Theistic argument run-down

In a recent blog post, Larry Moran raised the question: what are the best arguments for God? The subtext here is that apologists and "faitheists" are always claiming that there are sophisticated arguments for God out there, but rarely seem to be able to describe them.

One commenter, Martin, has risen to the challenge:

A few off the top of my head:

1. Kalam cosmological argument
2. Argument from contingency
3. Plantinga's modal ontological argument
4. Maydole's modal perfection ontological argument
5. Fine-tuning arguments
6. Argument from reason
7. Evolutionary argument against naturalism
8. Moral arguments
9. prosblogion.ektopos.com is loaded with arguments

Not bad, and kudos to Martin for actually coming up with some concrete claims. Ideally he would have said which of these arguments he finds most convincing, but that's a different issue. Let's have a look down the list.

1. The Kalam cosmological argument

This is a variant of the standard fine-tuning argument, employed by apologist William Lane Craig. The standard version takes as its premise that anything that exists has a prior cause. This lays it open to the reductio ad absurdum that, since God allegedly exists, He too must have a prior cause (a meta-God), who must also have had a cause (a meta-meta-God) and so on. Not a terribly elegant explanation.

The Kalam version simply states that everything that has a beginning has a prior cause. Since God is conjectured not to have had a beginning, He therefore doesn't need a cause. Since the universe is conjectured to have had a beginning, it does need a cause, and God fits nicely into the gap.

This argument has attracted a range of criticisms. In particular, it has been argued that things do appear without prior cause all the time in quantum mechanics. Various effects in QM only make sense if "virtual particles" are continually appearing from nothing (in pairs so as not to violate principles of symmetry) and vanishing again.

Craig's defence is that these events don't really count because the particles aren't coming from nothing; they're arising from fluctuations in the background energy field of the universe. This is technically accurate. But it means it's Craig's assumption is impossible to test. If anything within the universe can take the universe as its "prior cause", what exactly would count as a refutation?

There are of course other criticisms, but I only have the one evening. At the very least, though, this argument cannot be considered a "proof" in the same league as mathematical proofs or scientific theories. Like most extant philosophical proofs it is linguistically fuzzy, and it relies heavily on intuitions that are of dubious worth in a non-Euclidean universe.

2. Argument from contingency

A big topic in philosophy has been the study of the distinction between "necessary" truths (1+1=2 can't not be true) and "contingent" truths ("Lifewish is sitting in front of a keyboard" is true but could be false). There is an entire system of logic designed for drawing these distinctions.

The theistic argument from contingency (aka the modal cosmological argument) basically points out that it is really really difficult to reason from the existence of necessary truths to the existence of contingent truths. Basically, how did the first universe-like thing (whether that be this universe, another universe, or something more exotic like an M-brane) come about?

Since the universe is contingent, it is argued, there must have been something to start it off. God, who is assumed to be necessary, is considered a good candidate for this.

I haven't even looked into this one and already I can see a few refutations. For example, under what circumstances can necessary things give rise to contingent things? If it is easy for this to happen, could there not be a necessary thing other than God that's capable of the task? If it is hard, how come God can do it? Intuitively it seems odd that a necessary God could give rise to a contingent universe; how would He know which universe to create out of the various options?

It's also open to question in what sense the universe is contingent. Even if it is contingent, maybe it's part of a multiverse that is in some sense necessary. There are various other options to be considered, any one of which is enough to screw up the chain of logic.

Again, this argument is a nice philosophical tetherball to play with, but it is not terribly convincing to anyone who isn't already convinced. It exhibits basically the same cracks as all the other regress arguments, albeit with a slightly fancier wallpaper covering.

3. Plantinga's modal ontological argument

The classic ontological argument is: imagine the greatest God it's possible to imagine. If that God were real, He would be even greater. But then He wouldn't be the greatest God it's possible to imagine. For consistency with our initial premise, we have to assume that this God is real.

Plantinga's variant attempts to translate the fuzzy concept of "imagine" into more rigorous modal logic (the logic of "possible worlds"). First, assume that, in some possible world, there is a God that is "maximally excellent" (I love that phrase, it's very Bill and Ted).

But a maximally excellent God would presumably have the power to reach into other possible universes than their own (otherwise you can imagine an even more bodacious deity). So they'd be maximally excellent in all possible worlds, including our one.

This argument seems to have been absolutely slated by every philosopher who looks at it, including Plantinga himself. (See here for discussion.) Plantinga argues that, since the premises are "rational" (by which I think he means "not obviously daft"), the conclusion must be rational.

All I can say to that is: rational? You keep using that word. I don't think it means what you think it means. To me, and to most other skeptics, "rational" has a higher meaning than just "too complicated to understand, let alone critique". Security through obscurity is a bad principle to build a worldview on.

4. Maydole's modal perfection ontological argument

This is a relatively recent argument, and I hadn't come across it before. The original paper is behind a paywall, so I'm forced to rely on this forum post.

On investigation, this proof is like every other modal "proof" I've read: it smuggles in its conclusion via a complicated statement that sounds plausible until you think about what it actually means.

The statement: "If it's possible that there exists an x that is an F, then there exists an x so that it's possible that x is an F."

How it's being used: "If supremacy is possible then there must exist something that's potentially supreme."

Using this starting point, Maydole pulls a cunning trick. There is a standard theorem in modal logic that if something is possibly impossible then it's impossible. This makes more sense if you translate it differently: "If, from the viewpoint of some possible world, X is false in every possible world, then X is false".

By defining supremacy in terms of impossibilities, Maydole uses this theorem to create a sort of "potential world contagion" in a similar way to Plantinga's argument. Once the walls between possible universes are broken down, the possibility of God becomes the proof of God.

How to criticise this argument? Difficult without spending a full blog post on it - as with Plantinga's variant, the argument's main defence is its length (and I still only have the one evening). To start with, though, I would note that, in the version I linked to, statement P3 does not actually follow from statement M2.

I suspect that this error is a side-effect of the forum member's attempt to boil the argument down. But it demonstrates how fragile the argument is as a whole... and how little progress I can make without access to the original paper. I may research it in more depth at a later date if anyone is remotely interested.

5. Fine-tuning arguments

These have been refuted to death. The basic form is:

1) The universe (or some part of it) has a certain property with a certain value.
2) Human life wouldn't be able to tolerate a different value of that property.
3) Therefore God fine-tuned that property, because He cares about us so much.

Classic refutations:

1) Human life might not exist if the property were different... but some other wildly different lifeform might. In a universe with four dimensions, I wouldn't be typing this blog post. But a fifty-armed intelligent plasma cloud might be.

(See also Douglas Adams' puddle analogy).

2) Even if the property's value was an amazing slam-dunk, how many shots were there at the hoop? Many modern physical theories require there to be a ridiculously large number of alternate universes, each with slightly different attributes. Maybe we're just in the one of them that happened to be habitable?

(Note that there is no extant physical theory that requires God to exist...)

3) If God cares so much about getting the environment right for us, why is 99.9999etc percent of the universe uninhabitable vacuum? Why is 99.86% of the solar system's mass stuck inside the Sun, rather than being used to make more habitable planets? Why is 71% of the Earth's surface covered by relatively unhelpful water rather than fertile soil? God does not seem to be going out of His way to make things easy for us; why should the "fine-tuned" property be His one exception?

6. Argument from reason

Here I assume that Martin is referring to the transcendental argument. Roughly stated: in a Godless universe there's no obvious reason to think we'd be able to come to accurate conclusions. So, by arguing about anything (including God's existence), we are implicitly conceding that He exists.

I like to think of this as the Argument from It's My Ball And You Can't Play With It.

There are two really insanely obvious counters to this. Firstly, the ability to accurately model the behaviour of things confers a strong survival advantage. So we'd expect it to crop up occasionally in evolved species.

Such a creature might not be capable of discovering Ultimate Truths. But there's a pretty strong argument that we don't do that either.

Secondly, even if there were no Godless cause for rationality, this argument doesn't explain why God would be any more likely to create thinking organisms. Why would God not create mad creatures? Only by positing a very very specific God - a God that's naturally inclined to create sane humans - can we get to the conclusion. But then we might as well just posit a universe that is inclined to give rise to sane humans, and save ourselves the trouble of coming up with a proper causal explanation. This would make biology classes a lot shorter...

(In fact, many prominent believers have claimed that reason is in some way inferior. Why would God sully His hands with such an invention?)

Without dealing with both these counterarguments, the "argument from reason" is dead in the water.

