2 March 2024

Heuristics is a technique or method that is used to increase the knowledge of the human being through exploration and creative problem solving. The word heuristic comes from the Greek ‘εὑρίσκειν’ which means the art of finding, inventing and making discoveries.

This discipline is based on creativity, divergent or lateral thinking and personal or other experience to find the most viable solution to the problem. Heuristics apply to any area of ​​work related to invention and discovery. Keep reading and discover how to increase knowledge applying the heuristic method.

## What is the heuristic method?

This method of knowledge consists of using exploratory strategies and rules of thumb to arrive at a feasible solution. Especially in situations where finding a perfect or comprehensive solution is difficult or expensive in terms of time and resources.

The heuristic also proposes specific tactics or informal procedures for generating solutions and developing hypotheses.

Unlike other methods of knowledge, heuristics is not based on a thorough or complete examination of the problem. Rather, it is based on successive Approximations, considering the similarities of the case with other successful investigations. This method is useful to discard some aspects and work only on the possible solutions, and go directly to the resolution of the problem.

The heuristics method was popularized by the mathematician George Pólya, who proposed a four-step method of solving problems:

• Make a visual representation: draw a schematic of the problem to better understand it visually.
• To reason reverse of the problem to find its solution, devise a plan.
• study an example concrete if the problem is abstract, carrying out the plan.
• Review what has been done, what worked and what did not.

## What is heuristics in mathematics?

In the area of ​​mathematics, heuristics is used to describe methods for solving problems and equations, in order to find the concrete mathematical means in order to obtain a correct solution. Sometimes teachers teach heuristics, other times students discover them on their own.

In any case, these are usually more difficult than simple mathematical operations. Instead of using only simple formulas and basic operations like addition, subtraction, multiplication, and division, using the heuristic method in mathematics, students can use more visual media. In this case they use graphs and diagrams, problem modification and other unconventional methods in order to find the correct answer.

Other examples may include the use of a rule of thumb, an educated guess, intuitive judgment, stereotypes, or common sense. However, the most basic mathematical heuristics is considered trial and error.

In addition to problem solving as a strategy, which we will talk about later, mathematics teachers already use a series of heuristics in their classroom:

• The English acronym “FOIL” (first, outer, inner, last), which is used when developing algebraic expressions, is a widely used heuristic.
• It is also widely used The English acronym “BEDMAS” (parentheses, exponents, division, multiplication, addition, subtraction), which is used to solve an equation with multiple operations.

### Problem resolution

It is a set of heuristic strategies in mathematics that consists of reducing the number of mental operations. It also minimizes the information processing steps that a learner or student does to solve a problem.

Some of the most common heuristic problem solving strategies are:

• Encode: Transform the problem into a more familiar or simple language, using symbols, diagrams, tables, graphs, etc.
• Organize: Sort and classify the information relevant to the problem, eliminating unnecessary or redundant data.
• To experience: try different methods or possible solutions, using trial and error, induction or deduction.
• Analogy: find a problem similar or equivalent to the one you want to solve, and use its solution as a model or guide.
• Explore: analyze the problem from different perspectives or points of view, looking for patterns, relationships, properties or principles that characterize it.
• auxiliary elements: add or modify some data or condition of the problem to facilitate its resolution. Some examples are: a variable, an equation, a geometric figure, etc.
• Divide the problem into parts: Break down the problem into simpler or more manageable subproblems, and solve them separately.
• Search for regularities: identify and take advantage of the properties or characteristics that are repeated or remain constant in the problem.
• Assume problem solved: Imagine that you have the solution to the problem and work backwards to find the steps that led to it.

## What is heuristics in art?

In the artistic field heuristic can be understood as the use of creative, intuitive or experimental strategies. These are useful to generate or discover new forms of expression, communication or artistic representation.

Heuristics in art implies the ability to invent, innovate, explore, and solve problems. This is done through imagination, divergent thinking, analogy, experimentation, fiction, and imitation. In fact, not based on fixed rules or formal methods, but in the process of searching for original, plausible and credible solutions that respond to the artist’s intentions, emotions and visions.

### Creativity and culture

The creativity and culture are two fundamental elements for the development of heuristics in art. Below we summarize the actions that each of these heuristic strategies includes to enhance artistic creation.

• Creativity: implies the ability to invent, innovate, explore and solve problems. Here imagination, divergent thinking, analogy, experimentation, fiction and imitation are used.
• Culture: refers to considering the set of values ​​and beliefs that make up the historical, social and personal context of the artist and the public.

Creativity and culture feed each other, since the culture provides the resources and the challenges for creativity, and this contributes to transform and diversify culture.

## What is heuristics in philosophy?

In philosophy, heuristics is a method or approach to the discovery of new conceptsideas or theories that is based on exploration and experimentation.

The heuristic is used in different fields of philosophy such as ethics, epistemology and philosophy of science. For example:

1. In the ethicsheuristics can serve to guide moral decisions when there are no absolute principles or clear rules to follow.
2. In the epistemologyheuristics are used to answer questions about how we obtain knowledge and how we can overcome obstacles in the search for truth.
3. In the philosophy of science, heuristics are used to deal with the uncertainty and complexity that define scientific inquiry. New experiments are done and new theories are created in areas where understanding is not easy or there is a lack of information.

### cognitive bias

Heuristics in philosophy can be useful to help the artist to generate creative and innovative solutions. However, you can also file certain limitations that can lead to misprocesses and cognitive biases.

A cognitive bias occurs when the practical strategies or methods used to generate knowledge may be inaccurate, incomplete, or irrational. It is also presumed a cognitive bias when the basis of the investigation is supported only by approximations or assumptions.

## What is heuristics in science?

Heuristics constitutes, in the strict sense, a true theory of the development of science. Its strategy in this area is based on the experienceobservation, analogy, divergent thinking, fiction and imitation.

The heuristics as a scientific discipline, is applied to various areas of knowledge, such as physics, mathematics, biology, engineering, psychology and philosophy of science. In all these fields, the heuristic method seeks to provide answers to problems through innovative and simple methods.

### Logical Reasoning and Investigation

The heuristic strategies of logical reasoning and research in science are similarly applied to other areas.

It’s all about using practical, creative or intuitive methods to investigate and discover solutions to scientific problems. At the same time, it is used to create logical principles and rules to analyze and evaluate the arguments and the conclusions that are drawn.

For optimal results, it seeks to combine creativity and innovation with coherence and validity, in order to avoid cognitive biases or errors that can occur when using heuristics inappropriately.