Saturday, November 07, 2015

Emmy Noether































The Mighty Mathematician You’ve Never Heard Of
Albert Einstein called her the most “significant” and “creative” female mathematician of all time, and others of her contemporaries were inclined to drop the modification by sex. She invented a theorem that united with magisterial concision two conceptual pillars of physics: symmetry in nature and the universal laws of conservation. Some consider Noether’s theorem, as it is now called, as important as Einstein’s theory of relativity; it undergirds much of today’s vanguard research in physics, including the hunt for the almighty Higgs boson. ....... a brilliant theorist whose unshakable number love and irrationally robust sense of humor helped her overcome severe handicaps — first, being female in Germany at a time when most German universities didn’t accept female students or hire female professors, and then being a Jewish pacifist in the midst of the Nazis’ rise to power. ...... Through it all, Noether was a highly prolific mathematician, publishing groundbreaking papers, sometimes under a man’s name, in rarefied fields of abstract algebra and ring theory. And when she applied her equations to the universe around her, she discovered some of its basic rules,

like how time and energy are related

, and why it is, as the physicist Lee Smolin of the Perimeter Institute put it, “that riding a bicycle is safe.” ........ “You can make a strong case that her theorem is the backbone on which all of modern physics is built.” .... Noether came from a mathematical family. Her father was a distinguished math professor at the universities of Heidelberg and Erlangen, and her brother Fritz won some renown as an applied mathematician. Emmy, as she was known throughout her life, started out studying English, French and piano — subjects more socially acceptable for a girl — but her interests soon turned to math. Barred from matriculating formally at the University of Erlangen, Emmy simply audited all the courses, and she ended up doing so well on her final exams that she was granted the equivalent of a bachelor’s degree. ....... earned her doctorate summa cum laude ..... In 1915 Einstein published his general theory of relativity. The Göttingen math department fell “head over ear” with it, in the words of one observer, and Noether began applying her invariance work to some of the complexities of the theory. That exercise eventually inspired her to formulate what is now called Noether’s theorem, an expression of the deep tie between the underlying geometry of the universe and the behavior of the mass and energy that call the universe home. ........ Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see that it is angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move. ..........

Some of the relationships to pop out of the theorem are startling, the most profound one linking time and energy.

Noether’s theorem shows that a symmetry of time — like the fact that whether you throw a ball in the air tomorrow or make the same toss next week will have no effect on the ball’s trajectory — is directly related to the conservation of energy, our old homily that energy can be neither created nor destroyed but merely changes form. ........ “Energy, momentum and other quantities we take for granted gain meaning and even greater value when we understand how these quantities follow from symmetry in time and space.” ...... After meeting the young Czech math star Olga Taussky in 1930, Noether told friends how happy she was that women were finally gaining acceptance in the field, but she herself had so few female students that her many devoted pupils were known around town as Noether’s boys. ...... Noether lived for math and cared nothing for housework or possessions, and if her long, unruly hair began falling from its pins as she talked excitedly about math, she let it fall. She laughed often and in photos is always smiling. .......

When a couple of students started showing up to class wearing Hitler’s brownshirts, she laughed at that, too.

..... In 1933, with the help of Einstein, she was given a job

at Bryn Mawr College, where she said she felt deeply appreciated as she never had been in Germany.







Emmy Noether Google Doodle: Why Einstein called her a ‘creative mathematical genius’
Noether had risen against wall after wall of obstacles to work on such areas as ring theory; now she was counted among those in a most rarefied academic circle...... “Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.” –A.E. ........ Noether studied French and English as a girl growing up in Bavaria, but upon reaching adulthood, she followed her father (Max Noether) and a brother (Fritz) into math, and it was there she discovered and gave her full expression to the poetry of logical ideas. ........ Einstein called her two years at Pennsylvania’s Bryn Mawr “the happiest and perhaps the most fruitful of her entire career.” ..... “There weren’t any obstacles that would stop Noether from her studies. In this doodle, each circle symbolizes a branch of math or physics that Noether devoted her illustrious career to. From left to right, you can see topology (the donut and coffee mug), ascending/descending chains, Noetherian rings (represented in the doodle by the Lasker-Noether theorem), time, group theory, conservation of angular momentum, and continuous symmetries — and the list keeps going on and on from there! Noether’s advancements not only reflect her brilliance but also her determination in the face of adversity.”
The female mathematician who changed the course of physics—but couldn’t get a job
Noether's Theorem may be the most important theoretical result in modern physics. ...... Göttingen served as the center of mathematics for the Western world by this point, and Hilbert stood as one of its most notorious thinkers. He was a prominent leader for the minority of mathematicians who preferred a symbolic, axiomatic development in contrast to a more concrete style that emphasized the construction of particular solutions. Many of his peers recoiled from these modern methods, one even calling them “theology.” But Hilbert eventually won over most critics through the power and fruitfulness of his research. ......... Her father, Max, was a fairly prominent mathematician, and one of her brothers eventually attained a doctorate in math. In retrospect, perhaps the Noethers may be another historical example of a family with a math gene. ..... she had a facility with languages and was allowed to become certified as a language teacher. But Noether recognized her passion was in mathematics, and she decided to chase her dream and find a way to study the subject at the university level. ...... She also vigorously attacked her own research, forging a personal and original path through abstract algebra. Just a year after her doctorate, Noether's papers and the doctoral research that she was unofficially supervising gained her election to several academic societies, which prompted invitations to speak around Europe. Among those wanting her around, Hilbert reached out to bring Noether to Göttingen in order to tackle Einstein’s theory. ........

