The Show of Total Solar Eclipse, linking Mathematics in the Context

MathFest_Talk_GraphicThe following post was published on Mathematical Correlations Blog (a little before the day of total solar eclipse), and thought of linking it here.

In keeping with the enthusiasm of the incoming total solar eclipse, I want to revive my presentation at the Astronomical Society of the Pacific annual meeting last year on this very topic The eclipse that changed the picture of the universe. Here is the abstract, and linked to it is its utube video (find in the widget area of the blog). I recorded the video after the talk, and so the discussion following the talk is missing in this video.

The Eclipse that Changed the Picture of the Universe

The distinguished total solar eclipse of May 29, 1919, gave new window to the universe. That eclipse truly stood as Einstein favoring cosmic phenomenon, authenticating his general theory of relativity; that the spacetime is conformed via gravity, upending the hitherto upheld Newtonian picture—gravity as force between masses. The bending of light due to mass that the eclipse captured reformed our understanding: from spacetime dynamics to black holes to the recently detected gravitational waves. [Video]

My recent visit to Math Fest 2017 (Mathematical Association of America annual meeting) was interesting and inciting, and there will be opportunities to discuss the sessions in detail here. Following the meeting it occurred to me that there wasn’t a talk that addressed total solar eclipse, surely would have been captivating in the spirit of all the current anticipation of the show of 21st August. I could have brought up in my own talk. And yes, mathematics can very well be seen in the context. The dynamics of total solar eclipse lets us capture the mathematics of spacetime geometry; that we call Einstein’s general relativity in physics.

I have just uploaded my talk Exposing general audience to the voice of mathematics. Here is its abstract, and the video (find it in the widget area, just following the ASP talk).

Exposing general audience to the voice of mathematics

Under the theme of “Pursuit of Truth” at Saint Louis University I tried to shape up a TEDx talk on the subject of mathematics. From my perspective there isn’t a better subject to address reality than mathematics. Catching me off-guard, a facilitator in the rehearsal round frustratingly snapped for not to be able to follow anything. I scrambled to revamp the talk starting with plain and basic, such as squared and cubed number depictions, then moving to formulations of reality—first simpler of classical mechanics then more complex renderings, such as Dirac equation—to notice the audience cheerfully draw in into the farther intricacies of mathematics as detailed as the expressions in general relativity and quantum field. Foundational concepts and fitting analogies seems to be the key to garner enthusiasm. [Video]

A few important resources on now past total solar eclipse: NASA; Being in the shadow; Great American Eclipse. And the very recommended Sun Moon Earth by Tyler Nordgren has been worth a read by many that embarked to soak in the eclipse show.

Replies and suggestions welcome.

Hope all had rich time absorbing the phenomenon of total solar eclipse!


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Math Shaped

To prepare a talk for the upcoming MathFest, to be held in Chicago this year, I was ruminating over articulating a clean-cut yet telling narrative. Since the talk subject is on ways to effectively outreach mathematics to general audience, it should at least somewhat bring up core concepts of mathematics. Somehow allude to the essentiality of its graphical and revelatory power, compared to just an instrument to calculate. Meaning mixing in subtler forms of advanced math, even abstract ones. I am sensitive to oversimplifying anything (my take on popular writing). It’s like providing a forced picture—like peas and potato analogy of quantum and cosmic realms in The Theory of Everything—that is far from an actual picture, and importantly dampened down on beauty, and inspiration. The point of outreach is to convey the subject—its significance and elegance that lay in the eyes of those who swim in it—not recite a lullaby.  And in my experience audience from all backgrounds, even without math ones, show true enthusiasm only when prompted into intricate and advanced forms of mathematics, yearning for the real sense. It’s there where the real message is, of what mathematics actually is about.

In my experience outreaching an advanced scientific field effectively rests on two basic elements. First, tell it the way it is, don’t soften it. That’s the hard part because all those elaborate labyrinthine equations with functionalities, symbols, and notations floating all over them is the very thing that makes some of us flee. And thus the second, present them correlatively as physical entity: Numbers to space, Algebra to geometry, Calculus to continual smooth change, Group and matrices to potentiality of abstract objects, the list is endless, and that physics itself at the core is mathematics. All those preposterous looking equations are actually quite beautiful and insinuating if you understand that those terms are the pieces of the landscape. The tangled appearance of an equation, like Dirac’s, would dwindle away once one sees what a colossal argument the equation is making.


