oseph Stalin apparently coined the term "American exceptionalism" to denounce the heresy that Marx's universal historical laws would somehow not apply to the United States. Though it's now clear that every nation is an exception to the historical dialectic that was supposed to culminate in the triumph of the proletariat over the bourgeoisie, the U.S. remains an exceptional nation in other crucial ways. Anyone who becomes an American citizen is fully American, from that day forward. By contrast, a naturalized citizen of France, Japan, or Nigeria can live for decades in his new country, and his family can remain there for generations, yet many of the locals will still think of them as foreigners. To be sure, there is an American culture. When traveling around the world, one can often spot other Americans, and not only because of language; dress, deportment, and music often distinguish us. But when it comes to American nationalism, such things are relatively trivial. In America, politics, not culture, makes the nation.
The exceptional character of American nationalism confuses students of nationalism. According to a standard work like Ernest Gellner's Nations and Nationalism (1983), "nationalism uses the pre-existing, historically inherited proliferation of cultures or cultural wealth." Is American a nation in that sense? Not exactly. American identity is bound up with our Union, Constitution, and laws, rather than with tribe, clan, or culture. Thus, one of our early treaties asserted that the U.S. "is not in any sense founded on the Christian religion." That stipulation presumes that American identity is primarily political, denying as it does a massive historical and cultural fact—that the vast majority of America's citizens have been Christians. The cultural heritage of most Americans is Christian, and even the American creed draws upon the Judeo-Christian tradition in important ways. In the U.S., however, nation and culture are separate to an unusual degree. That reality, in turn, affects a range of important questions connecting what kind of government America will have to what kind of nation it will be.
We Americans often celebrate our ability to turn people from all over the world into Americans. That is not to deny that immigration policy has, periodically, roiled our politics. In the 1790s Federalists worried that refugees from European revolutions would bring their mistaken political ideas to America. The 1850s saw nativist animus against Irish immigrants and, more generally, against growing numbers of Catholics in what had been a predominantly Protestant land. In the early 20th century, popular and Progressive ideas of racial purity influenced the debate. Today, the issue is immigration from South and Central America.
These episodes hardly make America exceptional. All nations are, at least in some ways, xenophobic. Humans are group-creating beings by nature, and no group can have an inside without rejecting an outside. Even people who regard themselves as "cosmopolitan" usually define themselves against those whom they regard as narrow and provincial.
If the United States is unusual, it's not because our citizens sometimes wonder whether mass immigration is a boon—that's true of most nations that have mass migration. What sets the U.S. apart is how rare, relatively speaking, such episodes are, and, perhaps relatedly, how political are the questions we typically raise about immigration. Thomas Jefferson expressed this view in the Notes on the State of Virginia, where he wrote that American government was at its heart
a composition of the freest principles of the English constitution, with others derived from natural right and natural reason. To these nothing can be more opposed than the maxims of absolute monarchies. Yet, from such, we are to expect the greatest number of emigrants. They will bring with them the principles of the governments they leave, imbibed in their early youth; or, if able to throw them off, it will be in exchange for an unbounded licentiousness, passing, as is usual, from one extreme to another. It would be a miracle were they to stop precisely at the point of temperate liberty. These principles, with their language, they will transmit to their children. In proportion to their numbers, they will share with us the legislation. They will infuse into it their spirit, warp and bias its direction, and render it a heterogeneous, incoherent, distracted mass.
The founders understood the distinction between establishing the American Republic upon certain principles discoverable by reason, and creating a functioning nation dedicated to those principles. Teaching aliens not only the principles of liberty but also the habits of free men has never been easy. America's principles, as understood and applied throughout most of our history, have required us to try. Hence, the dominant trend in American history has been to welcome immigrants, teach them American ideas, and assimilate them to American norms. Whether such intentional acculturation is still possible in an age of multiculturalism is an open, and grave, question.
If we wish to see how exceptional America's treatment of immigrants has been, perhaps we need look no further than presidential statements regarding Jews. No other people has lived as foreigners in so many lands across so many centuries, yet Jews have found America to be a home from the start, a place they could live as free and equal citizens. Early in his presidency, George Washington wrote to the Hebrew Congregation of Newport, Rhode Island, that in the United States "all possess alike liberty of conscience and immunities of citizenship" because the government "gives to bigotry no sanction [and] to persecution no assistance." A nation where tolerance was not an indulgence but the recognition of a natural right allowed Washington to express the hope (quoting the prophet Micah), "May the children of the Stock of Abraham, who dwell in this land, continue to merit and enjoy the good will of the other Inhabitants; while every one shall sit in safety under his own vine and fig tree, and there shall be none to make him afraid."
