Low carb diets

"Wayne S. Hill" wrote in message
...
Elzinator wrote:

"OmegaZero2003" wrote...

This is very similar to the issues facing cancer
researchers. Three very different mechanisms/theories using
separate processes all interacting to produce the endpoint.

Biological systems are more complex than most realize:
feedback loops, negative and positive regulators, redundant
and overlapping pathways, etc.

And, they're all nonlinear.

Well - theyt are not *all* non-linear!

That is, they are rife with
thresholds and saturation effects. This makes them very, very
(very) complicated, but has a lot to do with their effectiveness
and robustness.

The property of non-linearity has less to do with properties of robustness
(robustness connotes graceful degradation upon error, no single point of
failure and survival in nonhomogeneous scenarios/contexts/environments) and
effectiveness (effective for what?), than that of being dynamical and
complex.

In fact, it is mathematically more problematic for a non-linear system to
hold coherence (e.g., biodynamics, soliton quantum lattices and soliton
binding energies), than for a linear system to do so in the face of
perturbation.

However, what non-linear dynamical systems *do* exhibit vs linear systems,
is the propensity for forming function/properties that are emergent,
synergistic or both; i.e., unable to be cast into the froth of the
eliminative materialists and reductionists with any expectation of success
due to the inforamtion_lossy process that reduction is.

Now, it is the case that certain non-linear systems have the robustness and
effectiveness properties you mention; but if you go deep into this matter, I
think you will find that such system have subsystems (linear) that enable
the robust functionality (you do not want either a far-from-equilibrium
system or a non-linear system in charge of foundational biophysics for
example, when linear feedback will suffice), or the effectiveness of the
system in an environmental context.

And it is the overall systemic complexity of systems that happen to have
non-linear subsystems, that more determines their funtional effectiveness.
It is the complexity of emergent dissapative structures that will lead to
robustness and effectiveness directly, not the property of having processes
that are describbale using PDEs/DDEs/etc *per e*.

I.e., ther are lots non-linear systems that are either chaotic, far-from
equlibrium, or do not exhibit either robust dynamics or effectiveness in
dealing with perturbation.



See

Nonlinear Science - Emergence and Dynamics of Coherent Structures by Alwyn
Scott (A master in this area - I have spoken with him a lot over the years.)

http://www4.oup.co.uk/isbn/0-19-850107-2#contents





--
-Wayne

"Elzinator" wrote in message
...


I don't agree. There is a threshold where insulin tissues can be
saturated, but a healthy individual would have to eat a buttload of
carbs ...

Is this what a tossed salad means on the menu at Gay nightclubs?

OmegaZero2003 wrote:

"Wayne S. Hill" wrote...
Elzinator wrote:
"OmegaZero2003" wrote...

This is very similar to the issues facing cancer
researchers. Three very different mechanisms/theories
using separate processes all interacting to produce the
endpoint.

Biological systems are more complex than most realize:
feedback loops, negative and positive regulators,
redundant and overlapping pathways, etc.

And, they're all nonlinear.

Well - theyt are not *all* non-linear!

Actually, if you want to argue mathematics, they are *all*
nonlinear, because linearity is such a special case that is
never achieved in practice. 8-p

I won't argue the rest here, except to say that my statement
stands: the threshold and saturation phenomena so common in
biological systems are related to the robustness of their
operation.

--
-Wayne

"Wayne S. Hill" wrote in message
...
OmegaZero2003 wrote:

"Wayne S. Hill" wrote...
Elzinator wrote:
"OmegaZero2003" wrote...

This is very similar to the issues facing cancer
researchers. Three very different mechanisms/theories
using separate processes all interacting to produce the
endpoint.

Biological systems are more complex than most realize:
feedback loops, negative and positive regulators,
redundant and overlapping pathways, etc.

And, they're all nonlinear.

Well - theyt are not *all* non-linear!

Actually, if you want to argue mathematics, they are *all*
nonlinear, because linearity is such a special case that is
never achieved in practice. 8-p

AND I LOVE to argue or debate or discuss Mathematics. Why, me and my trusty
Mathematica app have been through many wars together. Akk Steven Wolfram
about what that might mean.

You must be dreaming of another dimension.

Lineararity and non-linearity are different concepts *in principle*.

Qualitatively.

