On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

El origen de la construcción fenomenalista: Mach, Moore y Whitehead

It's usually believed that the idea of applying logical methods to constructivist phenomenalism was, --in general- a result of Russell's originality. In this paper is argued that some important ideas were in fact due to Mach, Moore and Whitehead. According to the author, Russell got from Mach the general idea of epistemology as an analysis of scientific concepts and, specially,the idea of sensations as the building blocks for his logical construction. Moore made Russell believe that only sensations are known in a direct way, and so, the existence of external objects as the cause of our perceptions is only inferred. Moreover, according to the author, Russell's views on sense data -his sensibilia- are also due to Moore. Finally, Russell got from Whitehead the idea of the phenomenical reconstruction as an alternative to the causal theory of perception, and also how the logical construction should be done. The author undertakes also a detailed analysis of some early works of Whitehead not very well known.

Book Review of Cetacean Societies: Field Studies Of Whales And Dolphins Edited by I. Mann, R. C. Connor, P. L. Tyack & H. Whitehead

Studying the sociobiology and behavioral ecology of cetaceans is particularly challenging due in large part to the aquatic environment in which they live. Nevertheless, many of the obstacles traditionally associated with data gathering on tree-ranging whales, dolphins and porpoises are rapidly being overcome, and are now far less formidable. During the past several decades, marine mammal scientists equipped with innovative research methods and new technologies have taken field-based behavioral studies to a new level of sophistication. In some cases, as is true for bottlenose dolphins, killer whales, sperm whales and humpback whales, modern research paradigms in the marine environment are comparable to present-day studies of terrestrial mammal social systems. Cetacean Society stands testament to the relatively recent advances in marine mammal science, and to those scientists, past and present, whose diligence has been instrumental in shaping the discipline.

God: Savior, Butcher, Or Oblivious Artist? The Theodicy Of Alfred North Whitehead

This paper is a critical examination of Alfred North Whitehead's attempt to solve the traditional problem of evil. Whitehead's conception of evil is crucial to his process cosmology because it is integral to his process cosmology because it is integral to his notion of creation in which evil is understood in relationship to the larger dynamic of God’s creative activity. While Whitehead’s process theodicy is interesting, he fails to successfully escape between the horns of the traditional dilemma. Whitehead is often criticized for treating evil as merely apparent. While some process philosophers, notably Maurice Barineau, have defended Whitehead from this charge, it can be shown that this is an implication of Whitehead’s approach. Moreover, Whitehead’s theodicy fails to address radical moral evil in its concrete dimension in respect to real human suffering. As a result, Whitehead’s theodicy is not relevant to Christian theology. My paper is divided into two parts. I will first briefly discuss the traditional problem of evil and some of the traditional problem of evil and some of the traditional solutions proposed to resolve it. The reminder of the paper will demonstrate why Whitehead’s theodicy addresses the traditional problem of evil only at the expense of theological irrelevancy.

A forgotten genius: Charles Whitehead. A critical monograph ...

"Chronological and bibliographical table". pp. [295]-297.

Warwickshire; painted by Frederick Whitehead, R. B. A.,

Plates accompanied by guard sheets with descriptive letterpress.