Beauty and Symmetry...

Figure 13.8, the center vertical position for the unusual mirrored structure in the parliament building in Berlin
Jim Zuckerman on Composition: Symmetry

Topics: Geometry, Mathematical Physics, Quantum Mechanics, Theoretical Physics

www.worldsciencefestival.com

DATE: Saturday, June 4, 2016

TIME: 2:00 PM-3:30 PM

VENUE: NYU Skirball Center for the Performing Arts

MODERATOR: John Hockenberry

PARTICIPANTS: Robbert Dijkgraaf, David Gross, Alan Lightman, Maria Spiropulu

From a bee’s hexagonal honeycomb to the elliptical paths of planets, symmetry has long been recognized as a vital quality of nature. Einstein saw symmetry hidden in the fabric of space and time. The brilliant Emmy Noether proved that symmetry is the mathematical flower of deeply rooted physical law. And today’s theorists are pursuing an even more exotic symmetry that, mathematically speaking, could be nature’s final fundamental symmetry: supersymmetry. Join some of the world’s preeminent scientists to explore the core role symmetry plays in our unraveling of nature’s deepest secrets—and catch a glimpse of profoundly important symmetries that may be awaiting us just over the horizon.

The Big Ideas Series is supported in part by the John Templeton Foundation.

Image Credit: Miles Verkade

Finitistic, Infinitistic...

Image Credit: Wylie Beckert for Quanta Magazine

Topics: Computer Science, Logic, Mathematical Models, Mathematical Physics

With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary.

The boundary does not pass between some huge finite number and the next, infinitely large one. Rather, it separates two kinds of mathematical statements: “finitistic” ones, which can be proved without invoking the concept of infinity, and “infinitistic” ones, which rest on the assumption — not evident in nature — that infinite objects exist.

Mapping and understanding this division is “at the heart of mathematical logic,” said Theodore Slaman, a professor of mathematics at the University of California, Berkeley. This endeavor leads directly to questions of mathematical objectivity, the meaning of infinity and the relationship between mathematics and physical reality.

Quanta Magazine: Mathematicians Bridge Finite-Infinite Divide, Natalie Wolchover

Pi Day and Einstein...

We're wearing them!

Topics: Blerd, Circle, Circumference, Geek, Geometry, Math, Nerd, Pi Day

...and yes as you can see, we have our official T-shirts!

Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits.

Ultimate nerd out: It's Albert Einstein's birthday! It's also the 100th anniversary of the General Theory of Relativity, that led to the discovery of Black Holes. Trivia: Black Holes was a subject - like quantum mechanics he couldn't bring himself to believe in, though his work contributed to both.

Info from Celebration Site: PiDay.org
Biography.com: Fascinating Facts About Pi Day & Birthday Boy Albert Einstein
NBC News Weird Science: Pi Day Hits a Milestone, Alan Boyle

Al-Jabr...

Image Source: Kevtak Algebra Readiness Classroom and Homework page

This reminds me of a student in one of my first math classes I taught at the high school level - Algebra 1 - stating emphatically he "didn't need math to be a mechanic." A visit to the web page for UTI, and that "troubleshooting" and electronic technology involves a considerable amount of math managed to refocus him successfully (the Pre-Calculus class was a bit older, and concentrated on graduating - I didn't need to do much "pep-talking").

A little history for perspective: we use it to balance chemical equations; the first high school physics you'll ever learn before you run into Calculus will be based on this foundation.

Image source: Famous Scientists

Muhammad al-Khwarizmi

Baghdad in the 9th century was a global center of culture and trade, a hub connecting India and China with the Mediterranean and Europe. It was a rich city, a center of learning, and scholars from all over the world would come to study at the House of Wisdom, a renowned library and academy where Muhammad al-Khwarizmi lived as a scholar.

Ideas traveled in consort with commerce along the roads of Baghdad, and al-Khwarizmi embodied the wide range of the city's global vision. The Muslim scholar expanded upon the work of Greco-Roman astronomers such as Ptolemy, created one of the oldest surviving treatises on the Jewish calendar and employed and popularized the Hindu number system of 1, 2, 3... (which, because of al-Khwarizmi's work, we now refer to as the Hindu-Arabic numeration).

