Friday, 1 October, 2010, 07:07 AM - Not TFTDThis should be one to look out for. The Festival of Dangerous Ideas is playing host to a mock trial of Pope Benedict. Geoffrey Robertson is prosecuting and Alan Dershowitz is defending.
Protect the Pope (a site recently dedicated to Mary, our immaculate Mother, St Maximilian Kolbe, and to the Venerable Pope John Paul the Great) is already getting hysterical.
Actually that's wrong, it's been hysterically funny from the start.
Enormously Reverend James Jones, Lord Bishop of Liverpool and Bishop of Prisons, Platitude of the Year Winner 2009
And in the news today, I've just come back from an important bishops' fact finding mission to Phoenix, Arizona. It's hot there, swelteringly hot. You just wouldn't believe how hot it is. It was hotter than what you'd normally call hot. Very hot indeed.
The big topic for discussion was immigration. Should Americans try to kill illegal immigrants fleeing across the desert, or should they be nice to them? The same goes for Europeans and any other parts of the world that people are trying to illegally immigrate to.
What would Jesus have done? Should we have a green card system? Should we only take rich, well educated, highly qualified people from poor countries? After all, they wouldn't miss them, would they? Should we have an open door policy? Should we have a closed door policy?
Thanks to my fact finding mission to the swelteringly hot state of Arizona, I am now able to suggest a solution based on the teachings of Jesus. When he drove the money changers from the temple, Jesus wanted the temple to be a place of worship for all nations, although for some reason only one nation ever went there, perhaps due to the lack of money changing facilities. I think this means that the Invisible Magic Friend (of whom Jesus was the visible middle bit), wants us to be nice to foreigners. So clearly Jesus advocates a "be nice" policy.
This advice should be of great help to politicians struggling with this complex issue.
Has anyone mentioned that there's a big Jewish festival on at the moment? We've been sitting in our damp bamboo huts, being holy, remembering our fictitious past.
Has anyone mentioned Ed Miliband yet? He wants a break with the past. New Labour is just looking so old now. But he doesn't really want to break with the past because that would mean rejecting several thousand years of European culture. He really just wants to break with New Labour and create a much brighter, glorious, New New Labour.
Now that we've got that bit of the news out of the way, let's get back to the big Jewish festival. Once the big Jewish festival is over, we start reading the Big Book of Magic Stuff all over again, just in case anything has changed since last time. Then there'll be some more big Jewish festivals where we remember the past, some of which isn't fictitious, until we get to the end of the Big Book of Magic Stuff and go back into our huts again. Then we do it all over again. But don't worry. If you forget, I'm sure one of us will remind you.
Has anyone menshioned the Milibandsh yet? There's a shtory (hic!) in the Blible like that. Jacob tricks hish father into beshtoling, bleshtowering (hic!) blishtering (hic!), giving the elder brother's rightful blessing to him. Which ish eshactly different frum Miliband the Younger being elected Labour leader (hic!).
Jacob and Esau both proshpered. Jacob founded (hic!) Ishrael and Seesaw founded everybody else. But even though the brothersh were reconsh... (hic!) reconshiled, Ishrael and everybody elshe didn't. They threw all their cuddly toysh at each other (hic!).
And another thing. Ishrael and everybody elshe are still at it today. They need to make up (hic!) and have a big cuddle like Jacon and Eeesawww did.
Howsabout that then? (Hic!) Two topical newsh shtories in under free minutes. God I'm on a roll. I'm the ex Bishop of Shruffock. S'wat I do. (Hic!).
Monday, 27 September, 2010, 08:13 AM - BillingsRating 3 out of 5 (Fairly platitudinous)
Harriet Harman says life begins at 60 (although not if the government has anything to do with it).
What are we retired vicars going to do with all this free time? After a lifetime of incredibly useful vicarring, how do we get used to just not doing very much? It's easy to become fearful of just becoming too tired or too passed it to do any sort of practical vicarring at all, where our bodies just aren't up to the task of hard manual vicarring any more.
