The Buddha’s ‘Anatta’ doctrine and mathematical thinking
Posted on March 12th, 2019

Bodhi  Dhanapala,  Quebec, Canada.

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 in Prof. Dharmawardana’s book on “A Physicists view of Matter and Mind” (World Scientific, 2024)   he 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 Buddhist  picture.

I have discussed the Buddhist doctrine of rebirth and Anatta in my blog (

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.

3 Responses to “The Buddha’s ‘Anatta’ doctrine and mathematical thinking”

  1. Charles Says:

    Dear Mr. Dhanapala,

    I read with interest your article The Buddha’s Anatta Doctrine and Mathematical thinking. It was an interesting article and it carries value as it comes from a Mathematician-–a scientist. I also read some of the articles in your Blog.

    I am just an ordinary Buddhist without any scientific background and I do not see the Anatta Theory, Rebirth, and Paticcasamuppada in the same way as you see it. For me Rebirth, Kamma,, and Paticcasamuppada are essential part of the teachings of the Buddha without which it would not be his teachings. By reading and scientific investigation of dhamma you get a better understanding of the teachings , but it does not provide the same awareness that comes from experiencing the Dhamma. I mean through meditation, which gives an insight into the teaching which no amount of reading and reflecting would give. This of course Mr.Dhanapala is my opnion and I do not intend to criticise you or challenge your arguments as you have a right to have your own opinion on the subject.

    But when we search to understand the Anathma theory we understand it as the Buddha had said without looking for any proof beyond what the Buddha has said. For instance in insight meditation on impermanence( anitya bhavana) we see the body without the mind as a composition of four elements, and at death separated from the mind the body decays in 9 stages and disappear. We also see that form, feelings,perception,mental factors and the Consciousness are all impermanent entities that constantly change and that there is no soul or any permanent entity that could be called a soul present any where.

    That is anatma. We also see that there is no creator as every conceptual phenomena follows a cause ( paticcasamuppada). That the birth is the result of a Kamma accumulated through ignorance(avidya) of the four noble truth. The effort in meditation (vipassana)is to make the mind deeply understand (avabhodhaya) that it has made an error in accepting the form (rupa) as a being, and that there is in reality no such permanent entity. That is there is therefore an anatma sangna- no soul.


  2. Ratanapala Says:

    Lord Buddha has given us a set of tools that would help to chart a course through the quagmire of Samsara and to develop a means to see through and transcend ‘views’ whether religious, scientific or mathematical. He told us ” I only show you the Way” – it is up to us to traverse to the end and see for oneself”.

    We, on the other hand, have built ever more beautiful and awe-inspiring camps on either side of this road and are trying hard to predict what is at the end – just as astronomers are building ever more powerful telescopes, scientists ever more powerful particle accelerators, and colliders and hypothesis to see the end or the beginning of this assumed reality and existence. Although the end always seems ‘just around the corner’, just as the horizon it recedes and presents us ever more complex vistas to ponder.

    It was just at the end of the 19th Century the famous mathematician Laplace said we now have all the tools to understand reality back to its beginning and as much further into the future as we want just with the understanding of Newton’s and Maxwell’s theories. However, this was not to be – the advent of the Theory of Relativity and Quantum Mechanics has put all this in disarray. During the whole of the twentieth century and a fifth of a century into the 21st, we are no closer to that elusive Ultimate Reality!

    What Lord Buddha said is that it is a Beautiful Path but at the same time a Lonely Path for one has to traverse it oneself till this continuum of ever-changing consciousness enters the Supreme Bliss of Nibbana! The “Views” however beautiful be they religious, scientific or mathematical are only views that will forever keep us entangled in the quagmire of Samsara.

  3. Charles Says:

    Dear Mr. Dhanapala,

    I thank you very much for your reply. It is said that to learn the teachings of the Buddha you should listen or read the discourses, reflect on what you have heard or read, and above all discuss what you have heard or read. Therefore it’s a great priviledge to be able to discuss the Dhamma with you as you look at it from a different dimension-scientifically, to which I am a stranger and traverse such paths with trepidation. We normally discuss Dhamma with people who are of equal understanding, but you offered me a chance to discuss what I know with you , and I see no reason why I should take a “kithul polla”.

    The Dhamma is timeless and it is open to any challenge. Buddha’s teaching is without contradictions, and it is by itself scientific; you see it in Abhidhamma which Buddha did not want to confuse the ordinary people by introducing it to them. Therefore, even if you see certain aspects of the Dhamma differently, the basic teachings of the Buddha remain the same and it is wrong to call it old fashioned Buddhism because you think Science is new to Buddha and his teachings become dignified by giving to it a modern scientific twist.

    I have listened to the American Scientists meeting in Dharmsalaa to discuss Buddhism with Dalai Lama and I found it interesting.

    The question about parental genes go to make a child, are physical variations. It is like planting a seed and from it a tree grows or it is like respiration or circulation of blood. They cannot be attributed to Kamma. But the conception itself is kammic which involves the kamma of the parents and that of the being conceived.

    After all what we learn from Dhamma purifies our mind to the extent of our understanding, and prepares the mind to be concentrated into the departing citta of a dying person(cuti citta), and it is the kammic force within it that makes it reach a fertile womb with similar kammic vibrations to join with a relinking citta( patisandhi citta) to create a nama-rupa- a being. That is absolute Kamma, according to paticcasamuppada.

    I do not think the Buddha had a problem with different people understanding his teaching differently provided he follows the basics correctly to enter the path of Nibbana. Afterall the Buddha did not “invent” the teachings he found a teaching that was already there. Every Buddha is born to revive that same old teachings, so it is not different if you learn the teachins of the Gautama Buddha or in future from the Metteiya Buddha.

    What is important is how much of Dhamma we have absorbed and what our reaction would be when we are faced with the vision of death( gati nimitta etc) when we are about to die. Will we have the mind concentrated, calm and aware of the impermanence to prevent attachment at that moment when the final cuti citta is about to depart ?

    Thank you Mr. Dhanapala to have given me the courage to enter into this simple Dhamma discussion with you,

    Wih metta,


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