Einstein’s Theory of General Relativity was undoubtedly beautiful. It was unlike any theory of nature yet imagined by humankind

...... The mass that determined the strength of the gravitational force was the same mass that appeared in Newton’s second law of motion, F = ma; gravitational mass was the same as the “inertial mass.” There was no apparent reason this had to be true, it simply was. ....... but Hilbert could not overcome the resistance of the humanities professors, who simply could not stomach the idea of a female teacher. ...... Noether immediately grasped the problem with Einstein's theory. Over the course of three years, she not only solved it, but in doing so she proved a theorem that simultaneously reached back to the dawn of physics and pushed forward to the physics of today.

Noether’s Theorem

, as it is now called, lies at the heart of modern physics, unifying everything from the orbits of planets to the theories of elementary particles........ the theorem uncovers a hidden relationship between symmetry and conservation, and that relationship is what came to unify all of physics. ....... If the equations that describe the universe changed as time passed, we could never make sense of anything. ..... Physics should be the same no matter where in space we are, if nothing else changes. The equations of motion need to be the same in New York or Göttingen. ....... Noether’s Theorem relates continuous invariants to conservation laws. A conservation law is a rule that says that some quantity remains numerically constant as the system evolves in time. Conservation of energy, momentum, and angular momentum from classical physics are famous examples. ....... conservation of energy was not discovered for almost 200 years after Newton published his laws of motion. ........

Noether’s Theorem proves that for every invariant, there is a corresponding conservation law. She also proved the converse, meaning that for every conservation law there must be an invariant behind it.

...... The theorem shows that conservation of energy is equivalent to time invariance in classical physics. This hard-won yet essential conservation law is directly implied by, and implies, a fundamental symmetry of nature. It shows that momentum conservation is equivalent to spatial invariance. It establishes the equivalence of other symmetries, more mathematical in flavor, with other conservation laws. For example, the conservation of charge is related to a gauge symmetry, a complex mathematical symmetry in the equations of electrodynamics. ...... It is the theorem’s power to derive new conservation laws from abstract symmetries that has guided physical theory up to the present day. Noether’s result is an important tool in contemporary areas like particle physics, and it’s likely to remain so. ........ Noether’s work helped shed light on the fact that Einstein’s gravity behaves as no theory devised before, in that the energy of matter moving in a gravitational field can not be considered separately from the energy of the field itself. There is a conservation law, but it involves taking all of matter and gravity in a region of space as a unified whole .......... Noether showed that Hilbert was correct­—normal local energy conservation did not hold in Einstein’s work. However, she discovered that this was because of the peculiar kind of symmetry in general relativity. In this radically new model of the universe, gravity altered the very geometry of space and time.

In a Euclidean world, the ratio of the circumference of a circle to its diameter equals π. But in Einstein’s universe, this ratio depends on where in space you happen to be.

.......... energy conservation in general relativity just could not take the form that it had in all previous physics theories. ..... classroom teaching wasn’t her strength, Noether proved to be a superb leader of small research groups. Her advanced students were devoted to her. .......

One-third of the mathematics professors, and three-fourths of the heads of Göttingen’s mathematics and physics institutes, were Jewish despite less than one percent of the German population identifying that way at the time.

