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A Logic Puzzle That Teaches a Life Lesson
Here are a couple classic logic problems, updated for the digital world.
Before we get to the brain teaser of the day — which does, as the headline indicates, carry a deeper meaning — here is a classic logic problem, updated for the digital world, to get you warmed up:
You find yourself in a dark chamber with two closed doors — one leading to bliss, the other to death, though you do not know which door is which. Two charged and ready iPhones — one programmed with Honest Omniscient Siri, the other with Lying Omniscient Siri — sit on a low table. (Honest Siri always tells the truth; Lying Siri always lies.) But the phones appear identical, and, again, you have no idea which is which. You must choose a door, and you are given permission to ask one of the phones a single question to help you make your decision. What question do you ask?
Tough one, right? Sweating a little? It would be easy as pie if you could ask two questions: one to establish which is Honest Siri (e.g., “What’s my name?”) and then one directed to Honest Siri to determine which door leads to bliss. But no such luck. You need to ask a single question with no idea which phone is the trustworthy one. Make it a good one.
Because your question needs to yield valuable information no matter whether you happen to address Honest Siri or Lying Siri, it should be a question that will give you the same answer no matter which phone you chanced to pick up. So here we go: “If I asked the other iPhone which door leads to bliss, what would Siri tell me?” Honest Siri will point toward the death door, which is what Lying Siri would in fact indicate. Lying Siri would point toward the death door as well, which is the opposite of what Honest Siri would tell you if you asked her directly. So you find out what you need to know about the doors without having to figure out which phone is which. Now that you know which is the door to your demise, you can open the other door with confidence that bliss awaits you on the other side.
In this problem, known as the two guards riddle, everything depends on several pieces of information you assume to be true: The doors really lead to divergent fates and one phone always lies while the other always tells the truth. But in the real world, such conditions are always subject to some degree of doubt.
A new puzzle from programmer Mark Dominus plays on this inevitable uncertainty, and contains a valuable lesson. He calls it the “annoying boxes problem.” Here it is:
There are two boxes on a table, one red and one green. One contains a treasure. The red box is labeled "exactly one of the labels is true." The green box is labeled "the treasure is in this box."
Can you figure out which box contains the treasure?
a. The treasure is in the red box
b. The treasure is in the green box
c. There is not enough information to determine the answer
d. Something else: __________________________
What was your answer? Before I share the correct solution and an explanation thereof, here is the rundown of how 506 people voted in early July when Dominus first posted the puzzle:
So if you said the treasure is in the red box, you are in good company: About two-thirds of respondents chose (a), by far the most popular response. But if you selected option (c) — not enough information — you arrived at the correct answer. But here’s the kicker: The treasure was in the green box. How could that be? Here is how Dominus explains the apparent contradiction:
If you said the treasure was in the green box, you were right, but you got the logic puzzle wrong. As Dominus points out, the question asks whether you can figure out which box the treasure is in. And the answer to that question is no. No points for lucky guesses.
If you selected (a), like most respondents, you might wonder why you’re wrong. Dominus goes into detail in his post, which you can read here. For me, the most interesting point Dominus makes comes in his explanation of why it’s a mistake to read too much (or to read anything, actually) into the labels on the boxes. They are “red herrings,” he writes, and are “worthless”:
[I]n the absence of additional information, there is no reason to believe that the labels give any information about the contents of the boxes, or about labels, or about anything at all. This should not come as a surprise to anyone. It is true not just in annoying puzzles, but in the world in general. A box labeled “fresh figs” might contain fresh figs, or spoiled figs, or angry hornets, or nothing at all.
The boxes puzzle is “annoying” because it unsettles our predilection to place faith in truth claims and use them as anchors when solving a puzzle—or navigating the world. But jogging our tendency to rely on labels is a valuable public service. Labels can mislead; they can confuse; they can be crafted to manipulate you to do something you wouldn’t otherwise do. Have you ever clicked on a link with an especially alluring headline that didn’t quite deliver? Selected a product labeled “all natural” at the grocery store without knowing whether it was really any healthier? Bought a sunscreen based on its stated sun-protection factor (SPF) with no idea what that really means?
