Dilution.
This is my first real idea. Here we go.
Take the image of a circle. Its motion through space should be fairly constant. When you look at it, you see that it is a circle.
Or, take any image. It doesn't matter. Then make it conceptually blurry. Not physically blurry. You can see the image, and it looks the same, but the way it is processed by mathematical functions changes according to some rule set. In this example, the points on the image are physically next to each other like in the original object, but not mathematically next to each other.
For example, in the original image, a red pixel will be next to a yellow pixel. But, if you look at them mathematically, they will be many units apart. They have causal linkage but not direct linkage.
After randomizing the mathematical location of each pixel in the image without changing its relationship to itself, you can create another graph with the pixels at their mathematical location but not their physical location. Then you can map the relationships between pixels using lines.
This is a dilution. The graph that is created from a causal linkage mapped over a mathematical spread of points that are not spatially related to each other in any way.
How can we use this?
It allows the mapping of a dataset with one sequential property and any number of non-sequential properties, while maintaining the representation of each.
A physical example of a dilution is a puzzle. Actually, that's all it is. But, in dilution, the puzzle is both put together and not at the same time. The graph of this function will look like a web connecting each puzzle piece to the next without connecting them spatially.
Analyzing this graph can give us some useful information about the nature of the puzzle.
That's all I can think of right now. Since math is a big field, and many, many very smart people have been creating new ideas for millennia, my concept of dilution has probably been thought of many times over. All I can say for myself is that I have not heard of this mathematical function before.
Which is not saying much.
Take the image of a circle. Its motion through space should be fairly constant. When you look at it, you see that it is a circle.
Or, take any image. It doesn't matter. Then make it conceptually blurry. Not physically blurry. You can see the image, and it looks the same, but the way it is processed by mathematical functions changes according to some rule set. In this example, the points on the image are physically next to each other like in the original object, but not mathematically next to each other.
For example, in the original image, a red pixel will be next to a yellow pixel. But, if you look at them mathematically, they will be many units apart. They have causal linkage but not direct linkage.
After randomizing the mathematical location of each pixel in the image without changing its relationship to itself, you can create another graph with the pixels at their mathematical location but not their physical location. Then you can map the relationships between pixels using lines.
This is a dilution. The graph that is created from a causal linkage mapped over a mathematical spread of points that are not spatially related to each other in any way.
How can we use this?
It allows the mapping of a dataset with one sequential property and any number of non-sequential properties, while maintaining the representation of each.
A physical example of a dilution is a puzzle. Actually, that's all it is. But, in dilution, the puzzle is both put together and not at the same time. The graph of this function will look like a web connecting each puzzle piece to the next without connecting them spatially.
Analyzing this graph can give us some useful information about the nature of the puzzle.
That's all I can think of right now. Since math is a big field, and many, many very smart people have been creating new ideas for millennia, my concept of dilution has probably been thought of many times over. All I can say for myself is that I have not heard of this mathematical function before.
Which is not saying much.
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