Pinwheel of Star Birth

Pinwheel of Star Birth (10/19/10)

This face-on spiral galaxy, called NGC 3982, is striking for its rich tapestry of star birth, along with its winding arms. The arms are lined with pink star-forming regions of glowing hydrogen, newborn blue star clusters, and obscuring dust lanes that provide the raw material for future generations of stars. The bright nucleus is home to an older population of stars, which grow ever more densely packed toward the center.

NGC 3982 is located about 68 million light-years away in the constellation Ursa Major. The galaxy spans about 30,000 light-years, one-third of the size of our Milky Way galaxy.

NGC 3982 – click for 984×1000 image

More: here

Splitting of prime ideals in algebraic number fields

Our series of articles on algebraic number theory is back again. Maybe this time it won't be so sporadic. Stranger things have happened. The previous installment, of which this is a direct continuation, is here. All previous installments are listed here.

When we left off, we were talking about how to determine the way a prime ideal factors in the ring of integers of a quadratic extension of ℚ. Such a field is of the form ℚ(√d) for some square-free d∈ℤ. We were using very simple elementary reasoning with congruences, and we found a fairly simple rule, namely:

If p∈ℤ is an odd prime (i. e., not 2), and K=ℚ(√d) is a quadratic extension of ℚ (where d is not divisible by a square) then

1. p splits completely in K if and only if p∤d and d is a square modulo p.
2. p is prime (i. e. inert) in K if and only if d is not a square modulo p.
3. p is ramified in K if and only if p|d.

The prime 2 behaves a little more weirdly, but the result is that 2 ramifies if and only if d≡2 or 3 (mod 4); 2 is inert if and only if d≡5 (mod 8); 2 splits if and only if d≡1 (mod 8).

One limitation was that our simple reasoning made it necessary to assume that O_K, the ring of integers of K, was a PID (principal ideal domain).

Let's review what we were trying to do. We were investigating the factorization of a prime ideal (p)=pO_ℚ(√d) in O_ℚ(√d). If O_ℚ(√d) is a PID, then there is a simple approach to investigate how p splits. If p splits then (p)=P₁⋅P₂, where P_i=(α_i), i=1,2. Any quadratic extension is Galois, and the Galois group permutes the prime ideal factors of (p). The factors are conjugate, so if α₁=a+b√d we can assume α₂=α₁*=a-b√d. Hence (p)=(α₁)⋅(α₁*)= (α₁α₁*)= (a²-db²).

Taking norms (to eliminate possible units ε∈O_ℚ(√d)) reduces the problem to a Diophantine equation of the form ±p=a²-db². With the problem thus reduced, a necessary condition for (p) to split (or ramify) is that the equation can be solved for a,b∈ℤ. A sufficient condition to show that (p) is inert, i. e. doesn't split or ramify, is to show that the equation can't be solved.

Let's look at how that might work. For example, let d=3. Looking at the equations modulo 3, we have ±p≡a² (mod 3). That is, either p or -p is a square modulo 3. Say p=5. The only nonzero square mod 3 is 1, and 5≢1 (mod 3). However -5≡1 (mod 3), so could we have -5=a²-3b²? Suppose there were some a,b∈ℤ such that -5=a²-3b². Then instead of looking at the equation modulo 3, we could look at it modulo 5, and find that then a²≡3b² (mod 5). If 5 divides either a or b, it divides both, and so 25 divides a²-3b², which is impossible since 25∤5. Therefore 5∤b. ℤ/(5) is a field, so b must have an inverse c such that cb≡1 (mod 5). Therefore, (ac)² ≡ 3(bc)² ≡ 3 (mod 5), and so 3 is a square mod 5. But that can't be, since only 1 and 4 are squares modulo 5. The contradiction implies -5=a²-3b² has no solution for a,b∈Z.

