An Upanishadic lesson for modern science?

Do the Bhagavad Gita and the Upanishads lack the “baggage of biography” – to borrow Amit Chaudhuri’s words – because we don’t know who the authors, outside of the mythology, are or – as Chaudhuri writes in a new essay – do these texts carry more weight than their authors themselves because Eastern Philosophy privileged the work over its authorship? Selected excerpts:

One might recall that the New Critical turn against biography is related to a privileging, in the twentieth century, of the impersonality, rather than the emotional sincerity or conscious intention, of the creative act. This development is not unrelated … to the impact that certain Indian texts had on modernity after they were translated into European languages and put into circulation from the late eighteenth century onwards. …

By the time the Gita’s Krishna was first heard in Europe, all judgements were deemed, by the Enlightenment, to be either subjective or objective. What kind of judgement escapes this binary by being at once passionate and detached, made in earnest without mindfulness of outcome? Immanuel Kant addresses this in a shift in his own thinking, in his writings on aesthetics in 1790 … Five years separate the Gita’s appearance in English, and three years its translation into French, from Kant’s intervention in aesthetics. It’s unlikely he’d have been unaware of the work, or made his sui generis departure without it. The second time such “disinterestedness” appears as a concept, when Matthew Arnold redefines what criticism is, the link to the Gita is clear, and doesn’t require speculation. …

The Gita’s practice of “impersonality” points to T. S. Eliot’s attack, in “Tradition and the Individual Talent” in 1919, on the idea that poetry is an “expression of the personality” or of “emotion”. It’s no accident that the final line of The Waste Land is the Upanishadic refrain, “shantih shantih shantih”, the Sanskrit word for spiritual peace or even-mindedness …

It’s uncertain in what way these conceptual departures would have existed in modernity if these texts hadn’t been put into circulation when they were. Yet a great part of this history of ideas remains unwritten.

Chaudhuri also sets out the relative position of the Upanishads in modernity, particularly their being in opposition to one of the fundamental tenets of modern philosophy: causality. Per Chaudhuri, the Upanishads “dismantle” the causal relationship between the creator and the creation and “interrogate consciousness” through a series of arguments that attempt to locate the ‘Brahman’ in human and natural logic.

He concludes this portion of his text by speculating that the Upanishads might in fact have been penned by “anomalous Brahmins” because in the Bhagavad Gita, which is contemporaneous with some of the Upanishads and followed the rest after more than a century, Krishna asserts, “Neither Vedas, nor sacrifices, nor studies, nor benefactions, nor rituals, nor fearful austerities can give the vision of my Form Supreme” – whereas just these rituals, and their privation, concern the typical orthodox Brahmin today.

While the essay provides much to think about, the separation of creator and creation – in terms of the Upanishads being disinterested (in the specific sense of Chaudhuri’s definition, to mean an ‘evenness of the mind’ akin to unfixation rather than uninterestedness) with both a godlike figure or rituals and making room for biographical details in their verses – is incredibly interesting, especially in relation to modern science.

As Chaudhuri writes,

… “the field of knowledge called “the history of Western philosophy” could just as easily be called “the history of Western philosophers”, inasmuch as Western philosophers are the sum total of their lives and works, and we often defer to both biography and thought when we interact with the philosophy. Each body of work has a personality, but so does its author; in almost every case, we can, literally, put a “face” to the work, whether that’s a photograph of Bertrand Russell or a fourth-century BC bust of Plato.”

Prof Gita Chadha alluded to the same trait in the context of science pedagogy – in The Life of Science‘s promised postscript to their webinar on July 10 about ‘geniuses’ in science. In response to a question by Mrinal Shah, as to how teachers and educators could disprivilege the idea of a ‘scientific genius’ at the primary school level, Chadha said (excerpt):

There is an interesting problem here … In trying to make science interesting and accessible to children, we have to use relatable language. This relatable language organically comes from our social contexts but also comes with the burden of social meanings. So then, what do we do? It’s a tricky one! Also, in trying to make role models for children, we magnify the individual and replay what goes on in the world of science. We teach relativity as Einstein’s theory, we teach laws of motion as Newtonian laws of motion. The pedagogic need to lend a face to an idea becomes counterproductive.

