from the world's big
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.
Andy Samberg and Cristin Milioti get stuck in an infinite wedding time loop.
- Two wedding guests discover they're trapped in an infinite time loop, waking up in Palm Springs over and over and over.
- As the reality of their situation sets in, Nyles and Sarah decide to enjoy the repetitive awakenings.
- The film is perfectly timed for a world sheltering at home during a pandemic.
Richard Feynman once asked a silly question. Two MIT students just answered it.
Here's a fun experiment to try. Go to your pantry and see if you have a box of spaghetti. If you do, take out a noodle. Grab both ends of it and bend it until it breaks in half. How many pieces did it break into? If you got two large pieces and at least one small piece you're not alone.
But science loves a good challenge<p>The mystery remained unsolved until 2005, when French scientists <a href="http://www.lmm.jussieu.fr/~audoly/" target="_blank">Basile Audoly</a> and <a href="http://www.lmm.jussieu.fr/~neukirch/" target="_blank">Sebastien Neukirch </a>won an <a href="https://www.improbable.com/ig/" target="_blank">Ig Nobel Prize</a>, an award given to scientists for real work which is of a less serious nature than the discoveries that win Nobel prizes, for finally determining why this happens. <a href="http://www.lmm.jussieu.fr/spaghetti/audoly_neukirch_fragmentation.pdf" target="_blank">Their paper describing the effect is wonderfully funny to read</a>, as it takes such a banal issue so seriously. </p><p>They demonstrated that when a rod is bent past a certain point, such as when spaghetti is snapped in half by bending it at the ends, a "snapback effect" is created. This causes energy to reverberate from the initial break to other parts of the rod, often leading to a second break elsewhere.</p><p>While this settled the issue of <em>why </em>spaghetti noodles break into three or more pieces, it didn't establish if they always had to break this way. The question of if the snapback could be regulated remained unsettled.</p>
Physicists, being themselves, immediately wanted to try and break pasta into two pieces using this info<p><a href="https://roheiss.wordpress.com/fun/" target="_blank">Ronald Heisser</a> and <a href="https://math.mit.edu/directory/profile.php?pid=1787" target="_blank">Vishal Patil</a>, two graduate students currently at Cornell and MIT respectively, read about Feynman's night of noodle snapping in class and were inspired to try and find what could be done to make sure the pasta always broke in two.</p><p><a href="http://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813" target="_blank">By placing the noodles in a special machine</a> built for the task and recording the bending with a high-powered camera, the young scientists were able to observe in extreme detail exactly what each change in their snapping method did to the pasta. After breaking more than 500 noodles, they found the solution.</p>
The apparatus the MIT researchers built specifically for the task of snapping hundreds of spaghetti sticks.
(Courtesy of the researchers)
What possible application could this have?<p>The snapback effect is not limited to uncooked pasta noodles and can be applied to rods of all sorts. The discovery of how to cleanly break them in two could be applied to future engineering projects.</p><p>Likewise, knowing how things fragment and fail is always handy to know when you're trying to build things. Carbon Nanotubes, <a href="https://bigthink.com/ideafeed/carbon-nanotube-space-elevator" target="_self">super strong cylinders often hailed as the building material of the future</a>, are also rods which can be better understood thanks to this odd experiment.</p><p>Sometimes big discoveries can be inspired by silly questions. If it hadn't been for Richard Feynman bending noodles seventy years ago, we wouldn't know what we know now about how energy is dispersed through rods and how to control their fracturing. While not all silly questions will lead to such a significant discovery, they can all help us learn.</p>
The multifaceted cerebellum is large — it's just tightly folded.
- A powerful MRI combined with modeling software results in a totally new view of the human cerebellum.
- The so-called 'little brain' is nearly 80% the size of the cerebral cortex when it's unfolded.
- This part of the brain is associated with a lot of things, and a new virtual map is suitably chaotic and complex.
Just under our brain's cortex and close to our brain stem sits the cerebellum, also known as the "little brain." It's an organ many animals have, and we're still learning what it does in humans. It's long been thought to be involved in sensory input and motor control, but recent studies suggests it also plays a role in a lot of other things, including emotion, thought, and pain. After all, about half of the brain's neurons reside there. But it's so small. Except it's not, according to a new study from San Diego State University (SDSU) published in PNAS (Proceedings of the National Academy of Sciences).
A neural crêpe
A new imaging study led by psychology professor and cognitive neuroscientist Martin Sereno of the SDSU MRI Imaging Center reveals that the cerebellum is actually an intricately folded organ that has a surface area equal in size to 78 percent of the cerebral cortex. Sereno, a pioneer in MRI brain imaging, collaborated with other experts from the U.K., Canada, and the Netherlands.
So what does it look like? Unfolded, the cerebellum is reminiscent of a crêpe, according to Sereno, about four inches wide and three feet long.
