Coordinate-free
"Coordinate-free" means we don't need to use numbers to describe where something is or how it looks. Instead, we can use things like shapes, patterns, or objects to explain it.
Imagine we have a puzzle with different shapes and colors, and we want to describe how it looks. We could say things like "there's a red circle in the middle", "there are two green squares on the sides", or "there's a yellow star on top". We don't need to say things like "the circle is at coordinate (3,3)" or "the squares are at coordinates (1,1) and (5,1)", which means using numbers to explain where things are.
Similarly, we can use shapes and objects to explain how something works or how it changes over time. For example, if we want to describe how a pendulum swings back and forth, we can use a diagram of a pendulum instead of a graph of measurements (which is using numbers).
Overall, using non-numerical descriptions like shapes and patterns can be simpler and more intuitive, and it doesn't require us to use specific units or scales of measurement. This is what it means to be "coordinate-free".
Imagine we have a puzzle with different shapes and colors, and we want to describe how it looks. We could say things like "there's a red circle in the middle", "there are two green squares on the sides", or "there's a yellow star on top". We don't need to say things like "the circle is at coordinate (3,3)" or "the squares are at coordinates (1,1) and (5,1)", which means using numbers to explain where things are.
Similarly, we can use shapes and objects to explain how something works or how it changes over time. For example, if we want to describe how a pendulum swings back and forth, we can use a diagram of a pendulum instead of a graph of measurements (which is using numbers).
Overall, using non-numerical descriptions like shapes and patterns can be simpler and more intuitive, and it doesn't require us to use specific units or scales of measurement. This is what it means to be "coordinate-free".
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