The Gödelian argument proceeds by reductio ad absurdum, it initially supposes that the mind is essentially mechanical in nature and then tries to draw a contradiction from this hypothesis, if such a contradiction can be reached then we know that the hypothesis that we initially assumed as true is actually false.  But what does it mean to be mechanical?  We answer this next question by invoking the Church-Turing thesis, which loosely says that all essentially mechanical phenomena can be modeled by a very precise mathematical abstraction known as a Turing machine.  However, Turing machines are equivalent to μ-recursive functions which are in turn objects of first-order logic, and since the incompleteness theorem has consequences for first-order logic it therefore follows (from a bird’s-eye view) that it might also have consequences for μ-recursive functions and their Turing machine equivalents.  So there is a deductive trail that suggests the potential for a connection between the incompleteness theorem and what we can say about a mechanistic theory of mind.

The Incompleteness Theorem

Truth, as a semantic concept, is a rather ephemeral beast that can be apprehended but never found, like Bigfoot its metaphysics are contentious, but unlike Bigfoot it cannot simply be ignored.  After all, what kind of man can claim to be rational while denying Truth?

This is where the broader project of reductionism enters the scene as it tried to bring this semantic concept of analytic Truth down from the Platonic heavens and confine it to a syntactic cage of language rules once and for all.  Gödel’s incompleteness theorem showed that this could not be done - that the semantic notion of Truth couldn’t be reduced to syntactic notions of proof - thus lending the reductionist program its first real defeat.  It did this by constructing an explicit sentence in first-order arithmetic that managed to be both true and unprovable.

One way of seeing how our intrepid German went about this is to first consider the paradox of the liar.  The liar is a logical sentence L that says of itself, “I am false.” In the conventions of logic we can represent such a sentence as follows:

L: ~True(⌈L⌉)

where ⌈L⌉ is meant to signify the name of L under some naming convention and Truth(•) is a predicate that accepts as input the names of logically admissible formula and evaluates their truth status

The reason that this sentence is paradoxical is because if you tried to semantically evaluate the truth status of this sentence you would get contradictory answers; for if L is false then it must be true (according to L) and if L is true then it must be false (according to L).  The situation is indeed paradoxical.

Gödel took this insight and went about constructing a provability predicate and a very peculiar sentence that says of itself, “I am not provable.” In a similar vein to that of the liar, we can represent this [Gödelian] sentence as follows:

G: ~Prov(⌈G⌉)

For the purposes of emphasis, the most technical part of Gödel’s proof of the incompleteness was in showing that such a naming convention and provability predicate could be constructed while remaining within the confines of first-order arithmetic.

Now if we try to semantically evaluate the truth status of G here is what happens; if G is false then it must be provable and therefore true (a contradiction) but if G is true then it is not provable and there is no contradiction.  Therefore, G must be both true and not provable and such a sentence has been demonstrably found.

What is going on here is that we’re playing a subtle game between the semantics of truth and the syntax of provability, it is a kind of game that is unique to these sorts of theorems and can’t be found in any other part of modern mathematics.  What is accessible to us semantically is the soundness of first-order arithmetic (i.e. what we prove is always true) but this is, evidently, not accessible to us syntactically, otherwise the Gödelian sentence would be an example of a paradoxical sentence in an arithmetic theory that we know is not paradoxical.

For the truly dedicated reader, all the technicalities of Gödel’s original proof can be cheaply found here.

The Church-Turing Thesis

“Nevertheless, an idealized abacus has precisely the power of a Turing machine...By parity of reasoning, they also both serve as models for the human mind.  Yet the thesis that the human mind is an abacus seems distinctly less plausible than the thesis that the human mind is a computer.  And for an obvious reason:  It is absurd.  It is precisely when things have been reduced to their essentials that the interaction between a human being and a simple machine emerges clearly.  That interaction is naked, a human agent handling an abacus with the same directness of touch that he might employ in handling a lever, a pulley, or an inclined plane.” - David Berlinski

In the early part of the 20th century first-rate mathematicians endeavored to understand this concept of mechanicity by developing their own models of what an effective procedure (or mechanical process) might look like and compare notes.  Church, Kleene, and Rosser had their μ-recursive functions; Alan Turing had his Turing machines; and Alonzo Church had his λ-calculus.  And then a most remarkable thing happened, as it turned out all of their abstract models were equivalent!  Not only that but it also has been subsequently shown that all known mechanical processes and/or algorithms that we might encode in a digital computer can be simulated by Turing machines; or equivalently μ-recursive functions; or equivalently statements in the λ-calculus.

