trials and error problem solving

Trial and Error

Trial and Error is a fundamental method of problem-solving, which involves attempting different solutions until the correct one is found. As a strategy frequently used in multiple fields, including psychology, science, and computer programming, its significance is profound and multifaceted.

Understanding the term

To fully appreciate the trial and error method’s value, let’s delve into its characteristics, process, and theoretical underpinnings.

Characteristics of the Trial and Error Method

The trial and error method is defined by two key elements: making attempts (trials) and learning from failures (errors). The process continues until a solution is found.

The Trial and Error Process

The process of trial and error consists of generating possible solutions, applying them, assessing their effectiveness, and revising the approach based on the results.

Theoretical Background

Trial and error has roots in behavioral psychology, where it’s often associated with Edward Thorndike’s Law of Effect. This law suggests that responses followed by satisfaction will be repeated, while those followed by discomfort will be discontinued.

Trial and Error in Everyday Life

The application of the trial and error method is ubiquitous, extending from our daily activities to complex scientific research.

Learning New Skills

When we learn to ride a bicycle, cook a new dish, or play a musical instrument, we use trial and error to master the skills.

Technological Advancements

In the tech industry, trial and error play a crucial role in software development and debugging, hardware design, and algorithm optimization.

Advantages and Disadvantages

The trial and error method, despite its universal application, comes with its pros and cons.

H3: Advantages

Trial and error encourages creativity and fosters resilience. It allows for the discovery of all possible solutions and can lead to unexpected yet effective outcomes.

H3: Disadvantages

However, trial and error can be time-consuming and resource-intensive. It may not be feasible when there’s a need for immediate solutions or when the risks of failure are high.

To better illustrate the concept of trial and error, let’s consider a couple of examples.

Example 1: Learning to Code

When learning to code, students often write a program, run it to see if it works, and if it doesn’t, they debug and modify their code. This is an example of trial and error.

Example 2: Medicinal Drug Discovery

In medicinal chemistry, scientists often synthesize and test numerous compounds before finding one that effectively treats a disease. This process embodies the trial and error method.

Enhancing the Trial and Error Process

While trial and error inherently involve some degree of uncertainty, some strategies can enhance its efficiency.

Learn from Each Attempt

Each trial, whether successful or unsuccessful, provides valuable information. Reflecting on each attempt can improve future trials and hasten the problem-solving process.

Embrace Failure

Viewing errors as learning opportunities rather than failures can foster resilience and creativity, essential traits for effective problem-solving.

In essence, trial and error is an indispensable problem-solving strategy that encourages creativity, resilience, and comprehensive solution discovery. By understanding its characteristics, benefits, and limitations, we can harness its potential more effectively in various domains of life. Remember, each trial brings you one step closer to a solution, and each error is a stepping stone to success.

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Thinking and Intelligence

Problem Solving

OpenStaxCollege

[latexpage]

Learning Objectives

By the end of this section, you will be able to:

Describe problem solving strategies
Define algorithm and heuristic
Explain some common roadblocks to effective problem solving

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

PROBLEM-SOLVING STRATEGIES

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( [link] ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

When one is faced with too much information
When the time to make a decision is limited
When the decision to be made is unimportant
When there is access to very little information to use in making the decision
When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link] ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

A four column by four row Sudoku puzzle is shown. The top left cell contains the number 3. The top right cell contains the number 2. The bottom right cell contains the number 1. The bottom left cell contains the number 4. The cell at the intersection of the second row and the second column contains the number 4. The cell to the right of that contains the number 1. The cell below the cell containing the number 1 contains the number 2. The cell to the left of the cell containing the number 2 contains the number 3.

Here is another popular type of puzzle ( [link] ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

A square shaped outline contains three rows and three columns of dots with equal space between them.

Take a look at the “Puzzling Scales” logic puzzle below ( [link] ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

A puzzle involving a scale is shown. At the top of the figure it reads: “Sam Loyds Puzzling Scales.” The first row of the puzzle shows a balanced scale with 3 blocks and a top on the left and 12 marbles on the right. Below this row it reads: “Since the scales now balance.” The next row of the puzzle shows a balanced scale with just the top on the left, and 1 block and 8 marbles on the right. Below this row it reads: “And balance when arranged this way.” The third row shows an unbalanced scale with the top on the left side, which is much lower than the right side. The right side is empty. Below this row it reads: “Then how many marbles will it require to balance with that top?”

PITFALLS TO PROBLEM SOLVING

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in [link] .

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

The first puzzle is a Sudoku grid of 16 squares (4 rows of 4 squares) is shown. Half of the numbers were supplied to start the puzzle and are colored blue, and half have been filled in as the puzzle’s solution and are colored red. The numbers in each row of the grid, left to right, are as follows. Row 1: blue 3, red 1, red 4, blue 2. Row 2: red 2, blue 4, blue 1, red 3. Row 3: red 1, blue 3, blue 2, red 4. Row 4: blue 4, red 2, red 3, blue 1.The second puzzle consists of 9 dots arranged in 3 rows of 3 inside of a square. The solution, four straight lines made without lifting the pencil, is shown in a red line with arrows indicating the direction of movement. In order to solve the puzzle, the lines must extend beyond the borders of the box. The four connecting lines are drawn as follows. Line 1 begins at the top left dot, proceeds through the middle and right dots of the top row, and extends to the right beyond the border of the square. Line 2 extends from the end of line 1, through the right dot of the horizontally centered row, through the middle dot of the bottom row, and beyond the square’s border ending in the space beneath the left dot of the bottom row. Line 3 extends from the end of line 2 upwards through the left dots of the bottom, middle, and top rows. Line 4 extends from the end of line 3 through the middle dot in the middle row and ends at the right dot of the bottom row.

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Review Questions

A specific formula for solving a problem is called ________.

an algorithm
a heuristic
a mental set
trial and error

A mental shortcut in the form of a general problem-solving framework is called ________.

Which type of bias involves becoming fixated on a single trait of a problem?

anchoring bias
confirmation bias
representative bias
availability bias

Which type of bias involves relying on a false stereotype to make a decision?

Critical Thinking Questions

What is functional fixedness and how can overcoming it help you solve problems?

Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

How does an algorithm save you time and energy when solving a problem?

An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

Personal Application Question

Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

Leadership & Flow

Global Research Program and Network

What is ‘trial and error’?

Trial and error is not a method of finding the best solution, nor a method of finding all solutions. It is a problem-solving technique that is used simply to find a solution.

‘ So, you screwed up? ’ – How many times have you heard this criticism when you failed? What this question often implies is that you are a loser , someone who lost its reputation or having difficulty managing a situation or a relationship. Hidden, this question sends the message: ‘You are not good enough’ .

No wonder, that it is inherently coded in us to fear failure and be ashamed when we fail. Even though every one fails sometimes in life, as failure is part of a learning process we cannot avoid. If we look deep inside, everybody would agree, that the failures that make us stronger and unique.

Studies show that the most successful people failed a lot. When testing concepts, ideas, solving new problems in the real world one cannot avoid making mistakes, or fall flat sometimes. Successful managers, leaders, and entrepreneurs all understand the importance of failure, indeed they are mastered in failing but:

they have learned to move on; and
learned from their mistakes, in other words, they truly understand the meaning of trial and error.

To me, failure and self-development come hand in hand. It is not a question if: ‘ Will you fail or not?’ , but rather ‘ What level of risk you take?’ when you fail . Successful managers and leaders suggest testing concepts, ideas in a low-risk environment to minimize risk associated with failure.

So, why not to use this ‘formula’ in teaching management and leadership?

Computer games and online simulations, such as FLIGBY offer to test and master leadership and management skills in a safe, low-risk environment and allows to experiment.

By playing FLIGBY the players can face with some of their lacking abilities, management or leadership skills. It is almost certain that they will fail someway or another as leaders/managers while playing the Game. Odd it might be, but true that failing in the Game motivates the player to play more in order to test and try out other alternative management and leadership styles and skills in order to succeed.

This is how FLIGBY unconsciously teaches new management and leadership skills and styles, teaches to accept failure as part of a learning process, and master in people management skills.

After all our whole life is based on ‘ trail and error’ , but no one can take away the experience we collect through truly experiencing life, including the mistakes we make!