Persuasion in an outreach effort usually employs an object central to disseminating pronouncements of the subject. I have been thinking of having an actual physical object, and the top two in the list were tesseract and Calabi-Yau manifold. Tesseract represents four dimensional cube—Mathew McConaughey materializing in tesseract after he plunges into the black hole in the movie Interstellar, making tesseract currently an object of popular demand. Calabi-Yau manifold is a mathematical thing of a projective plane, surmising six dimensions. Both, thus, though may connect to reality in theoretical outlooks, cannot crystallize in our 3-D view. They are abstractions of mathematics, and stand to be significant (very) fully in their own right.

Having a real physical model in the talk, I thought, would be pedagogical, and a neat way to draw in enthusiasm. On simply googling tesseract I bumped into a 3-D printing enterprise shapeways, offering a model of tesseract (a beautiful one). (I didn’t look for Calabi-Yau model. Didn’t think it was possible to have a model of such an intricate complexity.) To my amazement, here they offered a Calabi-Yau 3-D printout as well, in different colors, snapshots, and sizes.

In conveying the actuality of mathematics with its ultra sophisticated developments, Calabi-Yau manifold can be an epitome that embodies conceptions of advanced algebra, cutting-edge geometry, mathematical abstractions, and advancements of modern physics all in one exhibit. And it is aesthetically pleasing as well. I got it from them.

Here is the snapshot of the 3-D printout (Itself a 3-D snapshot of 6-D object). It was also nice to exchange a few productive words with Rick Russell—at the Shapeways, who generated this 3-D printout with an expert eye for math and its models—on this very enchanting object. Hope the audience will like the object as much as I do.


The model emerges from the graphic that was originally rendered by A. Hanson, Indiana University, and it has done a phenomenal job in making its appearance from the nooks of abstract algebra articles, to academic and popular literature, to the explanations of modern physics. Somewhat surprised that it hasn’t shown up in the mainstream media, at least not yet.

Be back shortly,


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Prime Numbers Paralleling Reality: Possible?

Post recently published in Science Blogs. Thought of posting it here to keep the blog readers current. Indulge in primes!

All non-trivial zeros of the zeta function have real part one-half

stated Bernhard Riemann in 1859, a German mathematician whose contributions to modern mathematics, and theoretical physics, is wide and deep—a commonly known one is in structuring the layout of Einstein’s theory of general relativity (spacetime conforms to gravity).

Riemann zeta function

The relatively simple form of Riemann zeta function (in the above statement),


is an infinite series converging on its limit—a mathematical articulation worked out utilizing tools of analysis. This function with some clever number juggling, directed by Euler, transforms itself into a product (∏), that is, a series involving multiplication—as opposed to the above summation (the summation symbol ∑ we are familiar with)—over all primes, bringing the quirk of primes in the scope of palpable. Here we have the most significant milestone in connecting the nature of primes to the tapestry of all numbers (recall that at surface we don’t see a clear scheme in the distribution of prime numbers). The magic lies in the relationship of “product (∏)” to “summation (∑),” known as Euler product formula, with prime numbers coming into play. The above zeta function is then also this:

equation2  (p: prime, over all prime numbers)

Conceiving the dynamics of this function would then help grasp the inner nature of prime numbers, which Riemann did by the above hypothesis. Indeed visualizing the dynamic interplay not only involves seeing the structuring of prime product but also seeing it in the light of playing of the summation function, which involves perceiving through scrupulous analytics and advanced calculus.1

Digging deep

Except for 1, the zeta function has values for both positive and negative numbers, and its value for every negative even number is a zero—but a trivial zero. (We will see what the zero of a function implies in a bit.) The availability of non-trivial zeros is the gripping point in the true portrayal of prime numbers, and it emerges from the zeta function only but under the guidance of complex field involving the above exponentiation with complex numbers (“a + bi” is a complex number, with a as real part and bi an imaginary where the standard i is taken to be √–1). The Riemann Hypothesis says that under the navigation of zeta function, the complex plane brings about a steadfast line that sits at a ½ real value, streaked all the way to infinity rendered by all non trivial zeros—known as the critical line (Figure 1). Infinitely many non-trivial zeros satisfy the Riemann hypothesis,2 and the first ten trillion of them are seen to conform to the hypothesis.3

The first few non-trivial zeros (known as Gram’s zeros) start approximately as:

½ + 14.134725i; ½ + 21.022040i; ½ + 25.010856i

See the ½ real in the complex plane with different “i”s. Important is to note that here all “i” comes to be an irrational number, that is expanding limitlessly without any pattern, but that’s another story, off from the point of this post.


