Logarithmic mathematical scales represent orders of Magnitude or proportional relationships. A measure like IQ however is linear and only applies to humans, though. And while some of life is linear—
Intelligence is a complex and multifaceted emergence, and not unique to humans. IQ has been more of a shorthand for convenience anyway, not capturing the full picture of multiple types, such as spatial or naturalistic, of intelligence and does not apply to other organisms. I realize that some may consider one form or just a few forms of human biological intelligence to be superior. Human intelligence, though, is the conglomerate of the evolution of other intelligences, from a great tapestry. And I consider the total intelligence of our biological lives completely amazing.
Here I consider other existing constructs that exhibit types of intelligence -from a modern day multidimensional viewpoint, that includes but is not limited to linear processes. Cognition or mind is increasingly shown as a quantum cloud, rather than a sequential computer. Although, algorithms are becoming more advanced in order to fulfill and aid more advanced problem solving in nature. Conversely, there are situations in which the pure logic of sequencing is advantageous, such as optimizing physical properties.
A natural elegant logarithmic expression occurs in the beautiful nautilus. Quite remarkably, as the animal grows, it adds new chambered sections to its shell in a way that follows a logarithmic spiral. The result is an intricate structure that provides buoyancy and protection for the nautilus. And it’s known for its relative longevity.
This logarithmic spiral pattern is also found in various natural phenomena, including certain plants, galaxies, and hurricanes.The form represents optimal packing and energy efficiency. And in a way, this can be considered a form of organizational intelligence.
The mathematical equation that describes a logarithmic spiral is r = a * e^(bθ), where “r” is the distance from the center, “a” and “b” are constants, and “θ” is the angle.(1)(2)
Another important logarithmic related phenomenon in nature is the inverse concept of exponential growth or decay.
While not so obvious in physical structure as a logarithmic spiral, exponential growth and decay processes are fundamental in various natural systems and can be described using logarithmic functions. This is important such subjects as biology, physics, chemistry, economics, earth science and computer science. Logarithms have also been important to optimizing algorithms for example.
Also from computer science is Moore’s Law, concerning exponential growth or doubling of transistors on a microchip. Its relevance is changing because it is unidirectional for one particular property, while technologies and materials are upgrading. That’s another branch of the story! (3)
Relative growth or “allometry” of patterns in the different realms of nature varies, from symmetries to stripes. And there are many manifestations of cyclical growth or transformation from the lives of stars to the ebb and flow of life with the seasons. (4)
Another interesting candidate for consideration of intelligence: Efficiency.
Efficiency can apply to structure as mentioned before, extending to energy and energy usage. Here’s a general formula for electric power efficiency in kilowatts:
Efficiency (η)= Output Power / Input Power)×100%
The human system is of course far more complex than say a solar array.(5)
In various applications, the specific form of this equation may vary. For example, in the context of a heat engine, the efficiency can be expressed using the Carnot efficiency formula related to change in temperature. These are but slices or aspect layers of the whole.
Another interesting metric is magnetic flux Density (B), a measure of the strength of a magnetic field. It is also commonly referred to as magnetic induction. The formula for magnetic flux density considers magnetic force or magnetic flux in a given area.
Magnetic flux density is also related to field strength (H) and permeability (μ) of the material. Then, electron density (n) is typically defined as the number of electrons per unit volume.
Overall, electromagnetic and electronic potential, in the context of electrons in a system, may be very compelling when considering intelligent life, along with geometric and mathematical, physical and mechanical properties, and energy efficiency.
There are many facets of intelligence to consider when it comes to different forms of life, including humans, and especially those as yet unknown — in the solar system, galaxy and beyond. It’s necessary to consider different orders of magnitude and relativity of structure and multimodal function. Forms of life on Enceladus or one of thousands of exoplanets have common elements but different parameters. And the layers of life on Earth can be much better appreciated and understood as well.
- https://www.americanscientist.org/article/twisted-math-and-beautiful-geometry
- https://mathworld.wolfram.com/LogarithmicSpiral.html#:~:text=The%20logarithmic%20spiral%20can%20be,1997%2C%20pp.
- https://www.economist.com/science-and-technology/2023/12/13/jensen-huang-says-moores-law-is-dead-not-quite-yet
- https://www.nature.com/scitable/knowledge/library/allometry-the-study-of-biological-scaling-13228439/
- https://biologydirect.biomedcentral.com/articles/10.1186/1745-6150-8-31
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