One of the many topics that was raised during the talk on the Thai translation of Matthieu Ricard’s and Trinh Xuan Thuan’s book concerned the relation between Buddhist thought and mathematics. There have of course been quite a lot of talks about how Buddhism and science are related, but not much at all on Buddhism and mathematics. So that was a welcome change. Unfortunately we did not spend much time on this fascinating topic.

It was credit to Ricard and Thuan that they spend one entire chapter on this topic. The idea is how mathematics is related to reality and what the Buddhists think of that. The eleventh chapter of the book is entitled “The Grammar of the Universe” or something like that. What is interesting is how mathematics is an accurate description of reality at all. Which comes first, mathematics or the world?

On the one hand, this is a very simple point. We all know that two plus two equals four. So you have two things, add another two, and count the result, which is of course four. But the premise of mathematics is that you cannot get mathematics (or logic for that matter) out of empirical observation. You just cannot form a general statement “2 + 2 = 4” from just observing two things and another two things. The reason is that you have somehow to know before hand that two plus two equals four in order for you to be able to get the conclusion that these two things and these other two make four! This is Kant’s main argumentative strategy in his entire critical philosophy. And for Kant mathematics is a prime example of what he calls “synthetic a priori” judgments, e.g., judgments that are true by virtue of their correspondence with some outside measuring point but which is known entirely through thinking alone.

We are not actually discussing Kant here; the point is that if the truth of mathematics does not come from observation, then it must come from inside. Ricard and Thuan discussed that perhaps this situation implies that there is some universal and all powerful mind whose thinking made all mathematical statements true (all the true ones, of course). It is this big mind that guarantees that two plus two equals four, that the sum of the squares on the side of the two legs of a right angle triangle is equal to that on the hypotenuse, that the law of modus ponens (‘p’ and ‘if p then q’ always implies ‘q’), and so on.

So this big mind might refer to God. So here the discussion went on to see what the Buddhists think about this. I don’t quite remember what Ricard, the Buddhist representative in the book, made of this, so I am going to present my own thought. I also did this during the talk last Saturday, but time was so limited then.

I think the main difference between the theistic religions like Christianity and Islam and non-theistic one like Buddhism might not appear as large as one might think. Buddhism would have no problem recognizing the Big Mind alluded to above, so long as that refers, not to some external being, but in fact to our own minds. It is us who create mathematics and it is ultimately speaking our own minds, working together collectively, that create the world such that it is true of mathematics. In other words, we could also say that we human beings are gods unto ourselves. There is a Big Mind that creates reality corresponding to math, yes, but that Mind is not apart from us.

Whether this is shocking or not depends on your view on theism. If you believe that humans are apart from God, then you’d find this shocking. However, this is entirely correspondent with the Buddhist attitude that salvation is ultimately the person’s own responsibility and lies entirely within the person’s power to achieve. The Buddha is only a teacher. You don’t need to follow his teaching. The Buddha has no power to drag you to Liberation. No being does. You have to do it yourself.

Coming down from theological discussion and back down to earth, we see that the idea that it is human mind itself that creates mathematics to which reality belongs makes quite a lot of sense. We form mathematics and we perceive the world according to the same conceptual structure that formed the math in the first place, so no wonder the world corresponds to it. However, even thought mathematics looks very certain, it does not describe what reality is like ultimately speaking. This is because all mathematics depends on concepts and language (so is logic), and once you have concepts, you have to divide reality into separate chunks. So at best mathematics is a model or a map, and no map can become identical to the reality it is the map of. This refers to the doctrine of Emptiness or sunyata. We can say that math can always approach that, but never reach it, because if it does, then it would cease to be the math that it is.

there is no relation between math and religion,especially Buddhism.

A lot of mathematics was invented in West Africa – very far from the Indian-sphere of influence, which also contributed to mathematics to some extent… but this was after the rise of Buddhism.

I would have to agree with hyti – but I gave a reason why!

Buddhists can now use math, and interpret their logic into the logic systems of mathematics… but the two were never created to be used simultaneously.

Buddhism might be built on voidness-principles… so math based on inequalities and zero as the sum would be good Buddhist math.

Buddhism and Physics, as i write in another article — leads to cosmological issues, and I would love to present my findings in a seminar!!!

Math and physics are related… so math and Buddhism… as a joint concept… math would be the measurement of the means… means in Buddhism as I might be implying relates to the wave/motion/time… the transitioning between factors… Abhidhamma uses mind-moments, and these are measured…

Invite me to a seminar to present my award-winning paper – that I never presented because of visa problems!!!!

Thanks for your comments. Perhaps there’ll be a chance for you to present your award winning paper. Let’s see what can be done.

I’d say mathematics and Buddhism are related in a much deeper way than that discussed here. Mathematics is really all about defining abstract things and determining the consequences of some set of definitions, so it is not really “about” reality in the Buddhist sense at all.

However, I do think that deep truths of mathematical logic lend strong support to Buddhist ideas. To put it pithily, it is mathematically true that a whole cannot know itself as an object, and that truth from the perspective of a whole is provably undefinable (http://en.wikipedia.org/wiki/Indefinability_theory_of_truth). In fact, no non-trivial piece of the whole (no piece which including the statement “that which is true is true and that which is false is false and the two are different”) can be known as an object of the whole (http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems).

Even formally manipulating symbols leads to recognition of anatta!

Thanks for your comments. I agree that mathematics is really not about any reality, but then it seems that we humans conceive of that reality through conceptual tools made possible by or abstracted in mathematics.

I like your reference to indefinability of truth and Goedel’s theorem a lot 🙂

I would say that Tarski’s theorem could be directly applied to the brain as the basis of conceptualizing the brain. The current model is circular where you have an observer that perceives it is independent of what it is observing that is false. That which conceptualizes cannot reductively define itself in any way. So this circular logic has not been directly addressed and how math can be applied to break this circle.I am shocked that this failed logic circle still stands and it’s the key to understanding consciousness. I’m not a mathematician or I would do it myself..LOL..But I see the failure of the base concept of the brain as it currently stands and that is totally wrong and bizaare. The current model goes back into the 1800’s and is totally Newtonian.

I am a strict empiricist, harsh evolution determinism, non dualist. Reality is simply explained as a concrete/abstract singularity. QM biology will prove this out to be true. I’m also what could be called a Religious naturalist. But I just call it rational.

Hi David, thanks for your comments.

thanks for a very interesting article. You can also apply the pythagoras theorem.

Practico budismo, pero tengo o siento una aversión hacia las matemáticas, al leer el artículo me queda más claro que así como yo soy la única que puedo solucionar mis problemas existenciales, de la misma manera, soy la única que puedo solucionar mis problemas matemáticos. ¿Pero por qué los creo más poderosos que yo? Seguiré entonando Nam miojo rengue kio para encontrar la solución,

Hi, I don’t know much Spanish at all, but thanks a lot for your comment.

I’ve once heard that Buddist said that if things would have gone differently in an historic way maths would have gone very differently that the ones nowadays known

It’s possible that mathematical truths, in general, would be relativistic: a certain mathemtical set would undoubtly exist, but the truth about the size of the set is impossible to know, hence is relativistic.

Yes. Perhaps. Thanks.

Is there any contradiction in believing in the or at least finding the mathematical universe hypothesis (MUH) (“Our external physical reality is a mathematical structure. “) and Buddhism, in your opinion?

Hi. It might be not related to Buddhism and Mathematics at all but I’ve tumbled upon a meta-mathematical truth some arithmetic truths about the natural numbers are relativistic. I’m actually in the process of writing a paper on this. I don’t mind sharing my thought/work on this.