Randall R Schulz wrote:
> On Friday 01 February 2008 19:18, Francis McCabe wrote:
>> ...
>>
>> Being deterministic is not the same as being predictable. Chaos
>> Theory/ Fractals tells us that; as does the weather.
>
> Chaotic behavior occurs only in continuous systems. Digital computers
> are discrete, and that is not an incidental or unimportant difference. (01)
But "discrete" digital systems can be programmed to respond to events
occuring in the outside world to the extent that they trigger sensors to
emit digital signals. That world is continuous, as is the change in
current and voltage in many sensors. As a consequence, if you scan the
same image twice, you don't necessarily get identical bit patterns from
the sensors, and algorithms that operate on the resulting image,
although they are completely deterministic, do not generate identical
results. In some cases, for example, the algorithm recognizes a feature
in one scan and not in another. (02)
> Digital systems don't exhibit the phenomena associated with nonlinear
> dynamics. There is no "sensitive dependence on initial conditions,"
> no "strange attractors," etc. (03)
In one of my earlier careers, I was a data communications expert. In
all real-time programming, and particularly communications, you get all
kinds of event patterns, and it is very typical to find "race
conditions" in deterministic code: If X occurs before Y, the software
does A; if X occurs after Y, the software does B. So first, when the
events occur nearly simultaneously, you get different results depending
on the exact timing. Second, it is not whether X occurs before Y but
rather whether X is detected in the algorithm before Y that determines
whether the result is A or B. (04)
[In one memorable case, a manufacturing workstation controller wired
into the factory broadband network had a simple 2-state detector (a
microswitch) in a parts receiving station. As soon as a tray of parts
was fed into the receiving station, it tripped the detector and the
workstation took action, and in some cases that action involved
communication with a higher-level manufacturing management system. When
the Automatic Guided Vehicle delivering the materials initiated an
unload, it informed the management system as well, unfortunately by a
very early wireless technology at 1200 bits per second. So when the
workstation asked (at 10 Mbps) the management system about the parts
that had just arrived, the management system was unaware that any had.
Of course, the AGV unload had to happen before the workstation detected
the insertion, but in the management system, the notifications of the
two events occurred out of order, and the software took the wrong action
(in effect, it said to the workstation: "there are no such parts", which
caused serious problems with the intended job).] (05)
The problem here is that people tend to think of digital computer
systems as being a single processor with a single, algorithmically
determined, "thread of control". The reality is that all modern
computational systems involve multiple communicating processors, even
inside the box, and many interesting systems involve communication among
multiple autonomous agents across boxes, intentionally and
unintentionally. (Unintentional communication occurs when some agent
takes a physical action that is detected by another.) (06)
And there is a related behavior that I think of as "the Heisenberg
effect" -- attempting to acquire information from a system provides
information and alters the system. When you access a web page, the fact
that you accessed it becomes part of the knowledge held (and possibly
used) somewhere on the Web. (07)
Now, algorithmic parsing of a given natural language text is perforce
deterministic, and even when the algorithm is Bayesian and covers a
corpus of multiple texts, it is still deterministic if the corpus is
fixed or carefully controlled. But if you allow the corpus to change
dynamically, the results of the deterministic algorithms are not
deterministic, and if reasoning algorithms are then employed, the
results are chaotic -- repeating the same experiment 3 seconds later can
produce contradictory results. Think of trying to date a piece of
ancient pottery while the Egyptologists are adding new timelines to the
literature, revising some respected sources, and burning "outdated" books. (08)
-Ed (09)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (010)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (011)
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