In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, return to a state arbitrarily close to (for continuous state systems), or exactly the same as (for discrete state systems), their initial state.
I’ve heard talk around the internet of people implying that this means some sort of immortality or cyclical existence. Is this true or it is just some flavor of the month fear by people that we could be immortal?
Hello DarkNeos. This is a fascinating attempt to bridge mathematical theorems with existential questions. However, if we examine the physical mechanics underneath this concept, a few structural questions naturally arise.
When Poincaré’s theorem speaks of returning to a state that is “arbitrarily close” but not strictly identical, how do we account for the sensitive dependence on initial conditions (often known as the butterfly effect)? Wouldn’t even a microscopic difference ensure that the subsequent trajectory of that specific life completely diverges almost immediately?
Furthermore, at the foundational level of physics, we inevitably encounter quantum randomness. Since true quantum events do not follow strict deterministic paths, wouldn’t the intrinsic randomness at the Planck scale guarantee that the system’s dynamics diverge entirely, making any true “recurrence” of a life impossible?
I point this out because I genuinely want to help you avoid a very common and unfortunate intellectual trap. Historically, the human mind has always generated deranged religious imaginations and classic superstitions to cope with the biological terror of death. Today, we see this exact same psychological panic desperately rebranding itself as “quantum mysticism”—or, in your case, a sort of “mathematical recurrence mysticism.”
As someone interested in philosophy, I am sure you want to protect your reasoning from collapsing into this kind of ultimate intellectual absurdity. So, I offer this question as a friendly safeguard: when we strip away the mathematical jargon, are we actually doing rigorous physics here, or are we simply watching the human ape invent a new pseudo-scientific church to avoid accepting its own biological finitude?
Theorems are theorems. Reality is reality. Theorems are not reality. Reality isn’t a theorem.
Here’s a simple version of Poincare’s recurrence theorem. Say there are 3 spots and 3 differently colored balls. We can create a nice triangle using these balls. How many different types of triangles can we create. \frac{3!}{3} = 2 (circular permutation). Repetition is a mathematical inevitability. So yes if we’re one of these 3 balls and there are 3 slots, and we’re \triangle’s we’re immortal. That felt nice.
I don’t think this is meant to be an escape from death but the conclusion is meant to inspire a sort of terror in the person because they are effectively “trapped” in reality and doomed to repeat it.
I’m going to step out on a limb here with my limited understanding of dynamical systems. As the quote included in the OP says this only applies to dynamical systems. What aspect of human longevity does that apply to? I’m pretty sure the answer is none.
The original strange attractor was identified by a meteorologist named Edward Lorenz. It represents the graph of three simultaneous differential equations consisting of meteorological parameter functions expressed as coordinates in a phase space. You would have to show that human longevity can’t be represented by a similar system of functions.
To start I’ll restate the limitations of my expertise in this area. That being said, here is a definition of a dynamical system from Wikipedia:
In mathematics, physics, engineering and systems theory, a dynamical system is the description of how a system evolves in time. For example, an astronomer can experimentally record the positions of how the planets move in the sky, and this can be considered a complete enough description of a dynamical system. In the case of planets there is also enough knowledge to codify this information as a set of differential equations with initial conditions, or as a map from the present state to a future state in a predefined state space with a time parameter t, or as an orbit in phase space.
In what sense could that apply to human longevity?