7. Evolutionary argument against naturalism

This is just Plantinga's rehash of argument #6, focusing on the question of whether evolution can give rise to "true" rationality. Given his complete lack of understanding of evolutionary biology, I'm going with "no"...

See here for more discussion, if you're really keen. If you're a veteran of the Darwin Wars, or you're familiar with the classical transcendental argument, there's not a lot of interest here.

8. Moral arguments

In brief: people do good stuff, therefore God.

We're really scraping the bottom of the barrel here, I'm afraid. The evolution of morality has been studied in truly obscene depth (see for example Matt Ridley's book The Origin of Virtue). It turns out that, in a vast range of situations, moral behaviour follows directly from evolutionary premises.

For example, around some coral reefs there are big fish who get food stuck in their teeth. There are smaller fish who clean their teeth for them (thus getting a free meal). But what's to stop the feeder fish from eating the cleaner fish that groom them?

It turns out this does occasionally happen. But the cleaner fish have got very good at distinguishing individual feeder fish, and can recognise a back-stabber they've seen previously. So any feeder fish that goes rogue soon runs out of targets. It also doesn't get its teeth cleaned, which is not good if you've got a hot date in the evening.

It's harder to account for "heroic" (read: suicidal) morality - people throwing themselves on grenades and so on. However, I'd like to draw your attention to the principle of overcommitment. This says: I will do what I've promised to do, and I will do it in a really over-the-top fashion.

This can have useful effects. For example, if you're the kind of person who goes psycho and beats the crap out of people if they spill your beer, no-one is going to come near your glass. The "mutually-assured destruction" of nuclear war is another example. Paradoxically, by gaining a reputation as a nutter, you can

The converse is also true. By becoming the very avatar of all that is nice and friendly, you can get people to give you more slack than you'd get any other way. Think of the respect people have for those who spend their lives and money on charitable causes. It's an excellent way to get girls.

The problem with this is that you have to keep doing it. The moment you throw a comrade on the hand grenade rather than jumping on it yourself, your cover is blown (even if you aren't...).

9. prosblogion.ektopos.com is loaded with arguments

Maybe so. But at this point I'll draw your attention to a famous quote by Einstein. On being informed that the Nazis had published a booklet called "100 Scientists against Relativity", he commented "if they were right, one would have been enough".

Similarly, if God existed, one truly solid demonstration would be worth a hundred of the half-baked "proofs" I've dissected above.
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Best skeptical film ever

Watson: You know, Holmes, I've seen things in war I don't understand. In India I once met a man who predicted his own death, right down to the number and the placement of the bullets that killed him. You have to admit, Holmes, that a supernatural explanation to this case is theoretically possible.

Holmes: Oh, agreed. But... It is a huge mistake to theorise without data. Inevitably one begins to twist facts to suit theories, rather than theories to suit facts.

- Sherlock Holmes (2009)

I am convinced that the scriptwriter for this film is a guerilla skeptic. It's bloody marvellous to see someone taking the mickey out of credulity, rather than the usual attitude of "it's not mainstream therefore it must be right".

Another great moment is the hilarious gypsy fortune-teller Holmes employs to try and scare Watson off getting married ("Oh, I see patterned tablecloths... oh... and china figurines, and... ugh! Lace doilies!"). And there's more, but first I should issue a SPOILER ALERT.

As it turns out, the villain (Lord Blackwood) has built an entire evil master-plan based on convincing people he has mystical powers. The first time we see him is overseeing the sacrifice of a young woman. When confronted by Holmes and Watson, he lures Watson into charging at him with violent intent.

And if Holmes hadn't been there, Watson would have died right then, untouched by human hand... Holmes stops Watson and points out the so-thin-it's-invisible skewer of glass extending from Blackwood's fingers to just in front of Watson's nose.

Trick 2: When in prison, Blackwood appears to put a spell of some kind on a warden, leaving him struggling in agony on the floor. This is a simple one to solve: the warden was bribed. Never underestimate the profit motive.

Trick 3: Blackwood is sentenced to death and hanged. But death is only the beginning! The stone on his tomb is broken, apparently from the inside, and his grave is empty (of Blackwood, anyway).

Holmes' solution: a special waistcoat with a hook near the throat, and the collaboration of the hangman (more bribery), allow Blackwood to survive his hanging. A drug-induced coma allows him to deceive the medical examiner. The tombstone was pre-broken then stuck back together with a water-soluble glue. When it rained the night after Blackwood's hanging, the glue dissolved and the stone fell apart under its own weight, releasing Blackwood.

Trick 4: It turns out that Blackwood's intended power base is a mystical (credulous) secret society that includes several MPs, judges, etc. One of the steps he uses to convince them of his "power" is to kill the Order's leader in his bath, again untouched by human hand.

Solution: A chemical painted round the rim of the bath that reacts with water to produce a rather nasty acid. Once the police drain the bath ("out of common decency" - idiots), the chemical is effectively undetectable. OK, so that's not exactly one you could figure out at home, but it's definitely another point for skepticism's scoreboard.

Anyway, you get the idea. There are some wonderful lines in it as well. My current favourite:

Member of the Order: "We know you don't believe in magic, Mr Holmes. We don't expect you to share our faith, merely our fear."
Holmes: "Of the two, fear is the more efficacious condition."

Well said, Holmes. Well said.
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Oh the horror.

Taxpayers are funding the purchase of pornography for sperm donors, screams The Sun, with its usual tone of faux outrage (remember, this is the newspaper that invented Page 3).

According to other reports, men who come in for sperm donation are routinely provided with "porn magazines, a cup of tea and a biscuit".

But this misses the most important question...

...What kind of tea, precisely? Earl Grey is one thing, but in my opinion Assam is a perversion of all things holy.
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In the news: Qur'an burning

Burn a Koran Day will go ahead.

OK, so I don't agree with fundamentalist Christians on a lot. Here's a list of exceptions to that rule.

1) They have every right to burn the Koran without fear of physical reprisal, either from their government or from other citizens.

2) They should have that right (and I'd feel the same if they were burning a book I valued).

3) People really are more afraid of upsetting Muslims than Christians.

4) Although I'm not terribly impressed by the individuals involved here, the real assholes of the piece are the folks in predominantly Islamic countries who whip up a riot at the drop of the hat.

Regarding point #4, can Gen. Petraeus & co please note: these people cannot be placated. They cannot be bought off by our silence on religious matters. And this is because they're not really doing it for religious reasons; they're doing it because it enhances their personal power in their local community.

As long as there are people who have a personal incentive to riot, riots will continue to happen. (If no excuse comes along, they'll make stuff up.) It's simple socioeconomics.

It's like trying to talk rationally with a belligerent drunk bloke who's accusing you of spilling his drink in a pub. It doesn't matter whether you really spilled his drink. He's not there to talk rationally, he's there to thump someone. All you can do is ignore, evade, or punch back.
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Was it something I said?

Last weekend, a gay guy tried to pick me up* at a club.

This doesn't bother me; if anything it's rather flattering. It's a free country and, although I happen to be straight, I'm not freaked out by people who aren't. I just did what I always did: acted friendly but noncommittal and ignored the fact that my forearm was being gently squeezed...

(Incidentally, this is great for helping me empathise with women in the same situation. But I digress.)

What does bother me is that this happens with curious regularity. Everywhere I go - pubs, clubs, bars - inebriated gay guys try to hit on me. I seem to have far more (inadvertent) success with homosexual males than I do with heterosexual females. Am I giving out mixed signals or something? Do I register a false positive on gaydar?

Inquiring minds want to know.

---

* Not literally, I'm 6'4" and 16stone so he'd have needed to be Arnold Schwarzeneggar. Who, as far as I'm aware, is not gay.
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Religion stuff

There's a middle-aged couple who run the dry-cleaners down the road from me. In the past I've been a regular there, financial jobs like mine having a high formal-suit quotient. So I've got to know them quite well.

They're lovely people. Immigrants from Rajasthan (largest state in India), they've been over here a couple of decades now. They're really friendly and always make me feel welcome.

They're also quite religious. Once upon a time that would have been a problem for me, not because it bothered me but because it would start me ranting. I'd debated the God question online for so long that the thread of the argument had burned its way into my brain. In recent years I've been trying to train myself to resist this compulsion.

So when we started chatting about it, I did my best to shut up and listen. And what I learned was quite interesting to me. I've always been fascinated by small religions, and this couple are both passionate about one I hadn't ever heard of before, called "Santmat" (roughly: the way of the saints).

