Tuesday, September 9, 2014

How infinity breaks a moral calculus

It has been a long time since I've blogged anything, and it's been a longer time since I've blogged anything about mathematics and its impact on theological thinking, but it has come time to change that.

The issue that started my thoughts along the present course relate to Islamic Jihad, but because I think it's a very complicated topic, I will reserve commentary on it until later. For my purposes, the odious Westboro Baptist Church (WBC) will serve as a useful point of reference, and so I will use that for the time being (largely because it's simpler than Jihadism).

The case I want to make is one I've been making ever since I saw two members of the Westboro Baptists interviewed by Russell Brand on his own show, perhaps a year ago or thereabouts, in which I finally connected with at least one of the reasons that members of the Westboro Baptist congregation are acting in love with their despicable demonstrations. You can see that interview here, if you'd like. The representatives of the church make it quite plain that their motivation is one based in love and how they arrive at that conclusion.

Before continuing, let me make a note that I am aware that it is possible, if cynical to assume, that the bottom-level motivations of the WBC may be largely financial gain, but that does not necessarily imply that the majority of the membership of the WBC believes something other than what they say. It is vastly more economical and honest simply to assume that the angry rubes believe what they say they believe.

But, But... Love?

Yes, love. I think the true-to-their-word members of the WBC are motivated to engage in all of their hatefulness out of love. No doubt this is controversial, and to unravel the apparent paradox, we have to take a diversion into the infinite.

Every number is smaller than most

One of the main themes I wanted to convey with my book Dot, Dot, Dot: Infinity Plus God Equals Folly, published around this time last year, is that infinity is non-intuitive not just in "how it works" but also in how big it is. Even without getting to infinity, because the counting numbers, 1, 2, 3, and so on, including 0 if we like since it counts empty sets, we arrive at the mathematical fact that every number is smaller than most. Here's some of how I put it in the fifth chapter of Dot, Dot, Dot, that whole chapter being dedicated to this peculiar idea.
In English, we only have names for numbers that are conceivably useful, with some extensions using prefixes attached to -illion after a time. By the time we reach numbers with a few scores of digits, we also run out of names for them except in special cases, even if we can represent them numerically. We have a name for huge numbers like the googolplex (the number written with a one followed by the number of zeroes that is a one with one hundred zeroes after it), but what do we call, for instance, the number with one less zero than that? That idea—that we've only named numbers that are, to speak very vaguely, conceivably useful—provides the clue to finding salience in our concept of “large numbers.” We can call numbers “large” when they're relatively large given the context.

These numbers we're naming, or even the ones beyond names, though, are not large in an absolute sense as mathematical abstractions devoid of context. While one quadrillion (one thousand trillion, that is, one with fifteen zeroes following it) dollars constitutes a very large number of dollars, one quadrillion is nothing compared against the vast majority (almost all, as it turns out) of the natural numbers. If we take any “large” number, say one quadrillion, and multiply it by one hundred, the result obviously dwarfs our original “large” number by one hundred to one, casting a shadow over what it meant to be “large” in the first place. But there's no mathematical reason that we have to limit ourselves to multiplying by one hundred. We could multiply by a quadrillion, or multiply by a quadrillion a quadrillion times, by which time our original “large” number is lost in a sea of far, far larger values. When we realize that one quadrillion was chosen arbitrarily, meaning that any number, including a quadrillion multiplied by itself a quadrillion times, could replace our initial choice with the same implications, we get an idea of what is meant by every number being very small.

These abstractions are hard to understand and very high-minded, bordering on the feel of nonsense. Sometimes it is useful to try to get our heads around these numbers, but this is very difficult to do. For instance, one quadrillion is roughly the number of grains of refined, white sugar that could be hauled in 134 full-sized (53-foot) tractor-trailers. That's (kind of) a lot of sugar, but bear in mind that this number is only 1,000,000,000,000,000 in our condensed notation.

To get an idea of the size of a quadrillion multiplied by itself a quadrillion times, we'd have to have a one followed by fifteen quadrillion zeroes just to write the number in the same very condensed notation (incidentally, this number is still inconceivably smaller than the googolplex). In 12-point font on standard 8.5-inch by 11-inch paper (with one-inch margins), printed on both sides of the paper, just writing down a quadrillion multiplied by itself a quadrillion times requires a stack of papers filled entirely with zeroes roughly 250,000 kilometers thick, that is, reaching 65% of the way to the moon! Again, that's just writing the number down in a standard, somewhat condensed notation.

