Asymmetrical Information

Some infinities are larger than others; n as n runs to infinity is smaller than n^2 as n runs to infinity.

Favorite bumpersticker: "In the case of Rapture, this car will be unoccupied."

Favorite rejoinder bumpersticker: "In the case of Rapture, I'm going to get a sweet new car."

That wacky God and his millions of simultaneous lethal traffic accidents!

Is this on-topic? I don't know, I couldn't understand word one of those two linked posts.

There are also (usually) theological reasons for avoiding death. These generally fall under the headings of "you're part of God's plan," and "your life isn't yours, it's God's." Many religions have prohibitions against suicide (at some point I'd imagine negligence becomes tantamount to suicide in the adjudication of mortal sin—for Catholics, sin is largely about intent.) There's also the fact that you don't have a 100% guarantee of going to heaven, you very well might go to hell; it'd be a gamble. And, yes, most Catholics have thought through (usually around 3rd or 4th grade) the plan wherein you go to confession, receive absolution, and—while still in a state of Grace—act reckless in the hopes of getting into a deadly accident. I'm pretty sure that, at best, that plan gets you a long time in Purgatory. Speaking of Purgatory, a longer time in this world gives you more time to obtain forgiveness for sin, indulgences, &c. to reduce Purgatory time and the chances of being thrown into the Pit of Fire.

All of this is to say that there are reasons economic and theological for concluding that God-believers should not necessarily have a higher accident rate (at least, they shouldn't have one as a direct consequence of believing that there may be a Place Prepared for Them.)

As a Catholic, and an amateur Thomistic [St. Thomas Aquinas]/Aristotelian philosopher, I would like to weigh in as being solidly ANTI-dying in traffic accidents.

Every thing has its nature, and the nature of the human being is to grow from conception to maturity in accord with the faculties that are uniquely human.

Therefore, willing oneself to die is immoral because it is against the natural law.

But it is in the nature of human life that it comes to an end. Therefore there is no objection to accepting death when it comes.

Treating infinity as a number is erroneous. In analysis we consider the convergence of infinite series and such, but adding to infinite quantities in the previous manner is a bit icky. As a previous commentor noted, not all infinite sets are equal, but the rest of his comment is useless at best. If we consider a set with cardinality aleph-0--that is a set with a one-to-one correspondence with the members of the set of integers we can show that given any finite set B, that aleph-0 + N = aleph-0. But there are noncountable infinite sets with higher ordinals.

I believe that they should pay higher rates, because belief in God leads to moral hazard. There are people who seriously believe that faith and prayer are substitutes for being careful. I can remember one woman who left work at a job near mine a few years ago who blindly cut me off at least once a week. On her bumper was a sticker saying "God is my Co-pilot". It would have been better is she switched seats and let him drive.

As a matter of actuarial science, the statistical observation is that adherents of at least one Christian community, Lutheranism, are less accident prone and live longer than non-members of the community—enough so that we have an entire insurance company, formerly "Aid Association for Lutherans" and now "Thrivent Financial for Lutherans"—whose existence and premiums reflect those actuarial results.

Do people who believe in God cost our healthcare system less? After all, if I look forward to eternity with God, I might be more willing to accept a diagnosis of cancer or other terminal diseases without winding up the healthcare Energizer bunny to get maximum results (i.e. extend life as long as possible, with increaseing attendant costs.)

Does being baptized a Lutheran count or do I have to have been confirmed?

SomeCallMeTim is wrong on the math. There are larger and smaller infinite sets, but the series n^2 has the same convergence as n. The set of all rational numbers is the same size as the set of all positive integers, and the proof of this is almost simple enough to give in a blog comment box; the set of all real numners (rational and irrational) is larger than the set of "natural numbers" or rational numbers; the proof of this I don't quite understand. But n^2 is definitely in the rational-numbers infinity.

The phrase should have been "To spend the rest of eternity with their Maker." Since you were born you can't spend infinity with the Heavenly Father, you have to spend the rest eternity with the Maker so dying earlier means you do get more time in the presence.

"Speaking of Purgatory, a longer time in this world gives you more time to obtain forgiveness for sin, indulgences, &c. to reduce Purgatory time and the chances of being thrown into the Pit of Fire."

On the other hand, Phillip, a longer time in this world gives you more time to do things which require forgiveness. It's probably largely a wash.

