Are We Enabling a Generation of über-dumpkopfs?

Well, according to author Mark Bauerlein (The Dumbest Generation), we are. In his book he depressingly documents how the under-30 crowd are foregoing knowledge-based maturity to wallow in a self-confected, solipsistic, social mirror world of their own egos and selves. The fallout includes their not even meeting basic standards of knowledge for employment, far less earning a degree that actually means anything. (A recent survey found a majority of Harvard grads flunked a basic test on American History. Given many of these may well become future leaders, we're really in trouble!)

According to one polling of University of Illinois-Chicago students by Northwestern University communications professor Esther Hargatti (op. cit., p. 135) the students’ choices were all too predictable. As Bauerlein puts it:

“At number one stood Facebook (78.1%) followed by MySpace (50.7%). Only 5% checked a blog or forum on politics, economics, law or policy”

As he adds, the “acclaimed empowerment” of the Web has gone entirely to “social stuff”.

Are these proportions surprising? Not really. As Bauerlein observes, 18-20 year olds love digital media because it “allows them to construct a reflexive surrounding.” While their boring job tires them and the classroom irks them, their twittering, facebooking, myspacing and video gaming “mirrors their own woes and fantasies, a pre-packaged representation of the world- a ‘Daily ME’”

Thus, the digital media used, whether Facebook,Twitter or just dumb cell messages all contribute to an artificial solipsistic world filtered by the egocentric dispositions of the users. Instead of being a channel of information and knowledge consolidation, the monitor screen becomes a mirror of the young users’ own limited selves and under-developed psyches.

Bauerlein (p. 137) underscores this by citing a quote from Facebook founder Mark Zuckerberg, in an interview with the Wall Street Journal, purporting to reveal the secret of his site in terms of never having to “hear a dissenting word’:

“ That’s kind of what we are doing here, but with ‘what’s going on in the world with these people I care about’. “

So, all the things that bother and bore them are blocked out. The people they don’t know and don’t want to know they can exclude at the touch of key. A new bomb may have been developed by Iran, and an earthquake may have killed thousands in China, but in the case of Facebook users it’s the old monkey show: “hear no evil, see no evil, speak no evil” .

A delimited reality is confected which deliberately excludes the harsh outside world, and confines the personalized reality to chirpy “how r ya’s”, or gossip, mainly in deformed English which Bauerlein ranks just above the reading level of pre-school children’s books (determined by the median frequency of rare or difficult words per 1000 – with print newspapers at the top with 68.3 and pre-school books at 16.3)

The entire mental superstructure was revealed in the words of one 16 year old girl quoted (p. 137-38) when asked by a journalist if she wasn’t worried that she was denied a broader picture. Her illuminating retort:

“I’m not trying to get a broader picture, I’m trying to get what I want”.

Out of the mouths of “babes”!

But are we really helping to engender a generation of über-dumpkopfs? Maybe, maybe not. At the very least we may be contributing to the emergence of a generation of pseudo-intellectual Babbits governed by their own opinions, supported by very little factual basis. How can they assimilate a factual basis when the language to describe much of what is happening in the world’s most critical domains exceeds the language difficulty level to which they’re accustomed?

Just take what is happening in the world of global finance right now, with events in Greece, Spain and Portugal that could affect all of Europe and even the U.S. I am talking about the degradation of their respective bond ratings (an assessment of how much debt they have and how likely they are to be able to deal with it). In the case of Greece, Moody’s and Standard & Poor’s ratings have reduced the country’s bond quality to being ineligible for any loans other than via the International Monetary Fund(IMF). As anyone who’s seen the IMF act before (I did, in Barbados in 1990-91) you know it means the loans come at great cost and some suffering – with many public services cut or privatized and civil servants’ wages cut. Meanwhile, the news in the financial press yesterday was that the rating agency Standard & Poor reduced Spain's bond rating to A-minus and set off much panic. Would Spain become another Greece? Will the "contagion spread"? Who knows, but certainly not most electronic media addicts, blissfully unaware that a Greek-style bond crash might see them pawning their laptops at the nearest pawn shop just to buy a few Mickey D burgers and fries!

How many of the Twitter-Facebook generation are aware of any of this? How many even think it’s relevant to their lives? (Well, maybe they will when their college loans are affected, new conditions applied- e.g. higher interest rates, or college tuition, room and board etc. are increased 50% or more).

I reckon not many Gen Y’ers care because their little digital world of tweets, Facebook “friending” and video gaming is what defines their limited universe. But as author Bauerlein notes (p. 138):

“For education to happen, people must encounter worthwhile things outside their sphere of interest and brainpower. Knowledge grows, skills improve, tastes refine and conscience ripens only if the experiences bear a degree of unfamiliarity.”

What that means, as he further observes, is one must move through and beyond the initial knee-jerk reaction: “I don’t get it! That’s not for me, not my cup of tea!”

because the intellectual effort in making it your ‘cup of tea’ will then be intellectually rewarding. Bauerlein again (ibid.):

“Nobody savors the process, but mature adults realize the benefits. Adolescents don’t and digital connections save them the labor of self-improvement…..the screen and cell bombard adolescents with youth trifles and the sporadic brush with challenging subjects that recall their shortcomings are quickly offset by a few minutes back in virtual comfort zones”

And – as the author warns, the “opportunity costs are high”. Imagine instead of wasting hours and days on pseudo-socializing (which I define in terms of digital contacts-communication, rather than face-to-face or the famous “bull sessions” such as we used to partake of in the 60s) the young adult pursued actual knowledge aims – learning the conjugation of Russian verbs, or Latin, or how to integrate around a pole using residue calculus, or …just learning about what’s transpiring now at the interface of politics and finance in terms of financial regulations and reform.

‘AWWWWWW……BOOOOOOOOORRRRRING!’

Well, yes, to the undeveloped and raw mind. But getting beyond that reaction is what molds and defines the adult. It is, if you will, the sine qua non rite of passage to adulthood in a civilization which generally foregoes such rites.

Neil Postman in his book, ‘The Disappearance of Childhood’ (1994) noted at that time how television was infantilizing children and many adults, and the more hours they viewed (without also being exposed to difficult reading) essentially kept them at the level of a child. Postman’s main contention (so germane today with the digital youth generation) was that only adults are privy to the secrets locked into the printed word. If a supposed adult wanted to emphatically separate himself from the world and concerns of the child, he had to demonstrate it by his reading fare. That meant accessing a realm in printed material that the child mind wasn't equipped to process or understand. Twitter all you want and "friend" a million buddies on Facebook, you're still a de facto, intellectual child. Now, go read the first chapter of Jean-Paul Sartre's Being and Nothingness or Charles Darwin's Origin of Species, or even William Shakespeare's King Lear, we will reconsider your status. (University degrees may or may not count given how inflated most grades are today, because of the teacher evaluation system).

Any person can basically access an electronic medium if they apply even minimal effort, that includes cell phones, tv, video games and twitter. Any person can also employ those media to blab nonsense, gossip or indulge in aimless chatter. But what defines the adult mind is whether it can tackle a serious print work such as Being and Nothingness, The Origin of Species, The Origins of the Federal Reserve System, or ‘Relativity’ – the popular rendering of special and general relativity by Albert Einstein. Thus, the barrier to adult intellectual capacity is breached once one proves he or she can handle the latter. (And no, the content isn't necessarily supposed to be such that it "synchs" with you!) Socializing on Facebook is accessible to any child, so is watching network TV (perhaps not cable TV special programs such as the recent ones on Discovery featuring physicist Stephen Hawking)

This blog, by the way, has as one of its aims the intention of putting up lots of material that may be unfamiliar to readers. The idea is to challenge blog readers to move beyond their intellectual comfort zones and stretch. That’s why so many blog pieces are on mathematics, as well as finance, and even philosophy (e.g. the blogs on The Truth Hurdle, Pts. 1 and 2)

In this way, I try to do my part to spur readers, hopefully older and YOUNGER to read more widely, think more deeply and formulate more opinions based on fact, as opposed to just childish, subjective feelings or immature impressions.

Another Supreme Court Abomination- and the Cheerleading of the Pseudo-Righteous

Sadly, it seems one abomination (Citizens United v. The Federal Election Commission) wasn’t enough for the conservatives on the Supreme Court, they now had to spit at the Establishment Clause as well. In their earlier, egregious decision (which readers may recall President Obama upbraided them for during his State of the Union Speech) the clique of Five basically overturned all limits on financial expenditures for corporations and their lackeys.

Unless reversed by a future court, or more likely nullified via congressional legislation, this insidious ruling will clear the way for total corporate rule, which of course, is the same as fascism (in its classic definition). This is made possible by the stupid expedient of conflating money with speech and assigning it as a right to corporate “persons” – itself an abomination from the 1886 Santa Clara ruling.

Now, in the latest ruling, an obvious sectarian marker (cross set up in the Mojave desert to honor WWI vets) which conveys an iconic message of one religion, has been deemed acceptable despite lower federal court rulings that it violates the Establishment clause. But what do these five care, driven as they are to steer us into a corporate fascist theocracy?

As Justice John Paul Stevens correctly observed in his dissent, there have been thousands and thousands of non-sectarian markers to honor ALL vets who fought and died. So why choose one now that offends and excludes those vets who are non-Christian? Don’t those vets count? Are they less worthy because they espouse the Jewish faith, or Buddhism, or Muslim or no faith at all?

Of course, in the middle of this there are those who couldn’t resist parlaying the existing abomination into some kind of pseudo-defense that the nation is actually founded on God or God’s laws, or some such nonsense. One such person is a certain irrepressible Florida Pastor who never misses an opportunity to try to compound a judicial folly or ruling into some kind of wise decision with constitutional backing.

