Does Neo-Darwinian evolution require change ?

I assume you're talking about the human genome. The estimates for the functional fraction of the human genome that I'm familiar with started around 100%, dropped to 20%, dropped to "at least 5%", and are now hovering in the range of 6 - 10%. I'm not aware of any secular trend in this estimate.

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Right now, anyone can safely say that at least 30% of the genome is functional.

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Well, you can safely say it in the sense that no one will throw a brick through your window for doing so, but I don't know of any geneticists who think that.

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What I said concerning ENCODE was simply that it ''opened up the possibility'' that the entire genome had a function. I'm not saying it proved anything, and I certainly know the difference between functional and transcribed.

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Yeah, but the entire genome almost certainly isn't functional, and even their estimates for the transcribed fraction were probably much too high (at least if what the people who do that sort of thing have told me is correct).

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Therefore, all I'm saying is that when seeing how genetics has been unravelling the secrets of previously thought ''junk DNA'', and how more evidence comes to open the possibility that maybe the whole genome is functional, I think it is the idea that any part of the genome is junk that should be regarder with great skepticism, not the other way around.

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Geneticists keep finding functional bits of noncoding DNA, and the bits they keep finding constitute only tiny fractions of the genome. Meanwhile, vast swathes of the genome look and act exactly like junk: transposons, pseudogenes, and the like, almost all showing no sign of selective constraint. The fact that a single experiment, using rather dubious methodology, concluded that much of the genome is transcribed shouldn't weight very heavy in your thinking.

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Draw a circle around the original individual and then draw the same size circles around a point on the circumference of that circle. The first circle represents the range of possible mutations away from the position of the parent individual, the second is the possible range of mutations away from one of the outermost the offspring -- how much of that outer offspring circle is inside the parent circle? I get 39.1%, which I do not count as extremely improbable, and that is the worst case.

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I haven't been following the argument here, but this analogy is not a good one. Mutations are, to a first approximation, orthogonal to one another, so you should be working in a much higher dimensional space. Imagine the 50 mutations to be fifty unit steps in 50 of perhaps a million dimensions. The next 50 mutations will be in another 50 random dimensions. The probability of heading back toward the peak (neglecting selection) is tiny.

Because the point of the analogy was clear, regardless of what argument it was deployed in, and that point was based on an error. You make the error explicit below. Yes, I gathered that. No, you can't. That's why your analogy is a bad one. My point was that there are many, many orthogonal directions to take away from fitness. In biological terms, there are an enormous variety of ways that you can screw up an organism which are nearly independent of one another; even if you already have mutations that cause some of those defects, the next set of mutations is still overwhelmingly likely to cause new defects, not to fix the old ones. Just think about how many sites there are for potential deleterious mutations in the genome. If you flip 50 of them to become sites for potential beneficial mutations (which is what your first round of mutations does), how much have you changed the overall number of deleterious sites? I know. But your analogy was about the selective landscape, not about how populations respond to selective pressures. I try.

No, I've always been this pedantic. Of course there are many directions that can take you toward higher fitness. But if the offspring are anywhere in the vicinity of the fitness peak (as real organisms almost always are), there are far more directions taking you away. This is the point your 2-d analogy gets wrong. In two dimensions, a random step in any direction is almost as likely to take you toward a specified point as it is to take you away (something you noted in your original use of the analogy). As the dimensionality increases, the probability decreases -- and fitness landscapes have very many dimensions indeed.