In practice as you say, given that measurement is an approximation, and
given that linearity lay on one extreme of a spectrum and total (what ever
that can mean), the other extreme, it may be the case that all of nature
exhibits non-linearity in the various processes that constitute its form and
function.

However, given category logic, one can see that at one point some distance
off the non-linear extreme to the extreme, would constitute "non-linearity"
in a given context. Ditto linearity.

That is where the principles play a part - in determining where to place the
points and what to consider in placing thouse points Now, it is likely a
tuplpe of considering complexity. Indeed, in practice, if you are
considering very low level desciptions (in terms of particle physics), one
need only look at the Lagrangian, for a complex system, and visualize that
alongside several other system-characteristic_describing "equations", and
one has some work to do!



I won't argue the rest here, except to say that my statement
stands: the threshold and saturation phenomena so common in
biological systems are related to the robustness of their
operation.

Related perhaps - but correlation DNE cause or a particularly close
relationship in any dimension. But I also note that you say it is the
robustness of the system is relarted to some "threshold and saturation
phenomena".
That is different than your first postulation. Which was:

"And, they're [biological systems in nature] all nonlinear. That is, they
are rife with
thresholds and saturation effects. This makes them very,
very (very) complicated, but has a lot to do with their
effectiveness and robustness."

That non-linearity itself has a lot to do with thier effectiveness and
robustness.

Perhaps you can elaborate. I would like to know what you thin thresholds
and saturation effects have to do with linearity such that they help
constitute a property or process of robustness and effectiveness. Note that
specifying the system/domian will help establish criteris with which to
robustness and effectiveness can be defined and measured.




thresholds and saturation effects. This makes them very,
very (very) complicated, but has a lot to do with their
effectiveness and robustness

I agree with your implicate approval of Elzi's take on such systems in
general though.





--
-Wayne

OmegaZero2003 wrote:

"Wayne S. Hill" wrote:

Actually, if you want to argue mathematics, they are *all*
nonlinear, because linearity is such a special case that is
never achieved in practice. 8-p

AND I LOVE to argue or debate or discuss Mathematics. Why,
me and my trusty Mathematica app have been through many wars
together. Akk Steven Wolfram about what that might mean.

Go argue it with him. Some people think he's really onto
something, but I have my doubts.

You must be dreaming of another dimension.

I see dead dimensions.

Lineararity and non-linearity are different concepts *in
principle*.

Qualitatively.

In practice as you say, given that measurement is an
approximation, and given that linearity lay on one extreme
of a spectrum and total (what ever that can mean), the other
extreme, it may be the case that all of nature exhibits
non-linearity in the various processes that constitute its
form and function.

However, given category logic, one can see that at one point
some distance off the non-linear extreme to the extreme,
would constitute "non-linearity" in a given context. Ditto
linearity.

OK, you can *sometimes* view a complex system as quasi-linear
around an operating point (but in some systems this is
literally useless), but even such systems can only be viewed
as piecewise linear. Ultimately, the system changes as you
move away from the operating condition, so what has
linearization taught you?

I won't argue the rest here, except to say that my
statement stands: the threshold and saturation phenomena
so common in biological systems are related to the
robustness of their operation.

Related perhaps - but correlation DNE cause or a
particularly close relationship in any dimension. But I
also note that you say it is the robustness of the system is
relarted to some "threshold and saturation phenomena".
That is different than your first postulation. Which was:

"And, they're [biological systems in nature] all nonlinear.
That is, they are rife with
thresholds and saturation effects. This makes them very,
very (very) complicated, but has a lot to do with their
effectiveness and robustness."

No, you're misreading me. I said the same thing both times.

That non-linearity itself has a lot to do with thier
effectiveness and robustness.

It does, but the nature of the nonlinearity has a lot to do
with it.

Perhaps you can elaborate. I would like to know what you
thin thresholds and saturation effects have to do with
linearity such that they help constitute a property or
process of robustness and effectiveness.

I really don't want to get into this too deeply (not why I
come here), but threshold and saturation phenomena remap an
infinite range of possibilities into a modest finite range.
Since a biological system can only act within such a range,
this permits the system to respond to very broad ranges of
environments. The system does this by employing different
mechanisms or strategies in different ranges of external
influence (with each mechanism triggered by its own threshold,
and limited by saturation). For example, for a room-
temperature environment, the body maintains core temperature
using different strategies than in very cold or very hot
conditions.

