“…The example of great scientists is the light which guides all workers in science, but we must guard against being blinded by it. There has been too much talk about the flash of discovery and this has tended to obscure the fact that discoveries, however great, can only give effect to some intrinsic potentiality of the intellectual situation in which scientists find themselves…”
Michael Polanyi, in an essay titled “My Time with X-Rays and Crystals” (1969)
In recent years, this has been one of the best books on the history of mathematics in India. The late Prof. Divakaran was a theoretical physicist and a scholar.
This book is also an excellent example of how a scientist can present historical facts and analyse them with rigour and nuance. Particularly, it puts the Indian contribution in the global context and shows how ideas are exchanged across the geography. The writing is jargon-free and can be understood by anyone interested in mathematics.
Unfortunately, the cost of the book ranges from Rs 8800 to Rs 14,000 (depending on the version), which is a shame. Part of the reason why scholarly books, particularly in India, don’t get the traction is because of such high cost. This needs to change for the betterment and penetration of knowledge in a vast society such as India.
There is a nice video by numberphile on Prof. Divakaran and his book:
I have been teaching polarization of light in my optics class. In there, I introduced them to matrix representation of polarization states. One of the standard references that I use for explanation is a 1954 paper in American J. Physics, by McMaster titled: “Polarization and the Stokes Parameters.”
While skimming through the pdf of the journal paper, I found an excerpt from a 1954 book, which quotes Fresnel writing to Thomas Young:
Further, I knew from the past that S. Chandrasekhar (astrophysicist) had a role in rejuvenating Stokes vector formalism in radiative transfer. Below is his description from AIP oral history archives (May 1977):
” I started the sequence of papers, and almost at the time I started it, I read the paper by Wick in which he had used the method of discrete coordinates,* and I realized at once that that method can be used in a large scale way for solving all problems. So that went on. I have always said and felt that the five years in which I worked on radiative transfer [1944 – 49] is the happiest period of my scientific life. I started on it with no idea that one paper would lead to another, which would lead to another, which would lead to another and soon for some 24 papers — and the whole subject moved with its own momentum.” (emphasis added)
He further states how he rediscovered Stokes polarization vector formalism:
“All this had a momentum of it own. Then suddenly I realized one had to put polarization in; the problems of characterizing polarized light — my rediscovery of Stokes original paper, writing on Stokes parameters and calling them Stokes parameters for the first time“
Chandra further adds that the Stokes formalism was almost forgotten for 50 years, and he had a role in resurrecting it.
Next, there was some noise on social media where some one questioned the utility of matrix multiplication. For them, below is a wonderful review article by McMaster (again), to explore from polarization viewpoint, and realize the power of non-commutative matrix algebra:
Finally, the original paper by Stokes on his formalism, which is hard to find (thanks to paywall). But, classic papers are hard to suppress, and I found the full paper on internet archives.
Below is a snapshot:
Enjoy your random walk !
Recently, I saw the following tweet from the well-known historian William Dalrymple.
Congrats to the listed authors, who deserve rewards (and the money) for their effort.
I have 3 adjacent points to make:
1) India badly needs to read (and write) more on science and technology. Here, I am not referring to textbooks, but some popular-level science books (at least). Generally, educated Indians are exposed to science only through their textbooks, which are mostly dull, or, in this era, YouTube videos, which have a low signal-to-noise ratio. Good quality science & tech books at a popular level can add intellectual value, excitement, and expand scientific thinking via reading, not just in students, but also in adults.
2) In India, most of the non-fiction literature is dominated by the social sciences, particularly history (as seen in the best-seller list). I have no problem with that, but non-fiction as a genre is a broad tree. Indian readers (and publishers) can and should broaden this scope and explore other branches of the tree. Modern science books (authentic ones), especially written in the Indian context, are badly in need. I hope trade publishers are reading this!
3) Most of the public and social media discourse in India does not emphasize (or underplays) the scientific viewpoint. Scientific literature and scientific discourse should become a central part of our culture. Good books have a major role to play. Remember what Sagan’s Cosmos did to American scientific outlook, and indirectly to its economic progress. The recent Nobel in economics, especially through the work of Joel Mokyr, further reinforces the connection between science, economics and human progress. This realization should be bottom-up, down to individual families and public places.
One of the great scientists, James Maxwell, is attributed to have said: “Happy is the man who can recognise in the work of today a connected portion of the work of life and an embodiment of the work of Eternity.…“
Science, with its rich, global history and philosophy, in the form of good books, can connect India (and the world) to the ‘work of eternity’, and make us look forward.
Embedding science within culture, in a humane way, can lead to progress. Science books have a central role to play in this.
