ARCHAEOLOGY: Archaeological Find Suggests Civilizations Embraced Mathematical Thinking

"Evolutionary anthropology has long portrayed human ingenuity as emerging through a slow, linear progression: from early hunter-gatherer societies, through the ‘Iron Age,’ and onward to increasingly complex civilizations culminating in the modern day. 

However, recent evidence suggests that some of the earliest societies possessed far more sophisticated ways of understanding the world than evolutionary anthropologists have traditionally depicted.

The Earliest Vegetal Motifs in Prehistoric Art: Painted Halafian Pottery of Mesopotamia and Prehistoric Mathematical Thinking (Yosef Garfinkel & Sarah Krulwich, Journal of World Prehistory, 5 December 2025). The authors of this paper found striking evidence that early civilizations possessed a “complex” awareness of

symmetry, precise spatial division, and geometric sequencing as expressed in artistic forms. These findings were derived from painted pottery vessels from the Halafian culture in northern Mesopotamia.
While the authors describe their findings as “rather surprising”, intelligent design and young earth creation perspectives interpret this differently: humans were created with intelligence from the beginning, fully capable of symbolic thought, measurement, and artistry. The Halafian pottery bears witness not of a slow evolutionary climb from ignorance, but to an innate creativity and mathematical capacity endowed by the Creator from humanity’s beginning.

Garfinkel and Krulwich’s archaeological dig discovered precisely imprinted motifs depicting flowers, shrubs, branches, and trees, arranged in mathematically significant sequences. The authors describe these motifs as depicting repeating multiples of 4, 8, 16, 32, and 64, thereby “creating a mathematical series,” and note that the patterns were “meticulously executed.” They express surprise at the level of artistry involved, explicitly linking it to the mathematical precision the designs required. As they write:

“The depictions of flower petals in the geometric sequence of the numbers 4, 8, 16 and 32, as well as 64 flowers in another type of arrangement, point to arithmetical knowledge.”

From a secular archaeological perspective, the authors express surprise that such sophisticated Halafian vegetal motifs are dated to the seventh millennium BC: well before the evolutionary anthropologists estimate the rise of writing or advanced mathematics. Yet the evidence demonstrates that these early communities possessed not only aesthetic sensibility but also a clear awareness of mathematical structure. This finding challenges the evolutionary model of cultural development, which assumes a slow, linear accumulation of knowledge from primitive beginnings to modern complexity.

Mesopotamia is precisely where Scripture places the emergence of post-Flood human culture following the dispersion of Noah’s descendants (Genesis 10). Moreover, by the time of Noah, Scripture already records the use of precise mathematical measurements in God’s instructions for building the Ark (300 cubits long, 50 cubits wide, and 30 cubits high), making it clear that persons of that era routinely understood the meaning of numbers and standardized measurements (Genesis 6:14-16).

As Ecclesiastes 1:9 reminds us, “What has been will be again, what has been done will be done again; there is nothing new under the sun.” Human creativity has always been part of God’s design." 

CEH

Creation Moment 2/1/2026 - Geometry and zygotic genome activation

As thou knowest not what is the way of the spirit, nor how the bones do grow in the womb of her that is with child: even so thou knowest not the works of God who maketh all. 

Ecclesiastes 11:5

"The findings, published in Nature Physics, demonstrate that the geometry of the fertilized egg itself, i

ncluding its curvature and volume, acts as an “instruction manual” guiding asymmetric cell divisions, mitotic waves, and zygotic genome activation. 

This study by Mishra et al. (2026) builds on earlier research on

Drosophila which identified “geometry as a key organizer of mechanical force generation during morphogenesis.” However, this new study found even more detailed evidence that geometry also plays a role in the development of larger-scale processes in development, for example, coordinated cell divisions and embryo patterning.

This discovery offers a compelling glimpse into yet another example of the fine-tuned processes woven into nature and raises even more profound questions for evolutionary explanations of life’s origin, highlighting the remarkable precision and order that underlie living systems.

