Sunday, 25 May 2008

Thinking about thermodynamics in Wales

I recently spent two nights in Wales with a friend who collects railways, crematoria and hats.

We didn't find any new hats, but did visit two railways and a crematorium.

We stayed in the Trefeddian Hotel, Aberdovey, a delightful establishment where the amenities included an 'adults only' lounge. We were pampered with strawberries, and of course lots more too, for breakfast, and delicious five course dinners in the evening. If one doesn't finish a bottle of wine, they keep it till the next day, so we ordered both red and white on the first night and finished them off on the second.

On the Talyllyn Railway I had a chat with a friendly fireman while the engine was getting up steam. He told me that all the steam is vented to the outside (extremely inefficient) and when I peeped inside the driver's cab I noticed that the maximum safe pressure was 150 pounds per square inch. That provided food for thought during, because it was the first time I'd seen any figures for a steam engine, and didn't know the conversion factor from pounds per square inch into anything useful

Although the scenery was very pretty, with wooded hills and waterfalls, I should have enjoyed the journey a lot less had I not been busy converting pounds per square inch into pascals - the answer is about 6900, so the engine operated at about a million pascals, or 10 atmospheres.

Once I got home I looked up the vapour pressure of water and discovered that that pressure corresponds to about 180 degrees C, and by making a rough estimates of work done by the expanding steam in the pistons, and the heat put in, I estimated an upper limit of 6% for the efficiency.That makes steam trains seem much less fun.

It is not because I'm an ardent environmentalist, but because I find waste aesthetically unappealing. Even though I can remember how unpleasant railway travel could be when steam was almost universal, I'm not immune to the superficial charm of the surviving steam railways. The technology is very old and yet it works, thus do we condescend to previous generations. Steam engines make a cheery chuff chuff chuff and whistle frequently, and those that survive often potter along through pretty countryside, but using 94% of the fuel to produce the steam and smoke, and only 6% to make the thing move seems an unreasonable preference for the superficial.

Sunday, 18 May 2008

The Ham and Cheese Sandwich Theorem

My patient plodding through the definitions and basic theorems needed to get Topology underway has at last been rewarded with substantial result. The formal statement is:

Given three finite volumes, U, V, and W in Cartesian 3-space, there is at least one plane that bisects all three.

The application to the bisection of a ham and cheese sandwich with one cut should be obvious. Note that no assumption is made about the way the ham and the cheese are distributed within the sandwich.

The proof is quite short and fairly easy to understand, though it does depend on the Borsuk-Ulam Theorem, which my book considers too hard to prove except in one special case.

Sunday, 11 May 2008

I almost forgot to watch the last episode of Dr. Who. At one time I'd have almost been counting the minutes to the next episode.

It isn't just the loss of suspense between episodes now that most programmes show a self contained story, though that is a factor. What spoils the new series for me is mainly a combination of over hasty development, and an excess of what the producers probably call 'human interest'.

Much of the excitement provided by good science fiction comes from following the solution to a puzzle, and one cannot enjoy the solution to a puzzle unless one is first given a chance to be puzzled by it.

Dr Who's adventures used to start with people notiving that something a little odd was happening. As the Doctor probed into events things appeared odder and odder, eventually revealing the, usually malign, source. But even when the culprits were revealed there was still the further puzzle of why they were doing it and whether they were acting on their own account or as agents of some even more sinister power. One used to be kept on tenterhooks for weeks, but no more, alas.

Something else science fiction can do is to show the universe from an unfamiliar, non-human point of view. I'm not sure how realistic it is for we human beings to try to adopt a point of view that can probably never really be ours, but the attempt can at least be thought provoking. Having Dr. Who falling in love makes it harder to develop such point of view, because our thoughts about love are an elaborate ideology of collective self deception.

Human society with its politics and morality is an elaborate mechanism that serves to increase the number of human beings, a sort of epiphenomenon of the reproductive instinct, what F. A. Hayek (Law Legislation and Liberty) would have called a Spontaneous Order. Insofar as love transcends the primal impulse to mate, it is a sort of megalomaniac desire to have descendants, and society is a compromise between the competing reproductive instincts of different people, hence the strange belief in the sanctity of life.

Because we are human we cannot easily escape from this point of view, and possibly cannot escape at all, but it is refreshing sometimes to contemplate the world as it might appear to one whose vision was not obscured by the ideology of love. It seems a pity to miss an opportunity.

Thursday, 8 May 2008

I have just revised the last chapter of my Philosophy notes and put it on my web site. I thought it would do justice to the oddity of the subject to delay a tentative answer to the question What is Philosophy? until the final chapter.

Having provided content for this posting by making that announcement, I feel that I can mention cannabis without delivering the ill-tempered rant I might have indulged in had that been my only subject.

I do not believe that any sane and thoughtful person can think it helpful to make recreational drugs illegal, and assume that the near unanimity in favour of that inanity among our politicians indicates dirty work of some kind behind the scenes.

The greatest beneficiaries of legal restrictions are those who deal in illegal drugs on a large scale, since illegality greatly inflates their profits. I surmise that drug profits in some way play a part in maintaining the present state of the law, but am not sure how. I doubt if there is overt bribery, at least not in Britain, but I think it would be interesting to examine the financing of drug charities. Do they have lots of anonymous donations ?

Monday, 5 May 2008

I've just signed two petitions on the Downing Street site.

The first concerns the action of police who, as part of a campaign against drugs, have been distributing in schools leaflets advertising an organisation called Narconon with links to the Scientologists.

For background information see a study by the Sunday Times

To sign the petition follow this link.

The second petition protests at a proposal in the current Criminal Justice Bill to make it illegal to posses what is ambiguously termed 'extreme pornography'.

More information is provided by this article.

To sign the petition go here.

50 years ago laws against 'pornography' were widely ridiculed and they were repealed in the 1960's, yet those laws were mild compared with what is being introduced now, because the old laws forbade only 'publication', showing the material to someone else. To criminalise mere possession is to prepare the way for an inquisition, and all to give self righteous hypocrites a chance to boost their pomposity !!

Sunday, 4 May 2008

During the last few days I've been strangely obsessed by the local elections. It is many years since I hoped that our political process might improve matters substantially, but I still find elections exciting, especially when the governing party does badly. There is some justification for that, because even if an election replaces some bossy people by others, at least it is a chastening experience for the defeated, but that alone does not justify the hours I've spent following the results. Partly it is a sort of numbers game, a bit like erratic Go on a large scale, and the election of Boris Johnson as Mayor of London is definitely like a move in a game. I was delighted to see him replace the vindictively self-righteous Livingstone, though there may be too many Livingstone disciples in the London administration to allow Johnson to be amusing as I should like.

Combined with a clamouring of tomato plants needing to be repotted into my home-made soil and compost cocktail, the elections not only led to my neglecting this blog, but even distracted me from the topology book I'm plodding through slowly, as recorded in the appropriate section of my home-page.