All that does show 5 doesn't split or ramify in ℚ(√3), hence it must be intert, but this approach is messy and still requires knowing that the integers of ℚ(√3) form a PID. We need to find a better way. Fortunately, there is one. But first let's observe that this elementary discussion shows there is a fairly complicated interrelationship among:

1. Factorization of (prime) ideals in extension fields,
2. Whether a given ring of integers is a PID,
3. Whether an integer prime can be represented as the norm of an integer in an extension field,
4. Whether an integer can be represented by an expression of the form a²+db² for a,b∈Z (in the case of quadratic extensions),
5. Whether, for primes p,q∈Z, p is a square modulo q and/or q is a square modulo p.

The problem of representing an integer by an expression like a²+db² is a question of solving a Diophantine equation, and more specifically is of the type known as representing a number by the value of a quadratic form. This question was studied extensively by Gauss, who proved a remarkable and very important result, known as the law of quadratic reciprocity, which relates p being a square modulo q to q being a square modulo p, for primes p,q.

We will take up quadratic reciprocity soon (and eventually much more general "reciprocity laws"), but right now, let's attack head on the issue of determining how a prime of a base field splits in the ring of integers of an extension field. We will use abstract algebra instead of simple arithmetic to deal with this question. For simplicity, we'll assume here that the base field is ℚ, even though many results can be stated, and are often valid, for more arbitrary base fields.

Chinese Remainder Theorem

The first piece of abstract algebra we'll need is the Chinese Remainder Theorem (CRT). Although it's been known since antiquity to hold for the ring ℤ, generalizations are actually true for any commutative ring.

Let R be a commutative ring, and suppose you have a collection of ideals I_j, for j in some index set, j∈J. Suppose that the ideals are relatively prime in pairs. In general that means that I_i+I_j=R if i≠j, and further, the product of ideals, I_i⋅I_j, is I_i∩I_j when i≠j. If R is Dedekind, then each ideal has a unique factorization into prime ideals, and they are relatively prime if I_i and I_j have no prime ideal factors in common when i≠j. Let I be the product of all I_j for j∈J, which is also the intersection of all I_j for j∈J, since the ideals are coprime in pairs.

The direct product of rings R_i for 1≤i≤k is defined to be the set of all ordered k-tuples (r₁, ... ,r_k), for r_i∈R_i, with ring structure given by element-wise addition and multiplication. The direct product is written as R₁×...×R_k, or &Pi_1≤i≤kR_i.

Given all that, the CRT says the quotient ring R/I is isomorphic to the direct product of quotient rings &Pi_1≤i≤k(R/I_i) via the ring homomorphism f(x)=(x+I₁, ... ,x+I_k) for all x∈R.

The CRT is very straightforward, since f is obviously a surjective ring homomorphism, and the kernel is I, since it's the intersection of all I_i. (It's straightforward, at least, if you're used to concepts like "surjective" and "kernel".)

Now we'll apply the CRT in two different situations. First let R be the ring of integers O_K of a finite extension K/ℚ, and I_i=P_i, 1≤i≤g, be the set of all distinct prime ideals of O_K that divide (p)=pO_K for some prime p∈ℤ. Then (p)=P₁^e₁ ⋅⋅⋅ P_g^e_g, where e_i are the ramification indices of each prime factor of (p). An application of CRT then shows that O_K/(p) ≅ Π_1≤i≤g(O_K/P_i^e_i). Recall that for each i, O_K/P_i is isomorphic to the finite field F_qi, where q_i=p^f_i for some f_i, known as the degree of inertia of P_i. (This field is the extension of degree f_i of F_p=ℤ/pℤ.) Further, Σ_1≤i≤ge_if_i=[K:ℚ], the degree of the extension. Check here if you need to review these facts. Specifying how (p) splits in O_K amounts to determination of the P_i and the numbers e_i, f_i, and g.