During the Civil War, Abraham Lincoln ensured that there were Jewish chaplains in the Union army. Early in the war General Ulysses S. Grant had issued an infamous order, which Lincoln soon voided, expelling all Jews from the Department of Tennessee. Grant "apologized for the order publicly and repented of it privately," according to historian Jonathan Sarna. "[T]he sense that in expelling them he had failed to live up to his own high standards of behavior, and to the Constitution that he had sworn to uphold, gnawed at him." During his presidency, Grant went out of his way to be a friend of the Jews in America and beyond its borders, speaking out against Romania's pogroms.
In 1925 President Calvin Coolidge contended that America's ability to welcome Jews—and peoples from all over the world more generally—derived from the principles of 1776:
Our country has done much for the Jews who have come here to accept its citizenship and assume their share of its responsibilities in the world. But I think the greatest thing it has done for them has been to receive them and treat them precisely as it has received and treated all others who have come to it.
If our experiment in free institutions has proved anything, it is that the greatest privilege that can be conferred upon people in the mass is to free them from the demoralizing influence of privilege enjoyed by the few. This is proved by the experience here, not alone of the Jews, but of all the other racial and national elements that have entered into the making of this nation. We have found that when men and women are left free to find the places for which they are best fitted, some few of them will indeed attain less exalted stations than under a regime of privilege; but the vast multitude will rise to a higher level, to wider horizons, to worthier attainments.
America has been a home for Jews and for so many other persecuted people and peoples because it has been a place where people have been, relatively speaking, free to rise or fall on their own merit. The government simply did not care that they were Jews, or Germans, or Swedes. (To be sure, America did not always extend that same courtesy to Asians.) Our political institutions strive to treat individuals as individuals, who relate to the government on that basis, rather than as parts of groups, castes, or classes. A regime dedicated to protecting the rule of law and the rights of men—including the right of each individual to make his own way in the world, and to keep the rewards he gains for his work and talent—was the key to making America a beacon for wandering peoples, and for immigrants in general.
In 1776 American revolutionaries decided to cease being British subjects in order to become American citizens. That radical step changed not just the allegiance of the colonists, but the nature of that allegiance. Under British law, all persons born on British soil were his majesty's subjects. One could cease being a British subject only with the king's consent.
The revolution represented a movement from subjects to citizens. Subjects, as the term implied, were subject to the laws, possessing rights because the government magnanimously granted them. Similarly, in English law, all real property ultimately belonged to the king. Most property titles were "use-holds," rather than true ownership. Citizens, by contrast, are freemen and equals, possessing rights by nature and binding themselves together, voluntarily, to forge a polity. In American law, we own private property outright.
Until the imperial crisis began in the 1760s, the colonists had been proud to be British subjects, enjoying the "rights of Englishmen," as their birthright. Those rights were, in fact, a practical approximation of the rights of men, but they were understood to be the rights of a particular people as well. Between 1761 and 1776, it became clear to Americans that the British did not respect the rights of Englishmen in America. Sir Francis Bernard, the crown-appointed governor of Massachusetts in the 1760s, held that "the rule that a British subject shall not be bound by laws, or liable to taxes, but what he has consented to by his representatives must be confined to the inhabitants of Great Britain only." His successor, Thomas Hutchinson, insisted that in North America "there must be an abridgment of what are called English liberties." These ideas, put into law, meant that the colonists had to choose between being British subjects and retaining their rights. The Americans chose their rights. As a result, American citizenship would be based upon the rights of men rather than the rights of Englishmen. The penchant for universals, and for the robust discussion of them that has been so long remarkable in American history, was affirmed and established.
The Revolution was not instantaneous; 1776 began a process that did not culminate until the establishment of a new, federal government in 1789. The Declaration of Independence begins with the subject of nationhood, describing the crisis as a moment when it has become "necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the laws of nature and nature's God entitle them" (emphasis added). The new people, the American people, would be constituted according to the principles outlined in the next paragraph: "that all men are created equal, that they are endowed by their Creator with certain unalienable rights," and that when governments fail to uphold those rights, men may rise up, and create new government "laying its foundation on such principles, and organizing its powers in such form, as to them shall seem most likely to effect their safety and happiness." These principles, and that process, would be at the heart of American nationhood.
