The Fourier transform describes how to transform between cyclic and non cyclic. Did Nāgārjuna describe this already several centuries before Fourier as described in Mūlamadhyamakakārikā 25:19-20?

A full translation to western terms is

न संसारस्य निर्वाणात् किं चिद् अस्ति विशेषणं
na saṁsārasya nirvāṇāt kiṁ cid asti viśeṣaṇaṁ
There is nothing whatsoever of the cyclic distinguishing (it) from the non cyclic.
ननिर्वाणस्य संसारात् किं चिद् अस्ति विशेषणं। १९
na nirvāṇasya saṁsārāt kiṁ cid asti viśeṣaṇaṁ| 19
There is nothing whatsoever of the non cyclic distinguishing it from the cyclic.
निर्वाणस्य च या कोटिः।कोटिः। संसरणस्य च
nirvāṇasya ca yā koṭiḥ koṭiḥ saṁsaraṇasya ca
(That?) is the limit which is the limit of the non cyclic and the limit of the cyclic;
न तयोर् अन्तरं किंचित् सुसूक्ष्मम् अपि विद्यते। २०
na tayor antaraṁ kiñcit susūkśmam api vidyate| 20
Even a very subtle interval is not found of (between) them.

4 Answers 4


Nāgārjuna was not a mathematician; he was an eminent buddhist philosopher. That is certainly enough, don't you think?

There is an interesting parallel here, perhaps — maybe even a useful analogy, though one that would only be meaningful to people who understand Fourier transforms — but that's all. The claim inside the question asked is mere puffery (great word, puffery), but if we puff Nāgārjuna up with undeserved praise we deflate that which he actually deserves praise for.

A thousand people can all look at the same thing and describe it in a thousand different ways. Laozi described it centuries before Nāgārjuna, but we wouldn't give Laozi credit for Nāgārjuna's vision, and we shouldn't give Nāgārjuna credit for Fourier's vision.

  • Did Lao Tzu discover the spectral theorem maybe? But you have a point. I should refrase the question but not sure to what. Is "Did Nāgārjuna discover features of the Fourier transform?" better? This is not primarilly about credit, but in regard to credits it seems like Nāgārjuna should have some of Fouriers credits. A complete merit field would contain more than those names and also have vacancies, since some questions regarding the transform are unanswered. Jan 4, 2021 at 19:34
  • @DavidJonsson: I'm not sure what the deeper question here is, either. All I can really do is point at Newton's famous phrase: "If I have seen further it is by standing on the shoulders of giants." Knowledge is cumulative, and everyone builds on the intuitions of those who came before them, sometimes knowingly, mostly not. We can trace so much of the modern world back to some unnamed caveman who first put an axle in a wheel, but you know... c'mon. Jan 4, 2021 at 19:43
  • Origination counts. That quote about shoulders of giants actually comes from the 12th century Bernard of Chartres: en.wikipedia.org/wiki/Standing_on_the_shoulders_of_giants Jan 4, 2021 at 21:51
  • @DavidJonsson: Understanding counts. Attribution is an aspect of ego. Jan 4, 2021 at 22:52

To our knowledge, Nāgārjuna never shared a precise formula for calculating the Fourier transform precisely, so we have no way of gauging his understanding of that particular equation.

The remarkable thing about Fourier transforms is that a "local" phenomenon such as a singleton wave can be equivalently represented by the sum of infinite waves of different frequencies. In essence, Fourier provides a simple mathematical proof that something that looks like an individual isn't really an individual. Fourier transforms take us from the local to the infinite with relative ease.

So if we say that samsara is the convention that a self exists, then nibbana might be understood as the insight that the self is an illusion arising out of infinite conditions in the quote:

There is nothing whatsoever of nirvana distinguishing it from samsara.

The nice thing about Buddhism is that calculus is not required as it is for Fourier. Also note that wisdom is not required to calculate Fourier transforms.

  • Is it necessary to provide a precise formula or can it be deduced from what has been mentioned? One might say that Nāgārjuna is more general since there are other cyclicities to transform back and form from, as @arthur mentioned. Jan 4, 2021 at 19:18
  • @DavidJonsson Fourier provides a mathematical basis for an initial understanding of some Buddhist concepts. For example, the cyclicity of rebirth is reminiscent of the periodicity of sine waves. However, the depth of Buddhism goes well beyond Fourier. Fourier doesn't address suffering. Buddhism does.
    – OyaMist
    Jan 5, 2021 at 15:10
  • Buddhism does not prevent quantisation of suffering. Most reactions of this page seems to be about quantisation. Jan 5, 2021 at 16:54
  • Buddhism introduces quantisation in the concept of "contact". Understanding that suffering is quantized actually helps deal with suffering. There's no suffering between contacts because feelings arise from contact. But that's probably for a separate topic.
    – OyaMist
    Jan 5, 2021 at 18:30

Well, Fourier Transform makes an assumption that the function of life is a smooth enough object. It must be at least continuous, and is a lot better if it is differentiable a couple of times or more. In case of none smooth points (like transitions taking place in case of death or birth for example), it makes a lot more sense to use some other bases, like Haar wavelets or smth. In this case you'll notice not only the oscillating parts but constant parts as well.

  • 2
    This answer is not related to Buddhism
    – ruben2020
    Jan 1, 2021 at 8:40
  • @ruben2020 The question is not if it is related to Buddhism or not. As a philosophy Buddhism applies to anything. The question is if Buddhism can be applied to that which the Fourier transforms are applicable to and if there is a difference in such applications. Jan 4, 2021 at 18:54
  • Smoothness or continuity is not a necessity since the Fourier transform exists in a discrete form, the discrete Fourier transform. Jan 4, 2021 at 19:13
  • @DavidJonsson, thanks for the support. I tried to do best out of the question and provide as useful answer as possible. Surely, there's a discrete form, thought for me it is the other way around: we do discrete transform to have things fast on a PC
    – arthur
    Jan 5, 2021 at 21:15

What this question does is commit the logical fallacy of false equivalence, which is colloquially known as "comparing apples and oranges".

The OP changed saṁsāra into "cyclic" and nirvāṇa into "non-cyclic", when these Sanskrit terms are never used in the mathematical or physical context of cycles or waves.

Suppose I change saṁsāra into "existence of matter" and nirvāṇa into "non-existence of matter".

Now the verse becomes:

There is nothing whatsoever of the existence of matter distinguishing (it) from non-existence of matter.

There is nothing whatsoever of non-existence of matter distinguishing it from the existence of matter.

(That?) is the limit which is the limit of non-existence of matter and the limit of the existence of matter;

Even a very subtle interval is not found of (between) them

And voilà! Now Nāgārjuna discovered the phenomena of quantum fluctuation in quantum physics.

This is another example of false equivalence.

3D visualization of quantum fluctuation from Wikipedia:

Quantum fluctuation

  • There is no support for you translation. Matter is sometimes described as cyclic and appears as such on smaller scales. "Features of" can not be understood as equivalence. Jan 5, 2021 at 16:51
  • Are you with this post saying that saṁsāra doesn't mean cyclic and nirvāṇa meaning cyclic? Cyclic and non cyclic is not only limited to mathematics or physics. Feb 17, 2021 at 15:07
  • @DavidJonsson Yes. I'm saying that you are stretching the meaning of these terms to fit your narrative.
    – ruben2020
    Feb 17, 2021 at 15:49

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