Algorithms solve problems for both humans and computers

An algorithm is a set of steps used to solve a problem, and it's something both humans and computers use regularly. The term originated from the 9th-century Persian mathematician Muhammad al-Khwarizmi, but the concept dates back over 4,000 years to the Sumerians. In simple terms, an algorithm is just a clear, step-by-step process to get a result, similar to how a recipe works. When you follow a recipe, you're using an algorithm—it gives you instructions that lead to the desired outcome, just like an algorithm helps you solve a problem.

We make decisions in daily life using patterns similar to intuitive algorithms, like when we're knitting a scarf, putting together IKEA furniture, or weighing the pros and cons of a job offer or a big investment. These algorithms aren’t exact but help us make the best choice when we're uncertain, such as comparing risks and rewards. While they may seem random or subjective, they essentially solve problems in a similar way to the precise algorithms computers use. For example, when apartment hunting, we usually have a list of needs, such as a certain amount of space, distance from work or school, and a maximum rent. Once a place meets these criteria, we make our decision, which is just like how a computer algorithm works.

Algorithms often dictate risk limits

Finding an apartment in a tough market can be challenging. It's hard to know when to accept an offer and stop looking. We often rush into the first option we find, thinking it's the best. Then the next one seems almost as good. The optimal stopping algorithm tackles these problems. It helps us make smarter decisions about when to settle on an apartment, rather than jumping at the first opportunity that comes along.

Mathematically, when faced with 100 options, optimal stopping advises reviewing the first 37 without committing to any. This initial step sets a benchmark, like excluding ground-floor apartments with small bathrooms. After evaluating these initial 37 options, the strategy suggests seizing the first one that meets these benchmarks. While this method doesn’t guarantee the absolute best choice, it significantly improves your chances compared to randomly guessing. This strategy isn't limited to apartments; whether you're choosing a car, seeking a job, or finding a potential partner, the principle remains the same: focus on the first 37 percent to make a more informed decision.

The Pitfalls of Mathematical Strategy in Gambling

Math can’t always tell us when to stop, especially in gambling scenarios like a simple coin flip. Imagine you start with four dollars, betting on heads or tails with a strategy where you triple your bet each time but risk losing everything you’ve won. If the odds are 50/50, half the time you’ll end up with nothing, and the other half with twelve dollars. On average, that’s six dollars in your pocket. The math suggests you should keep betting because the potential winnings increase each round — starting with twelve dollars, you could expect eighteen dollars, and so on.

However, this mathematical approach doesn’t guarantee success. Sooner or later, you could lose everything and the game ends abruptly. This shows that while math gives us probabilities and averages, it doesn’t always predict the outcome in real-life situations like gambling.

Algorithms guide exploring new ventures

Slot machines, also known as "one-armed bandits," captivate many casino-goers. Some stick to one machine, hoping for a jackpot, while others explore different options, gathering information to boost their chances. This dilemma mirrors decisions in dating or investing: when to persevere and when to move on. In mathematics, these dilemmas are akin to "multi-armed bandit problems," offering various strategies. One simple tactic for slot machines is "stay-win, lose-shift," suggesting you stay with a machine if you win and switch if you lose. However, this might not always be the best choice.

Stick with one slot machine when you're winning and switch to another if you start losing. But this strategy can mislead you because one loss doesn't predict your overall luck. Instead, try the Upper Confidence Bound (UCB) algorithm:

• Find the Best Machine: Look for the machine with the biggest jackpot.
• Track Your Wins: Note how much money you win compared to what's expected. If you consistently win less than expected, consider switching to the next machine with the next biggest jackpot.
• Continue Evaluating: Repeat this process until you find a machine where your winnings match or exceed expectations.

Algorithms take into account that even the best machines can sometimes make mistakes, which can actually increase your chances of winning. Another inspiration for solving multi-armed bandit problems comes from adaptive clinical trials in the pharmaceutical industry. When doctors test different drugs for an ailment, they continuously assess their patients and make changes to their testing plan as they go, sometimes even before the trial is over. If a drug isn’t effective, they stop using it immediately and focus on other drugs that show promise. They are always ready to use new information before the final results are available.

Practical Tip for Organizing Your Workspace

If you prefer a bit of organized chaos, you might find it helpful to not stress about keeping everything perfectly tidy all the time. The main goal of staying organized is to make it easier to find things when you need them. Spending lots of time sorting through papers can be a big drain on your energy, especially when you already know where everything is. So, find a balance that works for you to save time and stay productive!