Let’s look at some of the codswallop spouted on his most recent blog:


“Now , granted, we may not see the name of God in the U.S. Constitution; but we see the hand of God. “

This is totally egregious and no more valid than claiming there are actual faces in clouds, or Satanic images in the debris cloud from 9-11 (which observed from a slightly different angle disappear). Thus, the claim here is entirely subjective, without any objective support.

Undaunted he continues:

"In reality, God is found throughout the U.S. Constitution, for the very basis of justice and freedom begins with a morally perfect God. Any attempt to separate God from a desire for justice and freedom is the height of ingratitude and ignorance. "

Of course, no where does he give actual examples of “God found throughout the Constitution”, he simply makes the bald claim. As for “justice and freedom” these are human definitions, and even a superficial reading of the Constitution will make evident the hand of intelligent humans.

The very fact that the Constitution contains the basis for its own continual revision via additional amendments (Article V) discloses it to be a human document, which is subject to constant alteration and not set in stone – like the pastor’s KJV.

Further, we know that many of the tea party brigade (though they claim the mantle of Christianity) declare certain aspects of the Constitution off limits and not to be followed or accepted. For example, they blanch and froth at Amendment XVI which provides the basis for congress “to lay taxes on income”. But IF the Constitution is really a document of God, originating at a deity’s behest, then why would so many millions of tea baggers reject the taxation amendment? Obviously, because they recognize human hands at work in writing up, revising, then voting on additional amendments and not any "hands of a deity"! They certainly don't accept Amendment XVI like John 3:16!

Justice and freedom themselves are not even taken to be permanent by the Founders! They are seen to be tenuous at best, and indeed, in the Declaration of Independence the Founders even write in this provision:

“Governments are instituted among men, deriving their just powers from consent of the governed. That whenever any form of Government becomes destructive of these ends, it is the Right of the people to alter or abolish it, and to institute new government.”

So clearly, the founders recognized the ephemeral and provisional nature of ALL governments by acknowledging the possibility of their abolition and replacement. Further, via the very separation of powers inhering in the Constitution, they disclosed a wise precaution in applying and inserting cross-checks, hedges and impediments (e.g. 2/3 majority to pass an amendment) to prevent the document from ever being misused. If they did this ab initio, it clearly and logically meant they recognized an imperfect government predicated upon an imperfect document. So, is the goodly pastor finally admitting his deity isn’t perfect….or what? (Since if it can't be "separated" from the document then it must ipso facto be as imperfect as the document).

Indeed, to put a firmer point on this, Amendment IX of the Bill of Rights allows for the explication of “unenumerated rights” – ones not explicitly stated in the Constitution. The amendment reads:

“The enumeration in the Constitution of certain rights, shall not be construed to deny or disparage others retained by the people”

In other words, the authors –founders fully well foresaw that they might not be able to think of or identify every single right of the people. This amendment then served as the ultimate redundancy plan so no future tyrant could say: “No, that’s not a right, it isn’t listed in the Constitution!” Again, this example reveals the understanding of an imperfect document – a HUMAN document, that may not have covered all possible bases.

He goes on, in his pastor-preachy way:


"History has proven that atheism and evolution were the demonic ideologies behind brutal Communism , as well as Socialism . The common allegation that most of the wars throughout history were fought over religion, does not take into consideration the fact that most religions are FALSE RELIGIONS ! "


Actually, history has “proven” no such thing other than in the pastor’s feverish neurons. While again demonizing atheism, he neglects to mention that the Communist totalitarians – such as Mao and Stalin- killed more than 15 times as many atheists in their pogroms and political purges as they did Christians. (Mainly because not that many Christians were living in either place at the time of Stalin’s purges, or Mao’s “Cultural Revolution”). Atheists were slaughtered by the teeming millions in Russia if they were suspected of being Trotskyites (followers of Leon Trotsky, deemed to be not a “true communist believer”) and by the millions in Mao’s China for being “intellectuals” and “purveyors of foreign culture”.

But then, it’s much easier to spout shlock and hope people are dumb enough to swallow it than to attend to facts.

The last statement made is a neat copout. The pastor escapes the fact that most wars through history were fought over religion by artificially narrowing the definition of religion! In other words, we have most religions being “false” so only a few (like his, I presume) are “true”. Thus, if only the occasional “true” religions made or conducted wars, then it is no longer true that most wars throughout history were fought over religion”.

But this gets old fast. The fact is, there is an explicit definition of religion (from my Webster’s Encyclopedic Dictionary):

“Any entity or system comprising a group of like-minded persons who believes or accepts that a transcendent Being has created the world, or governs it, or controls its destiny and intervenes occasionally and which also mandates certain specific rituals, exercises, readings (from sacred texts) and prayers, either to fulfill a human need or propitiate the deity or transcendent being accepted”

Notice there is no specious declaration or artificial demarcation of what is “true” or what isn’t. Under the above rubric all the known world religions qualify: Islam, Judaism, Catholicism and Protestantism – under which rubric the pastor’s rigid KJV-based system belongs as a growing cult.

Under this definition, mankind’s history indeed has mainly been permeated by wars over religion or religious belief, or which group had the “true belief”

More codswallop:

"Some people blame God for everything. The God of the Bible is a fair and a just God. The Bible is brutally honest, and some people have a hard time coping with that - ESPECIALLY the atheists and the ACLU !"

Actually, as I’ve shown in numerous earlier blogs the Bible is a human interpretation of legends from long ago, many copied directly from antecedent pagan sources. (For example, Genesis was almost entirely plagiarized from much earlier Babylonian creation myths). Thus, the “God of the Bible” is a purely human invention and construction, a product of semi-literate and limited intellects – which makes total sense given he acts like a psychopath most of the time. (Which is why the savvy Gnostics referred to it as “demiurgos” and insisted it was a fraud, not to be worshipped by any sane human)


And predictably, we see this bit of nonsense:


"In other words , all mankind are divided into two parties or dominions; that which belongs to God, and that which belongs to the wicked one (i.e., Satan ). True believers belong to God: they are of God, and from Him, and to Him, and for Him; while the rest, by far the greater number, are in the power of Satan and his earthly demons; they do his works, and support his cause. This general declaration includes ALL unbelievers, whatever their profession, station, or situation, or by whatever name they may be called !"

Which is taken right out of the book of the Inquisition, or Oliver Cromwell! We must “divide” humanity into the sheep and the goats. And even the sheep must be further divided into those who are “true believers” (presumably so vetted by this pastor) and the others…."false believers" (most likely Catholics, Jews, Mormons, JWs, Buddhists, etc. – to go by his previous ‘false doctrines’ page on his I-Net All Souls church site)

To top it off, to put the icing on the cake, the ‘non-true believers” are all in “Satan’s grip” while the unbelievers are….what….well I guess actual agents of Satan. Or maybe allies of his “earthly demons”.

Ordinarily this tripe would be laughable, but then that assumes people don’t take it seriously. The problem is that so many interpret this claptrap as having an actual grain (or more) of truth.

And so, in that sense, the pastor follows right along in the ranks of Stalin (who separated “true communists” from the false ones), and Mao (who separated true believers in the Cultural Revolution from false ones) and the Inquisition (which separated true believer Catholics from the false ones or heretics – that didn’t cop to every doctrine).

And now – some apt quotes from one of the Founders, Thomas Jefferson:

"Our civil rights have no dependence upon our religious opinions more than our opinions in physics or geometry." --Thomas Jefferson: Statute for Religious Freedom, 1779. ME 2:301, Papers 2:545

"I am for freedom of religion, and against all maneuvers to bring about a legal ascendency of one sect over another." --Thomas Jefferson to Elbridge Gerry, 1799. ME 10:78

And finally, Article 11 from the Treaty of Tripoli:

http://www.stephenjaygould.org/ctrl/treaty_tripoli.html


“Art. 11. As the Government of the United States of America is not, in any sense, founded on the Christian religion; as it has in itself no character of enmity against the laws, religion, or tranquillity, of Mussulmen; and, as the said States never entered into any war, or act of hostility against any Mahometan nation, it is declared by the parties, that no pretext arising from religious opinions, shall ever produce an interruption of the harmony existing between the two countries."

The Cult of Speculation must be tamed

As I watched the Senate subcommittee grilling of Goldman Sachs speculators yesterday, I almost grew ill. Their defiant and cavalier attitude to how they’d legally gutted millions of people yet felt no remorse at all, made me physically ill. One particular miscreant who led their mortgage –CDO unit, when asked directly by Sen. Levin if he felt he’d done any wrong- merely feigned a look of mock surprise and said ‘No’.

What did these golden boys, including the notorious Goldman trader supreme Fabrice Tourre do? They sold packages of mortgage securities called CDOs (collateralized debt obligations) which they knew with 99% probability would fail, then bet on them to fail in the CDS (credit default swap) market to make money on the losses. While Goldman packed away the samolians, banks that bought the “toxic waste” (in trader parlance) were brought to the edge of ruin as the mortgage market melted down.

Is Goldman guilty of law-breaking? I doubt it. Why? Because since the helter-skelter Reagan speculator era (when the 1984 Bank Holding de-regulations went into effect) the speculators have been allowed free reign. Remember Michael Millken and his “junk bonds”? Laws full of loopholes were thereby engineered, often with the help of traders turned lobbyists, to give the “masters of the universe” plenty of latitude to take risk and get a perfectly legal 'Amscray! Get out of Jail free card'.

