## Something I didn’t know before now

I suppose I first noticed those “Energy Star” logos on computer equipment about a decade or so ago – but I did not realise until now that Energy Star is in fact a US government programme – as opposed to just a piece of marketing by the hardware companies themselves. We really do not expect such things from the US!

Energy Star also, I discovered, say that data centres account for 1.5% of US electricity consumption and that the volume (not necessarily the proportion) of demand will double every five years or so. I do not see how that – unless it is replacing something else (lights in shops on Main Street?) – could possibly be sustainable, certainly not without massive investment in renewables and nuclear: shale gas might be cheap but it is far from CO2 neutral.

## How many kilowatt hours have I burnt losing weight? Not that many

Here’s a slightly sobering calculation – both in terms of what it tells us about human energy use and human frailty.

Since I started working in the gym, about 18 months ago, I think I have lost about 40 lbs of fat (weight loss is a bit more than that, but I am concentrating on fat).

If human fat has a calorific value of about 4000 kilocalories per pound, this all works out at about 44 kilowatt hours – around £5 (\$7 or so) worth of electric power. (Or, judging by the winter gas bill I have just received this is around a day’s worth of gas usage).

Thinking of it another way – 100 watts on the exercise bike is fairly easy to maintain for a sustained period (I would not normally do more than half an hour on this but I am sure I could do this for several hours if all else fails) – this 444 hours.

Of course I have used far more than this to sustain this weight loss – but it puts our routine energy use into perspective to think that all that effort is just a day’s worth of hot water, hobs and central heating.

## More evidence of Bitcoin bubble

Few things attract fraudsters more than bubbles. When the market is rising then their crimes get hidden – especially as those speculating in the market are unlikely to want to have its legitimacy called into question.

So too with Bitcoin – the BBC reports that the ever inflating bubble in Bitcoin has attracted the criminals who run botnets. Although these things are generally not too computationally powerful they are big enough and the market inflated enough to make it worth the while of criminals to target “Bitcoin mining“: the computationally intensive task of generating a new Bitcoin (the equivalent of digging another sovereign’s worth of gold out of the ground).

A sure sign of the crazy nature of the Bitcoin market is that it has caused inflation in the price of setting up a Botnet. Spamming – the more usual use of a Botnet – relies on the low (close to zero) marginal cost of sending out a spam email – something that is itself a function of the cost of establishing and running a Botnet.

One delicious thing to look forward to when the Bitcoin bubble bursts is that the Botnet owners will be economically ruined along with all the other speculators.

## Euler’s formula proof

Reading An Introduction to Laplace Transforms and Fourier Series I reach the point where it is stated, rather axiomatically, that: $e^{ix} = \cos x + i \sin x$.

This is a beautiful formula and has always suggested to me some sort of mystical inner mathematical harmony (yes, I am a materialist, but I cannot help it).

But these days I also want to see the proof, so here is one:

We know that complex numbers can be described in polar co-ordinates:

$z = |z| (\cos \theta + i\sin \theta)$

So too $e^{ix} = r(\cos \psi + i \sin \psi)$ where $r$ and $\psi$ depend on $x$.

Now (and applying the product rule) $\frac{d}{dx}e^{ix} = ie^{ix} = \frac{dr}{dx}(\cos \psi + i\sin \psi) + \frac{d \psi}{dx}r(-\sin \psi + i \cos \psi)$

So we equate the real and imaginary sides of both sides of this equality we have:

$ie^{ix} = (\cos \psi \frac{dr}{dx} - r \sin \psi \frac{d \psi}{dx}) + i(\sin \psi \frac{dr}{dx} + r \cos \psi \frac{d\psi}{dx})$

Then, recalling $e^{ix} = r(\cos \psi + i \sin \psi)$, we have $ir (\cos \psi + i \sin \psi) = ir \cos \psi - r sin \psi = ( \cos \psi \frac{dr}{dx} - r \sin \psi \frac{d\psi}{dx}) + i( \sin \psi \frac{dr}{dx} + r \cos \psi \frac{d\psi}{dx})$

By inspection we can see that $\frac{dr}{dx} = 0$ and $\frac{d\psi}{dx} = 1$, giving us:

$ie^{ix} = - r \sin \psi + ir \cos \psi$ and multiplying both sides by $i$ we have: $-e^{ix} = -r \cos \psi - i r \sin \psi$

Reversing the signs: $e^{ix} = r \cos \psi + i r \sin \psi$

But what of $r$ and $\psi$? Well, we have $\frac{dr}{dx} = 0$ and $\frac{d \psi}{dx} = 1$.

So $r$ is constant with respect to $x$ while $\psi$ varies as $x$.

If we set $x = 0$ then $e^{i \times 0} = 1$ – a wholly real number, so $\sin \psi = 0$ and $\psi = 0$. Thus $r ( \cos 0 ) = e^0 = r = 1$ and we can replace $\psi$ with $x$ throughout.

Hence: $e^{ix} = \cos x + i \sin x$.

## When will the Bitcoin burst happen?

This chart is interesting:

Over the last five days we can see that the Bitcoin price has risen by 25% but that volumes have remain low except when prices fell.

