced it.
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"Another coincidence is that of the novel, Futility (1898), by Morgan Robertson about the unsinkable ship Titan that is shipwrecked with much loss of life when it strikes an iceberg on its maiden voyage. In 1912, the Titanic struck an iceberg at midnight on her maiden voyage and sank on 15 April with great loss of life. There are several correspondences between the two boats but these may be due to the fact that both the novel and the design of the actual ship were based on proposals that were being written about in the 1890s. The coincidence may not be as remarkable as appears on first sight."
Author is quite wrong, and unless Titanic were deliberately scuttled and falsely claimed to have hit an iceberg, the coincidence IS striking.
Unless, of ....
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