Category Archives: Physical principles

Shifting Ways of Science

Interstellar. Credit: Paramount Pictures/ Warner Bros

If one falls into a black hole, what would one encounter? Well, from our recollection of the movie Interstellar—Cooper (Matthew McConaughey) ended up in a tesseract, a 4-dimensional object, via which he made it back to his own 3-D world—we would hope to plod out through a higher dimension, as if making a choice back into a familiar world. But there’s a catch—a lot of!

Tesseract is a 4-dimensional object (mathematical, so far! Helping us understand deep details in modern physics). The higher-dimension—via which Cooper connected to another Cooper (Murph, his daughter)—implies stacking of a zillion spacetime points on top of each other. Remember the bookshelf behind which Cooper stood? But accessing higher dimension also means that you be part of the higher-dimension; you be manifest as higher dimension.

Tesseract

The first catch. There would be as many Coopers, both Coopers (father and daughter), as many as the innumerable book-shelfs, the books in them, and the watch that is relaying the message to the daughter. Anything as a 3-dimensional embodiment would be presented as all spacetime points up until the current one. All past spacetime points stacked up until then; that’s how Cooper accessed the past. In that higher-dimension he had all information timeline, that’s every “time” point—more accurately as Einstein had shown “spacetime”  point—arranged discretely, from his past to his current. That many “Coopers,” though accurately put, would have given a flustered set-up, demanding more questions, as well as the associated theoretical premise. All valid, that’s how science progresses. More answers we find, more questions become apparent. The movie, although fictional, relays various significant current theoretical understanding of how spacetime manifests and flows, and all the information inherently brings up new uncharted territory of questions.

All valid, that’s how science progresses. More answers we find, more questions become apparent.

We have come unimaginably far in scientific understanding of how the universe works, and operates. But never in the past had we as many conundrums rearing their heads as we have today. From black holes, dilemmas of event horizon, dark matter, dark energy to perpetually expanding universe, its origins and parallel forms, to the spacetime unifying principles, the picture that unifies gravity and quantum depiction, and what current theoretical understanding relay, especially the mathematical ones, like string theory and loop quantum gravity. All our findings to date must fall into a single unitary phenomenon. Our quest is how? Answers to our inquiries come with a package of additional set of questions, and off we march in all directions. Healthy feat!

We have come unimaginably far in scientific understanding of how the universe works, and operates. But never in the past we had as many conundrums rearing their heads as we have today.

Following a short stint at the Antibody Society, to scientific outreach their mission and goals, I landed myself in a specialized somewhat recently founded company Quantum-Si (Q-Si). My current interest in scientific communication and outreach is part of the reason how I got here. As Q-Si prepares to launch its first-of-a-kind protein sequencing instrument, a brief overview here would help us see how we navigate the current scientific quests and find answers to inquiries that would aid research and development. Q-Si technology stems from a multifaceted scientific endeavor that involves strategic developments of pixelated semi-conductor chip, which allows the parallel processing (thus the given name “Quantum;” although not a 100 % sure that’s where the name is coming from) of miniaturized wells to read individual peptides at an amino acid level resolution. Amino acid is a molecular building block of protein, and there are 20 different kinds of them. The technology combines customizations of chip, electrical circuitry, waveguide—as in fiber optics—laser pulsation, and fluorescent signals to read biophysical interaction. Multifaceted, because the single experiment subsumes fine fields of physics, engineering, biophysics, and if you want to see too far, mathematics, to follow a biological undertaking, or knowing something that could be of clinical relevance.

Multifaceted, because the single experiment subsumes fine fields of physics, engineering, biophysics, and if you want to see too far, mathematics, to follow a biological undertaking

Only a few decades earlier it wouldn’t have been possible to carry out something as complex that agglomerates and fine tunes discrete branches in science. But in the scientific landscape we have advanced to a level where the boundaries between specialized scientific fields are hazy. Soon after joining Q-Si, I have begun to realize how important it’s to have current awareness of all basic fields in order to not just carry out a given task, but also to appreciate the beauty that can be realized only when we see the integrated picture; not just a single aspect of it. To that end, I had reached out to a Physics magazine on my desire to shape a short note titled Teach Physics to Life Science Students. Will keep you posted on how that goes. But the point is in the current science landscape it’s imperative that we have a handle of basic understanding of all core areas in order to reach further, or even to appreciate the developments.

