golden ratio in nature
When a flower hasn't yet bloomed, it's easy to see evidence of the golden ratio.
The golden ratio even relates to the loop quantum gravity parameter to black hole entropy. Any unification model (“theory of everything”) must include these two theories. And it's thought to be extremely common in nature. The golden ratio (often represented by the Greek letter φ) is directly tied to a numerical pattern known as the Fibonacci sequence, which is a list composed of numbers that are the sum of the previous two numbers in the sequence. A resource in this sense can be a unit of electricity spent for a logic gate to be opened to activate a binary choice in a computer language, or a calorie or two of energy needed to make a mental choice of what shirt to wear. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. It's not hard to find examples of this logarithmic phenomenon in nature — whether it's a simple houseplant (like the aloe plant above) or an expansive spiral galaxy (like the spiral galaxy, Messier 83, seen below), they all originate from the same mathematical concepts. Emergence theory predicts a fundamental, natural phenomenon that is so strange yet so prevalent that, with no physics theory having ever explained it, has been largely ignored by the scientific establishment and often seen as the stuff of amateur scientists and hobbyists.
Clearly, the universe is in the business of expressing physical meaning. Upon learning of a golden ratio related fact, most scientists will often treat it as a coincidence. The golden ratio of growth seen in a sunflower head. This phenomenon is the ubiquity of the golden ratio in nature from the micro (including the Planck scale) to the macro scale. It's often just us seeing a very specific well-known pattern where there is actually a more general one. Fruits and Vegetables. It is an irrational number often symbolized by the Greek letter “phi” … A spiral aloe plant sits in a gardening pot. From the Pyramids to vegetables, from Renaissance art to mollusk shells, the number is seen time and time again. Similarly, languages with fewer letters require less resources for each choice of letter. This is one reason why this text you’re reading is expressed as binary code under the secondary level of English words. For example it appears, notably, in black hole physics: the golden ratio is precisely the point where a black hole’s modified heat changes from positive to negative, and it is part of the equation for the lower bound on black hole entropy. There are two main discussion areas when it comes to the ratio in nature – Fibonacci numbers and golden spirals.
What is the meaning of this? The value of the golden ratio is 0.618 or 1.618. It’s the only ratio in math that switch hits like this.
By continuing to use our website you consent to all cookies in accordance with our cookie policy. The curled up fronds of a young fern are known as fiddleheads. A chameleon tail is famous for its tight spiraling shape. The value of the golden ratio is 0.618 or 1.618. It would be news to many people, however, that the golden ratio makes many precise (100% accuracy) and near-precise (accuracy of and near 99.99…%) appearances in values related to astronomical bodies that are often surprising and interesting. Languages that have a lot of letters are costly. Sign up today to get weekly science coverage direct to your inbox. Time and motion could simply be ordered sequences of different 3D quasicrystal configurations, “played” rapidly like a 3D strip of film frames. Messier 83, a spiral galaxy located 15 million light-years away from Earth.
But suffice it to say that the golden ratio is a powerful tool for building physics. Typical meaning, such as humor, is very subjective, while mathematical and geometric meaning is less subjective. Mathematically this is better described by fractals, repetitive patterns that can end up producing logarithmic spirals.
Snail shells are a lovely example of the golden ratio in nature. Except it isn’t. The atomic radius of hydrogen in methane is the Bohr radius over the golden ratio.
And even this is still an approximation. The simplest way to do this is by giving simple instructions like “first grow, then turn a certain angle and grow again”.
