SearcharxivSearch

arXiv · 2209.14244

Lotka-Volterra Models for Extraterrestrial Self-Replicating Probes

Abstract

A sufficiently advanced extraterrestrial civilization can send out a swarm of self-replicating probes for space exploration. Given the fast-growing number of such a probe, even if there is only one extraterrestrial civilization sending out such probes in the Milky Way galaxy, we should still expect to see them. The fact that we do not consists part of the Fermi paradox. The suggestion that self-replicating probes will eventually mutate to consume their progenitors and therefore significantly reduce the number of total probes has been investigated and dismissed in the literature. In this work, we re-visit this question with a more realistic Lotka-Volterra model, and show that mutated probes would drive the progenitor probes into "extinction", thereby replacing them to spread throughout the galaxy. Thus, the efficiency of mutated probes in reducing the total number of self-replicating probes is even less than previously thought. As part of the analysis, we also suggest that, somewhat counter-intuitively, in designing self-replicating probes, one should not program them to stop replicating when sufficient mutation causes the probes to fail to recognize the progenitor probes as "self".

Explore related subjects

Keep this discovery

BibTeXRIS

Yifan Chen, Jiayi Ni, Yen Chin Ong. 2022-09-08. Lotka-Volterra Models for Extraterrestrial Self-Replicating Probes. https://doi.org/10.1140/epjp%2Fs13360-022-03320-3

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS