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Always Struggling With Hard Decisions? This Mathematical Formula Will Help You

Always Struggling With Hard Decisions? This Mathematical Formula Will Help You

Imagine this scenario: you’re a boss with a string of job candidates to choose from. You have to make the final decision on each candidate at the end of each interview. If you make an offer to a candidate, you cannot interview the others; if you don’t make an offer you can never hire that candidate again.

That’s a hard decision to make. With these kinds of constraints, how are you going to maximize your chances of hiring the best candidate?

At what point in the process do you say, “Alright, I’m just going to hire the next candidate that is better than the previous ones?”

This is the “Secretary Problem,” sometimes known as the “Marriage Problem” – and mathematician Martin Gardner solved it in 1960.

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The Solution to the Formula for Making Hard Decisions

Here’s the formula’s solution: after you have interviewed 36.8% of all the candidates, just hire the next candidate that is better than the previous ones.

Essentially, the formula proves that 36.8% is the optimal stopping point. Don’t hire or marry any candidate within the first 36.8% of the group, but after that, simply choose the first one that is better than the first 36.8%.

As a practical example, if you had to interview 50 candidates, starting from the 19th candidate onward, you should hire the next candidate that is better than the first 18 ones.

Note that this doesn’t mean you will always select the absolute best candidate (you may end up with second best if the very best candidate is in the first 36.8%), but this puts the chances of you doing so at 36.8%. Pretty decent odds given the situation, I would say!

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36.8%, by the way, is the value of 1/e, where e is the base of the natural logarithm. You may or may not have recognized that little alphabet from your high school math classes.

For the mathematically-inclined who want to know exactly how the solution was derived, you can read about it here. You can also check out the more reader-friendly Wikipedia page on the Secretary Problem.

How Practical Is the Formula Really?

Like all math problems and formulas, there are always some strict constraints that don’t make it as practical as we would like.

For example, if you were going over a list of job candidates, you could most likely just interview them all and call back the best one after. No need to make a definitive offer at the end of each interview.

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However, since there is always a risk that in the interim the candidate may accept another job offer, it might be wise to follow the 36.8% rule, especially if you know the candidates are in high demand.

Making Hard Romantic Decisions Using the Formula

What about when we try to apply it to the romantic department? Well, since you (probably) can’t date a whole string of people and then go back and select the best one like in the hiring process, the problem now is that you don’t know how many candidates there are in the first place!

How you can you determine 36.8% of a number if you don’t even know what that number is?

Good news, because mathematicians have figured that one out, too, and the answer is still 36.8%! Only now, it’s 36.8% of the total time.

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Here’s how it now works: let’s say you gave yourself a certain period to find a suitable lifelong romantic partner – 5 years for example. After 36.8% of 5 years, which is about 672 days (or 1 year, 10 months, and 3 days), you should just propose to the next romantic partner who was better than the previous ones.

This is known as the unified approach, and was proved in 1984 by German mathematician F. Thomas Bruss. You can read all the mathematical details on how this was derived in his paper here.

Making hard decisions is part and parcel of life; and no mathematical formula will be able to help you with all of them. That said, it is useful to know that in certain scenarios, there is a formula we can use to maximize our chances of obtaining the most favorable outcome.

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Ian Lee

Freelance Writer for Hire

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Last Updated on April 19, 2021

The Art of Taking a Break So You Will Be Productive Again

The Art of Taking a Break So You Will Be Productive Again

Think of yourself as a cup. Each day, you wake up full. But as you go about your day—getting tasks done and interacting with people—the amount in your cup gradually gets lower. And as such, you get less and less effective at whatever it is you’re supposed to be doing. You’re running out of steam.

The solution is obvious: if you don’t have anything left to pour out, then you need to find a way to fill yourself up again. In work terms, that means you should take a break—an essential form of revitalizing your motivation and focus.

Taking a break may get a bad rap in hustle culture, but it’s an essential, science-based way to ensure you have the capacity to live your life the way you want to live it.

In the 1980s, when scientists began researching burnout, they described this inner capacity as “resources.” We all need to replenish our resources to cope with stress, work effectively, and avoid burnout.[1]

When the goal is to get things done, it may sound counterproductive to stop what you’re doing. But if you embrace the art of taking a break, you can be more efficient and effective at work.

Here are five ways on how you can take a break and boost your productivity.

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1. Break for the Right Amount of Time, at the Right Time

When I started my first job out of college, I was bent on pleasing my boss as most entry-level employees do. So, every day, I punched in at 9 AM on the dot, took a 60-minute lunch break at noon, and left no earlier than 5 PM.

As I’ve logged more hours in my career, I’ve realized the average, eight-hour workday with an hour lunch break simply isn’t realistic—especially if your goal is to put your best foot forward at work.

