> The question is why "so many real-world systems are governed by differential equations" and "so many real-world systems involve periodic motion". > > Well, stable systems are can either be stationary or oscillatory. If the world didn't contain so many stable systems, or equivalently if the laws of physics didn't allow so, then likely life would not have existed. All life is complex chemical structures, and they require stability to function. Ergo, by this anthropic argument there must be many oscillatory systems.

I would say that the it's very difficult to imagine a world that would not be governed by differential equations. So it's not just that life wouldn't exist it's that there wouldn't be anything like the laws of physics.

As a side note chaotic systems are often better analysed in the FT domain, so even in a world of chaotic systems (and there are many in our world, and I'd argue that if there wasn't life would not exist either) the FT remains a powerful tool