....... Noether’s work seemed to unify the most abstract mathematics with the most basic physical intuition, unifying the earliest successful systems of physics with science yet unborn. The circumstances of her life provide a powerful example of the humanizing influence of science and mathematics. It was the exponents of these fields who were eager to welcome her into their fellowship without regard for her sex or ancestry; the men of philosophy, history, politics, and government sought to exclude her for these very reasons. ....... A street and school in her home town have been named after her, as well as a crater on the moon. And for her birthday on March 23, Google dedicated its coveted Doodle real estate to one of history's most under-appreciated minds.




Wednesday, November 04, 2015

The Evolving Cyberthreat

The Evolving Cyberthreat
Even baseball teams are hacking their rivals now. And the latest series in the CSI television franchise? CSI: Cyber, starring Patricia Arquette and Ted Danson. .... (the best antivirus software catches only 5% of online threats; 80% of hackers work for organized crime rings) ..... Chinese irons and teakettles that were illicitly outfitted with Wi-Fi cards, allowing the appliances to secretly join their owners’ home networks and spread viruses and spam. ..... killer robots to plagues that are genetically engineered to attack a specific person (say, a sitting head of state) ........ researchers were able to identify specific people in anonymized data sets by using “a receipt, an Instagram post, and a Tweet about a new purchase or a Facebook post that included the location of a favorite bar or a restaurant.” ....... the United States, unlike many other countries, doesn’t classify privacy as a human right; instead, its laws tend to address privacy only after it’s been violated—in the wake of a data breach, for example. So we are exposed to anyone with the know-how and the inclination to violate it, including our own government. ...... hackers can change their tactics far faster and more easily than we can update our defenses ..... They can sidestep security simply by changing their IP addresses or adding a few lines of code to their malware, and they relentlessly pick apart apps, websites, and devices to find security holes they can exploit. New ways to steal your money and personal information are being dreamed up as you read this. ........ Cybersecurity books are a 20th-century solution to a 21st-century problem, and the solution isn’t working .... far too many people are still using passwords such as “123456” and “password,” and cybercrime is worse than ever. ..... The bad guys are already working together, whether through a catalog of common internet-of-things devices and how to hack them, the live tech support that attends one of the most nefarious malware packages, or the organized cybercrime rings themselves.

Sunday, November 01, 2015

Individuals Getting Paid

Wanted -- No, Needed: Digital Philosophers
"We have stronger opinions about our hand-held devices than about the moral framework we should use to guide our decisions.” As a result, we are in serious danger of having these philosophies influence our future in ways we neither intend nor desire. ......... “Advertising is a natural resource extraction industry, like a fishery. Its business is the harvest and sale of human attention. We are the fish and we are not consulted.” ...... “The reason advertising is artificially cheap is that no one has to ask our permission to advertise at us. We are involved in the transaction only as the commodity that is being bought and sold… Our right to preserve our own attention and to make our own decisions about how we spend it and with whom our personal information is shared must become part of the political agenda.” ....... One commercial at a time leaves me in control: I can change channel, look the other way, mute, close my eyes for 30 seconds. But thousands of ads, following me around on my computer, on my tablet, on my phone, in the movies, in the toilet, overwhelm me. ..... “Is advertising morally justifiable?” Thanks to the exponential growth of digital technologies, we face, or should be facing, similar philosophical questions across a whole range of activity. Is data collection morally justifiable? Does privacy have inherent value? How do we measure security?


Companies like Google should pay local, state and national governments across the world in jurisdictions where they make money. It might only be an aggregate 10% of what they make, but they should pay. Companies like Google should also pay individuals. The money should show up in your Gmail account. Data is not free. Big Data definitely is not free. It might only be 30 bucks a month, but that is a living in many countries. Heck, that is the mobile phone bill in the richest. Google's data plan is cheaper. Small internet startups should be free from this. A tech company should have to achieve a certain scale before they are asked to pay. That would work like an incentive. More paying companies would get created in the process.

Three billion people might opt to pay for their internet access this way. They might say, Google, create a section in your Chrome browser where you show me targeted ads, and let me have my internet access. For "free."

If we can create this pay structure, the impending era of abundance brought forth by huge rises in productivity might give us a billion artists who basically are jobless, who do nothing but surf the web, and who create content, who create art. Or not. They simply enrichen the internet by being there, by surfing. The internet is lifeless without people. They can always choose to get a job, or even build a company. But they are not starving in the meantime.