As far as engaging in risky behavior, there isn't much of that that doesn't also put other people in harm's way, physically, financially or emotionally. Driving like an idiot endangers your passengers and people not in your car. Playing alone with rattlesnakes and grizzly bears will not kill anyone else, but you can leave your children orphaned and cause your mother tremendous suffering. Christians aren't supposed to do those things either, but are supposed to be loving and considerate of others.

"I say no, since there is no additional payoff to dying quickly!"

I dunno, sorta depends on the discount rate.

"SomeCallMeTim is wrong on the math. There are larger and smaller infinite sets, but the series n^2 has the same convergence as n."

Mea culpa. It's been a long while since I've done any math, and I'm unwilling (and perhaps unable) to go re-read the calc book. But I certainly find this pt. (as well as A.N. Randy's pt.) credible and compelling. (Am still unclear on Anthony's proof, I admit). Self-correcting comment sections; is there no end to the wonders of the blogosphere?

Time-Value-of-Utility.

For one who pretends to rationality, you certainly whiffed on this one. What's the present value of a perpituity?

"For one who pretends to rationality, you certainly whiffed on this one. What's the present value of a perpituity?"

Time for the lawyer to weigh in...

Relevance, your honor?? I respectfully remind the court that there is a rule against perpetuities.

Your witness.

Doesn't Christian theology hold that God exists outside of time anyway, in a kind of "eternal now"? Thus, whether one's life is short or long doesn't matter, because eternity encompasses temporal existence. From God's perspective (and accordingly, one assumes, from the perspective of a soul living with God) my death (hopefully) several decades from now occurs contemporaneously (if that word even applies outside of a temporal context) with that of a man who died today.

Re: Lutheran baptism vs. confirmation, I think it's worse than that: I think your name has to show up on current membership rolls. We Lutherans, being largely Germanic, are kinda scrupulous about keeping those kinds of records. But this could be wholly wrong: for all I know, Thrivent will cover non-Lutherans, but because their marketing is focused almost exclusively on Lutherans in the pews, the statistics still work out. Hmmm. I should investigate further.

Just to interject a Protestant view. We Protestants believe that Catholics are Christians like us. Thus, we essentially believe that we are here to be part of God's plan. And, I look forward to eternity.

Where we disagree, is in the matter of grace bestowed upon us by Christ's substitutionary death for our sins past, present, and future upon repentance and acceptance of him in our life. There is no fear of Hell or the unscriptural Purgatory for the once and always "saved" believer. I can't imagine what a miserable life, it would be if I was always afraid of messing up and going to Hell.

It seems very dangerous for a non-believer to opine on what motivates believers. "You believe in life after death, so you must not value life very much..." No. We consider life to be a gift from God. As such, life is sacred and we are obligated to protect and cherish it.

"You believe before the 2nd Coming of Christ the environment will be wrecked, so you must believe it's not important to protect the environment..." No. We believe we inherit the commandment God gave Adam and Eve to dress and take care of the "garden" He had prepared for them. Thus, we believe we have a duty to take care of the environment.

Etc.

Anthony & SomeCallMeTim,

Oh, but Cantor's proof is truly brilliant! And simple. Here's how I had it expained to me:

To compare the sizes of two collections, you do what some who wanted to know whether she had more apples or oranges would do if she couldn't count: pair an apple with an orange, another apple with another orange, and so on until either they were all paired up, there were leftover apples, or there were leftover oranges. So, for example, in SCMT's example of N and N^2, it's clear that the sets are the same size: pair 1 with 1, 2 with 4, 3 with 9 . . . every number has its square and every square has its root, so the sets are the same size.

But consider a slice of the real number continuum — take, for convenience, all the real numbers between 0 and 1. Now each of them can be represented as a decimal point followed by an infinite number of digits, right? Some will terminate (meaning that after some point all the following digits are 0); some will be infinite and recurring; the (literally) infinite fraction will be infinite and non-recurring, which is to say apparently random.

Now, suppose you think you have figured out a way to pair each of them with the set of positive integers, the way I paired the positive integers and their squares. It doesn't matter what the method is, only that it generates, in effect, an infinite numbered list, with a first number and a second number and a 798th number and a millionth number and so on. Here's how you generate a number that can't be on even this infinite list:

Write down a decimal point. Then for the first digit of the new number, put down the first digit of the first number on the list, minus 1. (If the first digit is zero, use 9.) For the second digit, put down the second digit of the second number on the list, minus 1. For the third digit . . . for the 798th digit . . . for the millionth digit . . .

