Scott Aaronson on Penrose's argument (why machines can't think)
scottaaronson.com
scottaaronson.com
- Consciousness is weird and we can't explain it.
- Quantum mechanics is weird and we can't explain it.
- Therefore, consciousness and human intelligence must come from quantum mechanics.
Yeah, yeah, I know, that's obviously not how he frames it, but it's close. I read his book a few years ago, expecting some great insight but seriously, that's all there is to it.
He actually claims that mathematicians have some magical ability to "see" in to a parallell universe of mathematical answers, an ability that computers lack. How can this argument even be taken seriously?
As a human, you can mentally rotate an object, recognize a face and do all these extremely expensive computations effortlessly. For doing that, you need to have a model of the local universe loaded up to your brain, which in addition is constantly filtering out hypothetical scenes and movements which do not satisfy the principle of least action (e.g., you don't think Steve Jobs is under your desk right now). Many of such computations, however, are of the kind that could easily be carried out by quantum computers, provided you would load them up with the correct model of their neighborhood. Now imagine that the many worlds interpretation of QM holds: All the things in the cosmos "span" multiple universes. There are an infinite number of replicas of yourself in ever so slightly different universes. If your brain is indeed a quantum computer, your brain is cross-linked to all your other brains. There is no need to load up any model anymore. All that you needed is to perceive the reality as it comes!
Of course this "argument" (I would call it a theory) is full of holes, but the topic makes for some interesting talks with philosophers.
The number of inputs is pretty much infinite, not finite like he says.
I emailed him this, I'll post here if he replies:
I think you are incorrect about the lookup table. Just
walking around a city will provide more input permutations
than any lookup table could possibly encode.
You assumed that responses are always deterministic, but
actually peoples behavior is influenced by what they have
seen recently. Or even what they have been asked recently!
Every lookup table will also have to include the result
of choosing any question from the lookup table - and in
what order.
The possible number of orderings of that grows far faster
than any finite lookup table could encode, because simply
asking a question in the lookup table changes the answer
to all further questions.For example; I hear a gunshot and see a flower. I'm not going to notice the flower. I only consider the gunshot and begin to process that information, deciding the give precedence to figuring out an escape route over botanical pondering.
Watch "Mind Control Marketing" by Derren Brown for proof.
And why have I never heard the term "advertising science" until just now?
A billion operations per billionth of a second for a billion years is still finite, it's just big.
My argument is that each time you add a question to the table, you need to encode an answer that depends on all the other questions asked.
Meaning the number of answers is exponential (actually factorial) to the number of questions in it. Such a table is essentially infinite.
i.e. if you have 10 questions you have 3 million possible answers. But with a million questions you have 8 x 10^5565708 answers. I hope you realize how big this number is.
Just to be clear, I'm totally in agreement with you that a lookup table based AI would not actually be possible in the real world, but I don't think any sane person would claim that.
I would have used the exact term from complexity theory, except I don't know what it is for n! - the highest they have is EXPSPACE which is 2^n (which is smaller - much smaller).
As large as that number may be, following up on a discussion from yesterday, I would bet BB(10) is quite a bit larger. (Failing that BB(20) certainly is, because I suspect the TM to directly simulate the situation I just named could fit within 20 states. Mere permutation isn't actually that Turing-complex.)
The human lookup table is a much smaller finite subset of that, for any definition of human you could name. Enormous, but also "enormously" smaller than the other things I've described.
> can the human mind somehow peer into the Platonic heavens, in order to directly perceive (let's say) the consistency of ZF set theory? If the answer is no -- if we can only approach mathematical truth with the same unreliable, savannah-optimized tools that we use for doing the laundry, ordering Chinese takeout, etc. -- then it seems we ought to grant computers the same liberty of being fallible. But in that case, the claimed distinction between humans and machines would seem to evaporate.
Wonderfully written. I may not understand Godel's Theorems or ZF, but i did gain an understanding about some faults in Penrose's argument.
If the answer is yes, I'd be puzzled. It's naive to think that computers in XXIII century will be anything like current ones. We are after all machines and I find no reason any complexity (quantum, midichlorians or whatever) that we have can't be introduced in the construction of future computers.
That's like a XIX scientist saying that a microscope will never be able to see atoms. Surely he could have demonstrated it with good math.
Rephrased. the argument should be "computers as are built now can't think" that is so obvious simply because lack of power.
A reasonable simulation of conscience that tries to resemble that of a living organism would need at the very least senses, pain/pleasure, feedback (if I want to move, I can,) all throwed in an integration layer that "feels" everything at once.
First we should see if we're able to simulate an ant, then a mathematician brain :-)
Current simulations of living beings or colonies have value for statistical studies, but they're nothing in which that impossibility assertions can base.
I don't know if it has ever been taken seriously by anyone who doesn't approach the problem from that point of view, though.
1. Humans can perform Turing-uncomputable operations (mathematicians mainly) 2. All of present day physics is computable 3. So there should be some uncomputable physics yet to be discovered. 4. Penrose feels this new physics should be in quantum mechanics.
A small video of Penrose's argument : http://www.youtube.com/watch?v=9Gl6aThSs1s
On one hand the very notion that a computing device is conscious is patently ridiculous. Why? Because everything computes something. Even my fan computes a function so does the engine of a car[1], but are those artifacts conscious? The only honest answer is to say that this is a difficult problem.
This is a very good interview of David Chalmers (the philosopher who originated the term "Hard problem of consciousness") that I found on HN sometime back
http://www.youtube.com/watch?v=NK1Yo6VbRoo
Obligatory XKCD reference: Can a bunch of rocks be conscious? http://xkcd.com/505/
[1] Very trivially they compute the function which describes their dynamics.
Humans aren't Turing-complete; they can certainly emulate a small, finite, Turing machine, but they can't emulate an arbitrary large one.
An individual human is not complete in any way; look at how many people have failed to proof Fermat's last theorem.
Finally, people aren't consistent; Robert Penrose can say "Penrose will never utter this statement" and the roof doesn't fall in.
Can anyone give me an example of such problems?