Santmat is a classic "medley" religion. Just as Sikhism originated in an attempt to meld Hinduism with Islam, Santmat claims that each of these groups has an equally valid handle on the truth. In particular, they each have genuine gurus, or saints - individuals in whom the spark of the divine burns most strongly.

In the usual three-blind-men-and-an-elephant fashion, these saints all perceive the same divinity, but interpret it to their followers in a way that is appropriate to the time and place in which they operate. Saying that one religion is truer than another is nonsensical; if each has a true saint at its heart, they are just as valid. If you don't find one religion convincing, that just means that you're not destined to become a follower of that particular guru.

For this reason, I'm not entirely sure that Santmat can be considered a religion in the normal sense. It's more a philosophy, a system for putting all the other religions in context. The part that does count as a religion is the Radha Soami Satsang Beas, which is a group formed around a particular lineage of saints.

Each of these gurus made more converts for the Radha Soami movement. The sociology of this is interesting. You must remember that in Santmat, the important thing is the saint you follow rather than the name you call your religion. So followers of each guru tend to see themselves as distinct from the other "waves".

For example, my friends from the dry-cleaners were converted by the guru Maharaj Charan Singh Ji. Although he passed away in 1990, I think they feel a stronger affinity for him and his "generation" of believers than they do for the current guru (Baba Gurinder Singh Ji, Charan Singh's successor). Certainly the religious literature they've been feeding me seems to focus on him. There's no acrimony; your choice of guru to follow is as personal as your choice of woman to fall in love with, and people aren't expected to have the same preference.

Generally a rather nice, innocent religious group, with no blots on its history. So do I find them convincing? Am I going to find a guru of my own?

Unsurprisingly, the answer is: probably not. Firstly, of course, I find their cosmology unconvincing. I don't see any particular reason to believe that we have souls, for example.

The Santmat rebuttal here is: I don't believe in souls because I listen to scientists; they do believe in souls because they listen to saints. We've just chosen different gurus.

But this misses the point. In short: how do you choose a guru?*

The Santmat approach is your basic touchy-feely "you just know he's the one" kind of thing. But this is a problem for me because, back in the material world, many people have felt like that about some very scary characters. Hitler was considered quite the role model at one point, as was Stalin (still is, in some circles).

So, in situations where we can test how good people are at picking good gurus, we find the answer is: not very.

But that's kinda nihilistic. If people are bad at choosing trustworthy gurus, how do I know my scientists can be trusted? After all, there are some scandals in the history of science too (cold fusion, Hwang Woo-suk's cloning research, I could go on all day).

The answer is nicely paradoxical. I trust the scientific community because I don't have to. They don't expect me to. When they tell me something, they also present me with the data to back it up, and the method that gave rise to that data, and I can go away and confirm it all for myself.

By and large I don't bother to check the data - it'd be very time-consuming and expensive. Fortunately, there are lots of other scientists who are generally willing to replicate experiments, especially interesting or controversial ones. Scientists keep each other honest.

I don't see any evidence that gurus have that kind of skeptical mindset. Until I do, I won't be believing in souls.

---

* I should mention that this question is explicitly raised in one of their books (ch2 of The Science of Spirituality). Sadly, I don't think they actually answer in plain language. As far as I can tell, the chapter just boils down to: you'll know him/her when you see him/her.
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What is evil?

Evil is trying to please yourself, or someone important or close to you, at the disproportionate expense of someone less important or close to you.

Discuss.
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Strategy

Jack of Kent asks "Is skepticism getting a reputation for arrogance and smugness?" I've just left a comment, which I think is worth reprinting here, with extra commentary.

I think the important thing isn't so much what you say as how you encourage third parties to spin it.

For example, IMO, the 10:23 campaign did a good job of branding itself. It came across as cheeky, cheerful disrespect (with a serious underlying message).

Sad though it may be [to accept this], gently taking the mickey out of someone is a vastly more effective strategy than engaging them in serious debate. Not because it makes the point any better, but because it is looked on more kindly by the framers in the media.

A rule-of-thumb used by many people is that, if you feel passionately about something, that is a point against your position. I can understand why they feel this way - in my experience, deeply-held beliefs are actually less likely to be right, because emotion tends to inhibit skepticism.

It's a pain in the arse for me, though, because I always aim to practice what I preach. So every debate I get into is (on some level) deeply personal. For example:

• If someone presents an argument for God that I can't refute, I'll spend one day a week in church for the rest of my life.
  
• If someone presents an argument for homeopathy that I can't refute, I'll use it as a treatment for my own conditions.
  
• If someone presents an argument against global warming that I can't refute, I'll... actually I have no idea what I'll do, but I'm sure it'll be significant.

This leads to a rather serious outlook on these matters.

As mentioned, though, I've come to the conclusion that seriousness is simply not an effective strategy if I actually want to convince people. It's a paradox: if you care, you must appear not to care.

As such, I'm going to make a change to my hierarchy of debate. Step #1 should now be split in two:

1) If someone has clearly done less reading up on the subject than me, I will try to judge whether they are willing to accept correction.

a) If so, I will gently try to explain what they've got wrong.

b) If not, I reserve the right to cheekily, cheerfully, ruthlessly take the mickey out of their dogma. Or just to ignore them completely.

Which approach I take will depend on whether there's anyone listening who might be influenced by the discussion, and how bored I am at the time.
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Yes, I play guitar

Well, "play" is kinda a strong word for something that sounds like our cat did right after he had the operation. But I muck about.

Current target of mucking about: I've been picking up a few classical pieces. Found a nice arrangement of Bach's Minuet in G, which I've memorised but am not yet up to full speed on. I learned Greensleeves a while back, which is harder on 'tar than you'd think.

I've also got a couple of less well-known ones under my belt: Sarabande from Robert de Visee's Suite in D minor, and the first piece from Giulani's Op. 71 No. 1. Both fairly easy by classical standards, but the de Visee piece in particular is lovely. The Giulani piece is a bit mechanical but a great warm-up.

I also tend to make a note of any chord sequences or arpeggios that catch my fancy. The following are a couple of my favourites.


Shamelessly ripped from the Inner Life of the Cell soundtrack:

--------------------------------
---6---6------------------------
--7---7----5---5---7---7---3---5
-7---7----7---5---8---8---5---7-
5--------7---5---8---8---5---7--
--------5---5---6-------3---5---

Variations on the chord set G, C6 (?) C, D:

3-3-0-2-  --------------2-3-  --------------3-3--
3-3-1-3-  ------3---1----3--  ------3---1----2-3-
0-0-0-2-  --0----0---0------  --0----0---0-2-----
0-2-2-0-  ---0--------0-----  ---0-2---2--0------
2-3-3-x-  ----3---3---------  -2--3---3----------
3-0-0-x-  3-----------------  3------------------

-----------0---2---  ---3---3---0---2(3)-
---3---3--1---3-3--  --3---3---1---3-3---
--0---0--0---2---2-  -0---0---0---2---2--
-0---0------0------  ------------0-------
----3---3----------  ----3---3-----------
3------------------  3-------------------

The rhythm should be more like 1--4--7-1--4--7- on the second one, and 1-34--7- on the last three. This explains why it appears not to scan properly*. The (3) is because, if you hammer down your little finger (which you'd need to get in position for the next repetition of the G chord, anyway) you can get a lovely ringing high G just on the edge of hearing.

Got a really boring scale on the bass strings? Slow it down by a factor of six and fill the gaps with arpeggio:

------------------------------------------------
---3-----3-----3-----3-----3-----3-----3-----3--
--0-0---0-0---0-0---0-0---0-0---0-0---0-0---0-0-
-0---0-0---0-0---0-0---0-0---0-0---0-0---0-0---0
------0-----2-----3-----------------------------
3-----------------------0-----2-----3-----3-----

---0-----0-----0-----0-----0-----0-----0-----0-----0--
--0-0---0-0---0-0---0-0---0-0---0-0---0-0---0-0---0-0-
-0---0-0---0-0---0-0---0-0---0-0---0-0---0-0---0-0---0
------------------------------------------------------
------------------------3-----3-----2-----0-----------
0-----0-----0-----0-----------------------------0-----etc

Next project: actually learn some !"£$%^& scales. I'm currently memorising music by throwing lots of neurons at the problem. Having some sort of framework in place would presumably make learning new stuff easier. Not to mention making improvisation easier. I suck at impro.

Also, my mum has requested that I get good at an arrangement of the Trout Quintet I came across. I hear and obey.

