Big Think's Top 25 +1 Videos

Mama, Don't Let Your Babies Grow Up To Deny Evolution

If adults want to deny evolution, sure. That’s fine. Whatever. But those adults better not make their kids follow in step because we as society need them to be better. Bill Nye, everyone's favorite Science Guy, explains the importance of promoting evolution education for America's future voters and lawmakers.

My Man, Sir Isaac Newton

Are you at least 26 years-old? If so, you are older than Isaac Newton was when he invented calculus... on a dare! (If you're younger than 26, better hurry up.) Big Think expert and overall cool guy Neil deGrasse Tyson explains why Newton is the greatest physicist who ever and likely will ever live.

Will Mankind Destroy Itself?

Theoretical physicist Michio Kaku sees two major trends today. One eventually leads to a multicultural, scientific, tolerant society that will expand beyond Earth in the name of human progress. The other trend leads to fundamentalism, monoculturalism, and -- eventually -- civilizational ruin. Whichever of these two trends wins out will determine the fate of mankind. No pressure, everyone.

Ricky Gervais on the Principles of Comedy

Comedy isn't just about making people laugh, says actor Ricky Gervais. It's about making people think. And while different forms of comedy require different approaches, the crux of any good performance will always be rhythm.

Reading the Bible (Or the Koran, Or the Torah) Will Make You an Atheist

Author and magician Penn Jillette was asked to leave his Christian youth group by a pastor who told his parents: "He's no longer learning about the Bible from me. He is now converting everyone in the class to atheism." The reason? Jillette did his homework and was turned off by the hostilities of the text. It can be intimidating to come out as an atheist, especially in a religious community. Jillette found that having "out" atheist role models helped him feel unalone.

Henry Rollins: The One Decision that Changed My Life Forever

Punk legend Henry Rollins describes the biggest turning point in his life: the moment he decided to leave his job as manager of a Häagen-Dazs store and eventually become the lead singer of Black Flag. It was the courage to take a risk, plus a whole lot of luck, that got Rollins to where he is today.

5 Programming Languages Everyone Should Know

Java is "heavyweight, verbose, and everyone loves to hate it," but programmer Larry Wall still thinks you should know it. In this video, he offers suggestions for people interested in learning languages, as well as suggestions for those significantly less invested in computer programming.

The Importance of Unbelief

If you assume there’s no afterlife, Stephen Fry says, you’ll likely have a fuller, more interesting "now" life. The actor and comedian details the positive influence philosophers have had on his life, as well as his journey of understanding both what he believes and why he believes it.

Why be happy when you could be interesting?

We don't really want what we think we desire, says philosopher Slavoj Žižek.

James Gleick on the Common Character Traits of Geniuses

This video is part of a series on female genius, in proud collaboration with 92Y's 7 Days of Genius Festival.

The personalities of Isaac Newton and Richard Feynman were, on one level, extremely different. Biographer and former New York Times reporter James Gleick says Newton was argumentative, had few friends, and likely died a virgin. Feynman, on the other hand, loved dancing and going to parties, and had many friends in the scientific community. But in regards to their working habits, both men were solitary and had the ability to concentrate with a sort of intensity that is hard for mortals to grasp. At bottom, Gleick says geniuses tend to have a yearning for solitude which, though fruitful for their professional work, made the task of daily living more burdensome.

The Importance of Doing Useless Things

From poetry and ballet to mathematics and being clever, life is laden with frivolous pursuits that hold no bearing on our ability to survive. Yet, insists Richard Dawkins, if it weren’t for the development of these impractical activities, we wouldn’t be here.

Why monogamy is ridiculous

Dan Savage: the idea that one instance of infidelity should ruin a relationship is a new—and misguided—notion.