Such tremendous theoretical and empirical success can only mean one thing; hence the Church-Turing thesis.  In the words of la wik, “Despite the fact that it cannot be formally proven, the Church-Turing thesis now has near-universal acceptance.”

The Gödelian Argument

“Gödel’s theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met.1 This I attempt to do.” - John Lucas

It’s worth noting that soon after Gödel proved the incompleteness theorem he speculated about the potential of such an argument and I am sure that it was no surprise to him when other philosophers and mathematicians started to formulate such arguments.  The first to do just that was British philosopher John Lucas in his opening salvo, “Minds, Machines, and Gödel”; more recently the esteemed Sir Roger Penrose presented his own rather refined version of the argument here and here.  Of course, there are many other such versions scattered throughout the literature and it would neither be practical nor necessary to list them all.

Unfortunately, the logical issues that surround this argument are of such a subtle and complicated nature that even people who’ve defended the argument over the years have conceded that they are not even sure of its truth, at least Lucas is on the record of saying as much.  But like all good questing Europeans such warnings do not deter us and I have endeavored to present a computational form of this argument with the intention of eliminating as many confusions and complexities as possible.

The Gödelian Argument

(H) The mind is essentially mechanical
(1) If the mind is essentially mechanical then its mathematical faculty is also essentially mechanical
(2) The mathematical faculty of the mind is essentially mechanical (using H and 1)
(3) The mathematical faculty of the mind can be represented by a Turing machine M (by 2 and the Church-Turing thesis)
(4) M is logically and knowably sound
(5) There is a knowably true statement that is accessible to us but not to M (by 4 and the Gödel-Turing-Penrose Theorem)
⊥

The contradiction comes from the fact that since M is supposed to represent the mathematical faculty of the mind its mathematical knowledge should be equivalent to that of our own, but statement (5) shows that this cannot be the case.  The only thing left to prove is the Gödel-Turing-Penrose Theorem, which I will now give:

Gödel-Turing-Penrose Theorem: If M is any logically and knowably sound Turing machine then there is a knowably true statement that is accessible to us but not to M

Proof (following Penrose): It is an elementary fact of Turing machines that we can enumerate the set of all Turing machines that accept one natural number as an argument by the natural numbers themselves: C₁, C₂, C₃, C₄, etc.

Consider a new Turing machine A such that A(q, n) stops if M can show that C_q(n) does not stop.

Therefore if A(q, n) stops then C_q(n) does not stop, by the previous sentence and the assumption on the soundness of M.

Therefore if A(n, n) stops then C_n(n) does not stop, by setting q=n in the previous sentence.  (α)

We now notice that A(n, n) is a Turing machine that depends on only one natural number.  Therefore there exists some natural number k such that C_k(n) carries out the same computation as A(n, n), seeing as how our enumeration covered all such Turing machines.

Therefore A(k, k) = C_k(k) - hence one computation stops if and only if the other stops - by setting n=k in the previous sentence.  (β)

Now if A(k, k) stops then C_k(k) stops by (β), but if A(k, k) stops then C_k(k) does not stop by (α).  Therefore we can conclude that A(k, k)=C_k(k) does not stop because if it did then we would get contradictory answers.

However, if the statement “C_k(k) does not stop” was accessible to M (or could be determined by M) then A(k, k) would stop by construction, which is a contradiction!  Therefore, arguing by reductio ad absurdum one more time, we can conclude that the statement “C_k(k) does not stop” is not was accessible to M.  So the sentence “C_k(k) does not stop” is both demonstrably true and not accessible to M.

QED

Philosophically, the structure of the Gödelian argument is evidently sound and the Gödel-Turing-Penrose Theorem that it uses in statement (5) is also clearly true, so the success of the Gödelian argument hinges on its two most nontrivial statements, (1) and (4).

In defense of (1), it would seem as if all human minds share a common mathematical faculty and so it seems reasonable to speak of such a faculty in the abstract.  Furthermore, the “if then” structure of the premise is also quite reasonable as it’s difficult to imagine how the mind could be essentially mechanical if even one of its faculties was not also essentially mechanical.