But we really shouldn't be too concerned about being useful all the time. Being useful is overrated in my book. I've spent a lifetime being useful and I'm thoroughly fed up with it. It's time to enjoy myself, take up train-spotting or stamp collecting. Something that's interesting and fun. You have no idea how bored I've been being a vicar. I'm looking forward to spreading my wings, becoming a new man, spending my time being completely useless.
Jesus said that in order to enter the Invisible Magic Friend's big house in the sky, you have to be like a little child. By that, I don't think he meant being innocent and gullible and believing any old nonsense that someone tells us. No, I think he meant that retirement was a time to let your hair down and have a good time.
Saturday, 25 September, 2010, 12:54 PM - Not TFTDMelvyn Bragg's superb programme, "In Our Time" did an episode on imaginary numbers this week. Interesting as it was, I don't think the utility of imaginary numbers really came across. As this blog occasionally deals with other imaginary items, I don't feel it's too off topic to try and provide a short explanation of imaginary numbers for the non-mathematically inclined out there.
"Imaginary" numbers are numbers that are multiples of the square root of -1, usually denoted by the letter i. For centuries, it was known that many solutions of equations, such as x squared = -1, required i. These were simply discarded as it was assumed they had no real meaning. There seemed to be no number that, when squared, could possibly equal -1.
Mathematicians simply invented the number i and started to play with it just as if it were one of the "real" numbers. When we add real and imaginary numbers together (e.g. 2 + 3i ) we get the so called "complex" numbers. Carl Friedrich Gauss was able to show (in his doctoral thesis no less) that all equations involving powers of x had solutions in the complex numbers. The algebra of complex numbers can, in this sense, be thought of as complete. This theorem goes by the rather grand title, "The Fundamental Theorem of Algebra".
The real usefulness of complex numbers only become apparent once we adopt a visual representation for them. Real numbers can be thought of as being placed on a line that goes from left to right,
stretching off to infinity in both directions. All fractions, irrational numbers (such as square root of 2) and transcendental numbers (such as pi) have their appropriate place on the line, but there is no number on the line that squares to -1. Several mathematicians had the idea of drawing another line at ninety degrees to the real numbers and placing the imaginary numbers there. This is called the Argand plane.
To add or subtract complex numbers you just add or subtract their corresponding real and imaginary parts. Multiplication is a bit more interesting. Here are two complex numbers:
1 + i and -1 + i
The absolute "length" of these numbers as plotted on the Argand plane is just found using Pythagoras' theorem:
square root (1 squared + 1 squared) = root 2.
They make angles of 45 degrees and 135 degrees with the positive real axis.
To multiply them we just use the normal distributive rule of ordinary arithmetic.
(1 + i) x (-1 + i)
= 1 x (-1 + i) + i x (-1 + i)
= -1 + i - i - 1 (remembering that i x i = -1)
This is a number that has a length which is the product of the two original numbers (root 2 times root 2 = 2) and the sum of their angles (45 degrees + 135 degrees = 180 degrees).
Although we've only shown it for a special case, a little bit of trigonometry shows it to be true in general. To multiply two complex numbers, you multiply their lengths and add their angles. But now consider complex numbers that all lie on a circle of radius one.
All these complex numbers have length one. Multiply any two of them together and you get another complex number with length one but with the two angles added together. Those of you who remember your logarithms and exponentials might see a connection here.
To multiply two exponentials of the same number, you just add their exponents. We have something very similar here with two unit length complex numbers: you just do an addition, but this time it's of their angles.
If you remember your basic trigonometry, you'll see that the complex numbers on the unit circle have real and imaginary parts corresponding to the sine and cosine of their angles.
So we can express any complex number of unit length in terms of a single parameter, namely its angle.
And we can multiply two of them simply by adding their angles. This connection between exponentiation and trigonometry gives us the incredibly useful formula (Euler's formula):
(e is the base of the natural logarithms).
Why is this so incredibly useful? The reason is that it is much much easier to manipulate exponentials than to manipulate trigonometric functions. Nature is full of periodic, wavelike phenomena. These can be broken down into sums of sines and cosines.