But his most influential work dealt with methods to solve complete equations. In "The Compendious Book on Calculation by Completion and Balancing," al-Khwarizmi demonstrated how to simplify equations by adding or subtracting an identical quantity from both sides. For example, adding 4x to each side of 6x = 40 - 4x reveals that 10x = 40. This "act of completion" - al-jabr - gave mathematicians a new tool: algebra.

From Time, Special Editions: Great Scientists - The Geniuses, Eccentrics and Visionaries Who Transformed Our World, Mathematics, page 21.

And, in the spirit of irony as well as completion: x = 4 (today).

Virtual Prototyping of Superconductors...

MIT visualization of Faraday's Law

"Virtual prototyping of superconducting devices," Jeremy Howard-Knight PhD

Modeling Stars in 3-D...

Volume rendering of the entropy of a differentially rotating and highly magnetized progenitor to a supernova in a full 3-D. Red colors indicate high entropy (hot) material while blue represents low entropy (cold) material. Strongly magnetized material is continuously launched from the surface of the proto-neutron star in the center but gets severely distorted such that, instead of a clean jet observed in the ultra-strong magnetic field case, two giant polar lobes are formed. The box size for the visualization is 2000km cubed.

Credit: Philipp Moesta, TAPIR, California Institute of Technology

[The following is Part eight in a series of stories that highlight recent discoveries enabled by the Stampede supercomputer. In parts one, two, three, four, five, six and seven, learn how the system is helping to advance research throughout science and engineering.]

Using the National Science Foundation-supported Stampede supercomputer, Philipp Moesta and Christian D. Ott from the California Institute of Technology succeeded in performing the first 3-D simulations of a collapsing star that takes into account the influence of general relativity and magnetohydrodynamics--the interplay of electrically conducting fluids like plasmas and powerful magnetic fields. The death of these collapsing stars leads to energetic, jet-driven supernova explosions.

Their findings show that the simulations behave very differently in full, unconstrained 3-D compared to the same model simulated with the assumption that stars are sperically symmetrical.

National Science Foundation: Everything is Better in 3-D

Rule of Threes...

Image Source: Link Below

More than 40 years after a Soviet nuclear physicist proposed an outlandish theory that trios of particles can arrange themselves in an infinite nesting-doll configuration, experimentalists have reported strong evidence that this bizarre state of matter is real.

In 1970, Vitaly Efimov was manipulating the equations of quantum mechanics in an attempt to calculate the behavior of sets of three particles, such as the protons and neutrons that populate atomic nuclei, when he discovered a law that pertained not only to nuclear ingredients but also, under the right conditions, to any trio of particles in nature.

While most forces act between pairs, such as the north and south poles of a magnet or a planet and its sun, Efimov identified an effect that requires three components to spring into action. Together, the components form a state of matter similar to Borromean rings, an ancient symbol of three interconnected circles in which no two are directly linked. The so-called Efimov “trimer” could consist of a trio of protons, a triatomic molecule or any other set of three particles, as long as their properties were tuned to the right values. And in a surprising flourish, this hypothetical state of matter exhibited an unheard-of feature: the ability to range in size from practically infinitesimal to infinite.

“It’s a pretty wild idea,” said Randy Hulet, a physics professor at Rice University in Houston. “You get this infinite series of molecules.”

Quanta Magazine: Physicists Prove Surprising Rule of Threes

Entropy and Life...

Why does life exist?

Popular hypotheses credit a primordial soup, a bolt of lightning and a colossal stroke of luck. But if a provocative new theory is correct, luck may have little to do with it. Instead, according to the physicist proposing the idea, the origin and subsequent evolution of life follow from the fundamental laws of nature and “should be as unsurprising as rocks rolling downhill.”