In defense of (4), it would seem that if the mathematical faculty of the human mind could be mechanized then it must be based on logically sound principles, otherwise how could any human mind engage in meaningful mathematical work without constantly creating contradictions.  In other words, what could account for the great success of our mathematics if it was built on principles that were not logically sound?  Furthermore, it would seem that whatever those principles might be that they could be knowably apprehended as being logically sound, for they are the principles that we would be using and we would not be using them if we did not, at the very least, believe them to be logically sound.

Concluding Observations

While each individual piece of the argument holds up rather well (or at least is not without natural justification) it cannot be denied that the sheer length and level of abstraction that it demands does weaken its effectiveness.  But what it lacks in effectiveness it more than compensates with admiration for its heroic attempt to bring together so many strands of 20th century thought for the purposes of sustaining a philosophical argument about the mind.

Lastly, of the four views considered in the introductory entry to this series only the first is nullified by this argument, which the Church-Turing thesis says is equivalent to the Strong AI hypothesis.  It is this latter observation that has personal significance to me as this was the argument that finally disabused me of the Strong AI hypothesis.

Latinos, Hispanics, and mestizos - whatever the gatekeepers of morality decide to call them - are free to organize, protest, and advance political goals strictly on the basis of race or ethnicity.  Consider some of the mission statements of these advocacy groups: The League of United Latin American Citizens (LULAC) is busy:

[a]dvancing the economic condition, educational attainment, political influence, health, and civil rights of the Hispanic population in the United States.

The National Council of La Raza:

is the largest national Hispanic civil rights and advocacy organization in the United States

... and:

works to improve opportunities for Hispanic Americans.

Note that the translation of “la raza” into English is “the race.”

Jews are free to advocate specifically and exclusively for other Jewish people.  Among other goals, the Anti-Defamation League:

defends the security of Israel and Jews worldwide.

The American Jewish Congress is:

organized to defend Jewish interests at home and abroad through public policy advocacy - using diplomacy, legislation and the courts.

Similarly, Asians are free to rally around race:

The Asian American Justice Center exists “to advance civil and human rights for Asian Americans.

Blacks have a multitude of race-based advocacy groups.  A special group for black practitioners exists for almost every professional occupation.  Furthermore, the Congressional Black Caucus exists as an exclusively black organization and is comprised of exclusively black Congressmen advancing exclusively black interests.

In fact, all “people of color” (meaning all non-White people) have an implicit license to politically organize according to racial identity.  The National Association for the Advancement of Colored People (NAACP) states:

The NAACP’s principal objective is to ensure the political, educational, social and economic equality of minority group citizens of United States.

Blacks, Jews, Asians, Hispanics, “people of color” - all of these groups advocate and organize on the basis of race or ethnicity.  Yet White Americans may do no such thing without an onslaught of defamatory remarks, negative press coverage, and accusations of “hate” or “extremism.”

The knee-jerk negative reaction to a White identity organization is not natural.  Suspicion regarding an explicitly White political group is the product of intense conditioning from a very young age.  The origin and methodology of this conditioning is too complicated to adequately explain herein, but much of it stems from public education, globalist elites, and the corporate media.  In short, from a very young age, White Americans are taught that love and admiration for the race and ethnicity of non-Whites is a healthy and sociable trait, but love and admiration for Whites by Whites is strictly forbidden.  White Americans are conditioned to scorn their own heritage and to fawn over all other races.  According to the ruling orthodoxy, admiration of non-Whites is tolerance and love but admiration of Whites is hate and bigotry.

No other group in America is taught or conditioned to have the same amount of self-sacrificial aims or self-loathing emotions.  In fact, most other ethnic groups are encouraged to have a deep and profound sense of heritage and ethnic identity.  Perversely, Whites are expected to enthusiastically jump on the non-White bandwagon while abandoning their own families.  Whites must celebrate the achievements of every other race and ethnicity.  Only Whites are forbidden from celebrating their own extended family, heritage, and history.  Any sense of pride or identity stemming from a genetic origin must only be experienced vicariously for White Americans.  An entire month has been dedicated to a celebration of the contributions to high culture, technology, art, philosophy, and civilization produced by black Americans.  If someone protests that an entire month seems like immense favoritism towards blacks, then calls of “racism” are certain.  Any opposition to the politically correct viewpoint is met with swift “justice” and the punishment is summary social execution.