We have no choice, but to rely on labels, of course. Radical skepticism about every label is a prescription for paralysis. But it’s still advisable to keep up our guard in the face of labels that seem outlandish, unlikely, inconsistent, or too good to be true — and Dominus’ annoying little logic puzzle is a nice reminder of that.
Image credit: Shutterstock
Follow Steven Mazie on Twitter: @stevenmazie
Northwell Health is using insights from website traffic to forecast COVID-19 hospitalizations two weeks in the future.
- The machine-learning algorithm works by analyzing the online behavior of visitors to the Northwell Health website and comparing that data to future COVID-19 hospitalizations.
- The tool, which uses anonymized data, has so far predicted hospitalizations with an accuracy rate of 80 percent.
- Machine-learning tools are helping health-care professionals worldwide better constrain and treat COVID-19.
The value of forecasting<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNTA0Njk2OC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYyMzM2NDQzOH0.rid9regiDaKczCCKBsu7wrHkNQ64Vz_XcOEZIzAhzgM/img.jpg?width=980" id="2bb93" class="rm-shortcode" data-rm-shortcode-id="31345afbdf2bd408fd3e9f31520c445a" data-rm-shortcode-name="rebelmouse-image" data-width="1546" data-height="1056" />
Northwell emergency departments use the dashboard to monitor in real time.
Credit: Northwell Health<p>One unique benefit of forecasting COVID-19 hospitalizations is that it allows health systems to better prepare, manage and allocate resources. For example, if the tool forecasted a surge in COVID-19 hospitalizations in two weeks, Northwell Health could begin:</p><ul><li>Making space for an influx of patients</li><li>Moving personal protective equipment to where it's most needed</li><li>Strategically allocating staff during the predicted surge</li><li>Increasing the number of tests offered to asymptomatic patients</li></ul><p>The health-care field is increasingly using machine learning. It's already helping doctors develop <a href="https://care.diabetesjournals.org/content/early/2020/06/09/dc19-1870" target="_blank">personalized care plans for diabetes patients</a>, improving cancer screening techniques, and enabling mental health professionals to better predict which patients are at <a href="https://healthitanalytics.com/news/ehr-data-fuels-accurate-predictive-analytics-for-suicide-risk" target="_blank" rel="noopener noreferrer">elevated risk of suicide</a>, to name a few applications.</p><p>Health systems around the world have already begun exploring how <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7315944/" target="_blank" rel="noopener noreferrer">machine learning can help battle the pandemic</a>, including better COVID-19 screening, diagnosis, contact tracing, and drug and vaccine development.</p><p>Cruzen said these kinds of tools represent a shift in how health systems can tackle a wide variety of problems.</p><p>"Health care has always used the past to predict the future, but not in this mathematical way," Cruzen said. "I think [Northwell Health's new predictive tool] really is a great first example of how we should be attacking a lot of things as we go forward."</p>
Making machine-learning tools openly accessible<p>Northwell Health has made its predictive tool <a href="https://github.com/northwell-health/covid-web-data-predictor" target="_blank">available for free</a> to any health system that wishes to utilize it.</p><p>"COVID is everybody's problem, and I think developing tools that can be used to help others is sort of why people go into health care," Dr. Cruzen said. "It was really consistent with our mission."</p><p>Open collaboration is something the world's governments and health systems should be striving for during the pandemic, said Michael Dowling, Northwell Health's president and CEO.</p><p>"Whenever you develop anything and somebody else gets it, they improve it and they continue to make it better," Dowling said. "As a country, we lack data. I believe very, very strongly that we should have been and should be now working with other countries, including China, including the European Union, including England and others to figure out how to develop a health surveillance system so you can anticipate way in advance when these things are going to occur."</p><p>In all, Northwell Health has treated more than 112,000 COVID patients. During the pandemic, Dowling said he's seen an outpouring of goodwill, collaboration, and sacrifice from the community and the tens of thousands of staff who work across Northwell.</p><p>"COVID has changed our perspective on everything—and not just those of us in health care, because it has disrupted everybody's life," Dowling said. "It has demonstrated the value of community, how we help one another."</p>
It's hard to stop looking back and forth between these faces and the busts they came from.
