Links: April 2014

Links from the last month:


  • Widely-reported astronomical discoveries included an asteroid with rings and the second object (after Sedna) ever to be found in the inner Oort cloud. Links go to the best articles I’ve seen on each topic.
  • Also in astronomy, a model of Enceladus’s ocean derived from gravitational anomolies. This doesn’t tell us much we didn’t already know, but it’s an interesting confirmation.
  • A lovely tribute to a strange sea slug.
  • And in more creature strangeness, a sexually-reversed insect.
  • A relatively obscure 17th century alchemist and inventor.
  • British Pathé released an extensive archive of historical television clips. It’s well worth a browse, and if you find some favourites I encourage you to link to them in the comments. Meanwhile, each of the following asterisks links to a different video to get you started: [********]. In my opinion the most interesting ones are often those that reflect changing social attitudes.


  • For when you have plenty of time: the original Cosmos series on Youtube.
  • Christie Wilcox shares a dream. (Have you ever dreamed about a new species of animal? One of mine last year featured a migrating desert snail monotreme, but even in the dream I didn’t get to touch it; just saw the news report.)
  • Cityscape timelapse with a difference.


Buying my second mobile phone

I typically publish links at this time of month, and the following personal update was drafted as a footnote below just such a collection. But on reflection I’ve decided to let the links accumulate for another two weeks before publishing them, so the wouldbe footnote is now the entire post.

So … recently I bought myself a new mobile phone, replacing the one I bought in 2008 and reported on this blog at the time. After almost six years, the ringtones in the old one stopped working in January (broken speaker I guess), and I’ve been procrastinating getting a replacement ever since.

The new phone is an android (Samsung GT-S7500T) and cost me about $150. I’ve installed the following apps: LocSMS, Battery Widget, Brightness ControlRocket Music Player, Date in Status Bar, File Shortcut, MuPDF [list updated July 2014].

For SMS notifications I’ve chosen the Pizzicato tone that came with the phone, and for incoming calls I’ve imported the ringtone I made for the old phone. To create wallpaper for the new phone, I rotated and trimmed one of my fractal images, and you can see the result below. (Incidentally, the same source image is also used in the background of my profile on Twitter, Gravatar and other places.)


Of course there have been disappointments — ranging from conspicuously absent features to Google doing funny business without my consent — but I don’t like to use the blog as a place to rant. Besides, my feelings about a new phone are not interesting; what’s important is how I’ll feel after I’ve had a chance to get used to it. If it lasts another five or six years I will, on balance, be happy.

Navigating the night sky

Which stars do you recognise when you look up at the night sky, and how do you find them?

I’ve been planning to re-introduce shorter, lighter blog posts on random topics, and one topic that seems fit for that purpose is to describe how I personally find my way around the sky at night. This is not meant as advice on how other people should navigate the sky; it’s just a description of how I do it, and you are welcome to reciprocate in the comments. It is also only a summary and not a guide, so please look things up if you need more information. Bear in mind that I’m in the southern hemisphere.

When the sky is not yet dark and only a few stars are visible, I like to identify those stars as early as I can. This requires being familiar with the shapes formed by only the brightest stars, without relying on dimmer ones for context.

I start by looking for the triangle formed by Sirius, Rigel, and Canopus, which is back-to-back with the triangle formed by Sirius, Rigel and Procyon. All of these stars are among the brightest in the sky, and Sirius is the brightest of all, so once you’ve identified Sirius you know that anything brighter is not a star. The angles between these stars can look quite different depending on whether they’re overhead or near the horizon, but I can usually identify them quickly. (From Sirius, the line to Canopus is longer than the line to Procyon, so I find it helpful to remember that this is the opposite of what you’d expect given that pro- invokes words like prolonged.)

Once I’ve identified Rigel I can easily find Betelgeuse, and thus predict where the belt of Orion will appear even before it is visible (good party trick). If the sky is dark with little light pollution, I also look nearby for the Hyades (a.k.a. the horns of Taurus) and identify Aldebaran.

My usual next step is to follow the zigzag line from Procyon to Sirius to Canopus and then take one more zag to Achernar. Achernar is the only bright star anywhere near its vicinity, so you don’t need much precision to find it. The line of best fit through these four bright stars I have nicknamed the false ecliptic, because if you didn’t know your way around the night sky you might assume they were planets.

We’ll come back to Achernar in a moment, but let’s now turn our attention to the stars of the Southern Cross (featured on the flags of many Southern Hemisphere countries) and the adjacent Pointers. These are easy to find, and not hard to identify individually. The Pointers are Alpha and Beta Centauri (also known as Rigel Kentaurus and Hadar, but I prefer the former names) and the stars of the Southern Cross are Alpha, Beta, Gamma, Delta and Epsilon Crucis. Telling them apart is easy when you know that the sequence from brightest to dimmest proceeds clockwise, and that they are named in that order.

