There is a debate about the possibility of mind-uploading – a process that purportedly transfers human minds and therefore human identities into computers. This paper bypasses the debate about the metaphysics of mind-uploading to address the rationality of submitting yourself to it. I argue that an ineliminable risk that mind-uploading will fail makes it prudentially irrational for humans to un...

It remains unclear if patients with different types of common mental disorders, such as adjustment, anxiety and depressive disorders, have the same irrational ideas. The aim of this prospective cohort study (n = 190) is to investigate differences in level and type of irrational beliefs among these groups and to examine whether a change in irrational beliefs is related to symptom recovery. Irrat...

Let α be an irrational and φ : N → R be a function decreasing to zero. For any α with a given Diophantine type, we show some sharp estimations for the Hausdorff dimension of the set Eφ(α) := {y ∈ R : ‖nα− y‖ < φ(n) for infinitely many n}, where ‖ · ‖ denotes the distance to the nearest integer.

In two-sided matching problem, there are overwhelming evidences that support peoples are also motivated by concerns for fairness and reciprocity. We will show that compromise which is individually irrational improves the welfare of the whole groups. The reasonable compromise level is obtained as the function of the size of the group so that the social utility should be maximized.

We study the T = 0 magnetization of the Hofstadter model. Near a rational flux the magnetization as a function of the chemical potential has the structure of a sequence of lines with quantized slopes, connected by lip-shaped regions. The lips admit a semiclassical description. This structure appears on all scales for irrational fluxes that are well approximated by rationals infinitely often.

Letting P k (n) stand for the k-th largest prime factor of n ≥ 2 and given an irrational number α and a multiplicative function f such that |f (n)| = 1 for all positive integers n, we prove that n≤x f (n) exp{2πiαP k (n)} = o(x) as x → ∞.

Let $K\subset\mathbb{R}$ be a self-similar set defined on $\mathbb{R}$. It is easy to prove that if the Lebesgue measure of $K$ zero, then for almost every $t$, $$K+t=\{x+t:x\in K\}$$ only consists irrational or transcendental numbers. In this note, we shall consider some classes sets, and explicitly construct such $t$'s. Our main idea from $q$-expansions.