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Sunday, 10 March 2019
"This time next year we could all be..."
If you would like to be a millionaire it’s simple. Just solve one of the current seven most difficult to solve mathematical problems and collect the £1m. prize from the Clay Foundation in the US.
Just call me Archimedes. Like the great man I have all my best ideas soaking in a hot bath and today so it nearly was, except I didn’t come up with a relevant indisputable result, but at least I formed the notion for this post. I was wrestling with the logistics involving train times, buses, cars, and walking distances for the next two sections of our straight line walking route from Blackpool to the east coast with BC. We are now nearly halfway through and facing a transition from private to public transport.
One of the Seven Last Great Problems is the classic Travelling Salesman calculation trying to work out the shortest route between a number of towns he must visit known as the P versus NP problem. If there are only four towns there are only six options - easy to see which is best by simple maths. If you scale up to ten towns the exponential number now becomes 3,628,800 (ten factorial).
Here is an extract from The Millennium Problems by Keith Devlin. Keith has made a brave attempt to describe the problems for the layman producing a book I found absorbing. That is saying a lot for me as one who failed O Level maths.
Keith goes on to explain the colossal increase in available routes by just adding one or two more cities - when you get to 25 you will have: 15,511,210,043,330,985,984,000,000 options to evaluate. Eventually the problem goes beyond present day computing ability. Even for ten cities Keith says if you took a minute to work out the mileage for all 3,628,800 possibilities it would take you just over twenty years! There is much more on this problem in the book, but you may be heartened by the following from Keith: "P versus NP puzzle is the most likely to be solved by an unknown amateur. Not only is it relatively easy to understand what the problem says, it is possible that all it will take to solve it is one good new idea."
Ok, I was only concerned with three destinations for this section of our route, and not particularly with shortest distances, but I enjoyed the catalyst to go back to a book that gave me pleasure a couple of years ago.
My title comes from Only Fools and Horses, and again I found myself pursuing further knowledge by identifying the source which I was not aware of, although my son W was familiar with it. From Vaudeville in the US the full line is:
"Only fools and horses work for a living"