Ten conspiracy theories for nerds (or conspiracy theory theory)

by on June 29, 2012 at 10:20 am in Uncategorized | Permalink

Not your usual cup of tea, here is one of them:

The Simulation Argument. This is legion in popular culture from “The Matrix” and “Inception” and other sci-fi, so we’ll just refer you to Nick Bostrom’s formulation of it. In theory we could tell the difference if something happened in the manner of The Truman Show where a light labeled “Sirius” falls from the sky. But are there any such events?

We offer one complexity-related observation. Although it is routine to say that classes like {\mathsf{P}} and {\mathsf{BQP}} have universal simulation, this isn’t strictly true. The universal function for {\mathsf{P}} doesn’t belong to {\mathsf{P}}—if it did, then {\mathsf{P}} would be in some fixed polynomial time bound, which it isn’t. Although proving this is technically murkier for “random” or “promise” classes like {\mathsf{BQP}}, the essential idea holds for any reasonable complexity class. Thus a universal simulation involves dropping down to a lower grade than the resources on which you draw. If our universe is convincingly universal, perhaps this is a well-motivated reason to reject the argument.

Perhaps the conspiracy is that so many people are intent on getting us to believe the simulation hypothesis.  Here is another one:

{\bullet } Factoring Really Is Easy. This is similar to the last, but now they can factor in polynomial time on a laptop, rather than need a quantum computer. Ken and I think this one has a much higher prior, almost on the order of “Breaking Engima Really Is Easy” in 1939.

If I understand properly, that is from a collaborative post from Pip and Ken Regan.

1 IVV June 29, 2012 at 10:39 am

In many ways, a simulationistic view is a theistic view. The entity running the simulation would, in essence, be a god of the simulation. Thus, proof of a simulation is proof of deity.

2 gwern June 29, 2012 at 12:03 pm

And of course, in many ways a simulation view is the exact opposite of a supernatural theistic view: a simulator has no properties shared with a god (eg. they’re certainly not omnipotent or omnipresent unless you covertly redefine the
‘omni’s to scope only over the simulation) and is an entirely naturalistic explanation.

3 Right Wing-nut June 29, 2012 at 1:44 pm

Not if you’re inside the machine. And, by assumption, you are.

4 Ricardo June 30, 2012 at 2:03 am

Sort of.

The simulator would appear all-knowing and all-powerful from our rather ignorant and limited perspective but wouldn’t necessarily be so in reality. It certainly would not establish a benevolent or merciful god as in some religions.

Proof of a simulation would establish the existence of some sort of god-like figure as imagined by the Greeks or Hindus who might be vain, temperamental and petty and would not necessarily be the uncaused cause, prime mover, all-knowing, all-powerful, etc. deity.

5 Hasdrubal July 2, 2012 at 4:24 pm

Couldn’t a simulator be omniscient, omnipotent and effectively omnipresent _relative_ the simulation. For omniscience, all they have to do is pause the simulation and look at the state of whatever he feels like. For omnipotent, well, he’s doing the coding and setting the initial values, and can likely adjust the live values as well. Omnipresent might be a little harder, though he could have subroutines to halt execution and alert him whenever something he’s interested in happens. Stopping execution shouldn’t be detectable within the simulation if all variables and states are preserved.

6 Adrian Ratnapala June 29, 2012 at 11:08 am

the order of “Breaking Engima Really Is Easy” in 1939.

I don’t know the truth of these things, but I’ve read that the Enigma cypher was naive. That is, the Germans were not caught out (only) by the existence of electronic number crunchers, but mostly be the fact that their code was easier to break than they imagined.

In the meantime, mz kezboard has gone German again.

7 Alex Godofsky June 29, 2012 at 11:12 am

The universal function for doesn’t belong to —if it did, then would be in some fixed polynomial time bound, which it isn’t.

I’m curious if this is actually proven, or just assumed. It’s certainly a reasonable assumption, but I can’t immediately sketch out a proof that there isn’t a hard upper bound on the asymptotic complexity of problems in P (given a particular machine).

