Did Nāgārjuna describe features of the Fourier transform?

Question

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

25:19–20
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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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: