>> “How is that possible?” <<
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Have you ever observed the spirals on the underside of pine cones? Or Agaves? Or the seeds in a sunflower?
How about the hexagonal stress relief in basaltic rocks?
The fact that Fibonacci sequences exist in nature is the result of physical processes. But we often look at the result and impose our own order on nature. The same processes that generate a logarithmic spiral in a Nautilus generate a Fibonacci sequence in the seed scales of a pine cone, because a logarithmic spiral is asymptotically equivalent to a Fibonacci sequence.
Without understanding the generating processes, the presence of number in nature can acquire a mystical significance, but often what appears to be a significant relationship is just an artifact of the mathematical conventions we use (as in the case of Fibonacci sequences being convergent to a logarithmic spiral). Another example: Real numbers are a necessary abstraction, although we cannot perceive their existence as actual quantities. They do not exist in the same sense that finite, countable quantities exist.
Don’t get me wrong- I use advanced mathematics extensively in my work. There are many cognitive biases that can result in bad models, and I attempt to be very rigorous in excluding them.
I suppose this is to say that I am an Aristotelean rather than a Platonist when it comes to mathematics. It amused me in graduate school to argue this issue with one of my professors- a Hungarian emigree who was proudly atheistic - who nonetheless maintained that canonical mathematical forms existed somewhere (heaven?).
And by saying this I am not rejecting the idea of Creation or design- it is evident everywhere, but our understanding of nature is still very superficial.