- A quarantine project gone wild produces the possibly realistic faces of ancient Roman rulers.
- A designer worked with a machine learning app to produce the images.
- It's impossible to know if they're accurate, but they sure look plausible.
How the Roman emperors got faced<a href="https://payload.cargocollective.com/1/6/201108/14127595/2K-ENGLISH-24x36-Educational_v8_WATERMARKED_2000.jpg" ><img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ2NDk2MS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYyOTUzMzIxMX0.OwHMrgKu4pzu0eCsmOUjybdkTcSlJpL_uWDCF2djRfc/img.jpg?width=980" id="775ca" class="rm-shortcode" data-rm-shortcode-id="436000b6976931b8320313478c624c82" data-rm-shortcode-name="rebelmouse-image" alt="lineup of emperor faces" data-width="1440" data-height="963" /></a>
Credit: Daniel Voshart<p>Voshart's imaginings began with an AI/neural-net program called <a href="https://www.artbreeder.com" target="_blank">Artbreeder</a>. The freemium online app intelligently generates new images from existing ones and can combine multiple images into…well, who knows. It's addictive — people have so far used it to generate nearly 72.7 million images, says the site — and it's easy to see how Voshart fell down the rabbit hole.</p><p>The Roman emperor project began with Voshart feeding Artbreeder images of 800 busts. Obviously, not all busts have weathered the centuries equally. Voshart told <a href="https://www.livescience.com/ai-roman-emperor-portraits.html" target="_blank" rel="noopener noreferrer">Live Science</a>, "There is a rule of thumb in computer programming called 'garbage in garbage out,' and it applies to Artbreeder. A well-lit, well-sculpted bust with little damage and standard face features is going to be quite easy to get a result." Fortunately, there were multiple busts for some of the emperors, and different angles of busts captured in different photographs.</p><p>For the renderings Artbreeder produced, each face required some 15-16 hours of additional input from Voshart, who was left to deduce/guess such details as hair and skin coloring, though in many cases, an individual's features suggested likely pigmentations. Voshart was also aided by written descriptions of some of the rulers.</p><p>There's no way to know for sure how frequently Voshart's guesses hit their marks. It is obviously the case, though, that his interpretations look incredibly plausible when you compare one of his emperors to the sculpture(s) from which it was derived.</p><p>For an in-depth description of Voshart's process, check out his posts on <a href="https://medium.com/@voshart/photoreal-roman-emperor-project-236be7f06c8f" target="_blank">Medium</a> or on his <a href="https://voshart.com/ROMAN-EMPEROR-PROJECT" target="_blank" rel="noopener noreferrer">website</a>.</p><p>It's fascinating to feel like you're face-to-face with these ancient and sometimes notorious figures. Here are two examples, along with some of what we think we know about the men behind the faces.</p>
Caligula<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ2NDk4Mi9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY3MzQ1NTE5NX0.LiTmhPQlygl9Fa9lxay8PFPCSqShv4ELxbBRFkOW_qM/img.jpg?width=980" id="7bae0" class="rm-shortcode" data-rm-shortcode-id="ce795c554490fe0a36a8714b86f55b16" data-rm-shortcode-name="rebelmouse-image" data-width="992" data-height="558" />
One of numerous sculptures of Caligula, left
Nero<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDQ2NTAwMC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY1NTQ2ODU0NX0.AgYuQZzRQCanqehSI5UeakpxU8fwLagMc_POH7xB3-M/img.jpg?width=980" id="a8825" class="rm-shortcode" data-rm-shortcode-id="9e0593d79c591c97af4bd70f3423885e" data-rm-shortcode-name="rebelmouse-image" data-width="992" data-height="558" />
One of numerous sculptures of Nero, left
A new study proposes mysterious axions may be found in X-rays coming from a cluster of neutron stars.
Are Axions Dark Matter?<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="5e35ce24a5b17102bfce5ae6aecc7c14"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/e7yXqF32Yvw?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span>
New research suggests you can't fake your emotional state to improve your work life — you have to feel it.
