Behold the Mandelbulb

Daniel White posts some amazing pictures of a 3D equivalent to the Mandelbrot set.  I’m not sure whether to compare it to a cave system, a coral reef or alien architecture.  The way he’s rendered it gives the ‘Mandelbulb’ an eerie, deserted look, with shadows, caverns and strange looming formations, quite unlike the brightly colourful swirls of the 2D set – but all, of course, covered in intricate fractal detail.  Go take a look.

(You don’t need to know the maths to appreciate the pictures, but if you’re interested, there’s a second page with the formulae, commentary and links.)

(via Philip Wadler)

Behind the scenes at the opening of the Berlin Wall

BBC News: How a blunder finished off the Wall: “Mr Schabowski's announcement was complicated and bureaucratic, and like many others that evening I puzzled over it before concluding that it signalled free travel… East Berliners were rather quicker off the mark. Tens of thousands of them started turning up at the border demanding to be let across.  But the guards hadn't been told anything - their standing orders were to stop anyone crossing. Until recently they'd been instructed to shoot to kill anyone who tried… The guards asked their headquarters for orders but the government ministries in charge of security told them nothing… The guards on the ground - at the time - made the critical decision. They ignored their standing orders. They said, ‘Open the border.’”

The 1989 “carnival of revolutions” is a story I will never get tired of hearing.

Units of measure in F#

The latest version of F# introduces units of measure.  Using this feature, you can indicate that a numeric value is in a particular unit – metres, seconds, etc. – and the compiler will track that as part of the data type and validate that units are being converted and compared correctly.

For example, we can declare the following values:

let distance = 1000.0<m>
let time = 400.0<s>

Give these the ol’ Intellisense mouse waggle, and you find that distance has type float<m>, and time has type float<s>.  Try to add them together, and you get a tasty compiler error:

let nonsense = distance + time

FS0043: The unit of measure 's' does not match the unit of measure 'm'

But divide them and the compiler recognises that it makes sense, and figures out and tracks the derived unit of measure:

let speed = distance / time

speed has type float<m/s>, and again the compiler enforces that operations on speed are compatibly typed:

let description =
  if speed > 10.0<m s^-1> then
    "fast"
  else
    "slow"

Notice that F# supports the Proper Science notation of negative exponents as well as the Way Everybody Really Does It of division notation.

Derived units of measure can have names: the type float<kg m s^-2> is the same as float<N> and values of these types are therefore compatible.

let mass = 1.0<kg>
let accel = 50.0<m/s^2>
let whompiness = mass * accel

let ouch = whompiness > 100.0<N>  // compiles

Where do units of measure come from?  Well, when a daddy unit of measure and a mommy unit of measure love each other very much… but we’ve already talked about derived units of measure.  In fact, there are no units of measure built into the F# language or core library.  So either you have to define the units you need using the MeasureAttribute:

[<Measure>] type m

or you can import a bunch of standard SI units (basic units like the metre, kilogram and second, and derived units like newtons) from the F# Power Pack DLL:

// after referencing FSharp.PowerPack.dll
open Microsoft.FSharp.Math.SI

The Power Pack also includes a bunch of physical constants:

open Microsoft.FSharp.Math

let description =
  if speed < PhysicalConstants.c then
    "it's science"
  else
    "it's science... fiction!"

Naturally, these are all declared with the correct units of measure so efforts to compare Planck’s constant to the speed of light will meet with ignominious failure.  To work around this, tell your boss you need $370bn for a new particle accelerator.

To be clear, F# doesn’t assign any actual semantics to units.  For example, if you declare imperial units (because if it was good enough for the Babbage Engine, it’s good enough for the CLR, by Jove):

[<Measure>] type ft

F# won’t let you combine feet with metres.  It has no way of knowing that ft is a length measure, or how it would convert to metres.  However you can of course create conversion functions for your units:

let feetToMetres(f : float<ft>) =
  f * 0.3048<m> / 1.0<ft>
let totalLength =
  100.0<m> + feetToMetres(100.0<ft>)

Notice that our metres-per-foot expression spells out 1.0<ft> rather than 1<ft>.  F# only allows units of measure to be applied to floating point values, not integers.

Finally, be aware that units of measure are erased during compilation.  At runtime, F# (or rather the CLR) sees only plain old floats.  Unit checking is part of the compile phase only.

If only he really had been

Shorter Nick Griffin: “Being asked questions by the public makes me the victim of a lynch mob – quite unlike people who’ve been beaten up or murdered by gangs of BNP thugs for having the wrong colour skin.”

Crushing souls for fun and profit

The BBC commemorates – I won’t say ‘celebrates’ – 25 years of PowerPoint.  And the statistics are alarming.

The average PowerPoint session, apparently, runs for 250 minutes.  More than four hours!  I still feel bad about a presentation that overran to an hour and a half.  I’d like to say I can’t imagine what it would be like to sit through an “average” 4-hour PowerPoint session, but I can.  All too clearly.

And the average PowerPoint slide shows 40 words.  Admittedly this figure is distorted by a former colleague, the splendid Jane Smith, whose average PowerPoint slide showed 265.4 words, but surely even Jane’s prodigious output can’t account for more than 0.07 of that average.

Anyway, the article does also offer a few basic tips on the dangers of PowerPoint and how to avoid them (plus, from the comments, the delightful coinage “PowerPoint karaoke,” which I am officially adding to my vocabulary), and I’ll throw in one anecdote of my own.

A few years back I did a “training the trainers” course.  Although this was well into the PowerPoint era, the lady who ran the course did all her slides on printed transparencies on an old-skool overhead projector, and made us do the same.  How strange, we thought: if you were projecting off a laptop you wouldn’t need to faff around taking one slide off, putting it carefully down, transferring the protective tissue paper to the other side and placing and adjusting the new slide on the projector.  You could get straight onto the next slide and completely avoid all that delay.  Ah, she explained, but the time between slides was an open space.  You, and your trainees, could and should use it to invite questions, discussion or just reflection.  The slow turnaround between slides wasn’t a bug.  It was a feature.

In that moment, I became enlightened.

Monopoly goes to war

More news of board games in World War II: “Before leaving for missions, British airmen were told that if they were captured, they should look for escape maps and kits in Monopoly boards and other games delivered by charity groups. They were told that ‘special edition’ Monopoly sets would be marked with a red dot on the free parking space… In addition to [a] concealed compass, tools and maps, real bank notes were hidden under the fake money.”

Cease this nonsense at once

Popped into the supermarket last night and there at the front of the shop was a display of festive wrapping paper and Christmas trees.

For goodness’ sake, it is the middle of September.

This is going to be a very long spring.

Code Camp Auckland - .NET languages talk

Thanks to everyone who came to the Auckland Code Camp, to all the speakers and especially to the hard-working organisers! Here are the slides from the .NET languages talk:

What's happening in .NET languages - slides (PPTX format)

The demos were basically pretty closely derived from the Expert F# book and can be got from the book's Web site.

TechEd 09 - Visualising data in Silverlight and WPF

Thanks to everyone who came along to the Silverlight and WPF session yesterday. Unfortunately the final demos got a bit rushed but here's the complete code to all the samples which I hope will make a bit more sense when taken with a bit more leisure!

Visualising Data in Silverlight and WPF - slides (PPTX format)

Visualising Data in Silverlight and WPF - demos

Sunday “cats in domestic appliances” blogging

With only a week to go until Code Camp Auckland, it has been “all hands on deck” to help polish my presentation for the big day.

I even had a volunteer to write a Perl demo.