Around this same period, a whole raft of mortgage securities emerged, which were piled into bond funds. These included CMOs, collateralized mortgage obligations (the forerunners of CDOs) and interest only strips (Ios) and other trash (e.g. inverse floaters). The inclusion of so much garbage in bond funds was a major reason why many of them performed poorly, though the gullible masses were led to believe “bonds were safe”. (Actually, bonds are safe- T-bonds! Not bond FUNDS!)

The same laws that protected the bundling of CMOs into bond funds in the eighties, also later (with re-workings and tweaks) protected the bundling of CDOs into mortgage securities. Were the late 1980s and mid 1990s bond fund purveyors obligated to disclose to clients the specific content? No, they were not. So you could say the law was an ass, or at least in the court of the speculators. In the same way, the law under its letter did not require the likes of Goldman to disclose to its buyers the content of its (falsely rated) mortgage securities.

By “falsely rated”, I mean that the implicit bond grade was just a level above junk (maybe BBB) if that, but the bond rating agencies (like Moody’s, or AIG), bought into the uber-trader spiel and rated them “AAA” – which generally is reserved for only the highest quality instruments, not toxic waste. E-mail content disclosed last week (in the WSJ) from some of the bond raters actually revealed the stress they were under in making these specious ratings, to the extent they likely knew they were playing the margins of what was legal, and certainly crossing ethical margins.

Where things went wrong, in my opinion, was Goldman legally being allowed to “short” (bet against) the very products they almost certainly knew would go bust (one choice “brand” named “Timber wolf” was described in one e-mail read at yesterday’s Senate hearings as “shitty” by a Goldman trader) and make the short with the instruments’ AAA tag on the bond markets. Of course, this was how Goldman made its money, or most of it. Was it legal? Evidently yes, especially after the 1935 Glass-Steagall protections were repealed in 1999, allowing investment banks and commercial banks to mix. Was it ethical? Hell no!

Sadly, the Goldman Sachs episode is just the tip of a noisome “iceberg” of speculation gone wild in this country. Even as some deluded citizens have preened and posited about what a “godly nation” we have, the speculator cult has virtually locked the U.S. into a vise with no sign of abating. The Federal Reserve is even content to feed this speculative mania by having interest rates so low the money is almost "free", at least for the speculators! Wonder why the DOW kept heading higher? That "low cost" money was one huge reason. And then, even in the midst of it, we beheld Ben Bernanke, fretting over the growing deficits like other elites, calling for possible cuts to Social Security & Medicare! Not so fast, Ben! Before making direct cuts to those programs, go and collect some of the $4.3 trillion in IOUs still owed SS!)

Indeed, according to a recent TIME piece, what Goldman did is nothing that others on Wall Street – including Morgan Stanley and Lehman- weren’t also doing: Using other people’s money to make insane, risky bets in an obscure credit derivatives market- governed by a ridiculous equation (the Gaussian copula) that attempted to link and quantify entities that weren’t remotely related.

In an earlier blog I mentioned how the speculator cult has mutated so much that it’s now become invested in ghoulish products, such as insurance securities in which investors “bet” on when a person will die. If the bet is timed well, and the former policy holder (i.e. who has sold the policy to the investor, or more likely had his policy packaged with others) dies on time, then money is made. Else, it becomes a gruesome waiting game. "Jeebus, look! It's eighteen months past his projected death date! We've lost $500, 000! When will he just kick the bucket so we can cut our losses!)

If people think that’s as bad as speculation has become in this forlorn country, think again. According to The Wall Street Journal (‘States Bristle as Investors Make Wagers on Defaults’, April, 27, p. C1) the latest speculation craze is for “investors to short sell or bet against countless cities, towns and bridges and more than a dozen states, including California, Michigan and New York”.

Again, enter the derivatives called credit default swaps. Only in this case, the rabid speculators (I won’t even dignify by the title ‘investor’ since no investor I know is a Vegas-style gambler) are betting on the cities or towns to fail, and also for their bridges to collapse. Never mind hundreds may get killed or injured, as occurred in Minneapolis some years ago, if a bet can be made which will make them money they will do it. Gruesome and macabre, but that’s what we’ve come to. Apparently, these crass speculators might be the "canaries in the coal mine", they see the imminent and literal collapse of the country and they're determined to at least make some money off it! And meanwhile, untold millions extol that the grand old US of A is a “Christian nation” despite its having deformed laws that permit this sort of perverted, ghoulish gambling.

In his terrific book, Arrogant Capital, author Kevin Phillips observed that the final phase of a collapsing nation is when it becomes embroiled in a speculative mania. Such a mania entails wild and immoral speculation on any and everything, even as the financial centers of the country come to depend upon sleazy and obscure instruments for advancing it. Phillips noted that the collapse of both the earlier Dutch and British Empires was immediately preceded by a phase of speculative frenzy that lasted from 10-50 years.

We are in that phase now. We have become a nation that depends on variable, phantom fiat money (which goes up or down with the P/E ratios in the stock market, or interest rates in the bond markets) as opposed to plain, old fashioned, and stodgy saving. We want it all and want it now. We want our Medicare and health reforms but prefer not to have any increased taxes to pay for it.

We are a people totally divorced from reality even as we make the next cynical bet that the towns and bridges of our fellow citizens will come crashing down. Or that the people whose insurance policies have been bundled into a new security will all die “on time” so we can collect on them.

But, never mind, “God” is still with us and his magic hand is steering us through.

The $64 question is: Which god?

Hawking’s Alien Speculations: Don’t Take Them Lightly!

Cysts of schistosoma in a patient's bladder. Aggressive alien colonizers could conceivably genetically engineer something similar to invade the human gut and extract nutrients - effectively starving the person to death. Sent in hollow robot probes to fresh water lakes and sources on Earth - the human population might be removed in 3-8 months.


On a new Discovery Channel series, the world famous theoretical physicist made bold speculations about the possible encounter of the human species with a colonizing alien intelligence. Hawking didn’t mince words or soothe fears that the encounter likely wouldn’t go our way, and compared it to what transpired to the native populations -mainly the Arawaks- after Columbus alighted on their beaches and islands. Not to put too fine a point on it, but within a few years the native population was decimated.

In a 1962 high school research paper, long before Hawking’s alien warning emerged, I showed how any encounter with a truly advanced alien intelligence would likely be disastrous for the human race. While scifi films (e.g. 'Earth vs. The Flying Saucers') up to then often painted the meetings or altercations in cartoonish terms, I reasoned a hostile future encounter was almost inevitable and that our (putatively) lesser civilization would fall to a much more advanced, alien one. It was impossible to avoid, and this may have been the basis of a 1960 Brookings Institution REPORT to that effect. (Which I cited in my paper)

The paper was innocuously entitled, "Peaceful Uses of Outer Space", but the Brookings Institution recommended prohibition of disclosure, with a warning against the revelation of the existence of extraterrestrial life to the people of America or the world. Brookings Institution thinkers feared social, economic and religious upheaval would result. The Brookings Institution's conclusions were largely based on the public reaction to the infamous Orson Wells' radio broadcast of "The War of the Worlds" and the local panic that ensued in 1938.

Less well known, buried deeper in the 1960 report, the authors cautioned that an actual encounter would likely lead to the end of human civilization since, “whenever a more technically advanced civilization encounters an inferior one, the latter is either absorbed or destroyed.” That, of course, is what Hawking was referencing in his invocation of the Columbus example – which has by now become iconic in a negative sense to all native peoples.

In the wake of the Hawking warning, however, what did we find? Well, mainly jiggles and giggles from the punditocracy with very few serious treatments. Even Keith Olbermann – generally known for presenting sober views on science issues- more or less treated this with a dismissive tone and played it mainly for laughs or levity. (Perhaps as needed balance for his preceding material on the odious Arizona immigration papers law, and the Goldman Sachs pillaging of investors by shorting mortgage securities sold to them). His astronomer guest, if I can call him that, was totally clueless, somehow convinced we humans had nada to worry about because any such encounter was “hundreds of millions of years off” if ever. I had to wonder what planet this character was on, further when he based advanced aliens’ knowledge of us from our diluting radio signals – which would only be “60 light years out by now”.

However, the man is living in a fool’s paradise. The diffusion of an advanced alien civilization based on applying known diffusion wave front equations to their spread (together with very pragmatic assumptions) was the basis for the paper ‘Galactic Civilizations: Population Dynamics and Interstellar Diffusion’ by William Newman and Carl Sagan, in Icarus, Vol. 46, June 1981, page 293.

The authors began with a standard diffusion equation, treating the spread of any colonizing civilization similarly to any medium that diffuses – for example, viruses, or general infections, or even human populations (say in the early colonizations of the New World).. The basic diffusion equation used was (p. 301, eqn.12):

d(rho)/dt = DIV(D(x,t,rho) x grad rho(x,t)

where, rho(x,t) describes the population density at time t, and position x, and D is the diffusion coefficient in terms of x, t and rho. The preceding equation is then tweaked and used as the basis for future refinements.

Rather than weary the reader with the dozens and dozens of equations leading to the Results section (page 314), I will simply commence at that section and then go from there.

The authors' first major computation is of N’, the steady state number of extant advanced civilizations in the Milky Way. This is essential to obtain because it is one of the key variables used to compute the mean distance between advanced civilizations in the Milky Way:

L_m = (2.5 x 10^11/N’)^1/3

Where the numerator refers to the number of stars estimated in the galaxy. The result is in parsecs, assuming the mean separation between stars in the galaxy is 1pc = 3.26 light years. (Bear in mind while our region near the outer rim is sparse with stars, the interior third of the Milky Way is teeming with them, very densely packed)

Based on a star –planet formation factor, f *~ 1, and a mean lifetime for an advanced civilization of 10^6 years, the authors obtain: N’ = f(10^6) = 10^6, or one million advanced civilizations in the Milky Way alone.

