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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
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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Even before publication, health agencies were asking the journal not to publish the research.
- A new study in the Annals of Internal Medicine found little correlation between red meat consumption and health problems.
- A number of organizations immediately contested the evidence, claiming it to be based on an irrelevant system of analysis.
- Beef and dairy production is one of the leading drivers of climate change, forcing humans to weigh personal health against the environment.
It is perhaps fitting that just as McDonald's introduces meatless burgers, a new study, published in the journal, Annals of Internal Medicine, is overturning years' worth of dietary recommendations that we eat less red meat. Not that everyone is taking the study as the final word, however.
A panel of fourteen researchers and three community members from seven countries (reporting no conflicts of interest), directed by Dalhousie University epidemiologist, Bradley Johnson, studied 61 articles on all-cause mortality that included a total of four million participants. The team also reviewed dozens of trials linking red meat to cancer, heart disease, and mortality. The team concluded that the evidence between red meat, both unprocessed and processed, and health problems is "low to very low."
The study took three years to complete. Researchers from a range of cultures were included to ensure diversity of thought, while each professional was vetted for perceived conflicts of interest. When considering both processed and unprocessed red meat, 11 researchers voted for adults (age 18 and over) to continue eating recommended allowances and not cut down. In each study, three researchers offered a "weak recommendation" for reducing intake.
For the record, the average American adult consumes an average of 4.5 servings of red meat per week.
Organizations such as The American Heart Association and the American Cancer Society immediately came out against the study, with some groups suggesting that the journal withhold publication. They believed that not only would this information contradict years of findings, but it would "erode public trust in scientific research."
To be fair, that's the nature of science: If evidence overturns pre-existing norms, that evidence should be considered. However, we need to take a more holistic look at this picture.
Gut Bacteria and Red Meat: Highlight from Cancer and Diet
Nutrition science is tricky. Not only do self-endowed "life coaches" and fitness trainers not certified in nutrition offer unsolicited advice, actual scientific bodies find it hard to come to conclusions. One of the biggest issues: It's nearly impossible to isolate macronutrients or entire classes of food given their interactions with all the other food you consume. A burger doesn't have the same effect on your body as a burger with mayonnaise on a bun; whether you drink water or soda to accompany that meal matters too.
The main contention comes from the type of analysis the researchers used. As Harvard nutrition scientist, Frank Hu, says, the GRADE systematic approach was introduced for evaluating drug trials, not nutrition science. Alongside his colleagues, Hu published an article countering the results of the meta-analyses, coming to four conclusions:
- The new guidelines are not justified as they contradict the evidence generated from their own meta-analyses
- The publication of these studies and the meat guidelines in a major medical journal is unfortunate because following the new guidelines may potentially harm individuals' health, public health, and planetary health
- This is a prime example where one must look beyond the headlines and abstract conclusions
- These studies should not change current recommendations on healthy and balanced eating patterns for the prevention of chronic diseases
Close-up of Impossible Whopper, a meat-free item using engineered, plant-protein based burger patty from food technology company Impossible, during a limited market test at a Burger King restaurant in the San Francisco Bay Area, Danville, California, June 26, 2019.
Photo by Smith Collection/Gado/Getty Images
As with many topics in American discourse, our diet has become polarized. Those that claim that humans were not designed to eat meat are ignorant of how our biology (and cultures) evolved. As primatologist Richard Wrangham writes, the greatest culinary advancement in history was fire. Cooking made nutrients available much more quickly—a burger on a grill is more nutritious than chewing on raw meat. And meat is something our ancestors definitively ate whenever they could.
What also doesn't help is a sentiment that has been batted around the holistic blogosphere: that meat is toxic. To be fair, growth hormones and factory farming have increased the potential for toxicity in our food supply. But meat itself is not inherently toxic to our digestive system. As Harvard paleoanthropologist, Daniel Lieberman, writes, given our ancestors' adaptation to diverse climates, there is no "optimal diet." We ate what we could source. That said, meat consumption offered a particularly important boon to our biology.
"By incorporating meat in the diet and relying more on food processing, early Homo was able to spend much less energy digesting its food and could thus devote more energy toward growing and paying for a larger brain."
Yet that doesn't mean we need to eat meat, at least not as much of it was we do. Beyond sating our biological impulse, industrial agriculture—specifically, beef and dairy production—is one of the biggest drivers of climate change. Beef is extremely taxing on the environment, much more so than chicken or pork agriculture.
From a climate perspective, plant-based diets are less taxing, though you often run into the problem of nutrient loss due to monocropping. Plant-based burgers might be all the rage, but that also doesn't mean they're healthy, which brings into question whether or not it makes sense to sacrifice personal health for a perceived environmental gain.
