Ideal vs Real Solutions: Understanding the Differences and their Implications

## Introduction

In every field of study, whether it be science, mathematics, or even philosophy, there are often idealized models or solutions presented to help understand and explain the workings of the world. These ideal models are perfect in every sense, and they provide a simple, easy-to-understand explanation of how things work. However, in reality, these models often fall short, and it is necessary to consider real-world solutions that are more applicable and practical. In this blog post, we'll explore the differences between ideal and real solutions, and the implications of each.

# Ideal vs Real Solutions

## Ideal Solutions

Ideal solutions, as the name suggests, are the perfect answer to a problem or the ideal way of doing something. These solutions are often used in the field of mathematics to describe perfect mathematical models, or in physics to explain how objects behave in a vacuum. Ideal solutions are typically simple and easy to understand, making them great tools for explaining complex phenomena.

For example, in physics, the ideal gas law is an equation that describes the behavior of an ideal gas. The ideal gas law assumes that the gas molecules are perfectly spherical, have no volume, and are in constant random motion. Although these assumptions may not reflect the reality of a real gas, the ideal gas law provides a simple explanation of the behavior of gases and is widely used in many applications.

Ideal solutions are also used in the field of engineering. For example, in civil engineering, an ideal beam is one that is perfectly straight, uniform, and free from any imperfections. Ideal beams are used as models to understand the behavior of real beams, which often have imperfections and deviations from the ideal model.

Ideal solutions have several advantages, including:

1.     Simplicity: Ideal solutions are simple and easy to understand, making them a great tool for explaining complex phenomena.

2.     Predictability: Ideal solutions provide a predictable outcome, which can be useful for planning and decision-making.

3.     Consistency: Ideal solutions are consistent and unchanging, providing a reliable reference for comparison and analysis.

4.     Ideal for teaching: Ideal solutions are often used as teaching tools, helping students to understand complex concepts in a simple and straightforward manner.

## Real Solutions

In contrast to ideal solutions, real solutions are practical and applicable to the real world. Real solutions take into account all the complexities and imperfections of the world and provide a more accurate and relevant answer to a problem.

For example, in civil engineering, a real beam will take into account the variations in the strength and stiffness of the material, as well as the presence of cracks, defects, or other imperfections. By considering these real-world factors, engineers can design beams that are more accurate and reliable in their behavior.

In the field of economics, real solutions often involve compromises and trade-offs. For example, a government may aim to achieve a balance between economic growth and environmental protection, rather than seeking the perfect solution for either one.

Real solutions have several advantages, including:

1.     Relevance: Real solutions take into account the complexities and imperfections of the real world, making them more relevant and applicable.

2.     Accuracy: Real solutions provide a more accurate answer to a problem, taking into account all the relevant factors and variables.

3.     Flexibility: Real solutions allow for trade-offs and compromises, making them more adaptable to changing circumstances.

4.     Practicality: Real solutions are practical and can be implemented in the real world, providing tangible benefits.