Geometry has long been recognized as playing a pivotal role in both biological development and cosmic organization. In particular, the repeating, scale-invariant patterns of fractals have received considerable attention in the literature as an underlying template for the structure of many organisms, including pineapples, sunflowers, fern leaves, and broccoli. These structures have been found to improve efficiency in resource distribution and to govern growth rules in these complex biological forms." 

CEH

Creation Moment 10/8/2025 - Interwoven Universe

And He is before all things, and by Him all things consist. Colossians 1:17

"Algebraic and Positive Geometry of the Universe: From Particles to Galaxies (Fevola and Sattelberger, Notices of the American Mathematical Society, September 2025 issue).
A Reflection on Design
In this article, mathematics researchers Claudia Fevola from Inria

Saclay and Anna-Laura Sattelberger from the Max Planck Institute for Mathematics in the Sciences, underscored the profound connection between physical observations and mathematics, emphasizing how elegantly mathematical frameworks can describe and predict physical phenomena. In their words:

“The relationship between mathematics and physics is profoundly symbiotic: mathematics provides the language and tools to describe and predict physical phenomena, while physics inspires the discovery and development of new mathematical concepts”.

The notion of ‘symbiosis’ highlights how the intelligibility of our universe has been interwoven into a language of numbers that enable predictability. 

--This directly contradicts the evolutionary concept of randomness and chaos. Instead, the comprehensibility and predictability of the universe suggest a pre-existing blueprint with logic, symmetry, and structure.
Q: But, where did this blueprint come from?" 

CEH

Creation Moment 9/4/2025 - Geometric Design of the Solar System

All things were made by Him; 

and without Him was not any thing made that was made. 

John 1:3

"Example of geometric design in the solar system arises from the mean orbits of our innermost two planets, Mercury and Venus. 

Their mean orbital radii are 0.387 AU and 0.723 AU, respectively, where 1.0 AU (astronomical unit) is the average distance of the Earth from the sun. We might ask why Mercury and Venus have these particular orbital radii (actually, these are the semimajor axes of their slightly elliptical orbital paths). Although their distances from the sun may seem arbitrary, we find that they fit a special geometric pattern.

We can see the pattern by drawing any three identical circles adjacent to each other so that each circle just touches the other two. 

Next, draw another circle that passes through the centers of the three touching circles. Call this the mean orbit of Mercury around the Sun, lying in the center of the drawing. Finally, draw a larger circle that just encloses the first three circles. Call this the average orbit of Venus around the Sun.
Using a bit of trigonometry, one can calculate that the ratio of the radius of the larger circle to the radius of the smaller circle is 1.866. Now, here’s the fun part — using NASA data for the average orbital radius of Venus and Mercury, we find that their orbital radii form a ratio of 1.868, matching our simple circle construction to 99.9 percent accuracy!

Another example of geometric design hidden in our planetary orbits relates to the average orbital radii of Earth and Mars. These can be matched to the geometry of two nested pentagons. Inscribe a circle within the inner pentagon so that the circle is tangent to each of the five faces of the figure. 

Call this the mean radius of Earth’s orbit. 

Then circumscribe a larger circle so that it touches the five corners of the larger pentagon. 

Call this the mean radius of Mars’s orbit. 

Using trigonometry, we find the ratio of these radii to be 1.52786, which matches the actual ratio of these two planets’ mA fascinating geometric number is the Golden Ratio (approximately 1.618), which is also the limiting ratio of consecutive terms in the Fibonacci series of numbers (0,1,1,2,3,5,8,13,21…). Returning to the example of Venus “lapping” Earth in its orbit, we find that Venus orbits to a position between the Earth and the Sun (an “inferior conjunction”) every 584 days, or 219 days more than one Earth year. The ratio of 219/365=0.6, so every time this alignment occurs, Earth and Venus are three fifths of a circle further around the Sun. Five such alignments bring us back to the starting point after 5×584 days = 2920 days, or 8.0 Earth-years (which turns out to be 13.0 Venus-years). The relevant numbers in this analysis are 5, 8, and 13, found in sequence in the Fibonacci series. Moreover, the ratio of the orbital periods of Earth to Venus matches the value of the Golden Ratio (99.5 percent).

