The Buddha's ‘Anatta’ doctrine and mathematical thinking

The Island newspaper has published several accounts of the Anatta doctrine by a number of writers, including Dr. Carlo Fonseka, an ex-Marxist free thinker who has an excellent  grasp of  Buddhism, as well as Dr. Upul Wijayawardena, an ex-cardiac surgeon with a deep critical mind. The learned Bhanthe Dhammika from Australia has supplied the authoritative account. Interestingly, one aspect of these comments with a diversity of backgrounds is the lack of use of  even a modicum of mathematical language – the supreme language needed for the exploration of subtle concepts.

So,  when Leo Fernando, who I believe is an old-timer Cambridge mathematician,  wrote a comment (25 February - Island) saying that he too "fails to understand the Anatta doctrine", I could not help feeling surprised, because, in my opinion,  the answer to the question  is found in elementary mathematics, known to everybody but rarely reflected upon.The Buddha, in his Anatta doctrine denied the existence of any unchanging entity whatsoever in any aspect of reality or  in a manifestation of what we call a "Person". This is contrary to the usual  Hindu or Abrahamic doctrine that there is an unchanging essential characteristic,identifiable as the SOUL or "Aathma" of an individual, uniquely associated with the person. In fact Prof.

Dharmawardana's book on Matter and Mind  states that the word "Athma" is  the source of the name "Adam", while "Jeeva" is said to be the source of the name "Eve". In the Christian doctrine, a soul is given to a person by divine intervention at the moment of his conception. This doctrine troubled St. Augustine enormously because, how can Providence acquiesce to giving a soul to children resulting from sinful fornication out of wedlock?  According to the Buddha, a person is an ever evolving sequence of Nama (N) and Roopa (R)  held together by a process of "clinging" caused by "Thanha" or "desire to persist".  Nama are mental processes, while Roopa are physical processes. They cohere together to make a living being. So, a person at the time T1 is just (N1+R1 at T1). At a later time this becomes a modified set of Nama and Roopa at time T2, i.e., (N2+R2 at T2). There is nothing which has remained unchanged. But the new state "originates" from the earlier state by causal laws. There is no room for miracles or prayer!

The time evolution from the moment labeled T1 to the next moment labeled T2 is said to be determined by physical laws as well as Karmic factors  ("habits") associated with that person, who is the composite sum of Nama and Roopa at any given moment.  Although there is no identifiable permanent entity, the time evolution occurs directly by the sequence ofNama and Roopa. The time evolution can be written down as a transformation "matrix" or "operator" that takes as input the state N1+R1 at time T1, and outputs the state  N2+R2 at time T2, immediately afterwards.This type of relationship is used all the time in mathematics, and it is called a functional relationship. Simple relationships that connect the situation at time T1 with the time T2 are called "Markovian". The Buddhist picture is more complex and Non-Markovian, involving so-called karmic links  into the deep past. Karmic action is old habits acting on you, and making you do things that depend on your past practices. Thus, if you have been a habitual liar or  killer, lying and killing become ingrained modes of action in your life. If you practiced compassion, that becomes ingrained as your life style. Life is of course, simply the time evolution of a set of Nama and Roopa temporarily identified as "YOU" by you and your associates. It is this temporary identification  that makes you come to the DELUSION  that there is a "permanent  self" or specific "soul" identifying you. It is the attempt to "satisfy"the desires of this "I" that leads to "Dhukka". The word  "Dhukka"  is often translated as "suffering", although it is only partially appropriate.   So, we can go from one instant to another, where a set of  Nama and Roopa (N+R) are evolving, and we recognize this set as some person "we know", who may be a family member. If we stay together we hardly notice the changes. But there is no permanent unchanging aspect of any of us that we can discern. In fact, if we had seen some one at an early age, we may not recognize that person if we only see that "person" only after a lapse of say,  40 years. There is no permanent person. Finally, when a so-called  person's  "Nama+Roopa" decay due to biological aging, the association collapses and there is physical death.

The N+R association breaks down just as a  soap bubble grows and finally breaks down after some time. But Buddhism says that just as the breakdown of the soap bubble may spawn a tiny new bubble, the collapse of N+R spawns a NEW Nama+Roopa, which is a NEW grouping of N and R.  This is a new "being" who will mature and then decay. This is the "cycle of rebirth as explained by the Buddha". It requires no permanent soul, but only  the existence of a PROCESS, or "becoming". Similar concepts are found in Henri Bergson's philosophy where there is an ever changing "elan vital" which plays the role of Nama +Roopa of the Buddhistpicture.     I have discussed the Buddhist doctrine of rebirth and Anatta in my blog ( which explains why the traditional rendering of the rebirth doctrine is not needed in Theravada Buddhism as found  in the First Sermon of theBuddha.

The first sermon of the Buddha explains how Naama and Roopa evolve in time in the doctrine of the "Patichcha  Samuthpada". At each moment, even in "this life"  there is a set of Nama and Roopa which persists for a short interval of time, and then it dies and a new set of Naama and Roopa appears and persists for some time, and so on. That is, "rebirth" is happening all the time, just as the cells of our body die and gets regenerated after persisting for a day. A female egg persists for one menstrual cycle, but it is not permanent although long-lived compared to most other cells of our bodies. We are dying and being born all the time,and that is SAMSARA, which exists even without invoking a "next birth".   In fact, a careful perusal of the First Sermon shows that the Buddha  limits himself to just that in his first sermon, and never mentions traditional "rebirth" anywhere in it.

When the Buddha says "ayam anthima jatha  natthi daani punabbbavo", the Buddha is referring to the end of the birth ("jathi") of "Thanha", and hence the traditional translation (into English etc.) as "this is my last existence, now there is no rebirth" is surely incorrect. For more details, please read  my blog referred to above.


Quebec, Canada.


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