Gurbani and Mathematics.
Dr. Sajjan Singh
About the relationship between the Formless (God) and mathematics or about the role of mathematics in describing God, the learned ones have expressed some views, most of which relate to the literary vocabulary and philosophical thought. The teaching of Gurbani, despite being in very clear and simple language, are based on the fragrance of divine virtues, unshaken faith and spiritual experiences. While, according to Sri Guru Granth Sahib, to remove the obstacles in the way to attainment of God, aberrations and misgivings, mathematical bent of mind is helpful, Gurbani exhorts us mainly that the formula, rule or law which applies to the creation, does not apply to the Creator.
All the scriptures and treatises say loudly that love, dwelling on His Name, detachment, His glory, singing of his praises, self-dedication, etc. divine virtues and divine deeds help the seeker of God and logic, arguments, conflict, and accounts thereof are the obstacles on the true path. Although it is difficult even to imagine about God and Mathematics for an ordinary person, the learned ones have expressed their views in writing.
Swami Ram Tirath says, ‘Abstract Mathematics leads to God Realisation, that is, the theoretical mathematics connected with subtle views, shows the way to God.’ According to a writing, ‘Plato regarded the contemplation of Mathematical Truths as worthy of Deity.’ He further says, ‘There is Mathematics, something which is necessary and cannot be set aside,….and if I mistake not, of Divine necessity’. According to this learned man, the knowledge of mathematics cannot be ignored. In fact, Concentraation of mind, Intuition, Power of Discrimination, Regularity, Punctuality, Turth, etc. are most essential elements of attainment of God and Mathematics. The supreme intellect can be described in this way only.
To be a spiritual is not to reject reason but to go beyond it. That is why, one traversing the road to spiritualism, does not oppose logic or argument but remains above it and aloof from it.
From the ancient times, the sages, holymen, saints, Bhagats and Gurus have mentioned three ways to attainment of God.
“Gyan dhyan kachhu karam na jana”,says Gurbani.
(I know nothing of knowledge, meditation and actions)
These three appear to be distinct from one another, but when someone works hard, all the three seem to be one, intermingled with one another. Keeping within determined limits, an attempt is being made at sharing of views about the ‘Gyan Marga’ (Path of Knowledge).
Guru Nanak Dev was not only a Philosopher, in fact God in human form, a psychologist, a poet and a scientist but endowed with the virtues like realism, firm determination and logic, a great mathematician also. Some writers of the modern age have not been able to, on the basis of their self-devised tests, appreciate the laudable traits of all embracing personality of Guru Gobind Singh and the beautiful coordination of mutually conflicting virtues. The reason thereof has been given by Guru Nanak by way of a beautiful argument:
Eiwad oocha hovai koye,
tis oochai kau jaanai soye.(P.5)
(One has to be as high as He is, to know Him)
Though these words have been used to describe the greatness of God, they apply in toto to Guru Nanak’s greatness also.
Numerous adjectives made use of in praise of God, describe his Infinity like ‘aganat'(beyond counting), adole (Firm), Asankh (countless), Apar (Beyond everything), Beant (Having no end), Aleek (beyond any line of dogma), Asambh (Impossible of being gauged), Agam (Inaccessible), Atole (Unmeasurable), Amole (Priceless), agochar (Beyond sight), etc. As the fish in the unfathomable ocean, blooms in the ecstacy of love, feels thrilled, and dives, in the same way, absorbed in the greatness of infinite virtues, the devotees seem to be enjoying the bliss of nectar, ecstasy and delight, when we seem them in tune with the totality of these virtues-
Alakh, apaar, agam agochar
Na tis kaal na karma.
Jati, ajati, ajoni sambhau
na tis bhao na bharma (p.597)
(Undescribable, Beyond all, In accessible, Far off
Not subject to death or accountable for His deeds or belonging to caste. He is casteless, unborn, self-created, has no attachment nor doubts.)
Parvdigar, apaar, agam beant toon.
Jinha pachhata sach chumma pair moon. (488)
(Thou art the sustainer, Beyond reach, Limitless, having no end. I touch the feet of those who realize this truth.)
Agam agochar alakh apaara,
chinta karahu hamari p.795)
(Thou art beyond reach, beyond description and beyond sight. Take care of us, O Lord.)
