Well at this point we
should all be pretty familiar with Pascal’s wager. Essentially, Pascal used his
mathematical background to construct a probabilistic proof to why it makes
sense to believe in god.
A quick recap for those
of you who aren’t math whizzes: an Expected Payoff is used in probability
theory to determine what is the best course of action to take and is calculated
by multiplying the payoff if an event occurrs by the likelihood it occurs. For
instance, if I told you I were to give you $10 if I flipped a coin and it
landed on head but I would give you $100 if it landed on tails your expected
pay off would be $55. {Pay of event 1}*{likelihood of event 1}+{Pay of event
2}*{likelihood of event 2} = 10*.5+100*.5=55.
Pascal approached the
idea of God in a similar way. He makes many assumptions, which can’t be avoided
in this situation, to draw the conclusion that the expected payoff from
believing in god vastly outweighs the expected payoff from not believing in
god. To look at it mathematically here are the two expected pay offs. But first
we need to make some assumptions.
Assumption 1: God’s
existence is like flipping a coin, 50% chance he exists, 50% chance he doesn’t
exist.
Assumption 2: The
payoff for living a life of debauchery would be 10 pascalians (a unit of
measurement for amount of dopamine released by a person throughout his/her
life), but it would be -1000 if God existed, as they would spend the rest of
their life in hell
Assumption 3: The
payoff for living a life of faith would be -10 during their living life, but
would be +1000 during the rest of their, which they spend in heaven.
So now let’s take a
look at the expected payoffs for the two courses of actions, spending your life
helping the less fortunate through good deeds or spending your life helping the
less fortunate through funding drug cartels and strippers.
Life of Debauchery: {pay off god when doesn’t exist}*{likelihood good
doesn’t exist}+{pay off when god does exist}*{likelihood god exists}
=10*.5-1000*.5= -495
Ok, not great. Let’s
check out scenario #2.
Life of Faith: {pay off god when doesn’t exist}*{likelihood good
doesn’t exist}+{pay off when god does exist}*{likelihood god exists}
=-10*.5+1000*.5 = 495
Well, looks like Pascal
was right. Probabilistically speaking, wayyyy better to just believe in God and
take your chances.
Well now that we know
we should believe in God to get into Heaven let’s take a closer look at the
fine print of getting to Heaven. Hmmm, well it appears that things are bit more
complicated than how Pascal made them out to be, turns out that there are roughly
4,200 religions. So which God do we believe in? Well, looks like it’s back to
the drawing board. Let’s try this expected pay off thing again with this new
information in mind. But first, two new assumption needs to be made:
Assumption 4: God is
equally as likely to be the god of any religion (50% he exists divided by
4,200)
Assumption 5: These
religions heavens are mutually exclusive (I mean come on, it's God, he’s all
knowing. You’re not going to show up to the pearly gates having lead your life
as a Christian and then be let in when you find out God’s Zeus because of some
loophole where certain aspects of Christian life over lapped with aspects of Greek
polytheistic life.)
Life of Debauchery: {Chance God doesn’t exist}*{Payoff of life of
debauchery}+{Chance God does exist}*{Payoff of Hell}
.50*10+.50*-1000= -495
Life of Faith: {Chance God doesn’t exist}*{Payoff of life of faith}+{Chance
God does exist and you chose the right religion}*{Payoff of Heaven}+{Chance God
does exist and you chose the wrong religion}*{Payoff of Hell}
.50*-10+.00012*1000+49.99988*-1000=
-50,004
Well, looks like
chances are we’re spending the remainder of our lives in Hell anyways. Might as
well get those extra 10 Pascalians why you’re still on Earth and lead a life of
debauchery.
Of course, many
assumptions have been made here and you could argue that by changing these
assumptions you change the outcome. But any argument that discredits the math
done above will also discredit Pascal’s math because his logic too is based on assumptions.
Removing the numbers Pascal essentially says the outcome of believing in God and having him be real is so much better than the outcome of not believing in God and having him not be real that you should play to the odds of God existing. Removing my numbers, I am essentially saying there are so many Gods that the chances of you believing in the right one are so low that you are probably going to hell anyways and should enjoy your time on earth.
I don't believe that the above math is substantial evidence to
say that it probabilistically makes more sense to not believe in God; but, I certainly do believe that it is substantial evidence to say you can’t decide whether or not to believe in
God based on probability. Using the concepts of probability Pascal proved you should believe in God, using the concepts of probability I proved you shouldn't believe in God. By definition this proves that you can’t use probability to prove
whether or not to believe in God.
