Is Omega Impossible? Can we even ask?

-8 mwengler 24 October 2012 02:47PM

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

 

  1. Can god make a square circle?
  2. 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 
  1. 2+2 = 5
  2. 1+1 = 2
  3. 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
  1. Omega is an infallible intelligence that does not lie
  2. 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
  1. Omega is an infallible intelligence
  2. 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?  

 

[LINK] blog on cryonics by someone who freezes things in a cell bio lab

5 mwengler 19 October 2012 06:35PM

http://www.strike-the-root.com/51/walker/walker12.html

Came across it pretty randomly, I found it quite intriguing.  Cryonics is "routine" for human embryos, not far-fetched for humans at all.  Makes the whole thing seem potentially very reasonable (and me someone who hasn't signed up and doesn't plan to).  

A Film about TransHuman Enterprises

9 mwengler 08 December 2011 06:36PM

More of a Robin Hanson thing than a lesswrong thing, but these are sister blogs (sibling blogs?) and Robin's has no forum for discussion. 

Amused to learn a play had been written and staged with Eliezer Yudkowski in its title, I searched to find info on this.  The play is by Robert Saietta, who's name lead me to an interesting funding site, where I came across Utopia.  This is a movie project about uploading people to machines.  The trailer is gorgeous. 

The director has about 8 days left to fund it.  I am a deliberately inefficient giver (I view charity as me purchasing things for my own amusement) so I can't recommend you give to this, but it could turn out to be an efficient thing to support.  Irrespective of supporting the film, the website has the trailer available, and it is gorgeous. 

"Add to Friends" does something or not?

8 mwengler 28 January 2011 12:45AM

If I click on a users name it brings me to a page like lukeprog's.  In the upper right of that page I see lukeprog's karma score, and I also see a button "add to friends."

Early in my use of this site there were some authors I wanted to follow, I thought perhaps "add to friends" would help me do that. 

But since then as near as I can tell, "add to friends" has absolutely no functionality.  Does anyone out there know any differently?

the Universe, Computability, and the Singularity

-4 mwengler 05 January 2011 05:19PM

EDIT at Karma -5: Could the next "good citizen" to vote this down leave me a comment as to why it is getting voted down, and if other "good citizens" to pile on after that, either upvote that comment or put another comment giving your different reason?

 

Original Post:

Questions about the computability of various physical laws recently had me thinking: "well of course every real physical law is computable or else the universe couldn't function."  That is to say that in order of the time-evolution of anything in the universe to proceed "correctly," the physical processes themselves must be able to, and in real-time, keep up with the complexity of their actual evolution.  This seems to me a proof that every real physical process is computable by SOME sort of real computer, in the degenerate case that real computer is simply an actual physical model of the process itself, create that model, observe whichever features of its time-evolution you are trying to compute, and there you have your computer. 

Then if we have a physical law whose use in predicting time evolution is provably uncomputable, either we know that this physical law is NOT the only law that might be formulated to describe what it is purporting to describe, or that our theory of computation is incomplete.  In some sense what I am saying is consistent with the idea that quantum computing can quickly collapse down to plausibly tractable levels the time it takes to compute some things which, as classical computation problems, blow up.  This would be a good indication that quantum is an important theory about the universe, that it not only explains a bunch of things that happen in the universe, but also explains how the universe can have those things happen in real-time without making mistakes. 

What I am wondering is, where does this kind of consideration break with traditional computability theory?  Is traditional computability theory limited to what Turing machines can do, while perhaps it is straightforward to prove that the operation of this Universe requires computation beyond what Turing machines can do?  Is traditional computability theory limited to digital representations whereas the degenerate build-it-and-measure-it computer is what has been known as an analog computer?  Is there somehow a level or measure of artificiality which must be present to call something a computer, which rules out such brute-force approaches as build-it-and-measure-it?

At least one imagining of the singularity is absorbing all the resources of the universe into some maximal intelligence, the (possibly asymptotic) endpoint of intelligences desiging greater intelligences until something makes them stop.  But the universe is already just humming along like clockwork, with quantum and possibly even subtler-than-quantum gears turning in real time.  What does the singularity add to this picture that isn't already there? 