Additional geometric designs are apparent in the orbits of the planets, moons, and asteroids of the solar system. One or two such patterns might be adequately ascribed to coincidence, even when not predicted by gravitational interactions between the orbiting bodies. But when multiple “coincidences” appear, a thoughtful observer has reason to suspect that a conductor has orchestrated the celestial harmonies, perhaps out of sheer delight in creating a masterpiece.

Geometric design in the solar system as evidence of intelligent design was the conclusion reached by the scientist whose work most fundamentally explained the force constraining the motions of objects in the solar system, Sir Isaac Newton:
"This most beautiful System of the Sun, Planets and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being." 

SCT

Creation Moment 8/11/2025 - Statistical Significance: An Abused Standard

It is better to trust in the LORD than to put confidence in man. Psalm 118:8

"In research, “statistical significance” is the odds-based method used to tell whether a finding is likely real or just chance. When a study claims p = 0.05, it’s essentially saying, “We’re 95% confident this is real.”

Since the early 20th century, when Sir Ronald Fisher formalized it,

statistical significance has been central to research credibility. Journals prefer it. Publishers know their readers trust it. Researchers know their careers depend on it.

Ordak points out that many scientists admit they worry non-significant results will hurt their chances of publication. This pressure leads to a dangerous cycle: researchers shape their methods—sometimes inappropriately—to produce significant results.

Some even defend flawed analysis in peer review simply because it “got significant results.” This isn’t just cutting corners. It’s gaming the system.

But the numbers tell a darker story:

*Cancer research: Amgen tried to replicate 53 high-profile cancer studies—only 6 held up. Bayer reported similar results in 2011, failing to replicate 75% of cancer biology studies they tested. (Naik, 2011) (Errington et al, 2021)

*Psychology: Of 307 prominent findings, only 64% replicated at all—and those that did showed effect sizes about a third smaller than first reported. (Nosek et al, 2021)

*Neurology & disease research: 100 potential ALS drugs that once showed promise failed entirely in repeat trials. In spinal cord injury research, only 2 of 12 replications validated the original findings—one weakly and one only under special circumstances. (Errington et al, 2021)

Overall: Machine learning analysis of 40,000 psychology papers suggested only 40% might replicate. John Ioannidis famously concluded, “Most claimed research findings are false.” (Youyou et al, 2023) (Ioannidis, 2005)
---And here’s the kicker: A 2021 UC San Diego study (Serra-Garcia & Gneezy, 2021) found that papers that can’t be replicated are cited 153 times more than those that can—because they’re “interesting.” In other words, the more sensational your finding, the more attention you get—even if it’s wrong.
Max Planck put it best:

“Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are a part of the mystery that we are trying to solve.” 

CEH

Creation Moment 5/9/2025 - Exploring the "mind" & Consciousness

And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. Genesis 2:7

"If the human mind has a transcendent ability to perceive

mathematical truth, placing it outside of mathematics, then Penrose has found a mechanism that can resolve the undecidability he found in the foundation of physics. 

In other words, Penrose has shown mathematically that the physical world requires a mind’s transcendent power in order to operate, at least within the two physical systems he has analyzed. 

So, the world isn’t matter. 

It isn’t energy. 

It isn’t even information. 

The world is fundamentally controlled by a mind. 

Talk about mind-blowing!

As you might expect, Penrose’s view is not without critics.

The common objections are:

The mind is not a complete mathematical system. It has some random and inconsistent elements which means it can prove its own Gödel sentence.
The mind is too complex and inscrutable for humans to ever identify its Gödel sentence.
If humans could understand the truth of the mind’s Gödel sentence, this would be a contradiction. Therefore, it is a logical impossibility for humans to understand the truth of the mind’s Gödel sentence.

Penrose thinks that only the second objection has significant weight.
Based on the universality of mathematical insight, it is impossible for the mind to have a Gödel sentence without resulting in a contradiction. Since the mind cannot have a Gödel sentence, then the mind cannot be a mathematical system. Therefore, Penrose believes, the mind is beyond mathematics and thus it can solve the undecidable problems at the foundation of reality." 

MindMatters

Creation Moment 4/16/2025 - Creator's Mathematical Fingerprints of ordered Structure even in Light

And God said, Let there be light: and there was light. 

