From the Platonic to the real

Continuing this post, the following from the same issue of Nature Communications, akin to the tenets of the MHC, which are at question. I've said much the same in the real/false reason thread, but not in these scientific terms.

"The appeal of scale-free networks came from complexity science—an umbrella term for many research directions trying to find hidden laws in the complex world around us, and simple rules to explain them. One such idea is emergence—the phenomenon that a multitude of interacting units can as a group behave in ways not predictable from the behavior of the units alone. […] Sometimes emergent patterns can be scale free, meaning roughly that they are organized similarly at different (e.g., spatial) scales [...with] power-law degree distributions. […] A final concept of complexity science that is important for understanding the success of scale-free networks is universality. Emergent patterns are often consequences of basic symmetries and behavioral rules of the constituents. […] This means that rather different systems can share emergent properties […] that the scale-freeness of networks is such a universal phenomenon."

"In the Platonic realm of simple mechanistic models, extrapolated to infinite system size, the concepts of emergence, universality and scale-freeness are well-defined and clear. However, in the real world, where systems are finite and many forces affect them, they become blurry. If you meditate in front of a broccoli, you will notice that even though the same principles of organization occur at different scales, there are also differences—you can guess how zoomed-in a picture of a broccoli is. This blurring makes complexity concepts less applicable to the real world. […] Critics made the point that although the degree distribution is scale free, the actual networks are not. They pointed out that power-law degree distributions and the preferential attachment mechanism were already discovered. Even more polarizing, however, was the claim that degree distributions rarely follow power laws."

From the article in the previous post:



"These results indicate that genuinely scale-free networks are far less common than suggested by the literature, and that scale-free structure is not an empirically universal pattern. […] These results demonstrate that scale-free networks are not a ubiquitous phenomenon, and suggest that their use as a starting point for modeling and analyzing the structure of real networks is not empirically well grounded. […] The variation of evidence across social, biological, and technological domains is consistent with a general conclusion that no single universal mechanism explains the wide diversity of degree structures found in real-world networks."