From the standpoint of physics, there is one essential difference between living things and inanimate clumps of carbon atoms: The former tend to be much better at capturing energy from their environment and dissipating that energy as heat. Jeremy England, a 31-year-old assistant professor at the Massachusetts Institute of Technology, has derived a mathematical formula that he believes explains this capacity. The formula, based on established physics, indicates that when a group of atoms is driven by an external source of energy (like the sun or chemical fuel) and surrounded by a heat bath (like the ocean or atmosphere), it will often gradually restructure itself in order to dissipate increasingly more energy. This could mean that under certain conditions, matter inexorably acquires the key physical attribute associated with life.

“You start with a random clump of atoms, and if you shine light on it for long enough, it should not be so surprising that you get a plant,” England said.

England’s theory is meant to underlie, rather than replace, Darwin’s theory of evolution by natural selection, which provides a powerful description of life at the level of genes and populations. “I am certainly not saying that Darwinian ideas are wrong,” he explained. “On the contrary, I am just saying that from the perspective of the physics, you might call Darwinian evolution a special case of a more general phenomenon.”

His idea, detailed in a recent paper and further elaborated in a talk he is delivering at universities around the world, has sparked controversy among his colleagues, who see it as either tenuous or a potential breakthrough, or both.

Quanta Magazine: A New Physics Theory of Life, Natalie Wolchover
AIP Paper: Statistical physics of self-replication
Jeremy L. England
Department of Physics, Massachusetts Institute of Technology

Mathematical Physics...

Physics Database: In this course from the Perimeter Institute Carl Bender introduces the basics of mathematical physics. The covered topics include: perturbation theory, asymptotics, Schrodinger equation, Shanks transform, eigenvalue problems, Euler summation, divergent series and others. For more physics lectures check out our lecture page.

Calculus of Fly Balls...

You just didn't know you were doing it. Baseball season is coming...

World Science Festival: The Calculus of Catching Fly Balls

Catharsis...

TECHNOLOGY REVIEW: The Doomsday Argument is the idea that we can estimate the total number of humans that will ever exist, given the number that have lived so far. This in turn tells us how likely it is that human civilisation will survive far into the future.

The numbers are not optimistic. Anthropologists think some 70 billion humans have so far lived on Earth. If we assume that we have no special status in human history, then simple probabilistic arguments suggest that there is a 95 per cent chance that we are among the last 95 per cent of humans that will ever be born. And this means there is a 95 per cent chance that the total number of humans that will ever exist will be less than 20 x 70 billion or 1.4 trillion.

These guys look at the scenario in which many civilisations have evolved throughout the universe, the so-called “universal doomsday” argument. “In that case, we should consider ourselves to be randomly chosen from all individuals in that universe or multiverse,” they say.

Now suppose that the world population stabilises at 10 billion and our life expectancy is 80 years, then the remaining humans will be born in the next 10,000 years. That’s not a long future for humanity. Today, Austin Gerig at the University of Oxford and a couple of pals put forward a new argument with a (slightly) happier ending.

These guys look at the scenario in which many civilisations have evolved throughout the universe, the so-called “universal doomsday” argument. “In that case, we should consider ourselves to be randomly chosen from all individuals in that universe or multiverse,” they say.

In the past, these universal arguments have been no more optimistic than the ordinary ones. They generally state that long-lived civilizations must be rare because if they were not, we would be living in one. What’s more, because long-lived civilizations are rare, the prospects for our civilisation ever becoming long-lived are poor.

This new approach approach allows Gerig and co to take a more fine-grained look at the odds that humanity will survive for much longer in future than it has existed in the past.

The results are complex but their main conclusion gives some reason for hope. “If [the number of existential threats] is not too large, the probability of long-term survival is about a few percent,” they say.

It's comforting to muse that we can actually know the future, and the likelihood of a predicted outcome. We guffaw when the weather anchor "gets it wrong," and somehow think that global warming means if the entire planet isn't becoming the Sahara Desert (and it snows somewhere), there's nothing to it. In the need for accuracy and truth, science revises itself through a rigorous process of peer review, and adherence to The Scientific Method. Modeling and probability always have a margin for error, so in reading the link, think of that.

