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Wednesday, July 30, 2014

Group theory

Group theory

From Wikipedia, the free encyclopedia
   
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Various physical systems, such as crystals and the hydrogen atom, can be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.

One of the most important mathematical achievements of the 20th century[1] was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.

History

 
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields. Early results about permutation groups were obtained by Lagrange, Ruffini, and Abel in their quest for general solutions of polynomial equations of high degree. Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory of groups and field theory. In geometry, groups first became important in projective geometry and, later, non-Euclidean geometry. Felix Klein's Erlangen program proclaimed group theory to be the organizing principle of geometry.

Galois, in the 1830s, was the first to employ groups to determine the solvability of polynomial equations. Arthur Cayley and Augustin Louis Cauchy pushed these investigations further by creating the theory of permutation groups. The second historical source for groups stems from geometrical situations. In an attempt to come to grips with possible geometries (such as euclidean, hyperbolic or projective geometry) using group theory, Felix Klein initiated the Erlangen programme. Sophus Lie, in 1884, started using groups (now called Lie groups) attached to analytic problems. Thirdly, groups were, at first implicitly and later explicitly, used in algebraic number theory.

The different scope of these early sources resulted in different notions of groups. The theory of groups was unified starting around 1880. Since then, the impact of group theory has been ever growing, giving rise to the birth of abstract algebra in the early 20th century, representation theory, and many more influential spin-off domains. The classification of finite simple groups is a vast body of work from the mid 20th century, classifying all the finite simple groups.

Main classes of groups

The range of groups being considered has gradually expanded from finite permutation groups and special examples of matrix groups to abstract groups that may be specified through a presentation by generators and relations.

Permutation groups

The first class of groups to undergo a systematic study was permutation groups. Given any set X and a collection G of bijections of X into itself (known as permutations) that is closed under compositions and inverses, G is a group acting on X. If X consists of n elements and G consists of all permutations, G is the symmetric group Sn; in general, any permutation group G is a subgroup of the symmetric group of X. An early construction due to Cayley exhibited any group as a permutation group, acting on itself (X = G) by means of the left regular representation.

In many cases, the structure of a permutation group can be studied using the properties of its action on the corresponding set. For example, in this way one proves that for n ≥ 5, the alternating group An is simple, i.e. does not admit any proper normal subgroups. This fact plays a key role in the impossibility of solving a general algebraic equation of degree n ≥ 5 in radicals.

Matrix groups

The next important class of groups is given by matrix groups, or linear groups. Here G is a set consisting of invertible matrices of given order n over a field K that is closed under the products and inverses. Such a group acts on the n-dimensional vector space Kn by linear transformations. This action makes matrix groups conceptually similar to permutation groups, and the geometry of the action may be usefully exploited to establish properties of the group G.

Transformation groups

Permutation groups and matrix groups are special cases of transformation groups: groups that act on a certain space X preserving its inherent structure. In the case of permutation groups, X is a set; for matrix groups, X is a vector space. The concept of a transformation group is closely related with the concept of a symmetry group: transformation groups frequently consist of all transformations that preserve a certain structure.

The theory of transformation groups forms a bridge connecting group theory with differential geometry. A long line of research, originating with Lie and Klein, considers group actions on manifolds by homeomorphisms or diffeomorphisms. The groups themselves may be discrete or continuous.

Abstract groups

Most groups considered in the first stage of the development of group theory were "concrete", having been realized through numbers, permutations, or matrices. It was not until the late nineteenth century that the idea of an abstract group as a set with operations satisfying a certain system of axioms began to take hold. A typical way of specifying an abstract group is through a presentation by generators and relations,
G = \langle S|R\rangle.
A significant source of abstract groups is given by the construction of a factor group, or quotient group, G/H, of a group G by a normal subgroup H. Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory. If a group G is a permutation group on a set X, the factor group G/H is no longer acting on X; but the idea of an abstract group permits one not to worry about this discrepancy.

The change of perspective from concrete to abstract groups makes it natural to consider properties of groups that are independent of a particular realization, or in modern language, invariant under isomorphism, as well as the classes of group with a given such property: finite groups, periodic groups, simple groups, solvable groups, and so on. Rather than exploring properties of an individual group, one seeks to establish results that apply to a whole class of groups. The new paradigm was of paramount importance for the development of mathematics: it foreshadowed the creation of abstract algebra in the works of Hilbert, Emil Artin, Emmy Noether, and mathematicians of their school.[citation needed]

Topological and algebraic groups

An important elaboration of the concept of a group occurs if G is endowed with additional structure, notably, of a topological space, differentiable manifold, or algebraic variety. If the group operations m (multiplication) and i (inversion),
m: G\times G\to G, (g,h)\mapsto gh, \quad i:G\to G, g\mapsto g^{-1},
are compatible with this structure, i.e. are continuous, smooth or regular (in the sense of algebraic geometry) maps then G becomes a topological group, a Lie group, or an algebraic group.[2]

The presence of extra structure relates these types of groups with other mathematical disciplines and means that more tools are available in their study. Topological groups form a natural domain for abstract harmonic analysis, whereas Lie groups (frequently realized as transformation groups) are the mainstays of differential geometry and unitary representation theory. Certain classification questions that cannot be solved in general can be approached and resolved for special subclasses of groups.
Thus, compact connected Lie groups have been completely classified. There is a fruitful relation between infinite abstract groups and topological groups: whenever a group Γ can be realized as a lattice in a topological group G, the geometry and analysis pertaining to G yield important results about Γ. A comparatively recent trend in the theory of finite groups exploits their connections with compact topological groups (profinite groups): for example, a single p-adic analytic group G has a family of quotients which are finite p-groups of various orders, and properties of G translate into the properties of its finite quotients.