Colliding Black Holes, 1.3 Billion Light Years Away

The detection of gravitational waves, the existence of which Einstein had predicted in 1916, in 2015 was the landmark of ultra-precision measurement in scientific experimentation. The measurement entailed detecting a sub-atomic level length change that occurred due to the collision of two black holes 1.3 billion light years away, meaning time it took for light to reach us to tell that happenstance. An arduous scientific feat was achieved. Incredible!            

The measurement entailed detecting a sub-atomic level length change that occurred due to the collision of two black holes 1.3 billion light years away

Every scientific branch geometrically expands, collide and bump into each other, and eventually, if we continue to progress, inevitably unite into a solitary landscape or phenomenon.

See you soon again,

Neeti.


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Getting back to blogging

After a pause of some two plus years, I’m inspired back into writing on this blog The Cosmic Landscape in Quantum Décor. The time sort of demands that the scientific outreach should be in some ways about things connected to the pandemic: the disease physiology; the viral mechanism; the long- & short-term impacts; the future projections; the cure development; the last, but not the least, the vaccines and its workings. In the today’s working of the world even physicist & mathematicians are pitching their intellectual skills on curbing the pandemic in ways that are novel & indeed needed. It’s an academic maneuvering how physics and mathematical tools can be utilized in contributing toward helping the pandemic. I have myself recently started working for The Antibody Society, and this is closest I came to helping toward bringing forth therapeutics or the related biological understanding. My work here involves scientific communication, liaising, and outreach, and I think there is thus some contribution, however slight, being made to the current scientific needs.

But as Brian Greene brought forth his Equation of the Day series: Entirely mathematical, and thus an outlook of physics, a premise that could be a pleasurable distraction that can bring a nerve calming comfort, at least for those who love physics, and even more so mathematics, for purely their beauty. Yes, I know you all find fascination in physics and mathematical equation just as much as in captivating words, painting, natural landscapes, and so forth. So, in coming back to my blog I would first revive all the back posts, which I wrote for their varied topics of enticing awe, while inviting us to learn something new about the world we inhabit. Most is to allure you into the beauty of mathematics, and its rendering of physics. The recent some of blog posts (will continue to post all in total of 3 batches):

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In bringing on your allurement of mathematical beauty, I want to bring in one the most fascinating equations, if not the most awe-inspiring mathematical rendition:

Eulers_Id

Stunning isn’t it. Even at a purely visual level. It’s more than stunning for ones who see the dynamics displayed in it. Foremost, it weaves five most important mathematical constants relating to each other in a single fabric. That’s what makes this tonality phenomenal. It’s as if this mathematical rendering speaks of all of the mathematics in a most short-cut form possible.

The interrelating constants:

“e” is Euler’s constant, a transcendental number (in a coming post I may say more on this) & a base of natural logarithm, which emerges naturally in phenomena innumerable like finance, exponential growth, statistical distribution, and is an inextricable part of higher-level mathematics that describes the universe we inhabit.

“i” is an imaginary unit of a complex number with property i = √-1, yet another topic of interest we might talk on in later posts.

“π” is transcendental as well, defined as, we all know, ratio of circle’s circumference to its diameter.

“1” seemingly simple but consequential in mathematical equations and understanding physical reality.

& if you rephrase to

Euler_Id2

“0”, indeed one of the most cherished constants that gives a defined order in the dynamics of higher mathematics, or any mathematics as such (we all know that).

This equation is known as Euler’s identity that directly emerges from from Euler’s formula, which relates e to sine and cosine in the field of complex numbers, devised by Euler (Leonhard Euler) himself.

I will leave it here for you to soak up on this. Leave a comment on your say on it, & I’ll write back soon.

Thank you,

Neeti.

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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),

equation1

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.

Figure1

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.

Figure2

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.

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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.

Figure3

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.

——————————————————

References:

  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: http://www.claymath.org/millennium-problems/riemann-hypothesis

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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.

Archway_FigI

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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.

Archway_FigII

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.

Neeti.

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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.

postxi

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.

postxi_2

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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,

Neeti.

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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

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Be back shortly,
Neeti.