---

* A limerick:
There was a young bloke from Milan
Who wrote poems that never would scan
When asked why this was
He said "it's because
I just like to fit as many syllables into the last line as I possibly possibly can."

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News from the trenches

Just a quick update from yours truly. In true blogger fashion, I'll start by making excuses for why I've been so slow posting lately:

1) Exams. I did three actuarial exams this sitting, which is generally acknowledged to be borderline suicidal. I would estimate I passed two out of three, but don't ask me which two.

2) New placement. I'm working on a redress project: figuring out how much people are owed due to a company's breach of FSA rules. The subject of this one is Pensions Switching, an issue that has a good chance of becoming the Next Big Scandal. So far the Daily Mail hasn't found out about it, though.

3) Crappy connection. Grrrr.

In other news, I've started studying for actuarial subject CT8. This is a good one for me - it covers all that stochastic modelling stuff I've been babbling about. I'm already halfway through the course. If all goes to plan, I'll be able to effectively finish it before the results from the last set of exams come out on 2nd July. The fact that I'm in danger of being overtaken on exams by several of my younger friends has absolutely nothing to do with this sudden spurt of action...

I'll write more about the new placement at some point. Not so much because of the actuarial content (nothing really interesting there) but because we're having to develop a complete set of spreadsheets from scratch. I seem to have wound up handling the quality control, which sounds boring but is actually the ideal role for a skeptic. Watch this space.
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An observation

Skeptics and scientists both attempt to employ the same scientific method. The difference is that scientists focus on hypotheses that are promising, whereas skeptics focus on hypotheses that are popular.

This can have ramifications. For example, I've noticed that a lot of people with first-hand scientific experience (inc. my dad, for what it's worth) don't have a lot of respect for Karl Popper's attempts to distinguish science from non-science and identify a distinct scientific process. They tend to see science as working in a more intuitive, less formalised, fashion.

That's for two reasons. Firstly, scientists are mainly surrounded by promising hypotheses generated by other competent scientists. Skeptics aren't - we deal with the daftest ideas that human ingenuity can devise. And secondly, if a scientist comes across a non-promising and unsupported idea, they are "allowed" to discard it out of hand. Skeptics aren't, because then the cranks and quacks start whining that we're not treating them fairly.

Going the other way, I know many skeptics* are disturbed by the climate science community's complete PR failure in the case of "Climategate" and other alleged scandals. "Why did they not see this coming?" we ask ourselves. "Have they never dealt with people like this before?"

No, they haven't. They're scientists, not skeptics. They spend all their time working through complex climate models and looking at atmospheric data. They've never argued with a creationist, or tried to talk sense into a Holocaust denier. They're not equipped for this kind of debate.

Scientists and skeptics are natural complements, and there is a lot of overlap between the two groups. Skeptics have always taken scientists seriously; hopefully in the future this will go both ways.

---

* By this I do not mean climate change pseudoskeptics. I should mention that I don't have the knowledge (yet) to evaluate the claims of modern climate science, so I can't comment on whether it's correct. But what I do know is that most of the main claims made by climate change deniers are ludicrously simplistic and/or just plain wrong.
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British law: Bloody inconsistent

It's been barely a month since the brilliant response by the Court of Appeals in the BCA vs Simon Singh case. Sadly, they can't all be gems. Paul Chambers has just been convicted.

In case anyone hasn't come across this case, Mr Chambers made a comment on his Twitter feed expressing frustration at the closure of his local airport:

"Crap! Robin Hood Airport is closed. You've got a week and a bit to get your shit together, otherwise I’m blowing the airport sky high!"

Pretty normal for Twitter, you'd think, and frankly rather mild for the Internet as a whole. Sadly, the Crown Prosecution Service didn't agree. When they got wind of this comment, they decided to prosecute him for sending a message on a public network that was "grossly offensive or of an indecent, obscene or menacing character".

Quite apart from the WTF that we have such a fuzzy law on our books, there is no evidence that Mr Chambers intended to menace anyone, or that anyone in fact felt menaced. This is apparently a case of the CPS deciding that Mr Chambers must be guilty of something, and then hunting up an obscure law to fit. (We actually have a law specifically dealing with bomb threats, but that would have required the CPS to make a more solid case so they (ab)used an obscenity law instead.)

Now, as an average netizen, I'd normally respond with a comment like:

"These vindictive fascist little jobsworths will be first against the wall when the revolution comes."

But given the CPS's apparent inability to recognise hyperbolic comments, I wouldn't dream of saying any such thing.
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Status report

Just so you're not surprised by continued silence on my part... the last post was by way of a stress outlet. I'm still not done with exams, I'm just past the point where I can bring myself to revise very hard.

Exams end in 1 week. The traditional post-exams hangover will take a bit longer. It usually takes me a couple extra weeks to reacquaint myself with the concept of a social life (and in particular with those parts of my social circle that like to drink large amounts of CH3CH2OH). So expect to hear from me within the month.
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Gazing towards Olympus

I don't normally write fiction because... well... I suck. No way of sugar-coating it, my writing stinks.

That said, I would rather it didn't always stink. So in recent months, in between episodes of screaming exam panic, I've been casting around for stories to experiment with. This one popped more or less fully-formed into my head. I think it was sparked by this Penny Arcade comic about the game God Of War III.

I actually have no idea what GoW3 is about. My version is probably cooler though.

---

Now, I know what you're thinking: a bird that talks? But the plain truth is, you can't live thousands of years without picking up a few things.

I'm not actually sure how long it was. Certainly in the early days I was just an eagle like any other. Every morning I'd glide over to that mountain, just as the dawn struck it, ready for another breakfast of liver-and-onions. Without the onions, obviously. And with a lot more screaming. But it was a simple life, with a noticeable absence of clocks and calendars. Could have been millennia for all I know.

I think it was some time during the Roman occupation that he started speaking to me. Not surprising really - you chain a guy to a sodding great big rock in the boiling sun for a few hundred years, he'll wind up talking to everything from stones to flying pigs. That's dehydration for you. Eagles is small fry by comparison.

But it was nice, you know? Even when I was just another dumb beast, it was soothing. I'll let you in on a little secret: even birds of prey can get a bit squeamish at times. Cute little lambs gambolling in the green meadows, claws out, whoosh... you'd have to have a pretty stony heart not to feel slightly sorry for them. Not to feel a touch of existential angst on occasion. It was reassuring to know that at least one of my victims didn't hold it against me.

So he spoke to me, and for a century or ten that was all there was to it. There's precedent, you know: prisoners in towers befriending the sparrows, and all that. Befriending the eagle that rips out your viscera every morning is a bit of a stretch, but he always was soft-hearted. That's how he got into this mess in the first place.

And, then as now, soft-heartedness can have some... startling effects. Some time just after they started building churches, it clicked. I began to understand what these funny sounds he made were in aid of. I'm still quite proud of that accomplishment. I mean, even Champollion had the Rosetta stone to help him, you know what I mean? And already spoke a language, for that matter. I was operating from a bit more of a standing start.

Of course this didn't really mean much for fifty years or so, the eagle throat not being noticeably designed for speaking back. But I think he realised I could follow him. He started trying to turn his ramblings into a dialogue, inviting me to nod my head or shake my tail or whatever. He was more than half-mad with hunger and thirst by this point, but we eventually worked out a sort of talon-tapping routine that could get the message across.

(Incidentally this proved to be a useful investment in fine motor skill. After all, how do you think I'm writing this? My typing speed isn't great, but as long as I can get access to a keyboard... Let's just say that some web-cafes shouldn't leave their skylight unlocked, haha.)

Actually he mostly talked about you lot. Humans I mean. He really couldn't get over whether he'd done the right thing or not, giving you fire. He would often ask me to go out and report back to him on how you were doing, what works of art you were producing, what buildings you were constructing. I remember spending a week one time trying to explain the Sistine Chapel to him. I mean, come on, the Sistine Chapel? In glorified Morse code? But he got the general impression at least.

Come to think of it, that was maybe not so tactful, showing him how the world had moved on. Zeus had traded his thunderbolts in for a new throne, the rest of the Pantheon had reinvented themselves as angels and saints and the like, and yet here he was still chained to a mountain. They'd forgotten him. And all the art of mankind, that he had helped bring into being, depicted him as a serpent or monster. You lot aren't exactly much for gratitude.