That’s why popular productivity techniques like the Pomodoro advocate for the “sprint” principle. Basically, you work for a short burst, then stop for a short, five-minute break. While the Pomodoro technique is a step forward, more recent research shows a shorter burst of working followed by a longer pause from work might actually be a more effective way to get the most out of stepping away from your desk.

The team at DeskTime analyzed more than 5 million records of how workers used their computers on the job. They found that the most productive people worked an average of 52 minutes, then took a 17-minute break afterward.[2]

What’s so special about those numbers? Leave it to neuroscience. According to researchers, the human brain naturally works in spurts of activity that last an hour. Then, it toggles to “low-activity mode.”[3]

Even so, keep in mind that whatever motivates you is the most effective method. It’s more about the premise—when you know you have a “finish line” approaching, you can stay focused on the task or project at hand.

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There are many applications and tools that can help you block distracting websites and apps (such as social media) for specific periods of the day. Similarly, you can also use some mailing apps like Mailbrew to receive all the social media content or newsletters you don’t want to miss in your inbox at a time you decide.

So, no matter how long you work, take a break when you sense you’re losing steam or getting bored with the task. Generally, a 10-15 minute break should reinvigorate you for whatever’s coming next.

2. Get a Change of Scenery—Ideally, Outdoors

When it comes to increasing a person’s overall mental health, there’s no better balm than nature. Research has found that simply being outside can restore a person’s mind from mental fatigue related to work or studying, ultimately contributing to improved work performance (and even improved work satisfaction).[4]

No lush forest around? Urban nature can be just as effective to get the most out of your break-taking. Scientists Stephen R. Kellert and Edward O. Wilson, in their book The Biophilia Hypothesis, claimed that even parks, outdoor paths, and building designs that embrace “urban nature” can lend a sense of calm and inspiration, encouraging learning and alertness for workers.

3. Move Your Body

A change of scenery can do wonders for your attention span and ability to focus, but it’s even more beneficial if you pair it with physical movement to pump up that adrenaline of yours. Simply put, your body wasn’t designed to be seated the entire day. In fact, scientists now believe that extended periods of sitting are just as dangerous to health as smoking.[5]

It’s not always feasible to enjoy the benefits of a 30-minute brisk walk during your workday, especially since you’ll most likely have less energy during workdays. But the good news is, for productivity purposes, you don’t have to. Researchers found that just 10 minutes of exercise can boost your memory and attention span throughout the entire day.[6]

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So, instead of using your break to sit and read the news or scroll your social media account, get out of your chair and move your body. Take a quick walk around the block. Do some jumping jacks in your home office. Whatever you choose, you’ll likely find yourself with a sharper focus—and more drive to get things done.

4. Connect With Another Person

Social connection is one of the most important factors for resilience. When we’re in a relationship with other people, it’s easier to cope with stress—and in my experience, getting social can also help to improve focus after a work break.

One of my favorite ways to break after a 30-or-so minute sprint is to hang out with my family. And once a week, I carve out time to Skype my relatives back in Turkey. It’s amazing how a bit of levity and emotional connection can rev me up for the next work sprint.

Now that most of us are working from home, getting some face-to-face time with a loved one isn’t as hard as it once was. So, take the time to chat with your partner. Take your kids outside to run around the backyard. If you live alone, call a friend or relative. Either way, coming up for air to chat with someone who knows and cares about you will leave you feeling invigorated and inspired.

5. Use Your Imagination

When you’re working with your head down, your brain has an ongoing agenda: get things done, and do it well. That can be an effective method for productivity, but it only lasts so long—especially because checking things off your to-do list isn’t the only ingredient to success at work. You also need innovation.

That’s why I prioritize a “brain break” every day. When I feel my “cup” getting empty, I usually choose another creative activity to exercise my brain, like a Crossword puzzle, Sudoku, or an unrelated, creative project in my house.

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And when I’m really struggling to focus, I don’t do anything at all. Instead, I let my brain roam free for a bit, following my thoughts down whatever trail they lead me. As it turns out, there’s a scientific benefit to daydreaming. It reinforces creativity and helps you feel more engaged with the world, which will only benefit you in your work.[7]

Whether you help your kids with their distance learning homework, read an inspiring book, or just sit quietly to enjoy some fresh air, your brain will benefit from an opportunity to think and feel without an agenda. And, if you’re anything like me, you might just come up with your next great idea when you aren’t even trying.

Final Thoughts

Most of us have to work hard for our families and ourselves. And the current world we live in demands the highest level of productivity that we can offer. However, we also have to take a break once in a while. We are humans, after all.

Learning the art of properly taking a break will not only give you the rest you need but also increase your productivity in the long run.

More on the Importance of Taking a Break

Featured photo credit: Helena Lopes via unsplash.com

Reference

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