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.
Read the full post
Showing posts with label religion. Show all posts
Showing posts with label religion. Show all posts
Wednesday, August 25, 2010
Monday, January 25, 2010
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:
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?
* 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.
Read the full post
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?
* 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.
Read the full post
Friday, July 10, 2009
Rituals of my people
Last Sunday I went to the christening of my cousin's second son. It was a full church service, and was rather well attended by various family members and friends of the proud parents. The kid is very sweet. All told, a nice day out.
So what's bugging me?
Well, like I say, this was a proper church service. It's actually quite a while since I've been to a church except as a tourist, so this took some getting used to. And, after spending years discussing religion in blogs and forums, I found myself with a very strong urge to hit the "reply" button...
I was amused by the Bible reading that included Matthew 13:47-49a and carefully airbrushed out the less family-friendly Matt 13:49b-50. I was mildly irritated by the liturgical question-and-answer format - what if you don't agree with the prescribed answer*?
And I was actually rather bothered by the content of the liturgy. There are several parts that to a non-Christian like myself are a bit disturbing. For example:
I'm sorry, but this child is not old enough to be considered one of "our number". He's part of your community, sure, but at his age you can't meaningfully say he subscribes to your beliefs. Beliefs come later. And he might not share your views even when he grows up. Talk about counting your chickens before they hatch...
The entire liturgy is founded on the assumption that, if you're born into a particular family or community, you're going to grow up as a Christian. I reject that assumption. The kid will follow his own path and, as a responsible relative, I'll support him whatever that path might be.
If he becomes an atheist then that's cool. If he becomes a Christian then fair enough. If he becomes a Muslim, Hindu, Buddhist or goat-sacrificing Satanist then I'll still be on his side. Any other attitude is reprehensible.
If atheism's popularity increases, I foresee a day when we'll start to develop rituals and liturgies of our own. When that day comes, there will be a lot we can learn from the Christian versions.
In the case of child baptisms, I hope we learn what not to say...
* I handled this situation by just not saying anything while everyone around me muttered their responses. Who says I'm not tactful? Incidentally, I'm pretty sure I saw some other folks doing the same thing.
Read the full post
So what's bugging me?
Well, like I say, this was a proper church service. It's actually quite a while since I've been to a church except as a tourist, so this took some getting used to. And, after spending years discussing religion in blogs and forums, I found myself with a very strong urge to hit the "reply" button...
I was amused by the Bible reading that included Matthew 13:47-49a and carefully airbrushed out the less family-friendly Matt 13:49b-50. I was mildly irritated by the liturgical question-and-answer format - what if you don't agree with the prescribed answer*?
And I was actually rather bothered by the content of the liturgy. There are several parts that to a non-Christian like myself are a bit disturbing. For example:
Faith is the gift of God to his people.
In baptism the Lord is adding to our number those whom he is calling.
People of God, will you welcome these children and uphold them in their new life in Christ?
All: With the help of God we will.
I'm sorry, but this child is not old enough to be considered one of "our number". He's part of your community, sure, but at his age you can't meaningfully say he subscribes to your beliefs. Beliefs come later. And he might not share your views even when he grows up. Talk about counting your chickens before they hatch...
The entire liturgy is founded on the assumption that, if you're born into a particular family or community, you're going to grow up as a Christian. I reject that assumption. The kid will follow his own path and, as a responsible relative, I'll support him whatever that path might be.
If he becomes an atheist then that's cool. If he becomes a Christian then fair enough. If he becomes a Muslim, Hindu, Buddhist or goat-sacrificing Satanist then I'll still be on his side. Any other attitude is reprehensible.
If atheism's popularity increases, I foresee a day when we'll start to develop rituals and liturgies of our own. When that day comes, there will be a lot we can learn from the Christian versions.
In the case of child baptisms, I hope we learn what not to say...
* I handled this situation by just not saying anything while everyone around me muttered their responses. Who says I'm not tactful? Incidentally, I'm pretty sure I saw some other folks doing the same thing.
Read the full post
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