The second situation where we apply CRT involves the ring of polynomials in one variable over the finite field F_p=ℤ/pℤ, denoted by F_p[x]. Let f(x) be a monic irreducible polynomial with integer coefficients, i. e. an element of ℤ[x]. Let f(x) be f(x) with all coefficients reduced modulo p, an element of F_p[x]. f(x) will not, in general, be irreducible in F_p[x], so it will be a product of powers of irreducible factors: Π_1≤i≤g(f_i(x)^e_i), where f_i(x)∈F_p[x]. Each quotient ring F_p[x]/(f_i(x)) is a finite field that is an extension of F_p of some degree f_i. In general, e_i, f_i, and g will be different, of course, from the same numbers in the preceding paragraph. But the CRT gives us an isomorphism F_p[x]/(f(x)) ≅ &Pi_1≤i≤g(F_p[x]/(f_i(x)^e_i)).

Now, here's the good news. For many field extensions K/ℚ, there exists an appropriate choice of f(x)∈ℤ[x] such that for most primes (depending on K and f(x)), the numbers e_i, f_i, and g will be the same for both applications of the CRT. Consequently, we will have O_K/(p) ≅ F_p[x]/(f(x)), because for corresponding factors of the direct product of rings, O_K/P_i^e_i ≅ F_p[x]/(f_i(x)^e_i). As it happens, most primes don't ramify for given choices of K and f(x), so that things are even simpler, since all e_i=1, and all factors of the direct products are fields.

We can't go into all of the details now as to how to choose f(x) and what the limitations on this result are. However, here are the basics. Any finite algebraic extension of ℚ (and indeed of any base field that is a finite algebraic extension of ℚ) can be generated by a single algebraic number θ: K=ℚ(θ), called a "primitive element". In fact, &theta can be chosen to be an integer of K. Then the ring of integers of K, O_K, is a finitely generated module over ℤ. (A module is like a vector space, except that all coefficients belong to a ring rather than a field.) The number of generators is the index [O_K:ℤ[θ]]. (ℤ[θ] is just all polynomials in θ with coefficients in ℤ.) If p∈ℤ is any prime that does not divide [O_K:ℤ[θ]], then the result of the preceding paragraph holds. If for some p and some choice of θ p does divide the index, then there may be another choice of θ for which p doesn't divide the index. Unfortunately, there are some fields (even of degree 3 over ℚ) where this isn't possible for some choices of p.

The situation is especially nice in the case of quadratic fields, K=ℚ(√d), square-free d∈ℤ. If d≢1 (mod 4); we can take θ=√d and f(x)=x²-d, since O_K=ℤ[√d]. If d≡1 (mod 4), then the index [O_K:ℤ[√d]]=2, and there's a possible problem only for p=2. However, we still have O_K/(p) ≅ F_p[x]/(x²-d) for all p≠2. From that it's obvious that, except for p=2, (p) ramifies if p|d, (p) splits if d is a square modulo p, or else (p) is inert. That is exactly the conclusion we began with at the beginning of this article, on the basis of elementary considerations. Only now we need not assume that O_K is a PID.

There are four important lessons to take away from this discussion.

First, there is a very close relationship between the arithmetic of algebraic number fields and the arithmetic of polynomials over a finite field. Not only do we have the isomorphism discussed above, but it turns out that a number of similar powerful theorems are true for both algebraic number fields and the field of quotients of polynomial rings over a finite field.

Second, a lot of the arithmetic of algebraic number fields can be analyzed in terms of what happens "locally" with the prime ideals of the ring of integers of the field.

Third, many of the results of algebraic number theory are fairly simple if the rings of integers are PIDs (or, equivalently, have unique factorization). Such results often remain true when the rings aren't PIDs, though they can be a lot harder to prove. Often the path to proving such results involves considering the degree to which a given ring of integers departs from being a PID.

Fourth, and perhaps most importantly, abstract algebra is a very powerful tool for understanding algebraic number fields – and it is much easier to work with and understand than trying to use "elementary" methods with explicit calculations involving polynomials and their roots.

We will see these lessons validated time and again as we get deeper into the subject.

So where do we go from here? There are a lot of directions we could take, so we'll probably jump around among a variety of topics.

