REFLECTIONS REFLECTIONS REFLECTIONS REFLECTIONS REFLECTIONS • No. 2 • JUNE 1994

Pradeep B. DeshpandeProfessor of Chemical Engineering

University of LouisvilleLouisville, KY 40292 U.S.A.

ZerZerZerZerZero and Infinityo and Infinityo and Infinityo and Infinityo and Infinity:Foundations of Spirituality or Mathematics?

Figure 1. G. P. Rao's Riemann Sphere

•

j •••••

•••••

•••••

0Atma"Soul"

- j •••••

ances- •- •- •- •- •

Param-atma"Almighty"

One hundred years after it first deliberatedin Chicago, the Parliament of World

Religions met again in the windy city duringSeptember 1993 to ponder the role of religion forthe well-being of the inhabitants of this planet. It isperhaps befitting at this time to review how thenotion of zero and infinity may have originated overfive thousand years ago. The Sanskrit hymn (1) thatelaborates the meaning of infinity is

Purnamadam Purnamidam Purnat Purnamudachyate Purnasyapurnamaday Purnamevavashishyate Om Shanti Shanti Shanti

The hymn says that Parabhamma is full and nomatter how much is taken away from it, only fullness

remains.

The synonyms of zero (1) taken from an ancienttext Saankhya Nighantu (Muhurtha Darpanam)are

Akasham Gaganam Shunyam Antariksham Marutpatham

Akasham refers to sky and shunyam is the mostpopular synonym for zero and thus even in theirdefinitions, zero and infinity appear to be tied.

Figure 1 shows Prof. G. P. Rao's interpretation ofthe Riemann sphere with zero and infinity markedon the opposite sides (1). The letter j denotes theimaginary number. The point at zero representsthe atma (Sanskrit for soul or the self) while thepoint on the opposite side of the globe representsthe param-atma (or the almighty). The followingfundamental points are worth learning from theRiemann sphere.

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1. The distance from zero to infinity is very greatindeed and thus the search for the almighty is a longand difficult task.

2. The line from infinity returns to zero meaningthat the search for God may be conducted withinoneself.

3. One can draw a large number of radial lines fromzero to infinity that eventually return to zero, mean-ing that multiple paths in search of God exist.

The ideas in (1) and (2) must have led great soulssuch as Gautama Buddha to extensive searchthrough meditation. In this context, the search forthe almighty (infinity) through meditation requiresthe practitioner to rid the mind of all thoughts(zero) and thus here too there appears to be a linkbetween zero and infinity. The idea in (3) assuresdevotees that the routes prescribed in their respec-tive faiths are perfectly valid approaches to achievethe desired objective, no matter how diverse thevarious paths may appear. Appreciation of theramifications of these simple ideas appear to holdthe key to peaceful coexistence in these troubledtimes. Hopefully, the reader will be impressed withthe profound wisdom of the ancients.

The presence of multiple paths implies that there isno need to assume human form for the almighty,male or female. Such forms are admissible if thefaithful chooses to assume them but there is cer-tainly no compulsion for the male form.

Multiple paths lead to various faiths, such as Chris-tianity, Judaism, Islam, Hinduism, Buddhism,Jainism, etc., each equally valid, none superior toany other. A famous verse from the three to fourthousand year old Rig Veda says

Ekam Sad Vipra Bahudha Vadanti(Reality is one, the wise call it by many names.)

In fact in the vedic culture certain paths are pre-scribed that are independent of which faith, if any,one may belong to. For example,

Karma Yoga, the yoga of selfless action, refers torealization through good deeds. Mother Teresawould be closer to realization than most of us canever be, even if she never attended the church.

Raja Yoga, the yoga of meditation, refers to real-ization through discipline of the mind and thesenses.

Bhakti Yoga refers to realization through intensedevotion and worship.

It is interesting too what apparently began as anexercise in spirituality laid the foundations of math-ematics and sciences.

ACKNOWLEDGMENTS

The interpretation of the Riemann sphere is due toDr. G. P. Rao, Professor of Electrical Engineering,Indian Institute of Technology, Kharagpur, India.Prof. Rao has used the Riemann sphere to derive anumber of interesting transforms. He also providedthe Sanskrit hymn and the synonyms of zero citedin the paper.

The author acknowledges the assistance ofBharatkumar Sanghvi, a graduate student at theUniversity of Louisville, with the word processing.

REFERENCES CITED

1. Rao, G. P., Private Communication, January1994.

Pradeep B. Deshpande is Professor and a formerChairman of the chemical engineering departmentat the University of Louisville where he also di-rects a Center for Desalination. He has over twentytwo years of academic and full-time industrialexperience. Dr. Deshpande is author, coauthor,or editor of four text books in process controland seventy papers. He has received severalawards for his work including the 1990 DonaldP. Eckman Award in process control educationgiven by I.S.A. Pradeep consults for severalcompanies in the U.S. and abroad and offerscontinuing education courses in several coun-tries. He is a member of AIChE, ACS, and aFellow of ISA.