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I debated whether or not to ask this question here or on History. I concluded to try it here because I'm fairly sure it was said by someone like Arthur C. Clarke or Isaac Asimov, and a great many of their fans will be here. However, if this is better suited for History, I'm not opposed to migrating it.

A very long time ago I read a phrase. I remember that phrase to be...

The only way to model an infinitely complex system is with that system, itself.

After so many decades, that's most likely a paraphrase of what I read. This is pretty much proven by the fact that it doesn't appear in any form I can think of via Google. I am searching for the original quote and an attribution. Does anyone know?

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    I don't know, but online searches for books that discuss the modeling of complex systems keep coming up with John von Neumann as a source. Dec 28, 2021 at 0:32
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    "The map is not the landscape" is a common maxim in geography and in the sciences. There is an extended corollary: if the map had all the detail of the landscape, it would be the landscape.
    – Lexible
    Dec 28, 2021 at 4:58
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    That's very likely a mis-quote, as any person that deals with such things would also know that no system is infinitely complex.
    – PcMan
    Dec 28, 2021 at 10:21
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    No one who truly understands what modelling is would say this. The whole point of modelling is to study specific aspects of something through complexity reduction. Dec 28, 2021 at 20:27
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    @RBarryYoung That's an intersting observation, but I'm an electrical engineer who's lived his life modeling things. There comes a point where (a) modeling won't provide the desired level of resulting detail and (b) that as things get smaller, modeling gets harder if you want to take full advantage of scale. So, I hope you'll forgive me, but I wonder how much modeling you've done in your career.
    – JBH
    Dec 29, 2021 at 19:56

3 Answers 3

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I think this comes from von Neumann's Hixon Symposium Talk at Pasadena in 1948. It is described in "Theory of Self-Reproducing Automata", edited and compiled by Arthur W. Burks, pages 53 - 54. In the lecture the complex behavior of the human eye and nervous system was described as a finite (von Neumann) automaton, and

Von Neumann seems to suggest that possibly the simplest way to describe the behavior of this finite automaton is to describe the structure of the automaton itself

and went on to suggest that other attempts to describe it will be more complicated than the system itself. The exact phrase from the talk is:

It is not at all certain that in this domain [i.e. systems of high complexity] a real object might not constitute the simplest description of itself, that is, any attempt to describe it by the usual literary or formal-logical methods may lead to something less manageable and more involved

Von Neumann reached this conclusion by appealing to Godel's theorem. Some comments of Godel on this are then given, where he tries to interpret this statement, but unfortunately he never had the chance to discuss it directly with Von Neumann before his death.

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    I find myself unable to select a single best answer. I believe Clara identified the ultimate source of the idea and TheHammer identified where I was originally exposed to it. Would that I could select both answers! Thank you to you both!
    – JBH
    Dec 29, 2021 at 20:01
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    I was at first puzzled that JvN would say this in 1948, because it seemed to me that Kolmogorov's work on algorithmic complexity had already established this point rigorously and formally. But I was surprised to learn that Kolmogorov's work wasn't published until the 1960s! Dec 30, 2021 at 18:23
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I believe this is from Asimov's Prelude to Foundation (1988) chapter 32;

"The LPS - that is, 'the least possible simulation' - gains in complexity faster than the object being simulated does and eventually the simulation catches up with the phenomenon. Thus, it was established thousands of years ago that the Universe as a whole, in its full complexity, cannot be represented by any simulation smaller than itself."

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    I find myself unable to select a single best answer. I believe Clara identified the ultimate source of the idea and TheHammer identified where I was originally exposed to it. Would that I could select both answers! Thank you to you both!
    – JBH
    Dec 29, 2021 at 20:01
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In his book The Island author Des Greene says:

To model complexity we can't short-circuit any step - each step must be enacted individually. This means in effect that complexity can never be modeled other than by itself.

Is this what you're looking for?

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    Probably a little too recent?
    – Spencer
    Dec 28, 2021 at 2:33

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