And I suppose that was the next big development. I started to see his point. He really did want the best for you, you know. Most of the gods spent their time hanging round mountaintops; he was down in the valleys with you. Depressingly keen on helping people, three thousand years before Robert Baden-Powell.

He didn't deserve his punishment. I don't know if Zeus had got up on the wrong side of the cloud that day or what, but damn. Chained to a rock with yours truly performing impromptu surgery on a daily basis. That's gotta sting.

I started eating less of his liver. Some days I'd just make a scratch, give him a bit of an appendectomy scar in case anyone dropped by to check. I brought him berries, fruit, water. Took a while to work out what he was able to stomach (I swear I didn't know about the peanut allergy!) but eventually he started to get healthier. You don't exactly shake off millennia of torment overnight, but he began to seem a little more like his old self.

Sadder, of course. Maybe wiser. Certainly more angry. But hey, at least he'd stopped screaming. My eardrums were endlessly grateful.

And that brings us up to the present day. Or at least up to the day - a week ago now - when he asked me to help him. When I agreed to take the final step.

It wasn't easy. People look at you funny if you, an eagle, walk into the local library and check out a book on lock-picking. And some of the other stuff he was asking for... well, normally if someone's packing that kind of hardware, any wise bird avoids them on pain of taxidermy. But there are ways. As I said before, you don't live for thousands of years without picking up a thing or three.

So here we are. Or here I am, anyway. His chains are empty, his rock is bare. I can see the indentation he wore in it from lying there so long. And I can remember the look in his eye as his hands caressed the rifle's stock. I remember how he gazed towards Olympus.

I guess I'm still waiting for the other shoe to fall. What happens if Zeus comes looking for me, afterwards? Or... what happens if he doesn't? Either way, it's going to be one hell of a light-show.

I never told Prometheus about the Crusades, or the Holocaust, or napalm, or the bomb. I couldn't stand to see the look on his face if he'd found out what that fire he carried had been used for. If he'd known the cost of giving fire to man. Eating his liver would have been nothing by comparison.

But I think I know what he would have said. The true fire, the true spark of warmth, is the one in the mind and the heart and the eyes. The physical hearth and forge, the technology, is just a conduit for the greatness in man. I understand this because I felt it too. I felt it when my beak fumbled with the lockpicks, when I dropped the heavy gun by his side.

He gave fire to man. I gave it back.

I hope we were right.
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Fluffy nonsense

I hate Business Economics, indeed. With a passion. I hate it so much because the cello part is the worst cello part ever written in the history of

Wait, wrong rant.

I'm currently studying for actuarial exam CT7* (Business Economics). Essentially, the purpose of Business Economics is to determine when a sale will occur and at what price. I've hated this subject from the get-go, but it's taken me some time to really articulate what I dislike about it...

What is Business Economics?

To understand Business Economics, the first thing you need to know is: price is determined by the demand for a product and the supply of that product. When the demand at a given price equals the supply at that price, the market is in equilibrium and all produce will be sold. Markets tend towards equilibrium.

The supply function is determined by the seller's return on investment at various prices. A seller will pick the price that maximises their RoI. You can draw a "supply curve" showing the amount that will be produced at various prices. This will be a fairly straight upwards-sloping line.

The demand function is determined by the buyer's utility function. This is a subjective measure of how much value a buyer gets from a product, denominated in currency (e.g. £). Buyers will seek to maximise their total consumer excess: their total utility minus the products' purchase price. You can draw a "demand curve" to show how the amount bought varies at different prices, which will be a fairly straight downwards-sloping line.

To really understand Business Economics, the second thing you need to know is: all of the above is counterfactual bollocks. Markets don't really work like that under any circumstances. You can't draw demand or supply curves, and they wouldn't look like their descriptions if you could.

Theology meets practicality

These two different views of BE are both presented in the same textbook. Chapters 4-7 and 9-12 describe everything about a business in terms of demand and supply. Chapter 8, however, discusses the marketing mix.

The marketing mix is a widely-referenced checklist of things to consider when selling a product. It lists the following components of a successful sale:

1) Product
2) Price
3) Placement (e.g. location, visibility)
4) Promotion (e.g. advertising)

The traditional demand/supply model handles the first two of these fine, but is completely blind to the last two. The only way to account for e.g. the effect of advertising is to say "well, that just means that the person's utility function is higher for this product than it would otherwise have been".

But this just highlights the problem with the demand/supply model. It's not answering the question of "what determines price". It's just restating it in a more sciencey fashion. It is theology rather than science: no more meaningful than answering the question "what created everything" with "God did it".

In short, it sucks.

What went wrong?

I'm not sure why it sucks so much. My best guess is that the people who came up with this theory of economics had "engineering envy". In engineering, you start with various general principles (the laws of science) and reason your way to specific applications of those principles (bridges, buildings, microcircuits, etc).

I would conjecture that the early economists rather liked this idea, so they came up with some vague principles (the "laws" of demand and supply) and tried to reason from them to specific conclusions. But because those broad principles were not reality-based, the effect is similar to a Christian trying to reason from the existence of the Trinity to the existence of an earthquake in Haiti. It's an exercise in applied fuzziness, goalpost-moving, equivocation and redefinition of terms that would shame a Jesuit***.

This entire approach sucks.

First Principles

I'm still working on my own Grand Unified Theory of Economics, and probably will be for some time. But I already know where to start looking.

Look at the big picture again, and start to zoom in. Zoom in on a single continent (Asia). Zoom in on a single country (India). Zoom in on a single region (Uttar Pradesh). Zoom in on a town (Agra, home of the Taj Mahal). Zoom in on a little shop selling tables made of marble, and inlaid with semiprecious stones. Zoom in on the room where a tourist and a salesman are sipping tea together.

That tourist is me. That salesman, I am fairly sure, overcharged me by an order of magnitude for what was, I must admit, a rather lovely souvenir for my parents.

When an economic model can explain what happened in that room, in concepts more meaningful than the data they abstract...

When an economic model can explain what happened in that room, in a way that helps me to identify and avoid such situations in future...

When an economic model can explain what happened in that room, in enough detail that I can see how to return the "favour"...

...then I will consider it worth learning for exams.

Rant over.

----------------------------
* "CT" stands for "Core Technical". To become a fully fledged Fellow of the Institute of Actuaries** I need to have completed:

9 x Core Technical exams
3 x Core Applied exams
2 x Specialist Technical exams (from a choice of 9)
1 x Specialist Applied exam (from a choice of 6)
1 x Partridge in a Pear Tree.

** In Britain, for historical reasons, we have both an Institute of Actuaries and a Fellowship of Actuaries (collectively known as the Profession). Most Cambridge grads join the IoA. This is so that, when we've claimed our congregational MA and achieved the rank of Fellow of the IoA, we can put the letters MA FIA after our name and pretend to be Sicilian dons.

*** Yes, I know that the Jesuits were actually quite science-minded for their time. Their reputation for inflicting "sophisticated" theological arguments on the uninitiated is probably still valid.
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Contagion effects

One interesting topic of financial research in recent years has been the concept of "contagion". This is the effect whereby (for example) financial troubles at one bank can lead to a "domino effect", potentially bringing down the entire damn economy...

(This sort of thing is very important from an actuarial perspective - it goes back to my discussion of stochastic asset models. It's common to try to invest in a low-risk fund when a policyholder nears retirement; however, in a contagion-ridden market, there may be no such thing as a low-risk fund!)

I have three comments on this:

1) At the same time I was in Cambridge last week, they were holding a conference on this very subject. I've been reading through some of the papers, and they're rather cool - I might summarise some on this blog later.

2) There seems to be a strong link to principles of ecosystem collapse (see for example this excellent paper from PLoS CompBio). I'm surprised there's not more cross-research going on. (Or maybe there is and I just haven't found it?)

3) Some kind of contagion principle seems to apply to the use of the term "in respect of". You can measure how heavily-regulated someone's industry is just by seeing how often they employ this phrase. After some consideration, I have decided that it can almost always be replaced with the word "for". This, of course, is vastly shorter, thus saving wear and tear on keyboards.

OK, so that third point didn't really relate to the other two, but it's been bugging me for a while. As someone with a love of the English language and its intricacies, I really hate it when people try to fake linguistic sophistication by use of stock phrases and pompous legal jargon. It's like I'm a fan of automobile engineering and they're the blokes from "Pimp My Ride".
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Interesting turn of phrase

I'm having a lazy day.

This is probably not a good idea - actuarial exams start in under 3 weeks. However, I'm still recovering from last weekend, when I received my congregational MA at Cambridge and got absolutely wasted on College port* with some old friends. I vaguely recall dancing on tables. And I had a busy week too, so what the hey.