Expressing them as complex exponentials makes possible much of the world of electrical and electronic engineering, heat flow, fluid flow, quantum mechanics. Almost anything that is periodic or wavelike would be incredibly hard to work with without Euler's famous formula.
It might be going too far to say that modern technology, science and engineering would be impossible without imaginary numbers, but it would certainly make life a lot harder.
Saturday, 25 September, 2010, 11:10 AM - TFTDThe Thought For The Day website doesn't seem to be getting updated any more. They are however maintaining a list of recent TFTDs as podcasts, so we can all continue to enjoy these daily moments of enlightenment long after we get out of bed.
I'll link to these as they become available. I have no idea how long the links will remain valid, or whether the BBC will delete them over time.
The old links were quite formulaic and I could include them in advance simply by adjusting the date. The new ones also include a timestamp, so I won't be able to link to them until they appear on the BBC website. It looks like some kindly person in the Holy Department of Religion wants to make my life a little bit more difficult. I can't think why.
Sadly, it looks like transcripts have been discontinued. I have no idea if this is a permanent change of policy or is merely a temporary glitch.
Mutt, who used to maintain the TFTD website, has also been absent from this blog for a while. I hope everything is OK.
Brian here, in Southampton, an associate lecturer at the London Institute for Contemporary Christianity where we envision and equip Christians, and the leaders, churches and organisations that serve them, with the biblical framework, practical resources and models to engage biblically, relevantly and vigorously with the issues they face in today’s world. Hi.
The Big Book of Magic Stuff tells us that brothers invariably kill, or at the very least, detest one another: Cain and Abel, Isaac and Ishmael, Jacob and Esau, Joseph and everyone else. Eventually these petty little family squabbles break out into civil wars. Let's hope the Miliband brothers (who come from a musical family so large that they must be measured in thousandths of a Band) will bear no such animosity to one another.
Jesus, the visible bit of the Invisible Magic Friend, asked who is my brother or my sister? Why everyone is and wouldn't it be nice if we could all just get along? That's where great religions like Christianity really help out, bringing people together rather than dividing them along silly tribal or dogmatic lines.
Today, when one of the Thousandths of a Band brothers assumes the leadership of the Labour Party, and the other becomes his lowly slave, they will have the opportunity to lead by example. Unless Dianne Abbott gets it of course.
The 15th Robot World Cup was dominated by Far Eastern teams last week. Speculation is rife, that by 2050, these robots will be good enough to challenge human players.
As androids become more and more skilled and their cognitive abilities increase, philosophers will have new questions to address about the rights and expectations of electronic brains. Theologians will be tasked with important questions such as, do androids have souls.
The answer is "no" - the Koran says so.
Banks need to do things the right way, says Lord Turner. Many banks have been doing things the wrong way. People who thought they were really clever and had eliminated risk from their financial products, sold those products around the world. Well who's laughing now, eh? The markets collapsed and all those clever people had to say sorry. Then they gave us all the money back.
That's what happens when people do things the wrong way. The Nazis believed they could improve things by killing all the people they didn't like. With the benefit of hindsight, this turned out to be a wrong belief. Communists also believed they could make things better by killing large numbers of people. This also turned out to be the wrong belief.
I have to admit, that on occasion, the Church has sometimes tried to improve things by killing large numbers of people too. However, thanks largely to the fact that we're not allowed to do it any more, we have now come to believe that this is the wrong thing to do.
Banks, Nazis, Communists, and the Church gone past but not the Church today, have all believed wrong things. Experience tells us that it is much better to believe right things. Believing wrong things can have terrible consequences.
Has anyone mentioned Blessed Cardinal Newman yet? He was a very wise man who understood that we often believe wrong things and that it is much better to change our minds and believe right things. In fact he changed his mind about being an Anglican and became a Catholic, so he ended up believing the wrong things.
We have to constantly test our beliefs in the light of new evidence, just like the Church does.