[ExI] singularity models, was RE: Not Immoral to Want to Be Immortal
Jef Allbright
jef at jefallbright.net
Sat Apr 26 17:20:47 UTC 2008
On Sat, Apr 26, 2008 at 7:47 AM, spike <spike66 at att.net> wrote:
> Jef, what I find frustrating about singularity theory is that I have no way
> to use my most powerful tools: mathematical modeling. I use math to
> understand everything that I feel I know about. Without equations, I am
> left trying to describe things with words. I like words, I'm a big fan of
> them, but they don't get the job done. I have yet to see, nor can I
> conceive of how to describe the singularity with variables and good solid
> system of simultaneous differential equations that can be solved to yield
> insights and predictions.
Spike, your response appears symptomatic of the very problem I tried
to emphasize (and which was elided with your characteristic tact.)
Your expectation that the dynamics be modelable in such terms presumes
a context greater than the system of interest. This is the
time-honored traditional approach to Proof of Understanding, and it's
perfectly valid but doesn't scale to describing and predicting the
behavior of complex (and I don't mean complicated) systems.
I'm sure you're familiar with modeling of complex dynamical systems,
such as those involving turbulent flow, but consider that in all such
cases the environment (the context) is assumed to be well-defined.
I'm not saying we should abandon our mathematical models -- indeed,
they become increasingly vital to effective decision-making in an
increasingly complex world -- but that they and their interpretation
must be a qualitative level more sophisticated and necessarily
probabilistic (and I don't mean statistical.)
In its more general sense, prediction is not about saying what
**will** happen, but about realistically constraining the
possibility-space of what may happen. Having a well-defined context
is only a special case.
> Example: engineers study a field of math called feedback and control theory.
I'm quite familiar with feedback and control theory, having worked in
scientific instrumentation close to three decades. All such theory
assumes a well-defined environment, simpler than the system of
interest.
Related to this theme is the observation that a key differentiator
correlated with troubleshooting experience (wisdom) is that
inexperienced troubleshooters will approach a complex problem asking
"what is it?" while more experienced troubleshooters approach in terms
of probabilities of what can be ruled out, until what remains is their
answer.
> Negative feedback is what prevents most physical systems from reaching
> singularities. A speaker/microphone system would explode without negative
> feedback. Aim the microphone toward the speaker, the system amplifies
> random noise until a howl is created, but that howl doesn't keep getting
> louder until the system explodes because of the negative feedback imposed by
> the physical limitations of the system.
>
> I hafta think there must be negative feedback in the singularity, but I just
> don't know what are those mechanisms.
Some pointers of possible interest:
* The IEEE paper I mentioned a week or so ago on growth of value of
networks as n(log n).
* Google 'logistic function'
* Google 'mathematics coevolution'
* Google 'mathematics "self-organization"'
- Jef
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