In particular, I'm taking the time to read up on a few blog archives, mostly related to skepticism in the UK. Of particular interest recently has been the Appeal Court decision in the trial of science writer Simon Singh. The (very senior) judges running the show apparently gave the legal version of two raised fingers to the British Chiropractic Organisation. A most welcome verdict.

(I actually walk past the BCA's head office on my way into work each day. I'm considering dropping some Sense About Science literature through their door in case they feel like signing up. Worth a try.)

One interesting thought for the day was in this pro-CAM comment on the Adventures In Nonsense blog. FYI, the blog author is the guy who sent out 500 complaints to the Advertising Standards Authority about chiropractors who claimed to treat infant colic.

The comment uses an interesting phrase: "open-minded skeptic". I am actually impressed that a pro-alternative-medicine commenter would use this phrase; many of them seem to think it's an oxymoron. But let's examine what it means to say a person is an "open-minded skeptic".

"Open-minded" = is willing to examine any new claim
"Sceptic" (with a C) = demands good evidence for any new claim before accepting it
"Skeptic" (with a K) = gets pissed off if he/she receives no good evidence and yet finds people still parroting the same sodding claim

On this basis, I would say that most of the folks on Simon Singh's side in this battle of public opinion are indeed "open-minded skeptics". I'm happy to quietly support them; I only wish I could do more.

------------------
* If you ever visit Christ's bar, do not buy the College red or white wine, it gives you a splitting hangover. The port, however, kicks ass but leaves neurons standing. There's also a cafe called Taffy's just out the College's side gate where you can buy a fry-up cure for what ails ya the following morning.
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Cheers, Mate

Thanks to this guy for cutting short my evening-long search for a way to rip CDs to MP3.

He's right, it is ridiculously hard on Linux. My understanding is that that's because That Can Get You Sued, and Canonical is probably big enough to be a tasty target for the MP3 patent holders.

Normally I would use the ogg format, but I just got a cheap mp3 player thingy and none of the cheap ones seem to handle ogg. I did check.
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How to do Stochastic Calculus

Context

I have recently had to learn a mathematical approach called "stochastic calculus" as part of my actuarial exams. As misery loves company, I've decided to share the details with you...

This post is a short tutorial in stochastic calculus, with an emphasis on getting to the point where we can solve practical problems and skipping as much foundational material as I can get away with.

What is stochastic calculus?

Stochastic calculus is a useful tool in financial maths. In normal calculus, you might take a function and find its derivatives (gradient, curvature, etc) as time changes. Or you might take a differential equation (an equation relating a function to its derivatives) and use it to figure out what the corresponding function looks like.

"Stochastic" just means probability-related. In stochastic calculus, you take a random variable and find its derivatives, or take a differential equation and find the random variable it represents.

An example. Let's say we're looking at the size (n_t) of a population of lemurs. We reckon that the rate of population change is directly proportional to the size of the population. In mathematical notation:
dn_t/dt = g.n_t
where g is a constant growth factor (or shrinkage factor if negative). If we solved this with differential calculus we'd find that:
n_t = n₀.exp(g.t)

But wait! Real populations don't work like that. They behave far more randomly, which can lead to very different results. In particular, you'll notice that, no matter how negative the growth rate is, the lemurs can never go extinct. Sadly this is not true of real animals.

How do we represent this uncertainty? One way is to add a "noise" term to the calculation. So:
dN_t/dt = g.N_t + v.W_t.N_t
where v is a constant volatility factor and W_t is a continuously-changing random variable - a "stochastic process". You'll note that we're now using N_t rather than n_t, to show that population size is probabilistic rather than predestined.

Brownian motion

Which stochastic process should we use for our noise term? This would depend very much on the situation - our team of biologists would need to research how species' populations change in practice. However, a very popular choice is based on "Brownian motion". It's typical to try to reframe any stochastic problem in terms of this process.

Brownian motion is named after the phenomenon of pollen grains bouncing around in water (they're small enough to be affected by the impact of individual water molecules). It is a "random walk" process, with several nice properties:

- it is distributed as N(0,t²) (e.g the standard deviation at time t is t^0.5)
- it has independent increments, so you can model B_2t as B_t + B'_t
- dB_t.dB_t = dt (please take it on trust that this is important, we'll see how it's relevant later)

In the case of our population equation, we might set W_t such that W_t.dt = dB_t. In other words, B_t is in some sense the integral between times 0 and t of W_t. This allows us to rephrase our equation as:
dN_t = g.N_t.dN_t + v.N_t.W_t.dt
= g.N_t.dN_t + v.N_t.dB_t

Interlude: What the hell is that?

I keep using terms like dB_t and dN_t to mean increments of random variables. Intuitively, this doesn't make a heck of a lot of sense. Random variables, even time-dependent ones, don't have fixed values - that's kinda the point - so how the blazes can they have well-defined increments?

The answer is: the increment is also a random variable, just an infinitesimally small one (in the same way that dt is an infinitesimally small deterministic variable). When we say (for example) I = ∫₀^t 1.ds, the answer is clearly: I=t. When we say I = ∫₀^t 1.dB_s, the answer is equally obvious: I = B_t, the sum of the random increments.

More complex expressions like ∫₀^t B_s.dB_s are quite hard to understand intuitively. Multiplying a random variable by an infinitesimal random variable and taking an infinite sum? Wtf? Basically, the purpose of stochastic calculus is to allow us to transform messy situations like this back into simple ones like the two in the preceding paragraph.

The Ito formula

So anyway, we now know what the stochastic differential equation looks like. How do we solve it? We use an equation called the Ito formula to figure out what it should look like, and then we forcibly bring the two forms together.

The Ito formula says that if:
dX_t = u.dt + v.dB_t
(u, v real numbers)

and:
Y_t = f(t, X_t) for some function f(t,x)

then:
dY_t = ∂f/∂t.dt + ∂f/∂x.dX_t + 1/2.∂²f/∂²x.dX_t.dX_t
using e.g. ∂f/∂x as a shorthand for ∂f/∂x(t, X_t)

Usually it makes sense to take X_t = B_t.

A simple example. Let's say we're evaluating I_t = ∫ B_t.dB_t. We can rephrase this as: dI_t = B_t.dB_t

The variable I_t will end up depending on time and on the effects of the random variable, so we can write: I_t = f(t, B_t). Therefore, by Ito's formula:
dI_t = ∂f/∂t.dt + ∂f/∂x.dB_t + 1/2.∂²f/∂²x.dB_t.dB_t
= (∂f/∂t + 1/2.∂²f/∂²x).dt + ∂f/∂x.dB_t because dB_t.dB_t = dt (see the section on Brownian motion above).

Since we know: dI_t = 0.dt + B_t.dB_t
we can say that: ∂f/∂x = x
and: ∂f/∂t = -1/2.∂²f/∂²x
From the first of these partial derivatives, we have:
f = x²/2 + g(t)
We can now rewrite the second equality as: ∂f/∂t = -1/2.1
giving: f = -t/2 + h(x)
So overall: f = x²/2 - t/2

Therefore (drumroll), we have: I_t = f(t,B_t) = B_t²/2 - t/2

That population equation

Now we've got the tools in place, let's solve that population equation. First assume that there is some function f(t,x) such that N_t = f(t,B_t)

We know that:
dN_t = g.N_t.dN_t + v.N_t.dB_t
and that:
dN_t = (∂f/∂t - 1/2.∂²f/∂²x).dt + ∂f/∂x.dB_t

Therefore:
∂f/∂x = v.f
f = exp(v.x).p(t)
(I'm using p(t) and q(x) as my dummy functions rather than g(t) and h(x), to avoid confusion between g and g(t))

And:
∂f/∂t + 1/2.∂²f/∂²x = g.f
∂f/∂t + 1/2.v².f = g.f
∂f/∂t = (g - v²/2).f
f = exp((g - v²/2).t).q(x)

So overall we can infer that:
f = C.exp(v.x + (g-v²/2).t) for constant C

In other words:
N_t = N₀.exp(v.B_t + (g-v²/2).t)

QED. This is similar, but not identical to what we'd expect from looking at the traditional differential equation.

How we can use this

Now, just having an equation is not terribly useful. But once we've got it we can start asking interesting questions such as "what is the probability that the population of lemurs will have shrunk at time t?"

