Integral Identities





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Is "scale insensitivity" destroying climate activism?

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Here's an image you're probably familiar with: it's the BBC News website banner.  The space between "InDepth" and "UK" is reserved for quick links to the most important issues of the day, and right now it reads "Israel-Gaza war | War in Ukraine | Climate".  It's fair to assume that the highest priority issues are closer to the left, based on how frequently these issues end up in the headline article. So, I wondered, how has the priority - according to the BBC - of the biggest issues changed over time?  I decided to sample the website using the wayback machine , once per year from September 2020 to September 2025, and here's the result:   Over these 6 years the BBC News banner has had between 1 and 4 quick links.  And it seems to be a consistent feature that whenever a new story comes along that threatens fewer lives, it takes a higher priority position in the banner.  "Climate" didn't turn up until 2022, and when it did it...
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Schroedinger from nothing

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When learning Quantum Mechanics the rules can seem very abstract, and also very arbitrary.  The starting point is often taken to be the Schroedinger Equation, a deterministic equation describing the rate of change of an isolated system's state, and the Born Rule, which describes how that state gives rise to probabilities for each outcome when you interact with the system by making a measurement.  These two form the axioms of quantum mechanics from which everything else flows. These axioms seem incredibly arbitrary, which makes accepting them harder.  In this post I will show that you can, in fact, start with much more basic axioms and then derive both the Schroedinger Equation and the Born Rule from them.  What's more, we'll be able to show how collapse of the wavefunction  emerges  from these simpler axioms as a  subjective  phenomenon.  This then deals with the measurement problem, which is that collapse appears  to require us to arbit...
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Keeping the lights on

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Ever since the blackout that affected much of Spain , I've been wondering how it's going to work when renewable power starts to approach 100% of the power supplied by the grid.  That blackout may have been caused by a number of different factors, but the forces of evil were quick to point out that one thing that  may  have caused it was that there was too much renewable energy in the grid at the time. Renewable energy such as solar comes naturally in DC whereas the grid supplies AC at 50Hz (in Europe anyway).  This means that before it can be fed into the grid it has to be passed through an "inverter" to turn it into AC.  This is typically done by phase-locking to the grid signal, which is fine until the supply approaches 100% renewable at which point the question becomes: but who is setting the frequency?  I'm not sure whether or not this really was an issue in Spanish blackout, but it's a reasonable question to ask. A pretty good answer was provided by a...
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