Genesis 1:3

*God's ordered DESIGN of the Universe, such as the Fibonacci Number, is even even in Light.

"Beams of light that can be guided into corkscrew-like shapes called optical vortices are used today in a range of applications. Pushing the limits of structured light, Harvard applied physicists in the John A. Paulson School of Engineering and Applied Sciences (SEAS) report a new type of optical vortex beam that not only twists as it travels but also changes in different parts at different rates to create unique

patterns. The way the light behaves resembles spiral shapes common in nature.

The researchers borrowed from classical mechanics to nickname their never-before-demonstrated light vortex an "optical rotatum," to describe how the torque on the light's corkscrew shape gradually changes. In Newtonian physics, "rotatum" is the rate of change in torque on an object over time.

In a peculiar twist, the researchers found that their orbital angular momentum-carrying beam of light grows in a mathematically recognizable pattern found all over the natural world. Mirroring the Fibonacci number sequence, their optical rotatum propagates in a logarithmic spiral that is seen in the shell of a nautilus, the seeds of a sunflower, and the branches of trees." 

Phys.org

Creation Moment 4/15/2025 - Scientists Question Whether they can ever fully understand the Universe

Where wast thou when I laid the foundations of the earth? declare, if thou hast understanding.
Job 38:4

"It may sound strange, but mathematicians have created an entire

ladder of infinities, each larger than the next. Now a new kind of infinity threatens to upset that order, and perhaps redefine the structure of the mathematical universe.

For centuries, mathematicians have categorized infinities into a kind of ladder. The infinite set of natural numbers — 1, 2, 3, and so on — sits on one rung. On a higher rung, the infinite set of real numbers, which includes decimals and negatives, dwarfs it. And from there, infinities cascade upward, forming an endless hierarchy.

Recently, researchers from Vienna University of Technology and the University of Barcelona uncovered two new layers of this vastness, and they don’t quite play by the usual rules.

These new types of infinities are called exacting and ultra-exacting cardinals. Unlike their predecessors, these cardinals refuse to slot neatly into the established hierarchy of infinities. 

---Their discovery forces mathematicians to reconsider what infinity really means — and whether chaos might lurk at its core.

Mathematicians have long categorized infinities into a hierarchy where some infinities are larger than others. For example, the infinity of counting numbers (1, 2, 3, …) is smaller than the infinity of real numbers, which includes an infinity of decimals between 0 and 1 (and beyond).

Mathematicians use “large cardinal axioms” to describe these layers, defining specific types of infinite numbers with unique and powerful properties. At the base of the ladder is the infinity of natural numbers, ℵ₀ (aleph-null). Climbing higher reveals infinities of increasing size and complexity: measurable cardinals, supercompact cardinals, and even so-called “huge” cardinals.

These axioms followed a predictable, linear progression. Each new “rung” of the ladder built on the one before it, creating a stable structure. 

But as these infinities grow, they stretch the foundational rules of

mathematics to their limits. Large cardinals, for instance, exist outside ZFC — the Zermelo-Fraenkel set theory with the Axiom of Choice, the framework underpinning nearly all modern mathematics.
Exacting cardinals are stronger (or “bigger”) in their properties than many previously known large cardinals, meaning they can interact with the mathematical universe in new and unexpected ways.

Ultraexacting cardinals are an even more powerful and restrictive version of exacting cardinals. Think of them as exacting cardinals with additional “superpowers” that make them interact with infinity in a way that amplifies their effect on the mathematical universe.

HOD, or Hereditary Ordinal Definability, proposes that infinitely

large sets can be defined by “counting up to” them. If true, it would bring order to the mathematical universe, aligning the Axiom of Choice with the largest infinities.
But these new cardinals muddy the waters. 

If these new cardinals are accepted, they could provide strong evidence against the HOD Conjecture. “It could mean that the structure of infinity is more intricate than we thought,” Aguilera said.

Q: Can we ever fully understand the universe if infinity keeps surprising us?"

ZimeScience

Creation Moment 2/16/2025 - 3 Linguistic Signs of Creation

"And God said, Let there be light: and there was light. And God saw the light, that it was good: and God divided the light from the darkness. Genesis 1:3,4. 