Monday Randoms.

source: unknown

Monday Randoms.

source: unknown, flickr, unknown

Friday Randoms.

source: unknown

I really like the middle one. I'll try my best to respond to formspring and comments over the weekend!

Arms

source: eme's flickr, unknown, unknown

Selected readings 11/28/10

Interesting reading and news items.

Please leave some comments that indicate which articles you find most interesting or that identify topics you would like to read about, and I will try to include more articles of a similar nature in the future

These items are also bookmarked at my Diigo account.

Bad seeds, bad science, and fairly black cats?

Geneticists have failed to remind the public what the word “genetic” actually means. Heritability implies that gene and environment work, or might be persuaded to work, together. Why, after all, are taxpayers spending money on the double helix if there is no hope of an environmental intervention—a drug, a change in lifestyle, or cancer surgery after the early diagnosis of a somatic mutation—to help those at risk from what they inherit? Everyone in the trade knows this although they fail to mention it except to their first-year undergraduate classes. Transcripts of their lectures should be sent out with every press release. [The Lancet, 10/23/10]

Cancer’s little helpers

No one would have predicted a decade ago that these microRNAs, as the hairpins are called, were involved in cancer, because no one even knew that they existed in people. Mere snippets of RNA — DNA’s underappreciated cousin — these micromolecules are about 22 chemical letters long. But their size belies their power. [Science News, 8/28/10]

Hogan’s holometer: Testing the hypothesis of a holographic universe

In 2008, Fermilab particle astrophysicist Craig Hogan made waves with a mind-boggling proposition: The 3D universe in which we appear to live is no more than a hologram. Now he is building the most precise clock of all time to directly measure whether our reality is an illusion. [Symmetry Breaking, 10/20/10]

The Brain That Changed Everything

When a surgeon cut into Henry Molaison's skull to treat him for epilepsy, he inadvertently created the most important brain-research subject of our time — a man who could no longer remember, who taught us everything we know about memory. Six decades later, another daring researcher is cutting into Henry's brain. Another revolution in brain science is about to begin. [Esquire, 10/25/10]

How Big is the Unobservable Universe?

Based on what we currently think about inflation, this means that the Universe is at least 10^(1030) times the size of our observable Universe! And good luck living long enough to even write that number down. ... All that we know, see, and observe is just one tiny region that slid down that hill fast enough to end inflation, but most of it just keeps on inflating forever and ever. [Starts with a Bang!, 10/27/10]

Revealing the galaxy’s dark side

“In our paper, we discussed a number of astrophysical possibilities for the origin of the signal, including a population of pulsars, cosmic ray interactions and emission from our galaxy's supermassive black hole,” notes Hooper. “And in the end, no combination of any astrophysical sources could give us the signal we’re seeing,” he adds. “Eventually we just got fed up and concluded there doesn’t seem to be a way to explain the signal except for one thing — we tried dark matter and it fit beautifully without any special bells or whistles.” [Science News, 11/20/10]

When Muons Collide

A new type of particle collider known as a muon collider considered a wild idea a decade ago is winning over skeptics as scientists find solutions to the machine's many technological challenges. [Symmetry, 10/1/10]

We all need (a little bit of) sex

Sex costs amazing amounts of time and energy. Just take birds of paradise touting their tails, stags jousting with their antlers or singles spending their weekends in loud and sweaty bars. Is sex really worth all the effort that we, sexual species, collectively put into it? [Scientific American, 11/2/10]

Glia: The new frontier in brain science

Glia, in contrast to neurons, are brain cells that do not generate electrical impulses, and there are a lot of them—85 percent of the cells in the brain. Yet, these cells have been largely neglected for 100 years. I call this new frontier of neuroscience "The Other Brain," because we are only now beginning to explore it. The new findings are expanding our concept of information processing in the brain. They are leading rapidly to new treatments for diseases ranging from spinal cord injury to brain cancer to chronic pain, and Alzheimer's disease. [Scientific American, 11/4/10]

