Re: Low carb diets [Archive] - WeightLossBanter

Lyle McDonald

December 18th, 2003, 07:44 PM

OmegaZero2003 wrote:
>
> "Lyle McDonald" > wrote in message
> ...
> > Mirek Fidler wrote:
> > >
> > > > and a standard low-calorie diet. Also, sticking to a low-carbohydrate
> > > > diet doesn't appear to be any easier than following other weight-loss
> > > > plans. People on the Atkins diet dropped out at a similar rate as
> > > those
> > > > following the low-fat diet. If dieters aren't getting the results they
> > > > want - anticipated weight loss - they drop out. This suggests that the
> > > > low-carbohydrate diet, like so many diets, is no easier to stick to
> > > long
> > > > term."
> > > >
> > > http://www.mayoclinic.com/invoke.cfm?objectid=EC6E90D1-C761-4F40-A099254
> > > FDF10BCB1
> > >
> > > I was thinking about this issue, as personaly for me low-carb menu seems
> > > to be much attractive than low-fat one.
> >
> > and that, IMO, is the bottom line.
> >
> > After all of these studies and 30+ years of research, the basic
> > conclusion is that all diets work, as long as people follow them. And
> > unless they are totally retarded, they all generate about teh same
> > weight/fat loss (and for the majority of dieters, small differences in
> > LBM retention are an irrelevancy; that only matters for athletes and
> > bodybuilders and tha'ts a tiny percentage of the dieting public).
> >
> > Meaning this: pick the dietary approach (which is going to depend on
> > personal food preferences, activity, etc) that YOU CAN BEST STICK TO. I
> > have been saying this for years.
>
> Oh I agree with this 100%.
>
> But it is interesting to look at the mechanisms and theories.

No doubt. But the more you look, the more you find it comes down, more
or less to the above.

I mean, fundamentally, weight loss is a function of

eat less (or eat differently so that you automatically eat less)
exercise (or not)
repeat
forever

most of the mechanistic stuff has to do with determining the details of
those 4 steps.

What to eat and does it even matter what the composition of the diet is?
Given a few requirements (which I stated previously), the differences
are minor approaching 4/5th of **** all (they certainly aren't that
important for your average obese individual; a few pounds either way may
be huge for an athlete or bodybuilder). So all diets basically work as
long as you reduce calories. One issue is whether or not the diet is
going to be strictly controlled or you're allowing ad-lib intakes. If
the latter, you need to pick a diet that spontaneously makes folks
reduce food intake. Both low-fat and low-carb approaches have studies
to back them (reducing fat tends to reduce calories in the short-term
because of the high energy density, in that carbs typically make up 50%
or more of the daily diet, reducing/removing them tends to reduce
calories as well). High-fiber is key and protein is turning out to be
the big player as it decreases hunger/appetite the most. A high fiber,
high protein, low GI carb, and low to moderate fat diet would probably
lead to the greatest spontaneous reduction in caloric intake.

Exercise. What type, how much, how often? Studies are showing that
exercise has a bigger role in preventing weight regain (but it takes a
lot) than in causing weight or fat loss per se. Of course, most
exercise studies use pretty paltry intervenions. Of course, the average
person won't do/can't handle intense exercise, at least not at first.

Repeat forever gets into adherence issues and is, IMO, where the real
meat of the matter lays. Face facts, losing weight is NOT hard. People
do it all the time. KEEPING the weight off is the problem and figuring
out how to do that is where the key solution is as far as I'm concerned.
That also ties in with diet composition: is a given diet relatively
harder or easier to stick to. Very low fat diets tend to have poor
compliance (so even though they generate weight/fat loss in the
short-term, people get tired of eating cardboard and go off of them), a
number of studies show that moderate fat diets (25-35% of total
calories) do better. I'm unaware of any long term studies on low-carb
diet adherence but I suspect it's going to be close to just as bad.
Moderate carb diets allow a lot more food variety and probably have an
advantage in this regards (compared to strict low carb diets). Same
with moderate fat, they taste better and allow more food variety.

On and on it goes. One of these days I'll write a real diet book and
adress all of the above issues in the anal retentive detail I'm known for.

Lyle

Doug Freese

December 18th, 2003, 08:14 PM

Lyle McDonald wrote:

> and that, IMO, is the bottom line.
>
> After all of these studies and 30+ years of research, the basic
> conclusion is that all diets work, as long as people follow them. And
> unless they are totally retarded, they all generate about teh same
> weight/fat loss (and for the majority of dieters, small differences in
> LBM retention are an irrelevancy;

If the focus is strictly on weight loss then what you both have said
seems obvious, at least to some of us. When one introduces
additional notions such as, likelihood of staying on it, overall
health concerns which dovetails into quality of life, sprinkle in
some exercise, the discussion gets interesting and sometimes heated.