Combinatorial and geometric group theory

Groups can be described in different ways. Finite groups can be described by writing down the group table consisting of all possible multiplications g • h. A more compact way of defining a group is by generators and relations, also called the presentation of a group. Given any set F of generators {gi}i ∈ I, the free group generated by F subjects onto the group G. The kernel of this map is called subgroup of relations, generated by some subset D. The presentation is usually denoted by 〈F | D 〉. For example, the group Z = 〈a | 〉 can be generated by one element a (equal to +1 or −1) and no relations, because n·1 never equals 0 unless n is zero. A string consisting of generator symbols and their inverses is called a word.

Combinatorial group theory studies groups from the perspective of generators and relations.[3] It is particularly useful where finiteness assumptions are satisfied, for example finitely generated groups, or finitely presented groups (i.e. in addition the relations are finite). The area makes use of the connection of graphs via their fundamental groups. For example, one can show that every subgroup of a free group is free.

There are several natural questions arising from giving a group by its presentation. The word problem asks whether two words are effectively the same group element. By relating the problem to Turing machines, one can show that there is in general no algorithm solving this task. Another, generally harder, algorithmically insoluble problem is the group isomorphism problem, which asks whether two groups given by different presentations are actually isomorphic. For example the additive group Z of integers can also be presented by
〈x, y | xyxyx = e〉;
it may not be obvious that these groups are isomorphic.[4]
The Cayley graph of 〈 x, y ∣ 〉, the free group of rank 2.
Geometric group theory attacks these problems from a geometric viewpoint, either by viewing groups as geometric objects, or by finding suitable geometric objects a group acts on.[5] The first idea is made precise by means of the Cayley graph, whose vertices correspond to group elements and edges correspond to right multiplication in the group. Given two elements, one constructs the word metric given by the length of the minimal path between the elements. A theorem of Milnor and Svarc then says that given a group G acting in a reasonable manner on a metric space X, for example a compact manifold, then G is quasi-isometric (i.e. looks similar from the far) to the space X.

Representation of groups

Saying that a group G acts on a set X means that every element defines a bijective map on a set in a way compatible with the group structure. When X has more structure, it is useful to restrict this notion further: a representation of G on a vector space V is a group homomorphism:
ρ : G → GL(V),
where GL(V) consists of the invertible linear transformations of V. In other words, to every group element g is assigned an automorphism ρ(g) such that ρ(g) ∘ ρ(h) = ρ(gh) for any h in G.
This definition can be understood in two directions, both of which give rise to whole new domains of mathematics.[6] On the one hand, it may yield new information about the group G: often, the group operation in G is abstractly given, but via ρ, it corresponds to the multiplication of matrices, which is very explicit.[7] On the other hand, given a well-understood group acting on a complicated object, this simplifies the study of the object in question. For example, if G is finite, it is known that V above decomposes into irreducible parts. These parts in turn are much more easily manageable than the whole V (via Schur's lemma).

Given a group G, representation theory then asks what representations of G exist. There are several settings, and the employed methods and obtained results are rather different in every case: representation theory of finite groups and representations of Lie groups are two main subdomains of the theory. The totality of representations is governed by the group's characters. For example, Fourier polynomials can be interpreted as the characters of U(1), the group of complex numbers of absolute value 1, acting on the L2-space of periodic functions.

Connection of groups and symmetry

Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This occurs in many cases, for example
  1. If X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups.
  2. If the object X is a set of points in the plane with its metric structure or any other metric space, a symmetry is a bijection of the set to itself which preserves the distance between each pair of points (an isometry). The corresponding group is called isometry group of X.
  3. If instead angles are preserved, one speaks of conformal maps. Conformal maps give rise to Kleinian groups, for example.
  4. Symmetries are not restricted to geometrical objects, but include algebraic objects as well. For instance, the equation
x^2-3=0
has the two solutions +\sqrt{3}, and -\sqrt{3}. In this case, the group that exchanges the two roots is the Galois group belonging to the equation. Every polynomial equation in one variable has a Galois group, that is a certain permutation group on its roots.
The axioms of a group formalize the essential aspects of symmetry. Symmetries form a group: they are closed because if you take a symmetry of an object, and then apply another symmetry, the result will still be a symmetry. The identity keeping the object fixed is always a symmetry of an object.
Existence of inverses is guaranteed by undoing the symmetry and the associativity comes from the fact that symmetries are functions on a space, and composition of functions are associative.
Frucht's theorem says that every group is the symmetry group of some graph. So every abstract group is actually the symmetries of some explicit object.

The saying of "preserving the structure" of an object can be made precise by working in a category. Maps preserving the structure are then the morphisms, and the symmetry group is the automorphism group of the object in question.

Applications of group theory

Applications of group theory abound. Almost all structures in abstract algebra are special cases of groups. Rings, for example, can be viewed as abelian groups (corresponding to addition) together with a second operation (corresponding to multiplication). Therefore group theoretic arguments underlie large parts of the theory of those entities.

