Integral points on elliptic curves and explicit valuations of division polynomials

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one integral multiple [n]P such that n > C. The proof is a modification of a proof of Ingram giving an unconditional but not uniform bound. The new ingredient is a collection of explicit formulae for the sequence of valuations of the division polynomials. For P of non-singular reduction, such sequences are already well described in most cases, but for P of singular reduction, we are led to define a new class of sequences called elliptic troublemaker sequences, which measure the failure of the Neron local height to be quadratic. As a corollary in the spirit of a conjecture of Lang and Hall, we obtain a uniform upper bound on h(P)/h(E) for integer points having two large integral multiples.Comment: 41 pages; minor corrections and improvements to expositio

Sensorimotor theory and the problems of consciousness

The sensorimotor theory is an influential account of perception and phenomenal qualities that builds, in an empirically supported way, on the basic claim that conscious experience is best construed as an attribute of the whole embodied agent's skill-driven interactions with the environment. This paper, in addition to situating the theory as a response to certain well-known problems of consciousness, develops a sensorimotor account of why we are perceptually conscious rather than not

A lower bound for the canonical height on elliptic curves over abelian extensions

Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prove that there is a positive constant C(E/K) so that every nontorsion point P in E(K^ab) satisfies h(P) > C(E/K)

[Review of] Juan F. Perea, ed. Immigrants Out!: The New Nativism and the Anti-Immigrant Impulse in the United States

Immigrants Out! offers a response to nativist sentiment in the contemporary discussion of immigration policy. Individually, each chapter in this edited volume charts the development of contemporary nativist sentiment, while identifying the themes that have nurtured nativism historically. Some important relationships are identified between issue oriented politics and more general theses that emerge from nativist thought. For instance, in several passages English-only laws are described as a small, although highly symbolic, component of a broader ideology based on separatism and isolationism. Similarly, proposals to place restrictions on social welfare benefits for immigrants are linked to the more general curtailment of human rights. Moreover, the current trend toward heightened restrictions on immigration and naturalization is paralleled with restrictive immigration policies of the past

[Review of] Bruce E. Johansen, (ed.) The Encyclopedia of Native American Economic History

The Encyclopedia of Native American Economic History offers a unique perspective on economic development in North America, primarily because it constantly reminds the reader of the fundamental contradictions that this process has entailed. A view of economic processes fundamentally different from orthodox scholarly analysis emerges in many of the volume\u27s entries. In total a picture of economic activity is projected that links consumption, cultural conflict, social and ecological reproduction, and the transformation of group identity. This volume takes exploratory steps toward the development of alternative explanations of economic growth and change in society, particularly as these processes relate to the meaning of race and ethnicity. The book\u27s strongest sections are those that offer a multi-faceted view of the overlapping effects of political, social, and economic institutions on Native American groups. The volume includes several entries of this kind dealing with topics such as the legal status of Native American lands, agricultural development, environmental degradation, and the manner in which Native American groups have organized cultural and economic life historically