Tag Archives: mathematical reality

Getting back to blogging

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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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The allure of mathematical subtleties: Do we see the otherwise unfathomable reality?

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This time it was a relatively long breach in our communication, and I have been contemplating on dropping a note or two for some time now. So here they are. A few updates for our reasoning and creative appetites.

–          Do read The Impenetrable Proof. An almost anecdotic article brings to light the alleged mathematical solution to one of the greatest unsolved problems of mathematics—the abc conjecture. The assumption relates to the game of prime numbers, and how their quirk plays out in the landscape of number field. Though the article mostly relates to the storyline of the mathematician Shinichi Mochizuki who claims to have solved the conjecture, and along the way he seemingly had to create a new outlook of the nature of mathematics itself. His newly created mathematical plot of inter-universal geometry is very enticing. High-ranking mathematicians have found themselves perplexed in following the proof for the truly different mathematical perspective that it adopts. It isn’t as rebellious as it sounds. The allure of seeing the truth (or imagery in this case, specifically) in the mesmerizing abstractness of advanced mathematics isn’t very new, and many of us before have plunged into these realms. Article nonetheless is worth to truly feel how the truth of mathematics is genuinely at work at subtler levels.

–          In relation to the fascinating prime numbers, a hypothesis that stands out is the yet unsolved legendary Riemann hypothesis:

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

A relatively bland on the surface, the playing of this articulation isn’t just riveting, it takes in intricately advanced features and gives forth exceedingly consequential messages. I have just written an article on it, in the context of mathematical reality of the universe. I should be able to post this article here shortly.
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–          In connection to the above, and with all the current buzz on mathematical reality of the universe, and our true nature, my book Physical Laws of the Mathematical Universe: Who Are We? has just come out. We are still working on the e-book, but do stop by and join in to let me know your views, or drop me a question.

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See you all soon,

Neeti.

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Grothendieck’s Deep Visions

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Alexander Grothendieck isn’t a household name in academic community, and at a general level hardly anyone would ever have heard of him. Among mathematicians he dwelt as persona of profound brilliance and finesse, colored with uncanny idiosyncratic taints. Not just efficient in clearing up of the most convoluted mathematical renderings, he held clear workings of the most abstractly mathematical landscapes—of algebraic geometry and topology—and advanced them to the level of fathomable depictions for us all.

As in many cases in the modern history, his deep mathematical insights seemingly came with a price. Apart from deep-seated crannies of complex mathematics, he, seemingly by choice, remained mostly disconnected from anything in the rest of the world, even the simpler branches of mathematics.

I read somewhere an anecdote about him on prime numbers, which he chose not to be worthy of attention. He apparently addressed, hopefully unwittingly,  number 57 to be a prime number, which it isn’t (it factorizes to 3 and 19, and is thus not a prime number). Since then in mathematics community 57 is referred as Grothendieck’s prime.

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Neeti Sinha

Magnifieduniverse.com

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The Mathematical Truth

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                Mathematics portraying reality isn’t a new insight. We have been sensing it ever since the preliminary structure of mathematics, and their formulations, appeared. Over time, as the language of mathematics evolved, the understanding that mathematics reflects the reality of universe immensely sharpened. From its practical utilities to its guidance in formulating the reality of space-time, the representations of mathematics seem to pitch the most accurate information about our universe, many of which we hadn’t have known if we hadn’t accustomed ourselves with the mathematical tone. That is why the prevailing notion: “Mathematics is a language that is discovered rather than invented.”

                The idea of mathematics depicting truth doesn’t point to the counts appearing in everyday life and universal organization, or numerology. It plainly says this: The way mathematics arranges is identical to the way universe structures. This holds true, whether we talk of simple arithmetical depictions or complex algebraic formulations—the ones by which we have learned some of the hidden meanings of the universe.

We can start out with messages at a very basic level:

The square and cube of a number imitate the 2-dimensionality and 3-dimensionality of the real world. The example of 3:

MathUni

                Want to know how universe arranges itself in even higher dimensions—that current findings and theoretical models are pointing to—ask mathematics:
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Image credit: A Hanson, Indiana University

is one example.

 

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