Gahir gambhir athah apaar aganat toon
Nanak vartai Ik, Iko Ik toon (P.966)
(Thou art so very deep, unfathomable. Far beyond, incapable of being assessed. The Only One though pervadeth everywhere, sayeth Nanak. )
Besumar athah aganat atolai
Jio bolavai tio Nanak daas bolai. (p.292)
(Countless, fathomless, beyond assessment, beyond measure art The, O Lord. Thy servant sayeth what Thou maketh him say.)
The essence of all these virtues can be given in these words that God is Infinite. In the form of noun, infinity is such a word or symbol assss is related especially to mathematics and not any other subject. There are some properties of inifinity in mathematics and on the other side, the Inifinite Power Waheguru (God)has His own Divine qualities, the mutual relationship of which can be understood, to some extent, but to put it to writing is a very difficult proposition.
From the heading of a book ‘In Time with Infinity’ one finds this indication and from Gurbani also it is seen clearly that infinity is the second name of Divinity. And in relation to this, a mathematician can say ‘Divinity and Infinity cannot be explained at all. If it can be done so, it can be only through mathematics. In other words, the Inifinite cannot be described, and if it is possible, it is only through the means of mathematics.
It is the experience of those traversing this path that the personal experiences of the seekers of Truth do not tally. Sometimes there is a confrontation also. There are some sums in mathematics also which have different answers. These sums are connected with the Concept of Inifinity. Generally this is not so without reason in Mathematics.
Influenced by many of such questions, great mathematicians got unnerved. Not paying due regard to inner mystery, indications and hints given therein, they had attacked ‘Infinity’, According to this book,
‘Not many years before, a successful attack was finally made on the problems of the Infinite, the Supreme. Nineteenth Century Mathematician Karlk Fredric, GAUSS expressed a horror of Infinite qualities. I protest against the use of Infinitge magnitude….which is never permissible in Mathmatics.’
He severely criticized and opposed such questions and said openly that the question conercning Infinity are not capable of being accepted in mathematics.
Those who understood the hints, they parted company with Mathematical Infinity and went over to Divinity. It is mentioned somewhere ‘There was a professor of Trinity Who found the Square root of Infinity. But in counting the digits He was seized with fidgets.Dropped Mathematics and took to Divinity.This writing speaks of change but not the mystery of change.
But when we go into the Divine Light Guru Nanak Dev’s knowledge of the Infinite, we can say emphatically and without hesitation that how nice would it have been if GAUSS, instead of criticizing, had found the reasons behind different conclusions and clarified them, which he could have done easily.
In the enlightened mind of Guruji, there is no scope for lack of clarity or perplelxity about the conclusions reached with regrd to the qualities of Infinity.Many references have been made in Gurbani to the qualities of the Infinite and there is exaggeration in explaining their import, that ‘The worldly mathematics begins with 1, remains in a limited sphere and ends with attaining inifinity. While Guru Nanak’s arithmetic begins with non-duality and mathematics from infinity.
Gurujis’ spiritual knowledge is perfect from all angles. It is knowledge of all knowledges; it is science as also simple knowledge of wondrous nature. There is unmeasurable power to understand quickly a truth without logic or citations. There is no conflict in his meaningful views. Of course, it is easy to understand a Universal Truth through some methodology. That is why the seeker of the essence spiritualty, should bear this in mind that to become spiritually knowledgeable there is no need to reject logic but to rise above it.
In the spiritual field, Guru Nanak has for the first time given the definition of Infinity. Of course it is not easy to define the definitions, but still it is essential to understand that the definition and quality do not have the same meaning. Definition is unique, and only one, even if it is done through different words. It completely represents the defined word, while the qualities can be more than one. The full knowledge of any form is not called definition in term of a quality. In the following pauri of Japuji Sahib Guru Nanak says –
Ant na sifti kehan na ant.
Ant na karnai dein na ant.
Ant na wekhan sunan na anti.
Ant na japai kya man mant.
Ant na japai keeta akaar.
Ant na japai paravar.
Ant karan ketai billahe.
Taka ant na paiye jahe.
Eh ant na janai koye.
Bahuta kahiai, bahuta hoye. (5)
(His praise has no end, no end in saying it. No end to doings and no end to giving. No end to seeing and no end to hearing. Can’t see the full form of expansion. Can’t hazard a guess of its vastness. Many have tried in vain to do so. But His Vastness can’t be measured. No one knows this Infinity The more one may say, the more does it seem.)
Infinity has no end, no limit, no ending. We may call God as much Great as we can, but He is greater than that. This is defined in Mathematics in this way-
‘Inifinity is not a definite number, it is higher than the highest conceivable number through our intellect’
In this way Infinity is above limits, count, and measure.God is Infinite, therefore, infinity is variety and distinctness. From material angle, some divine qualities appear to be opposed to one another. Being progressive it is firm, it has unity in diversity and diversity in unity.