Bear in mind again that writing down a quadrillion merely takes roughly two inches on one line of the page and yet represents the number of grains of sugar that could be carried by a small fleet of full-sized semi-trucks. Now remember that even a ridiculously, impossible-to-understand large number like a quadrillion multiplied by itself a quadrillion times is a pittance that amounts to essentially nothing. Indeed, a number represented by a book of concatenated zeroes reaching from here to the sun or to the Andromeda Galaxy, which are hardly any distances at all, leave a quadrillion to the quadrillionth power minuscule beneath even potential notice (and are still themselves inconceivably smaller than the googolplex, which has more than a thousand quadrillion times more zeroes than the estimated number of atoms in the observable universe).

The fact of the matter is that these numbers, when bereft of real-world context, are impossible to call “large.” Indeed, they are unimaginably small. Incredibly, this smallness is a property that applies to every single number there is. Even more incredibly, this implies, as we've discussed, that against the infinite, every number is equally small, which is to say infinitely small.
In simple terms, because we have infinitely many counting numbers, and any counting number we might think of is only so big, every number is smaller than most. Think about it for a second: the biggest number you can think of has only that many numbers coming before it but infinitely many to come after it, so the proportion of numbers no bigger than your number is, to cheat for simplicity, "your number divided by infinity," which is zero (or infinitesimal). NB: Of course I know you can't divide by infinity and how this has to be understood in terms of limits, which is why I said we're cheating for simplicity.

Measuring experience

Also controversial is the idea that we can measure experience, but I think this notion has enough real-world salience to be getting on with without having to elaborate endlessly into philosophical diversion about what it means to measure experience or how it might be done. I think we all have a sense that better is better, worse is worse, and that somehow over the span of our conscious experience, more better is better, more worse is worse, and that there's some vague notion of a calculus going on here that could, in principle, account for that idea.

If we agree to run with the idea that we can measure experience, however crudely, then we have the sense of what it means to put well-being and suffering into a metric that allows us to compare various possible outcomes of conscious experience. In other words, we get a sense that "the good life" actually means something measurable. And once we agree to be able to measure the quality of conscious experience, we are ready to start discussing how infinity, in the forms of Heaven and Hell, breaks a moral calculus.

Life is finite

It seems to be uncontroversial, despite various religious beliefs to the contrary, to say that life, at least as we usually conceive of it, is finite. Whether it starts at conception, some other prenatal stage, birth, or what-have-we, it starts at some point of time. Then it ends at death, and whatever religious beliefs we might hold insisting that we do not really die, it is utterly beyond dispute to recognize that our body, the life we are currently living, starts and ends at roughly identifiable moments in time (I know, this is complicated too, but... honestly).

If our lives are finite--and they are--then the total quantity of our living conscious experience is also finite. Although it's unlikely to be real, any extension of our conscious experience beyond our lives takes place in an afterlife, which takes place after life, and thus isn't a part of it. I've said all of this, of course, to carefully navigate tiresome bullshit around an obvious point: whatever our lives entail, the total good or bad that we experience in it only adds up to so much, to a finite value.

Afterlife is (conceivably) infinite

Though not every tradition accepts this idea, many embrace the idea that Paradise, and its attendant bliss, is eternal, as are the torments of Hell. These ideas are key selling points for religions because they tap into a very human desire to avoid suffering and find bliss, whatever that might mean, and to maintain that state as long as possible. In other words, for many traditions, the good-life score of Paradise is positive infinity, and the good-life score of Hell is negative infinity. These ideas resonate immediately with people, even if they do not make sense.

So let's summarize the big points we've established so far:
  1. Living conscious experience is finite;
  2. Afterlife conscious experience is alleged to be infinite, usually polarized to perfect goodness or absolute badness; and
  3. Every (finite) number is smaller than most.
Infinity breaks a moral calculus

Surely you already see it, then. If someone absolutely accepts and believes in the ideas of a literal Heaven or Hell, with its attendant infinite reward or limitless misery, then that person has introduced into his moral calculus an element that completely outweighs any and all living experience, no matter how good or bad it might be. Once we tack on various dogmas and other supertruths concerning what merits someone admittance into Paradise or condemns them to the Fire, we have on our hands a moral calculus that can only admit one path to ethical reasoning: that which maximizes the chances of someone going to Paradise and/or avoiding Hell maximizes good.

Let that sink in for a moment. For a member of the Westboro Baptist Church who truly believes that homosexuality is a sure condemnation to Hell, no amount of suffering by any number of homosexual, bisexual, or other decent people--no amount at all--compares with the suffering of even one of them going to Hell, or instead, repenting of their "sin" and reaching Paradise. If a Westboro Baptist congregant follows Jesus' instructions to love one another, even those they find loathsome, the only loving course is to do everything, no matter how heinous, to try to change even one of their minds. In other words, for all their hate, it is entirely possible that their real motivation is love, and the reason is that their moral calculus is completely perverted by pretenses on the infinite.