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The Title and its Storyline

Continued from the preceding post…

Foremost, we can’t keep from commemorating the 2016 Abel prize awarded to Andrew Wiles of Oxford University, for proving that the Fermat’s Last Theorem is indeed true (in the year 1995). Congratulations to Andrew Wiles, and Pierre de Fermat! Fermat did claim (in the 17th century) to have surmounted proving his own elegant equation by noting “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” The methodology Andrew Wiles employed is too advanced for the time of Fermat. Inspired at the age of ten, Andrew Wiles decoded the mystery of Fermat’s Last Theorem in the year 1995, a truly uphill task that was interspersed with a humiliating pitfall that ultimately lead to the glory and catharsis, as his humbled tears rolled out upon meeting the wish.

Whether or not did he have the proof (we will never know), Fermat would have cheered the breakthrough, and recognition.

Here is my take on it:

Well, I am more excited than many, first because of the Oxford University backdrop in the recognition, but mostly because it involves the elegance and depth of Fermat’s Last theorem, and seeing it to be accurate.

I delight in the simplicity of its statement (the equation), yet the far reaching and deep insights it casts. I include the insightful cadence of this equation in my book.

The excerpt from the book, following which is the award link:

Excerpt, Pg. 56: Physical Laws of the Mathematical Universe: Who Are We? (about the book: www.magnifieduniverse.com/aboutbook)

“Fermat’s Last Theorem: An Enigma, or Not

For its blunt accuracy and transparency, even though we didn’t have a valid proof at the time it was stated, Fermat’s last theorem became a cliché mathematical citation, appearing regularly in didactic and popular genres alike.5,6 The statement is elegantly simple, but the meaning conveyed is both sharp and profound. Drafted by a French mathematician, Pierre de Fermat, in the year 1637, it states,

FigVI

              where n is the exponent of 3and up. The phrasing tells us that the sum of two exponentiations cannot give rise to an exponentiated entirety for the powers of three and up. For example, 32 plus 42 structures into 52, but 33 plus 43, in accordance with Fermat’s theorem, does not evolve into an entirety of x33-D-fold. Fermat’s equation applies for any numerical grade—in fact, tellingly, for any digital combination—as long as the power is 3 or higher.”

The award; The recognition

Cheers everyone!
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Back to the storyline, and the central points of discussions:

Universe Needing to Inflate

The abrupt inflation of universe in our cosmic history, its interrelatedness with the detection of gravitational waves, and seeing the necessity and order of the event of inflation itself

            “As enigmatic as it may sound, the scenario of expeditious growth does have healthy outlooks to support of the way we envisage the universe based on scientific judgments.”

In the Name of Science

The question of how do we amass interest and enthusiasm in science, its concepts and methodology. Then move further to have us all interested in seeking the true order of reality.

Interstellar

Do not miss out, if you like edutainment, especially with small dosages of science. You might pick up serious bits without having to try!

Grothendieck’s Deep Visions

The gravity of mathematics, and its followers: Alexander Grothendieck as an ardent devotee of anything deep and mysterious in mathematics

Continued in the next…

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Magnified Universe: Cosmic Landscape in Quantum Décor

The theme accentuated: continued…

In discussing over the underlying gist of the blog Magnified Universe: Cosmic Landscape in Quantum Décor we skimmed through the overall idea of how the three components are indispensable if we are to envision the truest order of reality. Those components are:

1] Cosmic observations

2] Quantum observations

3] The nature of self

Cosmic observations impart a limited range, authentic nonetheless, picture. We only see what we can see. Quantum level reading broadcast a comprehensive picture: including every bit, and factual scenarios that we do not directly perceive. It is in quantum mechanical rendering that all the elements of reality can be seen to play. All-encompassing architecture—that subsumes infinitesimal bits of atomic and subatomic particles, even strings for the believers of string theory (I support the idea totally!), molecular, macromolecular and complex biological structures, cosmic arena, the entire of the universe, and also its parallel universes—at the foundational level boils down to the sweep of matter and the forces by which matter exists.

In a nutshell there only are two constituents to dovetail in seeing one flawless scheme—matter and the forces through which matter exists. Amazingly simple task, but exceedingly hard to surmount! Simply because the ultimate picture must pick up all of the methodic observations in one fell swoop, and explain the rationality behind contradictions, such as prodigiously expanding universe in the tethering field of gravity, or the existence of antimatter.

