So my brain is represented in the world represented in my brain.

And the world represented in my brain is represented in the world represented in my brain represented in the world represented in my brain.

And so on ad nauseam.

This sounds like a red herring to me. The representation of the world I have in my brain is very incomplete, and inaccurate even where fully fleshed out. It specifically doesn't contain any but the vaguest and sketchiest notion of how brains work in general, and almost nothing at all about my brain specifically. I very much doubt that this situation is different even for the Steven Pinkers and Susan Greenfields of the world.

It isn't even an hypothetical problem, since the world and your representation of it, and your representation of that representaion wouldn't be the same kinds of thing, even if you had them.

Also, didn't someone say: if the brain were simple enough for us to understand we wouldn't be able to?

Or have I missed the point? -- Keith Braithwaite

It seems you have both the points, Keith: Infinite Regression and Self Representation/Self Understanding. The first is analogous to the video camera taking a picture of its own output. As pointed out, the view we have of our own brains is very hazy, even first time around, so that this 'series' rapidly converges on next to nothing. The second point(s) is best discussed in the context of What Is Reality, which is from where Peter Merel cited it -- pgk

Could you explain how this relates to John Von Neumann? http://ei.cs.vt.edu/~history/VonNeumann.html Or is this not who you mean?

The von Neumann article you reference appears to provide the answer. Take the series of 'brains' and alternatively map each element in the sequence to the dynamic interactions of a fly and a train. The article describes how von Neumann found the solution to this sequence, by summing it in his head.

The only fly in the ointment of this analysis is that the article does not give von Neumann's answer. But, as von Neumann no doubt would have pointed out, the mathematics is simple, it is only life that is difficult.

Perhaps it is this type of analysis that should be described as a Von Neumann Catastrophe ...

Thanks for the explanation, but I'm afraid I still don't follow. The article didn't talk about brains and representations. The point of the fly-between-the-trains problem is that there's an easier way to solve it than summing the series, which you can spot by framing the problem slightly differently. The point of the anecdote in the article was that John Von Neumann was such a math whiz, he actually could sum the series in his head. I suppose these things have something to do with brains and representations, but I can't see how they relate to the story above. Please help! What is the point of the story above? What is the catastrophe?

I was trying to make some sense of the vonNeumann moniker attached to the page. Perhaps Peter Merel could provide his rationale for this choice of title? -- pgk

Von Neumann's catastrophe of the infinite regress was a math demonstration that quantum mechanics entails an infinite regress of measurements before the quantum uncertainty can be removed. It goes like this: any measuring device is itself a quantum system containing uncertainty; a second measuring device, used to monitor the first, contains its own quantum uncertainty; and so on, to infinity, or at least to the end of the experiementer's patience. Here I was addressing the notion on What Is Reality that reality pre-exists distinction. Since reality is taken as the ground of existence, it seems distinctly odd to suggest that reality itself exists ... and it begs the question of What Does Exist Mean. --Pete.

Thanks for the clarification. Perhaps, if I put my slant on a comment above, vonNeumann's catastrophe is in part just an example of Zeno Paradox. However, there may be a distinction. In the quantum 'topology' the standard process of mathematical convergence for an infinite series becomes meaningless. Once the required degree of approximation is less than quantum uncertainty (a loose phrase as I use it) either the series can be deemed to have converged after a finite number of steps, or the rest of the series becomes unmeasurable/unobservable or collapses to a 'point' on measurement.

And this provides part of a possible answer to the main point of reality/distinction, chicken/egg. Even if there is a required sequence reality->distinction->reality and so on, could it not take place within the uncertainty 'space' and hence be considered to have taken place at the 'same' time, at least in measurable terms and at least after only a finite number of iterations? Maybe this is the way we are conscious - within some quantum indeterminable fleeting instance there is a space/time lull that allows us to 'resolve' these paradoxes and we find the truth or at least make sense of what it is in a way that trudging computability will never allow us.

And thinking about the experimenter, is losing patience merely hitting the quantum indeterminacy in our lives? And if so, why is my personal Planck constant so much larger than nitpicking fools, and so much smaller than waffling management? -- pgk

Isn't this "observer" view of QM a bit old world anyway? These days, if I remember correctly, the interest is in the physical proceses that result in decoherence. I'll leave to Penrose the question of where, if at all, consciousness comes into it. -- Keith Braithwaite

[ Delete Me: Bad English Alert - 'an hypothetical'. -- "Frick", 15 Jan 2001 20:48

Hey, this is a wiki. If you see a boo-boo, feel free to fix it. However, I don't think this is a boo-boo. There are different conventions for a/an before h. ]

An example of Lurker Defenestration.