Extra neutrino flavor could be bitter end to Standard Model

What seems to have caught everyone's attention is the suggestion that this might be evidence of what are called sterile neutrinos. Although regular neutrinos barely interact with matter, sterile neutrinos can only interact via gravity, which (if they exist) is what has allowed them to escape our detection to date. Since they'd also be heavier than the regular neutrinos, they would make good dark matter candidates. [Nobel Intent, 11/2/10]

The Neanderthal Romeo and Human Juliet hypothesis

Scientists have had trouble reconciling data from analyses of human mitochondrial DNA and the male Y chromosome. Analyses of human mitochondrial DNA indicate that we all share a common female ancestor 170,000 years ago. Analyses of the Y chromosome indicate that we share a common male ancestor 59,000 years ago. How can we account for the idea that our common grandmother is 111,000 years older than our common grandfather? [Neuroanthropology, 10/26/10]

An idle brain may be the self's workshop

As neuroscientists study the idle brain, some believe they are exploring a central mystery in human psychology: where and how our concept of "self" is created, maintained, altered and renewed. After all, though our minds may wander when in this mode, they rarely wander far from ourselves, as Mrazek's mealtime introspection makes plain. [Los Angeles Times, 8/30/10]

Determining 500th Alien Planet Will Be a Tricky Task

At NASA's last count, astronomers had confirmed the discovery of 494 planets around alien suns. There are signs of dozens more, if not hundreds, but it will take time to weed out which of the detections are actual worlds and which are merely false alarms. [Space.com, 11/11/10]

Tracking Viruses Back in Time

How long have viruses been around? No one knows. Scientists at Portland State University have begun taking the first steps toward answering this question. [Astrobiology, 9/6/10]

Can a 1960s Approach Unify Gravity with the Rest of Physics?

In July mathematicians and physicists met at the Banff International Research Station in Alberta, Canada, to discuss a return to the golden age of particle physics. They were harking back to the 1960s, when physicist Murray Gell-Mann realized that elementary particles could be grouped according to their masses, charges and other properties, falling into patterns that matched complex symmetrical mathematical structures known as Lie groups. [Scientific American, 9/7/10]

Neuroscience: Settling the great glia debate

The consequences of this 'gliotransmission' could be profound. The human brain contains roughly equal numbers of glia and neurons (about 85 billion of each), and any given astrocyte can make as many as 30,000 connections with cells around it. If glia are involved in signalling, processing in the brain turns out to be an order of magnitude more complex than previously expected, says Andrea Volterra, who studies astrocytes at the University of Lausanne in Switzerland. Neuroscientists, who have long focused on the neuron, he says, would have to revise everything. [Nature News, 11/10/10]

This Is Your Brain on Metaphors

Symbols, metaphors, analogies, parables, synecdoche, figures of speech: we understand them. We understand that a captain wants more than just hands when he orders all of them on deck. We understand that Kafka’s “Metamorphosis” isn’t really about a cockroach. If we are of a certain theological ilk, we see bread and wine intertwined with body and blood. We grasp that the right piece of cloth can represent a nation and its values, and that setting fire to such a flag is a highly charged act. [New York Times, 11/14/10]

Tree or ring: the origin of complex cells

All complex life belongs to a single group called the eukaryotes, whose members, from humans to amoebas, share a common ancestry. Their cells are distinguished by having several internal compartments, including the nucleus, which shelters their precious DNA, and the mitochondria, which provide them with power. [Not Exactly Rocket Science, 9/12/10]

I am virus – animal genomes contain more fossil viruses than ever expected

Your closest fossils are inside you, scattered throughout your genome. They are the remains of ancient viruses, which shoved their genes among those of our ancestors. There they remained, turning into genetic fossils that still lurk in our genomes to this day. [Not Exactly Rocket Science, 11/18/10]