If your chaotic filing system makes you seem disorganized, algorithms offer practical solutions. Take the bubble sort, the simplest yet least efficient method. It sorts items pair by pair until everything is in order. For instance, imagine organizing your shelf of zombie books alphabetically. Start by focusing on books beginning with A. Compare each pair already in place, like "Albatross Zombies" and "Alligator Zombies," adjusting them until they're correctly ordered.

Sorting a large book collection manually, like arranging books by titles such as "Albatross Zombies," "Aardvark Zombies," and "Alligator Zombies," can be cumbersome. Instead of repeatedly rearranging shelves, two effective methods streamline the process.

• Insertion Sort Method: Remove all books from shelves and reinsert them one by one. Each book is placed in its correct position relative to those already sorted. This method ensures each book finds its place efficiently without constant rearrangement.
• Merge Sort Method: For extensive collections, divide all books into smaller groups. Sort each group alphabetically. Once sorted, merge these groups back together, ensuring the entire collection is in order from start to finish.

These methods simplify the task of organizing books, making it more manageable and less time-consuming. Whether you have a modest or extensive library, these techniques ensure efficient organization without unnecessary repetition.

Efficient Storage Solutions for Your Digital Needs

Now that your shelves are tidy, let's focus on organizing the papers and notes on your desk. These include important items like bills and urgent letters that you need quick access to. Computers manage their data using either a hard disk drive (HDD) or a solid-state drive (SSD). Each has its advantages: HDDs store large amounts of data, while SSDs retrieve data faster. Modern devices often use both types of drives. They store critical data on fast SSDs for quick access and use HDDs for storing large archives. This setup ensures you can find what you need swiftly and efficiently.

Computers store crucial data in a special memory layer called the cache. This cache holds the most frequently used information for quick access. Using a method known as Least Recently Used (LRU), the computer prioritizes storing recently accessed items at the top of the cache. This strategy helps predict which files might be needed next. Interestingly, this same concept applies outside of computers too. Just like keeping bills and important letters handy on your desk, where your most recent and vital items are readily accessible, the LRU algorithm keeps your digital workspace organized and efficient. So, next time you glance at your cluttered desk, remember: it's likely your most important documents are right on top, ready when you need them!

Just like our brains, if we don't use certain information for a while, it's harder to remember it. To improve your memory before a big exam or meeting, try reviewing your notes right before bedtime. This helps you recall the information more easily the next morning.

Master Productivity with Effective Time Management

To boost productivity, it's crucial to organize both your files and your time efficiently. Each day presents unique challenges, from meeting deadlines to remembering everyday tasks like taking your dog to the vet. Algorithms can help solve these scheduling dilemmas. For instance, when juggling multiple tasks, start with the Earliest Due Date algorithm. Begin with the task closest to its deadline to stay on track. If time starts running short and you can't complete everything, apply Moore's Algorithm. Skip the task that requires the most time, allowing you to finish more tasks overall.

Avoid falling into priority inversion where minor tasks consume all your time, leaving important work undone. Despite seeking quick fixes, most scheduling issues resist easy solutions. Spending excessive time on organizing your schedule can also diminish productivity. For clarity amidst complexity, rely on a straightforward approach: focus on actionable insights and limit time spent on scheduling to maximize efficiency. To boost your productivity, concentrate on one task without letting emails or other requests distract you. Constantly switching between tasks burdens your working memory and forces you to restart each time. Instead, ignore distractions and focus solely on the task at hand. Don't stress about the length of your to-do list; everything will be completed in due course. 

Predict Future Outcomes with Algorithms

Algorithms help us predict what might happen in the future, akin to seeing into the future itself. This ability traces back to eighteenth-century England with Reverend Thomas Bayes, who developed a method for forecasting likely events based on past occurrences, like predicting winning lottery tickets. Today, this method is applied to modern scenarios, such as analyzing scratch tickets. For instance, if you buy three scratch tickets, Bayes suggests starting with an assumption about the overall proportion of winning tickets in circulation. By using this assumption, you can calculate the probability of the results you observe among your three tickets.

If all three of your lottery tickets win, it suggests that all tickets in circulation may be winners. For instance, achieving a 100% success rate with three out of three winning tickets implies that all tickets likely offer a win. On the other hand, if only half of the tickets were winners, the probability of all three being winners would be much lower, at around 12.5%. Therefore, it's more plausible that all tickets are winners when such a streak occurs. Collecting more data allows for more precise hypotheses. Over time, advancements in mathematics have provided us with better tools for making accurate predictions. Understanding the distribution pattern of a phenomenon significantly aids in refining these predictions.