Someone realized that I post from sci.med.nutrition. I have been in
and out of SMN for years and regardless of the number of degrees and
experience there is very little agreement on nutrition. I listen in
and get a few weeks of my daddy can beat up your daddy and put it on
the back burner. I would say most people agree that simple carbs aka
empty calories could be eliminated from everyone's diet and lose
nothing but possibly some weight. We have churned for years the
amounts, contents and proportions of pro/car/fat. Anyone think over
the next 5-10 years anything will be concluded? Until that time
most pick their horse, dig up some justification studies, with the
studies themselves coming under fire, and ride their horse.

--
Doug Freese
"Caveat Lector"

Lyle McDonald

December 18th, 2003, 08:32 PM

Doug Freese wrote:
>
> Lyle McDonald wrote:
>
> > and that, IMO, is the bottom line.
> >
> > After all of these studies and 30+ years of research, the basic
> > conclusion is that all diets work, as long as people follow them. And
> > unless they are totally retarded, they all generate about teh same
> > weight/fat loss (and for the majority of dieters, small differences in
> > LBM retention are an irrelevancy;
>
> If the focus is strictly on weight loss then what you both have said
> seems obvious, at least to some of us. When one introduces
> additional notions such as, likelihood of staying on it, overall
> health concerns which dovetails into quality of life, sprinkle in
> some exercise, the discussion gets interesting and sometimes heated.

I mentioned that in a different post.
There are other issues that factor into optimal diet choice.

Activity is one, potential health issues is another, there are certainly others.

> Someone realized that I post from sci.med.nutrition.

Explaining why you are a total dip**** (I'm basing this on your moronic
carb and exercise arguments, just so you know).

> I have been in
> and out of SMN for years and regardless of the number of degrees and
> experience there is very little agreement on nutrition. I listen in
> and get a few weeks of my daddy can beat up your daddy and put it on
> the back burner. I would say most people agree that simple carbs aka
> empty calories could be eliminated from everyone's diet and lose
> nothing but possibly some weight. We have churned for years the
> amounts, contents and proportions of pro/car/fat. Anyone think over
> the next 5-10 years anything will be concluded?

Yes: Moderation in all things.

My grandmother knew this 50 years ago and many nutrition studies are
coming to the same basic conclusion. Both extremely low-fat and
extremely high-fat diets can cause health problems (low-fat can raise
triglcyeride levels and increase small LDL particles; high fat has a
separate set of problems although it depends on the rest of the diet).
Same for protein (tho the risk of 'high-protein' are drastically
overstated). High-carb diets (esp if the carbs come from refined
sources and, let's face it, they do in modern diets) cause all kinds of
problems. Lowcarbs can or can not be a problem depending on other specifics.

for the majority of individuals, I feel that a diet containing

1. ~25-30% dietary protein (in the realm of .8-1 g/lb LBM)
2. 25-35% dietary fat (from mostly healthy/monounsaturated sources): I
use .45 g/lb as a pulled out my ass value for now (it's about 25-30% at
maintenance calories)
3. the remainder carbs: preferably less refined. Meaning that, at most,
carbs are going to be 50% of total calories. They can go lower but,
unless you're talking about elite endurance performance, there's rarely
a need to go higher.
4. High fiber (goes with 3)
5. Allow one or two don't worry about it, eat whatever the **** you want
meals per week to get it out of your damn system.

is probably about right.

There are outliers to any such schema. Elite endurance athletes may
need relatively more carbs (of course, their total claorie intakes go
through the roof so their absolute carb intakes will go up). Folks with
severe insulin resistance may need to reduce carbs further for health
reasons and/or to control calories.

Lyle

OmegaZero2003

December 18th, 2003, 09:43 PM

You certainly cram a lot of good info into a short space - thanks!