Note that this is what makes neural networks into
computational engines. Without threshold and saturation
phenomena, a NN would be useless.

--
-Wayne

"Wayne S. Hill" wrote in message
...
OmegaZero2003 wrote:

"Wayne S. Hill" wrote:

Actually, if you want to argue mathematics, they are *all*
nonlinear, because linearity is such a special case that is
never achieved in practice. 8-p

AND I LOVE to argue or debate or discuss Mathematics. Why,
me and my trusty Mathematica app have been through many wars
together. Akk Steven Wolfram about what that might mean.

Go argue it with him. Some people think he's really onto
something, but I have my doubts.

I would not argue with Steve; he is onto something. He put it all together
and formulated another view of reality consistent with certain other current
views, yet enabling a look at complexity_from_simplicity that has heretofore
not been appreciated in its scope of applicability.


You must be dreaming of another dimension.

I see dead dimensions.

Dimensions see multiple dead yous.


Lineararity and non-linearity are different concepts *in
principle*.

Qualitatively.

In practice as you say, given that measurement is an
approximation, and given that linearity lay on one extreme
of a spectrum and total (what ever that can mean), the other
extreme, it may be the case that all of nature exhibits
non-linearity in the various processes that constitute its
form and function.

However, given category logic, one can see that at one point
some distance off the non-linear extreme to the extreme,
would constitute "non-linearity" in a given context. Ditto
linearity.

OK, you can *sometimes* view a complex system as quasi-linear
around an operating point (but in some systems this is
literally useless), but even such systems can only be viewed
as piecewise linear. Ultimately, the system changes as you
move away from the operating condition, so what has
linearization taught you?

I won't argue the rest here, except to say that my
statement stands: the threshold and saturation phenomena
so common in biological systems are related to the
robustness of their operation.

Related perhaps - but correlation DNE cause or a
particularly close relationship in any dimension. But I
also note that you say it is the robustness of the system is
relarted to some "threshold and saturation phenomena".
That is different than your first postulation. Which was:

"And, they're [biological systems in nature] all nonlinear.
That is, they are rife with
thresholds and saturation effects. This makes them very,
very (very) complicated, but has a lot to do with their
effectiveness and robustness."

No, you're misreading me. I said the same thing both times.

I copied and pasted your original statement.


That non-linearity itself has a lot to do with thier
effectiveness and robustness.

It does, but the nature of the nonlinearity has a lot to do
with it.

What does that mean?


Perhaps you can elaborate. I would like to know what you
thin thresholds and saturation effects have to do with
linearity such that they help constitute a property or
process of robustness and effectiveness.

I really don't want to get into this too deeply (not why I
come here), but threshold and saturation phenomena remap an
infinite range of possibilities into a modest finite range.
Since a biological system can only act within such a range,
this permits the system to respond to very broad ranges of
environments.

The possible system states have little to do with whether a system is linear
or non-linear.

However, complextity is all about such.

The system does this by employing different
mechanisms or strategies in different ranges of external
influence (with each mechanism triggered by its own threshold,

I agree with this. But how does that (threshold and saturation) affect
robustness and saturation directly. They are parameters constraining
response yes and I get your point here, but a response to a perturbation
using, say, Green's Theroem to determine such (where the result of solved
SPDEs will eventually converge to zero - meaning the system will reach a
minima on a mapping - energy/complexity/activity/etc), in terms of its
robustness to that perturbation (ability to so converge/relax), will not
have threshold and saturation terms in those equations. Similarly for the
effectiveness parameter(s) (again, in tems of? meeting a goal (if an
intensional system), surviving an environment?) . If what you mean *is* a
system's effectiveness in surviving perturbations of an environment without
becoming unstable, there are aharmonic mutivibrator-characterized systems
that can tend to chaos or to stable systems with zippo to do with. There are
many other complex systems that do not reach such extrema (saturation) in
their response, nor are they especially threshold-based system. For example,
the brain can detect one photon of light (via the VC) when such impinges
upon a photoreceptor. That is the smallest threshold one can imagine - a
pseudo-infinitely-small threshold in the *sense* that it is representative
of the quanta of em energy. No telling if any brain has actually detected
*only* one photon at a "time" of course, but the point is one of
threshold-based systems. You have to make a quantum leap to get to that
threshold arr, arr!