Dan Harris: Hack Your Brain's Default Mode With Meditation

Dan Harris explains the neuroscience behind meditation, but reminds us that the ancient practice isn't magic and likely won't send one floating into the cosmic ooze. He predicts that the exercise will soon become regularly scheduled maintenance, as commonplace as brushing your teeth or eating your veggies. Harris, an ABC News correspondent, was turned on to mediation after a live, on-air panic attack. His latest book is 10% Happier: How I Tamed the Voice in My Head, Reduced Stress Without Losing My Edge, and Found Self-Help That Actually Works--A True Story.

How Intellectuals Betrayed the Poor

For 40 years academics were duped into idolizing the idea of unfettered markets, says Cornel West, and now our society is paying a terrible price.

Why Some Races Outperform Others

A psychologist explains the latest research into education disparity.

Why It's So Hard for Scientists to Believe in God

Some scientists see religion as a threat to the scientific method that should be resisted. But faith "is really asking a different set of questions," says Collins.

Why Facebook Isn't Free

Internet pioneer Jaron Lanier argues that free technologies like Facebook come with a hidden and heavy cost – the livelihoods of their consumers.

How to Tell if You’re a Writer

For John Irving, the need for a daily ration of solitude was his strongest "pre-writing" moment as a child.

Your Behavior Creates Your Gender

Nobody is born one gender or the other, says the philosopher. "We act and walk and speak and talk in ways that consolidate an impression of being a man or being a woman."

Are You a Liberal Snob? Take The Quiz

Charles Mrray designed this quiz to have a salutary effect on bringing to people’s attention the degree to which they live in a bubble that seals them off from an awful lot of their fellow American citizens.

Why You Should Watch Filth

John Waters defends the creation and consumption of obscene films, and recommends some of his personal favorites.

What Are You Worth? Getting Past Status Anxiety.

Writer Alain De Botton says that status anxiety is more pernicious and destructive than most of us can imagine, and recommends getting out of the game altogether.

Sheila Heen on the Psychology of Happiness and Feedback

Sheila Heen, a Partner at Triad Consulting Group and a lecturer on Law at Harvard Law School, explains the psychology behind feedback and criticism. Heen is co-author of "Thanks for the Feedback: The Science and Art of Receiving Feedback Well."

Are You a Psychopath? Take the Test.

Psychologist Kevin Dutton presents the classic psychological test known as "the trolley problem" with a variation. Take the test and measure you response on the psychopathic spectrum.

Here's How to Catch a Liar, If You Really Want To

It’s very complex as to whether or not we really want to catch a liar. We think we do. What if we find out that both of our presidential candidates are lying? Then what do we do? I’m not saying they are; I never comment on anyone in office or running for office. Only after they’re out that they’re fair game. . . . Clinton said, "I didn’t have sex with that woman" and then gave her name. "That woman" is putting her at a distance from himself.

Why I Came Out at Age 81

As a teenager in the '40s, James Randi "would have gotten stoned" for being gay. But when he outed himself to the world in 2010, the reaction was "wonderful."

More playlists
  • Hackers' motivations range from altruistic to nihilistic.
  • Altruistic hackers expose injustices, while nihilistic ones make society more dangerous.
  • The line between ethical and unethical hacking is not always clear.

The following is an excerpt from Coding Democracy by Maureen Webb. Reprinted with Permission from The MIT PRESS. Copyright 2020.

As people begin to hack more concertedly at the structures of the status quo, the reactions of those who benefit from things as they are will become more fierce and more punitive, at least until the "hackers" succeed in shifting the relevant power relationships. We know this from the history of social movements. At the dawning of the digital age, farmers who hack tractors will be ruthlessly punished.

Somewhere on the continuum of altruism and transgression is the kind of hacking that might lead the world toward more accountable government and informed citizenries.

