but Y has solved the (interesting) problem of understanding how people write novels.
I think the whole point in AI research is to do something, not find out how humans do something. You personally might find psychology (How humans work) far more interesting than AI research (How to do things traditionally classified as 'intelligence' regardless of the actual method) but please don't generalize that notion and smack labels "uninteresting" into problems.
What's happened in AI research is that Y (which is actually AI) is too difficult, so people successfully solve problems the way program X (which is not AI) does. But don't let this confuse you into thinking that AI has been successful.
When mysterious things cease to be mysterious they'll tend to resemble the way "X".
Consider the advent of powered flight. By that line of argumentation one could write "We don't actually understand how flight works, There are hacks that allow machines to fly without actually understanding how birds fly." Or we could compare cars with legs and say that transportation is generally just a ugly uninteresting hack.
If something goes wrong and our learned rules and basic instincts aren't working, consciousness has to step in and try to cobble a solution together on the fly (usually badly).
Considering that we've so completely kicked ass against any other species that we haven't been even on the same playing field for thousands of years I'd say conciousness has done rather well for itself.
Ofcourse this is just in relation to other species, in absolute scale we probably are not that good.
but it just tells us that those problems are less interesting than we thought.
Extrapolating from the trend it would not suprise me greatly if we'd eventually find out that intelligence in general is not as interesting as we thought.
When something is actually understood the problem suffers from rainbow effect "Oh it's just reflected light from water droplets, how boring and not interesting at all". It becomes a common thing thus boring for some. I, for one, think go and chess are much more interesting games now that we actually know how they are played, not just how to play.
I merely wished to clarify the difference between conciousness and how it is implemented in the brain. I had no intention of implying that it was part of the discussion. On retrospect the clarification was not required.
It's just way too common for the two issues to get mixed up, as can be seen on the various threads.
Quantum computing in the brain might be happening, but if we want to understand conciousness it is irrelevant (Unless conciousness is noncomputable where it becomes a claim about quantum physics yet again). It's as relevant as details about transistors or vacuum tubes are for understanding sorting algorithms.
Naturally when considering brain prostheses or simulating a brain the actual method with which brain computes is relevant.
It is why I am hesitant to argue that there are no quantum effects of any sort in the brain (although the quantum effects people have suggested so far haven't been convincing).
Considering that quantum physics is turing complete (unless it's nonlinear etc) any quantum effects could be reproduced with classical computation. Therefore the assumption that cognition must involve quantum effects implicitly assumes that quantum physics is nonlinear or one of the various other requirements.
In this light the first question that ought to be asked from persons claiming quantum effects on brain is: What computation [performed in brain] requires basically infinite loops completed on finite time and based on what physics experiment they believe that quantum effects are more than turing complete.
It seems I was wrong about Dennett's claims and misinterpreted the relevant sentence.
However the original question remains and can be rephrased: What predictions follow from world containing some intrinsic blueness?
The topmost cached thought I have is that this is exactly the same kind of confusion as presented in Excluding the Supernatural. Basically qualia is assumed as an ontologically basic thing, instead of neural firing pattern.
The big question is therefore (as presented in this thread already in various forms): What would you predict if you'd find yourself in a world with distinct blueness compared to a world without?
You can do a Dennett and deny that anything is really blue.
I'd like to see what he'd do if presented with blue and a red balls and given a task: "Pick up the blue ball and you'll receive 3^^^3 dollars".
Even though many claim to be confused about these common words their actual behaviour betrays them. Which raises the question that what is the benefit of this wondering of "blueness"? What does it help anyone to actually do?
As there is the 1:1 mapping between set of all reals and unit interval we can just use the unit interval and define a uniform mapping there. As whatever distribution you choose we can map it into unit interval as Pengvado said.
In case of set of all integers I'm not completely certain. But I'd look at the set of computable reals which we can use for much of mathematics. Normal calculus can be done with just computable reals (set of all numbers where there is an algorithm which provides arbitrary decimal in a finite time). So basically we have a mapping from computable reals on unit interval into set of all integers.
Another question is that is the uniform distribution the entropy maximising distribution when we consider set of all integers?
From a physical standpoint why are you interested in countably infinite probability distributions? If we assume discrete physical laws we'd have finite amount of possible worlds, on the other hand if we assume continuous we'd have uncountably infinite amount which can be mapped into unit interval.
From the top of my head I can imagine set of discrete worlds of all sizes which would be countably infinite. What other kinds of worlds there could be where this would be relevant?
Considering how much stuff like convays game of life which bears no resemblance to our universe is played I'd put the probability much lower.
Whenever you run anything which simulates anything turing compatible (Ok. Finite state machine is actually enough due to finite amount of information storage even in our universe) there is a chance for practically anything to happen.