Seeing the looming “½” takes exceedingly complex renderings like Equation3 and Riemann’s vision. Significant mathematical maneuvering and background would be required to even come close to how the non-trivial zeros align, but there it is. By it we have a hold of a crisp order executed by prime numbers—the very numbers that at the surface hover haphazardly (Figure 2). And this schematic is written in a regular numerical language right in front of our eyes. The root of the natural number landscape comes to be the tenacious halo of primes.


Unifying Principles

Lucid as it is, we haven’t seen the apex yet. In this deep-seated scope of a clear scheme the prime numbers take us further. Their fabric is stunningly indicatory one. It is here we see the dovetailing primes portending the coordination of the physical universe at its inmost depths.

To cut a lengthy and exceedingly labyrinthine story short, the mathematics that goes in describing quantum mechanical landscape constructs on advanced dosages of matrices—a group in an array that abides by certain set principles—algebra, and group theory. Mathematical operators, which underlie the rendering of matrices, are utilized to chart out the statistical mechanical territory of quantum landscape. Every matrix is stamped with a signature algebraic equation. An algebraic equation is like a prescription, realizing which one can decipher the nature of the object. At mathematical level this means finding its roots: incorporating what values in the equation do we get a zero. For example, for an expression x2 – 3x – 4 (i. e. equation x2 – 3x – 4 = 0) the roots come to be –1 and 4. Replacing x with either number annuls the expression, or makes it zero. The degree of the polynomial (algebraic) defines the number of zero(s) the polynomial has. Thus the squared ones, like in the above example, will have two zeros, or roots.

It is in these roots we merge the math and universe. For mathematical operators that go in describing quantum field these algebraic zeros are referred as eigenvalues—rings a bell? Indeed, it points to the eigenvalues of energy in quantum mechanical setup—that only certain values of energy are allowed.4,5

It is here we have the natures unite. Some such specialized operators cast striking resemblance with the Riemann’s zeta function in a way that the operator’s eigenvalues coincide with the zeta function’s non trivial zeros. It is here that not only diverse mathematical branches meld but also mathematical and physical amalgamate (Figure 3), by the sharp correspondence of the quantum energy values (the eigenvalues) and the non-trivial zeros.


We now have prime numbers not only casing a universal principle of symmetry but also doing it in the well defined outlay of tactile quantum realm.5 Their symmetry isn’t on the surface but in the dynamical interplay—the aligning of zeta zeros—that the physical world at its roots dons.

The non-trivial zeros themselves fall in a pattern, and squeeze closer and closer, as we climb up the complex ladder of zeta function. The spacing of non-trivial zeros aligns with the spacing of the eigenvalues. The array of quantum eigenvalues constitutes the spectrum that the non-trivial zeros of zeta function bring forth.  Then, the deep-hidden order of primes is the language of quantum depictions.

This was more than expected!

It is even contemplated that the Riemann function itself can directly be prescribed by an operator which would model a physical system, i. e., a potency of seeing a physical system by the weave of Riemann operator—a physical system of semiclassical quantum chaos to be precise.4 Not chaotic chaos, but chaos of chaos theory which sees a crisp complexion in a rendering that at the surface appears completely erratic. The non-trivial zeta zeros of this operator would be eigenvalues of a semiclassical chaotic system.

The Riemann hypothesis not only substantiates the Prime Number Theorem, it exposes a stubborn structural identity to the prime numbers, and piece them in the all-embracing arena of symmetry. Indeed immense approximations are involved for us to see the diagrammatic of the hypothesis, but they are all with acute mathematical precision.

The nuance of the quantum world vindicates the hypothesis. Do we still need a proof!

The hypothesis isn’t proven or disproven yet,6 but it has incited a great deal of novelties and unified large swaths of mathematics and mathematical physics in the interim. The intricate interconnections that play out behind it is mesmerizingly suggestive, and offer deep insights of the natural structure that is both discrete and abstract at the same time.



