If you set the probability at zero, you won't be convinced when they actually are an operator from the seventh dimension. That is to say, you run into the opposite problem of being Pascal's Muggle [1].
> A wind begins to blow about the alley, whipping the Mugger's loose clothes about him as they shift from ill-fitting shirt and jeans into robes of infinite blackness, within whose depths tiny galaxies and stranger things seem to twinkle. In the sky above, a gap edged by blue fire opens with a horrendous tearing sound - you can hear people on the nearby street yelling in sudden shock and terror, implying that they can see it too - and displays the image of the Mugger himself, wearing the same robes that now adorn his body, seated before a keyboard and a monitor.
> [...] "Unfortunately, you haven't offered me enough evidence," you explain.
* Helping a googleplex of people immediately vs over a period of time are two different complexities of action.
* Recall that hypotheses are selected from an ambient pool of possibilities. Then we might imagine that some hypotheses dominate others, so that regardless of how much evidence is offered, we always insist that the evidence supports a simpler alternative. To wit:
"Well, if I'm not a Matrix Lord, then how do you explain my amazing powers?" asks the Mugger.
"Street magic," you say. "Very impressive sleight of hand. Perhaps some smoke, mirrors, lasers, assistants."
* A Matrix Lord asking $5 of a person on the street in order to commit miracles is inherently irrational. If they just wanted $5, or wanted to deprive the person of $5, or wanted to humiliate and embarrass the person, or force them to accept certain philosophical truths, then those all could be achieved via Matrix Lordery. Therefore the Lord in this story is being a pointless dick, and it's silly to expect rational arguments to be part of the conversation. To wit:
"Just give yourself $5. Give yourself any reward you like, for helping people; it's not my place to set or fulfill the price of such powerful entities, is it?" you ask.
"But...but don't you want the feeling of doing good?" asks the Mugger.
"Not really, no," you reply. "I have investments and equity already, and those dollars already have ripples that affect people far beyond my direct control. I don't feel much of anything about those investments. And it would be irrational for me to value a $5 investment more than $5. Really, if you can do all of this good, then you should turn yourself into an exchange-traded fund, and let people buy your time to do good in the world," you muse.
"But...but this offer is for you, and you alone," the Mugger insists.
"Okay, but why me? Let's talk about the Self-Sampling Assumption!" you say. The Mugger groans.
That's a good point: if the Mugger is an Operator from the Fifth Dimension and he has such great magickal powers, why does he need the 10lb in Pascal's wallet? Or, if he does need them, why can't he just get them?
Like, we are asked to believe that, given that the Mugger is an Operator from the Seventh Dimension, he has the power to offer 10 quintillion Utils to Pascal, but not the power to just take the 10lb from his wallet.
I think the whole paradox can still stand, given that the Mugger can then just offer an amount of Utils that compensates from the much smaller conditional probability of the Mugger being only sorta omnipotent.
On the other hand, I think we can easily resolve the paradox by inserting the Crowbar of Cynical Jadedness: If it sounds too good to be true, then its probability of being either good, or true is zero (it can be one or the other with a non-zero probability, but not both). 10 quintillion utils (or however many) sounds too good to be true, so it can't be true. A Used Car Salesman will never offer you a good deal. The Mugger is only lying to get Pascal's money.
Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)?
The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero. Where does a non-zero probability value come from?
Are you then saying that the probability of any reward should never be placed to zero because that would not maximise rewards?
Probability zero is the same as saying that it would take infinite evidence to convince you. Even if someone provides amazingly convincing evidence, better than you've ever seen, a flat 0 or 1 eats it.
> there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero.
I don't think that logic works. What if the claim was "I have a five dollar bill in my pocket"?
>> Probability zero is the same as saying that it would take infinite evidence to convince you.
That assumes I can't go back and change my earlier beliefs. But I don't see why that's necessary. If I have no evidence that X is true at time t, I assing a probability of 0 to it. If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X.
The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity?
>> I don't think that logic works. What if the claim was "I have a five dollar bill in my pocket"?
