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Abstraction

math Maturity 13-18

You can think about groups.

JerryFelix.JPG
JerryFelix.JPG
A cat and a ball are things. You can call them all "things." This helps us talk. It makes big ideas easy. It is like a game. Do you like to group things?

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Think about a leather ball.

JerryFelix.JPG
JerryFelix.JPG
You can call it a "ball." This is an abstraction. It means you look for what is the same.

You leave out the small details. You do not need to know it is leather. You only need to know it is a ball.

Conceptual graph for A Cat sitting on the Mat Hi-res.png
Conceptual graph for A Cat sitting on the Mat Hi-res.png
This helps us group things. We can group many cats into one idea.

People have done this for a long time. It helps us use words to talk. It makes big ideas easy to share.

It is a way to see patterns. This helps us understand our world.

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Imagine you see a leather soccer ball.

JerryFelix.JPG
JerryFelix.JPG
You could talk about its color or its feel. But you can also just call it a "ball." This is called abstraction. Abstraction is a way to find a big idea from small details. You pick out only the parts that matter for your goal. When you think of a "ball," you leave out the leather. You only keep the parts that make it a ball. This helps us group many things together. Many different cats can all fit into the idea of a "CAT."
Conceptual graph for A Cat sitting on the Mat Hi-res.png
Conceptual graph for A Cat sitting on the Mat Hi-res.png

Humans have used this skill for a very long time. Experts think it grew between 50,000 and 100,000 years ago. It helped us build language. Language lets us use words to map many experiences. Long ago, people in Iraq used clay tokens to count things. They used marks on clay to stand for numbers. This was a way to turn real items into ideas. Abstraction helps us turn many facts into one big theory.

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Have you ever looked at a leather soccer ball and thought only of the word "ball"?

JerryFelix.JPG
JerryFelix.JPG
When you do this, you are using a special mental tool called abstraction. Abstraction is the way we find a big, general idea from many small details. To make an abstraction, you filter out information that does not matter for your goal. For example, if you want to talk about a ball, you ignore the leather. You only keep the parts that make it a ball. This helps us group many different things together under one name.
Conceptual graph for A Cat sitting on the Mat Hi-res.png
Conceptual graph for A Cat sitting on the Mat Hi-res.png

This process works like a way of squeezing information down. We call this compression. You can take many different pieces of data and map them to one single idea. Think about all the different cats in the world. Each cat looks unique, but they all fit into the single idea of a "CAT." You can even move through levels of abstraction. You might start with a specific cat sitting on a mat. Then you move to the idea of a mammal. Finally, you reach the even larger category of an animal.

JerryFelix.JPG
JerryFelix.JPG

Humans have used this skill for a very long time. Scientists believe this way of thinking developed between 50,000 and 100,000 years ago. It likely grew alongside human language. Language helps us turn many experiences into short sounds or words. In the past, people in Iraq used abstraction for counting. Between 3200 and 3000 BCE, they used clay tokens to represent items like grain. Eventually, they used marks on clay tablets to stand for numbers. This turned physical objects into abstract ideas for keeping records.

Many famous thinkers used abstraction to change how we see the world. Francis Bacon wrote a book called Novum Organum in 1620. He encouraged people to collect specific facts to build general theories. This was different from older thinkers like Aristotle or Thales. Thales lived before 546 BCE and believed everything was made of water. He used a different way of thinking to move from water to ice or snow. Later, Isaac Newton used abstraction to explain how planets move. He built his ideas from the work of people like Copernicus and Kepler.

Abstraction is useful because it helps us organize our lives. It lets us compare things that are not the same. For example, money is an abstraction that lets us compare the value of different objects. We also use it in architecture to design buildings. We can think about the idea of a building before we ever lay a brick. While a physical rock exists in a specific place, an idea like "redness" does not. Ideas can exist in many places and times all at once. This makes abstraction a powerful way to understand everything around us.

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Abstraction is a mental process used to create general rules and concepts from specific examples. It involves taking many different, detailed things and finding the common threads that connect them. When you abstract, you are essentially creating a common noun that can describe a whole group of related things. This allows us to organize the world into categories, fields, or groups. By using abstraction, we can move away from the literal, concrete details of a single object to understand broader principles. It is a fundamental way that humans process information and communicate complex ideas.

To perform abstraction, a person must use a process of filtering. This means selecting only the aspects of an object or phenomenon that are relevant to a specific purpose. For instance, if you are thinking about a leather soccer ball, you might abstract the concept of a "ball." To do this, you focus on general attributes like shape and behavior. You intentionally exclude details like the leather texture or the specific color. This process is often described as compression. It maps many different pieces of constituent data onto a single piece of abstract data.

Conceptual graph for A Cat sitting on the Mat Hi-res.png
Conceptual graph for A Cat sitting on the Mat Hi-res.png

There are different ways to view the structure of these ideas. One way is through the type-token distinction. In this view, a "type" is an abstract concept, such as a "ball," while a "token" is a specific instance, such as "that leather soccer ball." Another way to view it is through levels of abstraction. You can move from neural impulses to basic shapes, then to specific objects like a cat, then to semantic ideas like "CAT," and finally to broad categories like "mammals." This creates a chain where each step excludes more specific detail to reach a higher level of generality.

JerryFelix.JPG
JerryFelix.JPG

Anthropologists and sociologists believe that abstract thinking is a key trait of modern human behavior. It is thought to have developed between 50,000 and 100,000 years ago. This development was likely closely tied to the rise of human language. Language allows us to map an infinite variety of experiences onto short noises or words. Max Müller even suggested that there is a deep relationship between metaphor and the development of abstraction in thought. This ability to think in symbols changed how humans interacted with their environment.

History shows a shift in how thinkers used abstraction. In the ancient world, philosophers like Thales used deduction. Thales believed everything came from water, and he specified this general idea into forms like ice or fog. However, in 1620, Francis Bacon promoted induction in his book, "Novum Organum." He encouraged scientists to collect specific facts first and then use induction to create general theories. This approach helped early-modern scientists like Isaac Newton. Newton derived the motion of planets by building on the work of Copernicus and Kepler. Galileo also used abstraction by compressing the results of one hundred experiments into the law of falling bodies.

Abstraction is also visible in how humans handle physical materials, such as money or accounting. Money is an abstraction that draws away from the specific value of items to allow different objects to be compared. In ancient Iraq, between 3200 and 3000 BCE, people used clay tokens to represent items like grain. Eventually, they began making marks on the outside of clay containers to represent these counts. These marks acted as material abstractions of a counting process. This eventually evolved into the use of clay tablets for record-keeping. This allowed people to communicate quantities without needing the physical items present.

Finally, abstraction helps us understand the different ways things exist. Physical objects, like rocks, occupy a specific place and time. In contrast, abstract properties, like the color red, do not exist in a specific location. An abstract idea can be "multiply instantiated," meaning it can exist in many different places and times at once. This makes abstraction a vital tool for science, philosophy, and daily life. It allows us to move from the messy details of the world to the clean, organized laws of logic and mathematics.

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File:Conceptual graph for A Cat sitting on the Mat Hi-res.png
Conceptual graph for A Cat sitting on the...
File:JerryFelix.JPG
JerryFelix.JPG
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