‘Geniuses’ are necessarily individuals – there are no ‘genius communities’. A genius’s status as such denotes at once a centralisation of power and authority, and thus influence; a maturation of intellect (and intellect alone) presented as a role-model to others; and, in continuation, a pinnacle of achievement that those who profit from the extraction of scientific work, such as universities and research funders, valorise.

This said, I can’t tell if – though I suspect that – the modern history of ‘Western science’ is largely the modern history of ‘Western scientists’, especially of the ‘geniuses’ among them. The creator causes the creation, so by contemplating the science, you contemplate the scientist himself – or, as the ‘genius’ would have it, by contemplating the science you necessarily contemplate the creator and his specific choices. And since the modern scientific enterprise was largely harmonised to the West’s methods in the post-colonial period, this is our contemporary history as well.

Chadha had previously noted, in response to a question from yours truly, that she struggles to argue for the non-separation of science and scientist in the context of the #MeToo movement. That is, our liberty to separate important scientific work from the (extra-scientific) actions of an errant scientist may not be so easily achieved, at least if one intends to the extent possible to not participate in the accumulation of power. Instead, she said, we must consider them together, and call out “unethical or non-inclusive practices” – and by extension “you will also call out the culture to which they belong, which will help you to restore the balance of justice, if I may say so.”

This resolves to some extent my issue with Lawrence M. Krauss (although not fully because while Krauss’s culture has been dismantled at his previous university, however temporarily, he continues to maintain an innocence grounded in distasteful convictions). However, I’m still adrift vis-à-vis the late Richard Feynman and others. As a physics journalist first, I can’t help but encounter Feynman in one form or another – but how do you call out a dead man? Or does calling out the dead man’s culture, as perpetuated by the likes of Krauss today, suffice?

Chaudhuri has a similar question: “What do we do with a philosophy when there’s no philosopher in sight?” This matters because the philosopher’s “absence constitutes a problem in giving, and claiming, value. Meaning and significance in Western culture are not just features of the work, but pertain to, and arise from, the owner of the work – the author is the work’s first owner; the author’s nation or culture (“Greece” or “Germany”, say; or “the West”) its overarching one.”

So as with the Upanishads, would we be better served if we concerned ourselves less with deities and their habits and more with the “impersonal” instruction and interrogation of what is true? This seems like a straightforward way out of the problem Mrinal Shah poses, but it doesn’t address, as Chadha put it, the “pedagogic need to lend a face to an idea” – while “impersonal” interrogations of what is true will wrongly ignore the influence of sociological forces in science.

However, all said, I suspect that the answer is here somewhere. The ‘scientific genius’ is a construct and a shared one at that. When we contemplate a body of groundbreaking scientific work, we don’t contemplate the work alone or the scientist alone; we contemplate the work as arising from the scientist but even then only in a limited, constructive sense. But there is more at play; for example, as Chadha said, “We need to critically start engaging with how the social location of a scholar impacts the kind of work that they do”. If I write an article calling X a ‘genius’, X wouldn’t immediately occupy that position unless he is held there by social and capitalist forces as well.

The Upanishads in this context encourage us to erase the binary of ‘creator’ and ‘creation’ and with it the causal perspective’s temptation to think the scientist and the science are separable. In their stead, there is I think room to compose a communitarian story of science – where good arises not from the one but the whole, where power becomes, in keeping with the Upanishads, impersonal.

Where the Indian infiniteness?

I didn’t know Kenneth Wilson had died on June 15 until an obituary appeared in Nature on August 1. He was a Nobel Prize winning physicist and mathematician whose contribution to science was and is great. He gave scientists the tools to imagine the laws of physics at different scales — large and small — and to translate causes and effects from one scale into another. Without him, we’d struggle not only to solve physics problems at cosmological and nuclear distances at the same time but also to comprehend the universe from the dimensionless to the infinite.

