Gardner’s Synthesis

Once in a while, during my research, I come across writing by scholars from other disciplines that gives me a perspective that not only helps me to grasp the complexity of learning across disciplines, but also resonates with some thoughts on education.

Howard Gardner is one such academic who works on developmental psychology and has researched extensively on cognition and education. He has written ~30 books and ~1000 articles, and blogs regularly, even at the age of 82 or so. His recent book is titled A Synthesizing Mind.

Howard Gardner is a renowned Harvard academic and, as his book describes him as follows:

“Throughout his career, Gardner has focused on human minds in general, or on the minds of particular creators and leaders. Reflecting now on his own mind, he concludes that his is a ‘synthesizing mind’—with the ability to survey experiences and data across a wide range of disciplines and perspectives. The thinkers he most admires—including historian Richard Hofstadter, biologist Charles Darwin, and literary critic Edmund Wilson—are exemplary synthesizers. Gardner contends that the synthesizing mind is particularly valuable at this time and proposes ways to cultivate a possibly unique human capacity.”

While exploring the book and the related material, I came across an interview with Howard Gardner. In there, he is conversing about the theme of the book and discusses the synthesis of thought across disciplines. One of the pertinent aspects of learning is to know how innovation can be fostered by cross-disciplinary exploration without diluting disciplinary rigour. As Gardner says:

“I am not opposed to disciplinary learning—indeed I am an enthusiastic advocate. Any person would be a fool to try to create physics or psychology or political science from the start. But if we want to have scholars or professionals who are innovative, creative—and innovation is not something that we can afford to marginalize—then they cannot and should not be slaves of any single discipline or methodology.”

As a physicist, I can relate to this thinking within my discipline, and how innovative ideas, over the ages, have emerged by bringing ideas from mathematics, engineering and biology into physics. Particularly, the combination of biology, physics and mathematics is one of the most exciting frontiers of human exploration today, and Gardner’s words apply well in this scenario.

Going beyond science, I am always intrigued and amazed by artists (especially musicians) who can create art that simultaneously draws the attention of specialists and generalists. This is not a trivial achievement, and as a scientist, I am always trying to understand how artists resonate so well with the public. Gardner, in the abovementioned interview, frames this problem by looking at the goals of science and arts, and draws a contrast that is worth noting:

“Most scholars and observers like to emphasize the similarities between the arts and the sciences, and that is fine. But the goals of the two enterprises are different. Science seeks an accurate and well supported description of the world. The arts seek to capture and convey various aspects of experience; and they have no obligation other than to capture the interest and attention of those who participate in them.

Of course, there are some individuals who excel in both science and art (Leonardo is everyone’s favorite example). But most artists—great or not—would not know their way around a scientific laboratory. And most scientists—even if they like to play the violin or to draw caricatures or to dance the tango—would not make works of art or performances that would interest others.”

I partially agree with this assessment, as I know a few scientists who are deeply involved in various forms of art (including music) and do it very well, even at the professional level. In a way, Gardner is re-emphasizing the “two cultures” debate of C.P. Snow. My own thoughts on this viewpoint are ambivalent, as I see science, arts and sports as important pursuits that cater to different facets of the human mind. Of course, when it comes to expertise, the division may matter. There is a lot more to learn about the interface of art and science, at least for me.

Anyway, Gardner is a fabulous writer, and his blogs and books are worth reading (and studying) if one is seriously interested in understanding how to synthesize thought across disciplines.

Since we are discussing synthesis of thought, which is a kind of harmony, and coming together, let me end the blog with a line from Mankuthimmana Kagga by the Kannada poet-philosopher D.V. Gundappa:

ಎಲ್ಲರೊಳಗೊಂದಾಗು ಮಂಕುತಿಮ್ಮ” (Eladaralongodhagu manku thimma)

which loosely translates to: oh fool…be one among all (blend into world, living in harmony).

Harmony of disciplines and minds – how badly the world needs it today?

