Why Does Nature Branch into Threes and Fours: Optimizing "Surfaces" Instead of Wires

"Nature abhors waste." This intuition arises when observing blood vessels, nerves, tree branches, plant roots, and coral structures. Using as little material as possible to reach as far as possible, to as many places as possible——. For many years, scientists have tried to explain this intuition through the mathematics of "shortest wiring" to describe the networks of life.

However, this mainstream model has stumbled repeatedly. The branching predicted by the theory tends to favor "basic bifurcation." Yet, in reality, nature commonly exhibits structures with trifurcations, quadrifurcations, or branches extending at "irregular angles." Anyone who has ever sketched a tree would immediately argue, "It's not just bifurcations." Phys.org

The Limitations of Viewing as "Wires"

The study introduced by Phys.org (based on an RPI press release) bluntly identifies the cause of this impasse. It suggests that we have been thinking of natural networks too much as "thin lines (wires)." Real blood vessels and nerves are not thread-like lines. They have thickness, surfaces, and at branching points, these surfaces must connect smoothly——in other words, they are "three-dimensional objects" rather than "one-dimensional." Phys.org

This shift in perspective is significant. The concept of "Steiner trees (Steiner graphs)," a representative of wire minimization, imposes strong constraints on the degree of nodes (how many branches intersect) and branching angles. In contrast, empirical data repeatedly observe high-degree nodes (e.g., degree 4 corresponding to trifurcations), branches extending at right angles, and asymmetric branching angles. The Nature paper also acknowledges "systematic deviations" from traditional predictions (length minimization, volume minimization) as a fact, arguing that they stem from ignoring the "3D shape cost." Nature

The Key is "Minimal Surfaces" —— The Mathematics of String Theory Comes into Play

Enter the mathematics derived from string theory. String theory is famous as a "candidate for the ultimate theory of the universe," but it remains "unverified" in terms of experimental validation. However, the mathematical tools developed there are extremely powerful, particularly the techniques for dealing with "minimal surfaces." The research team reinterpreted the branching of biological networks as "surface optimization," showing that this minimal surface framework remarkably reproduces the characteristics of branching. Phys.org

The point is that the "cost of nature" is not merely the "length of lines," but includes the "geometric cost of smoothly connecting as structures with surfaces." The Nature paper explains that this surface minimization can be mapped onto high-dimensional Feynman diagrams (a computational technique in string theory), allowing the handling of numerically intractable optimization problems with string theory tools. Nature

What Can Now Be Explained: Trifurcations, Quadrifurcations, and "Orthogonal Sprouts"

What makes this theory intriguing is its ability to naturally produce what is commonly found in nature.

• High-degree Branching (e.g., Trifurcations, Quadrifurcations)
  Traditional models tend to focus on bifurcations, but surface minimization allows for the stability of high-degree nodes. The Nature paper describes predictions where locally tree-like networks transition to configurations "unexplainable by length minimization" under certain conditions, resulting in phenomena like trifurcations. Nature

• "Orthogonal Sprouts"
  The Phys.org article introduces that this theory predicts branches (sprouts) resembling "dead-end thin sprouts," which are often observed in nerves and plants. It further states that in the human brain, 98% of such orthogonal sprouts terminate at synapses (connection points), interpreting it as a mechanism for local exploration with minimal material cost. 98% of such orthogonal sprouts terminate at synapses (connection points), interpreting it as a mechanism for local exploration with minimal material cost. Phys.org
  
  The Nature paper also includes the prediction that orthogonal sprouts are prevalent in real networks and contribute to functionality (synapse formation in the brain, nutrient access in plants and fungi). Nature
  
  
  
  

How Plausible Is It: Verified with Six Types of "Real Data"

To the question, "The theory is understood, but what about the data?" the article is quite specific. The research team used high-resolution 3D scans to compare six types of networks: **human nerves, fruit fly nerves, human blood vessels, tropical trees, corals, and Arabidopsis**, reporting that the branching patterns consistently align closely with the predictions of "surface minimization." Phys.org

Of course, living organisms are not made of physics alone. There are developmental programs, chemical cues, and multi-objective constraints like fluid efficiency. In fact, the Phys.org article mentions that "real networks can be up to 25% longer than the absolute minimum predicted by theory," suggesting that the theory is better positioned as arobust geometric criterion that emerges within multi-objective optimization rather than as the "sole determining factor of everything." Phys.org

It's Not About "String Theory Being Right" —— But Its Value Is Significant

A common misunderstanding here is the leap to "string theory explaining biology = string theory being the correct answer for the universe." The Phys.org article itself clarifies that while string theory remains unverified as fundamental physics, the mathematics developed there has "practically proven effective." Phys.org

In other words, this should be viewed as asuccessful example of "repurposing mathematical tools" rather than a statement on the "truth of physical theories."

Future Applications: Towards 3D Printed Tissues, Urban and Transport Networks

RPI/Phys.org also touches on applications. Understanding the design principles of branching could provide insights into designing 3D printed tissues with blood vessels or more efficient transport, piping, and urban infrastructure. The way biological systems "connect" is directly linked to how engineering systems can be "connected." Phys.org

Reactions on Social Media (Summary of Visible Trends)

At present, the spread of the article is accompanied by both "amazement" and "caution."

• Official Posts Highlight the Surprise of "String Theory Geometry Predicting Branching"
  Phys.org's official X emphasizes the point that the geometric principles of string theory can predict the complex branching of biological networks. X (formerly Twitter)
  Similarly, Phys.org's LinkedIn post highlights that "it can be explained not by one-dimensional optimization but by three-dimensional surface minimization." LinkedIn

• Comments Section Also Sees Reflexive Criticism of "String Theory Words"
  On LinkedIn, discussions sometimes veer off into "cosmology (such as multiverse)" associated with string theory, with comments challenging the "definition of 'universe.'" This suggests that the main focus of the research (geometric optimization of biological networks) can easily get mixed up with the cosmological image of string theory. LinkedIn

• "For Now, Just Share" Type of Spread
  Individual posts introducing the article via Newswise can also be found, showing signs of circulation due to its topicality. X (formerly Twitter)

• The Main Page of Phys.org Has No Comments at the Time of Article Release
  At least at the time of retrieval, it shows "Load comments (0)," suggesting that discussions may be flowing to the social media side. Phys.org