“…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 !
A cartoon from a 1947 edition of a US magazine
Source: https://archive.org/details/sim_factory_1947-08_105/page/112/mode/1up
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 !
‘There is a story about two friends, who were classmates in high school,
talking about their jobs. One of them became a statistician and was working
on population trends. He showed a reprint to his former classmate, The
reprint started, as usual, with the Gaussian distribution and the statistician
explained to his former classmate the meaning of the symbols for the actual
population, for the average population, and so on. His classmate was a
bit incredulous and was not quite sure whether the statistician was pulling
his leg. “How can you know that?” was his query. “And what is this
symbol here?” “Oh,” said the statistician, “this is π.” “What is that?”
“The ratio of the circumference of the circle to its diameter.” “Well, now
you are pushing your joke too far,” said the classmate, “surely the population has nothing to do with the circumference of the circle.”’
These are the opening lines of Wigner’s famous essay titled: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
More than 25 years ago, Prof. G. Srinivasan (RRI, Bengaluru), in an astrophysics class, narrated something that has stuck in my mind.
I am paraphrasing here.
He told us about a conversation he had with Prof. Jocelyn Bell, the discoverer of pulsars (rotating neutron stars).
When Jocelyn was asked: What is the most important quality to do scientific research?
She replied: ‘ability to wonder’.
For ages, human beings have been curious about stars. Telescopes as observational tools have changed how human beings have studied and understood astronomical objects. Below is a snapshot from a 1947 edition of popular mechanics that features someone named John Cartlidge from USA. He was a mechanical engineer and an amateur astronomer. The story reveals that he took 20 years to build the telescope, and the description text from the magazine is an interesting read. An amount of $600 plus, for that era, sounds expensive. But what is astonishing is the 20-year effort to build a telescope.
This instance of human effort to pursue curiosity connects well to a wonderful poem: ‘Curiosity’ by David Jilk, and below I reproduce a stanza from it:
“Your greatest teacher is the world itself
and glory comes to those who find her codes;
for she is coy, no book upon a shelf,
and must be queried via crab-walk modes:
your question is, which questions make inroads?
Instruction thus proceeds aesthetically
with obverse strokes of creativity.“
Amateur astronomy fosters that strokes of creativity. After all, sky is the only limit !
Today, in my optics class, I discussed optical forces due to momentum in electromagnetic waves. Towards the late 1800s, it was realized that light can impart momentum. This manifested as radiation pressure in the electromagnetic theory proposed by James Maxwell.
Pyotr Nikolaevich Lebedev (24 February 1866 – 1 March 1912) was one of the earliest to experimentally measure (~1899) the radiation pressure on a surface (link to his 1900 paper in German). In 1991, the Soviet Union released a 1 ruble coin (pictured above) to commemorate Lebedev’s scientific achievement.
The formula expresses the total momentum transferred per unit time ( radiation pressure, P) by a beam of N photons, each of energy hν, that is incident on a surface with a coefficient of reflectivity ρ. The constant, c, is the speed of light.
The discussion in the class was mainly related to Ashkin’s work. I have written about this in the past.
Shared below is a delightful lecture given by Ashkin at the age of ~96, after he received his Nobel prize.
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.
VISMAYA - History & Philosophy of Physics 