Paine Relief

It was a delight to meet up with Robert (Nick) Paine and his wife and daughter in Neptune's Hall over the festive period. I promised that I would share my solution of the Queasyjet problem - see earlier blog post.
Well here is how I see it:
Assume that there are n+1 passengers, then when the first (and actually special) passenger gets on he will choose from one of the n seats that does not belong to him.
This means that there is a 1/n chance that he sits in the last passenger's allocated seat, leaving no chance that it is correctly allocated. It also means that there is an (n-1)/n that he sits in a seat leaving both his own and that of the last passenger unoccupied.
This second situation is what I call a "steady state" because from here on, the probability that the final passenger gets their allocated seat is 1/2. To understand why it is important to understand the end game - the "game is over" when a passenger sits in the first passenger's seat (in which case the boarding continues smoothly and the remaining passengers, including the last get their allocated seats) or when a passenger sits in the last passenger's seat (in which case it is guaranteed that the last will not get their allocated seat). These two scenarios are equally likely because for each passenger k>1 either their allocated seat is available or they choose one of the endgame scenarios each with probability 1/(k-1).
So if there are n+1 passenger, the probability that the last one will get their seat is
P(doesn't get seat)= [(n-1)/n]*[1/2] = (n-1)/2n=[1/2]-[1/2n]

The DNA Delusion

Last Christmas a friend of mine bought me Richard Dawkins' book "The Greatest Show on Earth". I was staggered to find out how narrow minded this man is. I have not read his book "The God Delusion" nor will I waste my money on it. He articulates a well-reasoned treatise on how a living form could arise from the primordial soup and then with a sudden leap of faith says that consciousness is simply the result of the complexity of the molecules - I have to say that this viewpoint reflects an act of faith rather than reason. Descartes pursues the argument the other way around, saying that the rules of the universe are simple and elegant, therefore there must be a God. I have to say both viewpoints are interesting but not totally convincing.

How many zeroes at the end of 100!

I thought this was a fun question from one of the (Junior) Maths Challenge papers. It's a good way to reflect on prime factorisation.

QueasyJet Queueing

This weekend I got a message from an old friend of mine Robert Paine (better known in our maths class as Pean). He attached the following probability problem to his email knowing that I enjoy doing the occasional maths problem in my extensive free time.

There is a queue of passengers waiting to board a QueasyJet plane each with an allocated seat. The first person boards the plane and sits in a random seat which is not their allocated one. The next person gets on, and if their allocated seat is free they sit in it, otherwise they choose a seat at random from those remaining. Each person then follows that same rule: if their allocated seat is available they sit in it, otherwise they sit in a random free seat. What are the chances that the last passenger sits in their allocated seat?

It's the sort of thing that would turn up on a Maths Challenge paper but probably not a GCSE or A Level these days. It did prove a welcome distraction from the essay I have to write!

Viral Marketing?

I got an email this morning from Katherine Poll of Digeus Software the exact text of which is below. Now as my early blogs will attest, I do have an interest in the way internet will work for business and marketing in particular. This is a cool approach which I have not seen before. Digeus are offering what should be a useful software item for screen capture and asking in return to have their product mentioned on my blog. Now is it the fact that it is on my blog that interests them? Well of course the answer is in the postscript. You must not change the text Screen Capture Software which under the covers links this phrase with the company Digeus Software. So what you ask? Well I just typed "Screen Capture Software" into google and I got heaps of results as one might expect. I browsed through the first 6 pages and could not find a link for Digeus Software. If my suspicions are correct then if Digeus are successful in getting this link into a large number of blogs, Google's search algorithm will obligingly push them up the list. Viral marketing? Let's hope not!

"May I ask you to place the link below to our Screen Capture Software anywhere on your blog? If you agree, please send me the link where you placed the link and I will present you with a license for free.

Here is the link:
Screen Capture Software
You may place this link alone without description or on existing post or create new post with a short description (language and text is up to you)
Feel free to get information about product here: http://www.digeus.com/products/snapit/snapit_screen_capture_3_5.html
P.S. Don't change text in the link. It should be "Screen Capture Software".
Sincerely,
Katherine Poll"

Education, Education, Education!