The people of Massachusetts took a leading role in deriving practice from theory, sending delegates to a state constitutional convention in September 1779. Once assembled, the delegates created a committee to draft a document, a task ultimately assigned to John Adams. The rest of the convention then debated and revised Adams's work before sending the result to the people of Massachusetts for ratification. All subsequent American constitutions, most importantly the new national one of 1787, followed that model of special convention and popular ratification.
The Massachusetts Constitution made the connection between constitutional means and constitutional ends explicit. Its preamble declares:
The end of the institution, maintenance, and administration of government is to secure the existence of the body politic; to protect it, and to furnish the individuals who compose it with the power of enjoying, in safety and tranquillity, their natural rights and the blessings of life; and whenever these great objects are not obtained, the people have a right to alter the government, and to take measures necessary for their safety, prosperity, and happiness.
The body politic is formed by a voluntary association of individuals. It is a social compact by which the whole people covenants with each citizen, and each citizen with the whole people, that all shall be governed by certain laws for the common good. It is the duty of the people, therefore, in framing a Constitution of Government, to provide for an equitable mode of making laws, as well as for an impartial interpretation and a faithful execution of them, that every man may, at all times, find his security in them.
Here we see the connection between the right to revolution and American political identity. The constitution blended the political, "a voluntary association of individuals," with the "social compact" in which "the whole people covenants with each citizen." The body politic was, however, not the same thing as the government, which was elected to secure the legitimate needs of the citizens of Massachusetts. Politicians work for the people, not the other way around. National identity, from this perspective, was emphatically political, rather than cultural, tribal, or even geographic.
Given that line of reasoning, it is no surprise that John Adams, like James Madison and George Washington, regarded the Congress meeting under the Articles of Confederation as essentially a diplomatic assembly, rather than as a national government. The Confederation Congress represented 13 independent states joined together in permanent Union.
That changed in 1787 and 1788 when the people ratified the U.S. Constitution. Ratification made the Union "more perfect" and constituted the nation, formally speaking, making senators and congressmen representatives of states and districts within a single state, rather than representatives of sovereign governments.
Note how different this new nation was from Gellner's prototypical one. Most citizens of the new republic were descendants of British Protestants, but they shared no common ethnicity. In America, Scotsmen and Englishmen became brethren in a way they did not in Britain. In Pennsylvania perhaps 40% of the population was of German extraction. Plus the Union had many citizens from elsewhere. In lieu of common myths there was only a common, albeit contested, history of the American Revolution.
In time, as we know, the nation built upon the principles of 1776 became a home for individuals from around the world.
Against the World?
These principles caused problems from the start, and would ultimately play a central role in the War of 1812. Once the wars of the French Revolution began, the British Navy faced a severe shortage of sailors. Traditionally, British sailors were subject to impressment-forced conscription into the British Navy. Press gangs roamed port cities in Britain and around the world and pressed British subjects into service. But who was a British subject? By treaty, Britain had agreed that all citizens of the 13 United States as of 1783 were no longer British subjects. But what about British subjects who became U.S. citizens after that? In British law, they were still Britons, and, hence, subject to impressment. In 1797, Rufus King, the American minister to Great Britain, received a lecture from Great Britain's foreign secretary, Lord Grenville, on the matter:
No British subject can, by such a form of renunciation as that which is prescribed in the American law of naturalization, divest himself of his allegiance to his sovereign. Such a declaration of renunciation made by any of the King's subjects would, instead of operating as a protection to them, be considered an act highly criminal on their part.
British subjects, being born, not made, could only renounce their obligations to the king and his government if the king chose to let them. Absent royal consent, pledging allegiance to another nation would be "highly criminal." The principles of 1776 had implications for both joining and quitting a nation.
That conclusion compels us to wonder whether the Supreme Court got it wrong when it interpreted the nature of U.S. citizenship in the little known but still controlling case of U.S. v. Wong Kim Ark (1898). In that decision, the Court's majority ruled that soil—perhaps we should say location at birth—was the foundation of American citizenship. Chief Justice Melville Fuller and Justice John Harlan dissented. Harlan had penned his famous dissent in Plessy v. Ferguson, insisting on the "color-blind" Constitution, only two years earlier. It may be no coincidence that almost the same majority that gave usPlessy also gave us Wong Kim Ark. In both cases, the majority placed principles other than individual equality into the heart of American law and institutions. In Wong Kim Ark, the Court, heavily influenced by the common law, and by popular Saxon myths of the day, upheld a "birthright" basis for citizenship—those born on American soil were American citizens, even as those born on British soil were British subjects.