The mere accusation of “racism” is enough to ruin a career, sink a political campaign, cancel an entertainment show, or alienate an individual.  Perhaps this is a better explanation for the dearth of White political groups.  Most of the nonsensical “truths” that modern Americans are forced to swallow are nothing more than shibboleths.  If the shibboleth is met with anything other than the proper response, the “outsider” has been successfully identified, and swift countermeasures will be undertaken.

Instead of American spies inside Germany’s Third Reich being discovered by holding up the pointer, middle, and ring fingers to signify the number three, American citizens within the border are identified as racist outcasts by merely questioning the dubious notion that “diversity is our greatest strength.” Instead of asking a gringo to pronounce a Spanish word with a rolling ‘r’, ask the sociology professor who is up for tenure about her thoughts about the long-term viability of an increasingly diverse America.  She had better work on her “accent” and toe the party line if she wants to have a successful academic career.  Otherwise, she may infect future legions with the disease of critical thought, healthy dissent, or individuality.  Heaven forbid, she may even fail in her greatest duty - to indoctrinate her pupils with the glorious fonts of wisdom which are Political Correctness and Tolerance for Diversity.  Joseph Goebbels would be proud of this efficient method for political cleansing.  A Soviet apparatchik would shriek with joy at the simplicity of this plan for purging the undesirables from the New Plan for Humanity.

As non-White Americans are free to create political organizations for the sole purpose of advancing the interests of a specific ethnicity, and White Americans are forbidden to do so, non-Whites enjoy fundamental rights and benefits which are denied to Whites.  The logical implications of these thoughts and observations are non-controversial, but the act of drawing attention to it is definitely controversial.  It might even be . . . “racist.”

As White Americans are prevented from organizing, thinking, or acting in a unified manner, and yet all other non-White groups are permitted and encouraged to do so, White Americans are at a distinct political disadvantage.  Social pressure, media influence, legislation, and educational indoctrination combine to influence Whites against organizing or even thinking on the basis of race.  This injustice must not stand.  White Americans must organize to advance their own interests or they will fade into a dispossessed minority in the nation their forefathers carved from the unforgiving wilderness.  White Americans must regain the political power they have implicitly relinquished.  White Americans need not fear their own shadows any longer.  Instead, White Americans must take back the reins and restore the conditions that made the United States of America into an exemplary society and a first-order civilization.

Once my prostrate form had been pumped towards the ceiling and I had, as I always do on these occasions, resolved to reduce my sugar intake, I became a half-hour hero.

My dentist’s usual technique for putting me at my ease is to regale me with anecdotes of blood and pain from his long career inside the mouths of strangers, but this time, as he did his worst to my martyred molar, he confined himself to murmured instructions to the nurse, and now that there was only the filling to go in, it seemed I might be spared any dental garrulity. My bib on, my gums numb, the drilling done, and a matrix band secured, I was almost relaxed, and certainly unprepared for the torrent of obscenity that began thundering behind my head.

“Human variation is endlessly fascinating,” I heard him say. “Not merely the differences between individuals, but the differences between groups.”

The oxygen was stripped from the air and I was fighting for breath. My whole life flashed before me. I felt I was dying in a terrible place.

“Yes,” my evil dentist continued, “the mouth is the mirror to the racial soul.”

I inhaled deeply three times and returned from the brink.

“E carehull,” I said.

“Do you know, Mr. Bismuth ...”

“Hohessor,” I said, remembering the nurse was there too.

“Sorry, Professor Bismuth. You are the first White patient I’ve seen today.”

“Ohnt shay engy nore.”

“You’ll have to wait until the band comes off, I’m afraid. One of the perquisites of dentistry is that it offers a succession of captive audiences for the frustrated monologist. Not as many as you have at the university, I’ll be bound. Amalgam, please, Sarah. Yes, in Negroes’ mouths it’s much more common than in those of other races to find a tooth-count over thirty-two. And also in Negroes, the third molars, the wisdom teeth, are never impacted.”

“Artsy scung! Artsy scung!”

“Well, I’ve never seen a case. Next amalgam, please, Sarah. And there’s a developmental abnormality, often of the premolars, known as dens repaginates - look it up - which is found almost exclusively among Orientals. In addition to the Chinese and Japanese, it’s found among Eskimos and Red Indians. This is a particularly diverse practice.”

“Artsy scung! Artsy scung!”

“Not too uncomfortable, is it? Well, won’t be long now. Last one, please, Sarah. But you, Professor Bismuth, you have a typically Anglo-Saxon mouth. You, like 94% of your race ...”

“Artsy scung! Artsy scung!”

