Monday, September 3, 2007

philosophy of mathematics

Philosophy of Mathematics
Usually a child is taught to count 1,2,3,4….
But actually a person wellversed in mathematics will count 0,1,2,3,4 …..Only a civilization which has reached its zenith of knowledge can count zero in front of the series of natural numbers(swabhavika samkhyasreni)Bertrand Russell has said so in his Introduction to Mathematical philosophy..When India discovered zero ,India was proving that it has reached the zenith of knowledge or wisdom.
To say 4 cats,10 horses,1000hens,4000cows,6000 men is entirely different from saying 4 days,10 thithi,1000 years,4000 yuga,and 6000 kalpa.The number used is the same.But when we measure time(kaalapramaanam)the 4th dimension is included and hence it becomes transcendental.Music and astronomy shares this transcendental quality.Both are measuring rhythmic time.
How did India reach the philosophy of Advaitha with three concepts,Brahma,Jeeva and the prakrithy?Indian Dasamsa or decimal system of the vedic period recognizes only Brahma(symbol Brahma(symbol 0 )Prakrithy(symbol 1)and jeevan (symbol 1,as pinnai or successor or pingaami ,one who follows ).This is the same as the three basic ideas Peano put forward later on .(zero,number,successor)

In music it is the pranava,octave and the raga.The first children are basically 72 according to this.They are the parents of all the following janyaraaga as well.
Brahma prakrithy jeeva
0 1 1 1(2) 1 (3) 1(4) 1(5) …… 72possibilities.
ZERO ONE SUCCESSOR
All successors are zero(original brahma)and 1(Prakrithi)only.The qualities of these two parents are in everyone of us(in every raga).This theory is called the samkhyam in India,now called principle of mathematical induction.
Is it only 72 that we get from Brahma/No we can get anantham jeeva as successors .We can get karani as well as akarani,just like squareroot of two which is an akarani.Squareroot of 2 is the karnam or diagonal of a magical square with length of 1 unit.To solve this problem of asamkhyam or anantham one has to enter the realm of philosophy from mathematics.This was known to India from tim e immemorial,and in Greece it was Pythagorus who understood this fact.
We must understand that in the sreni(progression)the natural numbers are not always numbers but points in timespace,moments in time,all the life and its forms lived,living and will live in this universe etc.This ananthasreni (endless progression)of numbers is called the jeeva in Indian philosophy and successor by Peano .In musical sense they are the janakaraaga 72 and their multitudes of janyaraaga which are countless.
Sreni =0,1,2,3,4,5,6,7 ……n,n+1
Zero here is nullclass,the one or EKA who has none to equal ,not empty space as many people misunderstand.Inthis way mathematical induction affords the essential characteristics by which the finite is distinguished from the infinite.
This is called Nitya Anitya vasthuvivekam (distinguish the infinite from the finite)The anantha is represented as the om or the alef null or the serpent on which Vishnu sleeps in his eternal yoganidra(transcendental sleep)
The ananthasreni will be n+2n+2 2n…
If n = 9,
2 9 512,2 512 =512 times 2 is multiplied to get a number with 153 positions.This 153rd position is a null position called a thamosthaana,and this number considered as raahumanam or measure of Rahu ,the small serpent.While Anantha is the immeasurable serpent ,Rahu represents the one which can be measured through sun,moon and the earth’s orbit .
The world exists in our thoughts.If I am not thinking about you,that means you are not a part of your world.If I am constantly thinking about you,you have become an inseparable part of my world and of my being.That is why there are so many views and controversies on every subject,including cosmos and God and even the silliest gossip in the world.The concept of the EKAM and Anekam will persist because it is the inherent structure of the world.But if we understand the process we can develop tolerance.You can lead a fruitful happy peaceful coexistence with everyone else in the world.If I say
S=Y
I should have known both those if I am a scientist.Or I should have had experience of both S and Y.For that I should have done mental intellectual emotional preparation and hard work ,or tapasya.that is spiritual experience or wisdom.One can say an opinion on both S and Y without knowing both.But that is only a matham or abhipraayam(opinion)which anyone can have,Only the informed knowledge is acceptable to all.Uninformed is always controversial.The difference between objectivity and subjectivity is precisely this only.Who measures also is important .Because only a person wellversed in a particular subject can give an informed opinion on the subject.With what criteria was the measurement done?How did his consciousness grasp the topic?What language was used for communication?All this determine objectivity.
A person who talks in musical language does not understand the mathematical language.One who speaks the language of physics does not understand the medical language.The language of stars and planets,that of birds and nature all are different for those who know only one language.But for a person who understand all these and finds the interconnectedness of all ,there is a strong Advaitha or oneness.
If S=Y is the hermeneutics of scientific language,the corresponding hermeneutics of spiritual language is Tat Twam Asi.The hermeneutics of the mystical langage is Aham Brahmasmi.But all these are using the same mathematical formula or equations.
That=twam
Brahma=aham
S=Y
0=1
This .is the philosophy of mathematics Indians employ in their life.And because of this ,to allot anantham or sahasram names to the nameless zero is not an impossibility.