The sequence goes like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. Ideas like the invariance of the speed of light could be explained using new ideas like an update of the de Broglie electron clock model. A spiky shell with a golden ratio spiral. You might consider this an Ah-ha! And, for some reason, it does this in the most economical way possible, as though it’s interested in getting the biggest “bang for the buck” of whatever the foundational stuff of reality is. Learn more about the Fibonacci sequence and natural spirals in this fascinating video series by mathematician Vi Hart, who talks fast, but she's interesting and will remind you of the way your brain once hopped from subject to subject: As Hart explains, examples of approximate golden spirals can be found throughout nature, most prominently in seashells, ocean waves, spider webs and even chameleon tails! Such a spiral is created by increasing the spiral's radius by the golden proportion every 90 degrees. However, the statistical probability of the golden ratio’s unrelenting prevalence to such high accuracy is practically zero. It is also important to remember that from the point of view of physics, spirals are low energy configurations. The nautilus is often used to discuss the golden spiral, but it isn't one. Having an irrational value guarantees this, so the spirals we see in nature are a consequence of this behavior. Fibonacci numbers form a sequence where each number is the sum of the two preceding ones. The golden ratio is about 1.618, and represented by the Greek letter phi, Φ. Two numbers are in the golden ratio if the ratio of the sum of the numbers (a+b) divided by the larger number (a) is equal to the ratio of the larger number divided by the smaller number (a/b). Materialists say that stuff is “energy”, but they are not able to explain or define exactly how energy is anything other than abstract information. Petals and leaves are often found in this distribution, although not every plant behaves like this so we cannot claim that it's a universal property. Most can agree that the most foundational principle of physical reality is the principle of least action. Fibonacci numbers form a sequence where each number is …
If plants want to maximize the exposure of their leaves to the Sun, for example, they ideally need to grow them at non-repeating angles. And the only way to get networks of 1D codes to act as an interactive 3D network of 1D codes is to use the golden ratio. The ratio of two neighboring Fibonacci numbers is an approximation of the golden ratio. There are two main discussion areas when it comes to the ratio in nature – Fibonacci numbers and golden spirals. Often referred to as the natural numbering system of the cosmos, the Fibonacci sequence starts out simply (0+1= 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8...), but before long, you'll find yourself adding up numbers in the thousands and millions (10946+17711=28657, 17711+28657=46368, 28657+46368=75025...) and it just keeps going on forever like that. Working with it would be mentally difficult and would certainly not conserve choices.
Since reality is three dimensional, we suggest to look first to see if reality might be written in the code 3D quasicrystals. When a Fibonacci number is divided by the Fibonacci number that came before it, it approaches the golden ratio, which is an irrational number that starts out as 1.6180339887… The two geometric letters in a Fibonacci chain quasicrystal are lengths with a ratio of one to the other that is the golden ratio, where the long length has a ratio to the short length that is the same ratio as the long length to the sum of the long + short length. In 1993 Lucien Hardy of the Perimeter Institute discovered that the probability of entanglement for two particles projected in tandem is the golden ratio over negative 5. Because information is meaning conveyed by symbolism.
Likewise, similar spiraling patterns can be found on pineapples and cauliflower. For those philosophically inclined, even a universe made of consciousness might be interested in conserving that precious resource to express the most physical meaning. Expressed algebraically, for quantities a and b with a > b > 0, All these distributions follow logarithmic spirals, the general mathematical form of a golden spiral. Black holes are where general relativity and quantum mechanics converge at their limits. The golden ratio appears fundamentally in quantum mechanics and in black holes. When the golden ratio is applied as a growth factor (as seen below), you get a type of logarithmic spiral known as a golden spiral. Does it require more mental energy to choose between vanilla and chocolate or to choose from 100 delicious flavors of ice cream? A powerful language is one which has the ability to express the maximum amount of meaning with the least number of choices, since each choice requires resources. Imagine if the English language had 23 million letters! (Yes, quasicrystals are languages or codes because they fully meet the definition by having (1) a finite set of two or more symbols, (2) symbol matching rules and (3) syntactical degrees of freedom.) Continue below to see just a few of the ways these spirals manifest in nature. The shell of the nautilus, in particular, can be better described as having a spiral that expands by the golden ratio every 180 degrees. Catie Leary writes and curates visual stories about science, animals, the arts, travel, and the natural world. The “golden ratio” (sometimes called the “golden mean” or “golden section”) is a fundamental geometric ratio that appears in a circumscribed equilateral triangle. Math has a lot of special numbers but none capture the imagination quite like the golden proportion. In a geometric code, like the quasicrystal code nature might be using, a two letter code might be powerful as well. The three formulas respectively can be seen in this graphic: Therefore, the golden ratio may be the fundamental constant of nature. And a growing number of physicists, from the late John Wheeler to MIT’s Max Tegmark, tell us that it is trivially obvious from the implications of both classic and quantum physics that reality is indeed made of information. The fractal spirals of Romanesco broccoli (Brassica oleracea). Golden ratio spirals as seen from the bottom of a pinecone. A seashell is one of the most well-known examples of the golden ratio spiral in nature. moment, but there are still deeper mathematical connections between all living things. Both the Romanesco broccoli and the shell of the nautilus follow regular spiral structures but neither follow the traditional golden spiral. You can see the spiral of this Comfrey flower's stalk. In binary matrices, which were used by Heisenberg to describe quantum mechanics, the highest probability non-trivial eigenvalues are the golden ratio, and negative one over the golden ratio. Here's How It Could Change the World, Welcome to the Golden Age of Camp Cooking, 8 Natural Mysteries That Can't Be Explained, 5 Natural Events That Science Can't Explain, A Golden Era in Safer Chemicals Is on the Horizon, NASA, ESA, and the Hubble Heritage Team (STScI/AURA).
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