“Well, your sub-race ... you have second molars with four cusps, five being present in over half of the Chinese, for instance. And, looking at your X-rays, I see your molars have bent roots, a malformation that’s also more common among the Englishry.”

“Artsy scung! Artsy scung!”

“I can see you are fairly bursting to join in, but you will be a helpless listener for another minute or so. Open wide.”

“Artsy scung! Artsy scung!”

“The largest molars I have ever seen were those of an Australian aborigine. He had a dental arch as broad as an amphitheatre, and disproportionately small incisors that did not fill the available space, leaving a wide gap between his two front teeth, a condition known as midline diastema. Look that one up too.”

“Artsy scung! Artsy scung! Artsy scung! Artsy scung! Artsy scung!”

“There now, we can unscrew the instrument of audience capture. Don’t have any hard toast or sticky toffee for the next couple of hours or you’ll be prematurely back here for further monologues.”

When my mouth was returned to me, I ripped off my bib like a petulant toddler and threw it at his feet. I accused him of practicing hate-dentistry. How dare he know these extremist facts? As patients, we put our trust in caring professionals, and when we are at our most vulnerable we do not expect to find ourselves the playthings of drill-wielders with unsavoury data at their finger tips. Let’s be clear: there is no place in a decent society for the disturbing details of comparative oral anatomy. Any teeth that could be saved by an understanding of racial differences should be lost as a matter of principle. I told him I would be putting my complaint in writing to the General Dental Council and I had every hope that it would do its duty and declare him unfit to practice, thus protecting the public from being relieved of suffering by the practical application of racism.

Assume for the sake of argument that in a stunning reversal, political correctness dictates that Africans are racist oppressors.  Africans disproportionately enjoy material niceties, unfairly subjugate other races, and an invisible “African privilege” pervades the air which mysteriously oppresses all other races.  In this hypothetical world, institutional racism means that Africans are predisposed to success and worldly gain from birth, as a result of the current political power relationship.  Now, follow the usual prescription for healing with plans for coercive diversity and watch the fireworks begin!

The continent of Africa can solve “the race problem” by a massive influx of non-Africans.  These non-Africans will assimilate and interbreed with Africans over time.  The end result will be a utopia of mocha-skinned beauties - society without race by homogeneous default.  Everyone will hold hands in unity, hatred will be a thing of the past, and racial oppression will no longer be an option.

A sharp mind quickly realizes the solution to “the race problem” in the African example is actually the Final Solution for Africans.  That is, the systematic eradication of the African people - African genocide.  No rational Black man will agree with such a genocidal campaign.  No reasonable Black man will stand by and cheer on the destruction of his or her fellow Africans.  No race deserves genocide.  Every race has the right to exist biologically, ethnically, and culturally.

International law defines genocide as an international crime against humanity, with grave punishment for violations.  As far as the international recognition of the reality of race, ask the ghosts of Saddam Hussein or Wilhelm Frick if the Kurds or Jews, respectively, are mere social constructs.  Race is an internationally-recognized reality and is a major factor in the crime of genocide.  In the future, the political and economic elites that are responsible for the policies of White genocide may face trial before an international tribunal.  The 1948 United Nations Convention on the Prevention and Punishment of the Crime of Genocide, Article II states:

In the present Convention, genocide means any of the following acts committed with the intent to destroy, in whole or in part, a national, ethnic, racial, or religious group as such:

(a) Killing members of the group;

(b) Causing serious bodily or mental harm to members of the group;

(c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;

(d) Imposing measures intended to prevent births within the group;

(e) Forcibly transferring children of the group to another group.

The present immigration and political policies of many traditionally White nations, especially the United States, are in violation of part (c) and possibly part (d).  White nations have been subverted to conditions that heavily favor non-White immigration, restrict White birthrates, and encourage and support non-White birthrates, and are thus calculated to bring about the physical destruction of the White race.  There are many quotations of politicians, professors, and pundits advocating this very point - the end of the White race.  Genocide is not always an act of traditional murder.  The United Nations Convention on Genocide covers violent genocide with parts (a) and (b).  However, the remaining definitions cover indirect and incremental methods to clarify that any form of genocide is punishable under international law.

