Unintelligent Design - How the Appearance of Design in a Fibonacci Spiral Evolved

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Fibonacci fractal

Fossil study sheds light on famous spirals found in nature | The University of Edinburgh

One of the things that creationists unwittingly present as evidence of design (and therefore of a designer) is the spiral pattern known as a Fibonacci spiral that occurs throughout nature, from the pattern of florets in a sunflower, the arrangement of leaves in plants, the spiral of a hurricane to the shape of a spiral galaxy.

The irony is that a Fibonacci spiral is the result of a mathematical progression known as a Fibonacci sequence where the next is the sum of the preceding two numbers, 1,2,3,5,8,13,21,34... etc., so the appearance of design is in reality the result of a simple mathematical progression. In other words, it's not evidence of design at all but evidence of how the appearance of design can arise without a designer, intelligent or otherwise.

Who was Fibonacci?

It's also an example of how creationists employ post hoc reasoning and deduce their desired answer from ignorant incredulity and the false dichotomy fallacy - "I can't work out how this happened naturally, therefore it must have been done by [fill in the name of the god their mummy and daddy believed in]".

Of course there will be those who extend their post hoc rationalization and claim the existence of mathematical laws like the Fibonacci sequence shows there must be a law maker, i.e., [fill in the name of the god their mummy and daddy believed in], failing to understand the deference between the descriptive laws use in science, which simply describe what happens, and the proscriptive and prescriptive laws that humans make to control our behaviour in a society.

But then where would creationism be without this ignorance, failures of logic and post hoc rationalization, in the complete absence of any supporting evidence?

And now, as though to add to creationists' discomfort, scientists have found evidence that the Fibonacci spiral seen in the arrangements of leaves in many plants is an evolved feature which was not present in the earliest plants.

First, a description of how Fibonacci sequences arise naturally in nature:

A Fibonacci spiral is a logarithmic spiral that appears in the shape of a series of increasing squares, with the side lengths following the Fibonacci sequence. The Fibonacci sequence is a mathematical sequence in which each number is the sum of the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
The Fibonacci spiral is derived by drawing arcs connecting opposite corners of these squares, forming a spiral that expands outward. The curvature of the spiral approximates the golden ratio, a mathematical ratio of approximately 1.618, which is denoted by the Greek letter phi (φ). The golden ratio has a unique property that the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller part.

The occurrence of the Fibonacci spiral in nature is often attributed to the principle of self-similarity and efficient packing. Self-similarity refers to the repetition of similar patterns at different scales within an organism or structure. Efficient packing relates to the ability of living organisms to optimize their growth or structures while minimizing space and resources.

Many natural phenomena exhibit Fibonacci spirals or ratios close to the golden ratio. Some examples include:

1. Nautilus shells: The chambers of a nautilus shell often follow a logarithmic spiral resembling the Fibonacci spiral.
2. Sunflowers: The arrangement of seeds in the florets of a sunflower often follows spirals that approximate the Fibonacci sequence.
3. Pinecones: The scales on a pinecone exhibit spirals that conform to the Fibonacci sequence.
4. Pineapples: The pattern of scales on a pineapple follows a spiral that approximates the Fibonacci sequence.
5. Hurricanes: The overall structure and spiral cloud bands of hurricanes often resemble Fibonacci spirals.
6. Spiral galaxies: The arms of spiral galaxies, such as the Whirlpool Galaxy, often follow logarithmic spirals resembling the Fibonacci spiral.

The prevalence of the Fibonacci spiral in nature can be attributed to the underlying principles of growth and optimization. These patterns and ratios allow organisms and structures to efficiently pack and distribute resources, facilitate efficient energy flow, and promote structural stability. While the exact reasons for the occurrence of these patterns in nature are still a subject of scientific inquiry, they provide intriguing insights into the inherent mathematical beauty and order found in the natural world.

ChatGPT3 "What is a Fibonacci spiral and why does it occur so often in nature?" [Response to user question]
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The spiral pattern observed in a sunflower, specifically in the arrangement of seeds within the florets, can be explained through the concept of phyllotaxis. Phyllotaxis refers to the arrangement of leaves, petals, or other plant organs around a stem or axis.

In the case of a sunflower, the seeds are arranged in a spiral pattern known as a parastichy. The parastichy follows a pattern that approximates the Fibonacci sequence, resulting in spirals with a characteristic angle between them. Typically, the number of clockwise spirals and the number of counterclockwise spirals are consecutive Fibonacci numbers.

