Your lovely neighbours cannot be correct except by chance; if there was any validity to their predictions, it would imply not just that they knew the future of the weather, but that the future of the weather was knowable, which it certainly is not. Your tendency to see their predictions as accurate is likely a conflation of your confirmation bias and your choice-supportive bias.
Humans naturally search for meaning in chaos. That is all that their observations of caterpillars and trees and birds amounts to. They are trying to attach significance to a chaotic universe in order to reassure themselves that their place in the world makes sense. It does not. This is mathematically verifiable.
If the birds and the caterpillars and the apple trees could know the future of chaotic systems, it would imply that we live in a deterministic universe where birds and caterpillars and apple trees could not exist. QED.
"If the birds and the caterpillars and the apple trees could know the future of chaotic systems, it would imply that we live in a deterministic universe where birds and caterpillars and apple trees could not exist. QED."
Complex dynamics 101: life is a complex dynamical system. If the math of chaos is wrong, the processes underlying life would not operate as they do. Life would not exist as we observe it.
Also, your iPad would not work. As I said, QED. This is not controversial.
Or, perhaps that weather has cycles and is not an uncorrelated random walk, and that 50 years of living with your life strongly influenced by the weather, along with several lifetimes of your parents' wisdom gives some insight into deep patterns of nature that are not readily apparent. Perhaps these persistent stories about old people predicting things based on caterpillars and trick knees are hints that the world might be more complicated than you think. And if you aren't so quick to assume that you understand the world because you think you understand a theory, you might investigate these hints. Maybe you will find out that there is something actually going on, and you'll have an exciting new world to explore.
"it would imply that we live in a deterministic universe..."
You say this as though it's impossible. You may not believe we live in a deterministic universe, but, that's just, like, your opinion, man. The rational stance (I think) is to: (1) admit you don't know, (2) acknowledge the possibility of a deterministic universe, (3) for whatever chance the universe is deterministic, delude yourself into believing that it's not, because the illusion of free will is probably good for your mental health.
I think you're doing #3 really well, but skipped over #1 and #2.
Humans naturally search for meaning in chaos. That is all that their observations of caterpillars and trees and birds amounts to. They are trying to attach significance to a chaotic universe in order to reassure themselves that their place in the world makes sense. It does not. This is mathematically verifiable.
If the birds and the caterpillars and the apple trees could know the future of chaotic systems, it would imply that we live in a deterministic universe where birds and caterpillars and apple trees could not exist. QED.