(The author of this entry is Esztella Fazekas , member of the Leadership & Flow Research Team)

An Expert is Made by Trial and Error

In a world that often glorifies instant success and celebrates overnight sensations, the concept of expertise cultivated through trial and error can seem outdated or undervalued. However, behind every true expert lies a journey marked by countless trials, failures, and relentless perseverance.

“The only sure way to avoid making mistakes is to have no new ideas.” – Albert Einstein.

The path to mastery is seldom linear; it is a labyrinth of experimentation, setbacks, and incremental progress. In this blog, we delve into the profound truth that an expert is indeed made by trial and error.

The Nature of Expertise:

Before we explore the role of trial and error in expertise, it’s crucial to understand what expertise truly entails. Expertise is not merely about possessing knowledge or skills in a particular domain. It encompasses a deep understanding honed through experience, a nuanced ability to navigate complexities, and the wisdom to discern what works and what doesn’t in diverse situations.

Malcolm Gladwell popularized that it takes roughly 10,000 hours of deliberate practice to master any field. While the exact number may vary depending on the discipline and individual differences, the essence remains the same: expertise demands relentless effort and a willingness to embrace failure as an integral part of the learning process.

The Role of Trial and Error:

Trial and error serve as the bedrock upon which expertise is built. Every failed attempt, every misstep, and every setback provides invaluable insights that contribute to the refinement of skills and the deepening of understanding. Consider the example of Thomas Edison, whose relentless experimentation eventually led to the invention of the practical electric light bulb. Edison famously remarked, “I have not failed. I’ve just found 10,000 ways that won’t work.” His journey exemplifies the iterative nature of trial and error in pursuing excellence.

Similarly, in the realm of arts and creativity, trial and error play a pivotal role. Renowned painters, musicians, writers, and other artists often produce numerous drafts, sketches, and prototypes before arriving at the final masterpiece. Each iteration is a learning opportunity, allowing them to uncover new possibilities, refine their techniques, and push the boundaries of their craft.

Embracing Failure:

The willingness to embrace failure as a natural and inevitable part of the learning journey is central to the concept of trial and error. Society often stigmatizes failure as something to be avoided at all costs, fostering a fear of experimentation and risk-taking. However, true experts understand that failure is not the opposite of success but rather a stepping stone toward it.

Psychologist Carol Dweck’s research on the growth mindset highlights the importance of viewing failure as a temporary setback rather than a permanent condition. Those with a growth mindset perceive challenges as opportunities for growth and resilience. In contrast, those with a fixed mindset are more likely to interpret failure as evidence of their inherent limitations. By cultivating a growth mindset, individuals are better equipped to navigate the trials and tribulations on the path to expertise.

Interactive Learning:

At its core, trial and error represent an interactive approach to learning and problem-solving. Instead of expecting immediate perfection, experts recognize that progress often comes through incremental improvements over time. This iterative process involves a cycle of experimentation, reflection, and refinement, with each iteration bringing them closer to mastery.

In fields such as software development, iterative learning methodologies like Agile and Scrum have revolutionized how teams approach complex projects. Rather than attempting to design a perfect solution from the outset, Agile principles encourage continuous feedback and adaptation, allowing for rapid iteration and course correction based on real-world outcomes. This iterative approach fosters innovation and mitigates the risks associated with large-scale projects by breaking them down into smaller, manageable iterations.

The Importance of Feedback:

Feedback serves as a compass guiding the iterative process of trial and error. Whether from mentors, peers, or the outcomes of one’s actions, feedback provides valuable information that informs future decisions and actions. However, not all feedback is created equal. Constructive, specific, actionable, and empathetic feedback is most conducive to learning and growth.

In the context of expertise development, seeking feedback from trusted sources and being open to critique is essential for continuous improvement. Constructive criticism helps experts identify blind spots, refine their skills, and challenge their assumptions, ultimately propelling them toward more excellent proficiency in their chosen field.

Persistence and Resilience:

The most defining characteristic of true experts is their unwavering persistence in the face of adversity. The journey of trial and error is fraught with challenges, setbacks, and moments of self-doubt. It is easy to become discouraged when faced with repeated failures or slow progress. Still, it is precisely during these times that resilience becomes paramount.

In her research on grit, Angela Duckworth emphasizes the importance of perseverance and passion in achieving long-term goals. Gritty individuals possess a combination of resilience, determination, and intrinsic motivation, enabling them to weather the storms of uncertainty and setbacks. They understand that expertise is not achieved overnight but through sustained effort and dedication over time.

Here, I leave you 4 questions to journal about Trial and Error:

Reflect on a recent challenge or setback you’ve faced in your journey toward mastering a skill or achieving a goal. How did you initially respond to the failure, and what did you learn from the experience?
Consider a time when you received constructive feedback from a mentor, peer, or supervisor. How did you incorporate this feedback into your approach, and how did it impact your progress?
Think about a project or endeavour where you’ve applied an iterative approach, embracing trial and error to refine your work. What were some of the key insights or breakthroughs that emerged from this process?
Explore your mindset toward failure and adversity. Do you tend to view setbacks as opportunities for growth, or do you perceive them as indicators of your limitations? How might adopting a growth mindset influence your approach to challenges in the future?

In a world that often celebrates instant gratification and overnight success, the journey of expertise reminds us that greatness is forged through trial and error. Every failure, setback, and obstacle encountered is an opportunity for growth and learning. True experts understand mastery is not a destination but a lifelong pursuit characterized by relentless experimentation, resilience, and a commitment to continuous improvement. So, the next time you encounter failure on your journey, remember that an expert is made by trial and error. Embrace the process, learn from your mistakes, and keep moving forward toward mastery.

Embracing the journey of mastery requires courage, resilience, and a commitment to continuous improvement. Suppose you found value in exploring the transformative power of trial and error. In that case, I invite you to subscribe to my newsletter, “Flip it.” Through “Flip it,” we delve into the art of challenging and transforming limiting beliefs, empowering you to unlock your full potential and embrace a mindset of growth and possibility.

Moreover, consider signing up for my free email course, “Rise & Shine,” where we explore the creation of effective routines to support your journey towards expertise. By mastering routines, you’ll enhance your productivity and cultivate habits that foster resilience and perseverance in the face of challenges.

Join me on this journey of self-discovery and transformation. Let’s flip the script on our limiting beliefs while establishing empowering routines that propel us towards mastery. Subscribe today and embark on a path of personal and professional growth like never before.

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7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

Describe problem solving strategies
Define algorithm and heuristic
Explain some common roadblocks to effective problem solving

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

When one is faced with too much information
When the time to make a decision is limited
When the decision to be made is unimportant
When there is access to very little information to use in making the decision
When an appropriate heuristic happens to come to mind in the same moment

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
Analogy – is using a solution that solves a similar problem.
Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
Divide and conquer – breaking down large complex problems into smaller more manageable problems.
Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
Reduction – adapting the problem to be as similar problems where a solution exists.
Research – using existing knowledge or solutions to similar problems to solve the problem.
Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

1. Only one disk can be moved at a time.
2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
3. No disc may be placed on top of a smaller disk.

Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage (1990) suggesting that while collecting data for what would later be his book The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground. Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm: problem-solving strategy characterized by a specific set of instructions

anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic: faulty heuristic in which you make a decision based on information readily available to you

confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended

heuristic: mental shortcut that saves time when solving a problem

hindsight bias: belief that the event just experienced was predictable, even though it really wasn’t

mental set: continually using an old solution to a problem without results

problem-solving strategy: method for solving problems

representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards: heuristic in which you begin to solve a problem by focusing on the end result

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Trial and error

Imagine that you wake up in the morning, turn on your computer to do some study, and then discover your Wi-Fi isn’t working. First, you run a diagnostic test on your computer, but it doesn’t uncover anything. Next, you restart your computer, and still no luck. Lastly, you reboot your modem router, and… success!

The process you have just used is called trial and error, and it can be used to solve small problems like the one you had with your Wi-Fi. It can also be a powerful method in controlled situations for scientific breakthroughs, inventions, and developing new products. The idea is that you keep trying different approaches until you find one that works. The benefit of trial and error is that it allows you to test certain ideas (or hypotheses) to see if they are an effective solution to a problem. You can then take what you’ve learnt from your trials (and errors) and use it to make adjustments and to guide your next moves.

