10 paradoxes that will stretch your mind

From time-traveling billiard balls to information-destroying black holes, the world's got plenty of puzzles that are hard to wrap your head around.

  • While it's one of the best on Earth, the human brain has a lot of trouble accounting for certain problems.
  • We've evolved to think of reality in a very specific way, but there are plenty of paradoxes out there to suggest that reality doesn't work quite the way we think it does.
  • Considering these paradoxes is a great way to come to grips with how incomplete our understanding of the universe really is.

Human beings have a lot of accomplishments to celebrate. We've repurposed and reshaped our environment to suit our needs. We're even gearing up to settle other planets once we outgrow this one.

Being on top is a great place to be, but it's easy to forget our limitations. The human brain is, after all, hardwired to think in certain ways. While it's a powerful tool for making models of the world, those models are limited by the way we're naturally inclined to think. As a little reminder to remain humble about our cognitive powers, here are 10 paradoxes to try and wrap your head around.

Quick note before we get started: this list takes paradoxes from a number of different fields, all of which tend to use the word paradox differently. Some of these paradoxes are highly unintuitive but objectively true, while others seemingly cannot exist in reality as we understand it.

1. The paradox of hedonism

Image source: Wikimedia Commons

This may very well be one of the most practical paradoxes to understand. In utilitarian philosophy, hedonism is the school of thought that pursuing pleasure is the best way to maximize happiness. However, psychologist Viktor Frankl wrote, "[Happiness cannot] be pursued; it must ensue, and it only does so as the unintended side effect of one's personal dedication to a cause greater than oneself or as the by-product of one's surrender to a person other than oneself."

Constantly pursuing pleasure and happiness is neither pleasurable nor likely to yield happiness; therefore, the best way to be happy is to forget about trying to be happy and to simply let happiness occur on its own.

2. The black hole information paradox

In physics, apparent paradoxes are really just puzzles we have yet to figure out yet. One of the biggest puzzles in physics we have yet to figure out is the black hole information paradox.

Quantum mechanics (for a variety of reasons outside the scope of this article) states that information — things such as the mass and spin of a particle, the structure of atoms that make up a carbon molecule, etc — can never be destroyed. If you were to burn two different letters, putting them back together from ash would be nigh impossible, but not entirely impossible. The subtle differences in smoke, temperature, and the amount of ash would still retain information about the two different letters.

The trouble is, black holes suck things up and then, over a very, very, very long time, radiate that stuff out in the form of Hawking radiation. Unfortunately, unlike the smoke and ash from burning a letter, Hawking radiation contains no information about where it came from: all Hawking radiation is the same, which implies that black holes destroy information about the universe.

Physicists are getting closer and closer to resolving this puzzle, and Stephen Hawking himself believed that the information of particles that enter black holes does eventually return to the universe. If it doesn't, then we need to seriously rethink much of modern physics.

3. The catch-22

Photo by U.S. Air Force Photo/Airman 1st Class Hayden K. Hyatt

Joseph Heller gets credit for inventing this phrase in his eponymous novel, Catch-22. In the novel, a World War II pilot named Yossarian is trying to get out of military duty by requesting psychiatric evaluation, hoping to be declared insane and therefore unfit to fly. His doctor, however, informs him that anybody trying to get out flying in combat cannot possibly be insane; the insane thing to do would be want to fly into combat.

That's the catch-22: a situation that somebody cannot escape because of paradoxical rules. If Yossarian wants to be considered insane, he has to fly in combat. If he flies in combat, then being labelled as insane doesn't do him any good. It's like how young college graduates need experience to get a job but can't get a job without experience.

4. The Monty Hall problem

Photo by Fineas Anton on Unsplash

This paradox lies in how human brains tend to approach statistical problems. It's named after the host of a game show called Let's Make a Deal, which featured this classic problem. There are three doors. Behind one is a car, and the other two hide goats. You pick a door. The host then opens another door, revealing a goat, and asks if you would like to change your selection to the single remaining door.

Most people believe that there is no advantage to switching doors. After all, there's two doors, so there's a 50-50 chance that one has the car, right? Wrong. Switching doors actually raises your odds of picking the car to 66%. Because the host has to pick the remaining goat, he's provided you with extra information. If you've picked a goat on the first try (which will happen two out of three times), then switching will win you the car. If you've picked the car (which will happen one out of three times), then switching will cause you to lose.

5. Peto's paradox

NOAA Photo Library via Flickr

As in physics, paradoxes in biology really are just unsolved puzzles. Enter Peto's paradox. Biologist Richard Peto noticed in the 1970s that mice had a much higher rate of cancer than humans do, which doesn't make any sense. Humans have over 1000 times as many cells as mice, and cancer is simply a rogue cell that goes on multiplying out of control. One would expect humans to be more likely to get cancer than smaller creatures such as mice. This paradox occurs across all species, too: blue whales are much less likely to get cancer than humans, even though they have many more cells in their bodies.