God spoke the light into existence, 

He saw the light, 

and obtained information from the light, that it was good. 

God speaking the light into existence is a “motoric ”sign.

God seeing the light is a “sensory” sign. 

Seeing the light looking good is a “linguistic” sign. 

These three types of signs together form the material world of

ordinary existence, and they must remain consistent, just as they do in mathematics. 

Oller states that “the miracle of communication is so common that we almost always take it for granted.” 

In Genesis 1, God is communicating to us the nature of our origin and giving us an insight into the process. 

This orderly process is explained in mathematical terms, either directly or indirectly by association of what was created."

Derek Marshall

Creation Moment 12/29/2024 - How the Creator upholds the creation in the Language of Mathematics

And He is before all things, and by Him all things consist. Colossians 1:17

"A team of scientists at Australia’s Monash University has “discovered a new universal rule of biological growth that explains surprising similarities in the shapes of sharp structures” across a vast array of living things.

It seems that the growth of all sharp biological structures follows the same mathematical law, called a ‘power law’. This defines the relationship between the width and length of a structure as it grows—for example, an elephant’s tusk.
Such a huge sweep across vastly different life forms means evolutionists cannot use a common ancestor as an explanation. Rather, it suggests some pervasive physical reason.
Our universe is governed by many precise and universal physical-mathematical laws, reflecting its lawgiving Creator. Many medieval founders of science, such as Roger Bacon, Robert Grosseteste, and Thomas Bradwardine taught that the Creator upheld the creation in the language of mathematics." 

CMI

Creation Moment 11/23/2024 - Infinite Monkey Theorem tells us......

Professing themselves to be wise, they became fools.... 

Romans 1:22

"You’ve probably heard this argument: Give enough monkeys enough typewriters and enough time and they will type out Shakespeare. The Infinite Monkeys Theorem is meant to show that chance rules the universe.
If you sense a problem, you are right.
Q: What does “enough” mean here?

--The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labor. ..... the estimated world population of 200,000 chimpanzees types one key per second until the universe ends in about 10100 years (1 followed by 100 zeros).

Q: How far would the monkeys get with typing so many words in a correct sequence?
A: The results reveal that it is possible (around a 5% chance) for a single chimp to type the word ‘bananas’ in its own lifetime. 

However, even with all chimps enlisted, the Bard’s entire works (with around 884,647 words) will almost certainly never be typed before the universe ends. “Too short”

If the monkeys couldn’t type out Shakespeare within the life of the universe, human creativity is not just a matter of chance." 

MindMatters

Creation Moment 10/1/2024 - Brain Geometry of Consciousness

I will praise Thee; for I am fearfully and wonderfully MADE: marvellous are Thy works; Psalm 139:14

"Investigators at U-M who are studying the nature of consciousness have successfully used the drug to identify the intricate brain geometry behind the unconscious state, offering an unprecedented look at brain structures that have traditionally been difficult to study.

A study published in the journal Nature Communications and led by Huang, George Mashour, M.D., Ph.D. and Anthony G. Hudetz, Ph.D., of the U-M Center for Consciousness Science, outlines for the first time in humans how the connections among brain cells within those two important areas are modified by propofol. The paper is titled "Propofol Disrupts the Functional Core-Matrix Architecture of the Thalamus in Humans."

In healthy volunteers, they mapped changes in the brain's architecture before, during and after propofol sedation, guided by functional magnetic resonance imaging (fMRI).

At baseline, explained Huang, the thalamus has a balanced level of activity of both specific nuclei (clusters of brain cells) that send sensory information to highly defined areas of the cortex—known as unimodal processing—and nonspecific nuclei that send information more diffusely throughout a higher layer of the cortex, known as transmodal processing.

The team found that, under deep sedation, the thalamus showed a drastic reduction in activity in clusters of brain cells responsible for transmodal processing, leading to a dominant unimodal pattern—suggesting that while sensory inputs are still received, there is no integration of those inputs.

Next, they discovered the specific cell types that played a role in the shift to an unconscious state and their relationship to the change in thalamic processing. The thalamus contains at least two distinct cell types, said Huang, core cells and matrix cells.