GOP plans for 'era of abundance' in energy
“Today’s energy policies are lagging far behind and are better suited for the gas lines in the 1970s than this new era of abundance”
JAVIER CREUS: “WE ARE ENTERING AN ERA OF ABUNDANCE!”
My co-authors and I found over 300 examples from all over the world of citizens organizing themselves to serve their own needs, which was so inspiring! This experience was what sparked my interest for the open knowledge, p2p production and collaborative economy movements........ Collaborative practices have grown massively and become mainstream in many areas such as for programmers on Github or for the European youth on ridesharing platforms. The collaborative / sharing economy has become widely known as a concept thanks to the interest of the media and the visibility of its communities. In some industries, such as lodging or city transportation, the impact on incumbent businesses has provoked many reactions and forced public administrations to rethink how to regulate these new businesses to benefit the public good. At the same time, some advanced businesses have started experimenting and getting in touch with the collaborative economy themselves. ....... basic concepts like mine & yours, customer & producer, partner & competitor, value & revenue, trust & responsibility may change dramatically when you integrate collaborative production systems. My impression is that most businesses see the efficiency generated by sharing resources, but have a hard time adapting to a new mental framework. ...... I’ve been researching the growth patterns of 50 digital powered organizations (from Wikipedia, to Spotify or AirBnb) that have grown at least 50% per year (in users, revenue and impact) since 2008. As I had predicted, platforms that have taken advantage of the socio-technological landscape as well as distributed or common resources and have integrated these new agents into their system or empowered their customers to find new roles, have grown faster than centralized service organizations. ........ Collaborative economy and open source projects have been financed by crowdfunding and P2P up to a point, but for the time being it is difficult to think of alternatives to VC in specific stages of growth. On the other hand, professional investors gain a profound insight into the businesses they invest in and can see when a long term view serves it better. Crowdfinancing, project currencies or open value chains are still experimental but promising. ........

we are going to see major changes in the next fifteen years towards a more fair and open society. Technology will make us more connected and thus aware of interdependence, ecology will make us energetically as autonomous as we can, economy will embrace the benefits of contributing to commons, and transparency will bring us trust in institutions.

...... I usually define a community as a group of people who share a common resource. Till the invention of the world wide web, communities where mostly confined to local environments as trust had to be generated face to face. The distributed structure of the Internet has allowed this traditional form of organization to scale directly to a global dimension. We are seeing new commons arising in all domains, and effectively already are in the age of communities! .......

We are entering an era of abundance, absolute abundance of knowledge and relative abundance of material goods.

We need a new version of capitalism for the jobless future
Andreessen steadfastly believes that the same exponential curve that is enabling creation of an era of abundance will create new jobs faster and more broadly than before, and calls my assertions that we are heading into a jobless future a luddite fallacy. ........ it’s a matter of public policy and preparedness. With the technology advances that are presently on the horizon, not only low-skilled jobs are at risk; so are the jobs of knowledge workers. ...... The jobs that will be created will require very specialized skills and higher levels of education — which most people don’t have. ..... millions will face permanent unemployment. I worry that if we keep brushing this issue under the rug, social upheaval will result. ......

Within 10 years, we will see Uber laying off most of its drivers as it switches to self-driving cars; manufacturers will start replacing workers with robots; fast-food restaurants will install fully automated food-preparation systems; artificial intelligence–based systems will start doing the jobs of most office workers in accounting, finance and administration. The same will go for professionals such as paralegals, pharmacists, and customer-support representatives. All of this will occur simultaneously, and the pace will accelerate in the late 2020s.

....... With less need for human labor and judgment, labor will be devalued relative to capital and even more so relative to ideas and machine learning technology. In an era of abundance and increasing income disparity, we may need a version of capitalism that is focused on more than just efficient production and also places greater prioritization on the less desirable side effects of capitalism. ........ China will be the biggest global loser because of the rapid disappearance of its manufacturing jobs. It has not created a safety net, and income disparity is already too great, so we can expect greater turmoil there. ....... Carlos Slim Domit .. He predicted the emergence of tens of millions of new service jobs in Mexico through meeting the Mexican people’s basic needs and enabling them to spend time on leisure and learning. He sees tremendous opportunities to build infrastructure where there is none, and to improve the lives of billions of people who presently spend their lives trying to earn enough on which to subsist. ........ Countries such as India and Peru and all of Africa will see the same benefits — for at least two or three decades, until the infrastructure has been built and necessities of the populations have been met. ...... Then there will not be enough work even there to employ the masses........Slim’s solution to this is to institute

a three-day workweek

so that everyone can find employment and earn the money necessary for leisure and entertainment. This is not a bad idea. In the future we are heading into, the cost of basic necessities, energy, and even luxury goods such as electronics will fall low enough to seem almost free — just as cell-phone minutes and information cost practically nothing now. It is a matter of sharing the few jobs that will exist in an equitable way......... The concept of