6. The Fermi paradox

NASA Goddard Space Flight Center via Flickr

Named after physicist superstar Enrico Fermi, the Fermi paradox is the contradiction between how likely alien life is in the universe and its apparent absence. Considering the billions of stars in the galaxy like the sun, the many Earth-like planets that must be orbiting some of those stars, the likelihood that some of those planets developed life, the likelihood that some of that life is as intelligent or more intelligent than humanity, the galaxy should be teeming with alien civilizations. This absence led Fermi to pose the question, "Where is everybody?" Some answers to that question are unfortunately a little disturbing.

7. Polchinski's paradox

Pixabay

Who doesn't love a good old-fashioned time paradox? Theoretical physicist Joseph Polchinski posed a puzzle to another physicists in a letter: consider a billiard ball tossed through a wormhole at a certain angle. The billiard ball is then sent back in time through the wormhole and, because of its trajectory, strikes its past self, knocking the ball off course before it can enter the wormhole, travel back in time, and strike itself.

It's a more whimsical and less gruesome version of what happens when you murder your own grandpa in the past and are never born, or if you travel back in time to kill Hitler, thereby obviating any reason you would have had to travel back in time in the first place.

8. The observer's paradox

Photo by Nine Köpfer on Unsplash

Originally coined for the field of sociolinguistics, the observer's paradox is that, when observing a given phenomenon, merely observing it changes the phenomenon itself. In sociolinguistics, if a researcher wants to observe casual communication in a population, those being observed will speak more formally since they know their speech will be involved in academic research.

In a Western Electric factory, researchers wanted to see if improving the lighting of a production line would also improve efficiency. They found that improving the lighting did so, but then returning the lighting to its previous conditions also improved efficiency. Their conclusion was that observing the workers was itself the cause of the improved efficiency.

9. The paradox of intolerance

Photo by ZACH GIBSON/AFP/Getty Images

Without a doubt the most culturally relevant paradox on this list, the paradox of tolerance is the idea that a society that is entirely tolerant of all things will also be tolerant of intolerance. Eventually, the tolerated intolerant elements of a society will seize control, rendering that society a fundamentally intolerant one. Therefore, in order to remain a tolerant society, intolerance cannot be tolerated.

10. The intentionally blank page paradox

john.schultz via Flickr

My personal favorite and also the least consequential: Many official documents will print blank pages in order accommodate formatting concerns. To ensure that readers don't think that they've received a defective publication, the blank page will often include the phrase "This page has been intentionally left blank," providing the page with text that annihilates its status as a blank page.

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Want to forge stronger social bonds? Bring beer.

New research shows that a healthy supply of locally-sourced beer helped maintain Wari civilization for 500 years.

Culture & Religion
  • A new analysis of an ancient Wari brewery suggests chicha helped maintain the civilization's social capital for hundreds of years.
  • Civilizations throughout the ancient world used alcoholic drinks to signify kinship, hospitality, and social cohesion.
  • The researchers hope their findings will remind us of the importance in reaffirming social institutions and sharing cultural practices — even if over coffee or tea.

Beer is history's happiest accident. Though the discovery probably happened much earlier, our earliest evidence for beer dates back roughly 13,000 years ago. Around this time, the people of the Fertile Crescent had begun to gather grains as a food source and learned that if they moistened them, they could release their sweetness to create a gruel much tastier than the grains themselves.

One day a curious — or perhaps tightfisted — hunter-gatherer hid his gruel away for a safekeeping. When he returned, he found the bowl giving off a tangy odor. Not one to waste a meal, he ate it anyway and enjoyed an unexpected, though not unpleasant, sensation of ease. By pure happenstance, this ancestor stumbled upon brewing.

That's one possible origin story, but we know that our ancestors learned to control the process, and beer took a central role in Fertile Crescent civilizations — so central that Professor Patrick McGovern, a biomolecular archaeologist at the University of Pennsylvania, argues that beer, not bread, incentivized hunter-gatherers to relinquish their nomadic ways.

Beer may also be proof of a God who wants us to be happy (Dionysus?), because the beverage* would be independently rediscovered by peoples across the ancient world, including those in China and South America.

One such peoples, the pre-Inca Wari Civilization, made beer, specifically chicha de molle, a critical component in their religious and cultural ceremonies. In fact, a study published in Sustainability in April argues that the role was so important that beer helped keep Wari civilization intact for 500 years.

Brewing social capital

Twenty years ago, a team of archaeologists with the Field Museum of Natural History, Chicago, discovered a brewery in Cerro Baúl, a mesa in southern Peru that served as an ancient Wari outpost. The brewery contained original equipment, clay storage vessels, and compartments for milling, boiling, and fermentation.