The downsides are that it can take time to conduct these trials, and this technique can’t be used in all situations. In some cases, a simple error could lead to disaster. For example, if you work as a bomb disposal expert and you need to disarm an explosive, cutting wires until you find the right one probably wouldn’t be a good idea!

Can you think of another example of a situation in which it would not be a good idea to use trial and error?
What about a situation in which trial and error would be a good strategy to use?

Answer the following questions to identify in which situations trial and error would be a good problem-solving technique to use.

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4 Main problem-solving strategies

In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.

Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.

Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.

Problem-solving stages

What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.

To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:

Initial state

The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).

For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.

In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?

It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.

Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.

Initial theory in problem-solving

When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.

But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.

Problem-solving strategies

These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:

Trial and error

1. Algorithms

When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.

Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.

2. Heuristics

Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.

You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.

If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.

When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.

Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.

3. Trial and error

When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.

Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.

This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.

Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.

When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.

I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.

You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.

Pilot problem-solving

No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.

Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.

This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.

Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.

Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.

Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.

Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.

The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.

If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.

Getting your causal thinking right

Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.

All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.

As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.

I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:

“What caused this?” (Projecting present into the past)

“What will this cause?” (Projecting present into the future)

The first question is more relevant to problem-solving and the second to goal-accomplishing.

If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.

Hi, I’m Hanan Parvez (MA Psychology). I’ve been writing about Psychology for 9+ years. My work has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur . If you have any queries, use the contact form or reach out to me on my socials.

The Edisonian Method: Trial and Error

First Online: 02 January 2020

Cite this chapter

Ian Wills 12

Part of the book series: Studies in History and Philosophy of Science ((AUST,volume 52))

488 Accesses

3 Citations

The day after Thomas Edison died, Nicola Tesla, who worked for Edison in 1882–83, was reported as saying, “His method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calculation would have saved him 90 per cent of the labour”. The method that Tesla derided was trial and error, a method that became so closely associated with Edison that it sometimes referred to as the Edisonian method.

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Quoted in New York Times, “Tesla Says Edison Was an Empiricist,” 1.

TAEB 3:844n1.

TAEB 3:880.

Gorman and Carlson, “Interpreting Invention as a Cognitive Process: The Case of Alexander Graham Bell, Thomas Edison and the Telephone.,” 152.

TAEB 3:981n1.

TAEB 3:941.

TAEB 3:1016n1.

TAEB 3:1005.

TAEB 3:1107.

Richard G Berger, “With Edison’s Insomnia Squad,” Modern Mechanix , April 1934, 52.

Quoted in Conot, A Streak of Luck , 71.

Edison, His Life and Inventions . 262. ibid., 2: 615.

quoted in Hughes, American Genesis , 52.

Thomas Midgley (1899–1944) American mechanical engineer, chemist and inventor. Midgley is best known for discovering tetraethyl lead, a fuel efficiency booster for gasoline engines, and dichlorodifluoromethane, originally marketed under the trade name Freon, a chlorofluorocarbon (CFC). Dichlorodifluoromethane was the first refrigerant that was both safe and effective.

Steinle, “Experiments in History and Philosophy of Science,” 421.

quoted in Edwin T Jr. Layton, “Mirror-Image Twins: The Communities of Science and Technology in 19th-Century America,” Technology and Culture 12 (1971): 566.

Derived thus:

Area inside figure = pressure ∗ volume

Pressure = force / area

Area inside figure = force / area ∗ volume = force ∗ length

Mechanical work = force ∗ displacement = force ∗ length

So area inside figure = Mechanical work

TAED TI1:38, TAEB 3:882.

quoted in Dyer and Martin, Edison, His Life and Inventions . 620.

Friedrich Steinle, “Entering New Fields: Exploratory Uses of Experimentation,” Philosophy of Science 64, no. Proceedings (1997); “Experiments in History and Philosophy of Science.”

“Experiments in History and Philosophy of Science,” 419.

“Entering New Fields: Exploratory Uses of Experimentation,” S.67.

Ronald R Kline, “Science and Engineering Theory in the Invention and Development of the Induction Motor, 1880–1900,” Technology and Culture 28, no. 2 (1987).

quoted in “Tesla and the Induction Motor,” Technology and Culture 30, no. 4 (1989).

See, for example, ASHRAE, ASHRAE Handbook - Fundamentals (SI Edition) (Atlanta, GA: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc., 2009), 3.1–3.14.

Lewis F Moody, “Friction Factors for Pipe Flow,” ASME Transactions 66, no. November (1944): 671, 72.

Michael Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy , 1962 corrected ed. (London: Routledge, 1958), 95.

Harry Collins, “Tacit Knowledge, Trust and the Q of Sapphire,” Social Studies of Science 31, no. 1 (2001): 72.

Changing Order: Replication and Induction in Scientific Practice (Chicago: University of Chicago Press, 1992), 51–78.

quoted in ibid., 60–61.

TAEB 4:1251n3.

Thomas A Edison. Improvement in Dynamo-Electric Machines. US Patent 219,393, filed 10 July 1879, and issued 9 September 1879.

Improvement in Solutions for Chemical Telegraphs. US Patent 168,466, filed 26 January 1875, and issued 5 October 1875.

Rosanoff, “Edison in His Laboratory,” 404.

Ibid., 416.

Thomas Jr. Midgley, “From Periodic Table to Production,” Industrial and Engineering Chemistry 29, no. 2 (1937): 242.

Eli Yablonovitch, “Photonic Crystals: Towards Rational Material Design,” Nature Materials 2 (2003): 648.

Gooding, “How Do Scientists Reach Agreement About Novel Observations?,” 208.

Thomas Nickles, “Justification and Experiment,” in The Uses of Experiment : Studies in the Natural Sciences , ed. David Gooding, Trevor Pinch, and Simon Schaffer (Cambridge, Cambridgeshire; New York: Cambridge University Press, 1989), 301.

Peter Louis Galison, How Experiments End (Chicago: University of Chicago Press, 1987), 19.

Steinle, “Experiments in History and Philosophy of Science,” 419.

Giora Hon, “Going Wrong: To Make a Mistake, to Fall into an Error.,” The Review of Metaphysics 49, no. 1 (1995): 2.

quoted in ibid., 1.

Ian Hacking, “Experimentation and Scientific Realism,” in The Philosophy of Science , ed. J D Trout, Richard Boyd, and Philip Gasper (Cambridge, Massachusetts: MIT Press, 1991), 254.

David Collingridge, “Incremental Decision Making in Technological Innovation: What Role for Science?,” Science, Technology and Human Values 14, no. 2 (1989).

Israel, Edison: A Life of Invention , 170–71.

Ibid., 338–62.

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Wills, I. (2019). The Edisonian Method: Trial and Error. In: Thomas Edison: Success and Innovation through Failure. Studies in History and Philosophy of Science, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-29940-8_10

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v.117(47); 2020 Nov 24

Rapid trial-and-error learning with simulation supports flexible tool use and physical reasoning

Kelsey r. allen.

a Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139;

b Center for Brains, Minds, and Machines, Cambridge, MA 02139

Kevin A. Smith

Joshua b. tenenbaum.

Author contributions: K.R.A., K.A.S., and J.B.T. designed research; K.R.A. and K.A.S. performed research; K.R.A. and K.A.S. analyzed data; and K.R.A., K.A.S., and J.B.T. wrote the paper.

Associated Data

Many animals, and an increasing number of artificial agents, display sophisticated capabilities to perceive and manipulate objects. But human beings remain distinctive in their capacity for flexible, creative tool use—using objects in new ways to act on the world, achieve a goal, or solve a problem. To study this type of general physical problem solving, we introduce the Virtual Tools game. In this game, people solve a large range of challenging physical puzzles in just a handful of attempts. We propose that the flexibility of human physical problem solving rests on an ability to imagine the effects of hypothesized actions, while the efficiency of human search arises from rich action priors which are updated via observations of the world. We instantiate these components in the “sample, simulate, update” (SSUP) model and show that it captures human performance across 30 levels of the Virtual Tools game. More broadly, this model provides a mechanism for explaining how people condense general physical knowledge into actionable, task-specific plans to achieve flexible and efficient physical problem solving.