"We now have compelling evidence that the widespread connections of thalamic matrix cells with higher order cortex are critical for consciousness," says Hudetz, Professor of Anesthesiology at U-M and current director of the Center for Consciousness Science.

Imagining that the cortex is layered like an onion, core cells connect to lower layers while matrix cells connect to higher layers in a more spread-out manner.

By measuring mRNA expression signatures—like I.D. badges for the cells—they were able to see that a disruption in the activity of matrix cells played a greater role in the transition to unconsciousness than core cells. An additional surprise was that GABA, a major inhibitory transmitter in the brain usually thought to be key to propofol's actions, did not appear to play as prominent a role as expected.

"The results suggest that loss of consciousness during deep sedation is primarily associated with the functional disruption of matrix cells distributed throughout the thalamus," said Huang."
MedicalXpress

Creation Moment 9/29/2024 - From "cells to shells" the Tiling of Creation

In the beginning God created the heaven and the earth.
Genesis 1:1 

"Mathematicians have long enjoyed the study of shapes. Using sharp edges and plenty of points, they’ve dedicated centuries to seeing just how these shapes fit together for infinite tiling ability. But the equations used in mathematical shaping, with their hard lines and sharp points, don’t generally lead to a lot of crossover with nature.

A team of researchers from Budapest University of Technology recently announced that they have uncovered a new natural class of shape that tiles with curved edges. They uploaded their findings to the preprint server arXiv. Dubbed both “soft cells” and “z-cells,” these shapes lack the telltale corners of theoretical math, but still fit together in both two dimensions and three dimensions.

“A central problem of geometry is the tiling of space with simple structures,” the authors wrote. “The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedral in three-dimensional space are built with sharp corners and flat faces. However, many tilings in nature are characterized by shapes with curved edges, non-flat faces, and few, if any, sharp corners. An important question is then to relate prototypical sharp tilings to softer natural shapes.”

The team believes that they’ve solved the problem of dimensions with this new “infinite class of polyhedral tilings” that can smoothly deform into soft tiles and construct soft versions of cells generally associated with point lattices in both two and three dimensions.

“These shapes emerge in art, but also in biology,” study lead Gabor Domokos, told the New Scientist. “If you look at sections of muscle tissue, you’ll see the cells having just two sharp corners, which is one less than the triangle—it is a very special kind of tiling.”

“Remarkably, these ideal soft shapes, born out of geometry, are found abundantly in nature, from cells to shells,” the team wrote.

In two dimensions, these soft shell shapes are pretty easy to describe

—according to the paper, they are “cells with curved boundaries which have only two corners.” In the three-dimensional space, things get a little more complicated, but the goal is the same: let things be bendy and minimize the amount of “corners” present. In 3D, a soft cell shape can have no corners at all.
“We found that architects have found these kinds of shapes intuitively when they wanted to avoid corners,” Domokos said.

A central part of the paper shows how seashells emerge as a natural example of the shape. Known to form from multiple chambers, shell growth appears to follow a regulated pattern. Using a CT scanner, the team found that when they measured the shells in three dimensions, they couldn’t find corners, even though a two-dimensional view of the shell looked different. That led the team to believe that a seashell offers the prime example of the soft cell shape. 

It also shows how nature is far beyond our current understanding of geometry." 

Prevention

Creation Moment 8/22/2024 - The Brain Functions on a Bell Curve

I will praise Thee; for I am fearfully and wonderfully made:

Psalm 139:14

"Researchers taking part in the Human Brain Project have identified a mathematical rule that governs the distribution of neurons in our brains.

The rule predicts how neurons are distributed in different parts of the brain....In the wonderful world of statistics, if you consider any continuous random variable, the logarithm of that variable will often follow what's known as a lognormal distribution.

 Defined by the mean and standard deviation, it can be visualized as a bell-shaped curve, only with the curve being wider than what you'd find in a normal distribution.

A team of researchers from the Jülich Research Center and the

University of Cologne in Germany found the number of neurons in areas of the outer layer of neural tissue in different mammals fits a lognormal distribution.

