I hope you are both willing at least to say that the other's contrary stance tells you that there is a good likelihood that you are wrong.

If Robin knows that Eliezer believes there is a good likelihood that Eliezer's position is wrong, why would Robin then conclude that his own position is likely to be wrong? And vice versa?

The fact that Eliezer and Robin disagree indicates one of two things: either one possesses crucial information that the other does not, or at least one of the two have made a fatal error.

The disagreement stems from the fact that each believes the other to have made the fatal error, and that their own position is fundamentally sound.

Eric, it's more amusing that both often cite a theorem that agreeing to disagree is impossible.

It's only impossible for rational Bayesians, which neither Hanson nor Yudkowsky are. Or any other human beings, for that matter.

Maybe neurons are just what brains happen to be made out of, because the blind idiot god is too stupid to sit down and invent transistors.

Maybe transistors are just what computers happen to be made out of, because the idiotic short-sighted humans are too stupid to sit down and build neurons.

Isn't it a bit silly to complain that 'nonwood' is so vague as to be useless, when 'wood' is such a broad category that it alone conveys little useful information?

I don't think it's a major leap to guess that making the wagons out of balsa will be a bad idea, but it's a wood. So is pine - which contains highly flammable resins. If spontaneous combustion is an issue, knowing what kind of wood is used is important.

Likewise, selling nonapples is equivalent to saying we shouldn't sell apples but should continue to sell something. It conveys more than saying we should stop selling apples, which is compatible with ceasing to merchandise.

If vagueness is a valid complaint, how are we to interpret 'Coherent Extrapolated Volition'?

ReadABook, I would suggest archiving your posts on another site. Nothing posted to this site is safe.

Has anyone proved a theorem on the uselessness of randomness?

Clearly you don't recognize the significance of Eliezer's work. He cannot be bound by such trivialities as 'proof' or 'demonstration'. They're not part of the New Rationality.

Don't you get the same effect from adding an orderly grid of dots?

In that particular example, yes. Because the image is static, as is the static.

If the static could change over time, you could get a better sense of where the image lies. It's cheaper and easier - and thus 'better' - to let natural randomness produce this static, especially since significant resources would have to be expended to eliminate the random noise.

What about from aligning the dots along the lines of the image?

If we knew where the image was, we wouldn't need the dots.

To be precise, in every case where the environment only cares about your actions and not what algorithm you use to produce them, any algorithm that can be improved by randomization can always be improved further by derandomization.

It's clear this is what you're saying.

It is not clear this can be shown to be true. 'Improvement' depends on what is valued, and what the context permits. In the real world, the value of an algorithm depends on not only its abstract mathematical properties but the costs of implementing it in an environment for which we have only imperfect knowledge.

Caledonian: Yes, I did. So: can't you always do better in principle by increasing sensitivity?

That's a little bit like saying that you could in principle go faster than light if you ignore relativistic effects, or that you could in principle produce a demonstration within a logical system that it is consistent if you ignore Godel's Fork.

There are lots of things we can do in principle if we ignore the fact that reality limits the principles that are valid.

As the saying goes: the difference between 'in principle' and 'in practice' is that in principle there is no difference between them, and in practice, there is.

If you remove the limitations on the amount and kind of knowledge you can acquire, randomness is inferior to the unrandom. But you can't remove those limitations.

Caledonian: couldn't you always do better in such a case, in principle (ignoring resource limits), by increasing resolution?

I double-checked the concept of 'optical resolution' on Wikipedia.Resolution is (roughly speaking) the ability to distinguish two dots that are close-together as different - the closer the dots can be and still distinguished, the higher the resolution, and the greater detail that can be perceived.

I think perhaps you mean 'sensitivity'. It's the ability to detect weak signals close to perceptual threshold that noise improves, not the detail.

But it is an inherently odd proposition that you can get a better picture of the environment by adding noise to your sensory information - by deliberately throwing away your sensory acuity. This can only degrade the mutual information between yourself and the environment. It can only diminish what in principle can be extracted from the data.

It is certainly counterintuitive to think that, by adding noise, you can get more out of data. But it is nevertheless true.

Every detection system has a perceptual threshold, a level of stimulation needed for it to register a signal. If the system is mostly noise-free, this threshold is a ’sharp’ transition. If the system has a lot of noise, the theshold is ‘fuzzy’. The noise present at one moment might destructively interact with the signal, reducing its strength, or constructively interact, making it stronger. The result is that the threshold becomes an average; it is no longer possible to know whether the system will respond merely by considering the strength of the signal.

When dealing with a signal that is just below the threshold, a noiseless system won’t be able to perceive it at all. But a noisy system will pick out some of it - some of the time, the noise and the weak signal will add together in such a way that the result is strong enough for the system to react to it positively.

You can see this effect demonstrated at science museums. If an image is printed very, very faintly on white paper, just at the human threshold for visual detection, you can stare right at the paper and not see what’s there. But if the same image is printed onto paper on which a random pattern of grey dots has also been printed, we can suddenly perceive some of it - and extrapolate the whole from the random parts we can see. We are very good at extracting data from noisy systems, but only if we can perceive the data in the first place. The noise makes it possible to detect the data carried by weak signals.

When trying to make out faint signals, static can be beneficial. Which is why biological organisms introduce noise into their detection physiologies - a fact which surprised biologists when they first learned of it.