Proof Without Words: Integer Right Triangle Hypotenuses Without Pythagoras

Unitarity triangle without semileptonic decays.

The use of semileptonic decays has become standard in constraining the unitarity triangle. Since precise calculations of these are very challenging, we propose an entirely new approach. The ε{K} constraint, which depends extremely sensitively on |V{cb}|, is replaced by the interplay between ε{K}, BR(B→τν), and ΔM{B{s}}. Improvements on the B→τν branching ratio and on the lattice determinations ...

Understanding Without Words

To understand a sentence, the meanings of the words in the sentence must be retrieved and combined. Are these meanings represented within the language system (the lexical hypothesis) or are they represented in a general conceptual system that is not restricted to language (the conceptual hypothesis)? To erraluate these hypotheses, sentences were presented in which a pictued object replaced a wo...

Infinite words without palindrome

We show that there exists an uniformly recurrent infinite word whose set of factors is closed under reversal and which has only finitely many palindromic factors. 1 Notations For a finite word w = w1 · · ·wn, the reversal of w is the word w̃ = wn · · ·w1. This notation is extended to sets by setting F = {w̃ | w ∈ F} for any set F of finite words. A word w is a palindrome if w̃ = w. A set F of fini...

Words without Objects

Worlds Without Words

This paper points out a deficiency in virtual worlds as they are envisioned today. Several of the more important aspects of human communicative behavior are missing, since there is no way to accommodate natural linguistic interaction with and through the interface. We point out some explicit cases where natural language interaction would be useful in a VR framework, and identify some areas wher...