https://ashlag-cause-and-kook-affect.blogspot.com/2018/10/the-natural-scale-of-thing.html
https://mobile.twitter.com/normonics/status/1092827181263265792
Quick GMO complexity lesson:
A central challenge in complexity studies is understanding how microscopic properties and behaviors flow upwards in scale and produce macroscopic behaviors
So we could define a measure of a network, cluster. Different scale clusters, incorporate lower level clusters. Lets say we create a node that has edges to all the members of a group. What is the distance between that node and a member of the group? However, I think that node would be at the lower level. Seems like a nonsensical question. Since all members are connected equally. But if they are connected to varying degrees....Then it would make sense. I would be asking what is the membership quality of this particle in the group. But that is still a different question that: what is the distance between this particle and the group...in this case the node has collapsed to the lower level. How do I know? Because I connected it to the lower level via an edge!
[What would the law of large numbers say about levels...]
https://transportgeography.org/?page_id=6164
Hierarchy (h). The exponent of the slope for the power-law line drawn in a bi-log plot of node frequency over degree distribution. Networks characterized by strong hierarchical configurations, such as scale-free networks (few large degree nodes and many small degree nodes), often have values over 1 or 2. A value lower than 1 indicates the absence of scale-free properties and a limited hierarchy among nodes.
in truth Hierarchy seems to be a poor measure. Since a graph with very tight relationships between the nodes in local communities has a low 'h' since the average degree is even, but the relationships are very clear and produce well defined communities...
A better measure for me:
https://transportgeography.org/?page_id=6171
Transitivity (t). Also called clustering coefficient, it is the overall probability for the network to have adjacent nodes interconnected, thus revealing the existence of tightly connected communities (or clusters, subgroups, cliques). It is calculated by the ratio between the observed number of closed triplets and the maximum possible number of closed triplets in the graph. Another way calculating transitivity is to calculate the average clustering coefficient of all nodes. Complex networks and notably small-world networks often have a high transitivity and a low diameter. Because triplets are not the only way for looking at neighborhood density among nodes, this measure can be extended to cycles of length 4 and 5.
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what is the difference between attempting to measure the distance between to elements at the same level with different dimensionality vs. two elements at different levels?
Right now I think there is no difference.
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How Much Data Do You Need
https://arxiv.org/pdf/1802.05495.pdf
I am missing a reference to the difference scales of the data. So, a different version that we can answer: Given a data set, do we have enough observations to answer a question at a particular scale?
We may not have enough data to describe a student with 3 degrees of freedom, but if the data indicates that those 3 degrees can collapse to a single degree (they are highly correlated) then we do have enough data to answer the more abstract queries at the single degree of freedom scale.
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so, being practical. How many observations will you need depends on the distribution of the data. But we don't know a priori the distribution...but we do have a data set. So the question is:
Given a data set, do we have enough observations?
1. faddc the data set. determine the distribution type, two components, the number of clusters @ each scale and number of levels
2. based on (1) we can determine if we have enough data.
Basically the number of clusters at a particular level provide a dimensionality to the data in a normalized space (kinda Gaussian). And we have a rule of 10^d -- where d is dimension of data.
How does the structure of the levels answer the question...we need to answer (2) for each level and then say: with the data we can answer questions relevant for this level, however there is insufficient data to answer the questions at other levels.
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https://www.skepticalscience.com/weather-forecasts-vs-climate-models-predictions.htm
So if we measure a lower level fact, that exists in a high dimensional space it does not help us underside a higher level behavior. Unless we assume causative model which can only exist on the same level! -- maybe that is the point.
Also we need to assume a distribution, such as a normal/gaussian distribution. So we know how many observations we need.
Why can causation only exist on the same level? First, due to dimensionality mis-match it is not possible to measure distance between objects on different levels. Causation requires two objects to influence each other, relative to other objects in the space.
A simple example is trying to sort something in one-dimension based on two parameters. Sorting a group of people by height and hair color into a single row, does not work.
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Article in Scientific American sept. 2015
https://www.scientificamerican.com/article/what-einstein-really-thought-about-quantum-mechanics/
http://philsci-archive.pitt.edu/13311/1/LevelsRevised.pdf
Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. This paper proposes a unified framework for modelling levels. I give a general definition of a system of levels and show that it can accommodate descriptive, explanatory, and ontological notions of levels. I further illustrate the usefulness of this framework by applying it to some salient philosophical questions: (1) Is there a linear hierarchy of levels, with a fundamental level at the bottom? And what does the answer to this question imply for physicalism, the thesis that everything supervenes on the physical? (2) Are there emergent properties? (3) Are higher-level descriptions reducible to lower-level ones? (4) Can the relationship between normative and non-normative domains be viewed as one involving levels? Although I use the terminology of “levels”, the proposed framework can also represent “scales”, “domains”, or “subject matters”, where these are not linearly but only partially ordered by relations of supervenience or inclusion.
Levels: descriptive, explanatory, and ontological
Christian List
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deontology vs utilitarianism medical ethics and autonomous vehicles
Perhaps a better approach is to start with natural scale. And define that. Then check what the natural scale of public health is
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4778182/
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Interesting to think of utiliterianism as a method to provide equitable outcome
"For instance, under a utilitarian conception of equity, an increase in the provision of needed PMTCT services implies an improvement in equity of health outcomes. "
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5446714/