Ch 4 .Mind and infinity.
Imagine two serpents coiled upon themselves.These two ar e two zeroes (Brahma/prakrithy,Ekam/anekam)and in the figure of 8 pattrn they are the symbol of anantham eternity of existence.*ashtam,ashtadalapadma,octave etc)Hebrews called it alef null from which the symbol alpha (the one we use for meditational brain waves )originated.Westerners call this leminiscate.But they started to see the leminiscate as the symbol of eternity only in the 17th century.(Rudy Rucker.Dept of Mathematics .Randolph Macon women’s college –virginia)The father of eternity theory in modern mathematics is George Canter.He renamed it alef nulland introduced a new symbol.
Only in 16th century did Galileo understand in the western world that there is an eternal time,and discovered calculusCanter discovered three types of eternities.
1.The absolute (paramarthasatha)
2.Physical infinities (Time and the sky or timespace)
3.Infinity grasped by human mind
The last two were together called transfinites by Canter.In a figure of 8 the big bang and the big stop are continuing forever in a cyclical pattern as if in a coiling serpent and what is big stop is a big crunch the next moment.This consciousness within your heartspace(hridaakaasa)of the Brahmaprakrithy is always something transcendental,which you cannot express with ordinary language.The hridaakaasa of the Indian is now known as the mindscape by the western thinkers.
When Joshua Roys say that the mental image of one’s own mind must be infinite ,it is an echo of the mirror image universes of the ancient astronomers which are seen in successive generations of yogis as heartspace(in guruparampara).Our thoughts and views are within our mind ,and are like one mirror in front of another and like that an infinite number of mirrors reflecting the same truth.Here the word jeeva is changed to mind in a guruparampara.
Viswam darpanadrishyamaana nagai(sankaracharya)
Thus the world in our thoughts is the conscious world of ours and when the consciousness of a guru becomes one with the disciple they become one individual and not two. If all my thought processes and researches and books are considered as a single set ,mathematics is the science that study the qualities of my internal world with a set rules.My universe with the definite set rules are within me,and outside me as the cosmos and what is in meis a blueprint of what is outside me.The absolute truth cannot be grasped by the finite mind,but can be grasped by two ways
1.The rational way(vivekam).My commentaries on Prasthanathraya is my attempt to grasp absolute by rational logical scientific methods.
2.The mystical way(experience or Anubhoothy) My musical experiences, and dream experiences,my dhyana experiences and imagery in poetics etc is the result of the second method of knowing the absolute.
According to me the mystical experience through music and dream visions had been of more use for me to grasp or understand what little I have known of the absolute.Sankara also said that swanubhoothy is better than logic.Rudy rucker also says to understand infinity only mystical experiences can be relied upon.Hence the importance of Naadalayayoga or musical transcendental experiences in my consciousness.

What is realism?