What is deep acting?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNTQ1NDk2OS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxNTY5MzA0Nn0._s7aP25Es1CInq51pbzGrUj3GtOIRWBHZxCBFnbyXY8/img.jpg?width=1245&coordinates=333%2C-1%2C333%2C-1&height=700" id="ddf09" class="rm-shortcode" data-rm-shortcode-id="9dc42c4d6a8e372ad7b72907b46ecd3f" data-rm-shortcode-name="rebelmouse-image" data-width="1245" data-height="700" />
Arlie Russell Hochschild (pictured) laid out the concept of emotional labor in her 1983 book, "The Managed Heart."
Credit: Wikimedia Commons<p>Deep and surface acting are the principal components of emotional labor, a buzz phrase you have likely seen flitting about the Twittersphere. Today, "<a href="https://www.bbc.co.uk/bbcthree/article/5ea9f140-f722-4214-bb57-8b84f9418a7e" target="_blank">emotional labor</a>" has been adopted by groups as diverse as family counselors, academic feminists, and corporate CEOs, and each has redefined it with a patented spin. But while the phrase has splintered into a smorgasbord of pop-psychological arguments, its initial usage was more specific.</p><p>First coined by sociologist Arlie Russell Hochschild in her 1983 book, "<a href="https://www.ucpress.edu/book/9780520272941/the-managed-heart" target="_blank">The Managed Heart</a>," emotional labor describes the work we do to regulate our emotions on the job. Hochschild's go-to example is the flight attendant, who is tasked with being "nicer than natural" to enhance the customer experience. While at work, flight attendants are expected to smile and be exceedingly helpful even if they are wrestling with personal issues, the passengers are rude, and that one kid just upchucked down the center aisle. Hochschild's counterpart to the flight attendant is the bill collector, who must instead be "nastier than natural."</p><p>Such personas may serve an organization's mission or commercial interests, but if they cause emotional dissonance, they can potentially lead to high emotional costs for the employee—bringing us back to deep and surface acting.</p><p>Deep acting is the process by which people modify their emotions to match their expected role. Deep actors still encounter the negative emotions, but they devise ways to <a href="http://www.selfinjury.bctr.cornell.edu/perch/resources/what-is-emotion-regulationsinfo-brief.pdf" target="_blank">regulate those emotions</a> and return to the desired state. Flight attendants may modify their internal state by talking through harsh emotions (say, with a coworker), focusing on life's benefits (next stop Paris!), physically expressing their desired emotion (smiling and deep breaths), or recontextualizing an inauspicious situation (not the kid's fault he got sick).</p><p>Conversely, surface acting occurs when employees display ersatz emotions to match those expected by their role. These actors are the waiters who smile despite being crushed by the stress of a dinner rush. They are the CEOs who wear a confident swagger despite feelings of inauthenticity. And they are the bouncers who must maintain a steely edge despite humming show tunes in their heart of hearts.</p><p>As we'll see in the research, surface acting can degrade our mental well-being. This deterioration can be especially true of people who must contend with negative emotions or situations inside while displaying an elated mood outside. Hochschild argues such emotional labor can lead to exhaustion and self-estrangement—that is, surface actors erect a bulwark against anger, fear, and stress, but that disconnect estranges them from the emotions that allow them to connect with others and live fulfilling lives.</p>
Don't fake it till you make it<p>Most studies on emotional labor have focused on customer service for the obvious reason that such jobs prescribe emotional states—service with a smile or, if you're in the bouncing business, a scowl. But <a href="https://eller.arizona.edu/people/allison-s-gabriel" target="_blank">Allison Gabriel</a>, associate professor of management and organizations at the University of Arizona's Eller College of Management, wanted to explore how employees used emotional labor strategies in their intra-office interactions and which strategies proved most beneficial.</p><p>"What we wanted to know is whether people choose to engage in emotion regulation when interacting with their co-workers, why they choose to regulate their emotions if there is no formal rule requiring them to do so, and what benefits, if any, they get out of this effort," Gabriel said in <a href="https://www.sciencedaily.com/releases/2020/01/200117162703.htm" target="_blank">a press release</a>.