  1. John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, A Plume Book, 2003
  2. H. Hardy (a British mathematician) in 1914 proved that infinitely many non-trivial zeros satisfy Riemann Hypothesis (or lie on the critical line): Sur Les zeros de la fonction ζ (s) de Riemann. French. In: Comptes Rendus de l’ Académie des Sciences 158 (1914), pp. 1012-14. Issn: 00014036.
  3. Gourdon (2004), The 1013 First Zeros of the Riemann Zeta Function, and Zeros Computation at Very Large Height.

For an overview (4, 5):

  4. Barry Cipra, A Prime Case of Chaos

  5. Germán Sierra, The Riemann zeros as spectrum and the Riemann hypothesis

6. Clay Mathematics Institute Millennium Problems:

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Window of Mathematics: The Language of Prime Numbers

Along the theme of earlier post of mathematics as being a universal language of the reality itself, here we shall peek into the revelatory window of prime numbers—for their simplicity and uncertainty at the surface, alongside the intricacy and perfection underneath.

Underneath the uncoordinated display, the prime numbers incite well-structured tones—of mathematics and the universe in their finest resolutions

For their unbreakability primes are viewed as atoms of mathematics—they construct all other numbers of the natural domain. But their appearance at the surface appears arbitrary, for the lack of a recognizable pattern in their structure or intermediary spacing. In the landscape of numbers, the prime numbers crop without any fabric of symmetry, which mathematics and the universe otherwise blatantly seize in their manifestation or flow. Starting from 2, 3, 5, 7, 11, 13, 17, 19, 23, ¼,  Euclid of Alexandria around 300 BC showed that these asymmetric entities stretch to infinity—of which first 100 billion or so are crunched.

The Concept and a Deep Underlying Order

Neat schemes of reality often emerge in the territories elusive and outwardly inconsequential, and take subtler outlooks and deeper visualizations. The correspondence of antimatter, the underpinning of chaotic system, the essence of entropy, and the design in fractals of nature are some examples where principle plays underneath what seems a haphazard display. But, nowhere is this more obvious than in the instruction of prime numbers. It took both the magnetizing appeal of prime numbers and the sharp visionary intellect of the followers to stumble upon the spotless tone that underlie their superficial irregularity. In the abysmal subtleties of their materialization not only does reside a well-pressed systematic structure, its code is both mesmerizingly suggestive and hauntingly captivating.

Never get caught up with the deceptive lack of pattern—concept actually, in math or otherwise.

The number of primes up to a given max N is shown to be N/ ln N (ln: the natural log)* by a relatively analytical theorem known as the Prime Number Theorem, which was proven independently by Jacques Hadamard and Charles de la Vallée in 1896 employing elaborate mathematical measures. The theorem implies that prime numbers thin out as we climb up the number ladder. The clarity of thinning though becomes apparent only at gigantic magnitudes, seen over logarithmic scales (as log function in the above formula suggests). This is slightly reflected at the onset: There are 25 primes to count 100, and 168 to 1,000 (instead of 250 if it were a regular distribution). Then there are 1,229 to 10,000, 9,592 to 100,000, and 78,492 up to a 1 million: the number of primes isn’t expanding proportionally. The tapering effect can be appreciated for large series of crunched primes at a site like Albeit lightly, the Prime Number Theorem brings to light that underneath the mixed up display, the constitution of prime numbers and their mechanics appears to be a parameterized layout, but so far after centuries of effort a clear logic behind the mechanism remains obscure. But not, if we take the Riemann Hypothesis 1, 2, 3 to be not only authentic, but also natural.


The reason we aspiringly anticipate the involvement of design in occurrence and unfurling of prime numbers is the case of glorious Riemann Hypothesis:

“All non-trivial zeros of the zeta function have real part one-half.”

Incredibly simple, isn’t it? The statement is more like a tip of the iceberg though (my thoughts on conveying its potential to general audience), with not only immense and consequential cues lurking under it, it takes up full range of elements from basic arithmetic functions, analysis, calculus, analytic number theory, advanced algebra, probability, statistics, and a fair share of visionary mathematical sense—tailored in place 1 by Carl Friedrich Gauss, Leonhard Euler, Lejeune Dirichlet, and indeed Bernhard Riemann, who was also the one to conceive this interpretation.

