113,660 research outputs found
The Paradox of Self-Consciousness
I discuss Bermudez' minimalist approach to self-consciousness approvingly, connecting it with other positions in philosophy and trying to separate it from ideas about non-conceptual content
Product formulas for the 5-division points on the Tate normal form and the Rogers–Ramanujan continued fraction
Explicit formulas are proved for the 5-torsion points on the Tate normal form E5 of an elliptic curve having (X,Y)=(0,0) as a point of order 5. These formulas express the coordinates of points in E5[5]−⟨(0,0)⟩ as products of linear fractional quantities in terms of 5-th roots of unity and a parameter u, where the parameter b which defines the curve E5 is given as b=(ε5u5−ε−5)/(u5+1) and ε=(−1+5–√)/2. If r(τ) is the Rogers-Ramanujan continued fraction and b=r5(τ), then the coordinates of points of order 5 in E5[5]−⟨(0,0)⟩ are shown to be products of linear fractional expressions in r(5τ) with coefficients in Q(ζ5)
Should We Colonize Other Planets?
A critical exposition of plans to colonize other planets , especially Mars, and their costs. The final chapter links with issues about the value and future of human life. See the extended summary uploaded to this site
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