Dork Scratchings

The extended family I've been sharing digs with... See alt-text for code

Credit: NASA This article in the guardian points to some recent research.  The article begins: Planting billions of trees across the world is one of the biggest and cheapest ways of taking CO2 out of the atmosphere to tackle the climate crisis, according to scientists, who have made the first calculation of how many more trees could be planted without encroaching on crop land or urban areas. As trees grow, they absorb and store the carbon dioxide emissions that are driving global heating. New research estimates that a worldwide planting programme could remove two-thirds of all the emissions from human activities that remain in the atmosphere today, a figure the scientists describe as “mind-blowing”. and goes on to quote the lead scientist from ETH Zürich saying "This new quantitative evaluation shows [forest] restoration isn’t just one of our climate change solutions, it is overwhelmingly the top one" Let's test this claim with two tools everyone has at their disp

In 2018 the Intergovernmental Panel on Climate Change produced a report on 1.5 C of warming .  This is considered a level of warming that is 50% likely to trigger a tipping point beyond which further warming will be beyond human control. According to the report: "Global warming is likely to reach 1.5°C between 2030 and 2052 if it continues to increase at the current rate" Unfortunately, that's been taken by our politicians to mean we've got until 2050 to zero our emissions. Let's see if this is true: According to section C.1.3 "C.1.3. Limiting global warming requires limiting the total cumulative global anthropogenic emissions of CO2 since the pre-industrial period, that is, staying within a total carbon budget (high confidence). By the end of 2017, anthropogenic CO2 emissions since the pre-industrial period are estimated to have reduced the total carbon budget for 1.5°C by approximately 2200 ± 320 GtCO2 (medium confidence). The associated remaining budget i

Why does $\sqrt{2} \ne \frac{7}{5}$?  Well, if it did, we could draw a square of side 5 and diagonal 7 Not in proportion! Then, by removing 5 from the diagonal we could create a second square of side 2 and diagonal 3, which would mean $\sqrt{2} = \frac{3}{2}$, which is a  different fraction to $\frac{7}{5}$. Actually, we can easily generalize this argument to show that if $$ \sqrt{2} = \frac{a}{b} $$ for some whole numbers $a$ and $b$, then $$ \sqrt{2} = \frac{c}{d} $$ for some smaller whole numbers $c \lt a$ and $d \lt b$.  Repeating this argument over and over leads us to the conclusion that $\sqrt{2}$ is a whole number itself!  This is clearly incorrect and leads us to the conclusion that we can't in fact write $\sqrt{2}$ as a fraction. This is not a particularly modern way to prove the existence of irrational (non-fraction) numbers, but it is - supposedly - how the ancient Greeks originally did it!  Unfortunately the person who discovered this fact, Hippasus of Metapontum , fo

Here's a cartoon I made on my phone.  It's an explanation of what the Polar Jet Stream is and how it might be changing! The winter of 2019/2020 was the 5th wettest on record in the UK, and the spring of 2020 looks like it will turn out to be the driest.  This has been attributed to the polar jet stream being more wavy and slower to change shape than in the past.  This meant that we got stuck in a U bend all  winter and an $\Omega$ bend all spring! This may be due to climate change, specifically the higher rate of heating that is occurring in the arctic region as newly exposed sea water causes less sunlight to be reflected.  However, most climate models appear to suggest the opposite: that the Jet Stream will speed up and become less wavy. Some types of prediction in climate science are easy and others are hard.  That the Earth will warm up significantly this century is certain; exactly what that will do to the polar jet stream and local weather patterns is very uncertain.  All

Hobbit hole, Chalkney Woods (Homunculum cuniculum) Stinkhorn, Sandringham (Phallus Impudicus) Wild dog with pliosauroid fossil, Sandringham (Canis Poodiculous)

I'm old enough to remember when holograms first appeared commercially.  I remember being amazed and trying to look behind to see if it wasn't just a 3-dimensional object masquerading as a 2-dimensional object (masquerading as a 3-dimensional object).  It must have looked like when you show a chimp a mirror and it tries to reach behind it to touch its reflection.  (I guess the same would happen to a human if it saw a mirror for the first time as an adult.) I did one year of physics at university before switching to maths.  In general I didn't like the practical sessions because they were always at the end of the day, and very long and tiring.  However, on one occasion we got to make our own holograms, and that really did impress me.  IIRC mine was of a 2 pence piece. What I found really interesting, was finding out how they worked.  I don't think we were taught this as such - it was up to us whether we wanted to go off and find out for ourselves.  Anyway,

From: Learn To Speak Mafia About 15 years ago I was working for a small firm making telecoms equipment , and developing from scratch a Voice over IP box.  It was a very simple device to convert SIP internet calls to local analogue POTS lines (Plain Old Telephony Service) and there were just two of us working on the project: Mike the hardware engineer, and me, for the software. The box had a microprocessor running Linux (including a massively hacked version of Linphone for the SIP stack), and it had a DSP to support the codecs (short for Codify/Decodify).  It was quite a fun project (*) . A word about codecs and SIP:  SIP stands for Session Initiation Protocol (**) and is an internet standard allowing two internet peers to start a phone call.  One of the main tasks SIP has to perform is to co-ordinate on which codec to use.  One peer may support GSM, G.729, and G.711, and another may support G.726, GSM, and Speex - in which case the two peers would have to agree to use their on