However, there does prevail just one more vital element, executing in the overarching game of reality, admittance of which not only completes our picture of reality, it irons out perplexities of the empirical descriptions as well. That element is the ultimate nature of self. Physical Laws of the Mathematical Universe: Who Are We? not only pins down the ultimate nature of self, but extends to show its play in the all-encompassing scheme, and sharpens scientific picture along the way.

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Now a deep-seated aid at our hand in all of this! Behind the discrete show of the universe, there seeps a profound glue. A glue that interlocks disparate pieces into one compact description. We have seen it over and over, and many of us have guessed it correctly. It is the glue of mathematics. Why it comes to be that way? Simply put, mathematics is an algorithmic language that lets us read reality. Deeply engrossed in the formulas of mathematics, we forget as to what a mathematical formula actually is: the formulation of reality, or the structure of reality. Mathematics, which though at the surface is a tool to codify the interplay of discrete entities, at the most basic level is the structure of reality itself, the reverberations of which we haven’t fully figured out. Same as we haven’t all the way figured out how the universe structures and continues.

The discrepancies lurk; Inquiries linger; Bewilderment creeps.

However, the numerical language carries the highest of potentials to expose the truly real all-inclusive picture of reality, simply because mathematics crystallizes only by play of all the components. Simple to intricate examples are covered in the new title.

And it is in the deep subtleties of mathematics that we can not only pin down quantum dynamics and cosmic display, but also tease out the truest identity of self.

FigIV

In keeping with the blogging courtesy and your continual interest, I would need to take a pause here, and expand on this further in the subsequent posts.

Until then please also take a peek at one of my earlier posts to get a general idea that seeps underneath the parallelism between mathematics and the physical world.

See you soon,

Neeti

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Magnified Universe: Cosmic Landscape in Quantum Décor

Magnified Universe: Cosmic Landscape in Quantum Décor

The theme accentuated

The underlying gist of the blog Magnified Universe: Cosmic Landscape in Quantum Décor is to envision the truest order of reality, or the uttermost flow of reality to be precise—simply because “flow” allows for continual change. Envisioning of the truest order of reality is the biggest of all questions! It is akin to piecing every single bit there is into a crisp comprehensible picture. That would be an insurmountable task. In a hilarious cartoon by S. Harris—in fact so many of his sketches are truly humorous, very popular among physicists and mathematicians, and often appear in Stephen Hawking’s popular science books—a scientist claims to have arrived at a unified theory simply by putting a box around a set of equations that described reality.

Dovetailing every piece into a whole amounts to subsuming every shred there is. From infinitesimal bits of atomic and subatomic particles, even strings (that string theory claims to be of Planck length, 10-35 meters, in size), to molecular and macromolecular structures to day-to-day objects to planets, and their satellites, to stars to solar systems to galaxies, and their clusters, to the entire of the universe (about the diameter of 93 billion light years), not to mention the parallel universes that we discern to be existing based on quantum mechanical understanding.

Oh yes, the indispensable of consciousness, awareness, and our subliminal paraphernalia as well!

Did I leave out anything? Caution me!

Accounting for all of these is a truly herculean task. We do need to shove all of it in a box, and wrap it up!

Then as I discussed in my last two posts, the perplexities that we pick up as we surf the landscape of scientific endeavors: On the beginning of time; emergence of consciousness; existence of multiverse; accelerating universe; recently, the dark matter; dark energy, and interconnectedly, the understanding of gravitational force; the dwell of antimatter. We have to account for all of this as well, meaning how they play out, or the reasoning behind their play. They are all real facts: They do need to either take role or resolve themselves out.

The unification implies just that: Seeing a harmonious picture in which all elements of reality take role, and discrepancies resolve. But even before we embark on such a journey, we need to imbue ourselves with two paramount characteristics of reality:

1] The universe is unified: Matter exists through fundamental forces such as gravity and electromagnetism.

2] The universe is uniform: Forces through which matter exists are uniform. Matter exists by same rules, anywhere.

