Tag Archives: algebra

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.

Dirac_eq

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.

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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.

CY_Rot

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,

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

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Be back shortly,
Neeti.

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The Mathematical Truth

                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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CalY

Image credit: A Hanson, Indiana University

is one example.

 

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