Distribution Patterns in Data

• The "bell curve," based on normal distribution, applies broadly. For instance, when estimating the average age of a random group, most individuals cluster around the middle of the curve, with fewer at the extremes. This means that on a blind date, you're likely dining with someone closer to your age rather than an elderly person.
• On the other hand, power-law distribution differs significantly. Here, the median average is influenced by numerous observations below it and a few significantly above it. Wealth distribution serves as a prime example: the majority of people have limited wealth, while a small fraction owns a substantial portion of global wealth.

Solving Communication Challenges

Imagine two generals planning a joint attack on a city in a valley, each positioned on separate hills. They must agree on an attack time, but the valley blocks direct communication, risking the capture of messengers. This scenario reflects a real challenge in ensuring messages reach their destination reliably. Computer scientists have developed algorithms to tackle such problems, ensuring secure and effective communication in complex situations.

The first strategy, known as "retransmitted till breakdown," involves sending multiple messengers in succession, hoping that at least one will reach its destination without being intercepted. This method mirrors our persistence when repeatedly messaging or calling a friend until they respond.

However, in today's context, issues often differ from intercepted messengers. Imagine encountering an error message every time you check your email, indicating server overload. Here, the Exponential Backoff method proves useful. Instead of continuously refreshing, wait a few minutes for traffic to decrease. If the error persists, double the waiting time to four minutes before retrying, progressively increasing until successful.

Optimize Network Performance with AIMD Algorithm

To prevent network overload, use the Additive Increase, Multiplicative Decrease (AIMD) method. This algorithm helps determine the maximum data capacity a network can handle. It starts by sending a small amount of data, then doubles the amount each time until it detects overload. After pinpointing the overload point, it adjusts by incrementally increasing data transmission until optimal capacity is reached without causing failure.

The Prisoner's Dilemma: A Tough Choice

Imagine you and a partner successfully rob a bank. Later, the police bring both of you in for questioning and place you in separate rooms. They lack evidence for the robbery but can charge you with a minor offense, leading to a one-year sentence if you stay silent. But the police offer you and your partner a deal. If you testify against your partner while they stay silent, you go free while your partner gets ten years in jail. If both of you testify against each other, you each get a five-year sentence.

Game Theory

In game theory, a classic scenario involves prisoners deciding whether to cooperate or betray each other. If both betray, they each face five years in prison. The temptation to betray is strong because it offers a chance to avoid jail time, especially if the other prisoner also talks. Despite this, both usually end up betraying, resulting in both receiving a five-year sentence. This outcome benefits the police. Another aspect of game theory, called mechanism design, focuses on structuring choices to ensure desired behaviors without relying on hoped reactions.

Many employers face a common issue: employees not using their vacation time. This problem affects productivity because well-rested employees perform better than those who are overworked. For instance, Evernote attempted to address this by offering a thousand-dollar bonus for taking time off, but it didn't succeed. Applying mechanism design to this problem means focusing on practical solutions rather than convincing employees. Instead of brainstorming ways to persuade them, the key is to ensure they actually take their vacation days. The simplest solution? Make vacations mandatory!

Choose Effective Models for Complex Problems

When tackling complex issues like understanding obesity causes, it's crucial to use models that consider various factors. A sophisticated model that incorporates diet, genetics, and exercise offers more comprehensive insights than a simplistic one focusing only on diet. This approach ensures a thorough understanding and effective strategies for addressing complex problems. Complex models can pose challenges, especially when dealing with real-world issues where uncertainty and data errors are common. Typically, you start by analyzing a small data set and constructing an algorithm to predict outcomes based on it. The temptation arises to include more variables in the algorithm until it fits the data perfectly, even the errors. This practice, known as overfitting, causes issues when applying the same algorithm to new data sets. Essentially, the model becomes too rigidly tailored to the original data, losing its adaptability and performing poorly with different data.

For example, When studying obesity, you might find that certain regions have higher obesity rates. However, this correlation could be coincidental. If you adjust your model to prioritize location, it might not perform well on new data where location isn't crucial. Recognizing that no algorithm is perfect allows you to ease your expectations and aim for solutions that are good enough rather than flawless. This approach encourages practical learning and helps in developing models that balance accuracy with real-world applicability.

Finding the best route between multiple points without revisiting any location, such as across a state or country, can be incredibly complex. One effective approach is to allow the salesman to revisit some locations, even if it's more than once. This adjustment can lead to a near-optimal solution in a reasonable timeframe, though it may not be perfect.