Dork Scratchings

Dork Scratchings has finally decarbonised!  The first to go was the fossil fuel investing pension (this has been replaced by PensionBee's fossil fuel free plan ), then went the petrol car (replaced by an electric 208), and this week we got rid of the boiler. The new heating system is a Mitzubishi heat pump which heats water by extracting heat from cold air.  The laws of Thermodynamics set a limit on the amount of heat energy that can be produced per unit of electrical energy and the formula is $$ \frac{T_H}{T_H-T_C} $$ Where $T_H$ is the temperature of the hot water ($50^\circ C$ in our case), and $T_C$ is the temperature of the cold air outside the house.  Note that the temperatures have to be in Kelvin to make this work, and the value drops as the outside temperature drops.  For example, for $50^\circ C$ water, it is 12.9 when the outside temperature is $25^\circ C$ but only 6.5 when the outside temperature is $0^\circ C$.   The heat produced per unit of ...

  Curated by Dorkscratchings, 2024

Why is it tides are semi-diurnal ? That is, why do they occur every 12 hours when they are caused by the gravitational pull of a moon that we turn to face once a day?  The straightforward answer is that water bulges out on both the side nearest and the side furthest from the moon.  (We'll ignore the Sun for simplicity, but adding it in doesn't change anything.) The Earth rotates while the bulges remain in place, causing tides 12 hours apart.  However, this doesn't explain why there should be two bulges.  The reason becomes clear when you change the frame of reference.  Instead of thinking about a frame in which both the moon and the Earth rotate, set the origin to be the centre of mass of the two objects, and choose a rotating frame in which the moon is stationary.  In this frame there is a "fictional" centrifugal force of $\omega^2 r$ which combines with the gravitational force from the moon, $GM_{\text{moon}}/(r-r_{\text{moon}})^2$ The two forces match a...

In 1964 John Stewart Bell proposed an experiment to determine whether the results of quantum measurements were truly random, or governed by hidden variables, i.e. state that exists prior to the measurement, but which we don’t have access to. The experiment involved creating a large number of EPR pairs, and firing them at two observers, Alice and Bob, who measure their photon’s polarisation, choosing the $\updownarrow$ direction or the $\nearrow\llap\swarrow$ direction at random. Determining the result of the experiment involves doing a complex statistical calculation to see if something called Bell’s inequality is satisfied or violated. The Bell experiment was first performed by in 1982 by Alain Aspect, and the result, as most commonly interpreted, is that hidden variables can only exist if Quantum Mechanics is non-local, i.e. if it supports faster-than-light causality! Some time after Bell proposed his experiment, Greenberger, Horne, and Zeilinger suggested an alternativ...

In this post I argue that economic growth is not the normal state of affairs, it is a blip caused by the discovery of a one-off resource of non-renewable energy.   The logistic equation $$ \frac{dy}{dt} = y(1-y) $$ Here's a simple model.  Humans discover an exploitable but limited resource and start consuming it.  The amount consumed, $y(t)$, is a function of time.  The general form of the equation is $\frac{dy}{dt} = \alpha y (\beta - y)$, but if you choose the right units $\alpha$ and $\beta$ both become $1$. Why should this work, in principle? Early on, the factor $1-y$ is approximately $1$ and can be ignored.  So the model states that annual consumption $dy/dt$ starts off proportional to $y$.  In other words, $y$ grows exponentially at first.  This could happen if exploiting the resource enables further exploitation of the resource.  For example, suppose a few humans are shipwrecked on an island with 1000 trees: they take ages to cut down the ...

My first neural net Like everybody else I've been playing a lot with ChatGPT recently and I'm gobsmacked by how good it is!  This has led me to start researching how exactly these things work.  In particular I wanted to understand how neural nets - a core component of the technology - are trained. Running a neural net is simple.  The neural net consists of layers of nodes connected by weights and biases.  The first layer is an input layer and setting the activation levels of each node in that layer causes the next layer to adopt values determined by the weights and biases.  The second layer determines the activation levels in the next layer and so on until the final layer, which is interpreted as the output.