"Lyle McDonald" > wrote in message
...
> Doug Freese wrote:
> >
> > Lyle McDonald wrote:
> >
> > > and that, IMO, is the bottom line.
> > >
> > > After all of these studies and 30+ years of research, the basic
> > > conclusion is that all diets work, as long as people follow them. And
> > > unless they are totally retarded, they all generate about teh same
> > > weight/fat loss (and for the majority of dieters, small differences in
> > > LBM retention are an irrelevancy;
> >
> > If the focus is strictly on weight loss then what you both have said
> > seems obvious, at least to some of us. When one introduces
> > additional notions such as, likelihood of staying on it, overall
> > health concerns which dovetails into quality of life, sprinkle in
> > some exercise, the discussion gets interesting and sometimes heated.
>
> I mentioned that in a different post.
> There are other issues that factor into optimal diet choice.
>
> Activity is one, potential health issues is another, there are certainly
others.
>
>
> > Someone realized that I post from sci.med.nutrition.
>
> Explaining why you are a total dip**** (I'm basing this on your moronic
> carb and exercise arguments, just so you know).
>
> > I have been in
> > and out of SMN for years and regardless of the number of degrees and
> > experience there is very little agreement on nutrition. I listen in
> > and get a few weeks of my daddy can beat up your daddy and put it on
> > the back burner. I would say most people agree that simple carbs aka
> > empty calories could be eliminated from everyone's diet and lose
> > nothing but possibly some weight. We have churned for years the
> > amounts, contents and proportions of pro/car/fat. Anyone think over
> > the next 5-10 years anything will be concluded?
>
> Yes: Moderation in all things.
>
> My grandmother knew this 50 years ago and many nutrition studies are
> coming to the same basic conclusion. Both extremely low-fat and
> extremely high-fat diets can cause health problems (low-fat can raise
> triglcyeride levels and increase small LDL particles; high fat has a
> separate set of problems although it depends on the rest of the diet).
> Same for protein (tho the risk of 'high-protein' are drastically
> overstated). High-carb diets (esp if the carbs come from refined
> sources and, let's face it, they do in modern diets) cause all kinds of
> problems. Lowcarbs can or can not be a problem depending on other
specifics.
>
> for the majority of individuals, I feel that a diet containing
>
> 1. ~25-30% dietary protein (in the realm of .8-1 g/lb LBM)
> 2. 25-35% dietary fat (from mostly healthy/monounsaturated sources): I
> use .45 g/lb as a pulled out my ass value for now (it's about 25-30% at
> maintenance calories)
> 3. the remainder carbs: preferably less refined. Meaning that, at most,
> carbs are going to be 50% of total calories. They can go lower but,
> unless you're talking about elite endurance performance, there's rarely
> a need to go higher.
> 4. High fiber (goes with 3)
> 5. Allow one or two don't worry about it, eat whatever the **** you want
> meals per week to get it out of your damn system.
>
> is probably about right.
>
> There are outliers to any such schema. Elite endurance athletes may
> need relatively more carbs (of course, their total claorie intakes go
> through the roof so their absolute carb intakes will go up). Folks with
> severe insulin resistance may need to reduce carbs further for health
> reasons and/or to control calories.
>
> Lyle

Doug Freese

December 19th, 2003, 02:00 AM

Lyle McDonald wrote:

> Explaining why you are a total dip**** (I'm basing this on your moronic
> carb and exercise arguments, just so you know).

My god you hurt my feelings. That ok, until I read this post I
thought the same of you. Since you always address proteins first it
suggested your a muscle head and you probably post from m.f.weights.
Have we finished with the name calling?

> Yes: Moderation in all things.

I think I said that a few times.
>
> My grandmother knew this 50 years ago and many nutrition studies are
> coming to the same basic conclusion. Both extremely low-fat and
> extremely high-fat diets can cause health problems (low-fat can raise
> triglcyeride levels and increase small LDL particles; high fat has a
> separate set of problems although it depends on the rest of the diet).
> Same for protein (tho the risk of 'high-protein' are drastically
> overstated). High-carb diets (esp if the carbs come from refined
> sources and, let's face it, they do in modern diets) cause all kinds of
> problems. Lowcarbs can or can not be a problem depending on other specifics.
>
> for the majority of individuals, I feel that a diet containing
>
> 1. ~25-30% dietary protein (in the realm of .8-1 g/lb LBM)
> 2. 25-35% dietary fat (from mostly healthy/monounsaturated sources): I
> use .45 g/lb as a pulled out my ass value for now (it's about 25-30% at
> maintenance calories)
> 3. the remainder carbs: preferably less refined. Meaning that, at most,
> carbs are going to be 50% of total calories. They can go lower but,
> unless you're talking about elite endurance performance, there's rarely
> a need to go higher.
> 4. High fiber (goes with 3)
> 5. Allow one or two don't worry about it, eat whatever the **** you want
> meals per week to get it out of your damn system.

In a nut shell your 50/25/25 give or take a few. There is not a word
above that I disagree with so what did I say that you disagree with.

> There are outliers to any such schema. Elite endurance athletes may
> need relatively more carbs (of course, their total claorie intakes go
> through the roof so their absolute carb intakes will go up).

You don't have to be elite, even slow endurance will drive the
demands for carbs up higher. I'm probably 60/20/20 on average.

