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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Maps show how CNN lost America to Fox News

Is this proof of a dramatic shift?

Strange Maps
  • Map details dramatic shift from CNN to Fox News over 10-year period
  • Does it show the triumph of "fake news" — or, rather, its defeat?
  • A closer look at the map's legend allows for more complex analyses

Dramatic and misleading

Image: Reddit / SICResearch

The situation today: CNN pushed back to the edges of the country.

Over the course of no more than a decade, America has radically switched favorites when it comes to cable news networks. As this sequence of maps showing TMAs (Television Market Areas) suggests, CNN is out, Fox News is in.

The maps are certainly dramatic, but also a bit misleading. They nevertheless provide some insight into the state of journalism and the public's attitudes toward the press in the US.

Let's zoom in:

  • It's 2008, on the eve of the Obama Era. CNN (blue) dominates the cable news landscape across America. Fox News (red) is an upstart (°1996) with a few regional bastions in the South.
  • By 2010, Fox News has broken out of its southern heartland, colonizing markets in the Midwest and the Northwest — and even northern Maine and southern Alaska.
  • Two years later, Fox News has lost those two outliers, but has filled up in the middle: it now boasts two large, contiguous blocks in the southeast and northwest, almost touching.
  • In 2014, Fox News seems past its prime. The northwestern block has shrunk, the southeastern one has fragmented.
  • Energised by Trump's 2016 presidential campaign, Fox News is back with a vengeance. Not only have Maine and Alaska gone from entirely blue to entirely red, so has most of the rest of the U.S. Fox News has plugged the Nebraska Gap: it's no longer possible to walk from coast to coast across CNN territory.
  • By 2018, the fortunes from a decade earlier have almost reversed. Fox News rules the roost. CNN clings on to the Pacific Coast, New Mexico, Minnesota and parts of the Northeast — plus a smattering of metropolitan areas in the South and Midwest.

"Frightening map"

Image source: Reddit / SICResearch

This sequence of maps, showing America turning from blue to red, elicited strong reactions on the Reddit forum where it was published last week. For some, the takeover by Fox News illustrates the demise of all that's good and fair about news journalism. Among the comments?

  • "The end is near."
  • "The idiocracy grows."
  • "(It's) like a spreading disease."
  • "One of the more frightening maps I've seen."
For others, the maps are less about the rise of Fox News, and more about CNN's self-inflicted downward spiral:
  • "LOL that's what happens when you're fake news!"
  • "CNN went down the toilet on quality."
  • "A Minecraft YouTuber could beat CNN's numbers."
  • "CNN has become more like a high-school production of a news show."

Not a few find fault with both channels, even if not always to the same degree:

  • "That anybody considers either of those networks good news sources is troubling."
  • "Both leave you understanding less rather than more."
  • "This is what happens when you spout bullsh-- for two years straight. People find an alternative — even if it's just different bullsh--."
  • "CNN is sh-- but it's nowhere close to the outright bullsh-- and baseless propaganda Fox News spews."

"Old people learning to Google"

Image: Google Trends

CNN vs. Fox News search terms (200!-2018)

But what do the maps actually show? Created by SICResearch, they do show a huge evolution, but not of both cable news networks' audience size (i.e. Nielsen ratings). The dramatic shift is one in Google search trends. In other words, it shows how often people type in "CNN" or "Fox News" when surfing the web. And that does not necessarily reflect the relative popularity of both networks. As some commenters suggest:

  • "I can't remember the last time that I've searched for a news channel on Google. Is it really that difficult for people to type 'cnn.com'?"
  • "More than anything else, these maps show smart phone proliferation (among older people) more than anything else."
  • "This is a map of how old people and rural areas have learned to use Google in the last decade."
  • "This is basically a map of people who don't understand how the internet works, and it's no surprise that it leans conservative."

A visual image as strong as this map sequence looks designed to elicit a vehement response — and its lack of context offers viewers little new information to challenge their preconceptions. Like the news itself, cartography pretends to be objective, but always has an agenda of its own, even if just by the selection of its topics.

The trick is not to despair of maps (or news) but to get a good sense of the parameters that are in play. And, as is often the case (with both maps and news), what's left out is at least as significant as what's actually shown.

One important point: while Fox News is the sole major purveyor of news and opinion with a conservative/right-wing slant, CNN has more competition in the center/left part of the spectrum, notably from MSNBC.

Another: the average age of cable news viewers — whether they watch CNN or Fox News — is in the mid-60s. As a result of a shift in generational habits, TV viewing is down across the board. Younger people are more comfortable with a "cafeteria" approach to their news menu, selecting alternative and online sources for their information.

It should also be noted, however, that Fox News, according to Harvard's Nieman Lab, dominates Facebook when it comes to engagement among news outlets.

CNN, Fox and MSNBC

Image: Google Trends

CNN vs. Fox (without the 'News'; may include searches for actual foxes). See MSNBC (in yellow) for comparison

For the record, here are the Nielsen ratings for average daily viewer total for the three main cable news networks, for 2018 (compared to 2017):

  • Fox News: 1,425,000 (-5%)
  • MSNBC: 994,000 (+12%)
  • CNN: 706,000 (-9%)

And according to this recent overview, the top 50 of the most popular websites in the U.S. includes cnn.com in 28th place, and foxnews.com in... 27th place.

The top 5, in descending order, consists of google.com, youtube.com, facebook.com, amazon.com and yahoo.com — the latter being the highest-placed website in the News and Media category.
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