[YeGoblynQueenne]

I don't know the background to this but if I understand correctly, it kind of pivots on the probability that the mugger is indeed an Operator from the Seventh Dimension, that Pascal places at 1 in a quadrillion.

In that case, I have to wonder where this estimate comes from? I get that it's just an arbitrary number and that any number would do, as long as it wasn't zero, but that's exactly the point: why can't Pascal place the probability of his mugger being an Operator from the Seventh Dimension at zero?

Is there any evidence at all to support the mugger's claim? Is there any evidence at all that there is such a thing as a "Seventh Dimension" for which the only thing we know is that its "Operators" have magickal, utility-maximising powers?

And does the whole thing only work if we assume that the probability that there is such a place and such people is more than 0?

[Strilanc]

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].

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.

[lidHanteyk]

In no particular order:

* 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.

[YeGoblynQueenne]

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.

[YeGoblynQueenne]

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?

[Dylan16807]

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"?

[YeGoblynQueenne]

>> 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.

[Dylan16807]

> 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.

[YeGoblynQueenne]

>> 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.

[TeMPOraL]

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.

A longer explanation: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-ar....

See also https://en.wikipedia.org/wiki/Cromwell%27s_rule, mentioned by 'edflsafoiewq.

[YeGoblynQueenne]

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?

>> See also https://en.wikipedia.org/wiki/Cromwell%27s_rule, mentioned by 'edflsafoiewq.

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?

[joefourier]

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.

[joefourier]

Why, instead of the probability being 0 or 1 in a quadrillion, is the probability not simply undefined?

Maybe I am not well-versed in Bayesian thinking, but I am unable to understanding assigning probabilities to events that have not occurred before, and to which there is no related numerical data.

Making the probability of Pascal's number being undefined renders any calculation of the risk involved null and solves the problem, while making it possible for future evidence to assign a defined probability (say you were previously approached by 10 Pascal's muggers and 2 turned out to be telling the truth).

[edflsafoiewq]

> I beseech you, in the bowels of Christ, think it possible that you may be mistaken.

https://en.wikipedia.org/wiki/Cromwell%27s_rule

[YeGoblynQueenne]

I think this is the same idea in another comment, above, about Pascal's Muggle. I think there's a bit of a confusion here though. I can adjust the probabilities of any event given new evidence.

For example, at this point in time I believe that the probability that I can fly if I flap my arms up and down is zero. I have no evidence that this is possible and I understand enough of the relevant physics to know that this is not just improbable, it is impossible.

However, if tomorrow I flapped my arms and found that I could fly, there would be nothing stopping me from re-evaluating my belief and assigning a higher probability to the chance that I can fly if I flap my arms.

But I think the problems begin with the misguided ambition to be able to predict the future even when there is no evidence to support any prediction. You can't know what you can't know. You can assign any probability you like to what you can't know, but even if you end up assigning the right probability that will be the result of blind chance, not the result of correct reasoning.

Anyway this is why I prefer logical inference to probabilistic inference. I understand that I'm in a minority on this, but for me it makes a lot more sense to maintain a state of provisional belief with an absolute value (in {0,1}), provisional in the sense that new evidence can always change your belief, than to live in a perpetual state of uncertainty which never resolves itself no matter how much evidence you see, because there is always a chance that you're wrong. There always _is_ a chance that you're wrong but it just seems cumbersome to have to maintain a ledger of competing probabilities for everything that has happened, and everything that hasn't yet happened, just on the off chance that anything can happen, including mutually exclusive events.

In principle, anything might happen. In practice, not everything will. There must be a sensible way to figure out what we need to prepare for and what we can safely ignore. And the whole Pascal's Mugger paradox, while it's meant to attack Pascal's Wager's logic, ends up for me as an illustration of why proabilistic inference is deeply borked.