Random: having a state or value depends on chance.
So you can predict the sum of two die rolls? That isn't uniform. You can predict the position of someone on a snakes and later board on the second turn, after seeing the result of their first turn? That is correlated with the result of the first term.
You can predict the sum of two die rolls with better than an accuracy better than random chance. If you provide a confidence interval, you can provide an exact prediction.
I'm sorry I don't understand the 'snakes and later board' example.
I think Walter Wayne was saying that it is like a drunkard's walk, the whole trajectory is random, but depends on the past history.
jimbob said:
Indeed, and the biggest difference is that an ionisation smoke detector is not a chaotic system. A slight difference in the decay rate leads to a slight difference in the ionisation current, which leads to a slight difference in teh "apparent" smoke density ant the output signal. A slight difference in the gain (transconductance) in the amplifying transistor similarly leads to a slight difference in the sensitivity of the detector, so this is compensated for during factory testing.
With the smoke detector slight differences in inputs lead to slight differences in outputs.
Agreed. With the qualification that the output isn't a slight difference in measured signal, it is strictly 'smoke or no'.
<nitpick>
some smoke detectors do produce an oputput that is a "level of smoke" which is returned to the controller, wheich then assesses whether the whol system is indicitive of a
dangerous fire or a false alarm. For example ambient pollution, or cigarette smoke. In the industry, these are termed smoke "sensors" rather than "detctors" which do only have an alarm/non-alarm output, I have previously worked in (in the fire "detector" and "sensor" development area). </nitpick>
I've got a couple of points here.
#1 Just to be clear I understand this to be from the perspective of the 'history of evolution' or 'path of evolution'. If we're talking about evolution in the sense of how a species change in response to changes in its environment(which may or may not be chaotic or random) this point is inapplicable. (Ie doesn't apply to the argument made from Baysian logic some pages back)
True, and this is where I think a lot of the differences lie.
I have said that in a
stable environment, and over a long enough time, then you don't need to invoke randomness. This
does cover a lot of examples used when discussing how evolution works, for example the advantage of sight.
I would still argue that the
particular adaptations could still be random, e.g. compound eye vs simple eye, position of the retina etc... but the adaptation to the environment would be there.
However this stable environment is only a subset of the situations where evoution occurs, even if it
is the simplest to understand.
#2 The 'consensus' I got from the 'chaotic' thread was that the jury was still out with respect to whether weather was chaotic. Moreover the 'consensus' I got was that we couldn't tell if a system was chaotic unless we are talking about a mathematical model and are in agreement about its quality of fit to the evidence.
There is quite a bit of evidence that it is chaotic, but that is why I started the other thread...
#3 I appreciate your intuition on these issues, but is there any reason you believe these systems are chaotic?
#4 How do you know that these systems are not just complex?
Positive feedback loops tend to produce unstable systems, indeed they are often used to produce oscillators. Ecosystems have lots of positive feedback loops, which would predispose the system to chaotic behaviour.
#5 How do you know that, if these systems are chaotic, that they are sensitive to random inputs?
Because that is how the maths works out. If they depend on position or momentum, they will eventually depend on quantum effects.
#6 What do you contend these inputs are?
Anything that affects the reproductive success of an organism, so including: the weather, asteroid strikes (rarely), competition, availability of mates, fertility, predation, parasites, food supply, territory, water supply, volcanoes (rarely), lightning strikes, etc...
There are many positive feedback loops, one has been hypothesised for the non-recovery of the grand bannks cod fishery. The simple analysis being that the reduced adult cod population has reduced the predation of smaller fish. These smaller fish, in turn prey on the young cod fry. The reduced predation of the smaller fish has increased the predation of the cod-fry, which in turn acts to keep the cod population down.
#7 How do you know that these systems are not constrained by negative feedback in the form of energy limitations and physical landscape for ecosystems, in terms of intertia,viscosity, and energy for weather.
#8 What are the relative scales of the development rate of 'disruptive mutations' vs 'positive feedback' in speciation. How do we know the scales are comparable?
There are obviously negative feedback loops involved in ecosystems as well as positive ones, however looking at the history of evoution
I don't get your question here. "Disruptive" mutations are rare, but they can be significant. If you are talking about geological timescales, then random events become more important in affecting how the developmetnal course of the ecosystem.
If the ecosystem starts to change, then (almost by definition) the organisms in that environment will be less well adapted to the altering environment than they would have been to the previous, stable environment. This would mean that variations are more likely to be eneficial than when the organisms were well-adapted.
Some of the positive feedbaclk loops would be those that frive the evolution of symbiotic relationships, where particular flowers and insects co-evolve.
Earlier on, I described the course of evolution as similar in some respects to a river system, these are often chaotic, and the course can seem stable for long times, but they can also change suddenly. If the topography is steep the change is less likely, if the gradients are shallow, then change is more likely. Similarly, in locally flat regions of the fitness landscape, or minor "saddles", slight changes could tip the evolution of the organism's descendents down different routes.
#9 How do we know that this 'positive feedback' doesn't just affect the speed at which the solution is generated and not the substantive result of the solution.
Your assertions are all well and good, but they're just as hand-wavy as your assertions about chaos theory which were quite vigorously shot down. Unless you can answer these questions with evidence and reason, really all you are saying is that despite the testament of people in the field, you have the strong personal conviction, a feeling, that the results of evolution involve significant chaotic effects. Which, IMO, is terribly unpersuasive.
There is plenty of evidence for discussion of chaotic behaviour in population dynamics and in other areas relevant to evolution.
I would also disagree that the assertions were "vigorously" shot down. I still contend that most physicists think that the timescales for quantum uncertainty to affect the weather is quite short. When I studied physics, the consensus seemed to be about 6-weeks. My
very naive treatment of the numbers came to a conclusion that was not vastly different. Life has existed for over 3-billion years, so that is the sort of timescale that would be needed if random events didn't affect natural selection affecting the weather.