While trying to set up a tent on a camping trip, you realize that the ground is too hard for the tent stakes, and you have no hammer. What would you do? You might look around for a suitable hammer substitute, passing over objects like pinecones or water bottles in favor of a graspable rock. And if that rock failed to drive in the stakes at first, you might try a different grip or search for a heavier rock. Most likely, you would need only a handful of attempts before you found an approach that works. Determining how to pound in tent stakes without a hammer is an example of the flexibility and efficiency of more general physical problem solving. It requires a causal understanding of how the physics of the world work and sophisticated abilities for inference and learning to construct plans that solve a novel problem. Consider how, when faced with the tent stake challenge, we do not choose an object at random; we choose a rock because we believe we know how we could use it to generate sufficient force on the stake. And if we find that the first rock fails, we again search around for a solution, but use the knowledge of our failures to guide our future search. This style of problem solving is a very structured sort of trial-and-error learning: Our search has elements of randomness, but within a plausible solution space, such that the goal can often be reached very quickly.

Here we study the cognitive and computational underpinnings of flexible tool use. While human tool use relies on a number of cognitive systems—for instance, knowing how to grasp and manipulate an object or understanding how a particular tool is typically used—here we focus on “mechanical reasoning,” or the ability to spontaneously repurpose objects in our environment to accomplish a novel goal ( 3 – 5 ).

We target this mechanical reasoning because it is the type of tool use that is quintessentially human. While other animals can manipulate objects to achieve their aims, only a few species of birds and primates have been observed to spontaneously use objects in novel ways, and we often view these activities as some of the most “human-like” forms of animal cognition (e.g., Fig. 1 A and B ) ( 6 ). Similarly, while artificial intelligence (AI) systems have become increasingly adept at perceiving and manipulating objects, none perform the sort of rapid mechanical reasoning that people do. Some artificial agents learn to use tools from expert demonstrations ( 7 ), which limits their flexibility. Others learn from thousands of years of simulated experience ( 8 ), which is significantly longer than required for people. Still others can reason about mechanical functions of arbitrary objects but require perfect physical knowledge of the environment ( 9 ), which is unavailable in real-world scenarios. In contrast, even young humans are capable tool users: By the age of 4 years they can quickly choose an appropriate object and determine how to use it to solve a novel task (e.g., picking a hooked rather than a straight pipe cleaner to retrieve an object from a narrow tube; Fig. 1 C ) ( 10 ).

An external file that holds a picture, illustration, etc.
Object name is pnas.1912341117fig01.jpg

Examples of using objects to achieve a goal. ( A ) Bearded capuchin monkey opening a cashew nut with an appropriately sized stone. Reprinted from ref. 1, which is licensed under CC BY 4.0 . ( B ) New Caledonian crow using heavy blocks to raise the water level in a tube to retrieve food ( 2 ). ( C ) Toddler using a shovel to reach a ball. Image credit: YouTube/Funny Vines ( http://youtu.be/hwrNQ93-568?t=198 ). ( D ) One illustrative trial in the Virtual Tools game ( https://k-r-allen.github.io/tool-games/ ). ( D , i ) The player must get the red object into the green goal using one of the three tools. ( D , ii ) The player chooses a tool and where to place it. ( D , iii ) Physics is turned “on” and the tool interacts with other objects. The action results in a near miss.

What are the cognitive systems that let us use tools so flexibly and accomplish our goals so rapidly? It has been suggested that mechanical reasoning relies on mental simulation, which lets us predict how our actions will cause changes in the world ( 3 ). This general-purpose simulation is a necessary component that supports our ability to reason about objects in novel environments, but by itself cannot explain how we make and update our plans so quickly. We propose that another key to rapid tool use is knowing what sorts of actions to even consider—both from an initial understanding of what actions are useful and by updating this belief from observing the outcome of our actions, in simulation and in reality.

This paper makes two contributions. First, we introduce the Virtual Tools game, which presents a suite of physical problem-solving challenges and allows for precise, quantifiable comparisons between human and machine agents. Second, we present a minimal model of flexible tool use, called “sample, simulate, update” (SSUP). This model is built around an efficient albeit noisy simulation engine that allows the model to act flexibly across a wide variety of physical tasks. To solve problems rapidly, the SSUP model contains rich knowledge about the world in the form of a structured prior on candidate tools and actions likely to solve the problem, which allows it to limit its simulations to promising candidates. It further learns from its simulations and from observing the outcome of its own actions to update its beliefs about what those promising candidates should be. Across 30 Virtual Tools levels in two experiments, we show that an instantiation of the SSUP model captures the relative difficulties of different levels for human players, the particular actions performed to attempt to solve each level, and how the solution rates for each level evolve.

Inspired by human tool use, as well as mobile physics games ( 11 ), we propose the Virtual Tools game as a platform for investigating the priors, representations, and planning and learning algorithms used in physical problem solving ( https://k-r-allen.github.io/tool-games/ ). This game asks players to place one of several objects (“tools”) into a two-dimensional (2D) dynamic physical environment to achieve a goal: getting a red object into a green region ( Fig. 1 D ). This goal is the same for every level, but what is required to achieve it varies greatly. Once a single tool is placed, the physics of the world are enabled so that players see the effect of the action they took. If the goal is not achieved, players can “reset” the world to its original state and try again; they are limited to a single action on each attempt. We designed 30 levels—20 for the original experiment ( Fig. 2 ) and 10 for a validation experiment (see Fig. 7 A )—to test concepts such as “launching,” “blocking,” and “supporting.” Of the first 20 levels, 12 were constructed in six “matched pairs” which incorporated small differences in the goals or objects in the scene to test whether subtle differences in stimuli would lead to observable differences in behavior.

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Twenty levels used in the Virtual Tools game. Players choose one of three tools (shown to the right of each level) to place in the scene to get a red object into the green goal area. Black objects are fixed, while blue objects also move; gray regions are prohibited for tool placement. Levels denoted with A/B labels are matched pairs.

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Results on 10 additional trials. ( A ) Trials used for the second experiment. ( B ) The cumulative solution rate for participants and the SSUP model. ( C ) Comparison of the number of human and model actions by trial. ( D ) Comparison of human and model accuracy on each trial.

The Virtual Tools game presents particular challenges that we believe underlie the kinds of reasoning required for rapid physical problem solving more generally. First, there is a diversity of tasks that require different strategies and physical concepts to solve, but employ shared physical dynamics that approximate the real world. Second, the game requires long-horizon causal reasoning. Since players can interact with the game only by placing a single object, they must be able to reason about the complex cause and effect relationships of their action long into the future when they can no longer intervene. Finally, the game elicits rapid trial-and-error learning in humans. Human players do not generally solve levels on their first attempt, but also generally do not require more than 5 to 10 attempts to succeed. People demonstrate a wide range of problem-solving behaviors, including “aha” insights where they suddenly discover the right idea for how to solve a particular task, as well as incremental trial-and-error strategy refinement. Fig. 3 demonstrates how this occurs in practice, showing four different examples of participants learning rapidly or slowly and discovering different ways to use the tools across a variety of levels.

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Examples of participants’ behavior on three levels, representative of rapid trial-and-error learning: Initial plans are structured around objects, followed by exploring to identify more promising strategies and then refining actions until success. Objects start as shown by light blue/red outlines and follow paths traced out by colored lines. Possible tool choices are shown at Right . ( A ) In the Catapult level, a useful strategy is often identified immediately and rapidly fine-tuned. ( B ) Other participants first try an unsuccessful strategy but then switch to a more viable strategy and refine it. ( C ) The Launch ( B ) level is designed to prevent obvious solutions. This participant may have initially believed the ball would start rolling and attempted to use a tool as a bridge. When this failed, the participant realized the need to launch the ball but discovered only after several trials how to use a tool in a nonobvious way to accomplish this, via a hooking motion around the blocking ledge. The participant then took several more trials to fine-tune this action. ( D ) In the SeeSaw level, a participant realized on the second attempt the platform must be supported for the ball to roll across and then tried different ways of making this happen.

We consider the components required to capture both the flexibility and efficiency of human tool use. We propose that people achieve flexibility through an internal mental model that allows them to imagine the effects of actions they may have never tried before (“simulate”). However, a mental model alone is not sufficient—there are far too many possible actions that could be simulated, many of which are uninformative and unlikely to achieve a specific goal. Some mechanism for guiding an internal search is necessary to focus on useful parts of the hypothesis space. We therefore propose people use structured, object-oriented priors (“sample”) and a rapid belief updating mechanism (“update”) to guide the search toward promising hypotheses. We formalize human tool use with these components in the SSUP model ( Fig. 4 A ).