The classic way to find the South Celestial Pole is to draw a line through the long axis of the Southern Cross and another line passing between the Pointers at 90 degrees, and to find the point where those two imaginary lines meet. An alternative method — slightly more accurate but less often practical depending on what clouds and the horizon obsure — is to identify Beta Centauri (the lesser Pointer) and Achernar (which I promised we would return to), and find the point halfway between the two. It’s no bad thing to have two different methods for finding the Pole, because then you can verify one against the other and also use this as an alternative way to find Achernar.

In total, I can point to and name 14 stars in the night sky — Sirius, Rigel, Canopus, Procyon, Betelgeuse, Aldebaran, Achernar, plus the seven stars of the Pointers and Southern Cross. I’ve never made the effort to memorise any more. It’s perhaps worth noting that I live in a fairly light-polluted city, but spent most of my childhood on a farm with many more stars visible.

That’s about as much as I can say from a personal perspective; most other details are things you can look up. If you have a perspective you’d like to share, it is now your turn.

Links: Late March 2014

Here are some links that I’ve seen recently and recommend. It’s an intentionally short list; I’ve shared several more on Twitter.

The big news in physics this week is the detection of polarisation patterns in the cosmic microwave background radiation that match what is expected if inflation theory is true. However, I’m not able to recommend a single best article on this topic, so I’ll leave it out.


  • The origami microscope is amazing. The TED talk will probably leave you with unanswered questions, like “Huh?”
  • LONG article involving autism and cartoons. Worth the effort.
  • The role of sponges in oxygenating the early oceans. Article could be better written, but it’s an intriguing idea.
  • You probably already know why Americans are weird (and, at the risk of spoiling the joke, so are Australians). But read this anyway; it’s a well-written overview.


  • I tried out the demo version of Osmos — a game in which you play the part of a blob absorbing (or being absorbed by) other blobs. I like it a lot, but with one deal-breaking reservation: the game saves information files in the user’s Documents folder. I feel strongly that the Documents folder should be reserved for the user’s own files, and that any software that stores files there automatically (without letting the user select an alternative location) is intruding on their personal space. (Note: At the time of writing, the most recent Windows version is 1.6.0.)
  • Hilarious clip involving a dog at a restaurant.

Elke at 10 months

The last time I posted photographs of my sister’s daughter, Elke Adele Smith, she was six months old. She’s now ten months, and I have new photographs.

Here is my favourite, rolling about by the River Torrens in Adelaide:


More from the same place. Mum (her grandmother) also appears, in her role as chair and climbing frame. You can see Elke is trying to learn crawling, but her legs haven’t figured it out yet.






We passed through the Festival Theatre, where I made this video …

(I used Youtube’s frankly awful background music selection tool — which I’d rant about at length were it not for the fact that doing so would be incongruous in a blog post about a cute baby — but for a 30 second video it can be made to work)

… and took these photos:


Here we are walking by the Torrens and later reading a book:


Finally, more playing around. This time in the playground by the caravan park:






I see no need to add much commentary; the pictures speak for themselves. She’ll soon be a whole year old, which is pretty amazing.

Operational algebra

I vaguely remember wondering — as a child of seven or eight — how new mathematics became established. I pictured a long line of people in front of a guy with a desk (or maybe a tent), waiting to register their latest idea — such as a new mathematical operation.

I had one such idea myself. I knew by this age that multiplication consisted of repeated addition, so I thought why not define something else in terms of repeated multiplication? Thus I invented integer exponentiation. (It’s an obvious idea: I blame the Childcraft books for arousing my interest.)

When I was older and learned that exponentiation actually existed, I was troubled by a curiosity of language. When people talk about 104, they say “ten to the power of four” — and yet 102, 103, 104 are collectively referred to as “powers of ten”. In one context, the number after the “of” is the exponent, and in the other context, it’s the base. Why is this? Isn’t mathematics supposed to be consistent?

If I could answer my childhood self, I’d point out that the same ambiguity crops up in everyday language. We say that x-ray vision is one of the powers of Superman, but we also say that Superman has the power of x-ray vision. When we use terms like “power of” we are translating mathematical notation into English, which has no use for consistency.

I not surprisingly came to speculate about an operation defined in terms of repeated exponentiation, another operation defined in terms of that, and so on ad infinitum. Some of you will find this familiar.