The United States employed an explicitly pro-White immigration policy for the entirety of its two centuries of existence until the treasonous 1965 Immigration Act, which reversed this safeguard and subverted American immigration policy to discriminate against White Europeans in favor of non-White immigration.  Prior to the 1965 Act, American immigration policy favored White European immigration to maintain the status quo of the American population.  The behind-the-scenes architects of the 1965 Act realized that overwhelmingly non-White legal immigration would inevitably reduce the White American population over time.  The political front men of the 1965 Act, such as Ted Kennedy, falsely assured the American public that the new immigration policy would not upset the racial balance of America. In 1965, America was approximately 89 percent White.  Just a few generations later, America is around 65 percent White.  In one more generation, White Americans will be a minority in their own country.

Illegal aliens create further demographic chaos, as White Americans are crowded out and out-bred by millions of mestizo illegal aliens from South America.  Despite overwhelming public desire to seal the border and to deport and deny entry to illegal aliens, the federal government has willfully ignored its mandate to protect against all threats, foreign and domestic.  Non-White legal immigrants and tens of millions of mestizo illegal alien invaders will dispossess the White American majority in the next few decades.  White Americans will become a minority in their own nation.

Overwhelmingly non-White legal immigration and millions of non-White illegal aliens are inherently destructive to the White American population.  Welfare and social benefit policies financially reward the generally poorer non-White groups for having large broods of children.  Preferential hiring policies set aside jobs for non-Whites.  Lax enforcement of employment law allows non-Whites to undercut the wages of educated White American citizens.  The appalling aspect of these trends is that most of these policies, such as welfare, food stamps, and free emergency medical care, are predominantly financed by White American taxpayers.  These White American taxpayers labor under conditions calculated to bring about their genocide as the progressive income tax discourages the most productive White Americans from having children.

Educated, self-reliant, and law-abiding White American taxpayers face the greatest disincentives to having large families.  Instead, these White taxpayers work hard but are forced to financially support criminals, illegal aliens, and welfare abusers.  The taxes paid by hardworking White citizens are transferred to illiterate illegal aliens to bankroll large broods of anchor babies that will produce an ever-increasing amount of welfare obligations and future criminals.  The White American population dwindles while the non-White populations exponentially increase, further straining the welfare system, crowding prison cells, diluting educational standards, and destroying formerly safe White neighborhoods.  White Americans face incremental genocide by design, which is precisely why so many fail to recognize the creeping trend.  Genocide need not be associated with machetes, firing squads, or executions.  The type of genocide White Americans face is far more subtle, which makes it all the more dangerous.

To deny White citizens of White nations the right to preserve themselves - biologically, ethnically, and culturally - is the true example of racism and hatred.  Genocide is never acceptable.  What can be more racist than the systematic eradication of an entire race?  White Americans need not be ashamed of identifying on a racial basis, as every other race in America has a political license to do so.  La Raza, the League of United Latino American Citizens, the National Association for the Advancement of Colored People, and the Anti-Defamation League of the B’nai B’rith are all bound by racial or ethnic ties.

White Americans are now approaching minority status in the nation their forefathers fought for and built from the ground up.  If the current birthrates continue, White Americans will be a minority group in a few generations.  White Americans must be free to object to the immigration policy of White genocide without being shouted down as “racists”, a term which has lost potency due to its use as a political tool to silence White advocacy.  “Racist” is a thinly-veiled attempt to silence a person who wishes to protect his or her race from extinction - a person who opposes genocide.  “Racist” is an empty slur meant to shut down debate, silence White people, and obfuscate the reality of White genocide.

White Americans must be free to describe racial injustices committed against White people.  Introduce the term “anti-White” to mainstream political discourse in the only way possible - by starting with private conversation.  The mainstream media attempts to mold public opinion, but when there is an seismic shift in American thought, the press has no choice but to bow to popular pressure.  Demand an end to White genocide and anti-White policies.

White Americans have the same claims to identity, organization, advocacy, and existence as does any other group in America.  Take a principled, adamant, and vocal stand against White genocide.  Talk to neighbors and inform friends.  Write letters to editors, television producers, media figures, and especially politicians.  Let the muffled White voice clear its throat and speak up clearly and forcefully after decades of silence.  Turn the tables and take back the moral high ground.  The truth is dangerous, which is precisely why slurs like “racist” are currently used to shout down reasonable opposition to White genocide.  Brush aside such denunciations, or better yet, mount the offense with a counterattack.

