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VI) Scale -- hierarchy and distance metrics

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VI) Scale -- hierarchy and distance metrics

Judgements are phase transitions, they bring us to higher levels of representation.

Scale -- hierarchy and distance metrics


I wrote the following:
https://ashlag-cause-and-kook-affect.blogspot.com/2018/10/the-natural-scale-of-thing.html

Here is a snippet:
There can be no metric to measure the distance between two things across levels

Why not?  Well simply:
1. A metric to measure distance between two elements requires that the elements be in the same dimension
2. By comparing two elements at different levels we are reducing the higher dimensional object to the lower dimension, this will collapse the information in the system.

Here is an example:
1. Assuming I want to measure the health benefits of eating a balanced diet.
2. At a high level I can gather data in a three dimensional space, carbs, protein and fat, macro nutrients.
3. I can also gather data at a lower level that is in a higher dimensional space, we can breakdown protein to amino acids.
4. Now, if I want to compare the distance between two peoples diet, and measure their protein consumption.
5. What is the distance between a macro measure of protein and a micro measure of amino acids?
If I were to try, I could randomly/evenly distribute the macro content across all amino acids.
But that would be false.

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