**Rating**3 out of 5 (Fairly platitudinous)

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!).

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Monday, 27 September, 2010, 07:13 AM - Billings

**Rating**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.

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Saturday, 25 September, 2010, 11:54 AM - Not TFTD

Melvyn 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 + 3

*i*) 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)

= -2

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, 10:10 AM - TFTD

The 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.http://www.bbc.co.uk/podcasts/series/thought

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.

**Rating**3 out of 5 (Fairly platitudinous)

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.

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**Rating**2 out of 5 (A little platitudinous)

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.

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Thursday, 23 September, 2010, 07:22 AM - Dont do bad things, Tilby

**Rating**4 out of 5 (Highly platitudinous)

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.

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Wednesday, 22 September, 2010, 08:14 AM - Sacks

**Rating**4 out of 5 (Highly platitudinous)

Has anyone mentioned the Pope's visit yet? I got to meet him you know? It was very nice. We smiled and said "Hello" and said a few soothing words to each other.

Why were we all so nice, when we used to raise vast armies to fight wars and persecute one another? It would be nice to think that we had grown up and recognised a core of spirituality, but in reality, nobody much bothers about religion any more. We just can't muster the vast armies to wage war any more, so we've got no real option but to be nice to one another.

I think this is very nice. It brings the niceness back to religion, because religion isn't about being powerful. Apart from Mesopotamia, Assyria, Babylon, Egypt, Judaism in the few brief centuries where it exercised real power, Christianity for the vast bulk of its history, the Islamic Caliphates of Baghdad, Cordoba and the Ottoman Empire, religion has never really been about power. It's all about helping poor people and being nice.

There's a big Jewish festival coming up. You'll recall I told you all about it last year and the year before that and the year before that. Happily, on each and every occasion there's been a major event that just so happens to perfectly illustrate the true meaning of Sukkot.

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**Rating**3 out of 5 (Fairly platitudinous)

Hash anyone menshoned the Pope yet? (Hic!) Yesh the exshitement and plomp of the Pope'sh shtate visit's over and it's time to get back to the everyday, humdrum world of ex-bishopping.

Ishn't poverty just (Hic!) jusht terrible, eshpeshally when it'sh foreigners who are poor. I shaw a cartoon once you know. It washn't (Hic!) about poverty. It wash about thish bloke in a pinstripe suit bashing a wall down. And there wash thish other bloke. D'ye wanna know what he did? Well, I'll tell you what he did, he jusht shat there (Hic!) waiting for him to finish.

Now I know what you're thinking. You're thinking (Hic!) "Yesh, that'sh (Hic!) jusht like being poor that ish." That'sh what your thinking. And ye know what? You're right, absholutely shpot on you are.

There need'sh to be more help for poor people. All thish keeping people poor'sh jusht terrible it ish. Y'know it'sh (Hic!) not what God want'sh. No sirreee. God want'sh nobody to be poor any more. He want'sh evr'body to have a glash of sherry or two now and again.

Oh, yesh please. (Hic!)

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Monday, 20 September, 2010, 07:16 AM - Billings

**Rating**3 out of 5 (Fairly platitudinous)

Has anyone mentioned the Pope or Cardinal Newman yet?

Cardinal Newman was a really, really important Anglican theologian, who changed the world forever with his ground breaking discoveries of new bits of theology. Then he became a Catholic and the Pope was so delighted that he made him a cardinal. The current Pope was even more delighted. So much so that he has now promoted Newman to being nearly a saint.

In today's godless, spiritual wilderness, where people aren't really that bothered about religion, it's difficult to understand what all the fuss was about. But back in more godly Victorian times, changing religion was a really big thing. To go from wearing an Anglican dress to wearing a Catholic dress was considered a betrayal. It meant the severing of friendships, the break up of families and the sowing of discord and bitterness. Them were the days!

Nowadays people seem to wander aimlessly from one religion to another and even in and out of religion altogether. There's no sense of loyalty to a particular brand any more. I've had people in my congregation from all sorts of weird, mangled versions of proper Christianity. I suppose they bring a kind of novelty in perspective.

There was even an agnostic in my church that came just to listen to the music and soak up the atmosphere. How bizarre! I'll never understand these unbelievers. I mean, why would anyone come to a church just for the music?

Cardinal Newman was seen crying outside his old church once. I like to think that this was him being miserable for being such a treacherous turncoat against proper Christianity.

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