This turn to soil was entangled with the effort to secure citizenship for the former slaves. These Americans had been born in the U.S., had no other political allegiance, but nonetheless did not enjoy the rights of men before the Civil War, and, alas, often after the War, too. The 14th Amendment declared "all persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside." But, as Fuller and Harlan noted, it was not necessary to go as far as the Court did in Wong Kim Ark to ensure that the freemen enjoyed their rights. Moreover, it was not clear that "subject to the jurisdiction thereof" meant subject to any jurisdiction thereof. In formal grammar, "subject to the jurisdiction thereof" would imply full jurisdiction, the sort that members of the Indian tribes, foreign diplomats, and illegal aliens manifestly did not enjoy. By contrast, language indicating partial jurisdiction would be "subject to some [or any] jurisdiction thereof." That did not mean, however, that location at birth was irrelevant. There was, after all, a difference between allowing that location at birth was, as a rule, a good indicator of the citizenship of a child and suggesting, as the Court did, that it is the thing that makes someone a citizen. We see the absurdity of such a birthright in recent laws which suggest that Boris Johnson, the current Mayor of London, and a descendent of George II and James I, among others, may have to file a U.S. income tax return because his parents happened to be living in New York City when he was born. It's as if the IRS thinks that Johnson's money belongs to the U.S. government unless he can prove otherwise. That's how George III and Parliament saw it in the years before and after 1776.
In other words, it's worth asking whether a nation that makes soil central to citizenship can be as welcoming to immigrants as one that makes central the principles of 1776. Because America had very little immigration between the early 1920s and the mid-1960s, we are only now beginning to see the implications of this change for America's character. It might be that, in time, we will look more favorably on the English idea that people enjoy rights only because of their national identity, and not also because they are men. And when rights are understood to be the gift of government, they are much more liable to limitation and regulation than they are when they are understood to be the gifts of God and nature. In short, the debate over which people are Americans is inseparable from the debate over which principles define America.
An Extended Republic
If it is true that the political character of American nationhood has made it exceptional, it is worth asking about the implications of that mode of nationalism for American politics, broadly speaking. It seems that a political—as opposed to a cultural, tribal, or historic—nationalism has been the complement of a limited, constitutional republic. That is probably not a coincidence.
Jefferson and Madison made this point with particular clarity in some of their best-known writings. In his First Inaugural Address Jefferson connected "[a] rising nation, spread over a wide and fruitful land" with "a wise and frugal Government, which shall restrain men from injuring one another, [and] shall leave them otherwise free to regulate their own pursuits of industry and improvement, and shall not take from the mouth of labor the bread it has earned." Jefferson noted, as well, the character of the American nation: "possessing a chosen country,...entertaining a due sense of our equal right to the use of our own faculties, to the acquisitions of our own industry, to honor and confidence from our fellow-citizens, resulting not from birth, but from our actions and their sense of them."
What made this regime so good at welcoming immigrants? In part, as we noted earlier, it was because of America's self-understanding as a "voluntary association of individuals," rather than a nation of groups. Such a republic was characterized by the kind of government Jefferson described. Moreover, it would feature a robust civil society. Pondering the temperance movement of the early 19th century, Alexis de Tocqueville was, at first, both amused and baffled.
The first time that I heard in America that one hundred thousand men had publicly promised never to drink alcoholic liquor, I thought it more of a joke than a serious matter.... In the end I came to understand that these hundred thousand Americans, frightened by the progress of drunkenness around them, wanted to support sobriety by their patronage. They were acting in just the same way as some great territorial magnate who dresses very plainly to encourage a contempt of luxury among simple citizens.
Importantly, Tocqueville continued, "one may fancy that if they had lived in France each of these hundred thousand would have made individual representations to the government asking it to supervise all the public houses throughout the realm." Citizens do collectively, in the expansive American private sphere, what subjects ask the government to do for them. Citizens understand the duties that come with the rights they enjoy as men and citizens. Just as it was then the job of private citizens and local associations to take care of the poor, the widow, and the orphan, so too was it the job of private citizens to try to moderate excessive drinking. But if rights are understood as the gift of government to the people, then it is also the duty of government to regulate the use and abuse of those rights. And should our government take over that sphere, it changes the regime fundamentally.
An extensive national government with centralized administrative power is likely to be one dominated by what James Madison termed factions. "By a faction," Madison wrote, "I understand a number of citizens whether amounting to a majority or minority of the whole, who are united and actuated by some common impulse of passion, or of interest, adverse to the rights of other citizens, or to the permanent and aggregate interests of the community." A faction was a group, be it a minority or even a majority, that sought through government to secure its own interest, rather than the good of the community as a whole.
