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  • Makoto Shibuya

Magic Number 4

Geoffrey West and his team have discovered universal scaling laws that appear to govern our universe. These scaling laws seem to transcend domains that appear, on their surface, to be wildly diverse. West concludes that underlying networks are what explain these universal scaling laws. Furthermore, he found that many of the exponents follow a 1/4 power law:


"In biology, almost invariably, is a simple multiple of the number 1/4. So the number 4 seems to be a magic number that is constraining all of life around you." —Geoffrey West


I can't help but think that the number 4 constraining life is not magical but surprisingly logical with the right frame of reference.


To explain, I will reference the work of Buckminster Fuller.


The exponent of a power law represents the dimensionality of space in which the power law is observed.


Despite being trained to think about the world in three dimensions, Bucky Fuller proposed that the universe is structured in four dimensions. No, not the fourth dimension of time or a fractal dimension. The fourth dimension is tangible with properties like the other three.


Bucky Fuller observed that nature does not have a chemistry, physics, or biology department, yet somehow, everything in the universe was coordinating. He deduced that nature had an underlying system to coordinate everything. Similar to Geoffrey West, he concluded that there was a shared network underlying everything, but took one more step to physically model this network. He referred to the underlying network that he discovered as the Isotropic Vector Matrix (IVM). The IVM is a space-filling and scale-invariant network based on spherical, rather than Euclidian, geometry.

3 Dimensional Grid

Isotropic Vector Matrix (IVM)

So, what is the big difference?


Bucky Fuller's work shows that the universe does not use a Cartesian coordinate system of 3 dimensions at 90 degrees but rather a coordinate system based on 4 dimensions at 60 degrees. He argues that this difference is the root cause of some divergence between theoretical and practical mathematics.

This may be hard to visualize due to the way we have been taught to think about space, but it is actually very intuitive once you can visualize it. In simple terms, Cartesian space is often used to visualize physical space as an array of cubes that have 3 planes of reference, while the IVM is a collection of tetrahedrons that have 4 planes of reference.

3 Planes in Cartesian Space
4 Planes in IVM

Bucky believed, and I think sufficiently proved, that the structural module of the network that governs our universe is a 4-dimensional tetrahedron of energy events, not a 3-dimensional cube. This 4-dimensional network suggests why the power laws governing all of life invariably have an exponent constrained to this 4-dimensionality of space.

4 Planes in the IVM

I am not a physicist or mathematician, and I welcome all feedback regarding the 1/4-power law that appears to govern our lives.



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