life imitates art, modulo regeneration

At the end of the Doctor Who episode Fear Her (2006), the Doctor (in his David Tennant incarnation) carried the Olympic torch, and lit the flame.

This morning (2012), in Cardiff, IRL, Matt Smith carried the Olympic torch for one leg of its journey:

Olympic Doctor, by Peter Evans

Warning: time paradox imminent!

nugatory recommendation

Here's the latest in my collection of weird Amazon recommendations.  After reading Jo Walton's review at tor.com, I added "Debt: The First 5,000 Years" to my Amazon wish list.  So, based on this, Amazon recommended:

quote of the day

To all of you who don't realise we are already living in the future (albeit one without jet-packs), here's a thought from Charlie Stross:

"to the extent that mainstream literary fiction is about the perfect microscopic anatomization of everyday mundane life, a true and accurate mainstream literary novel today ought to read like a masterpiece of cyberpunk dystopian SF."

eclipse by proxy

I didn't get to observe the latest (annular) eclipse of the sun, but there have been some spectacular pictures on the web. My favourite, which I found on Astro Bob (well worth checking out), must be:

Eclipse watchers at Papago Park in Phoenix, Ariz. are silhouetted against the eclipsed sun.
Credit: Michael Chow/ Arizona Republic / AP photo

The Motherland Calls

Scalzi’s latest post on his Whatever blog is a competition result: someone had to guess what monument he was thinking of in order to win a copy of his latest book.

One reader from Norway correctly guessed it was "The Motherland Calls", a statue in Volgograd.

Scalzi provides a picture, and a link to the wikipedia page about the statue.  I looked at the picture, and thought, that’s a cool statue – great pose, lovely and dynamic, and with a sword, too.

But how on earth did anyone guess this answer from all the possible monuments Scalzi could have been thinking of?

I clicked through to the wikipedia page to find out more about it. 

commemorating the Battle of Stalingrad … blah .... Declared the largest statue in the world in 1967 … blah .... prestressed concrete blah …

It wasn’t until I scrolled down the page and saw the plot of “Approximate heights of various notable statues” that I realised what I was seeing, and the significance of "largest statue in the world", however.

It’s as big as the Statue of Liberty including its plinth!  

So I looked back at the main photo and realised that the noise around the base of the statue, which I had barely registered on my first look, is people.

ZOMG!!!  The statue is over 80m tall.  The sword is over 30m long.  It’s amazing.  How is it that I have never come across this before?

And now it’s a little more understandable that someone guessed it.

going to extremes

Last week I went to a talk by Jim Al-Kalili, called “9 Paradoxes” (which, not coincidentally, is the title of his latest book).

One style of paradox he talked about are the mathematical ones, where a plausible calculation is presented, but the conclusion is wrong.  He illustrated this with the Monty Hall problem, and the Missing Dollar puzzle.

I’ve written about the Monty Hall problem elsewhere, and how the resolution is much easier to see by taking a more extreme case.  The approach of changing the problem to an extreme case is not specific to the Monty Hall problem, but is a more widely applicable check.  In particular, is can be applied to help see through the Missing Dollar puzzle. 

The Missing Dollar puzzle is as follows:

Three friends book into a shared room at an hotel.  The rate is $30, so they pay $10 each.  Later, the clerk realises they have overpaid; the rate is actually $25.  He takes $5 from the till, and goes to give them their refund.  On the way he realises that he won’t be able to split $5 between the three, so gives them $1 each, and pockets the remaining $2. 

So they have each paid $10-$1=$9, which is a total of $27. With the $2 in the clerk’s pocket, that’s a total of $29.  The original payment was $30. What happened to the missing $1?

The answer is that this is the wrong calculation. They have paid $27.  Of this $2 is in the clerk’s pocket, and $25 is in the till to pay for the room.  The puzzle works because the two prices are so close, and so it isn't necessarily obvious on a fast telling of the puzzle that the $2 should be subtracted from the $27, rather than added to it.  Let’s use the same approach of taking it to extremes to make the problem more obvious.

Three friends book into a shared room at an hotel.  The rate is $3000, so they pay $1000 each.  Later, the clerk realises they have overpaid; the rate is actually $25.  He takes $2975 from the till, and goes to give them their refund.  On the way he realises that he won’t be able to split $2975 between the three, so gives them $991 each, and pockets the remaining $2. 

So they have each paid $1000-$991=$9, which is a total of $27. With the $2 in the clerk’s pocket, that’s a total of $29.  The original payment was $3000. What happened to the missing $2971?

It is much clearer now that is that this is the wrong calculation. They have paid $27.  Of this $2 is in the clerk’s pocket, and $25 is in the till to pay for the room.