Real is imaginary and vice versa

This week in my optics class, I have been teaching Kramers-Kronig (KK) relations of electric susceptibility. It is fascinating to see the causality argument emerge from the relationship between the real and imaginary parts of the complex susceptibility. Whereas the time domain explanation is relatively easier to appreciate (that dissipation follows perturbation in time), for me, the frequency domain implication in KK relation is fascinating: the fact that information about the real part of the function at all frequencies can give you insight into the imaginary part at any given frequency (and vice versa) makes it such a powerful mathematical and physical tool. For example, by knowing the absorption spectrum of a medium, you can find out the refractive index of a medium at a particular frequency that is not easily accessible in experiments.

Two inferences I draw:

1) Complex analysis combined with differential calculus is one of the most beautiful and powerful mathematical tools invented, and exploring its application in experimental scenarios has made physics intriguing, useful, and profound.

2) The KK relationship shows how causality and the structure of matter are connected to each other, and by studying them, one will be able to extrapolate the idea beyond the problem at hand and apply it to a different context in physics. It just shows how ideas hop from one domain to another and how mathematics plays a critical role in intellectual arbitrage.

Real is imaginary and vice versa. Complex numbers zindabad!

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.

Conversation with Arka Banerjee

Welcome to the podcast Pratidhavani – Humanizing Science

Arka Banerjee is a cosmologist and an Assistant Professor of Physics at IISER Pune. His research focuses on exploring the connections between fundamental physics at microscopic scales and the formation and evolution of large-scale structures in the Universe, such as galaxies and cosmic voids. To pursue these questions, he develops new simulation methods, constructs summary statistics for cosmological data, and generates forecasts for upcoming observational surveys.

In this episode, we explore his intellectual journey and research.

Spotify link

References:

“Arka Banerjee – Home.” n.d. Accessed August 23, 2025. https://arkabanerjee.github.io/.

“‪Arka Banerjee‬ – ‪Google Scholar‬.” n.d. Accessed August 23, 2025. https://scholar.google.com/citations?user=kLde9gcAAAAJ&hl=en.

“Arka Banerjee – IISER Pune.” n.d. Accessed August 23, 2025. https://www.iiserpune.ac.in/research/department/physics/people/faculty/regular-faculty/arka-banerjee/381.

“Arka Banerjee – INSPIRE.” n.d. Accessed August 23, 2025. https://inspirehep.net/authors/1671323.

Some Optical and IR observatories in India

Below are ‘locations of some of the optical and infrared observatories marked on the Indian map’.

from: Narendranath, Shyama, Shashikiran Ganesh, Dipen Sahu, et al. 2025. “Solar System Research Prospects for the Decade and Beyond.” Journal of Astrophysics and Astronomy 46 (2): 34. https://doi.org/10.1007/s12036-025-10060-0.

Happy Independence Day & de Broglie’s birthday

Happy Independence Day to my fellow Indians !

15th Aug also happens to be birthday of Louis de Broglie, the famous French physicist who played a critical role in understanding wave-particle duality in quantum physics, and laid an important foundation through his formula

λ = h / p ;

where, λ is the wavelength of quantum particle with momentum p and h is the Planck constant.

See here for more details.

de Broglie studied and discovered the wave nature of electron, for which he received the Nobel prize in physics in the year 1929. In 1920s, understanding light from a quantum mechanical viewpoint was a challenge. Reconciling light, both as a particle and a wave, was counterintuitive and required a leap of thought that was provided by de Broglie. On 12th Dec 1928, delivered his Nobel lecture and mentions:

“I thus arrived at the following overall concept which guided my studies:
for both matter and radiations, light in particular, it is necessary to introduce
the corpuscle concept and the wave concept at the same time. In other words
the existence of corpuscles accompanied by waves has to be assumed in all
cases. However, since corpuscles and waves cannot be independent because,
according to Bohr’s expression, they constitute two complementary forces
of reality, it must be possible to establish a certain parallelism between the
motion of a corpuscle and the propagation of the associated wave.

This duality still remains, as we try understand the nature of light and harness it for information processing.