8 Rahul June 29, 2012 at 1:10 pm

But are there any such events?

Thought it was impossible for the subjects to ever know if we were indeed in a simulation?

9 Tim June 29, 2012 at 1:46 pm

Alex, the short answer is http://en.wikipedia.org/wiki/Time_hierarchy_theorem .

I’ll try my best to explain a bit though. Suppose u is a universal function for P. Then we can decide any other problem x in P, for an input s (of length n) by using u to simulate x on s. Suppose u is in P, then there is some O(N^c) time machine for u. As the string for a machine for x is constant, we can build a machine from u using x as input that solves whether x accepts s that runs in time O(n^c). As the choice of x was not specific, we can solve any problem in P in time O(N^c). This is the fixed polynomial time bound. But… we can’t do this! See the link above.

10 Alex Godofsky June 29, 2012 at 4:28 pm

Got it, thanks. I just wasn’t aware of the relevant theorem.

11 Zach June 29, 2012 at 3:36 pm

This is similar to the last, but now they can factor in polynomial time on a laptop, rather than need a quantum computer. Ken and I think this one has a much higher prior, almost on the order of “Breaking Engima Really Is Easy” in 1939.

I can’t seem to find one right now, but in the past I’ve seen job postings from the NSA for quantum computing research. The approaches advertised suggested that the NSA isn’t any further ahead than anybody else.

12 sort_of_knowledgeable June 29, 2012 at 3:56 pm

But they could be advertising just to make people think that they are not further ahead. And also to hire anybody else who might get somebody else ahead.

13 Zach June 29, 2012 at 4:10 pm

If you’re advertising for someone with expertise in ultracold ion laser trapping, you either have a very enthusiastic dedication to obfuscating your approach, or you are indeed looking at ultracold ions.

Consider: if you hire ultracold ion specialists *and then don’t use them,* you have tipped your hand much more directly than if you simply never hired anybody in the first place.

14 John Faben June 29, 2012 at 7:22 pm

>Consider: if you hire ultracold ion specialists *and then don’t use them,* you have tipped your hand much more directly than if you simply never hired anybody in the first place.

Really? To someone outside the NSA, how does the NSA hiring someone and not using them look any different to hiring them and they using them?

15 sort_of_knowledgeable June 29, 2012 at 8:03 pm

I was mostly being facetious, since it is hard to imagine the NSA that much ahead of what the rest of the world would consider the leading edge, but I have heard of companies advertising for positions they didn’t intend to fill because they wanted to give the appearance they were growing. If they hired an ultracold ion specialists I would expect that he would be put work even if they had what seemed to be a better quantum computer just to keep him busy and on the off chance he might make a break through.

16 bifyu June 29, 2012 at 4:09 pm
17 TallDave July 1, 2012 at 1:24 am

We offer one complexity-related observation. Although it is routine to say that classes like and have universal simulation, this isn’t strictly true. The universal function for doesn’t belong to —if it did, then would be in some fixed polynomial time bound, which it isn’t. Although proving this is technically murkier for “random” or “promise” classes like , the essential idea holds for any reasonable complexity class. Thus a universal simulation involves dropping down to a lower grade than the resources on which you draw.

I guess I thought everyone just assumed that anyway.

If our universe is convincingly universal, perhaps this is a well-motivated reason to reject the argument.

Maybe we’re a simulation being run in a universe with less indeterminacy at tiny scales (i.e. higher resolution). Or does Bell’s inequality rule that out? Or (haha) maybe the higher universe obeys local realism and the reason we don’t is that we’re a simulation.

18 Nick July 1, 2012 at 9:54 am

The simulation argument presupposes that the Fermi Paradox doesn’t fall on the side of the “Great Filter” (which is embedded in Bostrom’s argument to be sure)

Enough evidence life on other planets and the odds of us being in a simulation plummet.

FWIW: I believe there’s good odd’s the simulation argument is right but I don’t particularly care 🙂

http://www.technologyreview.com/article/409936/where-are-they/

19 Charles July 12, 2012 at 1:19 pm

Its always great to see conspiracy news!

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