Sri Guru Granth Sahib is a great creation in the world, in which the Formless has been depicted on a very large scale in a Formless form. Something having form has some limits, and therefore its qualities are also limited while the knowledge of the Infinite is all embracing and infinite. Guruji says –
‘Sukh nidhan Pritam Prabhu mairai.
Agnat gun Thakur Prabhu tairai.(802)
(O treasure of comforts, my dear Lord.
Thou hast got countless qualities, my Master.)
Of these infinite qualities, only Mathematics (with which this write up is concerned) is under consideration. Guruji has only explained the theoretical aspect, which only a mathatician can vouchsafe, one whose bent of mind is interested in going into the mysteries of the Infinite.
The Formless God, who roots out the doubts and ignorance has the first quality about His symbol. He is symbol-less or He is beyond form or features. Guru Nanak says in Sidhgoshta :
Chihan varn nahi chhaya maya Nanak sabad pachhanai.(944)
(He has no symbol, hue or class,etc; he is known through Words)
He is without symbols, form, or a special Name. On the basis self-made definition, to enter into arguments about different Names, becomes an obstacle on the way to attain the Truth.
From the Mathematics point of view
Which can be written as
a= -P=1 or P= -1.
Which is quite absurd.
This senseless conclusion has been arrived at because supposing P as infinity, the mathematical operation was carried out.
See how strict warning has been given not to describe God through symbols because in this way, taking infinity as a form of calculation, we try to operationalise it.
Hari beant hau miti kar varnau
kya jaana hoye kaiso re.
Karau bennati Satgur apuna
mai moorakh dehu updaiso re. (p.,612)
(God is Infinite, but I describe him by way of measurement, though I do not know anything about Him. I pray to my True Guide to guide me, a foolish one as I am, as to what is right.)
Timeless (God) is a complete unit, not broken. He is unbreakable; He cannot be divided into parts or pieces. The digit ‘1’ symbolizes the common Light. Guru Gobind Singh describes this quality of God in this way –
(I salute Him Who has no holes I salute Him Who cannot be amassed. I salute Him Who cannot be broken.)
Waheguru is not the common Name for all the gods, nor is He Brahma, Vishnu, Mahesh, divided into three. He is the Divine Power and not an earthly being. Let us see by dividing Infinite Waheguru into three parts –
And divide this into three
And if we compare P and z, it would appear that z=3P
Or the part is three times the whole.
Guru Arjan Dev says in Sukhmani Sahib –
Abinasi nahi kichhu khand.
Dharan dhar rehyo brahmand (P.282)
(He is indestructible and can’t be broken into pieces. He sustains the universe.).
The history of ancient India tells us emphatically that by breaking God into parts, not only the parts began to be worshiped but the worshippers also got broken into parts (sects).
His special quality is that of eternal growth. God’s inexahusible stocks never deplete. There is constant increase therein and no shortfall. This divine Power has no peak, no top (climax). One treading this path is ever in high spirits, and never out of sorts. How wonderfully true is it that we receive countless bounties from the inexhaustible treasures of God, bus His treasure, goes on growing rather than depleting. Confined to a narrow cirlce the ignorant ones find it difficult to believe this. Gurbani says –
‘Khavahe kharchahe ral mil bhayei.
Tote na avai wadhdo jayee. (p.186)
(Consume and spend together as brothers. There shall be no dearth, but increase only.)
Because God’s bounties are inifinite and for ever and if we suppose–
And deduct from it the first four number, the remainder will be-
It would be clear then that Q>P.
Note: This formula does not apply to Finite series.
Formless God is Unique, Has no equal and Umeansurable. We may say, He is matchless. It is possible to draw a comparison with the worldy powers but drawing a comparison with Infinite is height of ignorance. In 1-Onkar, ‘1’ is the symbol of Oneness and imitating s it is a fool’s stubbornness.
Bahu beant ooch tai oocha.
Nanak apas kau apai pahoocha. (291)
The Infinite is higher than the highest.
Sayeth Nanak, He alone can reach His own Height.
Mathematically, length, width, height, depth have two ends, but no one is aware about the two ends of Waheguru:
Duha siriyaan ka aap suami.
Khailai bigsay antar jami.
(He Himself is the master of the two ends. He plays and delights in His own way He knows everything in everybody.)