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( A ) The SSUP algorithm. ( B ) A diagram of the model for the Virtual Tools game. It incorporates an object-based prior, a simulation engine for filtering proposals, and an update module that suggests new proposals based on observations “in the mind” and from actions taken in the world. ( C ) Illustration of the policy π ′ evolving while attempting a level. Colored patches represent the Gaussian policy for each tool as indicated by the Belief Color Key.

SSUP is inspired by the theory of “problem solving as search” ( 12 ), as well as Dyna and other model-based policy optimization methods ( 13 , 14 ). Crucially, we posit that structured priors and physical simulators must already be in place to solve problems as rapidly as people; thus unlike most model-based policy optimization methods, we do not perform online updates of the dynamics model.

We emphasize that we view SSUP as a general modeling framework for physical problem solving and present here only one instance of that framework: the minimal model (described below, with more detail in SI Appendix , section S2 ) that we think is needed to capture basic human behavior in the Virtual Tools game. In the Discussion we highlight ways the model will need to be improved in future work, as well as aspects of physical reasoning that rely on a richer set of cognitive systems going beyond the framework presented here.

At a minimum, the actions we should consider to achieve any goal should have the potential to impact our environment. We therefore incorporate an object-based prior for sampling actions. Specifically, the model selects one of the movable objects in the scene and then chooses an x coordinate in an area that extends slightly beyond the width of the object and a y coordinate either above or below that object ( Fig. 4 B : sample). For tool choice, we assume participants are equally likely to choose any of the three tools since all tools in the game were designed to be unfamiliar to participants. Samples from this distribution are used to initialize search.

To determine which sampled actions are worth trying in the world, we assume people use an “intuitive physics engine” ( 15 ) to flexibly imagine the effects of their actions. This engine is able to simulate the world forward in time with approximately correct but stochastic dynamics ( 16 , 17 ). Determining the effect of a proposed action therefore involves applying that action to one’s mental representation and using the intuitive physics engine to posit the range of ways that action might cause the world to unfold ( 18 , 19 ). Here we implement simulation using a game physics engine with noisy dynamics. People characteristically have noisy predictions of how collisions will resolve ( 16 ), and so for simplicity we assume uncertainty about outcomes is driven only by noise in those collisions (the direction and amount of force that is applied between two colliding objects). *

Since the internal model is imperfect, to evaluate an action we produce a small number of stochastic simulations ( n s i m s , set here at four) to form a set of hypotheses about the outcome. To formalize how good an outcome is (the reward of a given action), we borrow an idea from the causal reasoning literature for how people conceptualize “almost” succeeding ( 20 ). Almost succeeding is not a function of the absolute distance an action moved you toward your goal, but instead how much of a difference that action made. To capture this, the minimum distance between the green goal area and any of the red goal objects is recorded; these values are averaged across the simulations and normalized by the minimum distance that would have been achieved if no tool had been added. The reward used in SSUP is 1 minus the normalized distance, so that closer objects lead to higher reward.

Once the model finds a good enough action (formalized as the average reward being above some threshold), it takes that action “in the world.” Additionally, to model time limits for thinking, if the model considers more than T different action proposals without acting (set here at five), it takes the best action it has imagined so far. We evaluate the effect of all parameter choices in a sensitivity analysis ( SI Appendix , Fig. S1 ).

So far, we have described a way of intelligently initializing a search to avoid considering actions that will not be useful. But what if the prior still presents an intractably large space of possible actions?

To tackle this, we incorporate an update mechanism that learns from both simulated and real experience to guide future search toward more promising regions of the hypothesis space ( 21 ). This is formally defined as a Gaussian mixture model policy over the three tools and their positions, π ′ ( s ) , which represents the model’s belief about high-value actions for each tool. π ′ ( s ) is initialized with samples from the object-oriented prior and updated using a simple policy gradient algorithm ( 22 ). This algorithm will shape the posterior beliefs around areas to place each tool, which are expected to move target objects close to the goal and are therefore likely to contain a solution. Such an update strategy is useful when it finds high-value actions that are nearby successful actions, but may also get stuck in local optima where a successful action does not exist. We therefore use a standard technique from reinforcement learning: epsilon-greedy exploration. With epsilon-greedy exploration, potential actions are sampled from the policy 100 − ϵ % of the time and from the prior ϵ % of the time. Note that this exploration is used only for proposing internal simulations; model actions are chosen based on the set of simulation outcomes. This is akin to thinking of something new, instead of focusing on an existing strategy.

We analyze human performance on the first 20 levels of the Virtual Tools game and compare humans to the SSUP model and alternates, including SSUP models with ablations and two alternate learning baselines. We show that the full SSUP model best captures human performance. Access to the game and all data including human and model placements is provided at https://k-r-allen.github.io/tool-games/ .

Human Results.

Experiments were approved by the Massachusetts Institute of Technology Committee on the Use of Humans as Experimental Subjects under protocol 0812003014. Participants were notified of their rights before the experiment, were free to terminate participation at any time by closing the browser window, and were compensated monetarily for their time.

We recruited 94 participants through Amazon Mechanical Turk and asked each participant to solve 14 levels: all 8 of the unmatched levels and one variation of each of the 6 matched pairs (randomly selected).

Participants could choose to move on once a problem was solved or after 2 min had passed. See SI Appendix , section S1 for further details.

The variation in difficulty between levels of the game was substantial. Participants showed an average solution rate of 81 % (SD = 19%), with the range covering 31 % for the hardest level to 100 % for the easiest. Similarly, participants took an average of 4.5 actions (SD = 2.5) for each level, with a range from 1.5 to 9.4 average attempts. Even within trials, there was a large amount of heterogeneity in the number of actions participants used to solve the level. This would be expected with “rapid trial-and-error” learning: Participants who initially tried a promising action would solve the puzzle quickly, while others explored different actions before happening on promising ones (e.g., Fig. 3 ).

Behavior differed across all six matched level pairs. We study whether these subtle differences do indeed affect behavior, even without feedback on the first action, by asking whether we can identify which level variant each action came from. We find these actions are differentiable across matched levels in “Shafts,” “Prevention,” “Launch,” and “Table” on the first attempt, but not “Falling” or “Towers” (see SI Appendix , Fig. S11 and section S6A for details). However, participants required a different number of actions to solve every level (all t s > 2.7 , p s < 0.01 ). This suggests that people are paying attention to subtle differences in the scene or goal to choose their actions.

Model Results.

We investigate several metrics for comparing the models to human data. First, we look at how quickly and how often each model solves each level and whether that matches participants. This is measured as the correlation and root-mean-square error (RMSE) between the average number of participant attempts for each level and the average number of model attempts for each level and the correlation and RMSE between human and model solution rates. The SSUP model explains the patterns of human behavior across the different levels well ( SI Appendix , Table S2 ). It uses a similar number of attempts on each level ( r = 0.71 ; 95 % CI = [ 0.62 , 0.76 ] ; mean empirical attempts across all levels, 4.48; mean model attempts, 4.24; Fig. 5 A ) and achieves similar accuracy ( r = 0.86 ; 95 % CI = [ 0.76 , 0.89 ] ; Fig. 5 B ).

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( A ) Comparison of average number of human participants’ attempts for each level with average number of attempts for the SSUP model. Bars indicate 95 % confidence intervals on estimates of the means. ( B ) Comparison of human participants’ accuracy on each trial versus the accuracy of the SSUP model. ( C ) Comparison of human participants’ accuracy to all alternate models. Numbers correspond to the trials in Fig. 2 .

Across many levels, the SSUP model not only achieves the same overall solution rate as people, but also approaches it at the same rate. We measure this by looking at cumulative solution rates—over all participants or model runs, what proportion solved each level within X placements—and find that people and the model often demonstrate similar solution profiles ( Fig. 6 A ; see SI Appendix , section S6B for quantitative comparison).

