Stuff Councils, even the Fathers have erred

After this, that we may not be confident in the Gospel merely preached, nor think that faith only suffices us for salvation, He utters also another, an awful parable. Which then is this? That of the Net.

For the Kingdom of Heaven is like unto a net, that was cast into the sea, and gathered of every kind; which, when it was full, they drew to shore, and sat down, and gathered the good into vessels, but cast the bad away.

And wherein doth this differ from the parable of the Tares? For there too the one are saved, the other perish; but there, for choosing of wicked doctrines; and those before this again, for not giving heed to His sayings, but these for wickedness of life; who are the most wretched of all, having attained to His knowledge, and being caught, but not even so capable of being saved.

(St. John Chrysostom. Source, Google books.)

We mustn't think faith only suffices us for salvation. We are saved because we choose right doctrine, avoid wickedness and prove capable of being saved. Yeesh.

But he does hit on something true—it is entirely possible to be drawn into the church in the sense of a false confession of faith, perhaps by the songs and the preaching and the warm fuzzies on a Sunday, but yet without being a "good fish". When the wicked are separated from the righteous, whose righteousness will we attempt to plead?

The Protestant Revolution

I watched the first episode of "The Protestant Revolution" (BBC Four, on Wednesdays at some unholy hour of the morning [EDIT: actually, I discovered it's on about five times in the week, including Wednesdays at 9pm, which ain't so bad.]) this evening; it’s an interesting enough programme, with features from Rowan “Scotty Dog” Williams, Tony “Lapshed Methodisht” Benn and Diarmaid “Scottish, Honest” McCulloch, presented by Tristram Hunt. His thesis in this programme—that Protestantism foments rebellion against tyrannies spiritual and temporal—was kind of predictable enough, if a little bizarrely applied at points. His material at the very beginning on Luther seemed about reasonable to me (I could identify a few historical errors, but nothing particularly shocking), but when he got onto Calvin and the Puritans he was muddled: apparently, John Calvin was a Radical in the same vein as Muentzer, and non-conformists were oppressed and underground until about 1900.

Oh yeah, and the theme music is someone-or-other’s version of the Sanctus, which is somewhat amusing for a programme all about Protestantism.

This Wednesday’s programme is all about the Protestant attitude to family, contrasted with Catholic celibacy. Because, as every one knows, all Catholics are celibate while Protestants have ginormous families. Ho-hum. We'll see if it's any better.

The military covenant

Current political rumblings have reminded us that, a few years back, part of the Army Doctrine Publication (is this like their Bible?) introduced a written version of the long-standing 'military covenant', in which the country and Armed Forces have a mutual agreement that, basically, soldiers accept harsher conditions and certain privations while on service in exchange for a duty of care from a thankful civilian nation. Political disputes about whether this covenant is being kept aside, I have a few questions. Who is the covenant mediator? Did the parties cut a horse in two and walk down the middle? Are there any good, old-fashioned covenant curses? Does the promise propagate generationally? Inquiring minds etc.

We have JWs

Came round to visit this morning, and had a fairly interesting discussion for about half an hour or so. The chap is planning to make a return visit in a fortnight or three weeks, so any pointers towards some useful resources would be good. I think, unless the conversation winds differently, that we'll be discussing the relationship between faith and works, and the New Earth.

From particles to perpetuities

I'm on this particle physics summer school and we got to discussing the singularly odd fact that you can "show" that

Σ_nn = -¹/₁₂,

as you do. (There's, as with almost anything, a Wikipedia article on this rather bizarre mathematical trick. Perhaps one day I'll figure out how to type-set one of the more clever routes to the result.) There's a similar result which states that the sum of "1" is -1/2.

I was chatting about this with one of my colleagues, and mentioned that economists, of course, sum "1" to infinity and get a sensible result all the time. The vehicle they use is most often called a "perpetuity". The way it works is this: suppose that I offer you a deal where you pay me an amount of money now, and I'll pay you a pound every year in perpetuity—means, forever. It's important that it be forever, for theoretical purposes. Now, how much is that deal worth to you?

He was quite surprised to learn that it has a finite value, but you can think about it in at least two ways to see that it must be true. Route one is to say that "jam tomorrow" has a lower value than "jam today". This is certainly true, and the rate that economists use is normally something around the 1-10% mark. I tend to take 5% as a reasonable discount rate. If a pound next year is worth 95p today, then it is a very simple exercise (as in, at the level of a competent GCSE student) to show that a pound every year forever is worth £20.

Route two is more direct. A discount rate of 5% supposes that I know of some way of getting a guaranteed return of 5% per annum, so to get £1 a year, I'd need to invest £20. Easy!

The next interesting question is to suppose I've done this deal with someone, and they're paying me my pound a year, when I suddenly find myself in need of some money. I decide to cash in my perpetuity. How much money should I ask them for? The answer is probably obvious, unless you think about it too hard. It's £20, because a perpetuity never loses its value. It's in perpetuity, remember!

There are a few other conceptual questions which could be quite good to pursue in interviewing a candidate for a finance degree course, but the thing I'm pondering is this: a bond or gilt is a deal between two parties, in which party A pays party B an initial sum (the loan principal) and then party B pays party A a fixed sum annually (the interest) for a fixed period, at the end of which, party B also returns the principal. Generally, these things are sold in £100 units, so the Treasury 5% 2025 is a unit of the promise by the Government to pay £5 a year until 2025, and then to pay £100 and the promise comes to an end. The interesting thing to me is that the cashflows on this are equivalent to a perpetuity: you pay out, receive a fixed sum per year and then receive back your payout. Does that make them a perpetuity?

Sticking with the nominal cashflows, I think this is right. When your gilt matures, you can put the money back into a gilt and, ceteris paribus, achieve the same return again. But that word nominal provides a little snag. You see, the Government (and companies) float their loans, so that the promise of £100 actually costs something different (in the gilt example I gave, yesterday's price was £102.22). The £100 nominal means the face value of the unit, and the £102.22 is what you actually pay on the open market. Now, using the market price and the promised cashflows, I can work out the market's long-term discount rate. But my observation that a gilt can be transformed into a perpetuity makes me wonder: is it simpler than I thought?

You go where you're looking

"Let us fix our eyes on Jesus, the author and perfecter of our faith." (Heb. 12:2)

I'm learning to drive at the moment, and when I started, my instructor kept having to tell me not to look at the oncoming traffic. Instead, he told me to look at the gaps, to see if I could get the car into them. You see, he told me, what happens is that you end up crashing into things if you're looking at them rather than at the road. In short, he was saying, if you look where you're going, you'll go where you're looking.

Spiritually, we shouldn't look at ourselves to tell whether we're heading in the right direction; we keep our eyes fixed on Jesus, and then we certainly will strain towards the prize.