Effective Field Theory

"Effective field theory" is a technical term within quantum field theory, but it is associated with a more informal notion of extremely wide applicability. Namely: if we imagine dividing the world into "what happens at very short, microscopic distances" and "what happens at longer, macroscopic distances," then it is possible to consistently describe the macroscopic world without referring to (or even understanding) the microscopic world. [Cosmic Variance, 11/25/10]

Meet a superpartner at the LHC

Of the many ideas for new physics that can be tested at the Large Hadron Collider (LHC), supersymmetry is one of the most promising. The theory proposes that each fundamental fermion particle has a heavier bosonic superpartner (and vice versa for each fundamental boson) and by doing so, offers an extension of the standard model of particle physics that fixes many of its problems. None of the known particles appear to be superpartners, however, which leads to the daunting conclusion that if supersymmetry is correct, there are more than twice as many fundamental particles as we thought, but we have only been left with the lightest partners; that is, supersymmetry is broken. [Physics, 11/22/10]

Mafia Wars

An increasing amount of data is showing that the cellular battle between pathogens and hosts needs much more than a simple military metaphor to describe it—think undercover infiltration, front organizations, and forced suicide. [The Scientist, 6/1/10]

RSS access:
Blog posts labeled "readings"
Items saved at Diigo

Ribs.

source: unknown

Friday Randoms.

Sunday Randoms.

source: unknown

Disturbing climate change headlines

Yesterday Tom Yulsman at CEJournal came across a story in Fog City Journal that led to a brief post, on which I commented there.

The topic is the fraught question of what's the best way for scientists to respond to global warming Know-Nothingism. My first comment was followed by a response from Tom, and I've responded with a longer note that seems worth sharing here. It turns out that there is a great deal that needs to be said.

What follows is my second response, more or less verbatim.

Tom, I've read the Revkin article and the Feinberg/Willer paper. [See the press release for quick summary.] Thanks for the references. However, I don't find them very persuasive. Apologies in advance for the length of this note.

The Feinberg/Willer paper is based on the social psychology circle of ideas known as "Just World Theory" (JWT). Curiously, the book of the "founder" of JWT, Melvin Lerner, is entitled The Belief in a Just World: A Fundamental Delusion. Unfortunately, I don't have ready access to that volume, but I note that there is no question mark in the title, so I don't know whether Lerner himself actually regarded the underlying "just world" belief as a delusion.

Although the underlying belief that JWT deals with seems philosophically controversial (at best), JWT itself simply asserts that "many people" have this belief, and that certain consequences follow. One thing that concerns me is whether substantial evidence has been developed that quantifies how many people hold the underlying belief in the world's justness. At most it seems like just one dimension in a multidimensional space of belief systems.

It's clear enough that many people have religious beliefs that are incompatible with the idea that a "just" deity would allow the kind of climate developments that science predicts, and so such people deny the science. But that's a pretty broad feature of religion in general – it denies many kinds of science that clash with religion. So what's science supposed to do – give up and say, "Oops. we aren't really predicting what the evidence strongly indicates"?

The Feinberg/Willer paper argues that certain sorts of positive messages increase subjects' acceptance of the ideas (1) that the scientific evidence for global warming is good and (2) that science can find solutions to the problem. In other words, these messages are pro-science in a feel-good, non-threatening way. So of course it's not too surprising that the subjects who heard these messages exhibited greater acceptance of scientific conclusions. This is basic marketing theory.

One problem is that the part of the message that says science can find a "solution" to the problem is likely to be false. It's probable that there is no largely scientific solution. Mitigation of climate change is probably much more of an economic and political issue, because significant behavioral change and economic adjustment are likely to be necessary. Of course, this assertion is also open to debate.

I think that the best science has actually discovered a lot that suggests the threat of climate change is even more dire than some cautious observers assume. There is, for example, this: summary of ten rather disturbing types of climate threat reported in the past year.

You [Tom] wrote, "30 years of unrelenting fear appeals on climate change have gotten us, well, where? I would argue pretty much nowhere. If ever there was a prima facie case that fear appeals on climate change don’t work, this is it."