Galois theory uses groups to describe the symmetries of the roots of a polynomial (or more precisely the automorphisms of the algebras generated by these roots). The fundamental theorem of Galois theory provides a link between algebraic field extensions and group theory. It gives an effective criterion for the solvability of polynomial equations in terms of the solvability of the corresponding Galois group. For example, S5, the symmetric group in 5 elements, is not solvable which implies that the general quintic equation cannot be solved by radicals in the way equations of lower degree can.
The theory, being one of the historical roots of group theory, is still fruitfully applied to yield new results in areas such as class field theory.

Algebraic topology is another domain which prominently associates groups to the objects the theory is interested in. There, groups are used to describe certain invariants of topological spaces. They are called "invariants" because they are defined in such a way that they do not change if the space is subjected to some deformation. For example, the fundamental group "counts" how many paths in the space are essentially different. The Poincaré conjecture, proved in 2002/2003 by Grigori Perelman is a prominent application of this idea. The influence is not unidirectional, though. For example, algebraic topology makes use of Eilenberg–MacLane spaces which are spaces with prescribed homotopy groups. Similarly algebraic K-theory stakes in a crucial way on classifying spaces of groups. Finally, the name of the torsion subgroup of an infinite group shows the legacy of topology in group theory.
A torus. Its abelian group structure is induced from the map C → C/Z+τZ, where τ is a parameter living in the upper half plane.
The cyclic group Z26 underlies Caesar's cipher.

Algebraic geometry and cryptography likewise uses group theory in many ways. Abelian varieties have been introduced above. The presence of the group operation yields additional information which makes these varieties particularly accessible. They also often serve as a test for new conjectures.[8] The one-dimensional case, namely elliptic curves is studied in particular detail. They are both theoretically and practically intriguing.[9] Very large groups of prime order constructed in Elliptic-Curve Cryptography serve for public key cryptography. Cryptographical methods of this kind benefit from the flexibility of the geometric objects, hence their group structures, together with the complicated structure of these groups, which make the discrete logarithm very hard to calculate. One of the earliest encryption protocols, Caesar's cipher, may also be interpreted as a (very easy) group operation. In another direction, toric varieties are algebraic varieties acted on by a torus. Toroidal embeddings have recently led to advances in algebraic geometry, in particular resolution of singularities.[10]

Algebraic number theory is a special case of group theory, thereby following the rules of the latter. For example, Euler's product formula
\begin{align} \sum_{n\geq 1}\frac{1}{n^s}& = \prod_{p \text{ prime}} \frac{1}{1-p^{-s}} \\ \end{align} \!
captures the fact that any integer decomposes in a unique way into primes. The failure of this statement for more general rings gives rise to class groups and regular primes, which feature in Kummer's treatment of Fermat's Last Theorem.
The circle of fifths may be endowed with a cyclic group structure
  • In physics, groups are important because they describe the symmetries which the laws of physics seem to obey. According to Noether's theorem, every continuous symmetry of a physical system corresponds to a conservation law of the system. Physicists are very interested in group representations, especially of Lie groups, since these representations often point the way to the "possible" physical theories. Examples of the use of groups in physics include the Standard Model, gauge theory, the Lorentz group, and the Poincaré group.
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CLICHES OF PROGRESSIVISM

Freeman

 
 
 

#7 – The Free Market Ignores the Poor

(Editor’s Note: This week’s cliché was authored decades ago by FEE’s founder, Leonard E. Read, and originally appeared in the first edition of Clichés of Socialism. Barely a word has been changed and though a few numbers are dated, the essay’s wisdom is as timely and relevant today as it ever was.)
The Foundation for Economic Education (FEE) is proud to partner with Young America’s Foundation (YAF) to produce “Clichés of Progressivism,” a series of insightful commentaries covering topics of free enterprise, income inequality, and limited government.

Our society is inundated with half-truths and misconceptions about the economy in general and free enterprise in particular. The “Clichés of Progressivism” series is meant to equip students with the arguments necessary to inform debate and correct the record where bias and errors abound.

The antecedents to this collection are two classic FEE publications that YAF helped distribute in the past: Clichés of Politics, published in 1994, and the more influential Clichés of Socialism, which made its first appearance in 1962. Indeed, this new collection will contain a number of essays from those two earlier works, updated for the present day where necessary. Other entries first appeared in some version in FEE’s journal, The Freeman. Still others are brand new, never having appeared in print anywhere. They will be published weekly on the websites of both YAF and
FEE: www.yaf.org and www.FEE.org until the series runs its course. A book will then be released in 2015 featuring the best of the essays, and will be widely distributed in schools and on college campuses.

#7 – The Free Market Ignores the Poor

Once an activity has been socialized for a spell, nearly everyone will concede that that’s the way it should be.  Without socialized education, how would the poor get their schooling? Without the socialized post office, how would farmers receive their mail except at great expense? Without Social Security, the aged would end their years in poverty! If power and light were not socialized, consider the plight of the poor families in the Tennessee Valley!

Agreement with the idea of state absolutism follows socialization, appallingly. Why? One does not have to dig very deep for the answer.