a universal basic income

is also gaining popularity worldwide as it becomes increasingly apparent that declining costs and the elimination of bureaucracies, make it possible for governments to provide citizens with income enough for the basic necessities. The idea is to give everyone a stipend covering living costs and to get government out of the business of selecting what social benefits people should have. The advantage of this approach is that workers gain the freedom to decide how much to work and under what conditions. Enabling individual initiative in the work that people pursue, in fields ranging from philosophy and the arts to pure science and invention, will result in their enrichment of their cultures in ways we can’t foresee. ....... With sensors, new nanomaterials and composites, and 3D-printing technologies, we could be building massive smart cities that use energy more efficiently and provide a better quality of life for their inhabitants. ....... Another potential solution, the brainchild of Internet pioneer Vint Cerf and entrepreneur David Nordfors, is to develop A.I. software that matches jobs to the skills, talent, passions, experiences, and values of each individual on the planet. They say that there is an almost infinite amount of work that needs to be done and that only a fraction of all human capacity is being used today. People hate their jobs, consequently losing tremendous amounts of productivity. With jobs tailored to a person’s passions, we could create a work environment in which people give 100 percent of their capacity to work and the economy expands because more is being done......

We need to be prepared and to develop a new version of capitalism that benefits all.





The (Needed) New Economics of Abundance
Molecular manufacturing coupled with AI could bring about a “personal manufacturing” revolution and a new era of abundance. But abundance could be highly disruptive, so we need to design a new economics of abundance so society is prepared for it. .... For centuries, we have built cultures and economies around scarcity. Economics is the “study of how human beings allocate scarce resources”1 in the most efficient way and conventional wisdom agrees that regulated capitalism results in the most efficient allocation of those scarce resources. ...

But what happens if resources are not scarce?

....... Is there even a point to talking about the “economics of abundance” in a culture where economic equations are entirely oriented around scarcity? ..... “My college textbook, Gregory Mankiw’s otherwise excellent Principles of Economics, doesn’t mention the word abundance. And for good reason:

If you let the scarcity term in most economic equations go to nothing, you get all sorts of divide-by-zero problems. They basically blow up.”

......... molecular manufacturing as “the automated building of products from the bottom up, molecule by molecule, with atomic precision. This will make products that are extremely lightweight, flexible, durable, and potentially very ‘smart’.” And cheap. ........ “personal manufacturing”. Such personal nanofactories (PNs) already have been envisioned and are likely to be similar in look and ease of use as a printer or microwave oven. ..... The advent of PNs should bring the cost of most nonfood necessities to near zero.

Much of the raw material for most objects we commonly use can be found in air and dirt

...... If we build things from the molecules up (and conversely, break things down into their component molecules for reuse),

materials cost will nearly disappear.

Information would then become the most expensive resource. Meanwhile, computing power — information management — continues to expand exponentially even as its cost drops precipitously. ....... as true artificial intelligence (AI) approaches, computers will become self-programming, and information cost may drop even more dramatically. It’s already happening. .....

even food eventually could be manufactured on the kitchen countertop personal at practically no materials cost.

...... What would an economy based on abundance look like? What would we call it? Could we convince the lawmakers, the regulators, and those who currently benefit most from a system based on scarcity to relinquish what has worked so well for them? ...... we must drive toward an outcome whereby the benefits of molecular manufacturing accrue to the greatest number of people. War, poverty, and business drive my reasoning. .....

To date, all our technological and economic progress has produced a world at war and in poverty. War is largely fought over scarce resources. Widespread wealth (through universal distribution of PNs) would remove the apparent fuel for most wars.

...... 2.7 billion humans live below a level necessary to meet basic needs. The organization says that this kind of poverty includes hunger, lack of shelter, no access to medicines, and losing a child to illness brought about by unclean water ....... This discussion needs to happen now, before entrenched interests develop protections and harden regulations adapted for maximum short-term profits while stifling innovation. Market forces can be too slow. What’s needed is a means to produce broad and inexpensive licensing so that early breakthroughs in molecular manufacturing can quickly benefit a broad swath of humanity. ..... Over hundreds of years, we have developed the skills of how to allocate things in short supply. For widespread abundance, we have no experience, no projections, and no economic calculations. Abundance, paradoxically, could be highly disruptive. It is time to design a new economics of abundance, so that abundance can be enjoyed in a society that is prepared for it.

What Esther @kcolbin and Thomas Wells talk about here is part of why I care about web science. Must-read. And I think I'...

Posted by JP Rangaswami on Sunday, November 1, 2015