[Martin Taylor 2006.07.05.17.22]
[From Bryan Thalhammer (2006.07.05.1540 CDT)]
Getting back to PCT, and what Rick said, models are a way of abstracting real events, and mathematical ones work pretty well. What you are saying (?) is that a map is not the real event. I agree. A map is a tool for making predictions regarding real events. You can interact with a model to test it, to see if it works consistently. But the real test [of the controlled perception] happens as an event in the real world. Yes?
The metaphor I use for myself is that the maths is a skeleton. It gives the general structure of what to expect in the real world if the abstraction is done right, but there's no flesh on it, and it's the flesh that provides the actual shape. In simple situations the maths will get you close (there's not much more to be flesh), but most of the time it isn't close enough to rely on without further test (the simplest science is physics, and there, the math is usually close enough to rely on -- but not in biology, except when calculating limiting conditions such as those implied by conservation laws).
Martin
[From Bryan Thalhammer (2006.07.05.1700 CDT)]
Martin,
Yes, the math is the skeleton or engine. And in the note to Marc about the cholera map, it was the basis by which an intervention was suggested, and successfully performed.
Oh, and btw, math involves data vs. narrative that involve verbal descriptions. So by math I mean a dataset of pixels, incidents, paths, etc. So the math gives you that simple to complex skeleton on which to hang the words, instead of the opposite.
Not quite sure why math in biology is that different from that as used in physics, chemistry, etc. Tell us more?
--Bry
> [Taylor 2006.07.05.17.22]
>
>> [Bryan Thalhammer (2006.07.05.1540 CDT)]
>>
>> Getting back to PCT, and what Rick said, models are a way of abstracting real events, and mathematical ones work pretty well. What you are saying (?) is that a map is not the real event. I agree. A map is a tool for making predictions regarding real events. You can interact with a model to test it, to see if it works consistently. But the real test [of the controlled perception] happens as an event in the real world. Yes?
>
> The metaphor I use for myself is that the maths is a skeleton. It gives the general structure of what to expect in the real world if the abstraction is done right, but there's no flesh on it, and it's the flesh that provides the actual shape. In simple situations the maths will get you close (there's not much more to be flesh), but most of the time it isn't close enough to rely on without further test (the simplest science is physics, and there, the math is usually close enough to rely on -- but not in biology, except when calculating limiting conditions such as those implied by conservation laws).
···
> Martin
>
[Martin Taylor 2006.07.05.22.09]
[From Rick Marken (2006.07.05.1845)]
I think a quantitative analysis of all this could be done using the equations for a quasi-static analysis of control described in Powers' 1978 _Psychological Review_ paper. But they could be used only if we have a quantitative definition of efficiency. Maybe I'll give it a shot (using my own definition of efficiency) sometime before I leave for China. It is kind of an interesting question: does the efficiency of control (I would say in terms of how much energy it uses to produce a particular level of control) vary depending on the parameters of control? I would guess that it does. But I'll see if I can come up with a nice, clear analysis (if Martin doesn't come up with one first: hint hint Martin)
I don't know if it's possible in terms of mechanical energy. I'll have to think about it, but I suspect it isn't. It might be possible to do for any specific control problem, though. The issue is that energy involves force, distance, and time, whereas control involves only the opposition to the disturbance. The same degree of control can use quite different amounts of force, depending on the "muscularity" of the disturbance. The biological control system uses quite a lot of energy just to sustain itself, and that enters into the efficiency calculation.
I'm quite stressed for time right now, having got back from two weeks away that provided me with immediate work, plus what got backed up over the two weeks. But I'll think about it.
I will repeat, however, what I said in an earlier message, that evolution and reorganization will ordinarily favour solutions that with greater efficiency provide the same level of control over the same range of environmental situations. If that's true, Jim Dundon's observer will usually see biological control systems as controlling pretty efficiently, even though none of the observed control systems are themselves controlling for efficiency.
Counter to this is the normal antagonism between robustness and efficiency. Systems that are highly efficient usually break when confronted with circumstances outside their design parameters. Evolved systems are usually not THAT efficient -- just pretty efficient.
Now isn't that a nice mathematical description of the situation?
Martin