Dork Scratchings

  I've been thinking a lot about the limits to growth recently.  If you look up the non-renewable resources that our economy depends on it quickly becomes apparent that all of them, whether they be fossil fuels or metals like copper , are somewhere between 30% and 70% exhausted.  And the exhausted part is invariably the easiest to get to.  However, it has only recently occurred to me that land is also a non-renewable resource:  they're not making any more of it.... Checking out Our World in Data  one can see that nearly 5 billion hectares are currently in use by humans.  That compares with a total available of 13 billion hectares, if you discount the ice covered land.  So, in fact land falls into the same 30-70% exhausted range as everything else. I downloaded the data and produced a smoothed graph of growth (%) vs year and found something interesting: growth grew more or less exponentially until about 1956 at which point it fell sharply to zero....

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...

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...

I did a little embedded project recently.  Years ago I bought a binary coded decimal clock which no longer works, and I thought I could replace it with one I built myself.  (In reality this was simply an excuse to play with programming a Raspberry Pi Pico.) Broken BCD clock (left) and home grown replacement (right).  The LEDs are in 6 columns and represent time in hh:mm:ss format, with each decimal digit represented in binary. During the project I realised I needed to create a little Finite State Machine to enable setting of the time using the bootsel button.  So I searched around on the internet and found tens of different libraries, but each with its own drawbacks. Some required a wizard executable to auto-generate code which you then edit, which has the drawback that if you change the input to the wizard you then need to manually merge new auto-generated code with your changes.  Other libraries, had this strange thing where each state had its own "enter" and...

In my previous post  Building a tensegrity structure I implied that when the thread was pulled taut an icosahedron would form.  I didn't directly use the word "icosahedron" but I did claim that you needed to allow enough thread for a stick length to triangle edge ratio of $(1+\sqrt 5)/2$, which amounts to the same thing.

 My latest project   This turned out to be a bit more fiddly than I expected.  This is partly because I set myself the goal of building it using a single piece of string and it wasn't entirely obvious how to do that without missing or repeating some edges.  Here are my tips:   1. Cut 6 pieces of bamboo Obviously these should all be the same length.  Hollow them out before going any further. 2. Measure out the thread The thread will pass through each bamboo 4 times, plus there are 24 edges between bamboo ends.  The bamboo sticks are $(1+\sqrt 5)/2$$^{[\text{see footnote}]}$ times the length of the edges (i.e. the golden ratio!)  You will need a bit more than this to make it easier to tie the ends.  Place two marks on the thread with a pen to identify where the knot should fall.   3. Blue tack the bamboo pieces in place This means creating a ball of blue tack and attaching 3 parallel pairs of bamboo to it in such a way that each pair is at...

This is perhaps the greatest epiphany of my life.  The moment I realized how to neatly summarize my understanding of the science I was learning: Time does not exist. Of course, this is just an interpretation, and a personal one.  It may not be true but in it's defence I assert it is consistent with many physicists' view of the world (though they may put it a different way).  It may not even make sense to ask whether it is true or not: what does it mean to say that a thing we don't understand, and haven't clearly defined, doesn't exist.  But like a lot of ways of thinking about reality, the real question is: Is this helpful? The things we know exist in the world can be divided into two categories: those for which we have direct evidence, and those for which we have indirect evidence.  In the former category we have light, sound, touch, smell; in the latter planets, atoms, and waves.  Time also belongs to the latter category.  We think about the future w...

 

  Time series showing the decline of growth in advanced (or "fully grown"?) economies since the 1960s suggesting an end to growth within one generation.  Growth in developing economies increased enormously between 1990 and 2005 but is now showing the same trend towards zero as advanced economies suggesting the entire world is hitting the same resource limits.  This graph took me 10 minutes to plot using publicly available data, but the obvious conclusions for the feasibility of long term growth are beyond the imaginations of almost all political leaders today.  Are we in the midst of a societal-scale shared delusion? Which do you want first...? Let's start with the bad news.  The bad news is that growth in industrialized, high income economies has been falling for the last six decades and looks like it will reach zero sometime within a generation.  (That's assuming it hasn't already reached zero with the positive growth figures that countries report...

I'm still a bit obsessed with the GHZ experiment.  This is the one where you prepare a GHZ state $\lvert 000 \rangle + \lvert 111 \rangle$ and send one qubit to each of 3 protagonists: Alice, Bob, and Charlie.  (I will be ignoring shared normalizer constants throughout this post, as I find they don't add anything to the understanding.) If you do the maths it turns out that when all three choose to measure in the $\lvert + \rangle$, $\lvert - \rangle$ basis (shorthand for $\lvert 0 \rangle + \lvert 1\rangle$ and $\lvert 0 \rangle - \lvert 1\rangle$) then they are guarranteed to get a parity zero result.  On the other hand if only one measures in this basis and the other two measure in the $\lvert +i\rangle$, $\lvert -i\rangle$ basis (shorthand for $\lvert 0 \rangle + i\lvert 1\rangle$ and $\lvert 0 \rangle - i\lvert 1\rangle$) they are guarranteed to get a parity one result.  As I showed in an earlier post this appears to be incompatible with the outcomes being prede...

It has occurred to me that the cartoon I drew two days ago will appear to most people as absurd: Alice measures one half of an entangled pair and instantly splits into two versions of herself!  Bob measures the other half and also splits, but each Alice is paired with one of the Bobs in such a way that, should they meet later to discuss their results, everything remains consistent. Yet if you replace Alice and Bob with two qubits - to get a quantum circuit like the one below - no quantum computing expert would find this outcome absurd. The Einstein Podolsky Rosen experiment in circuit form with non-classical Alice and Bob Alice is qubit q0 and Bob is q3 .  Qubits q1 and q2 are entangled into the Bell state $(\lvert 01 \rangle + \lvert 10 \rangle)/\sqrt 2$ and then q1 is shared with Alice, and q2 with Bob.  In the standard (collapse-based, non-multiversal) description Alice and Bob measure q1 and q2 , collapse the q1q2 wavefunction, and find that one gets 0 while the...

I just read this article on phys.org which claimed to "resolve the paradox" that entanglement appears to imply faster than light communication.  I don't think it actually resolves the paradox, it just side steps it.  Here's how the argument goes (and I paraphrase): Alice and Bob share a pair of entangled qubits in a Bell state $\left( \lvert 01 \rangle + \lvert 10 \rangle \right)/\sqrt{2}$. When Alice measures hers it "collapses" the pair's state immediately even if Bob is a great distance away.  However, this does not imply faster than light communication because, although Alice now knows what Bob will measure, Bob does not know until he makes a measurement himself, or receives a message from Alice which can only travel at the speed of light. This argument misses the point somewhat.  If the state of both qubits changes instantly when Alice measures her qubit (e.g from $\left( \lvert 01 \rangle + \lvert 10 \rangle \right)/\sqrt{2}$ to $\lvert 01 \rangl...

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 ...