3,604 research outputs found

    Sensorimotor theory and the problems of consciousness

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    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

    Integral points on elliptic curves and explicit valuations of division polynomials

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    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

    Kickshaws

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    Readers are encouraged to send their own favorite linguistic kickshaws to the Associate Editor. All answers appear in the Answers and Solutions at the end of this issue

    Kickshaws

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    Readers are encouraged to send their own favorite linguistic kickshaws to the Associate Editor. All answers appear in the Answers and Solutions at the end of this issue

    Kickshaws

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    Readers are encouraged to send their own favorite linguistic kickshaws to the Associate Editor. All answers appear in the Answers and Solutions at the end of this issue

    Kickshaws

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    Readers are encouraged to send their own favorite linguistic kickshaws to the Associate Editor. All answers appear in the Answers and Solutions at the end of this issue

    Kickshaws

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    Readers are encouraged to send their own favorite linguistic kickshaws to the Kickshaws Editor. All answers known to the editor appear in the Answers and Solutions at the end of this issue

    Kickshaws

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    Readers are encouraged to send their own favorite linguistic kickshaws to the Associate Editor. All answers appear in the Answers and Solutions at the end of this issue

    The Big Challenge

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    In the November 1974 Kickshaws, we challenged Word Ways readers to select ten different letters from the alphabet so as to maximize the number of five-five letter-splits that could be anagrammed into words. We were careful not to specify rigid rules -- we dislike the Procrustean nature of most puzzle contests with cash awards, and we think that anyone willing to tackle this arduous research ought to have the privilege of determining xes own acceptable and unacceptable words. In the February Kickshaws, we suggested a simple weighting scheme designed to force readers to use common words whenever possible, and lightheartedly proposed a fictitious 12-volume set of logological goodies as a prize to the compiler of the best list
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