The team recently analyzed these on-site vessels to uncover the secrets of the Wari brewing process. Removing tiny amounts of material found in the spaces between the clay, they were able to reconstruct the molecules of the thousand-year-old drink. They then worked alongside Peruvian brewers to recreate the original brewing process.**

Their molecular analysis revealed several key features of the beer: The clay used to make the vessels came from a nearby site; many of the beer's ingredients, such as molle berries, are drought resistant; and though alcoholic, the beer only kept for about a week.

These details suggest that Cerro Baúl maintained a steady supply of chicha, limited by neither trade nor fair weather, and became a central hub for anyone wishing to partake. The Wari would likely make such trips during times of festivals and religious ceremonies. Social elites would consume chicha in vessels shaped like Wari gods and leaders as part of rituals attesting to social norms and a shared cultural mythology and heritage.

"People would have come into this site, in these festive moments, in order to recreate and reaffirm their affiliation with these Wari lords and maybe bring tribute and pledge loyalty to the Wari state," Ryan Williams, lead author and head of anthropology at the Field Museum, said in a release. "We think these institutions of brewing and then serving the beer really formed a unity among these populations. It kept people together."

The Wari civilization was spread over a vast area of rain forests and highlands. In a time when news traveled at the speed of a llama, such distinct and distant geography could easily have fractured the Wari civilization into competing locales.

Instead, the researchers argue, these festive gatherings (aided by the promise of beer) strengthened social capital enough to maintain a healthy national unity. This helped the Wari civilization last from 600 to 1100 CE, an impressive run for a historic civilization.

Bringing people together (since 10,000 BCE)

A Mesopotamian cylinder seal shows people drinking beer through long reed straws. Image source: Metropolitan Museum of Art.

Of course, the Wari weren't the first civilization to use beer to reaffirm bonds and maintain their social fabric. Returning to the Fertile Crescent, Sumerians regarded beer as a hallmark of their civilization.

The Sumerian Epic of Gilgamesh tells of the adventures of the titular hero and his friend Enkidu. Enkidu beings as a savage living in the wilderness, but a young woman introduces him to the ways of civilization. That orientation begins with food and beer:

"They placed food in front of him,
They placed beer in front of him,
Enkidu knew nothing about eating bread for food,
And of drinking beer he had not been taught.
The young woman spoke Enkidu, saying:
"Eat the food, Enkidu, it is the way one lives.
Drink the beer, as is the custom of the land."
Enkidu ate the food until he was sated,
He drank the beer — seven jugs! — and became expansive
and sang with joy.
He was elated and his face glowed.
He splashed his shaggy body with water
and rubbed himself with oil, and turned into a human
."

Tom Standage, who recounts this scene in his History of the World in 6 Glasses, writes: "The Mesopotamians regarded the consumption of bread and beer as one of the things that distinguished them from savages and made them fully human." Such civilized staples not only demarcated their orderly life from that of hunter-gatherers, they also served a key role in their culture's unifying mythology.

Furthermore, Standage notes, Sumerian iconography often shows two people sipping from waist-high jars through reed straws. The earliest beers were consumed in a similar fashion because technological limitations prevented baking individual cups or filtering the beverage. But the Sumerians had the pottery skills to make such cups and filter the dregs. That they kept the tradition suggests that they valued the camaraderie brought by the experience, a sign of communal hospitality and kinship.

The ancient Greek's similarly used alcohol as a means of maintaining social and political relationships — though their drink of choice was wine.

During symposiums, upper-class Greek men would gather for a night of drinking, entertainment, and social bonding. In Alcohol: A history, Rod Phillips notes that symposiums were serious affairs where art, politics, and philosophy were discussed throughout the night and could serve as rites of passage for young men. (Though, music, drinking games, and sex with prostitutes may also be found on the itinerary.)

Of course, we can amass social capital without resorting to alcohol, which has been known to damage social relationships as much as improve them.

In the 17th century, London's coffeehouses stimulated the minds of thinkers with their caffeine-laden drinks, but also served as social hubs. Unlike the examples we've explored already, these coffeehouses brought together people of different backgrounds and expertise, unifying them in their pursuit of ideas and truths. Thus, coffeehouses can be seen as the nurseries of the Enlightenment.

Relearning ancient lessons

The Field Museum archaeologists hope their research can help remind us the importance social institutions and cultural practices have in creating our common bonds, whether such institutions are BYOB or not.

"This research is important because it helps us understand how institutions create the binds that tie together people from very diverse constituencies and very different backgrounds," Williams said. "Without them, large political entities begin to fragment and break up into much smaller things. Brexit is an example of this fragmentation in the European Union today. We need to understand the social constructs that underpin these unifying features if we want to be able to maintain political unity in society."

So, grab a beer or coffee or tea, spend some time together, and raise a glass. Just try not focus too much on whether your friend ordered Budweiser's swill or an overpriced, virtue-signaling microbrew IPA.

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