Once an activity has been socialized, it is impossible to point out, by concrete example, how men in a free market could better conduct it. How, for instance, can one compare a socialized post office with private postal delivery when the latter has been outlawed? It’s something like trying to explain to a people accustomed only to darkness how things would appear were there light. One can only resort to imaginative construction.

To illustrate the dilemma: During recent years, men and women in free and willing exchange (the free market) have discovered how to deliver the human voice around the earth in one twenty-seventh of a second; how to deliver an event, like a ball game, into everyone’s living room, in color and in motion, at the time it is going on; how to deliver 115 people from Los Angeles to Baltimore in three hours and 19 minutes; how to deliver gas from a hole in Texas to a range in New York at low cost and without subsidy; how to deliver 64 ounces of oil from the Persian Gulf to our Eastern Seaboard—more than half-way around the earth—for less money than government will deliver a one-ounce letter across the street in one’s home town. Yet, such commonplace free market phenomena as these, in the field of delivery, fail to convince most people that “the post” could be left to free market delivery without causing people to suffer.

Now, then, resort to imagination: Imagine that our federal government, at its very inception, had issued an edict to the effect that all boys and girls, from birth to adulthood, were to receive shoes and socks from the federal government “for free.” Next, imagine that this practice of “free shoes and socks” had been going on for lo, these 173 years! Lastly, imagine one of our contemporaries—one with a faith in the wonders of what can be wrought when people are free—saying, “I do not believe that shoes and socks for kids should be a government responsibility. Properly, that is a responsibility of the family. This activity should never have been socialized. It is appropriately a free market activity.”

What, under these circumstances, would be the response to such a stated belief? Based on what we hear on every hand, once an activity has been socialized for even a short time, the common chant would go like this, “Ah, but you would let the poor children go unshod!”

However, in this instance, where the activity has not yet been socialized, we are able to point out that the poor children are better shod in countries where shoes and socks are a family responsibility than in countries where they are a government responsibility. We’re able to demonstrate that the poor children are better shod in countries that are more  free than in countries that are less free.

True, the free market ignores the poor precisely as it does not recognize the wealthy—it is “no respecter of persons.” It is an organizational way of doing things featuring openness, which enables millions of people to cooperate and compete without demanding a preliminary clearance of pedigree, nationality, color, race, religion, or wealth. It demands only that each person abide by voluntary principles, that is, by fair play. The free market means willing exchange; it is impersonal justice in the economic sphere and excludes coercion, plunder, theft, protectionism, subsidies, special favors from those wielding power, and other anti-free market methods by which goods and services change hands. It opens the way for mortals to act morally because they are free to act morally.

Admittedly, human nature is defective, and its imperfections will be reflected in the market (though arguably, no more so than in government). But the free market opens the way for men to operate at their moral best, and all observation confirms that the poor fare better under these circumstances than when the way is closed, as it is under socialism.
Leonard E. Read
Founder and President
Foundation for Economic Education, 1946–1983
 

Summary


  • Explaining how a socialized activity could actually be done better by private, voluntary means in a free market is a little like telling a blind man what it would be like to see. But that doesn’t mean we just give up and remain blind.
  • Examples of the wonders of free and willing exchange are all around us. We take them for granted. Just imagine what it would be like if shoes and socks had been a government monopoly for a couple hundred years, versus the variety and low cost of shoes as now provided in free countries by entrepreneurs.
  • Free markets open the way for people to act morally, but that doesn’t mean they always will; nor should we assume that when armed with power, our behavior will suddenly become more moral.
  • For more information, see:
 "The Man Behind the Hong Kong Miracle" by Lawrence W. Reed: http://tinyurl.com/mkkrcpu
"Can the Free Market Provide Public Education?" by Sheldon Richman: http://tinyurl.com/m8vjqvp
"Presidents and Precedents" by Lawrence W. Reed: http://tinyurl.com/pfrmbux
"The Miracle and Morality of the Market" by The Freeman: http://tinyurl.com/ocva6hu
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Letter: It is unfair to demonize fracking

Letter: It is unfair to demonize fracking

Posted:   07/29/2014 11:44:09 AM EDT

To the editor of THE EAGLE:
 
The Eagle's July 17 editorial ("Fracking on shaky ground:) made some pretty strong claims against fracking, but your readers would have benefited from some additional clarity and context.
For example, you claimed "four wells used for fracking" caused one out of every five quakes from Colorado to the Atlantic Coast. That is not true. The wells studied were disposal wells, which are not " used for fracking." Interestingly, your editorial later acknowledged the culprit was disposal wells, but not before presenting a demonstrable falsehood to your readers.
 
You also asserted, without basis, that " no one" knows what happens to wastewater after it is injected. That's an interesting claim, considering the fact that the U.S. Environmental Protection Agency has been monitoring and regulating disposal wells (categorized as Class II under the Safe Drinking Water Act) for decades. The EPA calls wastewater disposal a "safe" process.
 
Science supports EPA's position. The National Research Council, part of the National Academy of Sciences, concluded recently that "very few [seismic] events have been documented over the past several decades relative to the large number of disposal wells in operation." The Cornell study cited in your editorial also noted that "thousands" of disposal operate " a seismically." As for claiming "the burden is on industry" to prove disposal doesn't cause earthquakes: How can you prove a negative?
Leaving aside the fact that the vast majority of disposal wells do not and have not caused seismic events, suggesting an industry that employs hundreds of thousands of Americans is " guilty until proven innocent" is a dangerous road.
 