This pattern emerges due to the growth dynamics of the sunflower during its development. The sunflower's growing tip, called the meristem, produces new florets as it expands. As each floret develops, it is positioned to maximize exposure to sunlight and reduce shading from neighboring florets. This optimal arrangement allows efficient utilization of resources, such as light, water, and nutrients.

The specific angle between the spirals in a sunflower is related to the golden angle, which is approximately 137.5 degrees. The golden angle is derived from the golden ratio and helps ensure that each seed receives the maximum amount of space and light without interference from adjacent seeds. This arrangement minimizes overlap and maximizes packing efficiency.

It's important to note that not all sunflowers exhibit a perfect Fibonacci spiral pattern, as external factors like genetic variations and environmental influences can affect the precise arrangement. However, the Fibonacci spiral is a common tendency observed in many sunflower varieties.

Overall, the spiral pattern in a sunflower emerges as a result of the plant's growth and optimization mechanisms, allowing for efficient resource allocation and maximizing exposure to essential elements like sunlight.

ChatGPT3 "How does the spiral arise in, for example, a sunflower?" [Response to user question]
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References:

1. "The Golden Ratio: The Story of Phi, the World's Most Astonishing Number" by Mario Livio: This book explores the mathematical concept of the golden ratio and its presence in art, nature, and science.
2. "Phyllotaxis: A Systemic Study in Plant Morphogenesis" by Roger V. Jean: This comprehensive book focuses on the patterns and principles of phyllotaxis, including the Fibonacci spiral, in plants.
3. "Patterns in Nature: Why the Natural World Looks the Way It Does" by Philip Ball: This book examines the underlying mathematical and physical principles that shape natural patterns, including the Fibonacci sequence and spirals.
4. "The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture" by Gyorgy Doczi: This book explores the occurrence of proportional harmonies, including Fibonacci patterns, in various domains such as nature, art, and architecture.
5. "The Number Mysteries: A Mathematical Odyssey through Everyday Life" by Marcus du Sautoy: Although not exclusively focused on Fibonacci patterns, this book provides an engaging exploration of various mathematical phenomena, including the Fibonacci sequence and its connection to nature.

The team of scientists who found that Fibonacci patterns evolved were led by Dr Alexander (Sandy) J. Hetherington of Edinburgh University, Scotland, UK.

The news release from Edinburgh University explains the study and the significance of the team's findings:

Fossil study sheds light on famous spirals found in nature

A 3D model of a 407-million-year-old plant fossil has overturned thinking on the evolution of leaves. The research has also led to fresh insights about spectacular patterns found in plants.

Fibonacci spirals in the leaves of a monkey puzzle tree.

Leaf arrangements in the earliest plants differ from most modern plants, overturning a long-held theory regarding the origins of a famous mathematical pattern found in nature, research shows.

The findings indicate that the arrangement of leaves into distinctive spirals, that are common in nature today, were not common in the most ancient land plants that first populated the earth’s surface.

Instead, the ancient plants were found to have another type of spiral. This negates a long held theory about the evolution of plant leaf spirals, indicating that they evolved down two separate evolutionary paths.

Nature's Secret Code

Whether it is the vast swirl of a hurricane or the intricate spirals of the DNA double-helix, spirals are common in nature and most can be described by the famous mathematical series the Fibonacci sequence.

Named after the Italian mathematician, Leonardo Fibonacci, this sequence forms the basis of many of nature’s most efficient and stunning patterns.

Spirals are common in plants, with Fibonacci spirals making up over 90% of the spirals. Sunflower heads, pinecones, pineapples and succulent houseplants all include these distinctive spirals in their flower petals, leaves or seeds.

Why Fibonacci spirals, also known as nature’s secret code, are so common in plants has perplexed scientists for centuries, but their evolutionary origin has been largely overlooked.

Based on their widespread distribution it has long been assumed that Fibonacci spirals were an ancient feature that evolved in the earliest land plants and became highly conserved in plants.

Holly-Anne Turner the first author of the study started this project as a Plant Science Honours student.

Digital Reconstruction of a Plant Fossil

However, an international team led by the University of Edinburgh has overthrown this theory with the discovery of non-Fibonacci spirals in a 407-million-year old plant fossil.