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( A ) Cumulative solution rate over number of placements for participants vs. the SSUP model. ( B ) Distribution of model actions (background) versus human actions (points) on the first and last attempts of the level for a selection of four levels. The distribution of model actions is estimated based on fitting a kernel density estimate to the actions taken by the model across 250 simulations. Colors indicate the tool used, with the tools and associated colors shown at Right of each level. In most levels, the SSUP model captures the evolution of participants’ solutions well, including the particular actions chosen; in the few cases that it differs, there is no alternative model that systematically explains these differences.

We can look in more detail at how the model accomplishes this by comparing both the first actions that people and the model take and the actions that both take to solve a level ( Fig. 6 B ). Like our human participants, the model takes significantly different actions on the first attempt between matched level pairs ( SI Appendix , section S6A ). More generally, both people and the model will often begin with a variety of plausible actions (e.g., Catapult). In some cases, both will attempt initial actions that have very little impact on the scene [e.g., SeeSaw and Prevention (B)]; this could be because people cannot think of any useful actions and so decide to try something, similar to how the model can exceed its simulation threshold. However, in other cases, the model’s initial predictions diverge from people, and this leads to a different pattern of search and solutions. For instance, in Falling (A), the model quickly finds that placing an object under the container will reliably tip the ball onto the ground, but people are biased to drop an object from above. Because of this, the model often rapidly solves the level with an object below, whereas a proportion of participants find a way to flip the container from above; this discrepancy can also be seen in the comparison of number of attempts before the solution, where the model finds a solution quickly, while people take a good deal longer ( Fig. 5 A ). For comparisons of the first and last actions across all levels, see SI Appendix , Fig. S11 .

Model Comparisons on Virtual Tools.

We compare the full SSUP model against a set of six alternate models. Three models investigate the contribution of each SSUP component by removing the prior, simulation, or updating individually. Two models propose alternate solution methods: learning better world models rather than learning over actions (parameter tuning) or replacing the prior and simulator with a learned proposal mechanism (Deep Q Network [DQN, ref. 23 ] + updating). The parameter tuning alternate model uses inference to learn object densities, frictions, and elasticities from observed trajectories. The learned proposal mechanism corresponds to a model-free deep reinforcement learning agent ( 23 ) which is trained on a set of 4,500 randomly generated levels of the game ( SI Appendix , section S5 ) and then updated online for each of the 20 testing levels using the same mechanism as SSUP. This model has substantially more experience with the environment than other models and serves as a test of whether model-free methods can make use of this experience to learn generalizable policies that can guide rapid learning. Finally, we compare to a “guessing” baseline for performance if an agent were to simply place tools randomly. See Fig. 5 C and SI Appendix , Table S2 for these comparisons.

Eliminating any of the three SSUP components causes a significant decrease in performance (measured as deviation between empirical and model cumulative solution curves; all bootstrapped p s < 0.0001 ; see SI Appendix , section S6B and Fig. S6 for further details). The reduced models typically require more attempts to solve levels because they are searching in the wrong area of the action space (no prior), attempting actions that have no chance of being successful (no simulation), or do not guide search toward more promising areas (no updating).

DQN + updating performs worst of all plausible alternate models, using the most actions and solving levels at a rate barely over chance. Because this is equivalent to the no simulation model with a different prior, its poor performance suggests that generalized action policies cannot easily be learned from repeatedly playing similar levels ( SI Appendix , section S5 ).

Because the parameter tuning model is equivalent to the no updating model except that the properties of the dynamics model can be learned in parameter tuning, comparing those two models allows us to test whether we need to assume that people are learning the dynamics of the world in this game. The fact that both models perform roughly equivalently ( Fig. 5 C ) suggests that we do not need this assumption here.

Finally, we quantified how well each model captured the particular actions people took. Due to heterogeneity in participants’ responses, we were unable to cleanly differentiate models’ performance except to find that the DQN + updating model underperformed the rest ( SI Appendix , section S6C ). However, no model reached the theoretical noise ceiling, suggesting components of the SSUP framework could be improved to better explain participants’ actions ( Discussion ).

Validation on Novel Levels.

We conducted a second experiment to test whether the models generalize to novel levels and physical concepts without tuning hyperparameters. For this experiment, we created 10 new levels: 6 novel level types and 4 variants of the originals ( Fig 7 A ), testing an independent sample of 50 participants on all levels. The 6 novel level types were designed to test new physical strategies, including balancing, breaking, and removing objects from a ball’s path. All other experimental details were identical to the main experiment.

Without tuning any model parameters, we find a good correspondence between human and model solution rates ( Fig. 7 B ) and a strong correlation between the model’s performance and human performance across number of placements ( Fig. 7 C , r = 0.85 ) and accuracy ( Fig. 7 D , r = 0.95 ). Similar to the main experiment, we find a decrement in performance if the prior or simulation is removed or for the DQN + updating model (all bootstrapped p s < 0.0001 ; SI Appendix , Fig. S7 ). However, while numerically worse, we do not find a reliable difference if the update mechanism is removed ( p = 0.055 ) or swapped for model learning ( p = 0.346 ), suggesting that the particular reward function or update procedure might be less applicable to these levels ( SI Appendix , section S6B ).

We introduce the Virtual Tools game for investigating flexible physical problem solving in humans and machines and show that human behavior on this challenge expresses a wide variety of trial-and-error problem-solving strategies. We also introduce a model for human physical problem solving: sample, simulate, update. The model presumes that to solve these physics problems, people rely on an internal model of how the world works. Learning in this game therefore involves condensing this vast world knowledge to rapidly learn how to act in each instance, using a structured trial-and-error search.

Model Limitations.

Although the SSUP model we used solves many of the levels of the Virtual Tools game in a human-like way, we believe that this is still only a first approximation to the rich set of cognitive processes that people bring to the task. In particular, there are at least two ways in which the model is insufficient: its reliance on very simple priors and its planning and generalizing only in the forward direction.

We can see the limits of the object-based prior in the Falling (A) level ( Fig. 5 B ): People are much less likely to consider placing an object underneath the container to tip it over. Instead, many people try to tip it over from above, even though this is more difficult. In this way, people’s priors over strategies are context specific, which causes them to be slower than the model in this level. In other cases, this context specificity is helpful: For instance, in the hypothetical level shown in Fig. 8 A , there is a hole that one of the tools fits suspiciously perfectly into. Many people notice this coincidence quickly, but because the model cannot assess how tools might fit into the environment without running a simulation, it succeeds only 10% of the time. In future work, a more complex prior could be instantiated in the SSUP framework, but it remains an open question how people might form these context-specific priors or how they might be shaped over time via experience.

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Two problems that demonstrate limitations of the current model. ( A ) A “suspicious coincidence” that one tool fits perfectly in the hole. ( B ) Creating a “subgoal” to launch the ball onto the other side is useful.

People show greater flexibility than our model in the ability to work backward from the goal state to find more easily solvable subgoals ( 24 ). In the hypothetical level in Fig. 8 B , the catapult is finicky, which means that most catapulting actions will not make it over the barrier and therefore will never hit the ball on the left. Instead, the easiest way to increase the objective function is by the incorrect strategy of knocking the ball on the right to get close to the goal, and therefore the model solves the level only 8% of the time. Working backward to set the first subgoal of launching the ball over the barrier would prevent getting stuck with knocking the ball as a local minimum. From an engineering standpoint, creating subgoals is natural with discrete problem spaces ( 12 ), but it is less clear how these might be discovered in the continuous action space of the Virtual Tools game.

Related Cognitive Systems.

There is an extensive body of research into the cognitive systems that underlie the use of real-world tools, including understanding how to manipulate them and knowing their typical uses (e.g., refs. 3 , 4 , 10 , and 25 ). Here our focus was on “mechanical knowledge” of tools: how to use objects in novel situations. However, in real-world tool use, these systems work together with motor planning and semantic knowledge of tools. Future work can focus on these links, such as how novel tools become familiar or how our motor limits constrain the plans we might consider.

The Virtual Tools game presents a problem-solving task that blends facets of prior work, but encompasses a novel challenge. To rapidly solve these problems requires good prior knowledge of the dynamics—unlike complex problem solving in which the dynamics are learned in an evolving situation ( 26 )—and further iteration once a promising solution is considered—unlike the “aha” moment that leads immediately to a solution in insight problem solving ( 27 , 28 ). Unlike in traditional model-based or model-free reinforcement learning, in this task people bring rich models of the world that they can quickly tailor to specific, novel problems.

