When Chandra wrote to Hawking

Learning is a lifelong process, and even the best researchers have to update their knowledge as and when they come across new information. Subrahmanyan Chandrasekhar was undoubtedly one of the most accomplished mathematical astrophysicists in the 20th century, and his range of topics covered almost all aspects of astrophysics.  Chandra (as he was known) was a lifelong learner, and took up new topics within astrophysics, researched them deeply, and wrote definitive books on them, which are still of great utility even today. In his research process, Chandra consulted various scholars across the world, irrespective of their age, and learned new things.

In 1967, Chandra, aged 57, wrote a letter to a 25-year-old researcher, Stephan Hawking, to learn more about his work ‘on the occurrence of singularities in cosmology’. In this letter, which is written in a desperate tone, Chandra mentions that he is grappling with some mathematical aspects of Stephen Hawking’s work and is asking him for references that he can consult to understand his papers. Chandra describes reading Hawking’s papers as  ‘climbing a staircase moving downwards’. Below, I reproduce the letter (from the University of Chicago archives).

 To this letter, Hawking dutifully replies (see below), suggesting specific books on topology and differential geometry. Hawking also suggests some of his published papers. Hawking himself downplays his knowledge of mathematical aspects related to the work, and mentions that it improved after he consulted the mentioned books. Below, I reproduce the handwritten letter (from the University of Chicago archives).

There are two aspects that are interesting to note:  one is the fact that even accomplished researchers have to learn and relearn many things as they get exposed to new information, which calls for humility and setting aside egos, and the second aspect is that ideas are built on existing ideas available at that time, and a major part of it is to learn from papers, books and of course communicating with people, as Chandra did in this case.

Science, after all, is a human endeavor.

Sanskrit subhashita – don’t waste

Here is a Sanskrit subhashita that I like.

वृथा वृष्टि: समुद्रेषु वृथा तृप्तेषु भोजनम्।

वृथा दानम् धनाढ्येषु वृथा दीपो दिवाऽपि च॥

LLMs are getting better at translations.

Below is a comparison of translations on 2 platforms

English Translation from perplexity AI:

Rain over the ocean is wasted, food for those who are already full is wasted; Charity to the wealthy is wasted, and a lamp during the daytime is wasted.

English translation from ChatGPT:

Rain over the ocean is in vain, food for one who is already full is in vain; Charity to the wealthy is in vain, and a lamp during the day is also in vain.

Physics Nobel 2024 – anywhere to everywhere

The Nobel Prize in Physics 2024 was awarded to John J. Hopfield and Geoffrey E. Hinton “for foundational discoveries and inventions that enable machine learning with artificial neural networks“. There has been much buzz surrounding this prize, especially in the context of whether these discoveries are indeed in the realm of mainstream physics. Many science commentators have questioned the choice and have provocatively dismissed it as ‘not part of mainstream physics’.

This has also brought into focus an important question: What is physics?

This question does not have a simple answer, given the rich history of the subject and its applicability over centuries. What we now call engineering is essentially an extrapolation of thinking in physics. New avenues have branched out from physics that cannot be readily identified as mainstream physics; a case in point is artificial intelligence and machine learning.

One of the aspects of mainstream physics is that the intellectual investment in the contemporary scenario is mainly driven by discoveries happening in the realm of quantum mechanics and general relativity. One of the mainstream problems in physics is to combine quantum mechanics and gravitation, which remains an unresolved task. Therefore, significant attention is paid to understanding these theories and verifying them through experimentation. Other areas and sub-disciplines in physics have become loosely connected to these two important theories.

There is another dimension to physics that is equally important and has vast applications: statistical physics. In statistical physics, the motivation comes from multi-particle systems and their applicability as models to understand our world, including biological systems. One utilizes knowledge from mathematics and statistics, combining them with physical laws to predict, invent and understand new forms and assemblies of matter. This thinking has been extrapolated to abstract assemblies and hence applied to a variety of situations. This approach has led to a revolution in how we can understand the realistic world because a statistical viewpoint is very useful for studying complex systems, such as many-body quantum mechanical aggregates (such as groups of electrons), dynamics of molecules inside a cell and the evolution of the stock market. Statistical physics plays a dominant role in all these situations. It has become a ubiquitous tool, making it difficult to directly connect it to basic principles of physics as taught in college textbooks and classrooms. It reminds me of a saying: if you are everywhere, then you are from nowhere.