The team didn't physically unfold a cerebellum in their research. Instead, they worked with brain scans from a 9.4 Tesla MRI machine, and virtually unfolded and mapped the organ. Custom software was developed for the project, based on the open-source FreeSurfer app developed by Sereno and others. Their model allowed the scientists to unpack the virtual cerebellum down to each individual fold, or "folia."
Study's cross-sections of a folded cerebellum
Image source: Sereno, et al.
A complicated map
Sereno tells SDSU NewsCenter that "Until now we only had crude models of what it looked like. We now have a complete map or surface representation of the cerebellum, much like cities, counties, and states."
That map is a bit surprising, too, in that regions associated with different functions are scattered across the organ in peculiar ways, unlike the cortex where it's all pretty orderly. "You get a little chunk of the lip, next to a chunk of the shoulder or face, like jumbled puzzle pieces," says Sereno. This may have to do with the fact that when the cerebellum is folded, its elements line up differently than they do when the organ is unfolded.
It seems the folded structure of the cerebellum is a configuration that facilitates access to information coming from places all over the body. Sereno says, "Now that we have the first high resolution base map of the human cerebellum, there are many possibilities for researchers to start filling in what is certain to be a complex quilt of inputs, from many different parts of the cerebral cortex in more detail than ever before."
This makes sense if the cerebellum is involved in highly complex, advanced cognitive functions, such as handling language or performing abstract reasoning as scientists suspect. "When you think of the cognition required to write a scientific paper or explain a concept," says Sereno, "you have to pull in information from many different sources. And that's just how the cerebellum is set up."
Bigger and bigger
The study also suggests that the large size of their virtual human cerebellum is likely to be related to the sheer number of tasks with which the organ is involved in the complex human brain. The macaque cerebellum that the team analyzed, for example, amounts to just 30 percent the size of the animal's cortex.
"The fact that [the cerebellum] has such a large surface area speaks to the evolution of distinctively human behaviors and cognition," says Sereno. "It has expanded so much that the folding patterns are very complex."
As the study says, "Rather than coordinating sensory signals to execute expert physical movements, parts of the cerebellum may have been extended in humans to help coordinate fictive 'conceptual movements,' such as rapidly mentally rearranging a movement plan — or, in the fullness of time, perhaps even a mathematical equation."
Sereno concludes, "The 'little brain' is quite the jack of all trades. Mapping the cerebellum will be an interesting new frontier for the next decade."
What happens if we consider welfare programs as investments?
- A recently published study suggests that some welfare programs more than pay for themselves.
- It is one of the first major reviews of welfare programs to measure so many by a single metric.
- The findings will likely inform future welfare reform and encourage debate on how to grade success.
Welfare as an investment<p>The <a href="https://scholar.harvard.edu/files/hendren/files/welfare_vnber.pdf" target="_blank">study</a>, carried out by Nathaniel Hendren and Ben Sprung-Keyser of Harvard University, reviews 133 welfare programs through a single lens. The authors measured these programs' "Marginal Value of Public Funds" (MVPF), which is defined as the ratio of the recipients' willingness to pay for a program over its cost.</p><p>A program with an MVPF of one provides precisely as much in net benefits as it costs to deliver those benefits. For an illustration, imagine a program that hands someone a dollar. If getting that dollar doesn't alter their behavior, then the MVPF of that program is one. If it discourages them from working, then the program's cost goes up, as the program causes government tax revenues to fall in addition to costing money upfront. The MVPF goes below one in this case. <br> <br> Lastly, it is possible that getting the dollar causes the recipient to further their education and get a job that pays more taxes in the future, lowering the cost of the program in the long run and raising the MVPF. The value ratio can even hit infinity when a program fully "pays for itself."</p><p> While these are only a few examples, many others exist, and they do work to show you that a high MVPF means that a program "pays for itself," a value of one indicates a program "breaks even," and a value below one shows a program costs more money than the direct cost of the benefits would suggest.</p> After determining the programs' costs using existing literature and the willingness to pay through statistical analysis, 133 programs focusing on social insurance, education and job training, tax and cash transfers, and in-kind transfers were analyzed. The results show that some programs turn a "profit" for the government, mainly when they are focused on children:
This figure shows the MVPF for a variety of polices alongside the typical age of the beneficiaries. Clearly, programs targeted at children have a higher payoff.
Nathaniel Hendren and Ben Sprung-Keyser<p>Programs like child health services and K-12 education spending have infinite MVPF values. The authors argue this is because the programs allow children to live healthier, more productive lives and earn more money, which enables them to pay more taxes later. Programs like the preschool initiatives examined don't manage to do this as well and have a lower "profit" rate despite having decent MVPF ratios.</p><p>On the other hand, things like tuition deductions for older adults don't make back the money they cost. This is likely for several reasons, not the least of which is that there is less time for the benefactor to pay the government back in taxes. Disability insurance was likewise "unprofitable," as those collecting it have a reduced need to work and pay less back in taxes. </p>