Are you a realist or not?
When people ask that question ,I ask ,what is your realism?For them realism means only one entity.But for me realism is a multitude of entities.It is a corruption of reality(Wallace stevens)the most independent elastic and prodigious of critical terms.There is the fantastic realism followed by formal realism,ideal realism,infrarealism,ironic realism,militant realism,naïve realism,national realism,naturalist realism,objective,optimistic,pessimistic,plastic,poetic,psychological,quotidian,romantic,satiric,socialist,subjective,supersubjective,visionary realisms the adjectives neverending.Wimsatt and Brooks names low,high and drab realisms.Then there is a spiritual realism.Which one of these you mean when you ask ,”Are you a realist or not”In a way ,we all are realists.But in our own way.
Realism,a critical term adopted from philosophy .It is sath,dharma,or may be idealism.Originally meant for universalism.Opposite of it was conceptualism(universal exists only in the mind)and nominalism (which denied the existence of universalism .It is just a name)
Truth is either scientific or poetic.Scientific truth is discovered by a process of knowing ,through observation and comparisons.It is technically refered to as a correspondence theory.Poetic truth is created by a process of creation,and is a coherence theory.Science is the truth of a positivist determinist whose aim is to document ,delimit,define and correspondence theory defers automatically to the fact and requires that truth be verified by reference to it.It is taking confidence from substantial agreement of majority in its description of reality which it therefore calls objective.
Coherence theory deals with intuitive perceptions.Selfevidence is formost.Correspondence theory is semantic and coherence theory is syntactic conception of truth(Russell)and hence both are functions of our brain and are realistic in their own way.
It is the troubled conscience of socalled realists that accord a special value to documentary drama,facts and to confessional poetry.A value which is applied illegitimately from without instead of being generated from within .Pretensions are more awarded than real performance in it.Correspondence theory is conscience of literature and coherence theory is consciousness of literature.In the latter realism is not imitation of someone else,but is original creation.
In this sense ,poetry is the real thing ,but it is created in another real world.Thia world is a dictionary of Hieroglyphics.(Baudelaire)Transcendentalism in poetry involves idealism and expresses itself ultimately as symbolism in literature.For idealists the transcendental doctrine alone is true ,according to which the goal of humanity is the establishment of a higher consciousness(Ernest Renan 1890).Picasso said “your self is a sun with a thousand rays in your belly.The rest is nothing”Something like the sahasrasuryaprakasa
of vishnu in his nabhipadma.
Metaphor offers a kind of satisfaction to intellectual nostalgia for the predualistic stage of consciousness.But the puritanical realist and th enovean romancier reflects metaphor as a contrivance in his obstinate burrowing away from the light of the mind.Whereas realism of consciousness derives all its strength from its simplicity ,realism in its conscious phase depends upon an awareness of its own complexity.
The naïve realist guided by the light of conscience ignore the actual process of creation.The informed realist knows that he is guided only by the light of the mind,so the process itself assume great importance.(Diary 4.9.1994)

Godell’s incomplete theorem
There are several problems which mathematics can never solve .Man will never know the final secret of the universe,however much he/she try.Because so many simple problems are still there which mathematics cant prove.Wittgenstein like a Zen mystic said”we feel that even when all possible scientific questions have been answered ,the problems of life remain completely untouched.The solution of problem of life is seen in vanishing of the problem.In Godell’s book ,the consistency of continuum hypothesis,Canton’s continuous principle cannot be disproved from existing axioms of the set theory.
What is Cantons continuum problem?He wrote in it:Despite their remoteness from sense experience we do have something like a perception of object of a set theory ,as it is seen from the fact that the axioma force themselves upon us as being true.This kind of mathematical intuition or perception is better than any sense perception.They too represent an aspect of objective reality ,but their presence in us is due to another kind of relationship between us and reality(unlike our senses).Godells incompleteness theorems are on an importance comparable to Pythagorus proof that square root of 2 is irrational.Pythagorus said that no ratio of natural numbers can fully describe the relation between the diagonal and the sides of the square.Godell showed that no finitely describable theory can codify all mathematical thruth.Sets of all true statements about mathematics is finitely unnameable and thus essentially random and infinite.His theorem :”The rational thought can never penetrate to the final ultimate truth” is the same as that of Sankara who said that logic can never explain the absolute ,but swanubhoothy can.
When Godel say “I do objective mathematics”he meant,the mathematical entities exist independently of the activity of mathematician,just as the stars would be there even if there are no astronomers to watch them.For him mathematics ,even that of infinities ,was essentiall y an empirical science.According tothis standpoint we do not create mental objects we talk about ,instead we find them on some higher plane that the mind sees into ,by a process not unlike sense perception.Godel said ,possibility is observer-dependent and therefore real.Because it is not subject to our will.Any one can go and see the Tajmahal .It is there for anyone to see.Like that anyone who takes some trouble to learn mathematics can see set of natural numbers himself with an independent existence ,an existence as a certain abstract possibility of thought .Just like Brahma concept.It is there for anyone who takes trouble to enquire (Only for the enquirer it reveals).
But how to enquire and perceive an abstract possibility of thought?
The method is exactly that of the Brahmagnani.Godell says three things.
1.Close off all other senses by lying down in a quiet place and seek with your mind.(This is called chithavrithy nirodha)
2.It is a mistake to let everyday reality condition possibility and only to imagine combinings and permutations of physical objects.The mind is cpable of perceiving infinite sets.
3.Ultimate goal of such thought and of all philosophy is the perception of the absolute.
Kurt Godell thus shared with Einstein a certain mystical turn of thought.The central teaching of mysticism is Reality is ONE.The practice of mysticism consists in finding ways to experience this higher unity directly.The one has variously been called the Good,God,Cosmos,Mind,Void,Absolute.No door in the labyrinthine castle of Science opens on to the absolute.But it is possible to jump out of the maze (Bandhana)if one understands it,and expereience absolute oneself.
This is the reality of mystics,mathematicians,yogi and the Advaithi ,and both Einstein and Cantor belonged to this class ,like our Sankara.They did chithavrithinirodha,concentrated on absolute and experienced it.Therefore when Godell say that Mind is everywhere opposed to the being localized in the brain of people,it is the basic mystic teaching of ancient philosophers who used the same method.He came across the same discovery ,because he tried the same method(Travelled the same road so that he could see the Taj Mahal. )