You see? The resulting number is not on the list anywhere. If it were, it would correspond to an integer, say 2,388,568,305. But it can't be 2,388,568,305, because its 2,388,568,305th digit is different.

So the number of integers is a smaller infinity than the number of real numbers — aleph-0 and aleph-1 respectively. Aleph-2 I seem to recall is the number of all possible curves, but I never learned how that was proven.

Gaaah. Preview Is Your Friend. Sorry. "Explained," not "expained" (Jeez), and "someone," not "some" in the first sentence of the second graf.

Sir Hosis of the Liver wrote:

"I can remember one woman who left work at a job near mine a few years ago who blindly cut me off at least once a week. On her bumper was a sticker saying "God is my Co-pilot". It would have been better is she switched seats and let him drive."

Or let him ride with you, where he'd be safe(r).

The late great Brother Dave Gardner had a joke about that, the preacher in the Rambler.

Michelle, that's a very nice summary of Cantor's diagonalization proof. By the way, since we seem to be on the subject of the infinite and the divine, it's worth noting that Cantor named his orders of infinity after the first letter of the Hebrew alephbet, i.e. "aleph," precisely because of an interest in the Kabbalah. See The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity, an excellent bio of Cantor.

Paul Snively, thanks, both for the book recommendation and for the compliment. I love simple, elegant proofs like that (the one demonstrating the irrationality of the square root of 2 and the one proving there's no largest prime are favorites).

I realized after reading over my comment that I'd used capital N's rather than lower-case, and that was a shock: have I really been away from math so long that I don't instinctively use lower-case? (Short answer: yep. Longer answer: but in another blog comment only a day or two ago I used x and y automatically. Go figure.)

A truly fervid Christian would endeavor to follow the Lord's example by preaching the Gospel in a hostile environment, thereby attaining martyrdom and the Kingdom of Heaven in short order.
Many early Christians did so.
We lesser, tepid, modern Christians who might be tempted to tempt fate by careless motoring should remember this.

Gah, so many heathens!

ProudDuck is correct regarding God's existence outside of time as an element of *Catholic* theology. My dead grandfather and I are already reunited in God's presence, though I have yet to finish my time here and shuck off this mortal coil.

Furthermore, as David pointed out, life is a gift from Big G, and squandering it is contrary to our duty to live our lives in a state of Grace, and reckless living ain't attaining a state of Grace. While accidents happen, we are required to "endure to the end", so no suicide, no giving up in the face of terminal illness, no euthanasia, no self absorbed, reckless driving, etc.

And Philip was also correct in his hints about the nature of sin in that it is *largely* about intent. So, when I inevitably and absent mindedly eat a hamburger this Friday even though it is Lent, it is not (necessarily) a sin. If, however, I wake up with a hearty "Screw you, Lord" and plow through a bacon and sausage laden breakfast, I am commiting a sin in His eyes.

I'm wandering now. Post over.

Thrivent requires an individual member to be at least 16 and either a current or former member of a Lutheran congregation.

Michell: It's OK; I didn't automagically find myself thinking "Why is she referring to the set of natural numbers there?" :-)

Lurkin: that's more in line with what I thought; thanks for doing my homework for me!

One of your commenters already touched on this, but I think one should not confuse the idea of eternity with the idea of an endless succession of moments. I think in the religious sense one is talking about eternity as timelessness (the "eternal now", as The Proud Duck put it).
And to throw in one of Einstein's thought experiments - that is what a photon would experience, if it were sentient, is it not? No passing of time?

I should point out that empirically, religious people suffer fewer accidents, are more likely to survive accidents that do occur, experience better health and live generally live longer. It doesn't appear to matter exactly what the religion is, just that it emphasizes moderation, family and personal honesty. The practical effects of such behaviors are enormous

Religions that forbid intoxication, for example, would instantly grant protection from accidents and illness that result from intoxicants. Since intoxicants play a role in somewhere between 1/3 to 1/2 of all accidents, the benefits of avoiding intoxication are immediate and significant.

Jim Glass is absolutely correct. The biggest problem with Jane's analysis is that it doesn't consider discount rate. Getting to heaven quicker is more valuable than getting there later even if getting there quicker doesn't imply staying there longer.

I think Jane is wrong for another reason. If a person believes that he is already in God's good graces and bound for paradise, he might want to die sooner to avoid the possibility of committing a mortal sin. I'm reminded of the Seinfeld episode where George is up for a promotion at the Yankees and he decides to take a vacation. When Jerry questions that decision, George says "Being there can only hurt my chances." Likewise, if a person is already going to paradise, living longer can only hurt their chances.