There are also discontinuous processes that "jump" right over "thresholds".



Can you point me to a ref. where you are reading/getting this relationship
from?


and limited by saturation). For example, for a room-
temperature environment, the body maintains core temperature
using different strategies than in very cold or very hot
conditions.

Note that this is what makes neural networks into
computational engines.

That is one level of description - or -one view of what brain does among
several. I have a bit of experience constructing ANNs for process control
and there are levels of description of brain that are not also
characterizable as a TME (Turing Machine Equivalent).



Without threshold and saturation
phenomena, a NN would be useless.

Threshold is apparent in the neuronal characterization of all-or-nothing
firings (which itself is a function of humongous complexity); however, that
one aspect of the messenger processes (first or second) of the brain.

I cannot see where it has the import ascribed WRT robustness or
effectiveness (towards a goal for example).

Saturation is an example of an extrema - a perturbation causing a behavior
point, and subsequent behavior points that are the same or similar magnatude
until the system relaxes. The system simply has no differential response to
continuing stimula.

Again, this is orthogonal to robustness and effectiveness of a system (in
terms of - we have not defined except as my intial take on what each means
earlier.

Here is another thought. Man-made complex systems are engineered, usually,
to clamp to a safe value(s), all those parameters that may compromise safety
or efficiency/waste-control. That, and the other characteristics I mentioned
(no single point of failure, graceful degradation etc.) make a system robust
(in the face of error or failure). Threshold and saturation are not part of
that consideration except as knowledge that can be employed to determine
startpopints (states), endpoints (end states), and the PID coefficients
affecting operation. When a P/I/D/PI/PD/PID process goes awry, the PID and
any cascaded processes/points to which it is related/connected get reset to
some clamp value(s) and a good system will transfer control to simple
LL-based controllers and/or simple interlocks completely divorced from the
other control system (isolatability is another aspect of robustness).

A good ref on all of this is the classic N. Weiner's Cybernetics Second
Edition: or the Control and Communication in the Animal and the Machine

Any good book on control systems theory incorporating the good ole PID
controller strategy should give more insight into the parameters affecting
system control, especially systems with feedback.



--
-Wayne

"Wayne S. Hill" wrote in message
...
OmegaZero2003 wrote:

"Wayne S. Hill" wrote:

Actually, if you want to argue mathematics, they are *all*
nonlinear, because linearity is such a special case that is
never achieved in practice. 8-p

AND I LOVE to argue or debate or discuss Mathematics. Why,
me and my trusty Mathematica app have been through many wars
together. Akk Steven Wolfram about what that might mean.

Go argue it with him. Some people think he's really onto
something, but I have my doubts.

You must be dreaming of another dimension.

I see dead dimensions.

Lineararity and non-linearity are different concepts *in
principle*.

Qualitatively.

In practice as you say, given that measurement is an
approximation, and given that linearity lay on one extreme
of a spectrum and total (what ever that can mean), the other
extreme, it may be the case that all of nature exhibits
non-linearity in the various processes that constitute its
form and function.

However, given category logic, one can see that at one point
some distance off the non-linear extreme to the extreme,
would constitute "non-linearity" in a given context. Ditto
linearity.

OK, you can *sometimes* view a complex system as quasi-linear
around an operating point (but in some systems this is
literally useless), but even such systems can only be viewed
as piecewise linear.


BTW, as a PS to my other answer post, here are some linear systems.

- those characterizable by linear algebra. there are lots of these!
- Hamiltonian oscillators and like systems. (the direction field
specifically)
- continuous-time systems like electrical networks, many mechanical systems
- any discrete system with a transfer function whose input, response and
output functions depend on one variable
- any systems preserving homogeneity (output proportional to input) and
superposition (a way of combining linear functions such that the result is a
linear function)

Even non-deterministic systems can be modeled using statistics for linear
dynamics.

But the main point to not be belabored is that there are linear systems on
nature and manmade (1)

Most systems *are* non-linear but some of those are characterizable using
linear methods to some degree of accuracy; you did make something like this
point.

(1) Schwarz, Ralph J. and Friedland, Bernard, 1965, Linear Systems, New
York: McGraw-Hill Book Company, 521 pp.