What to talk of the powers of the Infinite, we cannot even draw a comparison with the limited powers.
. God is Self-Reliant, Sovereign and Self-Created, He is not controlled by any creature, He is independent, not confined to the sbondage of anyone. In Mathematics, y=f(x) means that with the change of x the value of 7 shall change and would be Unique but Waheguru is beyond any effect, the change of time or space or any outer influence cannot change His form. Of course, through His Own will ‘Jewad bhavai tewad hoye. Nanak jaanai Sacha soye. (As He Wills, He assumes the form But He, the True One, knows this mystery. . Waheguru is continuous, constsant and an even flow. A creature is part of Him, part of the Supreme Light, just as a dot is part of the line but it cannot gauge the extent thereof. In the same way a creature can go back to mingle with God but cannot describe Him fully.
Nadia atai wah pavai, samund na janiah. ( Rivers and streams flow into the sea, but cannot fathom it).
If a being is a zero, God is 1, a line. If a being is a line, God is a large surface. If a being is a surface, God is a sky of length, breadth, and depth beyond measurement, a space. Where does a mere creature of dot size stand in the vast space? This humble creature, a worm, is something which may have its nominal existenced, because it has no dimension, length,breadth or depth. Its value is zero which attains value by joing a digit. Millions of zeros put together are of no value, meaningless. As zero cannot divide anything (It cannot be increased or decreased) it cannot be reduced or increased. The cycle of time goes on, time changes, old things get worn out but truth does not age. It is ever new, firm and unshaken.
No uh wadhai na ghat-ta jaiye.
Akul niranjan aikai bhaiye. (343)
(He does not grow or reduce. He is without lineage, aboveillusion, Uniform.)
This quality of Infinite is quite amazing, meaningful and priceless. Singing the praises of the Unfathomable, or trying all the numerous wisdoms to change the Highest Power, cannot affect Him. Gurbani says –
Sachai Naam ki til wadyayee.
Akh sakai qeemat nahi payee.
Je sabh mil kai aakhan paiye.
Wada no havai ghat na jaye.
(Even an iota of the True Name cannot be sated or evaluated. If all the ones get together to say this, He would neither grow nor reduce).
Perfection has a special quality that it is not more than necessary. If it is more, it can be easily reduced or removed. If it is less than necessary there is scope for adding something to it. Bhai Gurdas says-
Poora Satgur janiai, poorai poora thaat banaya.
Pooraai poora tole hai,
ghatai na wadhai ghatai wadhaiya.
(True Guide is known to be perfect, the perfect one has created perfection. He is complete, in full measure, and beyond reduction or increase.)
In the History of Hindu Mathematics, Bhaskar II writes –
‘In this quantity consisting of that which has cipher for its divisor, there is no alternation, though many may be inserted or extracted as no change takes place in the Infinite and Immutable God (not liable to change).’
It is clear that Bhaskar II knew that according to Mathematics
a=a and a+k = a
a+k= a +k
= a + kd
= a+k+0 = a+O = a
0+l 0 0
It is a simple and golden rule the converse or use of which facilitates solution of knotty problems. There are many questions relating to this formula of Mathematics, which cannot be discussed any further here.
Guru Gobind Singh adding something to this rule, has explained it in greater detail. Describing the Divine Light (a) Saibhang and Anubhav Praksh (Self Illumination) Sarbatra Bhao (Omni presence), Nirbadh bibhootai (Without Interruption), (b) Saivang prabha namo nath poorai (Complete) ie meaningfulness (a) both these special qualities have been given a distinct place. Guru’s words are-
Zimin zaman kai bikhai samast eik jote hai.
Na ghat hai na badh hai, na khat badh hote hai.
(In the entire universe there is only One Light Which does not increase or decrease)
It would be meaningful to describe this beautiful sutra in these words –
God is so great that He remains
Unchanged, and unaffected regardless
Of any operation on him, it may be
Mathematical or non-mathematical.
God is so great that consequent on all kinds of operations, no change is caused in His existence.
To see the real form of the True Indescribable One Formless God or to describe Him is possible by the True Guide only (Satguru). The one with little wisdom, cannot explain God and His Greatness. He has only one prayer –
Hari ki wadyayee hau aak na saka
hau moorakh mugdh nichan
Jan Nanak kau Hari bakhas lai
mairai suami sarnagat paya ajaan(733)
(I can’t state anything about His Greatness, I am a fool and ignorant one. Forgive my shortcomings O Lord, I have come to Thy door to seek shelter. )