I'm afraid that by the very same sort of argument, 30 years of attempts to patiently and rationally educate the public on the science of climate change have also failed.

The real problem is that what's actually true is that different approaches work best with different types of people, depending on their undelying personality types and value systems. For example see Skeptics discount science by casting doubts on scientist expertise or the paper it discusses – Cultural cognition of scientific consensus.

One of the individuals that Revkin quotes in his article, Dan Kahan at Yale [and a founder of the Yale Cultural Cognition Project], states the problem quite well:

I think it [Feinberg/Willer] is good research, and maybe captures something that is going on in the real world debate. But it doesn’t capture what’s most important: the source of individual differences. People disagree about climate change; it is one of a cluster of science & policy issues that polarize citizens along cultural/political lines. "Just world" theory posits a general psychological mechanism that affects everyone. Necessarily, then, it can’t explain why one and the same set of informational influences (e.g., stories reporting "scientific consensus" on climate change) provoke different reactions in identifiable subcommunities. The theory that we need is one that identifies what the identifying characteristics of these communities are and how they are implicated in cognition of risk. No theory that focuses of [sic] generic or population-wide aspects of the psychology of risk perception (so-called "main effects") can do that.

In other words, a lot more needs to be done to steer public attitudes in the right direction. It is not a matter of simply finding the most comforting feel-good way to "frame" the issue, if that just entails obscuring the hard scientific facts. That is a vain hope.

I don't have a solution of the problem, but I think a solution should include a careful evidence-based appraisal of the kinds of messages that work best with different groups, combined with a plan for how to deliver the messages through different channels appropriate for different groups.

It's a lot like any other tough political campaign. Sometimes "negative" campaigning works very well, sometimes it doesn't.

I can see what's going on here. There are obviously efforts being made by a broad range of social scientists, communication experts, and journalists to shape an effective messaging strategy. For example: ClimateEngage.org. This is probably good. What is not clear is whether the people most involved will be able to identify a near-optimal strategy.

Just to name names, Matthew Nisbet [also here, here] (whom Revkin also quotes) is one with whom I find a lot to disagree – such as the whole "post-partisan" shtick. The elephant in the room is that most opponents of the necessity of acting on climate change – to say nothing of those who deny it even exists and/or is anthropogenic – have no intentions of operating in a reasonable and responsible "post-partisan" fashion.

There really is a war going on here. Climate scientists who don't face up to this reality are going to get the crap beat out of them. Just ask Phil Jones or Michael Mann [more here], for example. Much like Lt. Colonel George Custer at the Little Big Horn.

New Tribal Tattoos designs

Tribal Tattoos designs

New Tribal Tattoo designs

New Head Tattoo tattoo designs

Head Tattoo tattoo designs

Head Tattoo tattoo designs

Back Tattoos For Men

Back Tattoos For Men I know that many people have a bunch of trouble finding good back tattoos for men. Sure, there is a lot of artwork out thee to choose from, but all most people see is the generic, cookie cutter artwork that has littered the web. This happens mostly because of people's reliance on search engines, which are very bad at showing us where the quality tattoo artwork is. There is a much better way to find good back tattoos for men and I will share it with you.

If you are fine with choose a random, generic tattoo, then search engines will be your best friend. That's all that seems to pop up. It's page after page of websites that have the same low end artwork as two hundred other galleries. They are just trying to stuff their gallery with as much art as humanly possible, so they aren't worried about the quality of the designs they post on their pages. This has become a disturbing trend and search engines aren't doing you any favors by pulling a lot of it up when looking for back tattoos for men.

This is also one of the reason people end up rushing their decision and end up getting tattooed with artwork that they don't even fully like. People will get tired of sifting through so much bland stuff and end up picking the first half way decent back tattoos for men that they see. This is a terrible way to go about choosing the tattoo that you will ink on your body.