(* Note: my inclination is actually to increase f to ~ 2, based on the discovery of more than 370 actual extra-solar planets, which were unknown at the time Newman and Sagan published their paper. This would yield double the number of advanced civilizations, but we will retain the more conservative estimate)

Then, the mean distance between advanced civilizations in the Galaxy is:

L_m ={ (2.5 x 10^11/ (10^6)}^1/3 = [2.5 x 10^5]^1/3 = 63 pc = 205 Light years

Readers may well not appreciate this, but this is literally “next door neighbors” in terms of the galaxy!

The authors’ next task is to obtain the velocity of the colonization wavefront which they give as (Eqn. (79), page 316):

V = (v_k)(D g)^1/2


Here, (v_k) is a dimensionless constant of order unity(1), and g ~ 0.1 (based on the rate of migration of human populations today (Newman and Sagan estimated 0.01 /yr, but that was nearly 30 years ago before the age of globalization). The diffusion coefficient, D, they (very) conservatively estimate at: D ~ (2 x 10^-8 pc^2/yr).

Thus, the colonization wave velocity would be:

V = (1)[ (2 x 10^-8 pc^2/yr)(0.1 /yr)]^1/2 = 4.4 x 10^-5 pc/ yr

Which would imply 1.4 x 10^6 or 1.4 million years before the colonization wave reached Earth, assuming a 63 pc distance to the nearest advanced colonizers.

Now, before anyone gets too ecstatic, bear in mind:

1) Sagan and Newman based their diffusion coefficient on relatively low travel speeds (v much less than c) since anything near v ~ c would be enormously expensive in terms of shielding, propulsion (page 312). They opted then for speeds far below relativistic (e.g. ~ 40,000 km/h).

2)They deliberately assumed a “random walk” diffusion with directional bias “away from population centers".

Now, I personally believe the first is way too conservative and ignores the sort of ingenuity and enterprise that may well apply to a truly advanced civilization which is also space faring. And again, just because we can’t imagine humans attaining relativistic speeds, doesn’t mean advanced aliens couldn’t. So, just a shift (reduction) of the base travel time to about one ten thousandth of what the authors use enhances the diffusion wave speed, V to 0.004 pc/yr.

This reduces the time to encounter to 1.57 x 10^4 yrs. or just over 15,700 years. A blink of an eye.

Thus, if the alien colonizers commenced a journey in our general direction (the next thing I will deal with in (2)) from about 3ky before the Holocene geological era, then they’d be roughly 700 years away from finding us. (Give or take 1000 years in terms of uncertainties). This means the colonizers may well be “right around the corner”.

As for the authors’ assumption (2) that the directional bias is away from population centers, or populated planets, I suspect this is based on their beneficent view of colonizing aliens. Their take is that a true spacefaring civilization would have had to oust its aggressive tendencies for the most part, otherwise they'd not be able to have their civilization reach the stage of interstellar travel. They’d have destroyed themselves long before.

However, many other astronomers and physicists, e.g. Freeman Dyson in a 1972 speech, have expressed a less sanguine view: that some alien civilizations for whatever reason, may have discovered the engineering basis for practical interstellar travel long before their aggressive and conquistadore dispositions were bred out of them. In that case, to use Dyson’s words, they’d be “like a malignant, technological cancer spreading across the galaxy” and we’d do well not to wish for any meeting.

In 1978 the British Astronomer Royal, Sir Martin Ryle, pleaded for extreme caution in restricting any and all types of electro-magnetic signals and noise emanating from our planet. He warned that it would be foolhardy to be anything but passive listeners given we don't know anything about alien intentions - should they receive a calling card from another world. Of course, Sir Martin likely based his cautions on a paper in the journal Science two years earlier, which showed how an advanced alien civilization could put together a detailed picture of life on Earth, especially of our defense capabilities.

And if they came our way would we see an armada of alien ships hovering or landing, ray guns zapping us, and our missile defense reacting? Hardly! More plausibly, if they're intelligent enough to make it this far, and as aggressive as I suspect they'll be, they'd surreptitiously enter from the outer edge of the solar system (cloaking all EM signals). Next, they'd probably set up a standby base on Pluto's Moon, Charon, then dispatch robot probes laden with special, genetically engineered parasites to Earth, to remove us. They could probably send out a thousand or so hollow probes laden with billions of such creatures, and land them in fresh water lakes on Earth wherein they'd have the maximum effect.

The best design would be for the alien-engineered parasite to essentially deprive the human host of all key nutrients, leaving the cells to basically starve. (Or, maybe neutralize all electrolytes in the blood.) Using diffusion equations (or something similar) to what was already shown, they could then estimate or even calculate (given say 10 billion parasites deposited) how long before all humans would starve to death. This may be anywhere from three to eight months, depending on a number of factors -- but the patient aliens would simply bide their time and wait us out. No fuss, no ray guns, no ships in the skies. Just dead humans...eventually. Then the clean up crews enter, and the way is rendered clear for new inhabitants.

Grisly? Perhaps. But much more realistic than the shoot 'em up idiocy that now passes for the first encounters with an aggressive, intelligent alien predator species.

Even more grisly, humans wouldn't have a clue what was happening to them, until possibly too late. All they'd recognize is something that appeared to be a massive new plague. Eventually, some wizard might detect or locate the source - the actual parasite- but by then it might be too late, especially if capable of concealing itself in a secondary host - like the schistosomiasis fluke in the snail.

Laugh at Hawking's alien speculations if you will- giggles and jiggles. I will take them seriously in the spirit he intended.

Just WHO are the real "pinheads"?

The problem of origins, cosmic and human, is a trenchant one and generally calls for highly motivated and rigorous debate. Alas, there are too few prepared to deliver it. What one finds instead is a cheap, shallow substitute - maybe akin to that cheap jam spread you buy at the supermarket, that promises big taste, but ends up in the garbage.

The reason for the lack of standards in debates about origins isn't surprising. It is because most of those who try to pontificate don't know anything about actual science, but attempt to go exclusively by "common sense". However, as author Victor Stenger has pointed out ('You Can't Trust Common Sense', in Not By Design: The Origin of the Universe, Prometheus Books, 1988) this is a dangerous and deluded strategy.

In fact, the march of 20th century modern physics shows the degree to which "common sense" so called, is perhaps the worst criterion to use to judge the merits of an argument, or the nature of evidence. Take the Michelson-Morley experiment (which Stenger explores nicely) as but one example.

In our normal experience of motions, say if one is in a vehicle traveling at 40 mph down a highway, and another car moves ahead at 50 mph, then one agrees that the faster car is going 10 mph faster or +10 mph relative to your own car's moving frame of reference.

Now, consider a rocket in space which sends out a flash of light as it is travelling at half the speed of light. Given the light beam is supposed to travel at the velocity of light: c =186,000 miles per second, can we affirm that if it's dispatched by a rocket traveling ALREADY at 0.5c, it will then have to be going at c + 0.5c = 1.5c? No, we cannot! The light beam, irrespective of the medium from which its sent - a car headlight moving at 40 mph down a highway, or a rocket moving at half the speed of light, still travels at only the speed of light, c.


What about TWO rocket ships approaching each other at the speed of say 08.c? Surely then they will approach at a relative velocity exceeding the speed of light (e.g. 0.8c + 0.8c = 1.6c just as two cars traveling toward each other at 60 mph are approaching each other at a relative speed of 60 mph + 60 mph = 120 mph)?

Well, that's what common sense and ordinary laws of motion tell us, but it's wrong. The actual relative velocity for bodies approaching at relativistic speeds is obtained from:

V(R) = [v1 + v2]/ [1 + (v1)(v2)/c^2]

where v1 = v2 = 0.8c

But working it out: V(R) = [0.8c + 0.8 c] /{ 1 + (0.8c)(0.8c)/ c^2 } =

[1.6 c]/ 1 + (0.64c^2)/ c^2 = 1.6c/(1 + 0.64) = 1.6c/ 1.64 = 0.9756c

or stll less than c!

Even more mind boggling and at odds with common sense are the findings from special relativity, proven over and over again.

For example, the "clock" associated with a moving particle runs SLOWER the faster the particle travels. (Based on the well known muon experiments.) This example of what we call "time dilation" has no counterpart in our everyday world (where velocities are generally far below the speed of light) so we never encounter slower clocks. Even the old Concord jets, as fast as they were, couldn't move fast enough to disclose a pronounced time slowdown. Yet the equations of Einstein show it in no uncertain terms, and the muon experiments prove it!

Also in defiance of common sense is that the length of a rod shrinks in the direction of its motion as it travels approaching the speed, c. At that speed, the rod vanishes since its length is now zero.

What would the length (L) of a rod be for a ground observer, if the rod is moving at 0.9c? Before it moves, measurement shows it is 1 meter long, so L' = 1 m.

Then, by the relativistic contraction equation of special relativity: L = L' {[1 - v^2/c^2]^1/2}

So, to the ground observer the length L is:

L = 1m ([1 - (0.9c)^2/ c^2)]^1/2] = 1m{[1 - 0.81c^2/c^2)^1/2} = 1m (0.19)

or L = 0.436 m

Or, in terms of feet- given the original length was about 3.3 ' (since 3.3' = 1 m) then

L = 1.43'

In other words, the moving rod shrunk from just over 39 inches to barely 17 inches!

Other modern physics findings also fly in the face of common sense, such as:

1- The observed diffraction of electrons wherein on electron can pass through two slits at the same time,

2- The phenomenon of quantum tunneling whereby a low energy particle can pass through a high energy barrier via wave action.

3- Dark energy in the universe which allows for repulsion to occur between masses, and is responsible for the universe accelerating.

