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
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
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
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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Scientists discover the inner workings of an effect that will lead to a new generation of devices.
- Researchers discover a method of extracting previously unavailable information from superconductors.
- The study builds on a 19th-century discovery by physicist Edward Hall.
- The research promises to lead to a new generation of semiconductor materials and devices.
Credit: Gunawan/Nature magazine
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A trio of intriguing galaxy clusters<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQzNDA0OS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxNTkzNzUyOH0.0IRzkzvKsmPEHV-v1dqM1JIPhgE2W-UHx0COuB0qQnA/img.jpg?width=980" id="d69be" class="rm-shortcode" data-rm-shortcode-id="2d2664d9174369e0a06540cb3a3a9079" data-rm-shortcode-name="rebelmouse-image" />
The three galaxy clusters imaged for the study
Mapping dark matter<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="d904b585c806752f261e1215014691a6"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/fO0jO_a9uLA?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>The assumption has been that the greater the lensing effect, the higher the concentration of dark matter.</p><p>As scientists analyzed the clusters' large-scale lensing — the massive arc and elongation visual effects produced by dark matter — they noticed areas of smaller-scale lensing within that larger distortion. The scientists interpret these as concentrations of dark matter within individual galaxies inside the clusters.</p><p>The researchers used spectrographic data from the VLT to determine the mass of these smaller lenses. <a href="https://www.oas.inaf.it/en/user/pietro.bergamini/" target="_blank" rel="noopener noreferrer">Pietro Bergamini</a> of the INAF-Observatory of Astrophysics and Space Science in Bologna, Italy explains, "The speed of the stars gave us an estimate of each individual galaxy's mass, including the amount of dark matter." The leader of the spectrographic aspect of the study was <a href="http://docente.unife.it/docenti-en/piero.rosati1/curriculum?set_language=en" target="_blank">Piero Rosati</a> of the Università degli Studi di Ferrara, Italy who recalls, "the data from Hubble and the VLT provided excellent synergy. We were able to associate the galaxies with each cluster and estimate their distances." </p><p>This work allowed the team to develop a thoroughly calibrated, high-resolution map of dark matter concentrations throughout the three clusters.</p>
But the models say...<p>However, when the researchers compared their map to the concentrations of dark matter computer models predicted for galaxies bearing the same general characteristics, something was <em>way</em> off. Some small-scale areas of the map had 10 times the amount of lensing — and presumably 10 times the amount of dark matter — than the model predicted.</p><p>"The results of these analyses further demonstrate how observations and numerical simulations go hand in hand," notes one team member, <a href="https://nena12276.wixsite.com/elenarasia" target="_blank">Elena Rasia</a> of the INAF-Astronomical Observatory of Trieste, Italy. Another, <a href="http://adlibitum.oats.inaf.it/borgani/" target="_blank" rel="noopener noreferrer">Stefano Borgani</a> of the Università degli Studi di Trieste, Italy, adds that "with advanced cosmological simulations, we can match the quality of observations analyzed in our paper, permitting detailed comparisons like never before."</p><p>"We have done a lot of testing of the data in this study," Meneghetti says, "and we are sure that this mismatch indicates that some physical ingredient is missing either from the simulations or from our understanding of the nature of dark matter." <a href="https://physics.yale.edu/people/priyamvada-natarajan" target="_blank">Priyamvada Natarajan</a> of Yale University in Connecticut agrees: "There's a feature of the real Universe that we are simply not capturing in our current theoretical models."</p><p>Given that any theory in science lasts only until a better one comes along, Natarajan views the discrepancy as an opportunity, saying, "this could signal a gap in our current understanding of the nature of dark matter and its properties, as these exquisite data have permitted us to probe the detailed distribution of dark matter on the smallest scales."</p><p>At this point, it's unclear exactly what the conflict signifies. Do these smaller areas have unexpectedly high concentrations of dark matter? Or can dark matter, under certain currently unknown conditions, produce a tenfold increase in lensing beyond what we've been expecting, breaking the assumption that more lensing means more dark matter?</p><p>Obviously, the scientific community has barely begun to understand this mystery.</p>
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