This situation leads us back to the question: What is physics? John Hopfield himself offers an interesting definition related to this question, emphasizing that viewpoint is a crucial element. This perspective allows for greater freedom in using physics beyond conventional definitions. Among scientific disciplines, physics is always associated with its depth of understanding. This is a good opportunity to emphasize the breadth of physics, which is equally noteworthy.

In that light, the 2024 Nobel Prize in Physics should be welcomed as an expansion of the horizon of what constitutes physics. In a day and age where basic science has been questioned regarding its applicability to modern-day life and technology, this prize serves as a welcome change to showcase that basic science has played a fundamental role in establishing a contemporary tool of primary importance to society.

This point is particularly important because policymakers and politicians tend to focus on immediate issues and ask how they can influence them by using modern-day technology. Utility is central to this form of thinking. Given that basic sciences are often viewed as ‘not immediately useful’, this viewpoint diminishes the prominence of foundational disciplines: physics, chemistry, biology, and mathematics. In contrast, this prize reinforces the idea that building cutting-edge technology, which holds contemporary relevance and societal impact, has its roots in these foundational disciplines. In that sense, this prize is an important message because, like it or not, the Nobel Prize captures the attention not only of the scientific world but also of the public and, hence, of interest to politicians and policymakers.

Issac Asimov is attributed to have said: “There is a single light of science, and to brighten it anywhere is to brighten it everywhere.” The Nobel Prize in Physics 2024 fits that bill.

Physics is a point of view about the world

picture from : Hopfield, John J. “Whatever Happened to Solid State Physics?” Annual Review of Condensed Matter Physics 5, no. Volume 5, 2014 (March 10, 2014): 1–13. https://doi.org/10.1146/annurev-conmatphys-031113-133924.

The title of this blog is the closing line of an autobiographical essay written by John Hopfield (pictured above), one of the physics Nobel laureates today: “for foundational discoveries and inventions that enable machine learning with artificial neural networks.”

In this essay, he retraces his trajectory across various sub-disciplines of physics and how he eventually used his knowledge of physics to work on a problem in neurobiology that further connects to machine learning.

The title of the essay is provocative(see below) but worth reading to understand how physics has evolved over the years and its profound impact on various disciplines.

Reference: Hopfield, John J. “Whatever Happened to Solid State Physics?” Annual Review of Condensed Matter Physics 5, no. Volume 5, 2014 (March 10, 2014): 1–13. https://doi.org/10.1146/annurev-conmatphys-031113-133924.

Thanks to Gautam Menon for bringing the essay to my notice.

By the way, Hopfield and Deepak Dhar shared the 2022 Boltzmann medal, and after the award, he gave a wonderful online talk at IMSc, Chennai. Thanks to Arnab Pal of IMSc for bringing this to my notice on X.

Let me end this post quoting Hopfield from the mentioned essay:

What is physics? To me—growing up with a father and mother who were both physicists—physics was not subject matter. The atom, the troposphere, the nucleus, a piece of glass, the washing machine, my bicycle, the phonograph, a magnet—these were all incidentally the subject matter. The central idea was that the world is understandable, that you should be able to take anything apart, understand the relationships between its constituents, do experiments, and on that basis be able to develop a quantitative understanding of its behavior. Physics was a point of view that the world around us is, with effort, ingenuity, and adequate resources, understandable in a predictive and reasonably quantitative fashion. Being a physicist is a dedication to the quest for this kind of understanding.

Let that quest never die!

Sanskrit quote on learning..

आचार्यात् पादमादत्ते पादं शिष्यः स्वमेधया ।
सब्रह्मचारिभ्यः पादं पादं कालक्रमेण च ॥

One fourth from the teacher, one fourth from own intelligence,
One fourth from classmates, and one fourth only with time.

Happy Teacher’s Day.. learning is eternal..