So, given these examples, why is it so hard for some fundies to admit that they fail the physics crtieria to be able to cease relying on their common sense, when it comes to how the cosmos arose? In fact, they assert over and over that we (atheists) say the cosmos sprang from nothing, but that word is only figurative. The actual term is a sub-quantum vacuum within a brane space of at least five dimensions. Details were given in a number of previous blogs last year, but the basic idea is that the pre-cosmic bubble "exploded" in conformal spacetime yielding the event we have described as the Big Bang in normative space-time. (A sketch is shown, in which the vacuum bubble is shown as unstable just before spontaneous release. Also shown is a contous of the conformal bubble (cross section) with units given in terms of the Planck Length, ~ 10^-44 cm)

Despite this, we have unadulterated nonsense such as this, fulminated by a certain pastor:

"Contrary to what the pinhead atheists spew out of their filthy sewers , being CANNOT come from NON-being ! there is no potential for this . Even skeptic David Hume called this "absurd" - a scientific (real) impossibility . "

Of course, what the fundie fails to mention is that Hume was a product of an age (230- odd years ago) when science was still seeking to find its legs. Michael Faraday hadn't yet done his magnet experiments. James Maxwell hadn't even shown the existence of the invisible fields we call "electromagnetic" nor had he developed his powerful Maxwell equations based on them. Quantum theory's first tentative steps were still over 160 years away. The Hubble telescope and its findings, along with modern astronomy's opening vistas into the other regions of the spectrum, over 200 years. So, what's the point of citing this ancient? Well, mainly to distract!

And while asserting that "being can't come from non-being" he 's clearly unaware of the phenomenon of pair production. This is made possible by an uncertainty in the amount of energy(E) available, which is associated with the uncertainty in the time (t) and the Planck constant such that: dE ~ h/dt. (Where h = 6.62 x 10^-34 J-s)

Thus, if the time uncertainty is small enough, than an amount of energy dE can become available to allow production of electron-positron pairs from the vacuum. To find out what this time uncertainy needs to be, one merely has to obtain the total rest mass of the materialized (e-, e+) in terms of energy, then calculate dt, viz. dt = h/ dE

In the same way, using the same analogy, the original cosmic "burp" from the M-brane conformal back ground would be facilitated by an uncertainty in the conformal variable for t (likely posed as (-t) to be associated with the repulsion of dark energy resident in the vacuum). In his superb paper, ‘Universe Before Planck Time – A Quantum Gravity Model', in Physical Review D, Vol. 28, No. 4, p. 756.) T. Padmanabhan shows the instantaneous formation of the universe by a possible quantum fluctuation arises when the conformal part of space-time is treated as a quantum variable. The conformal factor uses the key variable:

alpha = S ^6 (t) w ^2 (t)


where S is the action, thereby fixing the state of the universe to be compatible with a harmonic oscillator of frequency w. It is also this basis that provides the model for the instantaneous formation of the universe by a possible quantum fluctuation that arises when a particular threshold is crossed near alpha = 0 (from quantum to classical domains) As Padmanbhan shows in his paper, such a cosmos can emanate from “nothing” (Actually, an M-brane "bubble"- the bubble residing inside the light cone of a point in de Sitter space. The point itself, and its light cone, are the big bang of the Friedmann model, where the scale factor goes to zero). Thus, his model is perfectly justified and follows from the basis of the equations, the light cone, scale factor restrictions and so on.

Another choice canard offered by the Pastor:

"Through the centuries , many believed that the universe didn't need a cause ; it was self-existent . They thought a beginningless / uncaused universe wasn't illogical or impossible . But now that contemporary cosmology points to the universe's beginning and an external cause , skeptics insist everything needs a cause after all ! "

A key deficiency here is that the pastor isn't aware of the nuances that underpin causality. (One reason that most specialists now demand necessary and sufficient conditions as opposed to causes. Mainly because too few people can distinguish between efficient and non-efficient causes, or proximate causes, and a disjunctive plurality of causes). Now, a key question is whether the Padmanabhan theory of the inception of the cosmos from a sub-quantal bubble meets the most primary causality criterion. According to philosopher Mario Bunge (('Causality and Modern Science', Dover):

"Giving reasons is no longer regarded as assigning causes. In science it means to combine particular propositions about facts with hypotheses, laws, axioms and definitions. In general, there is no correspondence between sufficient reason and causation".

In other words, the standard is met, since Padmanabhan's paper combines particular propositions (e.g. that the conformal part of space-time can be treated as a quantum variable) with facts about hypotheses and laws ( e.g. the conformal variable allows contiguity of the pre-- and pst Big Bang states, by virtue of the resulting universe being compatible with a harmonic oscillator form of solution, which we know has solutions in terms of Hermite polynomials H_ n (q))

Finally, in his last sentence the pastor evinces total confusion in terms of his criticism. He avers:

"now that contemporary cosmology points to the universe's beginning and an external cause , skeptics insist everything needs a cause after all ! "

But misses the point as to why the external cause needn't be his "god". Again, from John Allan Paulos ('Irreligion'):

"If someone asserts that God is the uncaused first cause and then preens as if he's actually explained something, we should inquire: 'Why can't the physical universe itself be taken to be the uncaused first cause? After all, Occam's Razor advises us to shave off unnecessary assumptions, so taking the universe itself as the uncaused first cause has the great virtue of not having to introduce the (unnecessary) hypothesis of God"

The issue with us skeptics then, isn't we are now 'changing our minds' and just asserting "everything has a cause", but rather saying that you have to constrain your causal options until you fully define and explicate the nature of the entity you claim is unique and causeless. To use Paulos' words again: "Either EVERYTHING has a cause OR there's something that doesn't." BUT- if there's something that doesn't, that doesn't ipso facto make it "God" (since you haven't provided the n-s conditions for it to exist yet!)

Failing that proviso, coughing up those pesky n-s conditions, then the theist is left with one fact alone: If everything has a cause then GOD must too! THAT is why it is logical to introduce that another agent had to create him. OTOH, if something exists that IS uncaused, it could as well be the cosmos emerging from a sub-quantual bubble vacuum, which proposal has at least been published in a peer-reviewed scientific paper.

So much for the pinheads, who seem to be those who exercise more "common sense" than scientific sense in arriving at the mandate their god must exist. Well, it does, in their temporal lobes!

Theodicy Redux: Why do Certain 'Pastors' not get it?

It’s amazing that despite numerous Brane Space blogs on theodicy, and the general problem of evil- there are certain folks (like a certain "pastor") who reference this blog for indirect attack, yet still fail to appreciate the serious problem it poses for their god-concept. According to this same pastor in a recent blog piece on the nature of evil:

“Frankly , God owes NO ONE any "explanation" for anything ! The atheists and followers of Satan want everyone to think that we should live in a perfect , sinless , evil-less world .”

This, of course, misrepresents our position, but what’s new? It’s always more convenient to attack a red herring than it is to deal with the actual, underlying themes and arguments. For one thing, we don’t want or expect a “God” (whose existence is dubious and debatable) to proffer any “explanation”. What we want is the particular GOD BELIEVER to advance cogent reasons WHY HIS God is inactive in the world, to the point of being superfluous.

We want this to be a serious exercise in logic and not a specious errand devoted to deflection and distortion. As in the trope that we “think we should live in a perfect, sinless world’. NO WE DO NOT! I already made it clear that evolution presumes an imperfect world, and thus once one accepts evolution then imperfection must follow. (A point also made by Bernard Haisch in his own God Theory)

What we are saying, according to the Leibniz ontological premise, is that IF God existed then It ALREADY WAS PERFECT as a perfect vacuum of nothingness. If ALREADY PERFECT THEN WHY CREATE SOMETHING (UNIVERSE AND BEINGS) MANIFESTLY IMPERPFECT?

Especially – if one ascribes omniscience – it would have to know even prior to its act of creation that it would have to allow billions to be tortured eternally in Hell (according to the fundagelical beliefs and those of many other Christians ). Thus, by the very choice of creating, it committed a monumental act of violence and did so in a pre-meditated fashion.

The atheist lacks this problem because we don’t pin the inception of the cosmos on a god but rather a spontaneous quantum 'bubble' erupting from a 5D enclosed brane into a 4D space-time under the impetus of immense dark energy.

However, the onus is on the Christian – especially the fundie, to account for why his deity had to depart from putative perfection to enable a world of manifest evil AND IMPERFECTION. Was he or It following orders from an evil counterpart?

But instead of addressing the core issue, this following sort of refuse is emitted:


“What Satan DOESN'T tell you , though , is that the world WAS PERFECT !! That is , until he tempted Adam and Eve to sin - and ever since then , sin and evil have been in the world - though , it will NOT always be that way”

And so we see that rather argue rigorously from reason, the evangel cultist has no option other than to reaffirm and invoke his fairy story again, of the “garden of Eden”. (Along with his favorite fictious bogeyman "Satan'.....wooohooooo...!) A & E is a corny story that used to be taught to kindergarten Catholic Catechism kids in the 50s and 60s but eventually dumped because the kids started getting too smart and asked tough questions:

“Teacher, how come snakes can talk? I don’t see no snakes talkin’ anywhere, even at the Zoo!”

In other words, the “Adam and Eve” story is a cop out for morons and very under-developed children. There was never any “Adam and Eve” just as there was never any “Garden of Eden”. The planet was always brutish and nasty from the time of its formation from the solar nebula – starting with a poisonous, reducing atmosphere of methane that was only changed over eons into one of oxygen and nitrogen.