Granting the well-groomed and weighty diagrammatic this statement brings forth—so much as to make the hypothesis a self-evident truth—how its intricate circuitry plays challenges even the shrewdest of mathematicians.

But before we question what the prime numbers tell us about the real universe (is it even possible?) and how Riemann hypothesis connects to the field of prime numbers, we need to first delve a little into the articulation of this Riemann message itself, and I will be back with that shortly.



* A tighter way of saying this is p (N) ≈ Li (N), where π is the Prime counting function (up to N), Li is logarithmic integral, ≈ is “tends to approximately equivalent” as N gets larger, that the ratio π (N)/ Li (N) tends to 1 as N gets bigger and bigger.


  • John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, A Plume Book, 2003
  • Marcus du Sautoy, The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, Harper Perennial, 2002
  • Roland van der Veen and Jan van de Craats, The Riemann Hypothesis, Mathematical Association of America, 2016


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True Beauty Resides in Fundamentals

As I had mentioned, here is my write-up on the Archway Publishing Blog, on communicating complex scientific ideas. I was excited to bring in the Riemann Hypothesis to point out a elaborate mathematical complexity that is just as visionary and captivating:

Translating Complex Science for a General Audience

The last few posts were dedicated to gear us on the total solar eclipse that is approaching in our sight. The excitement among the educators, eclipse chasers, and anticipators is palpable. I had mentioned the veritable organizations and devoted scientists/educators (1, 2, 3, 4) that remain in full swing in disseminating the information and advice to spur on the audience from all backgrounds. The sight of a total solar eclipse is phenomenal. (I am told by those having savored it first-hand, I haven’t seen it myself. So despite my truly appreciating the fundamentals behind this cosmic display, I am looking forward to it as any other enthusiast.)

Although the cosmic and worldly wonders captivate us, it is the peek into the fundamentals that ticks enthusiasm, and keeps it alive. ASP (Astronomical Society of the Pacific) annual meeting presentations are uploaded, and you can find mine on fundamentals by the window of total solar eclipse there (the video of the same). Whether talking of gravitational waves, Einstein’s theories of relativity, hidden black holes, the origins and the acceleration of universe, the enigma of dark matter and energy, or the spectacle of total solar eclipse, at surface they all stir up wonder, but the real lure lies in the fundamentals that help us visualize how things shape up—and appreciate the true beauty.

When it comes to methodic delineation even beauty has fundamentals behind it. How much we have figured that out is a different issue. This brings up a narrative book A Beautiful Question compiled by a renowned physicist Franck Wilczek on the conception of beauty and the forces it embodies. (I am just finishing reading it.) With big chunks of basic facts, and on laws governing the universe, the text unfolds the cast of beauty that seeps the natural world, and how reality and beauty can be seen synonymously. Written with ethereal tone, it is informative and enjoyable read for audience from all backgrounds.

Disseminating deep-seated scientific formulations and complex theories to all audience isn’t very straightforward, mainly for the fact that it’s in these very intricate renderings that the true sense of beauty can be sniffed. It is where an educator enthralls, and a scientist draws in. The play of symmetry in quantum mechanical enactment or deep views of mathematical physics is one such example. Simplifying beyond a point would necessarily dampen down on beauty, and in a way mutilate the truth.

I have been in touch with friendly staff of Archway publishing with the hope of writing a post on their Writer’s Blog. The post had to be on the process of writing and publishing. Disseminating scientific advancements to general audience seemed an appropriate topic, and I recited some of my thoughts on communicating intricate concepts of physics and mathematics without taming the aesthetics—A demanding thing. The post should be out soon, and I will let you know.

Whether abysmal structure of the universe, the abstractly play of quantum field, the order of nature, or the subliminal sense of aesthetics, in the core of all resides the commonality of mathematical voice. And I am always looking for opportunities to communicate on this very aspect of mathematical truth. To that end I have just started writing on Science Blog site, under the title Mathematical Correlations. Take a look and let me know your views.


Scientific, educational, pedagogic, and creative aspects of mathematics blend in MAA (Mathematical Association of America) annual meetings. This year it is held in Chicago, and I am hoping to speak on how to entice non-mathematicians into mathematics, especially those that are apprehensive of the subject.