All life is finite

This isn't redundant. This is the state of affairs that motivates both the WBC and the Jihadis that I started out talking about. It isn't that this person, that homosexual, the other sinner, or whoever, lives a finite life. It's that we all live a finite life. Add finite to finite to finite to finite for as many as you want, so long as that amount is actually a "many," i.e. also finite, and what you end up with is still finite. That is, to be specific, the aggregate experience of all seven-point-some-odd billion of us and the billions more to come is finite, which is to say that it is smaller than most values.

Especially, it is smaller than infinity, obviously and by definition. So, if the torment for a single person in Hell is infinite, or the reward for a single of the Saved in Paradise is infinite, untold, unimaginable suffering in the lives of every single living human present and future literally doesn't matter in comparison. On a moral calculus that includes infinite reward or infinite punishment, literally any amount of suffering inflicted upon any number of people (and animals) is perfectly justified and can be said to be motivated by love if the goal of the behavior inflicting that suffering is to bring even one person into the proposed right way to believe to earn Paradise and avoid the Fire. Read that sentence again.

People believe this

The question, then, is whether or not anyone in the world actually believes such things, and I believe that question has an obvious and resounding affirmative answer. The Inquisition said it was motivated by that very belief, for instance, and on the Russell Brand show, the representatives of Westboro Baptist affirmed it. Along with a particular complication, it is likely that the "extreme" end of Jihadis all embrace this peculiar vision of the universe as well. That is, not only do I think people believe these ideas; I believe a lot of them do.

Take, for instance, this short piece, written a few days ago on the CEMB, Ex-Muslim, forum by "Toona," who describes his upbringing in a Jihadist environment. He describes exactly what I've been trying to tell people at least for the last year, what people like Sam Harris have been going on about for more than a decade: people really believe in moral calculi involving infinite reward and punishment and use the resulting warped motivations to be as nearly perfectly horrible as human beings can be.

Jihadism

I said from the outset that Jihadism is a little more complicated than the case of the WBC, and the reason is the specific character of the doctrines of martyrdom in Jihadist Islam (or really, in Islam generally, not that everyone believes all of them). Those characters provide the martyr with specific benefits, benefits that "Toona" rightly identifies as being selfish motivations. The martyr gets a more glorious road to Paradise; the martyr gets special rewards in Paradise; the martyr secures a direct path to Paradise for many of his chosen kin (this last point probably being the most alluring, even more than the alleged "72 virgins" thing, for a variety of well-established psychosocial reasons).

What that means is that Jihadism is slightly more complicated via a self-serving element than the twisted other-serving idea of love that the representatives of the WBC painted for Russell Brand (though I suspect there are self-serving reasons contained within the WBC's approach as well--like that God will punish those who don't take every opportunity to try to save others from hellfire by whatever means might be necessary). That doesn't remove the other-serving notions within Jihadism, though, as "Toona" makes clear for us:
Think about it like this: the eternal fate of just one person is a far more important matter than the temporary suffering of the thousands of people that are killed in these attacks. I would rather save one person from being tortured in the worst way possible for trillions and trillions of years than to prevent the premature death of the thousands of lives that are lost in these attacks. The idea of eternal hell was so terrible that everything else paled in comparison.
What to do about it

The first and most important thing to do when it comes to dealing with religious beliefs of infinite reward and punishment, and the right and wrong ways to find or avoid them, is to stop pretending people don't believe them or that they're not legitimately part of the religions that teach them, a favorite hobby-horse of the Left. People do, and once people believe them, their moral calculus is skewed by them in a way that follows perfectly logically from even a childlike understanding of the infinite. The results are predictable, and the ways we can deal with it when it arises (e.g. with ISIS) are limited.

Another thing to do is realize that these people aren't bad people at the level of their motivations. Their motivations are "good." It's the moral reasoning informing those motivations that is skewed, and it is skewed by unsupported beliefs. Those beliefs are always held on faith, and so one extremely important thing to do is to continue to help people realize that faith is not a reliable way to support a belief. (This, of course, will not be terribly effective on most extremists and will have to work from the outside inward, but acknowledging that fact doesn't negate the importance of this action as much as beg for a strategic way to employ it.)

If we realize where these people are coming from, we're more likely to be able to successfully help them out of their faith. So long as we persist in pretending that people's beliefs cannot be that erroneous, we're likely to be hopeless, left reacting to reactionaries we refuse to understand.

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