And then near the end we see the prime copout of projecting the origin of evil onto those who question them, because they’re incapable of explaining it themselves:

“Much of the evil BEGINS with Satan's atheists and other non-believers , as well as the various anti-Christ religious denominations ."

So, it’s all on us then! We’re responsible for the serial killers, the rapes, the 9-11s, the assassinations, all the wars (never mind most of the U.S. military commanders now in Iraq & Afghanistan side with Jaysus and believe their god is “more powerful than Allah”), and I suppose even the recent eruption of the Icelandic volcano which discommoded 9.5 million air passengers. So – according to this lame brain pastor, what? I guess we owe all those passengers an apology?

But impervious to reason as usual, he goes on in his own inimitable way.

“So , the next time an atheist and their ilk want to point the finger at God for the evil in the world , just tell 'em to look in the mirror , and they'll see the finger pointing right where it should be - BACK AT THEM !!”


Actually, again, he’s too clueless to get things straight in his mind. We don’t point the finger at God” for evil in the world, because we don’t accept there is a GOD! We say that BECAUSE THERE IS NO GOD, THERE IS NO NEED TO ACCOUNT FOR WHY EVIL EXISTS!

It exists because no one’s controlling the global theater. People get away with whatever they do because NO ONE IS MINDING THE STORE! There is no “Papa God’ to STOP, FAR LESS correct the evil doers, or to prevent volcanoes from blowing molten glass into the sky to prevent air travel, or to prevent an earthquake that killed over 200,000 in Haiti. Everyone's in a giant pinball game, like it or not.

There's nothing there because we inhabit a purposeless, godless, random event universe. So we certainly can’t blame God! That’s like me blaming today’s snow storm in Colo. on the “sky duppies” who live in the clouds. It’s stupid and unproductive. Save it for the peanut gallery.

At least Bernard Haisch, though his God Theory is exotic and far from closed, has the sense and intelligence not to blame others for either natural or man-made evil in the world. He holds his own deity responsible but in a creative way, basically because an evolving manifestation of that deity prevents it from achieving the perfective state in how the world unfolds. It must unfold according to the laws and natural principles invested in its evolving creation, and since the manifest God is part of the imperfect unfolding, it can’t act to prevent human foibles, crimes, wars, troubles, or natural volcanoes, or mammoth quakes.

A beautiful, simple and elegant solution – though admittedly far from complete- though at least he’s an adult enough not to need to fall back on childhood stories of Eden.

But at least superior to a certain clueless pastor’s!

But what else do you expect from a clown who actually believes the “face of Satan” appeared in the cloud of detritus from the Twin Towers. (See the book, “Faces in the Clouds” for how humans project imagery because of a basic brain wiring defect in the frontal cortex)

The Cognitive Dissonance of Americans

In earlier blogs I made reference to the corporate media and the extent of their brainwashing, propagandizing power. Often, the degree to which this is manifested reflects in polls, surveys that show a fundamental cognitive dissonance in the responses. The classic one emerged sometime over the summer, ironically at a tea party meeting, when one of the tee-pees yelled out: “I don’t want government in health care, and KEEP YOUR HANDS OFF MY MEDICARE!”

Clearly, showing a mammoth disconnect, since Medicare is one of the biggest government run programs, and yet this person didn’t want to lose his! Well, why not? We know that before Medicare passed in 1966, 67% of seniors were below the poverty line, most often because their medical costs bankrupted them or left them impecunious. No one denies Medicare is a worthwhile program except the most rabid libertarians, who insist the elderly ought to sink or swim on their savings.

More recent polls (from CBS-New York Times) disclose an ongoing cognitive dissonance among the tee-pee crowd who keep uttering the mantra for “less government” but of whom two-thirds don’t want to have anyone touch their Medicare or Social Security. Question: How do you get to “less government” without going after the two biggest “entitlements” around? The tee-pees won’t say, only that they don’t want anyone touching theirs.

This brings up the possibility that the TPs’ opinions actually reflects a more nuanced position than portrayed by the media mavens and blow-dried himbos and bimbos: that is, Less government is fine, but not for THEM – rather for those parasites who don’t like working or collect food stamps, or welfare.

In other words, the “I got mine and to Hell with you” rubric and ethic.

In a way, this doesn’t surprise me, since the (cowboy) capitalist nature of the country, enforcing a relentless “dog eat dog” competition- with only winners and losers- ensures everyone will fight over ever diminishing scraps of the pie. Thus, those who fear their portion will be cut will go after those who they fear will benefit from the cuts. As Charles Reich observed ('Opposing the System', p. 103):

"Community is destroyed because we are no longer 'in this together' because everyone is a threat to everyone else. "

In effect, it is for THOSE miscreants and layabouts that the TPs want less government, since they are the primary threats to the TPs' future economic security. But this is too complicated for them or abrasive for others they prefer not to alienate, so they stick with the simplistic "less government" spiel.

Now, a new PEW Survey and poll shows even more cognitive dissonance. According to this poll (see WSJ, 4/22, p. A21 top) only 40% of Americans say the government should exert more control over the economy today, compared with 54% a year ago. What happened here? Have Americans THAT short a collective memory, or have they simply been drumbeaten into stupidity and gullibility the past eight months?

Most intelligent people a year ago, at least those who also studied any macro-economics, knew that the credit and housing crisis caused a massive meltdown in the demand side of the U.S. economy. That is, the side governing consumer purchases, company hiring, and bank lending.

Effectively, the toxic waste (known as credit default swaps) buried in securities and especially collateralized debt obligations (CDOs) caused a massive shutdown of the productive, income generating and lending sector- threatening to bring about a seizure in economic activity every bit as immense as the bank closures in the 1930s.

Every sane economist and student of economics realized (based on knowledge of past history) that we were headed for a second Great Depression unless a flood of money was poured into the demand side. Banks weren’t providing it, private companies weren’t (including not hiring) and consumers all but shut down their purse strings- incepting even more firings and layoffs since companies whose goods weren’t bought couldn’t afford to retain staff to sell it. Inventories across the nation piled up in the wake.

Predictably, we reached 10% unemployment by the middle of 2009. Fortunately, however, the worst was averted because of the infusion of demand side money as a result of the $787 billion stimulus package. However, rather than do the follow-up PR job they needed to, to inform the public of the benefits, the Dems cowered behind closed doors as critics appeared in every conceivable venue yakking about “bank bailouts”. Before you could say ‘Obama’, every manjack and yahoo had an opinion of the stimulus and it wasn’t favorable.

Add to that the government taking over GM, Chrysler, etc, and the word was out the “government was on a rampage” (never mind that because of the bankruptcy required by government, GM and Chrysler are now both beginning to pay back what they were lent, GM a hefty $5.8 billion, and Chrysler $1.8 billion).

But, if it weren’t for GM’s CEO going on the air and broadcasting that success, I’d never have known about it. So WHERE THE HELL ARE THE DEMOCRATS? Why aren’t they capable of defending the actions, policies of government when they are beneficial? I submit that this failure of nerve, of explicatory capacity is a major factor in why the Tea Party movement arose in the first place, and shy so many Americans now think government exerts “too much control”.

Again, the Democrats passed and facilitated these things, but failed to make the PR sale later.

Last night, on the Rachel Maddow (MSNBC) show, we also learned for the first time of the massive rallies FOR government involvement occurring across our country. Some of these have 400,000 people on the streets in one day. So WHY have we not heard about them, and only about the pouty, sulky and whiny teepee crowd? (Who only managed a stunning 1500-odd people in their DC tax day rally, according to Reuters reports).

Gov. Ed Rendell of PA put it to Rachel’s audience that the reason is two fold: 1) the corporate media has focused almost exclusively on the Teepees, mainly because they get wet dreams over the “fight” meme and the teepees represent some kind of fighting opposition to Obama. And (2) the Democrats have “cowered behind shower curtains” (Rendell’s words) rather than go out and defend their votes, policies and actions for government doing the RIGHT thing.

Why are the Dems so consistently ball-less? I go back to what was said in an earlier blog about their incapacity to fight or vigorously defend their positions: since starting to take –accept campaign contributions from the Avatars of the Neo-liberal (less security for citizens, more freedom for markets) Hegemony, the Dems have ceased to be partisan fighters for the cause- which includes defending government when appropriate. Calling out the idiots, like those who conflate the stimulus to a “bailout” and knocking them hard and often.

The Democrats, if they want to be a viable party in the future, have to cease being pusillanimous because their novel assertiveness might offend the corporate, neo-liberal "hands that feed them". (Better yet, stop being “fed” by them, and get money the old-fashioned way by massive fund raising efforts from the PEOPLE, or better, changing the laws so NO one goes to the corporate trough for campaign cash, and setting up a publicly funded election pool).

And on that note, may I also suggest to Obama – before he has the SEC take Goldman Sachs to court- that he return the $1 million 2008 campaign donation they gave him?

WHO occupies REAL Cult status?

It’s always a bit of an amusement to visit a certain blog (which shall remain nameless) to see (and laugh at) the latest bunkum posted by its blustering, huffing, undereducated and misguided owner. I guess you could call it a welcome diversion.

In my last, most recent foray into this backward, backwoods blog, the claim was made that “Catholics, JWs, Mormons, etc. were all CULTS” and moreover, the “red flag ought to go up whenever one sees them being “defended by an Atheist”. Really? How so?

Does “defending them” really mean supporting them? Does describing a possible basis for common cause imply "defending them"? Well, I imagine so in the derelict, fractionated brain of this pastor. As readers will recall, however, I have been every bit as hard on these religions as on the good pastor’s (which incidentally, I regard as the only Cult – for reasons I will proffer shortly).

What I did do is the following, to clear the air:

1- Never said one word about the Mormons, which I regard as no more or less a “cult” than the Christian evangelicals or their Charismatic- talking in tongues, KJV -banging brethren.