On Sun, 21 Dec 2003 06:29:45 GMT, "OmegaZero2003"
wrote:

BTW, as a PS to my other answer post, here are some linear systems.

- those characterizable by linear algebra. there are lots of these!
- Hamiltonian oscillators and like systems. (the direction field
specifically)
- continuous-time systems like electrical networks, many mechanical systems

Only simple RLC electrical networks fall into this category. And even
then, it's just a theoretical assumption over the useful operating
range. Too much current or voltage or flux will flux up your circuit.
Linear electrical networks only exist on paper.

- any discrete system with a transfer function whose input, response and
output functions depend on one variable
- any systems preserving homogeneity (output proportional to input) and
superposition (a way of combining linear functions such that the result is a
linear function)

Even non-deterministic systems can be modeled using statistics for linear
dynamics.

But the main point to not be belabored is that there are linear systems on
nature and manmade (1)

Most systems *are* non-linear but some of those are characterizable using
linear methods to some degree of accuracy; you did make something like this
point.

(1) Schwarz, Ralph J. and Friedland, Bernard, 1965, Linear Systems, New
York: McGraw-Hill Book Company, 521 pp.

---
Proton Soup

"If I drink water I will have to go to the bathroom and
how can I use the bathroom when my people are in bondage?"
-Saddam Hussein

Proton Soup wrote:

"OmegaZero2003" wrote:

BTW, as a PS to my other answer post, here are some linear
systems.

- those characterizable by linear algebra. there are lots
of these! - Hamiltonian oscillators and like systems. (the
direction field specifically) - continuous-time systems like
electrical networks, many mechanical systems

Only simple RLC electrical networks

and their analogs in other domains

fall into this category.
And even then, it's just a theoretical assumption over the
useful operating range. Too much current or voltage or flux
will flux up your circuit. Linear electrical networks only
exist on paper.

Exactly. They're (essentially) linear in a linear range.

--
-Wayne

OmegaZero2003 wrote:

"Wayne S. Hill" wrote...
OmegaZero2003 wrote:

AND I LOVE to argue or debate or discuss Mathematics.
Why, me and my trusty Mathematica app have been through
many wars together. Akk Steven Wolfram about what that
might mean.

Go argue it with him. Some people think he's really onto
something, but I have my doubts.

I would not argue with Steve; he is onto something. He put
it all together and formulated another view of reality
consistent with certain other current views, yet enabling a
look at complexity_from_simplicity that has heretofore not
been appreciated in its scope of applicability.

That's not clear to me.

No, you're misreading me. I said the same thing both
times.

I copied and pasted your original statement.

I must have been unclear the first time, because I intended
the same meaning both times.

That non-linearity itself has a lot to do with thier
effectiveness and robustness.

It does, but the nature of the nonlinearity has a lot to do
with it.

What does that mean?

Nonlinearity can arise in many different forms. Aside from
quadratic/cubic forms, which you might call "local"
nonlinearities (because the "slope" of the interaction varies
locally), the global behaviors of threshold and saturation
phenomena are common themes in biological systems.

Perhaps you can elaborate. I would like to know what you
thin thresholds and saturation effects have to do with
linearity such that they help constitute a property or
process of robustness and effectiveness.

I really don't want to get into this too deeply (not why I
come here), but threshold and saturation phenomena remap an
infinite range of possibilities into a modest finite range.
Since a biological system can only act within such a range,
this permits the system to respond to very broad ranges of
environments.

The possible system states have little to do with whether a
system is linear or non-linear.

Au contraire. If a system is linear, it must accommodate an
infinite range of input variables linearly. Thus, the output
range has to be of infinite extent, and cannot exhibit
different types of states.

However, complextity is all about such.

You've got to be careful here. I take it you're referring to
complex dynamical systems that exhibit self-organizing so-
called emergent behaviors. A mass of nitrogen molecules is a
counter example: it never does anything "emergent", and so
doesn't (normally) have distinguishably different states.
That is, given N molecules in a box of size V and temperature
T, it exerts a pressure P. This varies in a simple and smooth
manner from above the boiling point to the neighborhood of
dissociation. The difference between a "simple" complex
system and one capable of self-organization is the way it
approaches equilibrium in the face of large disequilibrium.