What was the remedy to that problem? "If a faction consists of less than a majority," he noted, "relief is supplied by the republican principle." A minority faction can simply be outvoted. The danger of majority faction, however, was real. That being the case, the best way to prevent majority factions was, he reasoned, an extended republic—"extend the sphere and you take in a greater variety of parties and interests; you make it less probable that a majority of the whole will have a common motive to invade the rights of other citizens." The larger the republic, the more likely it was that all factions would be easily tamed minority factions, seeking but never securing private advantages adverse to the common good.
But what if a majority faction is assembled by gathering together a coalition of minority ones? It seems to be a rule of politics that the more areas of our lives government is directly involved with, the easier it is to assemble such coalitions. That was one reason why so many Jeffersonians, including Madison, opposed most internal improvements. They viewed them as the entering wedge for government support of private interest. Still, there is a difference between a government that supplies actual public goods like roads, canals and the like, and a government that serves the private interests of self-seeking factions.
The Madisonian argument, in short, cuts against "pluralism," the idea that government functions in a democratic republic through relations with competing interest and ideological groups rather than with individuals. The pluralist model assumes out of existence the idea of a true, knowable common good. Instead, it presumes that the common good is the good of the dominant groups in society, which compete for support in a democratic process. Pluralism makes it perfectly reasonable for government to grow and grow, providing more and more support to more and more groups along the way, providing infrastructure for a more or less permanent majority coalition of factions.
When government sees its job as serving or servicing groups, it is likely that the smaller the group, the less it will get from government, as political life becomes a mad scramble of rent-seeking. Down that road lies hyphenated citizenship, as each American relates to the government not as an individual citizen but as a member of one or more factions. Moreover, it points us back toward aristocracy, where the government relates to the leaders of each group, rather than regarding individual citizens as the ultimate boss. It creates an America where "government is the only thing we all belong to," as the Charlotte, North Carolina, video welcoming delegates to the 2012 Democratic National Convention proclaimed. In that America we do not all belong to the polity as equal citizens, creating together the government by which we secure those public goods that cannot be secured any other way. When government does only a few things, and those things involve genuine public goods, the rent-seeking scramble is likely to be more trouble than it's worth—and when it does take place it is less likely to ruin those who refuse to kowtow to the administrators.
Toleration and Bias
In recent years, the United States has seen efforts to ban circumcision on the grounds that it is cruel to children and a violation of their rights. Similarly, we have seen efforts to ban the kosher slaughter of animals, on the grounds it is cruel to animals. It may very well be that these are the first salvos in what could be a long war. If these efforts are, in fact, the way of the future, America will be but the latest instance of the oldest pattern in history: nations who welcome the Jews and then, in time, cease to be so welcoming. Similarly, recent efforts to require all hospitals to provide birth control, abortion, and sterilization, will, if they remain on the books, challenge many Americans to be both loyal citizens and observant Catholics.
The more elements of our lives the national government regulates, the more likely it is that the government will intrude on matters that Jews, Catholics, and others regard as fundamental questions of conscience. Either big, factious government must carve out special exemptions, which themselves are a form of class legislation, or it must trample the rights of Jews, Catholics, and other recalcitrant citizens. Simply upholding the traditional definition of marriage could one day soon be regarded as evidence of hateful bias. It is not a coincidence that supporters of expansive government prefer to embrace an ideological idea of toleration rather than simply practice toleration—they believe that tolerant people must believe x, rather than that tolerant people accept that there is more than one possible opinion about x; and, as a rule, this ideology of toleration is understood as an effort to secure 21st-century "values." It builds upon the idea of History that is at war with American exceptionalism. In time, that definition of "toleration" will, quite probably, return free American citizens to the level of subjects, forced to conform their life, liberty, property, and pursuit of happiness to the official uses prescribed by government. To say the least, that development would make it less and less likely that divers peoples would still find a welcoming home in the United States of America. Down that road lies the end of American exceptionalism.
Here is a question I often give on exams:
What is the probability that the next child to be born will be a genius? Give me a number and fully explain your answer.
There is not, of course, a single correct answer. What I just said is an important point, so let’s not skip lightly over it: there is no correct answer; at least, there is no way anybody can know the correct answer.
That nobody can know with certainty answers to questions of this type is under appreciated. I want people to learn this because we are, as I often say, too sure of ourselves.
