Religions of the world describe the same world, therefore are at essence the same belief with different conditions imposed upon it. At some level, they all believe that there is something more than meets the eye, but it follows the rules of the universe not of humanity, so we need to focus our minds on it instead of ourselves for once.

When described that way, religion reveals an immediate utility. Humanity struggles with its half-computer half-animal nature and frequently falls into solipsism because we know the world through our minds, therefore confuse our minds with the world, and assume the world is a subset of our ideation not the other way around.

When we flip that around, we start to see the basis of religion: pattern recognition beyond the visible. This means that we see that there are causes which are not physical, but informational, therefore appear everywhere without having to be physically forced by an actor or deity.

Sometimes life reveals these subsurface patterns in such a way that we can see the logic behind how the world works:

Flagellar undulations make stripe patterns in space-time, generating waves that travel along the tail to drive the sperm and microbes forward.

Alan Turing is most well-known for helping to break the enigma code during WWII. However he also developed a theory of pattern formation that predicted that chemical patterns may appear spontaneously with only two ingredients: chemicals spreading out (diffusing) and reacting together. Turing first proposed the so-called reaction-diffusion theory for pattern formation.

Although not yet proven by experimental evidence, these patterns are thought to govern many patterns across nature, such as leopard spots, the whorl of seeds in the head of a sunflower, and patterns of sand on the beach. Turing’s theory can be applied to various fields, from biology and robotics to astrophysics.

When we scatter chemicals, they naturally spread out to fill every area, but when they interact, this causes a wave to appear in their shapes. This basic structure can then be replicated easily anywhere curved lines are needed through the opposing tendencies of matter to both react and diffuse.

On a numerological level, this is logical: a growing heap of numbers, when interacting with other things, enters into a kind of shuttle pattern that will produce curves. The opposing forces do not synthesize so much as fall into a balance like an alternating series of compromises that favor one side and then the other.

Another pattern emerges through the power law which governs linear expansion:

Relationships obeying power laws appear as straight lines on log–log plots since the prior equation becomes log(y)=k log(x)+log(a) upon logarithmic transformation which is in the same form as the equation for a line. Unlike fractals which deal with self-similar geometrical objects, power laws characterize scale invariance of multivariate relationships or frequency distribution for descriptive attributes of geographic phenomenon.

Power law relationships and the rank-size rule are identical in principle to Zipf’s law – a rank-size relationship for word frequency in texts – and the Pareto distribution, a power law distribution of allocation of wealth. Stochastic growth models involving positive feedback (i.e., ‘the rich get richer’) and self-organized criticality have been posited to explain power law distributions; however process mechanisms continue to be debated and investigated.

With a power law distribution, there is no characteristic scale (size) for the phenomena under investigation – it is ‘scale-free’. This contrasts with the normal, bell-shaped distribution for which the mean can be interpreted as the characteristic scale.

Contrast this to the normal distribution, a pattern that shows up in any single measurement of a trait in a group:

Normal distribution, also called Gaussian distribution, the most common distribution function for independent, randomly generated variables. Its familiar bell-shaped curve is ubiquitous in statistical reports, from survey analysis and quality control to resource allocation.

The graph of the normal distribution is characterized by two parameters: the mean, or average, which is the maximum of the graph and about which the graph is always symmetric; and the standard deviation, which determines the amount of dispersion away from the mean. A small standard deviation (compared with the mean) produces a steep graph, whereas a large standard deviation (again compared with the mean) produces a flat graph.

The infamous “bell curve” shows up in everything. Assess the height of everyone in a room and the pattern of numbers will form a normal distribution. This shows a concentration around a target range, with enough variation that there is always internal sorting, which avoids repetition or randomness.

Do we see the divine in such things? It may simply be logic: this universe is designed to forever create conflict that refines its parts into greater degrees of complexity. However, whatever invented that clearly has a farther-reaching intelligence, whether conscious or not, than humanity.

Tags: normal distribution, power law, reaction-diffusion, religion