Infinity: What Is It (And Where To Find One Of Your Own)

The Imagination

Infinity is big. In fact, it is very, very big. It is even bigger than the incalculable Graham’s number. Now Graham’s number is big. I mean it is really, really big. It even makes Douglas Adam’s view of the universe look small!

Graham’s number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes’ number and Moser’s number. Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham’s number, assuming that each digit occupies at least one Planck volume. Even power towers of the form  are useless for this purpose, although it can be easily described by recursive formulas using Knuth’s up-arrow notation or the equivalent, as was done by Graham. The last ten digits of Graham’s number are … 2464195387″ (1)

Continue reading “Infinity: What Is It (And Where To Find One Of Your Own)”

A Sideways View · Modern Times · Reality

The Real Meaning Of Christmas.

Why Celebrate The Longest Night Of The Year Anyway?


For most people Christmas means – if it “means” anything at all – running up debts and getting drunk. Long gone are the traditions in most families. The presents lie scattered by 5am and the tetchy children are driven to places they would rather not go to see people they would rather not see. Only to get stuck in a traffic jam for an hour or two.

So what happened to Christmas? What indeed! Was it anything anyway? Mere tradition doesn’t hit the mark any more with the iPad and xBox generation. Everything needs to be driven to them from outside, videos – games – food. The modern generation expect to be hand fed everything, and that includes Christmas.

Continue reading “The Real Meaning Of Christmas.”


Railways, Then And Now.

There’s good coffee even at small station in Germany.

So here I sit with a coffee at the station Hamburg Harburg. A train is late, so I get the chance to drink a coffee in the station restaurant. It is, as you can imagine, made with the help of a machine. That it tasted good and only cost a little more than one euro will give you an idea of what I want to delve into.

There was a time when Uelzen, Lüneburg, Harburg, and Salzwedel all had their own locomotive depots. Today there is one in Hannover and another in Berlin. This clearly demonstrates a massive improvement in efficiency. Machines, electric and efficient have overtaken the unwieldy and maintenance intensive steam engines. That you can jump on a train departing from Uelzen every hour or two in every direction bar Dannenberg is testament to this improvement in customer service. That it is also massively cheaper than in the past, and it is also noteworthy that it is competitive with travelling by motorcar.

Continue reading “Railways, Then And Now.”


When A Hunt Saboteur Needs A Fox Stole

Meet Emilia Fuchsenschwanz

Emilia-Viktoria-von-und-zu-Fuchsenshwanz-VorstrelitzEvery Lady needs a stole now and again. You may – or may not – be aware that a stole is a fox-skin worn as a scarf. You see, the problem is for the hunt saboteur who is of course, anti-hunting. Even the fur shaved from a fox would be unkind. I would not wish a fox to be running around naked. It would be indecent for one thing. The only reasonable alternative was to wear a live fox.

This necessitated catching one, or in my case attempting to own one. It quickly escalated to some interesting problems and her escape. This is the tale:

Brian, who is a friend of mine found my stole on his doorstep one morning, and thought of sending another home with it. It? No! Not, “it” I should have said “her“!

Oh, dear.

I had never really considered having more than one stole. The problem being of expense.

You must understand that whilst as an ordinary human being, I travel second class. I may be upper middle class, but that matters not a whit to a stole. However, Emilia, my stole having come from the renown Brandenburgerfuchsundstoleakademie zu Berlin, expects a lifestyle somewhat more fitting to her needs, not mine. So when travelling with my stole, then it is necessary for me to upgrade my seat to first class, and when travelling overseas ensure that the cabin is next door to the captain’s quarters in order that my stole feels at ease with the situation.

So you can imagine that travelling with Emilia can get expensive.

Now couple that to a fox’s natural ability to walk and run, then this of course offers different problems because of the local poultry population. There have been several occasions when I have had to pay for a number of poultry carcasses that were mauled in the characteristic manner of a Brandenburgerfuchsundstoleakademie zu Berlin stole. They were so cleanly plucked and beautifully prepared as to be ready to put in the oven directly.

That I had other plans for dinner that night made no difference to my stole, Emilia. The brussels sprouts and potatoes had also been found along with two bottles of Chateau de Mouton de Rothschild. They would have cost a fortune had my stole actually bought them rather than getting them as the result of a favour earned before she came into my employ. In short, a stole trained as a sous chef and wine cellar manager can be something of a nuisance at times, especially when they had failed the household planning training.

The resulting meal was well worth the effort, and serving my stole in the manner to which she has become accustomed to (silver cutlery, cut crystal decanters, silver candlesticks, etc) took quite a while. Even the remains were very tasty, because that is all she left me.

The first class dining car on a Geman ICE high speed train.
The first class dining car on a Geman ICE high speed train.

You will appreciate that Emilia has a three bedroom coat hook, with central heating, fitted bathroom, kitchen and of course the necessary wine cellar. Yours truly is employed to clean the place, when allowed.

In short, owning a stole of this quality and nature is no mean affair, and costs considerably more than I earn. Goodness, I did try to encourage her to stay with you … G xx

As a codicil, this was my response to Brian when my fox had arrived home:
It was very kind of you to send Emilia home from Hamburg by train. I must be very clear at this point: I cannot afford to keep this animal, my pet. To send her back by train was kind, only expensive. Not only her very necessary first class seat, but her chaperone too. After all, a fox stole will never travel without someone to wear.
Not only that but on the way home she felt a little hungry.
On arrival in the dining car, she was not entranced with the menu. On returning to her seat she met and pleaded with an acquaintance of hers to cook for her instead. This was no lesser personage than Thomas Bühner the celebrity chef.
She enjoyed the meal. He sent me the bill. All I can say is that I am thankful that in first class, the coffee is free.