Moreover, why should anti-fracking groups, whose agenda is so extreme that it has been rejected by the Obama administration and Democratic governors across the country, get a free pass to accuse the industry of whatever it likes without scrutiny? Facts and evidence should trump convenient scapegoats.
 
The industry supports additional research on this issue, and both scientists and industry have acknowledged that there are straightforward fixes for problematic wells, including reducing flow rates. In the meantime, while it's easy to score search engine hits from articles that demonize "fracking," we don't solve any problems by leaving out context and key facts purely to support a predetermined narrative.
STEVE EVERLEY
Washington, DC
 
The writer is team lead for Energy In Depth. According to its website, Energy In Depth is a research, energy and outreach campaign launched in 2009 by the Independent Petroleum Association of America.
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Less Water on Exoplanets than Expected


 

 

 

 

 

 

 

 

 

 

 

Less Water on Exoplanets than Expected

Posted by Tom Hartsfield July 30, 2014
Link:  http://www.realclearscience.com/blog/2014/07/how_do_we_detect_water_on_exoplanets.html
Distant stars are pinpoint specks, too small to resolve. Exoplanets are ten times smaller in diameter and don't emit light of their own. They're vastly fainter than any star; we couldn't even see a single one until 20 years ago.

That's what makes a painstaking new study completed using the Hubble Space Telescope so beautiful. It not only located three exoplanets, but painstakingly measured the water composition of their atmospheres. There's water, but it's less than we expected. How is this possible?
Astronomers often find exoplanets by watching the light of many stars. If the brightness of a particular sun has a tiny (usually 1% or smaller) flicker that repeats in a regular pattern, we can calculate whether a planet's continuous orbit crossing in front of the star is the cause. Astronomical techniques have now evolved to the point that we not only look for a flicker in the total light from the star: we can see precisely how much each and every color of the rainbow flickers.

This is a more difficult version of the way we've been investigating stars for a century. We know the chemical makeup of far away suns because of their absorption spectrum: the colors missing from the light they broadcast to us.

The searing hot plasma at the core of a massive star emits light of all colors in the spectrum. The elements in the atmosphere of the star absorb a little bit of that light however, leaving certain colors absent from the light that reaches us.

Due to the quantum nature of energy states in atoms and molecules, they only absorb and emit energy in certain exact amounts, i.e., with very certain electromagnetic frequencies.

Water molecules absorb and emit a certain group of wavelengths due to their quantum transitions too. Upon absorbing an infrared photon of the correct wavelength (1380 nm for example), the atoms of the molecule will be kicked into vibrating back and forth in a certain pattern. This picture shows what such states look like.

An exoplanet atmospheric survey first looks to see how much light the star emits toward us at the colors absorbed by water when nothing else blocks any of the light. When the planet passes between the star and our telescopes during its orbit, we look at each of these wavelengths of light and see how much of it has been blocked. A certain percentage will be blocked solely by the mass of the planet itself.

However, a small part of the star's light will pass through the atmosphere of the planet and escape to the other side. We then look at this light that has passed through the sky of an alien world to see if it is missing a greater amount of those wavelengths that water likes to absorb.

The amount of water present in the measured alien atmosphere was actually something around 100 times less than predicted. This could mean that our models of how elements are distributed and retained in planet formation need tweaking. It could also be due to patterns of cloud or haze in the atmospheres of the planets. Measurements like these are the payoff of incredible recent improvements in astronomical instruments and techniques.

If this trend continues, it may not be long before we begin to look at something even more exciting: the atmospheres of earth-like planets.

(AP photo)

Tom Hartsfield is a physics PhD candidate at the University of Texas.
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Big government is bad for the little guy.

Big government is bad for the little guy.

July 29, 2014 4:00 AM     

Kevin D. Williamson
I recently had a conversation with an intensely conservative businessman whose first foray into politics was fighting for a tax hike on his business and others like it. The little town where he lived as a young man had no paved roads, waterworks, or sewage facilities, and the men who had the most invested in the town knew that it needed these to grow, which of course it did. That’s part of what Barack Obama and Elizabeth Warren are referring to with their “you didn’t build that” rhetoric, though they draw the wrong conclusions. They are also sometimes wrong in the specifics, too: The gentleman I was speaking with organized a few other businessmen to install streetlights at their own expense, with the understanding that the town fathers would pay them back when they could afford it. If you’re looking for an example of how small government is good government, a handshake deal to put in streetlights is a pretty good one. That is government at a scale that people can control, manage — and keep an eye on.
 
It is important to keep government small, but scale is not the only concern: Even the pettiest bureaucracy can descend into indolence and corruption. We talk a great deal about the level of government spending, but pay relatively little attention to a much more basic concern: It matters — a great deal — what government spends that money on. Even the wooliest anarcho-capitalist must look with some sympathy and admiration upon the small-scale model of township government that once characterized New England and the West. “But who will pave the roads?” is a standing libertarian punchline (“The federal government spends enormous sums of money getting monkeys addicted to cocaine, the police have murdered your puppies — But who will pave the roads?”) and, as noted in a certain volume of political speculation, the first paved intercity road in these United States was in fact privately built, suggesting that private enterprise is more than capable of road-making. But it was as a matter of history largely governments that paved the roads, built the sewage systems, drained the swamps, etc. And there was a time when governments, particularly at the local level, did a pretty good job of it.