Let’s adopt the symbol ➀ for addition, ➁ for multiplication and ➂ for exponentiation, and let’s have ➊ for subtraction, ➋ for division and ➌ for the calculation of roots (although exponentiation actually has two inverse operations — the other being the calculation of logarithms — so we’ll leave that well alone).

Now we can specify operations using algebraic variables — and for that reason I referred to this system as operational algebra. I’ll use the symbol ✪ for “operation”, and write 2 [✪3] 5 to mean the same as 2 ➂ 5 which means the same as 25. For inverse operations I’ll insert a minus sign so that 2 [-✪2] 5 means the same as 2 ➋ 5 which means the same as 2/5. My original notation was handwritten, obviously, but this is a reasonable compromise. I won’t pretend it’s perfect.

For positive integers, higher-order operations can be defined as:

a [✪n+1] b = a [✪n] a [✪n] … [✪n] a {b terms}

But because exponentiation is non-associative, this presents us with a choice. If we bracket the expression from right to left — as in 2(2^(2^(2^…))) — then we are in the same realm as Knuth arrow notation (which I didn’t know about at the time). But if we bracket it from left to right — as in (((22)2)2) — then because (ab)c=abc, it follows under this definition that ➃ can be extended to non-integer operands using the formula a ➃ b = a(a^(b-1)), and then a ➄ b can be defined for non-integer a. I always used the latter (left-associative) definition.

As for higher operations in this sequence, I was convinced at the time that they could all be extended to non-integer operands, but my reasoning was faulty.

The fun wasn’t all at the high end, though. Early on I recorded the trivial fact that there is no zeroth operation. That is, no operation can be consistently defined such that a + b = a ✪ a ✪ … ✪ a {b terms}.

I don’t propose to share everything I did with this system. For one thing, a lot of it was wrong, and for another, I threw my notes away years ago. But here is something worth finishing on. Recall that an inverse operation can be defined such that:

(a [-✪n] b) [✪n] b = a

Now observe:

  • 2 ➊ 2 = 2 – 2 = 0
  • 2 ➋ 2 = 2 / 2 = 1
  • 2 ➌ 2 = sqrt(2) = 1.41421…
  • 2 ➍ 2 = [solution of nn = 2] = 1.55961…
  • 2 ➎ 2 = [solution of (n^(n^(n-1)) = 2] = 1.6498…

Based on this, it seems intuitively likely that if we could extend all higher operations to non-integer operands, then as n approaches infinity, we’d find that 2 [-✪n] 2 approaches 2, giving us a glimpse into the infinite operation. This intrigued me.

I abandoned my speculations in operational algebra around the time I left school and started university. I am vaguely aware that everything I explored (except the wrong bits) exists in established mathematics, if often subsumed under much more abstract generalisations. This makes no difference to the fact that a teenager had fun messing about.

As a final word: please don’t take from this blog post the idea that I’m good at maths. I lack the rigour to be good at it; I am merely playful.

Park pictures are preferable to politics

It was election day yesterday for the South Australian state government. The results are very close to a draw, and can’t be called definitively until more votes have been counted. But who cares? Nothing ever happens on the state level of politics anyway.

You didn’t come here for politics. So here, instead, is a photo of me and my wood nymph (aka winner of the ‘Most Huggable Tree’ competition) taken by a friend a few weeks ago.


And here is a photo of the friend, walking ahead of me:


That was a great day.

On the offchance that you did come for politics, there were only four candidates contesting my electorate in the House of Assembly, so that was no challenge. For the Legislative Council I chose to vote below the line, and this table shows exactly how I voted. The exact order is somewhat arbitrary (cobbled together after a few minutes’ research), but the trend is from parties I support to parties I’m ambivalent about to the major parties to the deep recesses of the loony bin.

There was no queue outside the polling place. But on my walk home it rained, and I did not bring an umbrella. So — good luck and bad in equal portion.

Links: Early March 2014

Here are some outstanding links from the last month to fascinate and delight you. After that, I have some words to say about this blog’s recent visitor stats.



  • Humorous, subversive fabric design that did the rounds on Valentine’s Day.
  • David Attenborough on curling. I’ve said for years that sport should be presented as a wildlife documentary, although I must say I had outdoor sport in mind.
  • Bouncy goats.
  • Paul Willis is off to Antarctica soon (leaving 11 March), and here you can request photographs you’d like him to take. I asked for “pareidolic monster carved in ice“.
  • 4D fractal journey.

This blog received a huge influx of visitors when my post If Conversation Were Chemistry was featured on Freshly Pressed —’s official editor-picked “Best Of” page. On February 22 it received 319 hits from 256 unique visitors, and the next day it recieved 478 hits from 143 visitors. The previous record was 295 views in a single day.