P(N_t < N₀) = P(N₀.exp(v.B_t + (g-v²/2).t) < N₀)
= P(exp(v.B_t + (g-v²/2).t) < 1)
= P(v.B_t + (g-v²/2).t < 0)
= P(B_t < (v²/2-g).t/v)

Since B_t ~ N(0,t), this can be worked out using a set of tables. For example if g = 5%, v = 2%, and t = 5, then:
P(N₅ < N₀) = P(B₅ < (0.0004/2 - 0.05)*5/0.02)
= P(Z < (0.0004/2 - 0.05)*5/0.02/5^0.5)
= P(Z < (0.0004/2 - 0.05)*5/0.02/5^0.5)
= P(X < -5.5678)

Past a certain point the population of lemurs is likely to go extinct (although this is not modelled well by the equation - N_t can never reach 0). If the population was declining, and we could figure out values of g and v, we could determine the probability of extinction. We could then allocate our animal conservation money appropriately.

Applying these principles to pension fund capital is left as an exercise to the reader.

Why is that not the full story?

There are several things I've left out here, two mathematical points and two practical points.

Firstly, W_t is not a "real" distribution. If you actually try to work out what dB_t/dt looks like, you find that it is infinite at infinitely many points. That is just plain weird.

Fortunately, there is a mathematical hold-all concept - the "extended distribution" that sweeps all that under the carpet. And since it all works out OK, the specifics aren't really a concern, any more than you need to know Real Analysis to understand differential calculus.

Or are they a concern? Point #2 is that there are actually several ways to define ∫...dB_t, which give mutually exclusive results. Explaining the differences is beyond the scope of this post. Suffice to say that the one we've been using - the Ito integral - is mathematically nice.

Practically speaking, what we've looked at here is only half the battle. As responsible scientists, we'd want to produce sensible values for g and v, and in general confirm that the population is behaving as the equation predicts. This calibration is a nightmarish task that I'm not even going to begin to discuss here.

And finally there's the question of whether our general approach - all founded, you'll recall, on Brownian motion - is remotely sensible. There has been a lot of muttering recently pointing out that extreme events are far more likely than the normal distribution would suggest. It is very hard to produce Brownian processes that can emulate this behaviour, and nigh-on impossible to calibrate. There is a strong suggestion that a broader family called Levy processes might be more plausible, but they are also a bugger to calibrate.

This sort of thing won't be solved any time soon.

References

I learned SC from the textbook by Bernt Oksendal (5th edition). In retrospect this was probably a mistake, as he goes very deeply into the mathematical fundamentals before covering anything remotely practical. If you can get past the first 3 chapters without falling asleep then it's not a bad book, although not terribly readable (even by maths book standards...).
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Sucks to be us

I get a lot of emails from the Institute of Actuaries, the professional organisation of which I am a (student) member. One running theme is a rather plaintive request for people to view actuaries as more trustworthy. They write endless editorials on actuarial ethics, they arrange super-special "professionalism" training, they commit us all to worryingly restrictive codes of conduct... the list is endless.

I've always been a bit surprised by this. I don't have a pension, I don't have life insurance, I don't have a car to insure, so pretty much my first contact with the actuarial profession was when I signed up to become one. I've been wondering for some time now what the fuss is all about...

Well, it turns out that they're not wrong to fuss. I just came across the following passage in a book on scams that I'm reading:

Hundreds of thousands, if not millions, have been disappointed and forced to complain about 'with-profits' bonds, endowments and pension plans. And these all come from highly respected - and really big - life insurance companies.

How do these complicated schemes work? Well, no one really knows, often not even the people who should know. It's all down to the 'experts' at the insurance companies which run these schemes. Using obscure mathematics coupled with a finger held up to the wind, they make up the numbers year on year.

Wait a minute. That's us he's talking about. This sucks.

Do actuaries deserve this slagging-off? Well, partly yes, partly no. (Equivocation never harmed anyone...)

Where's the money?

Let's take an example: that with-profits thing he mentioned. With-profits is superficially rather a clever idea. Let's say you're putting money into a pensions fund for your retirement. There are two main kinds of investment fund: fixed interest and unit-linked.

With a fixed interest fund you are guaranteed (say) a 3% per year rate of return. In a way this certainty is good - that money is as good as in the bank. But in a way it's bad, because you are going to get a very crappy rate of return. This is because, if the market crashes, that 2% is going to start looking like quite a large number. No fund provider wants to be caught out that way, so they will all low-ball their figures to compensate.

With a unit-linked fund, a certain amount of money is put into a pot for you. That money is used to buy shares in various companies, in the hope that their share price will go up. Usually you'll just specify some broad criteria ("I want all my money in Asian shares") and a fund manager will sort out the investment specifics. This approach generally gives a much higher rate of return - e.g. you might get 10% instead of 3%. But it is inherently risky - you might also get -50%.

As pensions actuaries, we want to get the best of both worlds. How can we do this? There are three main approaches (that I'm aware of):

1) Shuffle money from unitised to fixed-interest funds as the member approaches retirement (I mentioned this last time as a good use of SAMs)
2) Invest in an index-linked fund (see footnote*)
3) Invest in a with-profits fund

Technical interlude

A with-profits fund is where you take a fixed interest fund and strap a unitised fund to the roof. The fund provider will keep a pot of money, which it will invest in various companies etc. They will guarantee you a relatively low rate of return (3%, say) on your contribution to this pot.

Then, at the end of every year, they will take a look at how their investments have done. If the investments are doing much better than the guaranteed rate (10%, say), they will tell you "we declare a bonus of (say) 5%". The value of your investment will thus increase by 8%, with the remaining 2% being kept in the pot for a rainy day**.

The point is that, under the with-profits model, the fund provider doesn't need to plan ahead so carefully - if they overdo the bonuses this year, they can just make it up by under-doing it in future years. With-profits funds allow the provider to wing it. They don't have to be as cautious as they are with fixed-interest funds. And that reduced risk translates directly into better rates of return.

What are the characteristics of a with-profit fund? In any given year, there's a limit to how badly they can do (handy if a recession strikes just before you're due to retire). However, in the long term, they won't do as well as unit-linked funds (because they have that extra protection, which must be paid for). They're generally quite a good solution, and fill a very useful niche.

With-profiteering

Now, being smart people, you've probably noticed a gap in the above explanation: how precisely is the bonus calculated? That's an excellent question.

And the answer is very fuzzy. The provider's actuaries will look at the state of the market, look at the state of the fund, and make an educated guess as to what bonus they can afford. There is no hard-and-fast method, and no requirement to document their method. From the point of view of the paying public, the actuaries all go into a dark room and come out a week later saying "right, you're getting 8%". In the words of my generation: What The F***?

Now there are actually good reasons for some of this reticence. An example: many of these calculations use stochastic asset models (see last post) that are just too damn complicated to explain to the general public. Due to the huge pile of regulation hanging anvil-like over our heads, it can often be legally safer to shut up than explain what you're doing. Especially if there's any chance of being creatively misunderstood***.

Regardless of this, the opacity of the system - the secrecy, the lack of information, the argument from authority - definitely promotes suspicion. It's a fricken' invitation to conspiracy theory. I personally would be surprised if the bonus system had ever been abused too badly, just because there are so many people breathing down the average actuary's neck. But you can see how people could come to that conclusion, and there's no way to refute them. Skepticism FAIL.

What can the Institute of Actuaries do about this? Bugger-all, sadly. They don't have the power to compel all these companies to open up, which is really the only way to fix the situation. Hence the rather frantic "oh we're so professional and ethical" song and dance - it's the only thing the poor sods can do to stop their collective street-cred going down the pipe.

Who does have that power? The UK government (in the UK, anyway) and its regulator the Financial Services Authority. Will they act? On existing funds this is very unlikely - it would be too much of a can of worms to open. However, the general trend is towards greater transparency with financial information****. Maybe one day we'll get this mess sorted out.

And the profession will breathe a sigh of relief.

Disclaimer: I am not a subject matter expert, please take all the above with a pinch of salt.

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* An index-linked fund guarantees you (say) 1% plus your central bank's base interest rate per year. This removes some of the risk that the buying power of your money will fall (e.g. due to hyperinflation). So although the amount of money you'll get when you retire is uncertain, the number of mars bars you'll be able to buy with it is closer to being fixed.

In terms of returns, index-linked funds are less good than unitised funds, but not nearly as bad as traditional fixed-interest funds. In terms of risks, the order is reversed (as you'd expect).

** There are some complexities (e.g. various bonus types, market value reductions, etc) - this is just an overview not a technical manual.