There was more room for them to experiment in an era in which the federal government did relatively little. At the end of the 19th century, the largest single federal expense was veterans’ pensions, which accounted for nearly half of federal spending. As James Carafano notes, that pension system was a swamp of Republican graft, the original dependency agenda; but in real terms, the money lost to graft today in programs such as Medicare and Medicaid probably would have paid for all of the operations of the federal government in the late 19th century, with a surplus. So easy and profitable is Medicare fraud that New York’s Bonanno mafia clan set up a Florida operation specifically for that purpose. (Florida is the Augean stables of Medicare fraud.) Some of the graft is explicitly criminal, but much of it is perfectly legal: subsidies for cronies, sweetheart loans and generous tax treatment for politically connected businesses, etc. The Solyndra debacle may not have been a crime, but it was criminal.
Big government, big expenses, big corruption — big problem.
 
On the one hand, we have the small-town entrepreneur yearning for sidewalks and streetlights; on the other, we have dodgy “Five Aces” federal contracts and Al Gore’s federally enabled greenmongering. Between those two points there exists a spectrum of possible configurations of government, and the fundamental political debate of our time is whether we’re on the right side of that spectrum or the wrong side. Conservatives want to prune back the vines, and progressives want them to grow thicker.
 
How’s that working out in the laboratories of the Left?
 
Progressives argue that we need deeper government involvement in the economy in order to assuage the ill effects of economic inequality. But, as Joel Kotkin points out, inequality is the most pronounced in places where progressives dominate: New York City, San Francisco, Los Angeles, Chicago. The more egalitarian cities are embedded in considerably more conservative metropolitan areas in conservative states. “Part of the difference,” Mr. Kotkin writes, “is the strong growth of higher-paid, blue-collar jobs in places like Houston, Oklahoma City, Salt Lake, and Dallas compared to rapidly de-industrializing locales such as New York, San Francisco, Chicago, and Los Angeles.
Even Richard Florida, the guru of the ‘creative class,’ has admitted that the strongest growth in mid-income jobs has been concentrated in red-state metros such as Salt Lake City, Houston, Dallas, Austin, and Nashville. Some of this reflects a history of later industrialization but other policies — often mandated by the state — encourage mid-income growth, for example, by not imposing high energy prices with subsidies for renewables, or restricting housing growth in the periphery. Cities like
Houston may seem blue in many ways but follow local policies largely indistinguishable from mainstream Republicans elsewhere.” In Detroit, Chicago, and Philadelphia, African Americans earn barely half of what whites earn —  and in San Francisco, African Americans earn less than half of what whites earn. Hispanics in Boston earn 50 percent of what whites make; but it is 84 percent in Riverside County, Calif., a traditional Republican stronghold (it holds the distinction of being one of only two West Coast counties to have gone for Hoover over FDR and is Duncan Hunter’s turf), and the figures are comparable in places such as Phoenix and Miami.
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The Curious Evolution of Artificial Life

The Curious Evolution of Artificial Life

From:  http://www.technologyreview.com/view/529491/the-curious-evolution-of-artificial-life/?utm_campaign=socialsync&utm_medium=social-post&utm_source=google-plus
 
July 30, 2014
 
The term “Artificial Life” emerged in 1986 when the American computer scientist Christopher Langton coined it while organizing the first “Workshop on the Synthesis and Simulation of Living Systems.” Since then the idea of artificial life has spread through computer science into gaming, the study of artificial intelligence, and beyond.

One important factor in this spread has been the Web and the way it allows networked computing to generate complex environments in which artificial organisms can thrive and evolve. Today, Tim Taylor from Monash University in Australia outlines the history of artificial life on the Web and the way it might evolve in the future.

He divides the history of Web-based artificial life into two periods: before and after 2005, a characterization that corresponds roughly with the emergence of Web 2.0 and the collaborative behaviors that it allows.

One of the earliest networked artificial life experiments was based on the well-known A-Life system, Tierra. This was created in the early 1990s by the ecologist Tom Ray to simulate in silico the basic processes of evolutionary and ecological dynamics. After Ray began his work, he soon recognized the potential of the Web to create a large complex environment in which digital organisms could freely evolve. So he set up a project called Network Tierra to exploit this potential

The results of this experiment were mixed. One goal of Network Tierra was to reproduce the
Cambrian explosion in which single-celled organisms on Earth evolved rapidly into multicellular ones and then into more complex animals.

The in silico experiment began with a human-designed multicellular organism consisting of two different cell types. This survived under natural selection, a significant success in itself, but the number of cell types never increased beyond two.

Nobody knows how or why the Cambrian explosion occurred but artificial life experiments have the potential to throw some important light on the issue, despite Tierra’s limited success.
At about the same time, various researchers launched a variety of other Web-based artificial life projects. These included Technosphere, a project in which online users could design creatures, release them into a virtual world and then receive email updates at key moments in their lives, for example when they interacted with other artificial animals. At one point Technosphere had a population of 90,000 creatures.

The online virtual world of Second Life emerged at about the same time that the Web was transitioning from Web 1.0 to Web 2.0. This world attracted a couple of interesting artificial life experiments in which fully functioning ecosystem allowed various types of plants and animals to evolve.