Using digital reconstruction techniques the researchers produced the first 3D models of leafy shoots in the fossil clubmoss Asteroxylon mackiei – a member of the earliest group of leafy plants.

The exceptionally preserved fossil was found in the famous fossil site the Rhynie chert, a Scottish sedimentary deposit near the Aberdeenshire village of Rhynie.

Our model of Asteroxylon mackiei lets us examine leaf arrangement in 3D for the first time. The technology to 3D print a 407-million-year old plant fossils and hold it in your hand is really incredible. Our findings give a new perspective on the evolution of Fibonacci spirals in plants.

Dr Sandy Hetherington, corresponding author
Evolutionary Palaeobiologist and Project Lead
Institute of Molecular Plant Sciences
School of Biological Sciences,
University of Edinburgh, Edinburgh, UK.

The clubmoss Asteroxylon mackiei is one of the earliest examples of a plant with leaves in the fossil record. Using these reconstructions we have been able to track individual spirals of leaves around the stems of these 407 million year old fossil plants. Our analysis of leaf arrangement in Asteroxylon shows that very early clubmosses developed non-Fibonacci spiral patterns.

Holly-Anne Turner, first author Former Undergraduate Student
Institute of Molecular Plant Sciences
School of Biological Sciences
University of Edinburgh, Edinburgh, UK.

The site contains evidence of some of the planet’s earliest ecosystems – when land plants first evolved and gradually started to cover the earth’s rocky surface making it habitable.

The findings revealed that leaves and reproductive structures in Asteroxylon mackiei, were most commonly arranged in non-Fibonacci spirals that are rare in plants today.

Evolution of Plant Spirals

This transforms scientists understanding of Fibonacci spirals in land plants. It indicates that non-Fibonacci spirals were common in ancient clubmosses and that the evolution of leaf spirals diverged into two separate paths.

The leaves of ancient clubmosses had an entirely distinct evolutionary history to the other major groups of plants today such as ferns, conifers and flowering plants.

The team created the 3D model of Asteroxylon mackiei, which has been extinct for over 400 million years, by working with digital artist Matt Humpage, using digital rendering and 3D printing.

The team’s findings are published in Science, sadly behind a pay wall. However, the Abstract and Editor's summary are available:

Editor’s summary

Aerial parts of plants arrange their organs around stems, and this arrangement defines their structure. In most existing plant species, organs emerge at 137.5° from the previous organ. This results in continuous spirals of organs, with the number of clockwise and anticlockwise spirals forming consecutive numbers in a Fibonacci sequence. Reconstructing early lycophyte phyllotaxis from Rhynie Chert fossils, Turner et al. found alternative leaf arrangements suggesting that Fibonacci-style patterning was not ancestral to living land plants. The authors also found support for a hypothesis that lycophyte leaves originated from modified reproductive structures rather than evolving de novo. The work provides insight into how diverse early plants evolved into the plant forms seen today.

Maddy Seale

Abstract

Lateral plant organs, including leaves and reproductive structures, are arranged on stems in distinct patterns termed phyllotaxis. Most extant plants exhibit phyllotactic patterns that are mathematically described by the Fibonacci series. However, it remains unclear what lateral organ arrangements were present in early leafy plants. To investigate this, we quantified phyllotaxis in fossils of the Early Devonian lycopod Asteroxylon mackiei. We report diverse phyllotaxis in leaves, including whorls and spirals. Spirals were all n:(n+1) non-Fibonacci types. We also show that leaves and reproductive structures occurred in the same phyllotactic series, indicating developmental similarities between the organs. Our findings shed light on the long-standing debate about leaf origins and demonstrate the antiquity of non-Fibonacci spirals in plants.

Turner, Holly-Anne; Humpage, Matthew; Kerp, Hans; Hetherington, Alexander J.
Leaves and sporangia developed in rare non-Fibonacci spirals in early leafy plants
Science, 380,1188-1192(2023).DOI:10.1126/science.adg4014

@copy 2023 2023 The Authors,
Published by American Association for the Advancement of Science.
Reprinted with kind permission under licence #5572441490209.

And again, quite casually and without any intent to do so, scientists refute creationism just by revealing the facts. The appearance of design is no indication of design or of a designer because the appearance of design can be the result of an evolutionary process in a self-replicating organism.

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