That depends. I've seen five dollar bills coming out of peoples' pockets before (actually, I haven't because dollars are not common where I live but Ok). I don't have to assing a zero probability to that. I have some evidence that it's possible.
But I have no evidence that there even exists such a thing as a Seventh Dimension etc.
> If I acquire evidence that X is true at time t+1, I throw out the 0 and assign a higher probability to X.
> The world changes all the time. Why am I condemned to hold on to obviously unsound beliefs for all eternity?
Normally when you update a probability, how much you change it is based on the strength of the evidence. If your probability of something is ultra-low, and you see an event that's a million times more likely if that thing is true, your new probability is roughly a million times higher. And for a probability that's sufficiently close to 0 or 1, that pit is basically impossible to climb out of.
Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens.
> But I have no evidence that there even exists such a thing as a Seventh Dimension etc.
If you're setting a hard cutoff based on the silly Seventh Dimension stuff, then you still fall for the version where I come to your house and sign a document giving you a giant pile of money. That's how mortgages and business deals work every day after all.
> How about the statement "Hillary Clinton is the President of the United States"? What probability should I assign to that? I know that the PotUS is Donald Trump. Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?
Not for that reason. But you have to factor in the chance that you got confused, or your brain is failing to make new memories and it's actually 2022, or you just woke up from a really detailed dream about the wrong president.
>> Do you have an alternate method to suggest? What's the calculation you would use? Note that "I'm seeing this with my own eyes" should only give you so much change, because you might have accidentally taken a whole bunch of hallucinogens.
I don't understand. How would it happen that I've accidentally taken a whole bunch of hallucinogens? I never go near that kind of stuff.
>> Not for that reason. But you have to factor in the chance that you got confused, or your brain is failing to make new memories and it's actually 2022, or you just woke up from a really detailed dream about the wrong president.
I don't see how that would happen either. Why would my brain fail to make new memories? Why are you saying that this might be the case?
I think this is just enhancing the deep unreality of what you are proposing. If we need to assume that I'm in some kind of weird mental state that I have no reason to be in for your whole proposition to make sense then I really don't see the point of it, other than perhaps an interesting theoretical game.
You can't come up with a one in a billion scenario that you would accidentally take a hallucinogen?
You never ever have a dream that seems real for a few moments?
And failing to make new memories would be a specific but possible injury.
We're supposed to be working with very low probabilities here. That's the whole point of the thought experiment. If you're going to round anything below one-in-a-million to exactly zero then that's your prerogative, and it works in everyday life, but it's objectively wrong; it would falsely reject the idea of lightning strikes and winning the lottery.
> I think this is just enhancing the deep unreality of what you are proposing.
You didn't even reply to the part about removing all the silly stuff and cutting it down to just "guy offers to sign a document for lots of money"...
But I'm not hallucinating and I'm not dreaming either.
Also, I don't know why you're saying I'd round anything below one-in-a-million to zero. I wouldn't. But would assign zero probability to a mugger being an Operator from the Sevent Dimension because that's a patently absurd idea that I see no good reason to grace even with the slightest degree of belief.
I mean, if you take what you are saying here at face value I actually have to assume that there is a probability that there exists a Seventh Dimension with magikcally powerful Operators inhabiting it. In real life, not just in the context of Pascal's Wager. Because I can't assign zero probability to anything.
That just doesn't make any sense at all.
>> You didn't even reply to the part about removing all the silly stuff and cutting it down to just "guy offers to sign a document for lots of money"...
Apologies. I didn't understand what you meant with that and I didn't want to clutter the comment space with more clarifying questions.
> But I'm not hallucinating and I'm not dreaming either.
You've never been unsure if something actually happened for a moment? Because even if you only spend a few moments like that per month, we can assign it a probability.
> I mean, if you take what you are saying here at face value I actually have to assume that there is a probability that there exists a Seventh Dimension with magikcally powerful Operators inhabiting it. In real life, not just in the context of Pascal's Wager. Because I can't assign zero probability to anything.