The emergence of Web 2.0 allowed more vibrant collaboration and interaction. One of the key technologies that makes this possible is client-side storage and computation in which most of the work is done by the user’s browser. One example is Pfeiffer, a system in which snowflakes of different patterns evolve under the influence of the user’s selection. All the work is done in the browser.

Taylor’s favorite Web-based artificial life project is a project known as The Wilderness Downtown. This combines A-life technologies such as flocking with real-time animation superimposed on
Google Street View images of any address the user enters.

Taylor was clearly impressed when he first visited the site: “I was sure that what I had just witnessed would change the face of Artificial Life research.”

Indeed, The Wilderness Downtown was highly acclaimed and won many awards. But it’s fair to say that it hasn’t yet changed the face of artificial life research. One reason for this is that the commercial development of artificial life technologies are significantly ahead of academic work.
This is reflected in the success of a number of ventures that have gained Kickstarter funding. For example, WigglePlanet recently raised over $15,000 to fund the development of a project combining artificial life and augmented reality. Even more impressively, Steve Grand one of the early pioneers of artificial life games, has raised over $50,000 on Kickstarter to fund the development of a secretive A-Life project called Grandroids.

Perhaps commercial projects are the future for Web-based artificial life. But even so, there are many interesting scientific questions that artificial life could surely help to answer. Not least of these is the origin of the Cambrian explosion and a more detailed study of the factors and processes that have influenced evolution on Earth.

The fact that artificial life has fallen out of fashion in the academic world may be something to lament but it also provides an interesting opportunity.

Ref: arxiv.org/abs/1407.5719 : Artificial Life and the Web: WebAL Comes of Age
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White House Pushes Financial Case for Carbon Rule

White House Pushes Financial Case for Carbon Rule

By CORAL DAVENPORT
 
           

 
The report is part of the White House’s effort to increase public support for President Obama’s climate-change agenda, chiefly an Environmental Protection Agency proposal targeting coal-fired power plants, the nation’s largest source of planet-warming pollution. The E.P.A. will hold public hearings on the proposal, which are expected to be heated, this week in Atlanta, Denver, Pittsburgh and Washington.
 
The rule could lead to the shutdown of hundreds of power plants, a decline in domestic coal production, an increase in electricity rates and a fundamental transformation of the nation’s power supply. The White House has repeatedly sought to make the case that the long-term cost of not cutting carbon emissions — including longer droughts, worse floods and bigger wildfires that will damage homes, businesses and the nation’s infrastructure — will be higher than the short-term expense of carrying out the regulation.A Sierra Club volunteer, Alex Burke, outside an E.P.A. hearing in Denver. Brennan Linsley/Associated Press
 
Jason Furman, the chairman of the White House Council of Economic Advisers, said the report was intended to explain “why the administration is doing so many things on so many levels to deal with climate change.” He added, “Each decade we delay action results in added cost.”
The report concludes that climate-change costs will increase 40 percent for each decade that nations do not curb carbon emissions.
 
Americans for Prosperity, the Tea Party group backed by Koch Industries, the Kansas conglomerate run by Charles G. and David H. Koch, is planning demonstrations outside the hearings to protest the regulation aimed at coal-fired power plants.
 
“President Obama’s E.P.A. is waging a war on traditional affordable energy through burdensome regulations and unrealistic mandates,” the group’s president, Tim Phillips, said in a statement. “It’s time for the American people to stand up to this federal overreach, and send a message that they cannot afford to pay for Obama’s environmental ideology.”
 
The Senate minority leader, Mitch McConnell, Republican of Kentucky, a state that is heavily dependent on coal, is expected to speak at the public hearing in Washington about losses of coal-mining jobs under the proposal. The American Coalition for Clean Coal Electricity, which lobbies for the coal industry, said it would show videos criticizing the plan outside each hearing site.
 
The Environmental Defense Fund, which is in favor of the rule, is planning rallies that are intended to focus on the dangers of climate change.
 
The White House report adds to a growing stack of research linking climate change to economic costs. A report titled “Risky Business,” issued last month by a bipartisan coalition backed by Michael R. Bloomberg, the former mayor of New York, and Tom Steyer, the billionaire and environmental activist, among others, also concluded that the long-term costs of carbon pollution would be greater than the expense of cutting emissions.
 
Congressional Democrats are working on their own messages. The Senate Budget Committee, led by Patty Murray, Democrat of Washington, conducted a hearing on Tuesday to show the effect of climate change on the federal budget. Over the past decade, federal spending during droughts, floods and wildfires has reached record levels.
 
“It’s becoming clearer and clearer that if you care about the deficit, you need to care about climate change,” Ms. Murray said in a statement. “We’ve got a responsibility to leave a stronger country for our children and grandchildren, and that means addressing climate change to help the environment, help the economy and help the federal budget.”
 
Democrats hope that argument will win over some fiscally conservative Republicans. Most Republicans have said that the E.P.A. climate-change rules exemplify what they call the Obama administration’s overreach.
 
