Notes on Isaiah 1:18b and 7:14b-16

Math 118B Solutions

Homework Problems 1. Let (Xi, di), 1 ≤ i ≤ n, be finitely many metric spaces. Construct a metric on the product space X = X1 × · · · ×Xn. Proof. Denote points in X as x = (x1, x2, . . . , xn). Given x, y ∈ X define d(x, y) = d1(x1, y1) + · · · + d(xn, yn). Then clearly d(x, y) ≥ 0 and d(x, y) = d(y, x). Furthermore, if d(x, y) = 0 then each di(xi, yi) = 0. That is, each xi = yi and x = y. Final...

Notes on Lectures 1 - 5 Aleksey Zinger March 16 , 2010

Notes on Complexity Theory Last updated : October , 2011 Lecture 16

Let us begin by re-examining our intuitive notion of what it means to “prove” a statement. Traditional mathematical proofs are static and are verified deterministically : the verifier checks the claimed proof of a given statement and is either convinced that the statement is true (if the proof is correct) or remains unconvinced (if the proof is flawed — note that the statement may possibly stil...

Reading Isaiah Berlin in China1

A year before his death in 1997, Isaiah Berlin was invited by a Chinese scholar named Ouyang Kang to write a summary of his thought for the Chinese reading public. Berlin, as Dr Henry Hardy recalls, much valued this new readership, and therefore wrote his last essay, ‘My Intellectual Path’. It was first published in English in the New York Review of Books, and then included in The Power of Idea...

Isaiah 1:2-20 Reconstructed Original Orthography

In the scansion offered below, a reconstruction of the Isa 1:2-20’s original orthography is presented. It is based on the premise that the text derives from the late 8th or early 7th cent. BCE. The orthography mimics that of the Siloam inscription and other inscriptions of that period. Even if by definition the reconstruction is less than certain in a number of instances, it serves to highlight...