Is Omega Impossible? Can we even ask?

mwengler

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Is Omega Impossible? Can we even ask?

by mwengler

24th Oct 2012

2 min read

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EDIT: I see by the karma bombing we can't even ask. Why even call this part of the site "discussion?"

Some of the classic questions about an omnipotent god include

Can god make a square circle?
Can god create an immovable object? And then move it?

Saints and philosophers wrestled with these issues back before there was television. My recollection is that people who liked the idea of an omnipotent god would answer "omnipotence does not include the power to do nonsense" where they would generally include contradictions as nonsense. So omnipotence can't square a circle, can't make 2=3, can't make an atom which is simultaneously lead and gold.

But where do the contradictions end and the merely difficult to conceive begin? Can omnipotence make the ratio of the diameter to the circumference of a circle = 3, or 22/7? Can omnipotence make sqrt(2)=1.4 or 2+2=5? While these are not directly self-contradictory statements, they can be used with a variety of simple truths to quickly derive self-contradictory statements. Can we then conclude that "2+2=5" is essentially a contradiction because it is close to a contradiction? Where do we draw the line?

What if were set some problem where we are told to assume that

2+2 = 5
1+1 = 2
1+1+1+1+1 = 5

In solving this set problem, we can quickly derive that 1=0, and use that to prove effectively anything we want to prove. Perhaps not formally, but we have violated the "law of the excluded middle," that either a statement is true or its negation is. Once you violate that, you can prove ANYTHING using simple laws of inference, because you have propositions that are true and false.

What if we set a problem where we are told to assume

Omega is an infallible intelligence that does not lie
Omega tells you 2+2=5

Well, we are going to have the same problem as above, we will be able to prove anything.

Newcomb's Problem

In Newcomb's box problem, we are told to assume that

Omega is an infallible intelligence
Omega has predicted correctly whether we will one box or two box.

From these assumptions we wind up with all sorts of problems of causality and/or free will and/or determinism.

What if these statements are not consistent? What if these statements are tantamount to assuming 0=1, or are within a few steps of assuming 0=1? Or something just as contradictory, but harder to identify?

Personally, I can think of LOTS of reasons to doubt that Newcomb's problem is even theoretically possible to set. Beyond that, I can think that the empirical barrier to believing Omega exists in reality would be gigantic, millions of humans have watched magic shows performed by non-superior intelligences where cards we have signed have turned up in a previously sealed envelope or wallet or audience member's pocket. We recognize that these are tricks, that they are not what they appear.

To question Omega is not playing by the mathematician's or philosopher's rules. But when we play by the rules, do we blithely assume 2+2=5 and then wrap ourselves around the logical axle trying to program a friendly AI to one-box? Why is questioning Omega's possibility of existence, or possibility of proof of existence out-of-bounds?

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Is Omega Impossible? Can we even ask?

by mwengler

24th Oct 2012

2 min read

-12

EDIT: I see by the karma bombing we can't even ask. Why even call this part of the site "discussion?"

Some of the classic questions about an omnipotent god include

Can god make a square circle?
Can god create an immovable object? And then move it?

What if were set some problem where we are told to assume that

2+2 = 5
1+1 = 2
1+1+1+1+1 = 5

What if we set a problem where we are told to assume

Omega is an infallible intelligence that does not lie
Omega tells you 2+2=5

Well, we are going to have the same problem as above, we will be able to prove anything.

Newcomb's Problem

In Newcomb's box problem, we are told to assume that

Omega is an infallible intelligence
Omega has predicted correctly whether we will one box or two box.

From these assumptions we wind up with all sorts of problems of causality and/or free will and/or determinism.

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thomblake14y140

If Omega is only able to predict your answer with 75% accuracy, then the expected payoff for two-boxing is:

.25 * 1001000 + .75 * 1000 = 251000

and the expected payoff for one-boxing is:

.25 * 0 + .75 * 1000000   = 750000.

So even if Omega is just a pretty good predictor, one-boxing is the way to go. (unless you really need a thousand dollars or usual concerns about money vs utility)

vi21maobk9vp14y20

This seems an overly simplistic view. You need to specify your source of knowledge about correlation of quality of predictions and decision theory prediction target uses.

And even then, you need to be sure that your using an exotic DT will not throw Omega too much off the trail (note that erring in your case will not ruin the nice track record).

I don't say it is impossible to specify, just that your description could be improved.

4thomblake14y

For the curious, you should be indifferent to one- or two-boxing when Omega predicts your response 50.05% of the time. If Omega is just perceptibly better than chance, one-boxing is still the way to go. Now I wonder how good humans are at playing Omega.

-2mwengler14y

Interesting and valuable point, brings the issue back to decision theory and away from impossible physics. As I have said in the past, I would one-box because I think Omega is a con-man. When magicians do this trick the trick is the box SEEMS to be sealed ahead of time, but in fact there is a mechanism for the magician to slip something inside it. In the case of finding a signed card in a sealed envelope, the envelope had a razor slit which the magician could surreptitiously push the card in from. Ultimately, Siegfried and Roy were doing the same trick with tigers in cages. If regular (but talented) humans like Siegfried and Roy could trick thousands of people a day, then Omega can get the million out of the box if I two box, or get it in there if I one box. Yes, I would want to build an AI clever enough to figure out a probable scam and then clever enough to figure out whether it can profit from that scam by going along with it. No, I wouldn't want that AI to think it had proof that there was a being that could seemingly violate the causal arrow of time merely because it seemed to have done so a number of times on the same order as Siegfried and Roy had managed. Ultimately, my fear is if you can believe in Omega at face value, you can believe in god, and an FAI that winds up believing something is god when it is actually just a conman is no friend of mine. If I see Omega getting the answer right 75% of the time, I think "the clever conman makes himself look real by appearing to be constrained by real limits." Does this make me smarter or dumber than we want a powerful AI to be?

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