Having very recently read Galbraith’s The Great Crash 1929 – an essential classic – my gut feeling is that indicates the crash is pretty close. There plainly are a lot of people who will want to get out when they think the time is right and so they will stampede one another when a sell-off begins in earnest.

My instinct, for what it’s worth (I don’t trade in Bitcoin, I don’t intend to and I am nobody’s financial adviser), would be to sell now: don’t wait for the moment the market goes into a tailspin.

## Tinfoil and Bitcoin

The article I wrote on Saturday on the Bitcoin bubble has seen increasing traffic every day this week and now is the most read page on the site.

The interesting thing is that the way in which people get to the page is effectively hidden – no real referral tracks are visible. Though there has been an increase in the number of search driven visits where users have hidden the query (either explicitly and individually or because their search engine does this by default.)

If more evidence were needed that Bitcoin is an obsession of slightly strange people who think the modern world is a conspiracy against them, here it is.

The interesting thing, though, is that a few of them seem to be quite worried that Bitcoin is indeed a bubble and is likely to burst.

The Scientific American reports that the mass of the Higgs Boson indicates that our Universe is merely meta-stable and that, via quantum tunnelling it is possible that our universe could transition to a different, lower energy state: in other words the universe (as we know it) would end.

The half-life of our current meta-stable state is reckoned to be many, many billions of years and so, we are assured, the changes of this actually happening to us in any given time are essentially zero.

But surely, if we accept the “many worldsinterpretation of quantum mechanics, this means that our current universe has already decayed (and is, indeed, decaying all the time). We just hope and believe (based on the evidence) that we happen to live in a typical one of those many worlds and so the chances of us seeing our universe decay are negligible. But what if that were wrong?

## Centenary of Paul Erdős

Paul Erdős was born 100 years ago today.

As the most prolific mathematician of all time I am rather disappointed he hasn’t been deemed worth a “Google doodle“.

Erdős was victimised in the McCarthy era in the US and certainly seems to have had a warm relationship with the Hungarian Communist authorities (though there is nothing to suggest he was a spy), though eventually boycotted the country over its treatment of Israeli citizens.

To see some of his work have a look at the Erdős-Straus conjecture.

## Why I love Metapost

I am writing some stuff about Conway’s Game of Life (and Scratch) – thinking about whether it is possible to explain to adults the basics of programming a computer using the Scratch Life script an an example: Life is more suitable for adults than say the Code Club fish chasing game and anyway it gives me an opportunity to indulge my fascination with the game.

To write the text I need to draw diagrams that explain how the rules work and I tried in both Xfig and Dia to do this. But it was a nightmare.

In contrast I could manage it very quickly in Metapost, even though the natural inclination is to steer clear of that and stick with the “point and drool” GUI based alternatives.

beginfig(1);
prologues:=3;

for i=0 upto 4:
draw (0, i*20 + 10) — (100, i*20 + 10);
draw (10 + i*20, 0) — (10 + i*20, 100);
draw (200, i*20 + 10) — (300, i*20 + 10);
draw (210 + i*20, 0) — (210 + i*20, 100);
endfor;

pickup pencircle scaled 12;
draw (140, 40) — (150, 50)–(140, 60) withcolor red;
linejoin:=mitered;

path a, b, c, d, e, f, g, h, j, k, l, m;
a = fullcircle scaled 10 shifted (40,40);
draw a;
fill a withcolor green;
b = fullcircle scaled 10 shifted (40,60);
draw b;
fill b withcolor green;
c = fullcircle scaled 10 shifted (60,60);
draw c;
fill c withcolor green;
h = fullcircle scaled 10 shifted (60,40);
draw h;
fill h withcolor green;
j = fullcircle scaled 10 shifted (40,20);
draw j;
fill j withcolor green;
k = fullcircle scaled 10 shifted (60,20);
draw k;
fill k withcolor green;

d = fullcircle scaled 10 shifted (220,40);
draw d;
fill d withcolor green;
e = fullcircle scaled 10 shifted (240,60);
draw e;
fill e withcolor green;
f = fullcircle scaled 10 shifted (260,60);
draw f;
fill f withcolor green;
g = fullcircle scaled 10 shifted (280,40);
draw g;
fill g withcolor green;
l = fullcircle scaled 10 shifted (240,20);
draw l;
fill l withcolor green;
m = fullcircle scaled 10 shifted (260,20);
draw m;
fill m withcolor green;
endfig;

Gives me this: (actually the original EPS is better as it is a vector format and the PNG won’t scale in the same way)

Metapost is not widely known and under-appreciated.

## Waiting for the Bitcoin bubble to burst

The Guardian follows up the Economist’s piece earlier in the week examining Bitcoin and its role in greasing the wheels of Silk Road, the marketplace for drugs hidden behind Tor.

The most striking thing is a graph (the Economist produced a similar one) of Bitcoin’s price – here’s a more sophisticated version from Bitcoin Charts:

It’s the chart of a classic bubble. And bubbles always burst.

In the meantime the world’s monetary authorities should be doing their best to hasten that day. If banning Bitcoin is too difficult then making it unconvertible to cash is possibly easier and less heavy handed. No point in trying to launder illegal sales receipts through it if it is not possible buy anything other than drugs with it.