An easy answer? Not here.
One thing is clear: The current rate of beef production is unsustainable. Whether or not 4.5 servings of red meat will increase your risk of cancer or heart disease might remain a source of contention. But a more important question remains: If reducing your meat intake is better for the environment (and therefore everyone's health), isn't that a wiser decision to make?
It marks a breakthrough in using gene editing to treat diseases.
This article was originally published by our sister site, Freethink.
For the first time, researchers appear to have effectively treated a genetic disorder by directly injecting a CRISPR therapy into patients' bloodstreams — overcoming one of the biggest hurdles to curing diseases with the gene editing technology.
The therapy appears to be astonishingly effective, editing nearly every cell in the liver to stop a disease-causing mutation.
The challenge: CRISPR gives us the ability to correct genetic mutations, and given that such mutations are responsible for more than 6,000 human diseases, the tech has the potential to dramatically improve human health.
One way to use CRISPR to treat diseases is to remove affected cells from a patient, edit out the mutation in the lab, and place the cells back in the body to replicate — that's how one team functionally cured people with the blood disorder sickle cell anemia, editing and then infusing bone marrow cells.
Bone marrow is a special case, though, and many mutations cause disease in organs that are harder to fix.
Another option is to insert the CRISPR system itself into the body so that it can make edits directly in the affected organs (that's only been attempted once, in an ongoing study in which people had a CRISPR therapy injected into their eyes to treat a rare vision disorder).
Injecting a CRISPR therapy right into the bloodstream has been a problem, though, because the therapy has to find the right cells to edit. An inherited mutation will be in the DNA of every cell of your body, but if it only causes disease in the liver, you don't want your therapy being used up in the pancreas or kidneys.
A new CRISPR therapy: Now, researchers from Intellia Therapeutics and Regeneron Pharmaceuticals have demonstrated for the first time that a CRISPR therapy delivered into the bloodstream can travel to desired tissues to make edits.
We can overcome one of the biggest challenges with applying CRISPR clinically.
"While these are early data, they show us that we can overcome one of the biggest challenges with applying CRISPR clinically so far, which is being able to deliver it systemically and get it to the right place," she continued.
What they did: During a phase 1 clinical trial, Intellia researchers injected a CRISPR therapy dubbed NTLA-2001 into the bloodstreams of six people with a rare, potentially fatal genetic disorder called transthyretin amyloidosis.
The livers of people with transthyretin amyloidosis produce a destructive protein, and the CRISPR therapy was designed to target the gene that makes the protein and halt its production. After just one injection of NTLA-2001, the three patients given a higher dose saw their levels of the protein drop by 80% to 96%.
A better option: The CRISPR therapy produced only mild adverse effects and did lower the protein levels, but we don't know yet if the effect will be permanent. It'll also be a few months before we know if the therapy can alleviate the symptoms of transthyretin amyloidosis.
This is a wonderful day for the future of gene-editing as a medicine.
If everything goes as hoped, though, NTLA-2001 could one day offer a better treatment option for transthyretin amyloidosis than a currently approved medication, patisiran, which only reduces toxic protein levels by 81% and must be injected regularly.
Looking ahead: Even more exciting than NTLA-2001's potential impact on transthyretin amyloidosis, though, is the knowledge that we may be able to use CRISPR injections to treat other genetic disorders that are difficult to target directly, such as heart or brain diseases.
"This is a wonderful day for the future of gene-editing as a medicine," Fyodor Urnov, a UC Berkeley professor of genetics, who wasn't involved in the trial, told NPR. "We as a species are watching this remarkable new show called: our gene-edited future."
A new government report describes 144 sightings of unidentified aerial phenomena.
On June 25, 2021, the Office of the Director of National Intelligence released a much-anticipated report on UFOs to Congress.
The military has rebranded unidentified flying objects as unidentified aerial phenomena – UAPs – in part to avoid the stigma that has been attached to claims of aliens visiting the Earth since the Roswell incident in 1947. The report presents no convincing evidence that alien spacecraft have been spotted, but some of the data defy easy interpretation.
I'm a professor of astronomy who has written extensively on the search for life in the universe. I also teach a free online class on astrobiology. I do not believe that the new government report or any other sightings of UFOs in the past are proof of aliens visiting Earth. But the report is important because it opens the door for a serious look at UFOs. Specifically, it encourages the U.S. government to collect better data on UFOs, and I think the release of the report increases the chances that scientists will try to interpret that data. Historically, UFOs have felt off limits to mainstream science, but perhaps no more.
Three videos from the U.S. military sparked a recent surge in interest in UFOs.
What's in the UFO report?