Mathematics aside, a simple and important distinction is 

---the symmetry of the normal distribution bell curve 

---and the asymmetry and heavy right-skewed tail of the lognormal distribution, due to a large number of small values and a few significantly large values.

Brain structure and function depend on neuron numbers and arrangement. The density of neurons in different regions and layers of that outer tissue layer – the cerebral cortex – varies considerably.
"For instance, if the density of synapses is constant, regions with lower neuron density will receive more synapses per neuron." 

A lognormal distribution is a natural result of processes that multiply, just like normal distribution is a natural result of adding up many independent variables....suggests brain neural network variation is more than just a byproduct and may actively help animals learn in changing environments. And the fact that the same organization can be seen in different species and in most parts of the cortex suggests that the lognormal distribution is used for something." 

ScienceAlert

Creation Moment 8/6/2024 - Why do bees use hexagons in honeycombs?

For it is written, I will destroy the wisdom of the wise, and will bring to nothing the understanding of the prudent. 

1 Corinthians 1:19

"Why hexagons--- It’s a simple matter of geometry. If you want to pack together cells that are identical in shape and size so that they fill all of a flat plane, only three regular shapes (with all sides and angles

identical) will work: equilateral triangles, squares, and hexagons. 

Of these, hexagonal cells require the least total length of wall, compared with triangles or squares of the same area. So it makes sense that bees would choose hexagons, since making wax costs them energy, and they will want to use up as little as possible—just as builders might want to save on the cost of bricks.

If you blow a layer of bubbles on the surface of water—a so-called “bubble raft”—the bubbles become hexagonal, or almost so. You’ll never find a raft of square bubbles: If four bubble walls come together, they instantly rearrange into three-wall junctions with more or less equal angles of 120 degrees between them, like the center of the Mercedes-Benz symbol.

Evidently there are no agents shaping these rafts as bees do with their combs. All that’s guiding the pattern are the laws of physics. Those

laws evidently have definite preferences, such as the bias toward three-way junctions of bubble walls. The same is true of more complicated foams. If you pile up bubbles in three dimensions by blowing through a straw into a bowl of soapy water you’ll see that when bubble walls meet at a vertex, it’s always a four-way union with angles between the intersecting films roughly equal to about 109 degrees—an angle related to the four-faceted geometric tetrahedron.

Q: Like all of mathematics, the hexagons are all just a big accident, right?"
UncommonDescent

Creation Moment 6/5/2024 - Simple Mathematics in your Lungs

I will praise thee; for I am fearfully and wonderfully made.... Psalm 139:4

"Formally speaking, fractals are infinitely complex patterns that are self-similar across different scales. But, in an echo of their geometry, fractals can help us better understand the world on many levels.

Let’s start with the familiar: fractals in nature. “They are all around us – in trees, mountain ranges, river deltas and so on,” says Dave Feldman at the College of the Atlantic in Bar Harbour, Maine. Such ubiquity makes sense because of the way fractals are made: “a simple iterative process – repeated folding or branching – can produce fractals”, he says.

The inside of your lungs is fractal for a reason: such arrangements cram a huge surface area into a small volume of space.....maximizing the area of tissue that can absorb oxygen." 

Nature

Creation Moment 4/26/2024 - God’s attributes as seen through Math

For the invisible things of Him since the creation of the world 

--are clearly seen, 

--being perceived through the things that are made, 

even His everlasting power and divinity; 

that they may be without excuse. 

Romans 1:20 HNV

"What’s remarkable about the reality of universals as proof for God’s existence is that it points in a simple and clear way to some of God’s attributes, such as infinity, eternity, and omnipotence.

The Mind that contains them must itself be infinite.

*Because the Mind in which natural numbers exists is infinite, it is also omnipotent. 

*Limitations on power are finite and are inconsistent with an infinite Mind.

Because numbers exist independently of the material universe, they are eternal (e.g., the truth that 1+1=2 is independent of time) and thus the Mind that contains them is eternal.
Because mathematics can show infinity, eternity, and omnipotence, it can only have proceeded from a mind with those characteristics. That’s God."
UncommonDescent

Creation Moment 3/5/2024 - Orbital Resonance

Thus saith God the LORD, he that created the heavens,.... 

