Friday, 12 April 2013

This is REALLY Random

(using the 2013 edition of the word “Random” to mean weird, amazing and far out).

In my work, I use a clever piece of software that uses a statistical approach to model the reliability of equipment. The user defines stuff like “this pump has an average failure rate of once every 5 years” and “annual maintenance starts on this date”. By using a statistical approach, the software provides an idea of the expected overall performance and “uptime” of the whole plant in which the equipment is installed. Getting this right can save millions of dollars.

The statistical maths behind this program is called the Monte Carlo Method. It gets its name from a casino where the uncle of the guy who invented the maths used to gamble. Roulette for inspiration? You couldn’t make this stuff up if you tried!  Is that random, or is it just weird?

In reading the history and development of this, and related, maths I came across a book titled “A Million Random Digits” (on Amazon here) first published in 1955. In those days, random numbers were hard to generate in a computer (because nobody had a computer). This book, which literally contains page after page of numbers, was actually very useful. Amazingly it has been reprinted, so maybe it still has some application today. What a weird, random world we live in!

Now at this point I could choose to bore you with a discussion of why random numbers are really important, and why a computer can’t really generate really random numbers (it generates a sequence of numbers that look like they are random, but because they are a sequence, they aren’t really random – Sorry, I did bore you a little bit. Oops).

But I’m not going to bore you any longer. Instead, scroll down the Amazon page of “A Million Random Digits” and go to the comments. Even if you only have a vague idea of the mathematical beauty of randomness, I hope you will appreciate comments like :
“The book is a promising reference concept, but the execution is somewhat sloppy. Whatever generator they used was not fully tested. The bulk of each page seems random enough. However at the lower left and lower right of alternate pages, the number is found to increment directly.”
Or this:
“Even though I didn't really see it coming, the ending was kind of anti-climatic. But overall the book held my attention and I really liked the "10034 56429 234088" part. It's nice to know I'm not the only one who feels that way.”
Or this, my favourite:
“This book is ok as far as lists of digits go, but seriously limited. Its only a million digits. Its nothing in comparison to Graham's Digit's Bound (available from Cirius Cybernetics as the ratio of lengths of two pieces of bogonium, or as an RSS feed until the end of this and every universe.)
To be fair this set of digits is supposed to be random, but my guess is that you could find this exact set of digits or an encoding of this set as a set of digits in Graham's Digit's Bound. I could easily prove this if I could get a couple of minutes of time on the Aleph One.”
If you thought the references were random (i.e. you didn’t understand them), then you need to spend less time reading maths and more time reading literature, particularly Douglas Adams (link deliberately omitted so you have to do some of your own research).

Despite it’s awesome title, you won’t find “Graham’s Digit’s Bound” on Amazon though. It’s a reference to Graham’s Number. You will find the definition on Wikipedia here but this page should come with a warning like. “Warning! Explicit maths-p0rn – may upset some audiences – NSFW!!!”. For my non-maths-geek readers, Graham’s number is so big that mathematicians have difficulty finding symbols that can express how big its bigness is. Others have explained it far better than I will (still horror-movie brainmelt stuff) and here is a slightly more humane version, with a twist at the end).

This got me thinking. First about the fact that books of random numbers were actually published (and now hide wasted on people’s bookshelves). And second about the literary creativity in the comments on stuff that is available on Amazon. You can get some pretty random (meaning obscure) things on Amazon - like live ladybirds and wolf urine. That's worse than random! Truth is stranger than fiction. The comments are just brilliant (though you might need a dark sense of humour). Here are some more for you:

Barrenttine Methylated Spirits (Actual warning: Meths is nasty stuff).

The humble biro gets the comments treatment too, including this priceless gem: “the spellcheck for this device seems to be broken”.

Others have already written about these comments of literary genius in newspapers and blogs but to save you wasting your lunchbreak scraping the depths of Amazon’s database, some random reviewer has helpfully compiled a Listmania of them already: UK version here  and US version here.

That’s so random!

Wednesday, 10 April 2013

Reversing the Beeching Axe

In my student days, my dad asked me to prune a Buddleia in the garden. "Cut it right back" was the advice I'd been given, as that was apparently the right way to keep this plant in shape. I think I was more eager then as a gardener now, for I did indeed prune it right back - leaving barely half a metre of trunk left sticking out of the ground. The poor plant did not survive. But the memory of my gardening errors are perpetuated from time to time by my family.

In the 1960s, the "Beeching Axe" dramatically pruned Britain's railways. With hindsight, we see that this had a devastatting effect on our nation. Communities that relied upon the train for contact with the outside world were cut off, and some have dwindled to nothing. The loss-making branch lines suffered the clippers much more than the profitable main lines. It wasn't until a few years afterwards that people realised that the branch lines fed the main lines in the same way that leaves feed a tree. The promised increase in profitability of the main lines never happened, and passengers took to the roads instead.

Fifty years later, our roads creak under the weight of a traffic density they were never expected to carry, and more people travel by train than ever before. A few of those branch lines remained open. Some of them are now used by preserved railways (e.g. the Bluebell Railway). But the vast majority are unlikely ever to see trains along their routes again, because crucial parts of the track-bed were sold to property developers or were cut off by other infrastructure. Sadly, in most cases, the prospect of re-opening these branch lines to improve capacity on our railways is bleak.

Two branch lines exist near my home. There is a line from Watford Junction to St Albans Abbey, known as the Abbey Flyer. This line survived the pruning, and is relatively busy during the rush hour. At the Watford end, there are connections to Euston, Birmingham and to the London Overground. The route is single line all the way, which dictates a 45-minute gap between trains. I believe that this timetable is the main reason that it is poorly used: if a more frequent service were made available, I am certain that the success of this line would rise dramatically, challenging the main Thameslink service on the other side of town. To offer a more frequent service would require some practical changes, such as a passing-loop somewhere along the line, and these ideas are already under consideration.

The other branch line near my home is (or rather was) the onward line from St Albans to Hatfield. It was lost to the Beeching Axe. It is now a footpath and cycle path, known as the Alban Way. Since the line was removed in the 1960s, several short areas of this line have been developed which would make reinstatement of the line financially challenging. At least two housing estates now exist along the route. A road under-bridge has been modified so that cars go down less of a dip, and a short section near Hatfield has been lost to the development of the Galleria shopping centre and the A1M. Probably 95% of the line could be reinstated, but those last bits make it difficult to complete.

If it were possible to reinstate the Alban Way, then the East Coast Main Line (via Watford) would be re-connected to the West Coast Main Line (via Hatfield or Welwyn), via the Great Central line at St Albans along the way. All three routes are heavily used by commuters, and connecting them seems a beneficial thing to do. Routing the line past the Galleria might be seen as a challenge, or it might be a golden opportunity to shift shoppers from car to train. The issues of routing around housing estates and roads are more complex, but can also be surmounted. A fairly anonymous website describes some solutions to the problem, notably joining at the busier station at Welwyn instead.

This is just one branch line. There are of course thousands of others, and most will never see trains again. But there is hope. The tide appears to have turned, and Network Rail is actively re-opening some of those branch lines again. It's a small reversal of railway decline in this country, and changes such as these take time to implement, but it does appear that the tide has finally turned. It is like seeing fresh buds of a plant growing when you thought you'd killed it.