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Comment by jcr | Hacker News Reader

The trouble I have with Metcalfe's Law and similar is that all of them are far too optimistic. Most English speakers have heard the phrase, "Point of diminishing returns," and such points do exist. Worse yet, there's also the phrase "Collapse under its own weight," describing the point where something got so big or widespread to retain its integrity, so its groth essentially harmed itself and failed.

If you look around, you'll see this kind of diminishing returns and self destruction in a lot of different places, from "social" environments like this forum, to your over-flowing email box, to the constant interruption of your cell phone.

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It is definitely true that a vocal minority of users are destructive to any network they find themselves in. Examples of negative users include things like trolls and spammers.

Another problem is that the natural desire of the people running the network to monetize it creates incentives to weaken the experience.

Both of these can lead to sub-linear growth in overall value as a network grows. But measuring value is already hard. Modeling all of the ways to screw up a network is even harder, and I doubt that there is any simple approximate general law that describes it.

Same here. I've never seen a simple general law, rule, or even guideline to accurately predict the stagnation and decline of complex systems, or more accurately, growth-decay cycles. It's a bit like knowing the sun regularly rises somewhere over there (jcr points vaguely towards the "East-ish" direction) but having no idea why it does, and hence, having no way to accurately predict where it will rise. Trying to figure it out can be both fascinating and frustrating.

There was a mathematician or scientist who said, "To measure something is to know it," but unfortunately, I can't remember his name. Anyhow, I agree our inability to accurately measure and model (or even notice) a lot of the factors involved in complex systems results in our inability to describe or predict them.

BTW, I kind of look at "measuring value" and "modeling ways to screw up the network" to be mostly the same thing. In one case you're identifying, measuring, and modeling the beneficial (value-increasing) factors, and in other, you're identifying, measuring, and modeling the harmful (value-decreasing) factors. --I have a funny feeling that I've missed some thing obvious, so did I misunderstand your statement?

Our inability to accurately measure and model (or even notice) a lot of the factors involved in complex systems results in our inability to describe or predict them

Structured processes | SDIC [1] vs Resolution is a legitmate issue. Not at all processes can be modeled the same, like a "complicated" but ultimately simple one. In the latter, Logic helps "bridge" the resolution issues. Many deterministic processes cannot be brute-forced, though.

[1] ie, displaying Sensitive dependence upon initial conditions; just how accurate is your measure and can it ever be accurate enough to deduce an originating function?

Edit: If I may expand on the point above. Which may seem cryptic.

Complex systems are interisting in that they can be both predictable (in theory) and not predictable (in practice). What's more is that they can be mischaracterized by analyzing the data. Ie, this data is a mess, it must me unpredictable. There are a whole class of deterministic processes which generate these types of results. Whereas a normal, linear process can be infered from medium/high resolution data, even with higher-resolution data we can't infer the underlying logic of the complex system. We may, as a result, either oversimplify the model or proclaim the data to not support any deterministic process at all. The classic example is the class of processes that exhibit sensitive dependance upon initial conditions. ie, variations on the notion of deterministic Chaos. Their sesitivity is such that the resolution of the dataset required to deduce or infer the origination function would never be feasible if it was anything other than complete. Whereas, with deterministic processes that are more traditionally tractable, you can make progress in your knowledge with data-sets of increasing resolution. ie, you can run a regression to infer y=mx+b or a monte-carlo to fit a gaussian curve or what not. But you cannot "brute" force a fit to a choatic process from a montecarlo, becaue you will never have enough resolution nor enough precision in your data set to infer an origination function. [1]

The summary thought is tha sometimes gaps in data can be bridged with higher-level logic or heristic, but this is not always possible (either in theory or practice). Yet, we should not infer a problem is unsolvable or untractable just because of this. =D

[1] http://en.wikipedia.org/wiki/Chaos_theory#Sensitivity_to_ini...

Some complex systems can be described using simple laws e.g., complex interactions of gas molecules can be described using thermodynamics with aggregate terms such as temperature, pressure.

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