While a lot of people will "still" end up picking tattoo artwork on impulse wherever they go, there is a way to find tons of quality back tattoos for men. You can do this by using internet forums. The bigger forums throughout the web are always jam packed with topics about tattoo art. It's a fantastic community, which can help you find out exactly where other folks are locating some of the great artwork the internet has to offer. It's a great way to find a lot of the superb tattoo galleries that search engines just aren't showing you. Looking for good back tattoos for men should be a fun experience and this should help you on your journey.

No matter where you end up looking for back tattoos for men, just make sure you take your time and don't settle on anything less than "exactly" what you want.

New Angel Tattoo Designs

angel Tattoo

Angel Tattoo Designs

Butterfly Tattoo Designs

Butterfly Tattoo

Butterfly Tattoo Designs

The Top Tattoo Designs For Men

Top Tattoo Designs For Men There are millions of designs available for tattoos but some are classic topics and some designs come and go. Here's some ideas if you haven't made you mind up yet.
*Dragons and Snakes These used to be just for the men but now are becoming popular with girls as well.

*Skulls, Bones and Anchors Probably still a man thing but these pirate tattoos are becoming more common on the arms of girls as well.

*Celtic Crosses and Knots Always a favorite, some of these designs can be quite stunning.
*Ambigrams A lot of interest has appeared in these designs of words that can be read in different directions. These have become much more popular after the Angels & Demons movie.
*Tribal What tribe do you belong to, or want to belong to?
*Chinese or Sanskrit Chinese or Japanese phrases have always been popular but now Sanskrit, the ancient language of India, has started to be very desirable.
*Butterflies and Birds Used most often by girls some of these are in my opinion the most beautiful and sexy tattoos you can have.

There are a huge range and variations on these themes and you should really spend some time thinking about the design before getting a tattoo. People love to see something special and not just some straightforward design.

Bone Fish Hook Necklaces

One of the most popular Maori arts is bone carving. This type of Polynesian artistry goes back hundreds, even thousands of years ago. Even nowadays this craft is still alive. Moreover, it is flourishing because of the grown interest in indigenous cultures such as that of the Maori.

A special kind of bone carvings are the necklaces. These have been popular among boaters, surfers, and other water sports fans for decades. Also the many tourists visiting New Zealand are fond of these little works of art.

Many of the designs used in these carvings are authentically historic but a selection of the renowned Maori and New Zealand carvers make use of contemporary patterns or combinations in their works. Whatever your personal taste demands, here's some more info on bone Maori fish hook necklaces.

The Art of Maori Wood Carving

The origin of Maori woodcarving lies in the arrival of the first Polynesian canoes (waka) landing on the New Zealand shores in 1200 AD (estimate). A few hundred years later, aproximately around 1500 the unique distinctive Maori wood carving style had been developed.

Maori wood carvings are characterized by bold three-dimensional forms adorned with intricate, detailed designs. In Maori language this art form is called Whakairo Rakau, meaning; the Art of Woodcarving.

The typical designs represent traditional Maori culture and Maori legends. Also a large deal resembles remembrance of ancestors. Purpose of carving wood was to pass on tribal history, legends and stories of ancestors (whakapapa) This because the Maori had no written language (wood) carvings were an ideal means to capture historic events.

Some of the native woods commonly used are Kauri, Rimu and Totara wood. Objects subject to carving were porches of (meeting) houses, canoes but also smaller items such as walking sticks (tokotoko), weapons (such as the taiaha and wahaika), and ceremonial storage boxes. (waka huia)

A frequently occurring design are human like figures many of which have a provoking appearance . Their purpose was to ward of evil spirits as well as to scare off members of enemy tribes. For this reason they were placed strategically on the front of canoes and on houses. Many carvings were painted red, a sacred color in Maori culture.

Examples of the human-like figures are the tiki and tekoteko both with jutting tongue, also a sign of defiance. Heads were carved in different styles depending on the tribe and their geographical location. Examples are the Tai Tokerau style, Taranaki Style, and Wheku style.