Of course, it must be acknowledged that hackers are engaged in a whole range of acts, from the altruistic to the plainly nihilistic and dangerous. On the altruistic side of the continuum, they are creating free software (GNU/Linux and other software under GPL licenses), Creative Commons (Creative Commons licensing), and Open Access (designing digital interfaces to make public records and publicly funded research accessible). They are hacking surveillance and monopoly power (creating privacy tools, alternative services, cooperative platforms, and a new decentralized internet) and electoral politics and decision making (Cinque Stelle, En Comú, Ethelo, Liquid Democracy, and PartidoX). They have engaged in stunts to expose the technical flaws in voting, communications, and security systems widely used by, or imposed on, the public (by playing chess with Germany's election voting machines, hacking the German Bildschirmtext system, and stealing ministers' biometric identifiers). They have punished shady contractors like HackingTeam, HBGary, and Stratfor, spilling their corporate dealings and personal information across the internet. They have exposed the corruption of oligarchs, politicians, and hegemons (through the Panama Papers, WikiLeaks, and Xnet).

More notoriously, they have coordinated distributed denial of service (DDoS) attacks to retaliate against corporate and government conduct (such as the Anonymous DDoS that protested PayPal's boycott of WikiLeaks; the ingenious use of the Internet of Things to DDoS Amazon; and the shutdown of US and Canadian government IT systems). They have hacked into databases (Manning and Snowden), leaked state secrets (Manning, Snowden, and WikiLeaks), and, in doing so, betrayed their own governments (Manning betrayed US war secrets, and Snowden betrayed US security secrets). They have interfered with elections (such as the hack and leak of the Democratic National Committee in the middle of the 2016 US election) and sown disinformation (the Russian hacking of US social media). They have interfered with property rights in order to assert user ownership, self-determination, and free software's four freedoms (farmers have hacked DRM code to repair their tractors, and Geohot unlocked the iPhone and hacked the Samsung phone to allow users administrator-level access to their devices) and to assert open access to publicly funded research. They have created black markets to evade state justice systems (such as Silk Road on the dark web) and cryptocurrencies that could undermine state-regulated monetary systems. They have meddled in geopolitics as free agents (Anonymous and the Arab Spring, and Julian Assange and his conduct with the Trump campaign). They have mucked around in and could potentially impair or shut down critical infrastructure. (The notorious "WANK worm" attack on NASA is an early, notorious, example, but hackers could potentially target banking systems, stock exchanges, electrical grids, telecommunications systems, air traffic control, chemical plants, nuclear plants, and even military "doomsday machines.")

It is impossible to calculate where these acts nudge us as a species. Some uses of hacking — such as the malicious, nihilistic hacking that harms critical infrastructure and threatens lives, and the hacking in cyberwarfare that injures the critical interests of other countries and undermines their democratic processes — are abhorrent and cannot be defended. The unfolding digital era looks very grim when one considers the threat this kind of hacking poses to peace and democracy combined with the dystopian direction states and corporations are going with digital tech.

But somewhere on the continuum of altruism and transgression is the kind of hacking that might lead the world toward more accountable government and informed citizenries, less corrupt and unfair economic systems, wiser public uses of digital tech, more self-determination for the ordinary user, fairer commercial contracts, better conditions for innovation and creativity, more decentralized and robust infrastructure systems, and an abolition of doomsday machines. In short, some hacking might move us toward a digital world in which there are more rather than fewer democratic, humanist outcomes.

It is not clear where the line between "good" and "bad" hacking should be drawn or how to regulate it wisely in every instance. Citizens should inform themselves and begin to consider this line-drawing seriously, however, since we will be grappling intensely with it for the next century or more. My personal view is that digital tech should not be used for everything. I think we should go back to simpler ways of running electrical grids and elections, for example. Systems are more resilient when they are not wholly digital and when they are smaller, more local, and modular. Consumers should have analogue options for things like fridges and cars, and design priorities for household goods should be durability and clean energy use, not interconnectedness.

In setting legal standards, prohibiting something and enforcing the prohibition are two different things. Sometimes a desired social norm can be struck by prohibiting a thing and not enforcing it strenuously. And the law can also recognize the constructive role that civil disobedience plays in the evolution of social norms, through prosecutorial discretion and judicial discretion in sentencing.