One of the ways to "increase our odds" is addressing "existential threats" (meteors, nuclear war, pandemics, poverty), and becoming a space faring species. On "a few percent": Growing up under the "duck and cover" drills of the 60s during the Cold War (during which I never thought we had a snowball's chance), I'll TAKE that!

My Pascha post...

Physics arXiv: Universal Doomsday: Analyzing Our Prospects for Survival

Universality...

Students of Bhashyam Blooms explain a mathematical model at the maths exhibition in Guntur - The Hindu

In 1999, while sitting at a bus stop in Cuernavaca, Mexico, a Czech physicist named Petr Šeba noticed young men handing slips of paper to the bus drivers in exchange for cash. It wasn’t organized crime, he learned, but another shadow trade: Each driver paid a “spy” to record when the bus ahead of his had departed the stop. If it had left recently, he would slow down, letting passengers accumulate at the next stop. If it had departed long ago, he sped up to keep other buses from passing him. This system maximized profits for the drivers. And it gave Šeba an idea.

“We felt here some kind of similarity with quantum chaotic systems,” explained Šeba’s co-author, Milan Krbálek, in an email.

After several failed attempts to talk to the spies himself, Šeba asked his student to explain to them that he wasn’t a tax collector, or a criminal — he was simply a “crazy” scientist willing to trade tequila for their data. The men handed over their used papers. When the researchers plotted thousands of bus departure times on a computer, their suspicions were confirmed: The interaction between drivers caused the spacing between departures to exhibit a distinctive pattern previously observed in quantum physics experiments.

“I was thinking that something like this could come out, but I was really surprised that it comes exactly,” Šeba said.

Subatomic particles have little to do with decentralized bus systems. But in the years since the odd coupling was discovered, the same pattern has turned up in other unrelated settings. Scientists now believe the widespread phenomenon, known as “universality,” stems from an underlying connection to mathematics, and it is helping them to model complex systems from the Internet to Earth’s climate.

Simons Foundation: In Mysterious Pattern, Math and Nature Converge

I Prefer Double Twelves...

...versus double six and double nine sets: math is quicker, and more fun to play.

The stunt:


The schematic:

The math:

Physics arXiv: Domino Magnification
Site: CDT-domino.com

Brain and Universe...

Scientists have found through a computer simulation that the universe grows like a giant brain.

This research has been published online in the November 16th issue of the journal Nature’s Scientific Reports.

Scientists have found that there are some single basic laws, which are still unknown, are working from the tiny electrical firing of neurons to the expansion of the universe.

“Natural growth dynamics are the same for different real networks, like the Internet or the brain or social networks,” said study co-author Dmitri Krioukov, a physicist at the University of California San Diego.

Researchers made a computer simulation of the early universe by breaking it to the tiniest possible units even smaller than the sub-atomic particles. They linked any quanta – the smallest discrete quantity of a physical property – in the huge celestial network and found that more and more space-time was added to the universe as the simulation progressed showing that the “network” connections between the matter in the galaxies also grew.

Researchers found that the growth of social networks and brain circuits follow the same path as the growth of universe i.e. their networks expanded in the similar way. They maintain a balanced links between similar nodes with the ones that had already many connections.

Say People: Single unknown fundamental laws are controlling everything

The Universe as Simulation...

Technology Review

TECHNOLOGY REVIEW: One of modern physics' most cherished ideas is quantum chromodynamics, the theory that describes the strong nuclear force, how it binds quarks and gluons into protons and neutrons, how these form nuclei that themselves interact. This is the universe at its most fundamental.

So an interesting pursuit is to simulate quantum chromodynamics on a computer to see what kind of complexity arises. The promise is that simulating physics on such a fundamental level is more or less equivalent to simulating the universe itself.

There are one or two challenges of course. The physics is mind-bogglingly complex and operates on a vanishingly small scale. So even using the world's most powerful supercomputers, physicists have only managed to simulate tiny corners of the cosmos just a few femtometers across. (A femtometer is 10^-15 metres.)