You don't think there's any chance that you fundamentally misunderstand the universe and that there are powerful secrets being actively hidden from you? It doesn't have to be real 'magic', just something too beyond your understanding. I think there's some chance of that. I'd say less than 1% and more than 1 in a googolplex, to put some amusingly loose bounds on it. And then you have to factor in the chance the guy picks you in particular to mess with, but that's not an unreasonably large number.
> Apologies. I didn't understand what you meant with that and I didn't want to clutter the comment space with more clarifying questions.
You're objecting so specifically to the seventh dimension stuff, I thought it would be simpler to cut all that out. The point of the thought experiment is just a very likely but very positive act. And the way to have a productive conversation is to respond to the strongest form of the argument. So in that version, you can't just declare that the person in front of you isn't a rich guy screwing around and giving money to people that accept, because the probability of that is clearly not zero.
>> The point of the thought experiment is just a very likely but very positive act.
(You mean very _un_likely eh?)
The reason I'm objecting specifically to the seventh dimension stuff is that it's just something fanciful that someone came up with, so it's obviously fake and I don't have to believe it even a little bit.
The probability of someone just handing out money (if I read you correctly this time) is very low, but not zero, yes. But I'm contesting the claim that I'm never allowed to assign 0 probability to anything, because then I'm at risk of losing out. Sometimes, you don't risk being wrong by disbelieving something.
Anyway I'm getting more and more confused by this conversation. I don't think it's getting anywhere. Thanks for your patience- you have the floor.
As the saying goes, "zero and one are not probabilities". Like 'Dylan16807 says, they eat evidence. When doing maths, when transforming to log probabilities, 0 becomes -Infinity; when transforming to odds ratios, 1 goes to infinity.
Yes, I get the arithmetic, thank you. What I don't get is why I'm forced to perform it in the way that you say. Why do I have to hold on to that 0 probabilty no matter what happens? Clearly it's much more reasonable to change my mind given that the world has changed and assign a non-zero probability to an event for which I now have evidence. Why would I not?
How about the statement "Hillary Clinton is the President of the United States"? What probability should I assign to that? I know that the PotUS is Donald Trump. Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?
I'd say it's because the process of updating probabilities in light of new evidence involves multiplication, which yields you nothing new for 0 and 1. It's not resetting values of variables.
> Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?
Yes. And the justification for that is that there's tiny but non-zero possibility that she may really be the president, and it's your senses that deceive you. Perhaps you're the protagonist of your own's Truman Show. Or perhaps it's some peculiarity in your brain that prevents you from accepting who the real president is. Integrating other evidence around you, you can assign ridiculously low probabilities to these scenarios, but you can't assume zero probability. After all, there exist people with such problems, and they tend to end up in treatment when someone realizes what's going on with them.
And the nice thing about it, that not using 0 and 1 makes the whole thing add up to reality in an elegant fashion. Adding 0 and 1 breaks that.
>> And the nice thing about it, that not using 0 and 1 makes the whole thing add up to reality in an elegant fashion. Adding 0 and 1 breaks that.
I really don't see the "elegance" in having to accept that I may be in a strange mental state were reality is unkonwable, in order to describe reality.
I mean, at the end of the day, if you follow down that path you find yourself having to argue that Hillary Clinton might, actually, be the PotUS, and I may be brain damaged or something, you never know. That's just absurd and there's no practical point in it. It's just a waste of time.
I would agree, that is not enough evidence. Some sort of advanced display technology causing the apparition provides the exact same explainability, and would require no changes to our understanding of the universe and the laws of physics.
1: https://www.lesswrong.com/posts/Ap4KfkHyxjYPDiqh2/pascal-s-m...
> A wind begins to blow about the alley, whipping the Mugger's loose clothes about him as they shift from ill-fitting shirt and jeans into robes of infinite blackness, within whose depths tiny galaxies and stranger things seem to twinkle. In the sky above, a gap edged by blue fire opens with a horrendous tearing sound - you can hear people on the nearby street yelling in sudden shock and terror, implying that they can see it too - and displays the image of the Mugger himself, wearing the same robes that now adorn his body, seated before a keyboard and a monitor.
> [...] "Unfortunately, you haven't offered me enough evidence," you explain.