Valuebased education -Indian Gurukulam

Valuebased education in India

Max Muller changed many meanings,James Mill denied the antiquity of many books/scriptures and Macaulay made these two combined on the educationalreforms of India .The effects of Macaulay’s educational reforms still on Indian society.
What should be the aim of education in a free democratic nation?Should not the educational institutions create world class human beings?world class citizens?Is it just enough for serving under the government ,as Macaulay envisaged?Should not our methodologies add more weight to ability of institution to give values,create values,rather than merely perpetuate the brand myths?The people who show a will to cultivate a climate of innovations and constantly improve their processes give priority to create future leaders with values to the society.For this we have to assimilate new ideas ,technologies,practices without loosing the old values of our society.An effective leader is one who can chart out a clear growth strategy and make sure that the faculty members internalize it and work as a team.
How to build strong relationships with teammates,faculty members ,students,members of society /How to achieve it in a small group and in a large group?
There should be staff meetings (informal over a cup of tea)every day ,for 15 minutes.That will sort out day to day coordination functions.
Faculty council meetings every nmonth to monitor implementation of projects,midcourse adjustments if required.Debates and discussions on new ideas,achievements of faculty members to be celebrated during these meetings.
Long term strategic issues and visions discussed in annual retreats of faculty.

Perks ,incentives for good work,publications,restriction of workload to get enough time for research etc will boost the morale.
Curriculum review and update regularly based on industry output.
Employment of pedagogy to impart knowledge and skills (case method,live projects,gameplaying,roleplay,computer simulations etc)
Continuous evaluation programmes like quizzes,assignments,presentations,tests at regular intervals should replace the end term examinations.The concept of teamteaching in select courses where multidisciplinary focus is necessary.
Strong mentoring programmes to make correct choices (An industry mentor,alumnous menter,faculty menter for each student is ideal,if not possible at least one faculty menter)for councelling on academic ,career and personal concerns.


Valuebased:-Education is for full development of human life.Quality of schools,institutions,universities should be improved to increase the limitless inner potential of teachers and students within the institutions.Knowledge has three units-the knower,the known ,and the process of education or knowing.
The process of Knowing:1.Through sensory perceptions.Of the Knower.
2.Through the thoughts,intellectual analysis of the known object /subject and the knower.
3.Extrasensory perceptions of the knower.