Since then, the number of visitors has settled back to previous levels, but the number of views has remained far higher than usual. I used to rarely get more than two views per visitor; now I’m getting around ten each day. For example, yesterday (March 5) I had 170 hits from 19 visitors, or 8.95 views per visitor, whereas two weeks before that (February 19), I had 37 hits from 19 visitors, or 1.95 views per visitor.

Looking at what people viewed, we see that yesterday there were 151 views of the front page or archives (i.e. pages that display multiple posts at once), and only 19 views of specific posts. Exactly two weeks previously, there were 6 views of the front page or archives, and the other 31 were views of specific posts. The number of hits on specific posts has not changed at all (the difference between 31 and 19 is within normal variation), but the front page and archives have received a dramatic increase in views.

If we look at where the views are coming from, we see something remarkable. Of the 170 views received yesterday, a whopping 144 came from Germany, and only 26 from all other countries put together. And it has been a similar story every day. In the last 7 days, I’ve received 890 hits from Germany — an order of magnitude more than from any other country. The runners-up are 72 from the United States and 28 from Australia.

To summarise:

  • The number of views has increased dramatically, but the number of unique visitors has not.
  • The increase has overwhelmingly been in views of the front page and archives, not of individual posts.
  • The increase has overwhelmingly been from computers that identify themselves as based in Germany.

It looks very much as though ONE person in Germany has been visiting this blog more than a hundred times a day, every single day, ever since I got Pressed.

Before I invite this mysterious German to introduce themselves in the comments, there is an alternative hypothesis. Apparently German law forbids websites from collecting visitor statistics, and it’s possible that what I’m seeing is an artifact of that. Maybe all visitors from Germany are counted as the exact same visitor, or maybe some people who are not really in Germany find it convenient to pretend that they are.

But if you’re reading this from Germany, do say hello. And maybe you’d like to browse my photographs from last time I was there.

Fragments of song

There are several old posts on this blog about music that I composed when I was younger. But as a teenager in the nineties I also composed some fragments that never became complete songs, and I’ve not yet blogged about those.

So here is a selection. The lyrics are brimming with teenage angst, and are also rich in words I thought of as inherently poetic at the time. If any of them inspire you, you’re welcome to adapt them in your own creative works. All I ask is that you let me know.

Most of the recordings below were made expressly for this blog post, and are not polished performances. Their purpose is simply to demonstrate the tune.

The first one is the chronologically oldest, and here is a tune I recorded some years ago, followed by lyrics:

What I feel is a kind of torture
Every moment reminds me of a thought that once occured
And I feel nothing less than torture
When I remember that the thought is too absurd.
I cannot justify the course this tension’s leading;
I wait unsatisfied, in pain and almost screaming.
Waiting for some release from torture
To release my mind, a thought that’s not absurd
And I feel nothing less than torture
When I remember that the thought has not occured.

The next fragment is intended to sound like some old folk song. It’s rich in metaphor and open to interpretation.

There is no place so distant as my only world;
There is no sound so faint as our most piercing scream.
What shall I build, here where a thousand stones are hurled,
And where the wind erodes away each worthless dream?

This one is about being abandoned by a valued friend. The second verse would have included the line, “And I’ll walk to infinity again today” (invoking a sense of aimlessness).

Every healing word I know is void;
Watching silence greet every desperate cry.
Everything we shared, everything we said;
Watching memories freeze as they pass me by.

A few years ago I wrote the above fragment into a story — as previously mentioned here — and also included this one.

How do I build from impossible stones —
Where’s the ground to hold them?
How do I walk from infinity home
After wandering there?

To finish, a fragment that is only one line long, but which I’ve always thought has potential for a pop song.

Unwelcome conclusion of a painful illusion.

I hope these brought you pleasure, and that they don’t evoke your current state of mind. But you have my sympathy if they do.

If conversation were chemistry

Today’s blog post is for the geeks. Seriously, if you don’t think frequency analysis for its own sake can be fun, you probably won’t enjoy this much.

Stan Carey has a blog post about the length of the chemical name of the largest known protein, considered as though it were a word. It takes three and a half hours to read aloud, so it would easily be the longest word in the English language were it not for the fact that it doesn’t count.

I decided to play around, so I started by taking the chemical name, and (after removing hyphens/whitespace from raw text) ran it through a character frequency analyser. This told me that the letter L occurs 14645 times, accounting for 22.9% of the text. At the low end, the letter D occurs a measly 238 times, which is just 0.4%. Letters not present at all are B, F, J, K, Q, W, X and Z.

Noticing that the chemical name contains a multitude of components ending in ‘yl’, I inserted a space after each occurence of that pair, then fed the result through a word frequency analyser. It gave me the following totals for each component word. Read the rest of this entry »