The natural scale of a thing

[The attempt to measure the distance across levels feeds #pseudoscience #badscience #fakeScience,@John Ioannidis and @Christian List]

Everything can be characterized by two properties:
1. Intrinsic qualities and relationships with other things (extrinsic qualities).
2. The intrinsic qualities of a thing, best characterize the thing, if they are as different as possible, i.e. orthogonal.

3. The number of orthogonal qualities is the dimensionality of the thing.

A thing's relationship with other things provides a scale with which to analyze the thing

Everything has a natural scale.

There are two characteristics that define the scale of a thing:

1. The dimensionality of the things at that scale; and

2. The hierarchical relationship between different levels.

A higher level thing has a lower dimensionality than the dimensionality of the lower level things that it is related to.

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.

Seems axiomatic. Do I need a proof?

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.

Perhaps it is better to define the scale with a graph, social network.

Participation in two identities at the same scale is impossible

1. I can belong concurrently to different identities at different scales, but not multiple identities at the same scale.
2. The reason is that there is no conflict between different scale identities, they are disjoint.
3. Yet if I open my boundary, create an edge between nodes at different scales I will create a conflict.

That is the definition: If you have an edge you are at the same level.

Here is an example:
1. If I participate in a local network, my family, can I concurrently participate in a different family?
2. no! but I can participate in different scale identities.
3. I am both a member of my family and a member of my community.