Why do we recognize patterns? Maybe it's because we are all part of the same pattern and see what we are familiar with.
Even before we see the pattern with our eyes, the pattern and the equation describing it are already in our minds.
Imagine that the universe is a very big picture. Let's just call the complete image "truth". We are part of this "truth", just like a dot on the canvas. We can't get rid of this painting and expect to see a complete image. You can't see the truth from the outside
Next question, can we see the truth from consciousness?
We are all made of stardust, so how can things from the same element provide power for the furnace of stars to evolve consciousness? But then again, we're here, we've been there, so it's possible.
However, separating consciousness from the physical field and making it a new entity is a challenge to our way of reasoning. It is a fascinating idea to think that there is an entity wandering in our minds, visiting in our dreams and showing us the equations of the universe, but it is also difficult to accept. Unless we invite another guest, a person who is essentially "sacred".
Different views/explanations on the golden ratio.
Mathematics-the most irrational number, nothing special, nothing more.
Physics-no application (at present)
Art-can be found in painting, ancient architecture, music, etc.
Biology-found in sunflowers, nautilus shells, etc.
Mysterious Art/Other-Creation, Penrose Tiles, E8, Best Fractal, Galaxy, DNA, Human Body, etc.
The golden ratio itself is not important. Why is it common in nature? This is a more interesting question. It is undeniable that the golden ratio exists in nature, but for some reasons, it is difficult for people to understand its importance. It's like the air we breathe. We know it exists because it keeps us alive, otherwise we will be in a strange place, but we can't see it.
As mentioned earlier, this ratio itself is not important. Therefore, it is futile to say that the golden ratio is x2-x- 1=0 and try to apply it to the physical world. Although mathematics can be used to deal with equations and describe the physical world to some extent, it should not be the starting point of physical observation. Please note that mathematics belongs to the abstract field, not the exact physical reality.
To put it more clearly, the golden ratio (phi) is only a part of the physical equation, not the equation itself. And (pi) are not equations of sphere volume, but part of the equation.
In order to give physical meaning to this ratio, we must first find an equation that describes the physical phenomenon that contains this ratio, and then use this ratio to describe other phenomena.
Now comes the tricky part ... how is this equation derived? We should not use axioms to deduce, because we are dealing with physical phenomena.
Another method is to use a proven scientific method, that is, "guess" it-calculate the result of the guess-and compare it with the observation result (R. Feynman).