*** In the UK, the life office Equitable Life went bankrupt at least partly because A) people managed to creatively misunderstand their pensions' guarantee structure, and B) a court decided to hold them to the most expensive interpretation.

**** For example, under the new Solvency II requirements (basically saying how much money an insurer needs to put by in case everything goes wrong at once), the rather complicated models used by each company to calculate their funding requirements must be disclosed. I consider this a very positive step, not least because I want to play around with the models (and possibly blog about them!).

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Actuarial theology? Wait a second...

It's funny how different subjects can overlap. This point was forcibly brought home to me by a paper I was reading which compares different "stochastic asset models" (SAMs).

Would you expect a topic like this to tie directly into the philosophy of religion? I didn't. But guess what I found...

Meet SAM

SAMs are bits of mathematics and/or computer code that are used to predict roughly what possible values an asset could hold in future. Actuaries use these to guesstimate how much money you need to put into a pension scheme to get a given payout, and how that money should be invested in the meantime.

As a very simple example, we generally stick money in high-interest (high-risk) assets to start with, and then move it into low-risk (low-interest) assets later on. That's because, as someone approaches retirement, there's less time to recover from disasters - if the market crashes two days before they hit 65, we want to ensure that the piggy-bank is still reasonably full.

Normally the asset ratio is taken to be a simple linear function of time. So for someone retiring at 65, you might say: put min(1,(65-age)/10)*100% of their money into a high-risk fund (e.g. Asian shares) and max(0,(age-55)/10)*100% into a low-risk fund (e.g. government bonds). This is a nice simple linear relationship.

However, it is also a very rough rule of thumb pulled straight out of our actuarial buttocks. The problem is, we don't know how the assets are likely to behave over time, so we can't come up with a more realistic strategy. SAMs are intended to fill that hole.

A SAM will normally be a set of difference equations (or differential equations) with a bit of randomness ("innovations") thrown in for good measure. The equations are intended to codify the relevant bits of economic theory - for example we expect that retail prices will be affected by inflation. The model is then initialised with numbers estimated from the last few years' worth of real-world economic data.

Whoops

The problem* is, these models can sometimes have "interesting" side-effects. For example, the paper I'm reading refers to a type of model which it calls a "random walk variant with alpha-stable innovations". I think I know what that means, but anyway the interesting bit is the following quote:

"The alpha-stable distribution [...] is in some ways the most intellectually satisfying possibility. [...However, they are] not satisfactory for the pricing of derivatives because the prices of simple options are theoretically infinite [...]"

Yeah, that'd be a problem.

An option is a simple kind of contract - basically a form of insurance. If I run a sawmill, I want to ensure that I can get some logs cheaply no matter what. One approach would be to arrange a "future" contract - a contract which sets a price and time at which I can and must buy the wood.

However, this isn't perfect: what if the price of wood drops massively? In that case I'll be paying good money for something I could buy cheaper elsewhere. Instead of a future, I could arrange an "option" contract, which sets a price and a time at which I can - but don't have to - buy the wood**. This gets me the best of both worlds - no risk of excessive gain or loss. I'll normally have to pay a bit of a premium for the privilege, of course.

These options are vital tools of business, and to be told that they should be infinitely expensive is disturbing. How can that be the case?

Wtf?

As far as I can tell, the logic seems to be: extreme market events are more likely than you'd think. Let's consider a simple case, an option to buy a tonne of wood for £100. We need to work out how much loss the option seller expects to suffer. This will depend on the probability distribution of the lumber's cost C at the option's expiration date.

If we knew for sure that the cost would be £150, we could say P(C=150) = 1. The option seller would then have to buy wood at £150, and sell it to me for only £100. Her loss would be £50, so she'd presumably charge me at least £50 for this (rather useless) option***.

If we guessed that the option price would either go up or down by £30, and that the odds were the same, we could say P(C=50) = P(C=150) = 0.5. If the price went down, I'd be daft to exercise the option, so the seller's expected loss is 0. If the price went up (as it would 50% of the time), the seller would lose $50 as before. £50 × 50% = £25, so the option would probably cost a bit more than £25.

Let's consider a more complicated case:
P(C<=100) = 1/2
P(C=200) = 1/4
P(C=300) = 1/8
P(C=500) = 1/16
P(C=900) = 1/32
...
P(C = 100*(1+2^n)) = 1/4 × 1/2^n for n between 0 and infinity

It's easy to prove that 1/2 + 1/4 + 1/8 + 1/16 + ... = 1, so this is a valid probability distribution.

In this case, what is the option seller's expected loss? It will be:
0×P(C<=100) + (200-100)×P(C=200) + (300-100)×P(C=300) + (500-100)×P(C=500) + ...

This can be rewritten as:
Sum[n = 0 to infinity] { 100 × 2^n × 1/4 × 1/2^n }
= 25 * Sum[n = 0 to inf] { 1 }

But if you add ones together an infinite number of times, you get infinity! This is what's known as a "fat-tail" effect - the "tail" of the distribution is so long and wide that it completely overwhelms the rest of the calculation.

Wager 2.0

From a practical economic perspective, this is a disaster for the model. It's implausible that the value of anything can be infinite - there isn't that much money on the planet.

But I'd like to draw your attention to something. Here we have a model - a belief system of sorts - which, if true, can grant us amazing rewards. All we need to do is act on this belief (e.g. buy an option) and our expected gain goes up to infinity.

Does that remind you of anything?

Pascal's wager is one of the oldest arguments for God. It states that, if you believe in God, you could get to go to Heaven - an infinitely valuable reward - and at worst you'll lose a finite amount of time spent praying etc. If you don't believe, you definitely won't go to Heaven. The "fat tail" of Heaven's infinite goodness is supposed to overwhelm the mere finite rewards you can get from living a happy Godless life.

By the same logic, the infinite return we can expect from buying an option under the alpha-stable model should overwhelm our mere finite uncertainty about whether the model is actually valid. There is no way we can be infinitely sure that the alpha-stable model is wrong - statistics just doesn't work like that. So (in theory) the logic will always hold.

I've given some thought to Pascal's wager, and I think I've found a fair number of holes in it. I haven't thought much about option pricing yet; the same holes may be present there. But in the meantime, a single thought is buzzing round and round in my head:

Should I buy an option?

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* OK, so there are all sorts of other problems. But I'll save them for another post.

** Actually this is only one type of option (a European call, to be precise). For more information, see the Wikipedia page.

*** I'm ignoring interest here as it's not really relevant to the point.
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What actuarial is really about

See here. Also here, only less so.

Enjoy.
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Hierarchies of debate

I've just read an interesting post by a guy called Daniel Loxton on James Randi's accidental endorsement of pseudoscience.

I agree with Loxton that only informed debate is useful in scientific matters. But I think his hierarchy of debate as written is a bit too close to an argument from authority. I'd phrase it slightly differently...

1) If someone has clearly done less reading up on the subject than me (e.g. someone saying that evolution cannot add new information, which I know from studying information theory is complete mince), I will vocally disagree with them.

2) If someone has clearly done more reading than me (e.g. they're a Professor of Atmospheric Dynamics at a reputable uni), I will quietly challenge them in the hope that they'll help me improve my understanding. If they appear unable to do so then I'll jump to step #4.

3) If someone appears to have roughly the same level of knowledge as me, I'll aim to trade information with them via debate until we can reach a consensus.

4) If I can't judge whether someone is more or less competent than me, I'll go away and read basic science textbooks until I can judge. (Or I'll shut up. But I don't like shutting up.)

I'm currently at step #4 with my dad on climate change. He's normally more scientifically literate than me, but he's also an AGW skeptic, which seems to go against the consensus. I think it's likely he's just been getting information from dodgy third-hand sources, but I've been getting my information at third hand as well so I can't really protest about that. Yet. I'm working my way through the IPCC report as we speak, and looking up references where possible.

I'm at step #2 with my actuarial science course notes. I have a suspicion that basically the entire financial economics community is taking an approach of "these are the kind of mathematical models we know how to use, therefore we'll assume finance really behaves like that". But I need to do a lot more background reading and questioning, in a state of humility, before I can say for sure.

I consider myself to be at step #1 with the "does God exist" debate, but only because the majority of theists seem to be stuck at step #4 (without the shutting up part). There are some with better knowledge than me, but they tend to be like Henry Neufeld, who freely admits that he believes in God on essentially non-rational grounds.

What hierarchies do you guys use?
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