Xavier -

I'd think that someone in their late 20s might believe that they are likely to lead a less-sinful life in the future than they had in the past, and, if Catholic, that living long will allow them plenty of time to properly atone for their more youthful sins.

Regarding discount rates, a perpetual stream of income does have a net present value so long as the discount rate is positive. In particular, for a continuous, semi-infinite flow of benefit of amount 'p' in time 't', with a discount rate of 'i' over a period of 't', the net present value P = p/i. In the theological case, this may not be terribly meaningful, as 'p' is likely to be presumed to be infinite, as well.

What, dear Christians, does one do in eternity with God? Does one have a job, attend concerts,
play soccer, travel to exotic parts of the Kingdom? Are there literally "many mansions" and
do they each have a pool? Kidding aside, what do you image existence in Heaven is like?

Paul the Apostle addressed this one when writing to the Christians at Philippi. Quoting from Chapter 1 of Philippians (quoting from the ASV translation):

(20) "according to my earnest expectation and hope, that in nothing shall I be put to shame, but that with all boldness, as always, so now also Christ shall be magnified in my body, whether by life, or by death.
(21) ¶ "For to me to live is Christ, and to die is gain. (22) But if to live in the flesh, —-if this shall bring fruit from my work, then what I shall choose I know not. (23) But I am in a strait betwixt the two, having the desire to depart and be with Christ; for it is very far better: (24) yet to abide in the flesh is more needful for your sake."

He sets up a key principle there: Whether in life or death, Christ is to be glorified; so on what basis can he choose? If he goes to be with the Lord, that is far better; but if he remains here, it is because the Lord has service for him to perform unto his fellow Christians.

The wildcard is that not everyone who claims to be a Christian believes the Bible (oddly). So some, for example, might believe they can get into heaven by works (contra Isaiah 64:6), in which case a long life of good works would be desired; but then others believe they can get kicked out on account of works (contra Ephesians 2:8-9 and Titus 3:5), in which case a quick death immediately after salvation might be preferred.

You can probably make extrapolations like this for any other religion, too. Muslims believe in God, for example; and as we have seen, Muslims can range from reasonable people who want to live a normal life all the way to fanatics who willfully end their own life, and preferably those of many others, through combustive vaporization.

So I think the question, as framed, is fundamentally bogus. "Belief in God" so broadly defined is generally no more, and no less, likely to predict responsibility of behavior. If you narrow the focus sharply, then you might find significant trends.

Kidding aside, what do you image existence in Heaven is like?

How about eternity with Jesus Christ, source of all blessing and good, and all other believers across the history of mankind; gathered in a location where time does not exist, love permeates everything, there is true joy and true peace, and true beauty; there is no night, no tears, no death, no sickness, and nothing at all that defiles? (Read Revelation 21 and 22 if you wish, although be advised that like most biblical prophecies, it makes heavy use of symbolic imagery.)

I remember a homily from my childhood (one of the VERY few I remember from the days when I actively tried not to listen). The priest described both heaven and hell, and while his descriptions were not perhaps what Creech is after, they've stayed with me for going on thirty years now:

Hell, he said, is a banquet. There's a long, long table, at which is seated every soul in the place. There's food, food in abundance, beautiful, aromatic, food so wonderful-looking that you just KNOW it's going to be the most delicious thing you've ever tasted. And at each person's place-setting: a plate, and a pair of five-foot-long chopsticks. So in hell, everyone is in torment, able to pick up this amazing food but unable to bring it to his mouth.

Heaven, he went on, is a banquet. There's a long, long table, at which is seated every soul in the place. There's food, food in abundance, beautiful, aromatic, food so wonderful-looking that you just KNOW it's going to be the most delicious thing you've ever tasted. And at each person's place-setting: a plate, and a pair of five-foot-long chopsticks. But in heaven, there's joy and satiation, because each person has learned to feed the person across the table from him.

Jamie: And where do people who eat with their hands go? ;-)

Seriously, most descriptions of heaven I've heard sounded like a crashing bore, and an eternal banquet with someone else shoving food in my mouth doesn't sound any better.

Good christians don't act recklessly, commit crimes, or overindulge, so as long as the chances of martyrdom are slim, they'll live longer. However, in the USA at least, the reckless, criminal, or addicted people that don't live so long are mostly bad Christians, not atheists. That is, they believe in God, if anything more than the average American, but have trouble conforming their behavior to their beliefs...