विज्ञान (Vignana) should transform to ‘We’gnana !
ಕನ್ನಡ ರಾಜ್ಯೋತ್ಸವದ ಶುಭಾಶಯಗಳು
Reproducing one of Da. Ra. Bendre’s Kannada poems titled “ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?” which translates to Have You Seen the Bird Flying?
A comment on the poem: In my reading, this poem is a metaphor for the exploration of the universe through the exploration of a bird. The poet periodically asks: “Have you seen the bird flying?”, thereby motivating the reader to observe what the bird may be seeing and doing. It is a poem read by school children, but there is a deeper philosophical meaning in asking humans to look up at the sky and realize the flight of a bird in themselves. YouTube also has the original audio of Bendre reciting the first few lines of the poem, and it is worth listening to.
Below is the poem, followed by a decent translation.
“ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?”
ಇರುಳಿರುಳಳಿದು ದಿನದಿನ ಬೆಳಗೆ
ಸುತ್ತಮುತ್ತಲೂ ಮೇಲಕೆ ಕೆಳಗೆ
ಗಾವುದ ಗಾವುದ ಗಾವುದ ಮುಂದಕೆ
ಎವೆ ತೆರೆದಿಕ್ಕುವ ಹೊತ್ತಿನ ಒಳಗೆ
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?
ಕರಿನೆರೆ ಬಣ್ಣದ ಪುಚ್ಚಗಳುಂಟು
ಬಿಳಿ-ಹೊಳೆ ಬಣ್ಣದ ಗರಿ-ಗರಿಯುಂಟು
ಕೆನ್ನನ ಹೊನ್ನನ ಬಣ್ಣಬಣ್ಣಗಳ ರೆಕ್ಕೆಗಳೆರಡೂ ಪಕ್ಕದಲುಂಟು
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?
ತಿಂಗಳಿನೂರಿನ ನೀರನು ಹೀರಿ
ಆಡಲು ಹಾಡಲು ತಾ ಹಾರಾಡಲು
ಮಂಗಳಲೋಕದ ಅಂಗಳ ಕೇರಿ
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?
ಮುಟ್ಟಿದೆ ದಿಙ್ಮಂಡಲಗಳ ಅಂಚ
ಆಚೆಗೆ ಚಾಚಿದೆ ತನ್ನಯ ಚುಂಚ
ಬ್ರಹ್ಮಾಂಡಗಳನು ಒಡೆಯಲು ಎಂದೋ
ಬಲ್ಲರು ಯಾರಾ ಹಾಕಿದ ಹೊಂಚ
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?
Translation (ChatGPT):
Have You Seen the Bird Flying?
(by D. R. Bendre — English rendering)
Night after night melts into day,
All around, above and below —
the world moves on and on,
as the moment of awakening opens —
Have you seen the bird flying?
It has a tail dark as rainclouds,
and feathers white, shining bright;
its wings on either side
are tinted with colors of gold and light —
Have you seen the bird flying?
It drinks the silvery water of the moon,
to play, to sing, to soar;
it enters the courtyard of the blessed world —
Have you seen the bird flying?
It’s touched the edge of the horizon,
stretched its beak to the farthest reach;
who knows — since when it has tried
to break open the universe itself —
Have you seen the bird flying?
Some writing advice (mainly physics) I shared with my undergraduate class. This may be useful to others.
Also, below is another blog related to written assignments.
A nice article by @RutujaUgale in @Sci_Rio that discusses public engagement by scientists as influencers of scientific thought.
Thanks, Rutuja, for profiling my blog, ‘Vismaya’.
Here is my quote from the article:
“For me, there are two implications of doing science. One is that science is extremely useful to society, and the second is that it is a good, thoughtful way of living one’s life. Communicating the second implication is important to me, and I do this by researching, writing, and podcasting about the history and philosophy of science (physics in particular). This path helps people understand the human element of doing science and reveals a context. Some of my blogs (filtered here) discuss why I do science and how I do it. More than ‘influencing’ the audience, I am interested in inviting them to explore science by themselves via their own curiosity. That is one reason why my blog is called VISMAYA.”
Link to the full article.
Meghnad Saha (6 October 1893 – 16 February 1956), of the fame of Saha’s ionization formula, was born this day. In 1993, a postage stamp in India was released commemorating his birth centenary.
Saha was an astrophysicist with a broad knowledge and appreciation of various branches of physics. One of the earliest English translations (1920) of the papers on relativity by Einstein and Minkowski was written by Meghnad Saha and S.N.Bose.