The system does this by employing different
mechanisms or strategies in different ranges of external
influence (with each mechanism triggered by its own
threshold,

I agree with this. But how does that (threshold and
saturation) affect robustness and saturation directly. They
are parameters constraining response yes and I get your
point here, but a response to a perturbation using, say,
Green's Theroem to determine such (where the result of
solved SPDEs will eventually converge to zero - meaning the
system will reach a minima on a mapping -
energy/complexity/activity/etc), in terms of its robustness
to that perturbation (ability to so converge/relax), will
not have threshold and saturation terms in those equations.
Similarly for the effectiveness parameter(s) (again, in tems
of? meeting a goal (if an intensional system), surviving an
environment?) . If what you mean *is* a system's
effectiveness in surviving perturbations of an environment
without becoming unstable, there are aharmonic
mutivibrator-characterized systems that can tend to chaos or
to stable systems with zippo to do with. There are many
other complex systems that do not reach such extrema
(saturation) in their response, nor are they especially
threshold-based system. For example, the brain can detect
one photon of light (via the VC) when such impinges upon a
photoreceptor. That is the smallest threshold one can
imagine - a pseudo-infinitely-small threshold in the *sense*
that it is representative of the quanta of em energy. No
telling if any brain has actually detected *only* one photon
at a "time" of course, but the point is one of
threshold-based systems. You have to make a quantum leap to
get to that threshold arr, arr!

There are also discontinuous processes that "jump" right
over "thresholds".

True.

Can you point me to a ref. where you are reading/getting
this relationship from?

Sorry, I just made it up (but it happens to be true).
Remember, I see dead dimensions.

and limited by saturation). For example, for a room-
temperature environment, the body maintains core
temperature using different strategies than in very cold or
very hot conditions.

Note that this is what makes neural networks into
computational engines.

That is one level of description - or -one view of what
brain does among several. I have a bit of experience
constructing ANNs for process control and there are levels
of description of brain that are not also characterizable as
a TME (Turing Machine Equivalent).

True, but I'm referring to much simpler ensembles of neurons.
The computational capability of a NN is directly traceable to
the threshold and saturation characteristics of the neurons.

Without threshold and saturation phenomena, a NN would be
useless.

Threshold is apparent in the neuronal characterization of
all-or-nothing firings (which itself is a function of
humongous complexity); however, that one aspect of the
messenger processes (first or second) of the brain.

I cannot see where it has the import ascribed WRT
robustness or effectiveness (towards a goal for example).

Then open your eyes.

I think we're arguing past each other, something that wouldn't
happen if we actually discussed this in person.

Saturation is an example of an extrema - a perturbation
causing a behavior point, and subsequent behavior points
that are the same or similar magnatude until the system
relaxes. The system simply has no differential response to
continuing stimula.

Right, and this is really important: beyond a narrow range,
the cost of responding linearly to external stimuli would be
too taxing to the organism. Consequently, the organism lets
that mechanism saturate, and turns on a different one.

Again, this is orthogonal to robustness and effectiveness of
a system (in terms of - we have not defined except as my
intial take on what each means earlier.

No, it's key.

Here is another thought. Man-made complex systems are
engineered, usually, to clamp to a safe value(s), all those
parameters that may compromise safety or
efficiency/waste-control.

This is a simple form of saturation.

That, and the other
characteristics I mentioned (no single point of failure,
graceful degradation etc.) make a system robust (in the face
of error or failure). Threshold and saturation are not part
of that consideration except as knowledge that can be
employed to determine startpopints (states), endpoints (end
states), and the PID coefficients affecting operation. When
a P/I/D/PI/PD/PID process goes awry, the PID and any
cascaded processes/points to which it is related/connected
get reset to some clamp value(s) and a good system will
transfer control to simple LL-based controllers and/or
simple interlocks completely divorced from the other control
system (isolatability is another aspect of robustness).

You don't see the analogy?

A good ref on all of this is the classic N. Weiner's
Cybernetics Second Edition: or the Control and Communication
in the Animal and the Machine

Any good book on control systems theory incorporating the
good ole PID controller strategy should give more insight
into the parameters affecting system control, especially
systems with feedback.

Well, yeah, but they provide little insight into profound
nonlinearity.

--
-Wayne