Interestingly, de Broglie was one of persons who nominated CV Raman for the Nobel prize in 1930 ! Below snapshot is from the Nobel prize nomination archives.

A bit of advice…to students

To paraphrase something I tell my students, especially when they are starting a research project –

There are certainly many people in the world who think better than us. But the competition reduces when it comes to the people who take their thoughts and ‘do’ something with them. Novelty of ideas is in the novelty of connections of ideas. There is always more scope for new connections of old ideas.

Generally, the game is won not in out-thinking, but in out-doing. This does not mean that doing excludes thinking. In fact, many times, doing fosters thinking.

Conversation with Kollegala Sharma

Welcome to the podcast Pratidhavani – Humanizing Science

Kollegala Sharma is a renowned science communicator and prolific Kannada writer, celebrated for making science accessible through articles, books, radio dramas, podcasts, and translations. A former chief scientist at CSIR-CFTRI Mysore, he has received prestigious awards for his exceptional contributions, including pioneering India’s first Kannada science podcast and editing the state’s popular science magazine, Kutuhali.

In this conversation (in English), we discuss what motivates him to do what he does so well…communicate science…

Spotify link

References:

Akka TV, dir. 2022. Lecture 107 | Science Journalism : Introduction | Shri. Kollegala Sharma. 44:38. https://www.youtube.com/watch?v=031_4I0W9I8.

“Amazon.In.” n.d. Accessed August 6, 2025. https://www.amazon.in/Books-Kollegala-Sharma%60/s?rh=n%3A976389031%2Cp_27%3AKollegala%2BSharma%2560.

“CFTRI.” n.d. Accessed August 8, 2025. https://cftri.res.in/faculty_detail/2062.

Falling Walls Foundation, dir. 2020. Breaking the Wall to Language, Geography and Social Separation. 05:12. https://www.youtube.com/watch?v=_nscnJFd–8.

Kollegala Sharma | Mysuru Literature Festival. n.d. Accessed August 6, 2025. https://www.mysuruliteraturefestival.com/lit-fest-2024/kollegala-sharma/.

Mandram, dir. 2018. Science and Language – Dr Kollegala Sharma. 27:49. https://www.youtube.com/watch?v=dSqO-AOu9io.

Spotify. n.d. “Learn and Unlearn.” Accessed August 6, 2025. https://open.spotify.com/show/1JYHPAvzx3RuWcO8hL6Cjy.

X (Formerly Twitter). 2025. “(4) Kollegala Sharma (@kollegala) / X.” July 27. https://x.com/kollegala.

YouTube. n.d. “Kollegala Sharma.” Accessed August 6, 2025. https://www.youtube.com/channel/UCCtB6my4ohaYOnQvBRnPEuA.

Light as EM wave – in Maxwell’s words

Every year, I teach an optics course to physics majors (including physics iPhD students and MS Quantum Tech students). In the process of introduction, I discuss how light was discovered to be an electromagnetic wave. One of the thrills of this topic is to quote Maxwell from his legendary 1865 paper1, in which he makes this monumental connection. Every time I teach this, I get an intellectual kick, even after doing this for almost 1.5 decades.

The highlighted text is the famous statement. Before that, Maxwell compares his result with two experimental results and confirms his prediction. I follow this up with Hertz’s experiment.

Note: Electric waves and telegraphy were already known before Maxwell’s paper. There were papers that discussed about velocity of light and its connection to electric waves. See this paper2, for example. However, these interpretations were not as comprehensive as Maxwell’s case, and importantly, the field theory viewpoint needed Faraday’s experiments and Maxwell’s interpretation.

  1. Maxwell, James Clerk. 1865. “VIII. A Dynamical Theory of the Electromagnetic Field.” Philosophical Transactions of the Royal Society of London 155 (January): 459–512. https://doi.org/10.1098/rstl.1865.0008.
    ↩︎
  2. https://www.ifi.unicamp.br/~assis/Weber-Kohlrausch(2003).pdf ↩︎