At the beginning of the book, Mahalanobis introduces the topic with a historical introduction. He begins with a thoughtful discussion on experiments that eventually ruled out the presence of ether, and it sets the stage as follows:
“Lord Kelvin writing in 1893 in hig preface to the English edition of Hertz’s Researches on Electric Waves, says many workers and many thinkers have helped to build up the nineteenth century school of plenum, one ether for light, heat, electricity, magnetism; and the German and English volumes containing Hertz’s electrical papers, given to the world in the last decade of the century, will be a permanent monument of the splendid consummation now realised.”
Ten years later, in 1905, we find Einstein declaring that “the ether will be proved to be superflous”. At first sight the revolution in scientific thought brought about in the course of a single decade appears to be almost too violent. A more careful even though a rapid review of the subject will, however, show how the Theory of Relativity gradually became a historical necessity.
Towards the beginning of the nineteenth century, the luminiferous ether came into prominence as a result of the brilliant successes of the wave theory in the hands of Young and Fresnel. In its stationary aspect, the elastic solid ether was the outcome of the search for a medium in which the light waves may “undulate.” This stationary ether, as shown by Young, also afforded a satisfactory explanation of astronomical aberration. But its very success gave rise to a host of new questions all bearing on the central problem of relative motion of ether and matter.“
Saha, in various capacities, took a stance against British colonialism. Although it affected some opportunities, he continued to do science and was recognized for his outstanding contributions. As Rajesh Kochhar mentions:
“Saha had wanted to join the government service, but was refused permission because of his pronounced anti-British stance. For the same reason, the British government would have liked The Royal Society to exclude Saha. It goes to the credit of the Society that it ignored the pressures and the hints, and elected him a fellow, in 1927. This recognition brought him an annual research grant of £300 from the Indian government followed by the Royal Society’s grant of £250 in 1929 (DeVorkin 1994, p. 164).“
Saha led a tough life. He not only had to face suppressive British colonial rule but also academic politics and battles (versus Raman, no less). His knowledge of physics, his contributions to Indian science, and his commitment to people (he was a politician too) were significant. Let me end the blog with a few lines from Arnab Rai Choudhuri’s article, which nicely summarizes Saha’s work (specifically his ionization formula), and his scientific life:
“Saha’s tale of extraordinary scientific achievements is simultaneously a tale of triumph and defeat, a tale both uplifting and tragic. Saha showed what a man coming from a humble background in an impoverished colony far from the active centres of science could achieve by the sheer intellectual power of his mind. But his inability to follow the trail which he himself had blazed makes it clear that there are limits to what even an exceptionally brilliant person could achieve in science under very adverse circumstances.“
India and Indian science should remember Meghnad Saha.
Today is the birth anniversary of Satish Dhawan (25 September 1920 – 3 January 2002). He was probably India’s best scientist-administrator who headed institutions such as the Indian Institute of Science and the Indian Space Research Organization. With a PhD from Caltech, he came back to India and set up a marvellous research enterprise on fluid mechanics, including aerospace science and engineering. He mentored some of the outstanding scientists of India and led scientific institutions with vision, openness and informality, which is still a great benchmark to emulate1.
Below are a couple of historical documents related to Dhawan:
The first one is a lecture note from 1979, on making a case for a national satellite system and how it influences science and scientific activity (a copy of this note has been reproduced in a wonderful tribute to Satish Dhawan written by P. Balaram on his birth centenary2).
The next one is a beautiful perspective article written by Dhawan on ‘Bird Flight’ from an aerodynamics perspective3. It is a detailed overview of the dynamics of bird flight and shows Dhawan’s interest and ability to bridge two facets of science. It is a prototypical example of interdisciplinary research.
Finally, let me end the blog with a quote from P. Balaram on Satish Dhawan4:
“Dhawan mentored some remarkable students and built the discipline of aeronautical engineering at the Institute. He influenced aeronautical research and industry in India in a major way. He shepherded the Indian space programme following Vikram Sarabhai’s untimely death. He served the Indian scientific community in many ways. His stewardship transformed IISc. How then do we describe such a man? Dhawan studied English literature obtaining a Master’s degree in his youth. It may therefore be appropriate for me to borrow a 16th century description of Sir Thomas More:
‘[Sir Thomas] More is a man of an angel’s wit and
singular learning. I know not his fellow. For where is
the man of that gentleness, lowliness and affability?
And, as time requireth, a man of marvelous mirth and
pastimes, and sometime of as sad gravity. A man for
all seasons.’Satish Dhawan was truly a man for all seasons.”
Happy Birthday to Prof. Satish Dhawan!
References:
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?
VISMAYA - History & Philosophy of Physics 