Xander,
ReplyDeleteI enjoyed reading your analysis on Pascal's wager, and I want to challenge your notion that "by definition you can't use probability to prove whether or not to believe in God." Am I mistaken to believe that you meant to say you can't use probability to prove whether or not God exists, however you can use the concepts of probability to decide whether or not to believe in God. Using the example of climate change, let's challenge this notion:
As you've previously mentioned, we don’t need to be 100% sure that the worst fears of climate scientists are correct in order for action to be taken. What is most important are the consequences of being wrong. Let’s assume that there is no human-caused climate change, or that the consequences are not that serious. What’s the worst that can happen?
Well, at best we’ve made major investments in renewable energy. This is an urgent issue even in the absence of global warming, as the International Energy Agency has now revised the date of “peak oil” to 2020. Not far from now...
And what if we're wrong and global warming is real and very serious? There will be droughts, floods and other extreme weather, species loss, and economic and social harm, etc etc.
It really is like Pascal’s wager. On one side, the worst outcome is that we’ve built a more robust economy. On the other side, the worst outcome really is a sort of hell on earth. In short, we do better if we believe in climate change and act on that belief, even if we turned out to be wrong. So is it really productive to use the concepts of probability to decide whether or not to believe in climate change (or God), versus balancing the probability of the consequences?
In response to the "Am I mistaken to believe that you meant to say you can't use probability to prove whether or not god exists", my answer is yes, you are mistaken in that assumption. I am not making a statement on whether or not God exists. I am only making a statement on whether or not someone should believe in God based on probability theory.
DeleteYour global warming example mirrors Pascals. Pascals analysis draws the conclusion using probability that you should believe in God. My analysis draws an opposite conclusion using the same basic ideas of probability. Two opposite analyses of the same situation using the same mathematical model but with two different assumptions proves that the mathematical model is not robust enough and too much is unknown of the situation to draw a clear conclusion. By drawing an opposite conclusion with the same approach I simultaneously disprove myself and Pascal. If the same approach can be used in the same situation to reach two different conclusion, than that approach is not sufficient for that situation. It is for this reason why I believe probability theory can't be used to decide whether or not one should believe in God, not because I don't understand the premise of Pascal's wager.
I think my favorite part about this post is that you created your own unit of measure and named it after Pascal. However, I think that you missed out on a really great opportunity by not naming the unit of dopamine after yourself. If you had done so, the chasian would have henceforth been known as the source of all debauchery the world over. You could have been in an exclusive club along with Richter, Ohm, Joule, Hertz, Apgar, Fujita, and... Pascal!! Really, it hardly seems fair for one person to have their name forever associated with both pressure and pleasure.
ReplyDeleteI do unfortunately, however, have to take issue with your analogy of the existence of god as a coin toss. In the case of a coin toss, provided uniform density of the metal and a nearly perfect disc shape, the probability of either heads or tails is predictable based upon thoroughly-observed phenomena of physics. In the case of the existence of god, all we have is the word of man as evidence. Out of the roughly 4,200 religions in the world, presumably many of them rely exclusively on some circular doctrine of faith as proof of their own supremacy. Since we're using mathematical probability, it would seem as though we would have to adhere to the Scientific Method in all aspects of this experiment. Without being able to measure and repeat any evidence of the existence of a given religion's god or gods, mustn't we discount that religion and reduce the probability of the existence of god by 1/8,400?
If you're on board with that, I would propose that the formula for the payoff for a life of debauchery be adjusted thusly:
{payoff of life of debauchery}*{.50+.00012*disqualified religions}+{payoff of hell}*{.50-.00012*disqualified religions}
So in order to balance the probabilistic scales towards us sinners, we'd have to disqualify a certain number of the world's religions. We'll call that number j, as in Jack Daniels:
10* {.50+.00012j} > -1000*{.50-.00012j}
Cheating a little bit here, we know that the number of pascalians associated with the afterlife is 100 times the number associated with living a really awesome life on Earth so we'd have to reduce the likelihood of the existence of god from 50% to 1% to eliminate statistical risk of a net negative payoff. That means excluding 98% of the 4,200 world religions, or 4,116 religions. While I'm sure that it would be possible to do this (I mean even if there is a god, she can only be fully represented by a maximum of one religion, right?), that seems like a lot of work. So instead I vote that we instead spend that time drinking bourbon, eating bacon, and treating our neighbor with the same love and respect with which we would want them to treat us. If Zeus isn't into that kind of life, I probably wouldn't want to hang out with him for eternity anyway.