Quantum Joint Configuration article: need help from physicists

15 mwengler 22 December 2010 06:32PM

EDIT: 1:19 PM PST 22 December 2010 I completed this post.  I didn't realize an uncompleted version was already posted earlier.  

I wanted to read the quantum sequence because I've been intrigued by the nature of measurement throughout my physics career.  I was happy to see that articles such as joint configuration use beams of photons and half and fully silvered mirrors to make its points.  I spent years in graduate school working with a two-path interferometer with one moving mirror which we used to make spectrometric measurements on materials and detectors.  I studied the quantization of the electromagnetic field, reading and rereading books such as Yariv's Quantum Electronics and Marcuse's Principles of Quantum Electronics.  I developed with my friend David Woody a photodetector ttheory of extremely sensitive heterodyne mixers which explained the mysterious noise floor of these devices in terms of the shot noise from detecting the stream of photons which are the "Local Oscillator" of that mixer.  

My point being that I AM a physicist, and I am even a physicist who has worked with the kinds of configurations shown in this blog post, both experimentally and theoretically.  I did all this work 20 years ago and have been away from any kind of Quantum optics stuff for 15 years, but I don't think that is what is holding me back here.  

So when I read and reread the joint configuration blog post, I am concerned that it makes absolutely no sense to me.  I am hoping that someone out there DOES understand this article and can help me understand it.  Someone who understands the more traditional kinds of interferometer configurations such as that described for example here and could help put this joint configuration blog post in terms that relate it to this more usual interferometer situation.  

I'd be happy to be referred to this discussion if it has already taken place somewhere.  Or I'd be happy to try it in comments to this discussion post.  Or I'd be happy to talk to someone on the phone or in primate email, if you are that person email me at mwengler at gmail dot com.  

To give you an idea of the kinds of things I think would help:

1) How might you build that experiment?  Two photons coming in from right angles could be two radio sources at the same frequency and amplitude but possibly different phase as they hit the mirror.  In that case, we get a stream of photons to detector 1 proportional to sin(phi+pi/4)^2 and a stream of photons to detector 2 proportional to cos(phi+pi/4)^2 where phi is the phase difference of the two waves as they hit the mirror, and I have not attempted to get the sign of the pi/4 term right to match the exact picture.  Are they two thermal sources?  In which case we get random phases at the mirror and the photons split pretty randomly between detector 1 and detector 2, but there are no 2-photon correlations, it is just single photon statistics.  

2) The half-silvered mirror is a linear device: two photons passing through it do not interact with each other.  So any statistical effect correlating the two photons (that is, they must either both go to detector 1 or both go to detector 2, but we will never see one go to 1 and the other go to 2) must be due to something going in the source of the photons.  Tell me what the source of these photons is that gives this gedanken effect.  

3) The two-photon aspect of the statistical prediction of this seems at least vaguely EPR-ish.  But in EPR the correlations of two photons come about because both photons originate from a single process, if I recall correctly.  Is this intending to look EPRish, but somehow leaving out some necessary features of the source of the two photons to get the correlation involved?

I remaing quite puzzled and look forward to anything anybody can tell me to relate the example given here to anything else in quantum optics or interferometers that I might already have some knowledge of.  

Thanks,
Mike

 

A fun estimation test, is it useful?

5 mwengler 20 December 2010 09:09PM

So you think its important to be able to estimate how well you are estimating something?  Here is a fun test that has been given to plenty of other people.  

I highly recommend you take the test before reading any more.  

http://www.codinghorror.com/blog/2006/06/how-good-an-estimator-are-you.html

 

The discussion of this test at the blog it is quoted in is quite interesting, but I recommend you read it after taking the test.  Similarly, one might anticipate there will be interesting discussion here on the test and whether it means what we want it to mean and so on.  

My great apologies if this has been posted before.  I did my bast with google trying to find any trace of this test, but if this has already been done, please let me know and ideally, let me know how I can remove my own duplicate post.

 

PS: The Southern California meetup 19 Dec 2010 was fantastic, thanks so much JenniferRM for setting it up.  This post on my part is an indirect result of what we discussed and a fun game we played while we were there.  

 

 

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