Going to extremes doesn't work for everything, but it is quite a powerful argument sanity-checker.

FatFonts

Edward Tufte advocates using minimum ink to maximum effect in displaying quantitative information, and designing graphic displays to have both macro (distant) and micro (close-up) readings.

One technique he describes that fits his philosophy is the "stem and leaf" plot. Let’s say you have two sets of 50 exam marks as percentages, and you want to examine the data.  One way to see the spread is to plot the marks, maybe as a histogram. That shows the distribution, but loses the information of the specific scores.  The stem and leaf plot provides the best of both worlds: a graphical overview and close up values.  The "stem" shows the tens values, and the "leaves" show the remaining digit values.

stem and leaf plots, of 50 values generated randomly from a normal distribution, with:

 (a) mean 50, std dev 20; (b) mean 70, std dev 10

This plot looks like a histogram from a distance, but closer inspection shows that the bars are made from digits with meaning.  So we can easily see that in the first case, the marks range from 9 to 96, and in the second case, the marks range from 54 to 94. 

Stem and leaf plots can also be used to good effect for bus and train timetables. In this case the "stem" shows the hours, and the "leaves" show the minutes when the transport is due.  For example, Nottingham tram timetables use this approach.

You can immediately see, with a distant macro-reading, on weekdays the most trams are at rush hour, on Saturdays they are more evenly spread , and they are rather more infrequent out of hours and on Sundays.  Then you can look closer for a micro-reading, and see the actual tram times.  

These plots have been around for a long time.  The latest New Scientist (2 May 2012) reports an analogous approach for greyscale plots: "FatFonts", conceived and developed by Miguel Nacenta, Uta Hinrichs, and Sheelagh Carpendale.

the "Rotunda" FatFont

With a FatFont, the amount of ink used to print a digit is proportional to the value of the digit: so a 9 uses nine times the ink as a 1, for example.  Instead of plotting a greyscale pixel on a graphic, plot the actual value using the FatFont.  For more numerical resolution, simply use a second digit one-tenth the area of the first (and a third digit, one tenth smaller again, if needed, and so on, until resolution fails). From a distance, the macro-reading is a greyscale image; closer up, the micro-reading shows the digits, showing the numerical values. 

Here's an image of the terrain around Etna on Sicily, from the FatFonts galley page: 

A FatFont plot is to a greyscale image what a stem and leaf plot is to a histogram.

Typewriter art, ACSII art, and photo mosaics achieve a given picture (macro-reading) by using very many small characters or picture "tiles" chosen to have the right density or colour.  But with those techniques, the micro-readings are not usually of interest.  FatFonts, on the other hand, give a useful graphical tool.

It’s a really neat idea.

April showers

We have an official drought here in the south of England; ironic in a country famed for its rain.  Of course, that's part of the problem: why bother to store something that's in constant supply.  So it takes only two dry years in succession to cause a problem. However, recently we've also had a lot of very heavy rain, or so it seems.  Is it really much wetter than usual, or have we simply  forgotten how wet it usually is?

Last year was the driest since records began.  Well, since our records began in June 2005, when we started collecting rainfall statistics in our Cambridgeshire garden.  The annual rainfall (in mm) since then shows last year very dry, with 2010 on the dry side.

annual rainfall, in mm

Actually, it isn't the total rainfall over the year that's important for droughts, it's the rainfall over the winter.  Summer rain evaporates more; winter rain soaks in.  So here's the rainfall month by month, averaged since (our) records began:

average (mean and median) monthly rainfall, in mm

So the wettest month by far is August, closely followed by May: neither exactly winter months. Also, the driest month by far is April: so much for it being famed for "April showers".  Yet it is this April that has been so seemingly wet.

However, plotting both mean and median points out an anomaly in the April value.  Its mean is much higher than its median, indicating a skewed distribution.  Let's look at April in more detail:

April rainfall, in mm

So, for three years we detected no rain at all in April, and in 2010 only 1mm.  Two further years were around 10mm.  Then this year, 72mm!  That's some outlier.  Not only has it been wet this April, it's been significantly wetter than the average for any month, and it's been over three times wetter than all those other Aprils put together! 

So yes, it really has been wet. And it's not only our garden, and our short measurement span.  It has in fact been the wettest April in the UK for over a hundred years.  But it's still officially a drought.

overheard on the train

I wasn't actually listening to the people next to me on the train the other day; in fact I was trying not to listen, so that I could concentrate on my book.  However, I couldn't help but hear their concluding sentence:

I'll see you then, then.

That is, "I'll see you at that time, in that case".  Not as good as the three thats, but enough to make me smile (into my book).