2- Justified the Catholic Church, warts and all, as a true and valid religion primarily by virtue of its historicity and seniority. In other words, it commenced well over fourteen centuries before the pipsqueak Protestant Johnny come latelies began their revolt (over 1500+ years before King James and his corrupted bible, based on an erroneous script by Erasmus). To assert, therefore, that "Catholics form a cult” is as disingenuous and ignorant as asserting that the U.S. is a real, independent nation – but Great Britain (from which the U.S. revolted)is merely a "colony".

3- Justified considering the Jehovah’s Witnesses as possible “comrades in arms” given the same pompous pastor had waylaid them with a 10-12 blog attack, thereby taking his odious sights temporarily off atheists. (However, at no point did I “defend” any JW beliefs, though my conversations with them have disclosed they don’t buy into a literal “Hell” like this corny –cornpone “pastor”. )

Now, again, what constitutes a cult and what doesn’t? Unless the specific attributes are known and accepted, one will go round and round the bend on this, so let’s revisit those criteria which I discussed in a February blog. (Note: whether one accepts a particular rendering of scriptures, e.g. KJV bible or other, is NOT a cult criterion. What is, is whether one embraces it as a SOLE FONT of truth!)


Generally, four characteristics can be used to make an identification:

1-A belief system that is independent of facts, logic, or even one’s own intuition. In other words an absolute and blind acceptance of specific literature (generally a bible) as undeniable fact.

2-A pre-meditated choice to isolate from the rest of society, usually justified by the assertion that those outside of the faith are wicked, lost, hellbound etc.

3-The compulsive need to recruit others into the cult- called by different names, e.g. witnessing,.

4-The complete loss of individuality, logic, and objectivity. The only reasons for continued existence becomes the serving of the cult’s raison d’etre.

Let’s look at each in turn to see whether JWs or Catholics meet the respective criteria (clearly Atheists do not, since we harbor no belief systems independent of logic, nor adopt any specific SINGLE piece of literature (e.g. like the KJV bible by fundies), nor do we “isolate from society” or declare our opponents bound for atheist hell, oh and we don’t need to “witness to others”! We also extol individuality, rather than steamrolling it under a pile of superstitious mush).

Catholics by way of their magisterium (teaching office) have always allowed for extending one’s insights beyond one or several books. (This is one reason why, for a long time, the Church discouraged reading the bible and scriptures, because it was felt the lower classes and especially the less educated would invest too much time and energy in them to the exclusion of other works- like The Confessions of St. Augustine.)

On this basis alone the Catholic Church can’t be a cult. Second, the Church doesn’t isolate from the rest of society, but rather extends its missions and outreach programs all over the world. Third, the Church has no “witnessing” or proselytizing program like the fundies-evangelicals do. Last, there’s no loss of individuality because many priests and bishops readily allow that certain teachings (e.g. banning artificial contraception) can be judiciously ignored without risk of grave sin. Millions of Roman Catholics actually take communion each day and still practice artificial birth control, since they understand the teaching on it issued from the magisterium and not the infallible office of the papacy.

ON all these counts, like it or not, The Catholic Church comprises no cult.

What about the JWs? I can’t make as certain a contention here, because I’ve never belonged to that religion. I can only go by my interactions with assorted JWs online (AARP 'Is There Life After Death?' forum - from 2007-2008) . But from those interactions I found: 1) at no time did any "JWs" attempt to insist only one book (e.g. their NWT bible) was the correct one, like the fundies insist their KJV is; and 2) they all agreed that Darwinian evolution correctly explains nature and human biology, and 3) they never issued any hell threats or warnings. On just this limited basis, the JWs therefore, can’t be called a cult. Maybe a “sect” but not a cult. At the very least, bare minimum, the JWs are no more a cult than the KJV-dominated evangelicals who want to pin the word on them. Speaking of whom.....

What about Fundies? Let’s look at why THEY DO MEET the critera:

1) All Fundies (ok, 99.9999999999%) believe their ONE book is “inerrant” so they simply masticate what’s in that bible (usually the corrupted KJV) and declare it provides not only ALL their truth, but EVERYONE ELSE'S. In terms of facts and logic, seldom, if ever, do Christian Evangelicals make their own conjectures about nature, the phenomenon of life and morality. They accept without question everything imparted to them by their pastors or bibles- even when the information is contradictive of science, history, logic, or basic intelligence. In its place they impose and insinuate their own corrupted and debased information, which is actually carefully crafted propaganda- though they don't realize it. The very fact they embrace ONE BOOK as holding ALL truth means they ascend to undeniable culthood.

Note: the one exception to this I've beheld was an Evangelical pastor in Florida who recently stated that evolution is possible, and should not be excluded automatically. For that bit of independent thought he was rousted from his position. Again, the same thing we beheld over and over with the Rev. Jim Jones cult in Guyana! The attribute of a CULT.

2) The choice to isolate themselves is pre-meditated, because the Evangelical-Fundie accepts the world is evil, and only those who accept HIS version of the Christian faith will be saved from eternity in Hell. Some actually assert their bible requires that they separate and ISOLATE themselves from all “Satanic religions” – which of course means any religion that doesn’t share their particular code of accepted beliefs or bible. They also mandate the benefits of ISOLATION from ("non-born again") family who may otherwise "speed them to Hell." Worse, they can't see their monumental arrogance and self-righteousness in all this.

After declaring an entity "wicked and wayward", the Christian fundagelicals will use boycott and even public protest to show disdain for a wide range of institutions.All of this behavior is exactly the same as we have documented at Jonestown, where certain books, people, movies etc. were to be shunned. Pastor Jones declared what was acceptable and what wasn’t.

3) All cults feel they have to validate their existence by recruiting others into their insanity and mental slavery. For the Christian Fundie this amounts to a subtle terrorist tactic called “witnessing”.Using this process, they believe god has charged them with the task of turning everyone in the world into a ‘Saved” – Born Again Christian who embraces John 3:16. After all, they must save people from the otherwise certain fate of “Hellfire’. (Odd, because their own good Book, in the New Testament (Matt. 7:1-5) enjoins them not to judge “lest ye be judged”. And in deeming people hellbound they are emphatically making their own judgments!)Christian Fundamentalists believe it is the will of the divine that they make every effort to recruit (witness to) every other human being on the planet into their religious organization. The idea of simply letting each worship his own God, observing his traditions, and allowing the rest of the world to do the same is unacceptable

4) In respect of this attribute it’s easily seen that the Christian Cultists’ identity is totally vested in his belief system – which is based exclusively on the King James Version of the Bible. Criticize his belief system (or KJV) and he construes it as an attack on himself personally as well as charging "blasphemy". Predicated on the foregoing, Christian Fundamentalism- Evangelicalism can be seen as one enormous cult. Further, its belief system can be seen as a form of fear-based mind control. These people feel that they can’t even be friends with an “unbeliever” unless the ulterior purpose enters of getting him to see “God’s word”.

Thus, they lack any manner of independence to even choose their friends – even if these people are family members. Their poisonous, toxic belief system prevents it. How people choose to think, believe, and even act is completely up to them, of course, but when any group has a clear and aggressive mission of subverting and disrupting the rights of other people in an effort to impose its edicts upon the masses it ceases to be religion but becomes a cult – especially if its members are impervious to argument and logic.

Pastor Jim Jones was the same, and he saw enemies and an "evil" opposition throughout his life, leading inexorably to the perception that an exodus to Guyana (in South America ) was the only escape. Arguably, Jones totally lost whatever was left of his mind long before he issued the order for mass suicide in Christ’s name and his own. Because the vast opposition to him was feared to be gaining strength, he commanded all his gullible minions to take their own lives rather than inhabit a “Satanic-loving, politically correct world”.

Sad, but this is the lot for those prepared to sacrifice their minds, brains to the commands and edicts of a CULT, or to its claimed leader-pastor-Reverend. People inclined to do this might do well to consult the bible they hold so dear and the sections referring to "wolves in sheep's clothing" and "FALSE PROPHETS" who will lead them astray. Because make no mistake, anyone grounded in all the essential cult attributes and yet prepared to fling the c-word at all other religions, beliefs or non-beliefs, is definitely a cultist. Worse, a cultist who doesn't even recognize he's a cultist: the worst kind! Rather than consuming so much of their time and energy on blustering castigations of others and their beliefs, these religious misfits and miscreants would do better to apply the same time and energy to feeding the homeless, or attending to poor seniors in a nursing home. At least then they'd prove to us they aren't cultists and aren't isolated.

Another Reason to Steer Clear of Stocks

In a number of previous blogs I warned about the dangers of stock market investment- from market timing tricks used by big institutional investors, to the presence of unregulated derivatives, to the fact that we are in the midst of another stock bubble which bursting could have worse consequences than the last episode (tied to the credit default crisis) in 2008. This bubble is tied directly to the Fed's continued low interest rates (~ 0.25%) which creates a "cheap money" surplus that entices much more risk as well as speculative recklessness.

The good news is many investors, especially with 401ks needed for retirement, are playing it safe this time, despite incessant cajoling and pressure from the usual suspects (business cable networks, Wall Street Journal stock humpers, financial pundits at the major networks) to “get off the sidelines”. As usual, many of these cite the inflation risk to keeping money in minuscule interest earning instruments such as CDs and money market accounts. (Not money market funds, since those aren’t FDIC-insured, though they are also earning pitiful interest).