Wau Holland told the young hackers at the Paradiso that the Chaos Computer Club was "not just a bunch of techno freaks: we've been thinking about the social consequences of technology from the very beginning." Societies themselves, however, are generally just beginning to grapple with the social consequences of digital technology and with how to characterize the various acts performed by hackers, morally and legally. Each act raises a set of complex questions. Societies' responses will be part of the dialectic that determines where we end up. Should these various hacker acts be treated as incidents of public service, free speech, free association, legitimate protest, civil disobedience, and harmless pranksterism? Or should they be treated as trespass, tortious interference, intellectual property infringement, theft, fraud, conspiracy, extortion, espionage, terrorism, and treason? I invite you to think about this as you consider how hacking has been treated by societies to date.

A financial shot in the arm could be just what is needed for Americans unsure about vaccination.

On May 12, 2021, the Republican governor of Ohio, Mike DeWine, announced five US$1 million lottery prizes for those who are vaccinated. Meanwhile, in West Virginia, younger citizens are being enticed to get the shot with $100 savings bonds, and a state university in North Carolina is offering students who get vaccinated a chance to win the cost of housing. Many companies are paying vaccinated employees more money through bonuses or extra paid time off.

The push to get as many people vaccinated as possible is laudable and may well work. But leading behavioral scientists are worried that paying people to vaccinate could backfire if it makes people more skeptical of the shots. And ethicists have argued that it would be wrong, citing concerns over fairness and equity.

As a behavioral scientist and ethicist, I draw on an extensive body of research to help answer these questions. It suggests that incentives might work to save lives and, if properly structured, need not trample individual rights or be a huge expense for the government.

In the United States, incentives and disincentives are already used in health care. The U.S. system of privatized health insurance exposes patients to substantial deductibles and copays, not only to cover costs but to cut down on what could be deemed as wasteful health care – the thinking being that putting a cost to an emergency room visit, for example, might deter those who aren't really in need of that level of care.

In practice, this means patients are encouraged to decline both emergency and more routine care, since both are exposed to costs.

Paying for health behaviors

In the case of COVID-19, the vaccines are already free to consumers, which has undoubtedly encouraged people to be immunized. Studies have shown that reducing out-of-pocket costs can improve adherence to life-sustaining drugs, whether to prevent heart attacks or to manage diabetes.

A payment to take a drug goes one step further than simply reducing costs. And if properly designed, such incentives can change health behaviors.

Payments and cash prizes have been shown effective in encouraging blood donations, adherence to blood thinner drugs, blood glucose monitoring, physical activity and smoking cessation.

And for vaccination in particular, payments have been successful for human papillomavirus (HPV) in England; hepatitis B in the United States and the United Kingdom; and tetanus toxoid in Nigeria. The effects can be substantial: For example, for one group in the HPV study, the vaccination rate more than doubled with an incentive.

For COVID-19, there are no field studies to date, but several survey experiments, including one my group conducted with 1,000 Americans, find that incentives are likely to work. In our case, the incentive of a tax break was enough to encourage those hesitant about vaccinations to say they would take the shot.

Coercion concerns

Even if incentives will save lives by increasing vaccinations, there are still other ethical considerations. A key concern is protecting the autonomous choices of people to decide what they put into their own bodies. This may be especially important for the COVID-19 vaccines, which – although authorized as likely safe and effective – are not yet fully approved by the Food and Drug Administration.

But already people are often paid to participate in clinical trials for drugs that have not yet been approved by the FDA. Ethicists have worried that such payments may be “coercive" if the money is so attractive as to override a person's free choices or make them worse off overall.

One can quibble about whether the term “coercion" applies to offers of payment. But even if offers were coercive, payments may still be reasonable to save lives in a pandemic if they succeed in greater levels of immunization.

During the smallpox epidemic nearly 100 years ago, the U.S. Supreme Court upheld the power of states to mandate vaccines. Compared with mandating vaccination, the incentives to encourage vaccines seem innocuous.