Curiously, I think the answer is that human males are generally monogamous. Before getting on to that we should ask: what is the excess adipose tissue carried by females of the human species actually for?  There are two naive answers which I've heard expressed in the past: To provide milk for the human infant To attract a mate Neither of these explanations hold water.  Every other mammal that I'm aware of only has swollen glands whilst the offspring are young enough to breastfeed. At all other times the females look more or less similar to the males.  The second explanation leaves open an obvious question too.    Why should a male be attracted to these things in the first place? What does seem to be true, is that - all other things being equal - possession of the aforesaid is an encumbrance, as any well-endowed cave-woman that has ever tried to flee a sabre-toothed tiger might attest. There are cases in nature, however, where encumbrances are carried purely to i

Lockdown reading My lockdown reading list consists of just one book. This might last a long time I thought, so it's my opportunity to make a 2nd stab at understanding Quantum Field Theory. Last time, I bought "Quantum Field Theory for the gifted Amateur" and I learned a lot from it. Mainly that I am not gifted! I got three chapters through it and then gave up on the book, and on quantum field theory. This time round I did my research better and found a much more gentle book: Student Friendly Quantum Field Theory, by Robert D. Klauber . It covers the same material, but takes pains not to lose the reader, by spelling out every ambiguity and subtlety. I'm half way through and feeling quite chuffed with myself. Here I am studying hard, on a sunny day in Lockdown Britain: No, the weights are not mine In this book, and every other in the QFT literature there is a concept of some particles being virtual. What's this about?  Why are some virtual and o

I decided to watch Contagion on the telly the other night.  I thought it might be fun to see how Hollywood's idea of a pandemic matched reality....  Anyway, can you spot the glaring mistake in this clip? That's right!  He said math  when he should have said maths .  Math ith a roman catholic thervith! There was another problem too.... In the exponential phase the numbers infected increases by the same factor each day, rather than squaring each day.  Or to put it another way, the sequence should have been $$ x_n = 2^n $$ and not what he said, which was $$ x_n = 2^{2^{n-1}} $$ Dear Hollywood, I am happy to offer my services as on set math(s) consultant.  I am very cheap.

When it comes to getting action on the climate crisis I think no-one has been more successful than Extinction Rebellion .  I remember at a party one time showing the NASA CO2 graph to a lady who didn't believe it could be real.  "If this were true people would be running around in the streets screaming" she told me.  That's why XR's tactics actually work.  You can hear day in day out about the urgency and severity of the crisis, but while people are carrying on as before it's difficult for the information to break out from the intellectual part of your brain, and occupy the bit that can actually make a difference. I don't have an issue with XR's tactics, but I do worry about how we often talk to the public when we do have their ear. The pie chart above is completely made up, but I think it's about right. A tiny proportion of the general public make up their minds by looking up facts and figures; a slightly larger - but still tiny - number ar

[Or was it the editing...?]  At first glance it appears that this recent news article on the BBC is going to be a complete hatchet job on Professor Jem Bendell, author of the Deep Adaptation paper.  The paper is an honest, if uncomfortable appraisal of the likelihood of civilisational collapse caused by the climate crisis, and a blueprint for how we can work together to survive it as best we can. The first indication it's going to be hatchet job is the title: "The 'climate doomers' preparing for society to fall apart" Clearly, calling someone a "doomer" is a way of dismissing their point of view without actually challenging it.  Of course the BBC have taken the approach of distancing themselves from any responsibility by putting 'climate doomers' in quotes.  That's a standard trick for when you want to say what you think without having to justify it. The first paragraph of the article is in bold , and is highly dismissive of Ben

This reminder has been on a wall in my house for ~15 years As a programmer for 22 years I've fixed thousands of bugs, and created many times more.  Very often it appeared that the problem I was trying to fix had multiple independent causes.  However I have found - almost invariably - that if you dig long enough you'll find a single cause for all the problems you are seeing.  In fact the moment you hit on the right theory is often really obvious because it suddenly explains a whole bunch of other things that have been going wrong!  But, I wondered, can this observation be proven mathematically?  It turns out it can! The Debugger's Theorem If a system that usually works currently isn't working, then it is more likely than not that there's just one thing causing all the observed problems. Proof Let $P_0$ be the probability that the system has no problems, $P_1$ be the probability that one independent problem has occurred, $P_{2+}$ the probability that two

Article in the Telegraph... And now, the punchline...

How fast would you have to fire a cannonball for it to never hit the ground? Newton's very first ideas about gravitational orbits are said to have come about from a thought experiment. A cannonball was known to lose 5 metres of altitude a second after being fired horizontally, but the Earth - being round - curves away from the cannonball as it flies forward. So it occurred to Newton to ask: How fast would the cannonball have to be fired for the curvature to completely compensate for the vertical loss? If a cannonball was fired at this speed it would never lose any altitude, and end up orbiting the Earth. The diagram above shows that the answer can be found using simply trigonometry and comes to $$ \begin{align} v &= \sqrt{gr} \\ &= \sqrt{9.81 ms^{-2} \times 6.371\times 10^6 m} \\ &= 7868\space ms^{-1} \\ &= 17603\space mph \end{align} $$ In general, (non-relativistic) orbits are elliptical The next stage was to look at more general orbit