At a hearing last week, Senator Jeff Sessions of Alabama, the ranking Republican on the Senate Budget Committee, told the E.P.A. administrator, Gina McCarthy: “You don’t run the country. American people run the country.”
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The Atmospheres of the Solar System

The Atmospheres of the Solar System

07/25/2014 from http://www.compoundchem.com/2014/07/25/planetatmospheres/
 
Atmosphere Chemistry of the Solar System Planets
 
We’re heading out of this world for today’s post, to examine the atmospheric compositions of the other planets in the solar system, as well as our own. Practically every other planet in our solar system can be considered to have an atmosphere, apart from perhaps the extremely thin, transient atmosphere of Mercury, with the compositions varying from planet to planet. Different conditions on different planets can also give rise to particular effects.

Mercury
Mercury doesn’t really have an atmosphere in the strictest sense of the word – its incredibly thin atmosphere is estimated to be over a trillion times thinner than Earth’s. Its gravity is about 38% that of Earth, so it isn’t capable of retaining much of an atmosphere, and in addition, its proximity to the sun means that the solar wind can carry gases away from the surface. Particles from the solar wind, coupled with the vapourisation of surface rock as a result of meteor impacts, are probably the largest contributors to Mercury’s atmosphere.

Venus
Venus is similar to Earth in several respects: its density, size, mass, and volume are all comparable. The atmosphere is where the similarities end, however. The atmospheric pressure is around 92 times that found at sea level on Earth, with the main gas being carbon dioxide - the result of previous volcanic eruptions on the planet’s surface. Higher in the atmosphere, the planet also has clouds which are a mixture of sulfur dioxide and sulfuric acid. There is a thick layer of carbon monoxide (DJS note:  should be "dioxide") below these clouds, which subjects the surface of the planet to an intense greenhouse effect. Surface temperature on Venus is around 480˚C – much too hot to sustain life as we know it.

Earth
Earth’s atmosphere is composed primarily of nitrogen and oxygen, which are essential for the life which inhabits the planet. The composition of the atmosphere is a direct consequence of the plant life. Plants take in carbon dioxide and expel oxygen through photosynthesis, and without them doing so, it’s likely that the percentage of carbon dioxide in the atmosphere would be significantly higher.
The greenhouse effect that carbon dioxide is partially responsible for is the result of molecules of greenhouse gases absorbing infrared radiation, which is re-radiated towards the surface of the planet and surrounding atmosphere. Without this natural warming effect, temperatures on Earth would be significantly lower worldwide. The greenhouse effect is not the same as global warming – this is the intensification of the natural greenhouse effect via the emission of further greenhouse gases into the atmosphere by human activities. Venus is an extreme example of the runaway consequences of increased global warming!

Mars
The atmosphere of Mars is, much like Venus, composed primarily of carbon dioxide. Having mentioned the extreme greenhouse effect present on Venus as a consequence of the high carbon dioxide levels, it may seem puzzling that the surface temperature of Mars reaches a maximum of 35˚C. This is because the atmosphere of Mars is significantly thinner than that of Venus, so although the proportion of carbon dioxide is comparable, the actual concentration is much lower. The dustiness of the atmosphere gives Mars its characteristic appearance.

Jupiter
Jupiter is the first of the gas giants, and the largest planet in the solar system. Its atmosphere is, interestingly, fairly similar to the composition of the Sun. Unlike the inner planets, there isn’t a clear point at which the atmosphere of Jupiter stops, and the liquid interior of the planet beings. Around a third of the way towards the planet’s core, the pressure is high enough for hydrogen to exist as a metallic liquid, which can conduct electricity and is responsible for Jupiter’s electromagnetic field. Jupiter’s banded cloud system contains varying amounts of ammonia, water, and ammonia-sulfur compound clouds, and also complex sulfur, phosphorous and carbon compounds.

Saturn
Much like Jupiter, the upper clouds in Saturn’s atmosphere are thought to be composed mainly of ammonia ice, with clouds of ammonia hydrosulfide and water lower down. The sulfur present in the atmosphere gives a pale yellow hue to the ammonia clouds. Although not present on the graphic, Saturn’s moon Titan has possibly the most intriguing atmosphere in the solar system, which is the only nitrogen rich atmosphere outside of Earth’s. It’s the only other body in the solar system on which stable surface liquid has ben confirmed, as well as the only other body where it rains – though the rain is liquid methane, rather than water, and it’s estimated there are centuries between each rainfall at specific locations on the surface.

Uranus
The atmosphere of Uranus is, like Jupiter and Saturn, mostly hydrogen and helium. However, the slightly higher levels of methane, particularly in the upper atmosphere, cause greater absorption of red light from the sun, in turn causing the planet to appear a blue-cyan colour. Uranus has the coldest atmosphere in the solar system, at approximately -224˚C, and its atmosphere contains much more water ice than Jupiter and Saturn as a consequence of this.

Neptune
As with Uranus, the blue colouration of Neptune is partially a consequence of the presence of methane – however, as Neptune is a deeper blue, it’s thought that some unknown constituent of the atmosphere must also contribute towards the colour. As the stratosphere of Neptune contains more gaseous hydrocarbons than Uranus, its temperature is marginally higher. Neptune is also home to the strongest winds in the solar system, with their speeds potentially as high as 600 metres per second.

Pluto
Pluto hasn’t been a planet for a fair few years now, but that’s no reason to leave it out of the fun. On that note, after posting this, I threw this graphic together, so that Pluto doesn’t feel left out in the cold:
Pluto Atmospheric Composition
 
 Here’s the atmospheric composition of Titan, where it rains methane every few centuries:
The Atmosphere of Titan
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