Exploitation and paternalism

Yet some still worry. Bioethicists Emily Largent and Franklin Miller wrote in a recent paper that a payment might “unfairly" exploit “those U.S. residents who have lost jobs … or slipped into poverty during the pandemic," which could leave them feeling as if they have “no choice but to be vaccinated for cash." Others have noted that vaccine hesitancy is higher in nonwhite communities, where incomes tend to be lower, as is trust in the medical establishment.

Ethicists and policymakers should indeed focus on the poorest members of our community and seek to minimize racial disparities in both health outcomes and wealth. But there is no evidence that offering money is actually detrimental to such populations. Receiving money is a good thing. To suggest that we have to protect adults by denying them offers of money may come across as paternalism.

Some ethicists also argue that the money is better spent elsewhere to increase participation. States could spend the money making sure vaccines are convenient to everyone, for example, by bringing them to community events and churches. Money could also support various efforts to fight misinformation and communicate the importance of getting the shot.

The cost of incentives

Financial incentives could be expensive as a policy solution. As in Ohio, lottery drawings are one way to cap the overall cost of incentives while giving millions of people an additional reason to get their shot.

The tax code could also allow for a no-cost incentive for vaccination. Tax deductions and credits are often designed to encourage behaviors, such as savings or home ownership. Some states now have big budget surpluses and are considering tax relief measures. If a state announced now that such payments would be conditional on being vaccinated, then each person declining the shot would save the government money.

Ultimately, a well-designed vaccination incentive can help save lives and need not keep the ethicists up at night.The Conversation

Christopher Robertson, Professor of Law, Boston University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

  • It appears that Earth has a geologic "pulse," with clusters of major events occurring every 27.5 million years.
  • Working with the most accurate dating methods available, the authors of the study constructed a new history of the last 260 million years.
  • Exactly why these cycles occur remains unknown, but there are some interesting theories.

Our hearts beat at a resting rate of 60 to 100 beats per minute. Lots of other things pulse, too. The colors we see and the pitches we hear, for example, are due to the different wave frequencies ("pulses") of light and sound waves.

Now, a study in the journal Geoscience Frontiers finds that Earth itself has a pulse, with one "beat" every 27.5 million years. That's the rate at which major geological events have been occurring as far back as geologists can tell.

A planetary calendar has 10 dates in red

Credit: Jagoush / Adobe Stock

According to lead author and geologist Michael Rampino of New York University's Department of Biology, "Many geologists believe that geological events are random over time. But our study provides statistical evidence for a common cycle, suggesting that these geologic events are correlated and not random."

The new study is not the first time that there's been a suggestion of a planetary geologic cycle, but it's only with recent refinements in radioisotopic dating techniques that there's evidence supporting the theory. The authors of the study collected the latest, best dating for 89 known geologic events over the last 260 million years:

  • 29 sea level fluctuations
  • 12 marine extinctions
  • 9 land-based extinctions
  • 10 periods of low ocean oxygenation
  • 13 gigantic flood basalt volcanic eruptions
  • 8 changes in the rate of seafloor spread
  • 8 times there were global pulsations in interplate magmatism

The dates provided the scientists a new timetable of Earth's geologic history.

Tick, tick, boom

Credit: New York University

Putting all the events together, the scientists performed a series of statistical analyses that revealed that events tend to cluster around 10 different dates, with peak activity occurring every 27.5 million years. Between the ten busy periods, the number of events dropped sharply, approaching zero.

Perhaps the most fascinating question that remains unanswered for now is exactly why this is happening. The authors of the study suggest two possibilities:

"The correlations and cyclicity seen in the geologic episodes may be entirely a function of global internal Earth dynamics affecting global tectonics and climate, but similar cycles in the Earth's orbit in the Solar System and in the Galaxy might be pacing these events. Whatever the origins of these cyclical episodes, their occurrences support the case for a largely periodic, coordinated, and intermittently catastrophic geologic record, which is quite different from the views held by most geologists."