I am happy to see Facebook visitors, and appreciate their stopping by for scientific nuggets.

See you all soon.


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Total Solar Eclipse and the Picture of the Universe

Few are aware of the imminent cosmic phenomenon that sweeps all across USA in its splendor and rarity—the wonder of total solar eclipse. August 21st of this year will mark its occurrence after a void of almost 100 years, when it had painted the entire nation in the year 1918 (In the year 1979 it touched a tiny spot in the northern USA before veering off northbound). The whole effort of this year’s annual ASP (Astronomical Society of the Pacific) meeting was to spread out the word, engage as many science followers as possible into the majesty of this celestial display; urge them on into once in a lifetime kind of show.

There were stimulating talks disseminating the scientific background, and the enormous efforts that have been put in to popularize, educate, and incite on the appearance and experience of a total solar eclipse itself. And the ASP plans to upload all the talks on their website, in the hope to spur on a wider enthusiasm and interest.  Here is some useful set of information to help you prepare and indulge if you feel interested: NASA (1), Being in the Shadow (2), Great American Eclipse (3).

I being an ardent proponent of the physical sciences indeed tuned in, and pitched my own take on the subject of total solar eclipse, and how this phenomenon has played a vital role in revealing the basic principles of how the universe structures and continues. So here is my talk—The Eclipse that Changed the Picture of the Universe—at the meeting, in case you feel inspired.

Total solar eclipse takes place when the earth, moon and sun together strike a perfect alignment such that the moon situated in the middle fully blocks out the sun for a brief moment in space and time, leaving out the halo of corona—the usually invisible sun’s outer atmosphere—a brilliant ring that glows from behind. For that brief period we remain under the shadow of the moon while the radiating corona flags the sun’s only identity in the sky. It is the only instance in time when although the sun is present in our view of the sky, its intense glare remains occluded. Albert Einstein around the year 1915 realized that this relatively rare instance gives us an astonishing window into the nature of reality. How? In the year 1915 Einstein had proposed—by his theory of general relativity—that spacetime conforms to the force of gravity. Simply, gravity gives geometry to the universe. And if this is true then matter bends light.


An event of a total solar eclipse extends us a perfect window into which we can verify such bending of the light. The ultra bending of the light reaches a detection level only when caused by a massive cosmic body, such as sun. The bending of the light by the sun is ascertained by measuring the shifts in the positions of the background stars—the deflections of stars as the sun passes through (Picture 1). Measured in arcseconds—an extraordinarily miniscule amount—this deflection, however, would be impossible to pin down due the intense glare of sun on a usual day. The event of a total solar eclipse thus gives us a perfect window for studying sun’s gravitational field without being bedazzled by the blinding glow.


The total solar eclipse of May 29, 1919, became a legendary eclipse (Picture 2) that attested the bending of light by matter, theorized by Einstein. The discovery of spacetime curvation by the force of gravity led us to a bigger and finer picture of the universe: From the way the universe might have begun to the existence of black holes to theory of wormhole to the pulsation of gravitational waves, recently detected by LIGO (Laser Interferometer Gravitational-Wave Observatory).

The new picture emerged, and Einstein celebrated, by the mechanics of the natural grandeur.


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The Upcoming 2017 Solar Eclipse, Sweeping America on its Totality

The simple mechanics of total solar eclipse exposes deep-seated fundamentals of spacetime. Total solar eclipse occurs in an event of earth, moon, and sun alignment such that moon fully blocks out the sun, casting its shadow on earth on the zone of totality. What remains on sky is sun’s corona shimmering behind the bulbous moon: Includes a rendering imaginatively known as diamond ring. On August 21, 2017 we will transit such a mesmerizing and momentous (literally!) event, and the eclipse experts, chasers and broadcasters have their bits and takes on this. Here are some genuine picks  (1, 2) for those interested in details, and here is an interactive map of the upcoming totality. This year the ASP (Astronomical Society of the Pacific) is holding its annual meeting just for the purpose of convening the ideas and topics around the wonder of total solar eclipse, particularly toward preparing the upcoming 2017 one. Those interested in cosmic magnificence, and like to partake in grasping the nature of reality, would truly benefit from the event.