Wilson won his Nobel Prize in physics in 1982 for his work with phase transitions — when substances go from solid to liquid or liquid to gas, etc. Specifically, he extended its study to include particle physics as well, and was able to derive precise results that agreed with experiment. At the heart of this approach lay inclusivity: to think that events not just at this scale but at extremely large and extremely small scales, too, were affecting the system. It was the same approach that has enabled many physicists and mathematicians take stock of infinity.

The idea of infinity

As physicist Leo Kadanoff’s obituary in Nature begins, “Before Kenneth Wilson’s work, calculations in particle physics were plagued by infinities.” Many great scientists had struggled to confine the ‘innumerable number’ into a form that would sit quietly within their theories and equations. They eventually resorting to an alternative called renormalisation. With this technique, scientists would form relationships between equations that worked at large scales and those that worked at small ones, and then solve the problem.

Even Dirac, renormalisation’s originator, called the technique “dirty”. And Wilson’s biggest contribution came when he reformulated renormalisation in the 1970s, and proved its newfound effectiveness using experiments in condensed matter physics. Like Wilson’s work, the idea was interdisciplinary. But how original was it?

The incalculable number

Kenneth Wilson did not come up with inclusivity. Yes, he found a way to use it in the problems that were prevalent in mid-20th century physics. But in the Mahavaipulya Buddhavatamsaka Sutra, an influential text of Mahayana Buddhism written in the third or fourth century AD, lies a treatment of very large numbers centered on the struggle to comprehend divinity. The largest titled meaningful number in this work appears to be the bodhisattva(10^37218383881977644441306597687849648128) and the largest titled number as such, thejyotiba (10^80000 infinities).

The jyotiba may not make much sense today, but it represents the early days of a centuries-old tradition that felt such numbers had to exist, a tradition that acknowledged and included the upper-limits of human comprehension while on its quest to deciphering the true nature of ‘god’.

Avatamsaka Sutra, vol. 12: frontispiece in gold and silver text on indigo blue paper, from the Ho-Am Art Museum. Photo: Wikimedia Commons
Avatamsaka Sutra, vol. 12: frontispiece in gold and silver text on indigo blue paper, from the Ho-Am Art Museum. Photo: Wikimedia Commons

The Mahavaipulya Buddhavatamsaka Sutra itself, also known as the Avatamsaka Sutra, also contains a description of an “incalculable” number divined to describe the innumerable names and forms of the principal deities Vishnu and Siva. By definition, it had to lie outside the bounds of human calculability. This number, known as the asamkhyeya, owes its value to one of three arrived at because of an ambiguity in the sutraAsamkhyeya is defined as a particular power of a laksha, but there is no indication of how much a laksha is!

One translation, from Sanskrit to the Chinese by Shikshananda, says one asamkhyeya is equal to 10 to the power of 7.1-times 10-to-the-power-of-31. Another translation, to English by Thomas Cleary, says it is 10 to the power of 2.03-times 10-to-the-power-of-32. The third, by Buddhabhadra to the Chinese again, says it is 10 to the power of 5.07-times 10-to-the-power-of-31. If they have recognisable values, you ask, why the title “incalculable”?

Lesser infinities

For this, turn to the Jain text Surya Prajnapati, dated c. 400 BC, which records how people knew even at that time that some kinds of infinities are, somehow, larger than others (e.g., countable and uncountable infinities). In fact, this is an idea that Galileo more famously wrote of in 1638 in his On two New Sciences:

So far as I see we can only infer that the totality of all numbers is infinite, that the number of squares is infinite, and that the number of their roots is infinite; neither is the number of squares less than the totality of all numbers, nor the latter greater than the former; and finally the attributes equal,’ ‘greater,’ and ‘less,’ are not applicable to infinite, but only to finite, quantities.

Archimedes, whose Syracusani Arenarius & Dimensio Circuli predated the Avatamsaka Sutra by about 300-400 years, adopted a more rationalist approach that employed the myriad, or ten thousand, to derive higher multiples of itself, such as the myriad-myriad. However, he didn’t venture far: he stopped at 10^64 for lack of a name! The father of algebra (disputed), Diophantus of Alexandria, and the noted astronomer Apollonius of Perga, who lived around Archimedes’ time, also stopped themselves with powers of a myriad, venturing no further.

