U.S. tells embassy staff in Israel to leave now if they want amid Trump threats to attack Iran

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How this addresses the real-world failures from earlier

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A Riemannian metric on a smooth manifold \(M\) is a family of inner products \[g_p : T_pM \times T_pM \;\longrightarrow\; \mathbb{R}, \qquad p \in M,\] varying smoothly in \(p\), such that each \(g_p\) is symmetric and positive-definite. In local coordinates the metric is completely determined by its values on basis tangent vectors: \[g_{ij}(p) \;:=\; g_p\!\left(\frac{\partial}{\partial x^i}\bigg|_p,\; \frac{\partial}{\partial x^j}\bigg|_p\right), \qquad g_{ij} = g_{ji},\] with the matrix \((g_{ij}(p))\) positive-definite at every point. The length of a tangent vector \(v = \sum_i v^i \frac{\partial}{\partial x^i}\in T_pM\) is then \(\|v\|_g = \sqrt{\sum_{i,j} g_{ij}(p)\, v^i v^j}\).

We’ve entered into a Faustian pact with these companies: “While it’s brilliant to have access to high-quality products and software, very often for ‘free’, it’s important to remember that there is a trade-off involved – often of our personal data and privacy,” says Lisa Barber, tech editor at Which? We give these companies our attention and our information, which they then turn into big bucks and apparently unassailable monopolies.

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