As profound as the cosmic phenomenon itself is, total solar eclipse has been pivotal in our understanding of the way universe shapes and continues, and a linchpin in rubber stamping a revolutionary theory to be a truly authentic reality. On the May 29 of 1919, an English astronomer, physicist, and mathematician, Arthur Eddington, captured total solar eclipse on the island of Principe to validate Albert Einstein’s theory of general relativity. General relativity offered to blend gravity in the earlier picture of Einstein’s own special relativity, showing that gravity is the geometry of spacetime itself. The endeavor set out by Eddington and his team pinned the precise bending of light that occurs due to the presence of a massive body, in accordance with the principle of general relativity, thus fully endorsing Einstein’s Magnum Opus. Sun as a massive body too bends light that travel from distant stars, but we cannot verify such bending simply because sun’s intense glare blocks out the positions of distant stars. The shade of a total solar eclipse enables us to measure such deflections in the position of stars, as the sun observes its gravity.


The ramifications of general relativity are wide and far reaching, many we are still trying to fathom: From the origin of the universe to the existence of black holes (remember the fascinating Interstellar Gargantua), the phenomenon of wormhole, the prodigiously expanding universe to speculations of dark matter and dark energy to the recent detection of gravitational waves that employed state of the art technological sensitivity (10-16 cm in 4 km). General relativity has stood a century of experimental verifications, one recent with the validation of gravitational waves by LIGO (Laser Interferometer Gravitational-Wave Observatory), and some tests are still brewing that involve extraordinary precisions to further endorse general relativity, like appraising the contortions due to the black hole at the center of our galaxy or seeing the free fall of different materials in space missions.


The theory has shown the way universe propels, but also made our lives efficient on a daily basis. General relativity is a part of GPS navigation that we employ every day. Two well crafted titles that shed light on this deeply enriching theory are 1) The Perfect Theory by Pedro Ferreira, and 2) Big Bang by Simon Singh.

The first real validation of general relativity was ticked by the 1919 total solar eclipse. I will be attending the ASP meeting, and in the context of total solar eclipse, I will be speaking on the fundamental architecture of spacetime that the general relativity imparted.

For those interested in cosmic mechanics, deeper universal structure, or just scientific outreach to a wider community, it will be a good venue to participate and connect.

See you soon,


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Einstein in Fiction

Starting with the elegance of mathematics, here is an article the followers of mathematics will like—the true patrons of ‪mathematics see its reality in the deep-seated concepts.

At the Book Expo America in Chicago this year, as I explored flamboyant publishing setups and flashy book banners, an interesting title The Other Einstein caught my attention, and I was pulled in. After noting that the title refers to Einstein’s wife Mitza Maric as the other Einstein, and that the story narrates of her own potentials in understanding the ways of spacetime that Albert Einstein set forth, I became somewhat curious. I decided to meet up with the author. Even though the book itself is a novel, for it touches spotless territory of spacetime that Einstein established, the story can be seen as rather bold. Anyway, there I was, inquisitive enough to get a copy.

OtherEinstein    PostIX

As I was handed a copy, I spoke briefly with the author on fictionalizing a landscape that is so firmly established and deeply revered, by scientists and laymen alike. The author had her takes on it for the extent of fictionalization, and I was curious enough to give it a try. Fiction isn’t my usual read. Barring a very few known titles, like by Paulo Coelho for instance, I haven’t read much in current fiction. As I said The Other Einstein drew me in, first to just get a copy at the BEA, and then to read it, for the obvious reason. Not only do I have a background in physics, I am an ardent proponent of physics and mathematics for exposing the reality we live in. And for these reasons I am deeply aware of Einstein’s contributions and his legacy, so much so that for me to see that his special relativity theory is referred as being conceived by someone else—even in fiction—seems almost sacrilegious. Having said that, the story is crafted well, and once I started it I was hooked to finish. If the aim was to formulate a page-turner, the title has it.

For us scientists it might have been nicer if the extent of fictionalization was in some way hinted. To the author’s acknowledgement, this fiction weaved some of the real historical bits—time, space etc. Author’s  efforts in assimilating Einstein’s theories, and the scientific structures on which they rest, as it’s penned in the fabric of storyline, is certainly appreciable.

But the aficionados of pure physics/mathematics, or the sincere advocates of Einstein’s efforts, aren’t probably its best readership target.