As we all know and understand, yearly inflation – even at say 2%- will quickly eat up returns averaging barely 1.3% (For example, in the money market account I am currently in.) Over time, losses pile up. Thus, a $10,000 1-yr. CD earning 1% a year interest ($100) will lose $200 to inflation, for a net loss on that account of ~ $100 per year. (If the CD is rolled over and the conditions not changed). Thus, the following year, one commences with $9,900 and the net loss is:$200 – 99 = $101 etc., and that’s assuming no increase in inflation.

For bank savings and checking accounts the losses can be much greater, mainly because they pay a pittance in interest. In one of my (joint) bank CDs the interest is about 0.0025% a year, meaning I’m getting taken to the cleaners via inflation. However, I keep the (low amount) CD because it means I have to pay no bank fees at all. Sure I could look for a credit union or such, but that would be wasteful of energy – since this bank is only a block away and one can use the “two foot express” as opposed to driving eight miles to the nearest credit union each time. (As for online banking, sorry, don’t trust their systems! Despite all their soothe-saying and assurances, too much potential to be hacked!)

Anyway, the bottom line is one takes the risks where they make most sense to him. My question is this: Which makes more sense, losing $500-$1000 a year to inflation from all one’s fixed interest accounts, or losing $50,000- $100,000 in a large and even well diversified stock account? I say the former tableaux makes much more sense, since to lose the latter will likely mean taking years to reach the break even point.

As the DOW now climbs toward 12,000 many think they’ll make back what they lost in 2008, but they’re living in a fool’s paradise. First, as PARADE resident genius Marilyn vos Savant once pointed out in answer to a question, the market volume is geared so that only 10-15% can redeem in time and make their money back. All the rest will lose. This also applies to stock mutual funds. The reason is that most of the stock inflation and pump up is due to high P/E ratios, while REAL money is poured in to purchase them. In effect, one is gambling using his real, hard earned bread that he will hit the P/E high note and get that money out without suffering losses. Think again!

Most big institutional investors from pension fund holders to corporations use some form of market timing to get the news of companies’ stocks and their “bottom lines” before the little guy can read about it in the Wall Street Journal (usually the following day).

Now, with high frequency trading(HFT), it’s much worse. Because of the nature of the trades, buyers (or sellers) can know what you’re doing and react to it almost before you can get to a telephone to call your broker. HFT allows one group of investors to see the data on other people's orders ahead of time and use their supercomputers to buy in front of them. It's called front-loading, and it goes on every day.

In an interview on CNBC, HFT-expert Joe Saluzzi was asked if the big HFT players were able to see other investors orders (and execute trades) before them. Saluzzi replied:

"Yes. The answer is absolutely yes. The exchanges supply you with the data, giving you the flash order, and if your fixed connection goes into their lines first, you are disadvantaging the retail and institutional investor."

So, with HFT even the “big guy” (institutional investor) is placed in a marginal position in terms of the capacity to say redeem the stock phantom money (usually based on a very high P/E ratio) and capture actual real money at the cash out end.

Does this even begin to paint the warp and woof of the problem? Nope! Here’s another newsflash for the ordinary, non-HFT pipsqueaks still in stocks or considering them: The deep-pocket bank/brokerages actually pay the NYSE and the NASDAQ to "colocate" their behemoth computers ON THE FLOOR OF THE EXCHANGES so they can shave off critical milliseconds after they've gotten a first-peak at incoming trades. It's like parking the company forklift in front of the local bank vault to ease the transfer of purloined cash.

How can a new buyer be affected, for example? In a recent post, ‘Zero Hedge’ blogger Market Ticker explained some fine-points of HFT, such as, how the banks/brokerages probe the exchanges with small orders in order to find out how much other investors are willing to pay for a particular stock. He asserted:

"Let's say that there is a buyer willing to buy 100,000 shares of Broadcom with a limit price of $26.40. That is, the buyer will accept any price up to $26.40. But the market at this particular moment in time is at $26.10, or thirty cents lower."

So the computers, having detected via their "flash orders" that there is a desire for Broadcom shares, start to issue tiny "immediate or cancel" orders - IOCs - to sell at $26.20. If that order is "eaten" the computer then issues an order at $26.25, then $26.30, then $26.35, then $26.40. When it tries $26.45 it gets no bite and the order is immediately canceled.

Now the flush of supply comes at $26.39, and the claim is made that the market has become "more efficient." Balderdash! In fact, there was no "real seller" at any of these prices! This pattern of offering was intended to do one and only one thing - manipulate the market by discovering what is supposed to be a hidden piece of information - the other side's limit price!

With normal order queues and flows the person with the limit order would see the offer at $26.20 and might drop his limit. But the computers are so fast that unless a buyer owns one of the same speed devices, his order is immediately "raped" at the full limit price! Losses like this can pile up, and we aren’t even looking at the “sell” end which is often more critical if little guys need to get their moola out in a hurry so junior can go to college, or to pay off medical bills or whatever.

Again, my best advice? Stay out of the stock market unless you have money you can afford to lose. Especially with all the literal gaming still going on, and the fact that unregulated derivatives still pervade stocks and we all saw what those can do!

Looking at Groups

When I first taught mathematics in Barbados (Peace Corps) I quickly discovered my class was most fascinated by the mathematical entities known as groups. I'm not sure why this should have been the case, but suspect that a number of the (simplified) examples - using "clock arithmetic" I presented, had them linking groups to games! Irrespective of the reason, they took to groups like ducks to water and their math marks averaged highest whenever groups were tested.

In this blog we’ll be looking at these most fascinating and useful mathematical creatures. This will mainly be done at a basic, intuitive level (about the same as the level I taught 2nd formers in Barbados) though at the end I will give some examples and illustrations of exotic groups including from modern physics.

1. Definitions:

A GROUP is a set G with one binary operation defined on it , and G satisfies the axioms:

(a) Associative law: a· (b · c) = (a· b) · c
(b) Identity element (e): there exists an element e { G such that: e · a = a for all a { G and a · e = a

(c) Inverse element: For any a { G there exists an element a^-1 {G such that: a · a^-1 = a^-1 · a = e

d) Commutativity[1]: Only if there exist elements a, b { G such that (a · b) = (b · a), then G is said to be an Abelian Group.

2. Generating Simple Groups:

A) Clock Groups:


These are amongst the simplest of all, and easiest to generate – they also represent a nice introduction to modular arithmetic, the Euclidean Algorithm etc.

Let a clock group representation be denoted as shown in the diagram of Figure 1.

We seek to construct a group from the above, which is closed under addition. As we can see there are four members, 0, 1, 2, and 3. The process of addition is defined by adding elements – starting with 0- in a clockwise sense. Doing this we should be able to find a complete closed set of addition operations for all the elements. For example, we find 0 + 1 =1, and 0 + 2 = 2 and so forth. Similarly, we find 1 + 1 = 2, 1 + 3 = 0, 2 + 3 = 1 and so on. Each result obtained by adding the portion of the cycle from the starting element. From here, we may set out the group under addition (+) (Fig. 1- right top)

The reader should easily be able to check each of these and demonstrate for himself that the table is valid. Is G+⊕ (4) a group? Yes, because it obeys all the properties for a group.

Problem: For the same group, develop a table to show it is closed under multiplication (x). Hint: Simply extend the principle of addition to the case of multiples, and start all multiple entries counting clockwise from 0. For example, 2 + 2 + 2 amounts to three two’s counted from 0. (Three sets of two). One such counting set leads to 2, and two leads to 0 and three leads to…? Obviously, 2.

Thus: 4 + 4 = 0 and 4 + 4 + 4 = 0 so that 3 x 4 = 0

What about: 3 + 3 + 3?

By inspection and using the clock graphic we obtain: 3 + 3 + 3 = 1 so that 3 x 3 = 1

We thereby arrive at the (x) table for the group G+⊕ (4) (Bottom right in Fig. 1)

Is this group commutative? Some checks of the operation using pairs of elements will confirm that it is (E.g. 2 x 3 = 3 x 2). Hence, we can aver it is an Abelian group.

Problem: Set out a clock group with five elements (G+⊕ (5)), and prepare tables to show the group is closed under (+) and (x).

Solution:

The correct diagram is shown in Fig. 2, along with the tables for multiplication and addition.


B) Cyclic Groups and Sub-groups

A more advanced variation on the simple clock group is what's called a "cyclic group" which we will see can also be a sub-group. To clarify definitions here - let G denote a group, and let H be a subset of G (H ( G) - then H is a sub-group of G if: H is closed under the same operation as G, for each element x there exists the inverse element, x^-1, and these are related to an identity element I such that: (x)(x^-1)= I.


A relevant theorem- Lagrange's Theorem:

Let G be a group of finite order n, then let a be any element of G. Then the order of the element divides the order of G.

Proof:

Let H be the set of all powers of a:

H = {a, a^2, a^3, a^4...........a^n}

But, H must have a finite number of distinct elements.

Then: a^n = a^m (for some m

a^n(a^m)^-1 = a^(n-m)* a^m(a^m)^-1 = a^(n-m) *I

Is the cyclic group closed under (x)? Check by consideration of C_4, the cyclic group of order 4. To see an example of C_4 simply take the diagram for the clock group, G+⊕ (4), and re-assign it elements as follows:

0 -> 1

1 -> a^1 = a

2 -> a^2

3 -> a^3


Now, what will the multiplication table look like?

Solution: the result is shown in Fig. 3. Not especially how the table differs from the (x) table for the clock group, G+⊕ (4).


Practice exercise:

Using the diagram for the clock group G+⊕ (5) in Fig. 2 as a template, work out the elements for the cyclic group C_5. Prepare a table for (x) applicable to its elements. If C_4 a sub-group of C_5? Why or why not?



[1] This is not a critical, or indispensble group property. If it does apply, we say the group is Abelian.