Assuming the researchers' calculations are at least roughly correct — the authors note that different statistical formulas may result in further refinement of their conclusions — there's no need to worry that we're about to be thumped by another planetary heartbeat. The last occurred some seven million years ago, meaning the next won't happen for about another 20 million years.

  • A new study finds the oldest galactic wind yet detected, from 13.1 billion years ago.
  • The research confirms the theory that black holes and galaxies evolve together.
  • The galactic wind was spotted using the Atacama Large Millimeter/submillimeter Array in Chile.

An enormously powerful galactic wind generated by a supermassive black hole 13.1 billions years ago has been discovered by researchers. The scientists used the Atacama Large Millimeter/submillimeter Array (ALMA) in Chile, which combines 66 radio telescopes, to make the find. The results are published in the Astrophysical Journal.

This is the earliest example of this type of wind yet spotted that underscores the role of black holes in the formation of galaxies. Research has shown that galactic winds affect redistribution of metals around the galaxy and impact start formation.

Black holes and galaxies evolve together

In previous studies, scientists have noticed an unexpected proportional relationship between the mass of a supermassive black hole at the center of a large galaxy, which can grow up to billions of times more massive than the sun, and the mass of the galaxy's central area (known as a "bulge"). The proportionality of the masses is especially unusual considering that galaxies and black holes are so different in size, with the bulge generally being orders of magnitude larger. This led the researchers to conclude that galaxies and black holes developed together through coevolution, which involved some physical interaction courtesy of the galactic wind.

As ALMA's press release explains, a galactic wind starts coming into existence when a supermassive black hole gobbles up giant quantities of matter. It is then moved at such a high speed by the black hole's gravity that it radiates intense energy, which in turn, pushes surrounding matter away, creating the galactic wind.

Takuma Izumi, the paper's lead author and a researcher at the National Astronomical Observatory of Japan (NAOJ), says an important question is: "When did galactic winds come into existence in the universe?" Finding this out can lead to understanding how galaxies and supermassive black holes coevolved.

Finding an ancient galactic wind

The researchers used NAOJ's Subaru Telescope to locate over 100 galaxies that existed more than 13 billion years ago that featured supermassive black holes. They then used the high sensitivity of ALMA to analyze the gas motion in these galaxies, finding that the dust and carbon of one of them (dubbed J1243+0100) emitted radio waves. This allowed the scientists to detect the presence of an intense galactic wind that rushes forth from the supermassive black hole at about 1,118,468 miles per hour (500 km/second). The energy of the wind, the oldest found so far, is so strong that it pushes away stellar materials, preventing stars from forming.

Interestingly, the mass of the bulge in J1243+0100 was found to be about 30 billion times larger than that of the sun, while the mass of the galaxy's supermassive black hole was estimated to be about 1 percent of that. This ratio is essentially the same as the mass ratio of black holes to galaxies in today's universe. To the scientists, this demonstrates how essential black holes are in affecting the growth of galaxies, supporting the notion of coevolution from the early period of the universe.

"Our observations support recent high-precision computer simulations which have predicted that coevolutionary relationships were in place even at about 13 billion years ago," explained Izumi.

The scientists are planning to observe a large pool of space objects in the future, with the goal of clarifying "whether or not the primordial coevolution seen in this object is an accurate picture of the general universe at that time," further commented Izumi.

  • Most parts of everyday life involve accepting and applying various rules, from the words we speak to the cultural norms we insist on.
  • These rules are learned largely by observation of others and are very rarely taught explicitly.
  • Saul Kripke asks us how it is that we can ever be sure that we're following the rules correctly? And does it matter?

Imagine you're out with some friends and you have to, for whatever reason, add up two numbers: 432 and 222. It's easy, you think! You were great at calculus in school, and you won't even need to get out your phone. In a confident voice, you say, "Oh, that's 654."