Traits that uphold the integrity of a person and the progress of society
.1Enlightened selfinterest
2.reliability
3.compassion
4.justice
5.breadth of vision
These are associate dwith liberal education.Teaching profession touches the future of the society,nation and the world and hence teachers should be well chosen(The Guru)
Quality of a really educated person is not his degree or his positions.They are
1.Listening,hearing ,or reading(with concentration),speaking,feeling the content of the communicated word(by speech or by writing).Communication skills
2.Can read more than the words spoken or written.Through great works of art ,music etc for the sheer joy of it.
3.can communicate with anyone irrespective of age ,caste,gender,nationality etc.at a very broad range.(written,verbal,nonverbal communication skills)
4.can solve problems of society or nation or the world,for the common good of all and with no selfish motive or prejudice
5.rigor and truthseeking.Love for learning ,respect for learning and learned people.
6.Tolerance ,open liberal attitudes.Honour own culture.Respect other cultures and the diversity of cultures
7.strives to make the world a better place to live in.
8.Nurtures and empowers.The triumph of one person becomes the triumph of all ,-Belong to the world,to human race,
9.Education is all about connecting and communicating .Make sense of the world by making connections .Communicating values,positive thinking ,culture etc.
Education comes from universities,schools and colleges ,institutions,books but most importantly from people.From inter and intrapersonal relationships and experiences shared.
When two people live or work together they communicate.Stimulate the quest for knowledge and truth in the other .Create values together.This dynamic evercontinuing process is real education.Starts from home(parent-child)Gurukula(guru/disciple)society(person to person)man-woman(husband-wife)etc.Even simple facts are made meaningful by positive communication.This experience is the most valuable part in any educative process.The positive thoughts and emotions are evergreen in the memory of every human child and adult and they cherish and respect it.And the people who gave those valuable experiences.The human relations create experiences and hence we need model human beings in our midst to create valuable experiences to society,not just books and computers.
Who is a valuable human being?
A valuable human being is a noble being with freedom of will and expression ,happy to do and speak and communicate to the world,honest and loving,compassionate to all living things ,peaceful to all situations in life,responsible for what he/she says,writes thinks or does,is tolerant to other’s views,finds unity in life.In other words.simple life and high thoughts and noble ideals and deeds characterize a really educated and valuable human being.(Even if he/she doesn’t have a degree/position).
Every individual has a self organizing map(SOM),an algorithm to visualize and interpret large highdemand data sets –A regular grid of processing units ,the neurons.How efficiently this works in different persons is different (individual variations).But essentially the potential is in every member of the human race.Therefore a valuebased educationist has to set a model of himself/herself in front of the world to show how much of the potential is utilized by him./her and those who comes in touch with him./her.That is how a Guru gets more and more acclaim far and wide and good valuable disciples come to him/her .The valuebased eduation education takes away the pressures ,stress ,strain,anxiety of life from children /students/people and make them frustration-free individuals.When frustration is taken away we become more efficient .
The Gurukula of India was devised with this aim.
Caring for the roots of life
An important aspect of valuebased eduation is the caring for roots of life Our root of life does not stop at the geneology of our own family.But goes to the oldest ancestor of the human race.It even goes beyond that to all the living creatures,to genes,aminoacid sequences,elements of which aminoacids are made of,atoms and subatomic particles with which elements are made of.And ultimately to energy .The bio and cosmic energy are thus one in origin.The entire cosmos with its multitude of forms ,seen and unseen,become integrated in the “I “or AHAM of the sage since it is equivalent to Brahma.The root of all is ONE.Protection of thoughts of ancestors(books,manuscripts,cave writings,etc)civilizations,histories,monuments etc for coming generation is to learn and experience the beauty of our existence on it.To learn our roots.The need for disciplining and balancing the inner personality and concentrating on such valuable activities characterize an educated civilized person.
When such aims are in the thought process of any individual ,that individual naturally becomes a good human being ,a good world citizen,a role model to be emulated by others.We want such broadminded individuals .Such teachers for our children.Part of a valuebased educational system is thus to devise a curriculum for this .We need visionaries in all fields of art and science ,in all wakes of life ,in education and research to carry on the world on its path to fulfillment of such an aim.
In UNESCO report of 21st century ,learning is defined as atreasure.within the reorientation of preservice and inservice teacher /parent educatonfor enabling them to aquire the intellectual and emotional qualities that the nation wants to be developed in a citizen /child/society.
National policy of education(NPE)and programme of action (1992)has identified 10 core elements as the integral part of curriculum but as it is it remains in the papers only

One can raise one’s response to an electromagnetic wave(visual)or an auditory wave(sound)by rousing one’s level of subconscious and conscious mind to a higher level of consciousness(superconscious state).That means,emotions are not in the stimulus given alone,but in the receiving mind also.Both Guru and Shishya are having an equal part in creating knowledge,in the curriculum,experience of aesthetic generation etc.One has to improve that quality to become a valuebased educationist.