Unlike the efforts recorded in the Avatamsaka Sutra, however, Archimedes’ work was mathematical. He wasn’t looking for a greater meaning of anything. His questions were of numbers and their values, simply.

In comparison — and only in an effort to establish the origin of the idea of infinity — 10^64 is a number only two orders of magnitude higher than one that appears in Vedic literature, 10^62, dated 1000-1500 BC. In fact, in the Isa Upanishad of the Yajurveda (1000-600 BC: Mauryan times), a famous incancation first appears: “purnam-adah purnnam-idam purnat purnam-udacyate purnashya purnamadaaya puram-eva-avashisyate“. It translates: “From fullness comes fullness, and removing fullness from fullness, what remains is also fullness”.

If this isn’t infinity, what is?

In search of meaning

Importantly, the Indian “proclamation” of infinity was not mathematical in nature but — even if by being invoked as a representation of godliness — rooted in pagan realism. It existed together with a number system, one conceived to keep track of the sun and the moon, of the changing seasons, of the rise and fall of tides and the coming and going of droughts and floods. There is a calming universality to the idea — a calming inclusivity, rather — akin to what a particle physicists might call naturalness. Inifinity was a human attempt make a divine being all-inclusive. The infinity of modern mathematics, on the other hand, is contrarily so removed from the human condition, its nature seemingly alien.

Even though the number as such is not understood today as much as ignored for its recalcitrance, infinity has lost its nebulous character — as a cloud of ideas always on the verge of coalescing into comprehension — that for once was necessary to understand it. Infinity, rather infiniteness, is an entity that transcends the character typical of the inbetweens, the positive numbers and the rational numbers. If zero is nothingness, an absence, a void, then infinity, at the other end is… what? “Everythingness”? How does one get there?

(There is a related problem here in physics, similar to the paradox of Zeno’s arrow: if a point is defined as being dimensionless and a one-dimensional line as being a collection of points, how and when did dimension come into being? Incidentally, the earliest recorded incidence of infinities in Early Greek mathematics is attributed to Zeno.)

The lemniscate

As it so happened, the same people who first recorded the notion of infiniteness were also those who recorded the notion of a positional numbering system, i.e. the number line, which quickly consigned infinity to an extremum, out of sight, out of mind. In 1655, it suffered another blow to its inconfinable nature: John Wallis accorded it the symbol of a lemniscate, reducing its communication to an horizontal figure-of-eight rather than sustaining a tradition of recounting its character through words and sense-based descriptions. We were quick to understand that it saved time, but slow to care for what it chopped off in the process.

Of course, none of this has much to do with Wilson, who by his heyday must have been looking at a universe through a lens intricately carved out of quantum mechanics, particle physics and the like. What I wonder is why did an Indian scientific tradition that was conceived with the idea of infinity firmly lodged in its canons struggle to make the leap from theoretical to practical problem-solving? There are answers aplenty, of course: wars, empires, scientific and cultural revolutions, industrialisation, etc.

Remembering too much

Wilson’s demise was an opportunity for me to dig up the origins of infinity — and I wasn’t surprised that it was firmly rooted in the early days of Indian philosophy. The Isa Upanishad incancation was firmly implanted in my head while I was growing up: the Brahminical household remembers. I was also taught while growing up that by the seventh century AD, Indians knew that infinity and division-by-zero were equatable.

It’d be immensely difficult, if not altogether stupid, to attempt to replace modern mathematical tools with Vedic ones today. At this stage, modern tools save time — they do have the advantage of being necessitated by a system that it helped create. Instead, the Vedic philosophies must be preserved — not just the incantations but how they were conceived, what is their empirical basis, etc. Yes, the household remembers, but it remembers too specifically. What it preserves has only historical value.

The Indian introspective and dialectic tradition has not given us just liturgy but an insight into the modes of introspection. If we’d preserved such knowledge better, the epiphany of perspectives that Wilson inspired in the late 1970s wouldn’t be so few nor so far between.

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This piece was first published in The Copernican science blog on August 6, 2013.