Anyone who opposes a return to traditional American immigration policies is pro-White genocide.  Anyone who supports amnesty for tens of millions of illegal aliens is pro-White genocide.  The current American immigration policy discriminates against White Europeans and is pro-White genocide.  There is nothing more racist than genocide, because it is the destruction of an entire race.  If someone shouts “racist!” in a petty attempt to silence debate, explain that a real racist is someone who wants to commit genocide against the White race.  Stop White genocide one conversation, one talking point, one letter, one complaint, one comment, one remark, and one person at a time.  Stay on a consistent message against White genocide.

The White race of the future, if there is to be one, will be grateful.

We proceed by an induction argument.

Induction Hypothesis (H1): If there are at least N blue-eyed people on the island then no one will leave the island for the first (N-1) nights.
Induction Hypothesis (H2): If there are N blue-eyed people and M brown-eyed people on the island then all the blue-eyed people will leave the island on the Nth night.

Proceed by induction on N, which is the number of blue-eyed people on the island.

First the base case N = 1.  Clearly, the blue-eyed person will leave the island on the first night for he knows that someone on the island has blue eyes (via the guru) and he knows that everyone other than himself does not have blue eyes, which establishes (H2) for the base case.  (H1) is trivially true for the base case.

Now suppose that everything else is the same except there are (N+1) blue-eyed people and M brown-eyed people on the island (where N ≥ 1 and M ≥ 1).  The blue-eyed people don’t leave the island for the first (N-1) nights by the induction hypothesis (H1).  The blue-eyed people also don’t leave the island on the Nth night for the same reason that no brown-eyed person leaves the island on the Nth night for the case of N blue-eyed people and (M+1) brown-eyed people on the island, which we know is true by the induction hypothesis (H2) and (A).  Therefore no one leaves the island on the Nth night by the preceding statement and another application of (A), which establishes (H1) inductively.

After the Nth night of no one leaving the island each blue-eyed person knows that there are more than N blue-eyed people on the island by another application of the induction hypothesis (H2), but since each blue-eyed person sees only N other blue-eyed people he can discern that there must be (N+1) blue-eyed people in total and that he is the (N+1)th such person.  Therefore, all (N+1) blue-eyed people leave the island on the (N+1)th night and (H2) is established inductively.

We can arrive at our final solution for the puzzle in the case of N = 10 blue-eyed people and M = 10 brown-eyed people.

But now a much more subtle question presents itself.  The guru doesn’t say anything that the islanders don’t already know; after all, each of them can see at least 9 other blue-eyed people.  So what piece of information is the guru providing that logically enables the blue-eyed people to leave the island on the 10th night?  For if the guru had not spoken no one would ever be able to leave the island.

Note: I by no means have a monopoly on this brain teaser as multiple treatments of it already exist on the web and are formulated in a similar way

Addendum:

I had to add an extra assumption to the puzzle in order to come up with an inductive proof that is both completely rigorous and economical, which might make it the only one of its kind.

George W. Bush’s No Child Left Behind has been recognized as a failure, though not officially stated as such. Instead, Obama wants to start over though his educational reforms have not been clearly defined as of yet. But there is another player in town with Bill Gates jumping into the fray. Bill Gates in 2000 implemented a program to improve education by breaking up large schools into smaller schools. Unfortunately, it was determined that student body size had little effect on achievement. Back to the drawing boards.

The Gates Foundation now has turned its attention on the teachers. It has selected several school districts and plans to reward or punish these school teachers according to how well they perform in raising student performance. This sounds like a rehash of the No Child Left Behind program where teachers quickly adopted “teaching to the test,” providing the duller students with additional schooling, or keeping them in school through the summer so they wouldn’t forget what they have learned, to out-and-out cheating on standardized tests. When a teacher is encumbered by innately less intelligent students, they will naturally manipulate the system to protect their own monetary interest. And why shouldn’t they? Is it their fault that they are teaching either above average or below average students?

Public teachers are unionized and so far they have been able to blunt the effects of holding individual teachers responsible for the poor performance of below average students. However, as home schooling, vouchers, charter schools, and other non-union competitors vie for public funds, there will be increasing pressure for the eventual privatization of education as each program fails to improve the performance of failing students. And it is not as if this is all new. Educational reforms are just the re-mixing of tried and failed remedies because the empirical data, if vigorously applied to education, would lead to the one conclusion that has been consistent for over 100 years—if you want to have children learn more you need to have smarter children to start with. And even if you can raise scores in children by teaching to the test and providing more instruction, when they become adults they will only be as intelligent as their genes permit.