See you all soon,


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Nonfiction Science

Pleased to see a sizable enthusiasm for the title Physical Laws of the Mathematical Universe: Who Are We? I had set a giveaway at the Goodreads, and was charmed to see so many avid readers of nonfiction science entered, while many tagged the title as to-be-read. I with fervor packaged individual copies, included short notes, and mailed them off. So yes the 10 winners should be receiving their copies shortly. It’s on the way. A short recap, the title discusses an overarching scheme of how the universe and its parallel forms, exist and continue, and how we ourselves are part of the continuum that physical sciences reverberate.


I am still getting familiar with the Goodreads, and it is nice to find abundant science titles covered there, including many currently prominent science author profiles marking the widespread landscape of readership from all genres. Science surely has caught on as a choice read in recent times. Not science fiction, but the real hard core nonfiction science. If we cover its depths, the real science is far more awe inspiring, even mystical. Go into the depths of quantum mechanics, and you will see what I am implying. This isn’t to say that the creativity of fiction science is redundant. Fiction lets mind wander wherever it wants to wander. Nonfiction on the other hand gives so many fresh perspectives, and insights. Do take a look at the Goodreads for nonfiction. You may start from the few books I just commented on.

Popularity of nonfiction science isn’t as across-the-board on other places. I recently attended the illustrious Book Expo America 2016—mostly because my title Physical Laws of the Mathematical Universe was included for display at the Archway Publishing booth. Thousands of titles emblazoned the most prolific of booths—Simon and Schuster, Penguin, Random House, Harper Collins. A few nonfiction non-science titles caught my attention enough for me to mark them as to-be-read, and I have already read a couple of them, and they are engaging. But mostly, by nature and choice, I was inclined to scavenge for scientific tiles there. Thus the University booths, Oxford, Cambridge, Princeton, MIT, Chicago, Basic Books (known for publishing popular science titles in physical science; I have some very good titles from them) and a few others were a definite targets to be explored bit by bit. And I did get a bunch of interesting reads, and some good math fun books, but mostly hard core science (even popular) was missing across the whole show. The ones included were either in youth section, or very toned down popular. We need to go a little way to build up the real science ardor. I was swept with a feeling that my title at the Archway Publishing was perhaps the only one that extended into the serious scenes of physics and mathematics. I would still call it popular science. At the Simon and Schuster – Archway Publishing authors reception on the day two of the event, a few authors did tell me that they are going to read it!


See you all soon,


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Mini Takes on Titles I Recently Read

The Universe in the Rearview Mirror: How Hidden Symmetries Shape RealityThe Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality by Dave Goldberg

My rating: 4 of 5 stars

Liked the mathematical connotation, and the broad overview, not so much of toning down to meet extensive readership, but understandable for a popular genre.

Unknown Quantity: A Real and Imaginary History of AlgebraUnknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire

My rating: 4 of 5 stars

Methodically done. Crisply portrayed. Framed for general audience (must love mathematics though) yet doesn’t dampen down on analytical rigor.

When Breath Becomes AirWhen Breath Becomes Air by Paul Kalanithi

My rating: 4 of 5 stars

Deeply heartening, and hauntingly gripping. Out of the two main sections–one on the personal experience with medicine, practice, and residency, and the later on his transition between life and death–the later stands out to be utterly original, and consummately engaging, for its strength, beauty, determination, and melody in the face of life that displayed its end.

For the messages in the first section, I happen to see a clearer dynamics via Atul Gawande’s titles, especially “Being Mortal.” The text although is delicately literary.

An Invisible Thread: The True Story of an 11-Year-Old Panhandler, a Busy Sales Executive, and an Unlikely Meeting with DestinyAn Invisible Thread: The True Story of an 11-Year-Old Panhandler, a Busy Sales Executive, and an Unlikely Meeting with Destiny by Laura Schroff

My rating: 3 of 5 stars

Nice warm story. Well done narrative, but at times excess on religious overtone.

Also it’s good to know that 626 people so far requested the title: Physical Laws of the Mathematical Universe: Who Are We?

Goodreads Book Giveaway

Physical Laws of the Mathematical Universe by Neeti Sinha

Physical Laws of the Mathematical Universe

by Neeti Sinha

Giveaway ends May 24, 2016.

See the giveaway details
at Goodreads.

Enter Giveaway

Be back shortly,

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