</p><p>Across three studies, she and her colleagues surveyed more than 2,500 full-time employees on their emotional regulation with coworkers. The survey asked participants to agree or disagree with statements such as "I try to experience the emotions that I show to my coworkers" or "I fake a good mood when interacting with my coworkers." Other statements gauged the outcomes of such strategies—for example, "I feel emotionally drained at work." Participants were drawn from industries as varied as education, engineering, and financial services.</p><p>The results, <a href="https://psycnet.apa.org/doiLanding?doi=10.1037%2Fapl0000473" target="_blank" rel="noopener noreferrer">published in the Journal of Applied Psychology</a>, revealed four different emotional strategies. "Deep actors" engaged in high levels of deep acting; "low actors" leaned more heavily on surface acting. Meanwhile, "non-actors" engaged in negligible amounts of emotional labor, while "regulators" switched between both. The survey also revealed two drivers for such strategies: prosocial and impression management motives. The former aimed to cultivate positive relationships, the latter to present a positive front.</p><p>The researchers found deep actors were driven by prosocial motives and enjoyed advantages from their strategy of choice. These actors reported lower levels of fatigue, fewer feelings of inauthenticity, improved coworker trust, and advanced progress toward career goals. </p><p>As Gabriel told <a href="https://www.psypost.org/2021/01/new-psychology-research-suggests-deep-acting-can-reduce-fatigue-and-improve-your-work-life-59081" target="_blank" rel="noopener noreferrer">PsyPost in an interview</a>: "So, it's a win-win-win in terms of feeling good, performing well, and having positive coworker interactions."</p><p>Non-actors did not report the emotional exhaustion of their low-actor peers, but they also didn't enjoy the social gains of the deep actors. Finally, the regulators showed that the flip-flopping between surface and deep acting drained emotional reserves and strained office relationships.</p><p>"I think the 'fake it until you make it' idea suggests a survival tactic at work," Gabriel noted. "Maybe plastering on a smile to simply get out of an interaction is easier in the short run, but long term, it will undermine efforts to improve your health and the relationships you have at work. </p><p>"It all boils down to, 'Let's be nice to each other.' Not only will people feel better, but people's performance and social relationships can also improve."</p>
You'll be glad ya' decided to smile<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="88a0a6a8d1c1abfcf7b1aca8e71247c6"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/QOSgpq9EGSw?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>But as with any research that relies on self-reported data, there are confounders here to untangle. Even during anonymous studies, participants may select socially acceptable answers over honest ones. They may further interpret their goal progress and coworker interactions more favorably than is accurate. And certain work conditions may not produce the same effects, such as toxic work environments or those that require employees to project negative emotions.</p><p>There also remains the question of the causal mechanism. If surface acting—or switching between surface and deep acting—is more mentally taxing than genuinely feeling an emotion, then what physiological process causes this fatigue? <a href="https://www.frontiersin.org/articles/10.3389/fnhum.2019.00151/full" target="_blank">One study published in the <em>Frontiers in Human Neuroscience</em></a><em> </em>measured hemoglobin density in participants' brains using an fNIRS while they expressed emotions facially. The researchers found no significant difference in energy consumed in the prefrontal cortex by those asked to deep act or surface act (though, this study too is limited by a lack of real-life task).<br></p><p>With that said, Gabriel's studies reinforce much of the current research on emotional labor. <a href="https://journals.sagepub.com/doi/abs/10.1177/2041386611417746" target="_blank">A 2011 meta-analysis</a> found that "discordant emotional labor states" (read: surface acting) were associated with harmful effects on well-being and performance. The analysis found no such consequences for deep acting. <a href="https://doi.apa.org/doiLanding?doi=10.1037%2Fa0022876" target="_blank" rel="noopener noreferrer">Another meta-analysis</a> found an association between surface acting and impaired well-being, job attitudes, and performance outcomes. Conversely, deep acting was associated with improved emotional performance.</p><p>So, although there's still much to learn on the emotional labor front, it seems Van Dyke's advice to a Leigh was half correct. We should put on a happy face, but it will <a href="https://bigthink.com/design-for-good/everything-you-should-know-about-happiness-in-one-infographic" target="_self">only help if we can feel it</a>.</p>
Archaeologists discover a cave painting of a wild pig that is now the world's oldest dated work of representational art.