The No. 1 thing the report focuses on is the lack of high-quality data. Here are the highlights from the slender nine-page report, covering a total of 144 UAP sightings from U.S. government sources between 2004 and 2021:
- “Limited data and inconsistent reporting are key challenges to evaluating UAP."
- Some observations “could be the result of sensor errors, spoofing, or observer misperception."
- “UAP clearly pose a safety of flight issue and may pose a challenge to U.S. national security."
- Of the 144 sightings, the task force was “able to identify one reported UAP with high confidence. In that case, we identified the object as a large, deflating balloon. The others remain unexplained."
- “Some UAP many be technologies deployed by China, Russia, another nation, or non-governmental entity."
UFOs are taboo among scientists
UFO means unidentified flying object. Nothing more, nothing less. You'd think scientists would enjoy the challenge of solving this puzzle. Instead, UFOs have been taboo for academic scientists to investigate, and so unexplained reports have not received the scrutiny they deserve.
One reason is that most scientists think there is less to most reports than meets the eye, and the few who have dug deeply have mostly debunked the phenomenon. Over half of sightings can be attributed to meteors, fireballs and the planet Venus.
Another reason for the scientific hesitance is that UFOs have been co-opted by popular culture. They are part of a landscape of conspiracy theories that includes accounts of abduction by aliens and crop circles. Scientists worry about their professional reputations, and the association of UFOs with these supernatural stories causes most researchers to avoid the topic.
But some scientists have looked. In 1968, Edward U. Condon at the University of Colorado published the first major academic study of UFO sightings. The Condon Report put a damper on further research when it found that “nothing has come from the study of UFOs in the past 21 years that has added to scientific knowledge."
However, a review in 1998 by a panel led by Peter Sturrock, a professor of applied physics at Stanford University, concluded that some sightings are accompanied by physical evidence that deserves scientific study. Sturrock also surveyed professional astronomers and found that nearly half thought UFOs were worthy of scientific study, with higher interest among younger and more well-informed astronomers.
If astronomers are intrigued by UFOs – and believe some cases deserve study with academic rigor – what's holding them back? A history of mistrust between ufologists and scientists hasn't helped. And while UFO research has employed some of the tools of the scientific method, it has not had the core of skeptical, evidence-based reasoning that demarcates science from pseudoscience.
A search of 90,000 recent and current grants awarded by the National Science Foundation finds none addressing UFOs or related phenomena. I've served on review panels for 35 years, and can imagine the reaction if such a proposal came up for peer review: raised eyebrows and a quick vote not to fund.
A decadeslong search for aliens
While the scientific community has almost entirely avoided engaging with UFOs, a much more mainstream search for intelligent aliens and their technology has been going on for decades.
The search is motivated by the fact that astronomers have, to date, discovered over 4,400 planets orbiting other stars. Called exoplanets, some are close to the Earth's mass and at just the right distance from their stars to potentially have water on their surfaces – meaning they might be habitable.
Astronomers estimate that there are 300 million habitable worlds in the Milky Way galaxy alone, and each one is a potential opportunity for life to develop and for intelligence and technology to emerge. Indeed, most astronomers think it very unlikely that humans are the only or the first advanced civilization.
This confidence has fueled an active search for extraterrestrial intelligence, known as SETI. It has been unsuccessful so far. As a result, researchers have recast the question “Are we alone?" to “Where are the aliens?" The absence of evidence for intelligent aliens is called the Fermi paradox. First articulated by the physicist Enrico Fermi, it's a paradox because advanced civilizations should be spread throughout the galaxy, yet we see no sign of their existence.
The SETI activity has not been immune from scientists' criticism. It was starved of federal funding for decades and recently has gotten most of its support from private sources. However, in 2020, NASA resumed funding for SETI, and the new NASA administrator wants researchers to pursue the topic of UFOs.
In this context, the intelligence report is welcome. The report draws few concrete conclusions about UFOs and avoids any reference to aliens or extraterrestrial spacecraft. However, it notes the importance of destigmatizing UFOs so that more pilots report what they see. It also sets a goal of moving from anecdotal observations to standardized and scientific data collection. Time will tell if this is enough to draw scientists into the effort, but the transparency to publish the report at all reverses a long history of secrecy surrounding U.S. government reports on UFOs.
I don't see any convincing evidence of alien spacecraft, but as a curious scientist, I hope the subset of UFO sightings that are truly unexplained gets closer study. Scientists are unlikely to weigh in if their skepticism generates attacks from “true believers" or they get ostracized by their colleagues. Meanwhile, the truth is still out there.
This article has been updated to clarify that the report was produced by the Office of the Director of National Intelligence.
Gain-of-function mutation research may help predict the next pandemic — or, critics argue, cause one.