It seemed more than appropriate that, as I began my third University level course of education, I should be sitting in front of my laptop waiting for an on-line tutorial to begin. The tutorial, part of a PGCE teacher training course, was about "Professional Studies". This part of the course looks at the history of education, and amongst other things the role and evolution of the National Curriculum. Dennis Almeida of Exeter University showed the YouTube video "Shift Happens" to set the scene for our discussions; it is an interesting collation of various statistics which reflect our fast changing and technological world, and should certainly inform our approach to education.
Having reflected on this I have settled on three threads of thinking; invariants, vocational training, multi-culturalism.
For me, mathematics and basic science, and literacy and good literature will always be the core of education. Understanding the ways to reason rigorously and natural language skills are the gateways to new learning. Good literature is the route to understanding the human condition beyond the world or worlds that we can experience directly [I like Shakespeare, Tolstoy, Dostoyevsky and even Jane Austen who has to be admired for having written the same book so many times!] These things are the invariants for me.
The second thread is vocational training. This one is always difficult. For one, it is very expensive to set up good vocational training facilities (compared to the chalk and blackboard needed to teach mathematics), and secondly everything in this arena is going out of date so quickly. When I left school they were still training printers to typeset with lead typeblocks. Later, I witnessed armies of Cobol programmers being trained. As the video so clearly noted, many of the jobs of the future do not exist today. So what is the solution? I think the main job to be done is to try to reveal a seam of passion within the individual, and to then encourage that individual to nurture and exploit that passion. This may seem vague, but its vagueness is what will allow it to adapt to the inevitable change.
For me the multi-cultural UK is missing out on a trick if it does not embrace and exploit its multi-cultural nature. If I were able to change the curriculum in some way it would be to include more of the history of civilisations, how humanity arose from Africa, the early civilisations in Mesopotania, the Arabs, Indians and Chinese and so forth. I have been delighted to see that the increasing number of programmes on science and mathematics give due credit to the various cultures responsible for the development of these subjects. I would also like to see some different languages taught in schools not just the French and German, how about Polish, Arabic, or Punjabi?
As a final observation, we need to be able to teach our children the benefits of perseverence. From my experience it takes about 10 years to become good at anything; a sport, musical instrument, foreign language, technology or whatever. I have been most fortunate to witness the perseverence of my own children in the fields of mathematics, languages, music and drama. I hope in my future role as a teacher I will be able to help others too.

Climate Change - Now It's Official

The last of the most hardened sceptics were finally convinced of the reality of climate change as most of the UK enjoyed good weather over the Whitsun bank holiday. Michael Fish, well-known weather reporter commented "Our forecasting software at the met office has bad weather set as a constant for bank holidays. We can normally only rely on Bank Holiday Tuesday for fine sunny weather. Our scientists are having to rethink our system from first principles". Bernie Madeoff, speaking from an unnamed location in South America said "I'm putting my money, or rather the money of my former clients, back into the market. Riding on the tidal wave of climate change, I'd recommend investments in British Wine and in the luxury seaside resort of Margate". A pity that Alan Sugar's potential apprentices did not pick up on this.

A Day of Internet Therapy

I spent a very therapeutic day yesterday trawling through Linkedin looking for old friends. It really does seem to be the case that we are each only five people away from knowing everyone in the world (like 90% of statistics, that was made up). The approach that I took was to scan the contact lists of all my contacts and look for names that I remembered; it certainly seems to have born fruit.

It was particularly pleasing to find John Giannandrea once again. Dubbed "John, Jean and Andrea" by still ST-resident wit, and excellent engineer Julian Wilson, the name was particularly appropriate as John did have the productivity of at least three good engineers. It was John who asked me to pay for a connection to the internet and thus gave INMOS (and subsequently ST) its first internet connection; it didn't take long to see how this world-wide email connection was going to change the way we did business. Sadly, through this connection I learned of the recent death of Jeff Mock who worked on the Pixar Renderman Engine when Pixar were using transputers and came to INMOS for a 6 month sabbatical. He provided us with the C run-time library to support multi-threading in our C development system. He was a great guy personally and participated in many of our lively technical debates. We were also priviledged to see some of the early images, such as the baby, that appear in their later blockbusters like toy story.

Of course the internet and email was one part of the story, and this arrived before web browsers arrived on the scene. It was some years later in 1994 that Mario Guanziroli gave me a demo of Mozilla in Cagliari; being slow on the uptake, it took some time (and explanation) for me to appreciate the significance of the "document" that we appeared to be browsing being distributed across various researchers' desktop machines.

As an unexpected side-effect of this trawl I have been delighted to have received so many good wishes from friends and past colleagues. I must apologise for the short notice I gave for my leaving drinks at the Cambridge Arms; it did of course result in a saving worthy of a Corporate Finance VP. I hope to be able to make amends over time.