Physics arXiv: Constraints on the Universe as a Numerical Simulation

Fractal Calculus...

Purdue physicist Erica Carlson stands in front of an illustration of the fractal clusters present in copper-oxygen based superconducting material. (Purdue University photo/Mark Simons)

WEST LAFAYETTE, Ind. - Many researchers studying superconductivity strive to create a clean, pure, perfect sample, but a team of physicists found that some flaws might hold the key to a material's unique abilities.

Erica Carlson, a Purdue University associate professor of physics, led a team that mapped seemingly random, four-atom-wide dark lines of electrons seen on the surface of copper-oxygen based superconducting crystals. The team uncovered a pattern in these flawed lines, which are separate from the expected structure of the material, and discovered that they exist throughout the crystal. The findings suggest the lines could play a role in the material's superconductivity at much higher temperatures than others.

"This material is ceramic, like your dinner plates, and it has no business conducting electricity, but under the right conditions it conducts electricity perfectly with zero energy loss," Carlson said. "A better understanding of how and why this superconductor works could help us design better ones. If we can create a superconductor that works at high enough temperatures, it could transform how we use and generate energy."

Purdue University News: Superconductor 'flaws' could be key to its abilities
Related link: Mandelbrot Set Tripping
Wolfram Mathworld: Fractals

Ray Palmer's Realm...

Quantum computers are still years away, but a trio of theorists has already figured out at least one talent they may have. According to the theorists, including one from the National Institute of Standards and Technology (NIST), physicists might one day use quantum computers to study the inner workings of the universe in ways that are far beyond the reach of even the most powerful conventional supercomputers.

DC Wiki: Ray Palmer
NIST: Quantum Computers Will Be Able to Simulate Particle Collisions

The Queen of Sciences...

Discover Magazine

1 The median score for college-bound seniors on the math section of the SAT in 2011 is about 510 out of 800. So right there is proof that there are lots of unsolved math problems.

2 The great 19th-century mathematician Carl Friedrich Gauss called his field “the queen of sciences.”

3 If math is a queen, she’s the White Queen from Alice in Wonderland, who bragged that she believed “as many as six impossible things before breakfast.” (No surprise that Lewis Carroll also wrote about plane algebraic geometry.)

4 For example, the Navier-Stokes equations are used all the time to approximate turbulent fluid flows around aircraft and in the bloodstream, but the math behind them still isn’t understood.

5 And the oddest bits of math often turn out to be useful. Quaternions, which can describe the rotation of 3-D objects, were discovered in 1843. They were considered beautiful but useless until 1985, when computer scientists applied them to rendering digital animation.

My favorite Calculus problem:

More at the link below:

Discover Magazine: 20 Things You Didn't Know About...Math

Zilch...Nada...and a little more...

Space Foundation Overview

View more presentations from Space Foundation

New Scientist: The Nature of Nothingness

A 501(c)3 organization, The Space Foundation mission is "to foster, develop and promote, among the citizens of the United States of America and among other people of the world ... a greater understanding and awareness ... of the practical and theoretical utilization of space ... for the benefit of civilization and the fostering of peaceful and prosperous world."

Perhaps...the world could one day "work [somewhat] like Star Trek." Imagine that.

Physics...and Basketball...

Dunking: Mid Flight

Though it is technically football season, this is pretty interesting. It points out that physicists and scientists are part of the rest of the world, and pay attention to sporting events: like football and basketball.

Hint: It's probably not a good idea to bet against them in an office pool!

We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk₁. The time between successive scoring events follows an exponential distribution, with little memory between different scoring intervals. Using this random-walk picture that is augmented by features idiosyncratic to basketball, we account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead. By further including the heterogeneity of team strengths, we build a computational model that accounts for essentially all statistical features of game scoring data and season win/loss records of each team₂.

1. Wolfram Mathworld: Random Walk
2. Physics arXiv: Random Walk Picture of Basketball Scoring, Alan Gabel and S. Redner, Center for Polymer Studies and Department of Physics, Boston University