Distilling rich world knowledge to useful task knowledge is necessary for any agent interacting with a complex world. One proposal for how this occurs is “learning by thinking” ( 29 ): translating knowledge from one source (internal models of physics) to another, more specific instantiation (a mapping between actions and outcomes on this particular level). We show how SSUP instantiates one example of learning by thinking: by training a policy with data from an internal model. Evidence for this sort of knowledge transfer has been found in people ( 30 , 31 ,) but has focused on simpler discrete settings in which the model and policy are jointly learned.

Virtual Tools as an AI Challenge.

In preliminary experiments with model-free reinforcement learning approaches ( 23 ), we found limited generalization with inefficient learning across almost all of the Virtual Tools levels ( SI Appendix , section S5 ) despite significant experience with related levels.

Based on our human experiments, we believe that model-based approaches will be required to be able to play games like Virtual Tools. Such approaches are becoming increasingly popular in machine learning ( 32 ), especially when combined with “learning-to-learn” techniques that can learn to adapt quickly to new tasks ( 33 , 34 ). Learning these models remains challenging, but approaches that incorporate added structure have excelled in recent years ( 35 , 36 ). Within the AI and robotics communities, model-based methods are already popular ( 9 , 37 , 38 ). Remaining challenges include how to learn accurate enough models that can be used with raw sensor data ( 39 ) and how to handle dynamic environments.

Virtual Tools adds to a growing set of environments that test artificial agents’ abilities to predict and reason using physics, such as the concurrently developed physical reasoning (PHYRE) benchmark ( 40 ) and others ( 41 – 43 ). In contrast, our focus is on providing problems that people find challenging but intuitive, where solutions are nonobvious and do not rely on precise knowledge of world dynamics. By contributing human data to compare artificial and biological intelligence, we hope to provide a testbed for more human-like artificial agents.

Future Empirical Directions.

This work provides an initial foray into formalizing the computational and empirical underpinnings of flexible tool use, but there remains much to study. For instance, we do not find evidence that people learn more about the world, perhaps because there is little benefit to additional precision here. But there are cases where learning the dynamics is clearly helpful (e.g., discovering that an object is abnormally heavy or glued down), and we would expect people to update their physical beliefs in these cases. When and in what ways people update their internal models to support planning is an important area of study.

Children can discover how to use existing objects earlier than they can make novel tools ( 10 ), suggesting that tool creation is more challenging than tool use. Yet it is the ability to make and then pass on novel tools that is theorized to drive human culture ( 44 ). It is therefore important to understand not just how people use tools, but also how they develop and transmit them, which we can study by expanding the action space of the Virtual Tools game.

Understanding how to flexibly use tools to accomplish our goals is a basic and central cognitive capability. In the Virtual Tools game, we find that people efficiently use tools to solve a wide variety of physical problems. We can explain this rapid trial-and-error learning with the three components of the SSUP framework: rich prior world knowledge, simulation of hypothetical actions, and the ability to learn from both simulations and observed actions. We hope this empirical domain and modeling framework can provide the foundations for future research on this quintessentially human trait: using, making, and reasoning about tools and more generally shaping the physical world to our ends.

Supplementary Material

Supplementary file, acknowledgments.

We thank Leslie Kaelbling, Roger Levy, Eric Schulz, Jessica Hamrick, and Tom Silver for helpful comments and Mario Belledonne for help with the parameter tuning model. This work was supported by National Science Foundation Science Technology Center Award CCF-1231216; Office of Naval Research Multidisciplinary University Research Initiative (ONR MURI) N00014-13-1-0333; and research grants from ONR, Honda, and Mitsubishi Electric.

The authors declare no competing interest.

This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sciences, “Brain Produces Mind by Modeling,” held May 1–3, 2019, at the Arnold and Mabel Beckman Center of the National Academies of Sciences and Engineering in Irvine, CA. NAS colloquia began in 1991 and have been published in PNAS since 1995. From February 2001 through May 2019, colloquia were supported by a generous gift from The Dame Jillian and Dr. Arthur M. Sackler Foundation for the Arts, Sciences, & Humanities, in memory of Dame Sackler’s husband, Arthur M. Sackler. The complete program and video recordings of most presentations are available on the NAS website at http://www.nasonline.org/brain-produces-mind-by .

This article is a PNAS Direct Submission. N.K. is a guest editor invited by the Editorial Board.

Data deposition: Access to the Virtual Tools game and all data including human and model placements is provided at GitHub, https://k-r-allen.github.io/tool-games/ .

*We also considered models with additional sources of physics model uncertainty added but found that the additional parameters did not improve model fit, so we do not analyze those models here.

This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1912341117/-/DCSupplemental .

The Use of Trial and Error To Solve Problems

Some complex problems can be solved by a technique that is called trial and error. Trial and error is typically good for problems where you have multiple chances to get the correct solution. However, this is not a good technique for problems that don’t give you multiple chances to find a solution.

An example of situations where you wouldn’t want to use trial and error are diffusing a bomb or performing an operation on a patient. In these situations, making an error can lead to disaster. Trial and error is used best when it is applied to situations that give your large amounts of time and safety to come up with a solution. In addition to this, trial and error is also a great way to gain knowledge. Basically, a person that uses the trial and error method will try to a method to see if it is a good solution. If it is not a good solution, they try another option. If the method works, the person using it has acquired the correct solution to a problem. However, there are some situations where there are too many options, and it is not feasible for a person to go through all of them to find out which one works the best. In this event, a person will want to use the option that has the best possible chances of succeeding. If this doesn’t work, they can try the next best option until they find a good solution. There are a number of important factors that makes trial and error a good tool to use for solving problems. The purpose of trial and error is not to find out why a problem was solved. It is primarily used to solve the problem. While this may be good in some fields, it may not work so well in others. For example, while trial and error may be excellent in finding solutions to mechanical or engineering problems, it may not be good for certain fields which ask "why" a solution works. Trial and error is primarily good for fields where the solution is the most important factor. This is often the case in math courses which are taught in high school or college. Most math teachers place an emphasis on using trial and error to find a solution to problems, and many of them don’t spend a whole lot of time explaining "why" a solution works. One reason for this is because most math teachers have time constraints. However, some students who take advanced math classes in college may learn more about why certain solutions work. Another good aspect of the trial and error method is that it does not try to use a solution as a way of solving more than one problem. Trial and error is primarily used to find a single solution to a single problem. Trial and error is not a method of finding the best solution, nor is it a method of finding all solutions. It is a problem solving technique that is simply used to find a solution. One of the most powerful advantages to this technique is that it does not require you to have a lot of knowledge. However, it may require you to have large amounts of patience. Trial and error is typically used to discover new drugs, and it also plays an important role in the scientific method as well. Some also feel that organic evolution is a form of trial and error, because random mutations will occur until they are successful.

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Advantages and Disadvantages of Solving a Problem Through Trial and Error

Back to: Learning and Teaching – Unit 2

Introduction

E.L. Thorndike propounded the theory of trial and error. He believes that behavior is the result of a response to a stimulus. According to him, learning is associated with responses, impressions, and a sense of action. Thorndike’s views are often referred to as connectionism as it believes in the connection of stimulus and response. Thorndike referred to it as connecting and selecting or trial and error theory since learning results from repetition. Thorndike proposed three laws of learning namely, the law of readiness, the law of effect, and the law of exercise.

The disadvantages of solving a problem through the trial and error method are as follows:

Creative Approach

Trial and error is considered to be a creative approach for solving tasks because it makes individuals use both the right and left hemispheres of their brain.

Less Time Consuming

The trial and method consume less time to solve tasks that do not have a great depth of difficulty.

Division of Tasks

The trial and error method involves the division of tasks which makes it possible for individuals to search for a quick solution.

Allows one to Learn

It is not possible to get everything right on the first try due to trial and error is a good method to encourage learning.

Mistakes are Allowed

In the trial and error theory, mistakes are a part of learning. When people make errors, they can reflect on them and make changes to get better.

Disadvantages

Consumes a lot of energy.

The trial and error method can be a bit energy-consuming since it uses a lot of energy due to which it can limit the quantity of learning.

Emphasizes Rote Learning

The theory includes the use of repetition and therefore, encourages rote learning.