No one has yet mentioned the reason I might expect the really religious to have a shorter lifespan: if they can believe in one huge heap of horse manure, why aren't they deluded about other things, such as medicine or the laws of physics?

However, Christians who pray when they ought to be going to the doctor are pretty rare - much rarer than people who skip church, drive too fast, drink too much, or are addicted to hard drugs.

I'll note that two of my grandparents were Jehovah's Witnesses and they died in their 60s. My lukewarm Congregationalist grandparents did much better; grandpa died at 87, and grandma is 93 and still breathing. However, there is also an immense socioeconomic difference there that explains the difference more than the JW aversion to certain medical procedures: the JW's were basically hillbillies who barely qualified as working class and lived where the ambulance might take hours to find you, while the Congregationalists were suburban upper middle class who could afford the best medical care available.

Tim, it's not n^2 that's larger than n (where you've defined n as infinity), it's 2^n. That really _is_ larger, as the Cantor proof shows.

markm:

You seem to be confusing devoutness with some kind of fundamentalism... I've known fundamentalists (a few - they're not common among my coreligionists but I do get out sometimes). I myself am not a great fan of literalism, though (not having all the answers myself) I can't deny the possibility that G*d makes billions of individual decisions from moment to moment about how the world will work.

However, it's entirely possible to be deeply religious, at least to be deeply Christian (I'm insufficiently familiar with non-Christian religions to make this claim, though I'm fairly certain it holds readily in Judaism too, at least), and simultaneously to acknowledge the wonderful gifts of a universe that obeys discoverable laws and the intellect to discover them. Some of us think the two are, in fact, inextricable from one another.

Incidentally, my priest was speaking allegorically, which I certainly hope you figured out.

Xavier wrote:

"... Likewise, if a person is already going to paradise, living longer can only hurt their chances."

Isn't this, as other similar notions expressed here that it's better to die sooner than later so one can sooner reside with God for eternity, just another version of the Albigensean Heresy?

Yeah, some people don't so much long for a better world as hate this one. Christianity and Buddhism lean that way (the only 2 religions with monks and nuns, tellingly.)
Some Christians and Buddhists (and some more obscure sects like the Albigenseans you mentioned, or 'Heaven's Gate' for that matter) focus so hard on the evils or inadequacies of this world that they risk degenerating into death cultists.
Tendencies like that are, of course, self-limiting.
Teaching your followers to proselytize and not use birth control is a much better plan, if you care about your religion's evolutionary fitness.
God, of course, allows all of us to approach Him (or not) in whatever manner we see fit. And God will kill us all, in due time, and God will judge.
Like the t-shirt says: 'Life is short. Pray hard.'

However, Christians who pray when they ought to be going to the doctor are pretty rare - much rarer than people who skip church, drive too fast, drink too much, or are addicted to hard drugs.

Try this one: "(14) Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord: (15) And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him" (James 5:14-15).

It helps to know that when that was written, annointing the head with oil was a common medicinal practice. Or IOW, if a medicine happens to be available, use it; just don't put your faith in it.

anony: It also helps to know that when that was written, there wasn't a whole lot doctors could do about most illnesses - and too much of what they did do was harmful. So having the church elders perform a magical ceremony was at least harmless, and didn't pile financial worries on top of an ailing man's sickness. (Although I think the ancient Greek and Roman-era doctors weren't as dangerous as later ones. They believed in learning from experience although not in controlled experiments, bleeding wasn't yet considered a cure-all, and they believed in cleanliness for it's own sake - unlike medievals who thought too much washing was unchristian, and even most 19th century doctors.)

I don't think it makes a significant difference.

Muslims believe that if you kill yourself on purpose, you will end up in hell. Christians are challenged to kill themselves if they honestly believe that they will go straight to heaven once they die. They should want to kill themselves because then they can enter paradise earlier (because believing Jesus is God is meant to save u, regardless of anything else you do). They never do kill themselves, however. Still, those who would kill themselves would not allow it to happen on the road, they would keep it to themselves.

Attempting to rationally consider sets of inherently irrational beliefs is neither rational nor productive.

Most people don't actually believe in the things they claim to believe. They merely believe they believe those things. That's why religious hypocrisy is so widespread.

But what if you don't believe in believing you don't believe what you really believe?
Is that as bad as believing in disbelief in beliefs one doesn't truly believe?

Most callow, sophomoric types haven't thought through ontology or epistemology to any great effect.
That's why they often rush from nursery tales to a sophomoric, puerile athiesm.

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