There's a pause as everyone looks at you oddly. "You serious?" someone says. Of course you are. That's how addition works, right?

Or is it? According to Saul Kripke, how do you know that you're doing addition correctly?

The games people play

In everyday life, we all follow a series of rules, whether we know it or not. These can be the rules of etiquette, like "don't burp in public" or "don't cook fish in the office microwave," but there are also unspoken rules that apply to our use of words and concepts. For instance, consider the words "anxious" and "scared." The two are similar but there are also very specific rules for when we cannot use them interchangeably.

Sociologists, anthropologists, and linguists have varying names for these rules, but Austro-British philosopher, Ludwig Wittgenstein, called them our "form of life." Although the term is a bit ambiguous, it's taken to mean those rules that we accept to go about our public interactions. They're a bit like the rules of a game before everyone plays — "don't pick up the ball" or "start running when you hear the gun."

We all belong to various forms of life, which give us the values we have and the language we use (which in turn influences how we think). It might be, for instance, that your family has a very particular word for the remote control that other families find odd. Or a certain country might have cultural norms that others do not. It's curious how Scandinavians tend to eat their evening meal around 4 or 5pm, while Spaniards eat nearer 9 pm.

Let's return to the opening example. Mathematics is no different. There are certain rules we have to learn and understand, and then we apply them to new situations. We have axioms, parameters, operators, coefficients, and so on, all of which constitute the "form of life" of mathematics.

Do any of us know what we're doing?

Kripke was a card-carrying Wittgensteinian. He argued that while we go about applying these rules all the time, he raised the question of whether we can ever be entirely sure that we're applying them correctly.

For example, if a child or a non-native speaker is learning a language, they will often be corrected by competent speakers. In fact, it's important that they are corrected so that they can, themselves, become the ones who will enforce those rules later. As a speaker learns the proper rules of a language, they will recalibrate what Kripke calls their "rule following consideration." And yet, it's quite conceivable that someone could misunderstand a word, but use it correctly all the time, by luck, perhaps.

In my own case, I remember using the word "reprehensible" quite correctly for a long time, thinking it meant one (slightly off) thing. I was simply lucky enough to use the word only in the contexts that fit my understanding. I was never "caught out." Most adults have a vocabulary of around 30,000 words, and most haven't taken the time to look up even a fraction of those. And, even if you did, what would that prove? Lexicographers are always playing catch up — words morph and evolve as well as die, and new ones are born every day.

But, this skepticism is not limited to words. It applies, too, to things like mathematics. No one is ever shown "addition." What happens is that we're given a list of discrete examples of addition at work and are expected to just understand. We say, "2+2=4, 4+3=7, 9+7=16. You got it yet? Good, now go and do that on your own."

A teacher or a group of people competent at math might correct us as we're finding our feet, but it's a wonder how we latch on to the principle of addition. And then we assume that we're doing it right all along.

But what if addition isn't what you think it is? In the opening example, what if addition works differently if the second addend is three repeated numbers? What if addition works differently after you reach a certain number? It might be that you've just never encountered this before.

I don't care — it just works

There are some Wittgensteinians who think Kripke misses the point. They argue that when you are part of a form of life, or when you wholesale accept a system of rules, part of doing that means that you don't question it. When you play chess you don't spend all your time asking, "But why do the knights move this way? It makes no sense!" You just play the game.

Likewise, when we speak to each other, we're not crippled by doubt that we might be choosing the wrong word. We just assume that we're right and get on with it. So, too, with Kripke's "rule following considerations." To understand a rule is to accept it, not to doubt it. Addition is no different.

But, that being true, it's still an interesting thought: How do you know that you're doing anything properly? We all think that we're competent and intelligent, but what if we're just monumentally lucky? What if one day, we're exposed as poseurs?

Jonny Thomson teaches philosophy in Oxford. He runs a popular Instagram account called Mini Philosophy (@philosophyminis). His first book is Mini Philosophy: A Small Book of Big Ideas