In this paper, we shed light on the dynamic characteristics of rational group behaviors and the relationship between monetary policy and economic units in the financial market by using an agent-based model (ABM), the Hurst exponent, and the Shannon entropy. First, an agent-based model is used to analyze the characteristics of the group behaviors at different levels of irrationality. Second, the...

The strategy of this paper is to throw light on rational cognition and epistemic justification by examining irrationality. Epistemic irrationality is possible because we are reflexive cognizers, able to reason about and redirect some aspects of our own cognition. One consequence of this is that one cannot give a theory of epistemic rationality or epistemic justification without simultaneously g...

Moore’s paradox in belief is the fact that beliefs of the form ‘p and I do not believe that p’ are ‘absurd’ yet possibly true. Writers on the paradox have nearly all taken the absurdity to be a form of irrationality. These include those who give what Timothy Chan calls the ‘pragmatic solution’ to the paradox. This solution turns on the fact that having the Moorean belief falsifies its content. ...

We demonstrate that also the second sum involved in Apéry’s proof of the irrationality of ζ(3) becomes trivial by symbolic summation. In his beautiful survey [4], van der Poorten explained that Apéry’s proof [1] of the irrationality of ζ(3) relies on the following fact: If a(n) = n

We give a proof of the irrationality of the p-adic zeta-values ζp(k) for p = 2, 3 and k = 2, 3. Such results were recently obtained by F.Calegari as an application of overconvergent p-adic modular forms. In this paper we present an approach using classical continued fractions discovered by Stieltjes. In addition we show irrationality of some other p-adic L-series values, and values of the p-adi...

In 1978, R. Apéry [1], [2] has given sequences of rational approximations to ζ(2) and ζ(3) yielding the irrationality of each of these numbers. One of the key ingredient of Apéry’s proof are second-order difference equations with polynomial coefficients satisfied by numerators and denominators of the above approximations. Recently, V.N. Sorokin [3] and this author [4], [5] have got independentl...