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PostIII_Figure

After this assimilation, we can pretty much see that we as a scientist would want to see resolve any fact tossed at us into the above overarching picture of reality. Empirical observations, their disagreements, their quandaries, how we fit and continue, the mental bearings, and at a subtle level even the methodic concepts that we come to rely on, should all swimmingly be the part of the grand scheme.

If we leave scientific facts behind, the picture isn’t just fuzzy and disconcerting, it can be delusional. On the other hand, if we leave out the other elements of reality—the nature of self for instance—the scientific picture, wouldn’t be fully readable, and its perplexities wouldn’t resolve. Plainly because all the elements play in the construction of the full-length picture, again more precisely, flow. To see any kind of picture, scientific or otherwise, all pieces should be accounted for.

And those pieces are:

1] Cosmic observations

2] Quantum observations

3] The nature of self

I will continue with the theme of this blog in the next post, and also bring up the idea behind title itself—Magnified Universe: Cosmic Landscape in Quantum Décor.

Till then feel free to pitch in your views.

See you soon,

Neeti

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Proving it or Making Sense, Part II

Scientific Argumentation and Universal Logic in understanding the Universe

Part II

We were talking about how the alignment of “proving it” and “making sense” goes haywire with descriptions of deeper orders of reality, at times so much so that only the scientist in us happens to stomach them, and part of us still crave for an overarching clearer picture—causing an ever greater rift between the scientific endeavors and seeing the all-encompassing picture of reality, where we also reside. The reality is one, scientifically or otherwise. Science in no way takes us to a hazy confounding zone, but to see a true order we have to look at the scientific data with a broader, overarching perspective.

It’s just that with prodigious scientific advancements intricate details seep in, and “making sense” starts to fall outside the boundaries of scientific endeavor: because now it involves “us” seeing it differently. Like the tangled issue of the beginning of time that I brought up in the last post. No matter what rationality, the beginning of the universe via black hole, or the time having no beginning or end, as we are now learning, glaring quandaries nudge us for clarity—like what banged in the big-bang, or what’s the true nature of this timeless space-time.

As quirky as it gets, the beginning of time, whether through black hole or big bang (the linked article in the previous post argues for black hole as an alternative scenario of big bang), in the end could only be as mysterious as a colorblind entity chewing over the beauty of a rainbow. In seeing the reality, the time having a beginning seems a graver scenario than the case of an overarching continuum that flows eternally—simply because the earlier case incites further perplexities. The obvious one is how the time itself emerges out of nowhere. Some other blatant questions.

Arriving at the reality might take boxing of all the inputs and thinking outside the box. I would again have to pass on saying more on this here for the sake of space and post, and for the sake of you reading the book Physical Laws of the Mathematical Universe: Who Are We? instead.

In the earlier post I brought up the other mystifying subject that is infiltrating the bounds of scientific understanding—the emergence of consciousness in the continuum of space-time. An indispensible description, if we are to see a full meaning in the picture that has sprung from centuries of research and contemplation. Here again though we are struck with the oddity of joining a clear empirical deduction, from cosmological and quantum physics, to an order that appears to be abstractly—the nature of consciousness. We are puzzled over sewing part-science part I-don’t-know-what together.
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PostII_Figure

I was looking forward to a recently held debate on the topic of Death contested between two teams of scientists, one arguing for the existence of life beyond death, and the other against. I happened not to watch the debate, but after finding out that the team against the idea won, I out of curiosity glanced bits of the video. You can watch it in Sean Carroll’s blog under the post Afterlife Aftermath. The neuroscientist who was trying to make his argument—upholding the existence of life beyond death—based on personal experience and neurological understanding belonged to the loser team [no pun intended]. The forlorn look of the neuroscientist was pitiful [not taking sides]. His struggle might have to do with our lack of scientific vocabulary to illustrate the subtleties of defining consciousness or our experiences, which could, in the end, provide a full picture of reality. The reality that science proves and we feel confounded about.

But in the end, in understanding the uttermost reality, the question of us or consciousness undeniably leads to the query of the truest nature of self. Read on Physical Laws of the Mathematical Universe: Who Are we?

Ultimately “making-sense” becomes foundational after certain threshold of “proving” is attained, for us to move forward, on scientific ground or otherwise. And basically it is “making sense,” at a common level, that not only authenticates but also translates the empirical doctrines.

All reasoning welcome,

Neeti.

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