Isaiah 45:2

"Planets orbit their parent stars while separated by enormous distances – in our solar system, planets are like grains of sand in a

region the size of a football field.....sometimes, their orbits display striking patterns. 

For example, astronomers studying six planets orbiting a star 100 light years away have just found that they orbit their star with an almost rhythmic beat, in perfect synchrony. Each pair of planets completes their orbits in times that are the ratios of whole numbers, allowing the planets to align and exert a gravitational push and pull on the other during their orbit. 

This type of gravitational alignment is called orbital resonance, and it’s like a harmony between distant planets. 

Researchers have discovered over 5,600 exoplanets in the past 30 years, and their extraordinary diversity continues to surprise astronomers. 

In the solar system, Neptune and Pluto are in a 3:2 resonance. There’s also a triple resonance, 4:2:1, among Jupiter’s three moons: Ganymede, Europa and Io. In the time it takes Ganymede to orbit Jupiter, Europa orbits twice and Io orbits four times. 

Resonances occur naturally, when planets happen to have orbital periods that are the ratio of whole numbers. Musical intervals describe the relationship between two musical notes. In the musical analogy, important musical intervals based on ratios of frequencies are the fourth, 4:3, the fifth, 3:2, and the octave, 2:1. Anyone who plays the guitar or the piano might recognize these intervals.

The star Gliese 876 has three planets with orbit period ratios of 4:2:1, just like Jupiter’s three moons. Kepler 223 has four planets with ratios of 8:6:4:3.

The newest example of a resonant chain is the HD 110067 system. It’s about 100 light years away and has six sub-Neptune planets, a common type of exoplanet, with orbit ratios of 54:36:24:16:12:9." 

Astronomy

Creation Moment 2/5/2024 - PHANGS

When I consider thy heavens, the work of Thy fingers, 

the moon and the stars, which Thou hast ordained; 

Psalm 8:3

"NASA’s Webb Depicts Staggering Structure in 19 Nearby Spiral Galaxies (NASA, 29 Jan 2024). Spiral galaxies, the public’s favorite deep-sky objects, are beautiful for their symmetry. The project combines data from multiple wavelengths from orbital and ground-based telescopes.

"These Webb images are part of a large, long-standing project, the

Physics at High Angular resolution in Nearby GalaxieS (PHANGS) program, which is supported by more than 150 astronomers worldwide. Before Webb took these images, PHANGS was already brimming with data from NASA’s Hubble Space Telescope, the Very Large Telescope’s Multi-Unit Spectroscopic Explorer, and the Atacama Large Millimeter/submillimeter Array, including observations in ultraviolet, visible, and radio light. Webb’s near- and mid-infrared contributions have provided several new puzzle pieces."

This image of spiral NGC 628 shows how the information from Hubble (lower right) and JWST (upper left) complement one another to permit physicists to analyze the processes that create the “staggering structure” inherent in spiral galaxies.

The caption of the JWST full image notes a peculiar fact: “The spiraling filamentary structure looks somewhat like a cross section of a nautilus shell.” 

The similarity relates to the Fibonacci Series, a mathematical

relationship of numbers that is found in many apparently-unrelated phenomena, from spiral galaxies to hurricanes to pine cones and sunflowers. 

*No one fully understands why such disparate structures, from a spiral galaxy to a nautilus shell, follows this relationship despite differing in size by many orders of magnitude. 

One thing, though, is certain: humans find the structures to be beautiful. They relate also to the “Golden Ratio” proportions that architects and artists know are most pleasing to the eye. 

For an exquisite animation showing Fibonacci numbers in nature." 

CEH

Creation Moment 10/27/2023 - The Mathematician

So where does this leave the philosophers, the scholars, and the world’s brilliant debaters? God has made the wisdom of this world look foolish. 1 Corinthians 1:20 NLT

"The interpretation of a physical theory partakes of a dark art, one in

which mathematical concepts are ceded dominion over the physical world. In practicing this art, the mathematician, like the necromancer that he is, is always liable to the temptation of confusing the structures over which he presides with things in the real world."
David Berlinski, Was There a Big Bang? 1998