Ineffective for Bright Learners

Learners who do not focus on rote memorization and learn things quickly may find this method ineffective.

Ineffective for Higher Classes

The theory fails to provide adequate guidance for learners belonging to higher classes.

Losing Popularity

The trial and error method has been losing popularity in the modern age due to which its use might not be relevant in the future.

The trial and error method has various benefits for solving tasks but there are certain limitations that impact its prevalence.

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Computer Science > Computation and Language

Title: boosting of thoughts: trial-and-error problem solving with large language models.

Abstract: The reasoning performance of Large Language Models (LLMs) on a wide range of problems critically relies on chain-of-thought prompting, which involves providing a few chain of thought demonstrations as exemplars in prompts. Recent work, e.g., Tree of Thoughts, has pointed out the importance of exploration and self-evaluation in reasoning step selection for complex problem solving. In this paper, we present Boosting of Thoughts (BoT), an automated prompting framework for problem solving with LLMs by iteratively exploring and self-evaluating many trees of thoughts in order to acquire an ensemble of trial-and-error reasoning experiences, which will serve as a new form of prompting to solve the complex problem. Starting from a simple prompt without requiring examples, BoT iteratively explores and evaluates a large collection of reasoning steps, and more importantly, uses error analysis obtained from the LLM on them to explicitly revise prompting, which in turn enhances reasoning step generation, until a final answer is attained. Our experiments with GPT-4 and Llama2 across extensive complex mathematical problems demonstrate that BoT consistently achieves higher or comparable problem-solving rates than other advanced prompting approaches.

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Trial and error
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Donate
What is Trial And Error?
Understanding the Concept of Trial and Error: An Accessible Guide in Everyday Language, Crafted by Expert Psychologists, Professors, and Advanced Students. ... provides valuable information. Reflecting on each attempt can improve future trials and hasten the problem-solving process. Embrace Failure. Viewing errors as learning opportunities ...
Problem-Solving Strategies: Definition and 5 Techniques to Try
In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness. 4. Working backward. Working backward is a problem-solving approach often ...
The Trial and Error Code: How to make the best decisions
Author: Lewis Harrison is a futurist, and professional forecaster.He is the Executive Director of the International Association of Healing Professionals, an educational organization that offers ...
Trial and Error: The Path to Success in Problem Solving.
Problem-solving is an integral part of human cognition and innovation. From the simplest tasks to complex challenges, our ability to navigate problems effectively is a key factor in our personal ...
Problem Solving
Solving Puzzles. Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link]) is a 4×4 grid.
Trial and error
Studies show that the most successful people failed a lot. When testing concepts, ideas, solving new problems in the real world one cannot avoid making mistakes, or fall flat sometimes. Successful managers, leaders, and entrepreneurs all understand the importance of failure, indeed they are mastered in failing but: they have learned to move on; and
Trial and Error: Your Guide to Learning and Growing
Find out why trial and error-based progress is so important and get tips to make the best out of it. Read more in this blog post.
7.3 Problem-Solving
Additional Problem Solving Strategies:. Abstraction - refers to solving the problem within a model of the situation before applying it to reality.; Analogy - is using a solution that solves a similar problem.; Brainstorming - refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal ...
Trial and error
The process you have just used is called trial and error, and it can be used to solve small problems like the one you had with your Wi-Fi. It can also be a powerful method in controlled situations for scientific breakthroughs, inventions, and developing new products. The idea is that you keep trying different approaches until you find one that ...
4 Main problem-solving strategies
These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are: Algorithms; Heuristics; Trial and error; Insight; 1. Algorithms. When you follow a step-by-step procedure to solve a problem or reach a goal, you're using an algorithm.
Problem Solving Strategies: Insight, Trial-and-error, and Algorit
How do you solve problems in different situations? Do you rely on insight, trial-and-error, or algorithms? This webpage explains the advantages and disadvantages of these three problem solving strategies, and provides examples and exercises to help you improve your skills. Whether you are a student, a professional, or a curious learner, you will find this webpage useful and engaging.
The Trial and Error Method: When to Use it and When to Avoid it
The trial and error method is a problem-solving technique that involves trying different approaches or solutions until you find the one that works best. This method ...
The Edisonian Method: Trial and Error
1 "His Method Was Inefficient in the Extreme". The day after Thomas Edison died, Nicola Tesla, who worked for Edison in 1882-83, was reported as saying, "His method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of ...
Delegating trial and error
Introduction. Trial and error, an approach commonly used in problem solving, is frequently delegated. Pharmaceutical companies outsource drug development to contract research organizations, hedge funds hire researchers to mine data for profitable trading strategies, and governments task consultants with finding creative solutions to novel problems.
Rapid trial-and-error learning with simulation supports flexible tool
To rapidly solve these problems requires good prior knowledge of the dynamics—unlike complex problem solving in which the dynamics are learned in an evolving situation —and further iteration once a promising solution is considered—unlike the "aha" moment that leads immediately to a solution in insight problem solving (27, 28). Unlike ...
Trial and error
Trial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued until success, or until the practicer stops ...
Delegating trial and error
1. Introduction. Trial and error, an approach commonly used in problem solving, is frequently delegated. Pharmaceutical companies outsource drug development to contract research organizations, hedge funds hire researchers to mine data for profitable trading strategies, and governments task consultants with finding creative solutions to novel problems.
The Use of Trial and Error To Solve Problems
This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website.
Advantages and Disadvantages of Solving a Problem Through Trial and Error
Advantages and Disadvantages of Solving a Problem Through Trial and Error » E.L. Thorndike propounded the theory of trial and error. He believes that
trial and error problem solving Crossword Clue
Give us an answer to any clue and we'll show all the clues that share that answer. Search millions of clues. Wordplays has answers to Quick puzzles, General Knowledge puzzles, Cryptic Crossword Puzzles, and Variety puzzles.
Boosting of Thoughts: Trial-and-Error Problem Solving with Large
The reasoning performance of Large Language Models (LLMs) on a wide range of problems critically relies on chain-of-thought prompting, which involves providing a few chain of thought demonstrations as exemplars in prompts. Recent work, e.g., Tree of Thoughts, has pointed out the importance of exploration and self-evaluation in reasoning step selection for complex problem solving. In this paper ...
How To Use "Trial And Error" In A Sentence: Diving Deeper
By understanding the grammatical rules and the different parts of speech that "trial and error" can take on, you can confidently incorporate this phrase into your writing, effectively conveying the idea of learning through experimentation.

Trial and Error

Understanding the term

Characteristics of the Trial and Error Method

The Trial and Error Process

Theoretical Background

Trial and Error in Everyday Life

Learning New Skills

Technological Advancements

Advantages and Disadvantages

H3: Advantages

H3: Disadvantages

Example 1: Learning to Code

Example 2: Medicinal Drug Discovery

Enhancing the Trial and Error Process

Learn from Each Attempt

Embrace Failure

Problem Solving

Learning Objectives

PROBLEM-SOLVING STRATEGIES

PITFALLS TO PROBLEM SOLVING

Review Questions

Critical Thinking Questions

Personal Application Question

What is ‘trial and error’?

An Expert is Made by Trial and Error

“The only sure way to avoid making mistakes is to have no new ideas.” – Albert Einstein.

The Nature of Expertise:

The Role of Trial and Error:

Embracing Failure:

Interactive Learning:

The Importance of Feedback:

Persistence and Resilience:

1 thought on “An Expert is Made by Trial and Error”

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7.3 Problem-Solving

PROBLEM-SOLVING STRATEGIES

Additional Problem Solving Strategies :

Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Answers to Exercises

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Trial and error

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4 Main problem-solving strategies

Problem-solving stages

Initial theory in problem-solving

Problem-solving strategies

1. Algorithms

2. Heuristics

3. Trial and error

Pilot problem-solving

Getting your causal thinking right

The Edisonian Method: Trial and Error

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Rapid trial-and-error learning with simulation supports flexible tool use and physical reasoning

Kevin A. Smith

Associated Data

Human Results.

Model Results.

Model Comparisons on Virtual Tools.

Validation on Novel Levels.

Model Limitations.

Related Cognitive Systems.

Virtual Tools as an AI Challenge.

Future Empirical Directions.

Supplementary Material

The Use of Trial and Error To Solve Problems

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