What I want to see in the answer is acknowledgment of the ambiguities. First, what is a genius? Surely that word is overused to a remarkable extent. For example, this list says, with a straight face, authoress JK Rowling and movie maker Stephen Spielberg are geniuses. I often have the idea that to not call some eminence a genius is nowadays taken as a slight. However, a moments’ thought suffices to show that people exaggerate—if you are willing to take that moment.
The next step is to think of some geniuses for the sake of comparison. It’s best to think of dead ones so that you are not overly influenced by current events. After all, only history can truly judge genius. If you agree with even part of this, you will have made the next most important step: admitting that you can be biased.
How about some dead geniuses? Einstein pops into nearly everybody’s head first. Then, for me, Mozart, Beethoven, Shakespeare, Newton, and the guy who invented beer. No, I’m not joking about that last name. The point is my historical knowledge is modest, and most of the names I pick are men from the last 500 years, and most are from Western culture. Humanity is older than 500, of course, and there are other cultures besides our own, so I know that my knowledge of who is a genius is limited. That’s what got me to thinking about the brilliant soul who invented beer. He did so, probably in Sumer, before people wrote down incredible deeds of this sort.
This line of thought eventually leads to other cultures (Confucius, maybe Lao Tzu) and other times where writing was non-existent (was there just one person responsible for the wheel and agriculture?). There must be a lot of geniuses I don’t know, and some that nobody can ever know.
Next step is to count, and to acknowledge that exact counting is an impossibility. Still, we can count to the nearest order of magnitude. This means “power of 10”, and it represents an enormously popular method of approximation. If you can get your answer to within “an order of magnitude” (a power of 10), you are doing good. The first power of 10, or 101, is just 10. The second power is 102=100, and so on.
So how many geniuses? Certainly more than 10, definitely less than 10,000, or the 5th order of magnitude. Could there have been a 100 geniuses? Given my above list, I say yes. 1000? I’m less likely to believe this number, but since I have said that there were lots of geniuses who went unsung, I can’t exclude it. Still, an order of magnitude more than this seems too large.
We have done a lot so far, but we still haven’t answered the question “What is the probability that the next child to be born will be a genius?” The answer will look something like # of geniuses who have ever lived / # of people who ever lived. Coming to this equation is crucial. This is because the question implies—I emphasize, it does not explicitly state—we are asking a question about all humanity. And all humanity certainly means all humans who have ever lived.
Thus far, we have nailed down the numerator in this equation to the nearest order of magnitude or so (102 to 103). How about the denominator?
What evidence do we have? Well, there about about, to an order of magnitude, 1010 or 10 billion people alive today. 100 years from now, nearly of these people will be dead and a new set, probably the same order of magnitude will take its place. Anyway, 100 billion people alive 100 years from now feels way too large to me, and 1 billion way too small, especially given recent population trends.
100 years ago, there were about an order of magnitude less people alive (nearly all of them different from the set we have today), or about 109 or 1 billion. How many 100s of years can we go back? About 2000, since the best guess is humanity arose about 200,000 years ago. That’s close enough; it’s within an order of magnitude. Without doing any math—just going by gut—we can guess that adding today’s 1010 to last century’s 109 (11 billion so far), and to the previous 199 centurys’ diminishing contributions (each previous century had fewer people), we arrive at about 1011, or 100 billion.
Was that larger than you had first guessed? This number usually surprises most people. But having a guess gives us our denominator as that we can finally solve our equation, which is
—— = 10-9
of, if there were 103 geniuses, 10-8. In words, it’s anywhere from 1 in a billion to 1 in 100 million.
Not very good odds, right?
This was a lot of thinking for such a simple question, wasn’t it? If you would have written down, as student’s often do, an answer “1 in a 100” or “1 in 1000” you would have got the answer wrong. Both answers imply that we should be flooded with geniuses, an answer which no observation supports.
Of oft-heard complaint among professors is that students don’t think about the answers they give. I agree with this, but I think it’s more than just students. It holds for professors and ordinary civilians, too.
“1 in a 100” is absurd, and far too certain. Just a few moment’s thought shows this. How many answers that we give in life are just as absurd?
Some kids will write, “I don’t know.” I usually give them 1 point for this because, after all, it is the strictly correct answer. But that answer is too certain itself. We do know something about the answer and we can answer it partially. We should always quantify uncertainty in any question and not seek the easy way out by given answers that are too certain.
Here, for fun, is another question I give:
How many umbrellas are there in New York City?