--
Doug Freese
"Caveat Lector"

Elzinator

December 19th, 2003, 02:48 AM

"OmegaZero2003" > wrote in message >...
> "Lyle McDonald" > wrote in message
> ...
> > After all of these studies and 30+ years of research, the basic
> > conclusion is that all diets work, as long as people follow them. And
> > unless they are totally retarded, they all generate about teh same
> > weight/fat loss (and for the majority of dieters, small differences in
> > LBM retention are an irrelevancy; that only matters for athletes and
> > bodybuilders and tha'ts a tiny percentage of the dieting public).
> >
> > Meaning this: pick the dietary approach (which is going to depend on
> > personal food preferences, activity, etc) that YOU CAN BEST STICK TO. I
> > have been saying this for years.
>
> Oh I agree with this 100%.
>
> But it is interesting to look at the mechanisms and theories.

Dude, mechanisms rool. (Lyle only likes endpoints ;)

Elzinator

December 19th, 2003, 03:14 AM

Lyle McDonald > wrote in message >...
> OmegaZero2003 wrote:

> > > Meaning this: pick the dietary approach (which is going to depend on
> > > personal food preferences, activity, etc) that YOU CAN BEST STICK TO. I
> > > have been saying this for years.
> >
> > Oh I agree with this 100%.
> >
> > But it is interesting to look at the mechanisms and theories.
>
> No doubt. But the more you look, the more you find it comes down, more
> or less to the above.
>
> I mean, fundamentally, weight loss is a function of
>
> eat less (or eat differently so that you automatically eat less)
> exercise (or not)
> repeat
> forever
>
> most of the mechanistic stuff has to do with determining the details of
> those 4 steps.

Which has more relavence for pathophysiologies and age-related issues
than the general populace. I agree that mechanistic knowledge is not
as important for the general populace, and, as you mention later in
your post, it is easy to attain weight loss (and maintain it) by
adjusting the two components: diet and exericse. However, age-related
changes in gene expression and metabolism alter the effects of both
diet and exericse. Pathophysiologies are often associated with genetic
mutations and resulting congenital or acquired phenotypes in which the
effects of diet and exercise may be dissimilar with normal
individuals.

After the symposium that I attended today on lipodystrophy, the
multifactorial nature of these pathophysiologies was very apparent;
not one treatment or therapy will result in equal response in all
individuals.

This is why pursuing mechanistic studies in diet and exercise and
weight regulation is imperative. And why I find it so fascinating and
challenging.

> What to eat and does it even matter what the composition of the diet is?
> Given a few requirements (which I stated previously), the differences
> are minor approaching 4/5th of **** all (they certainly aren't that
> important for your average obese individual; a few pounds either way may
> be huge for an athlete or bodybuilder). So all diets basically work as
> long as you reduce calories. One issue is whether or not the diet is
> going to be strictly controlled or you're allowing ad-lib intakes. If
> the latter, you need to pick a diet that spontaneously makes folks
> reduce food intake. Both low-fat and low-carb approaches have studies
> to back them (reducing fat tends to reduce calories in the short-term
> because of the high energy density, in that carbs typically make up 50%
> or more of the daily diet, reducing/removing them tends to reduce
> calories as well). High-fiber is key and protein is turning out to be
> the big player as it decreases hunger/appetite the most. A high fiber,
> high protein, low GI carb, and low to moderate fat diet would probably
> lead to the greatest spontaneous reduction in caloric intake.
>
> Exercise. What type, how much, how often? Studies are showing that
> exercise has a bigger role in preventing weight regain (but it takes a
> lot) than in causing weight or fat loss per se. Of course, most
> exercise studies use pretty paltry intervenions. Of course, the average
> person won't do/can't handle intense exercise, at least not at first.

Exercise also plays a large role in other traits, such as
cardioprotection and aiding the immune system. Reduction of diabetes
and CVD risk, ETC. What we don't know is what exercise prescription to
assign for each of these, or all for that matter. I suspect that it is
a combinatin of resistance and aerobic training. Each confers benefits
the other may not.

> On and on it goes. One of these days I'll write a real diet book and
> adress all of the above issues in the anal retentive detail I'm known for.

Uh, yeah....

Allow me to paste in the introduction of a very recent review authored
by one of my favorite reserchers in molecular/cellular biology of
exericse, Dr. Frank Booth (who up until a few years ago, was in
Houston) and a co-author:

"On a superficial level, many would consider it intuitive to
make the statement that exercise in general is a good thing.
However, when the layers of the exercise onion are peeled, the
answer to the question of how exactly at the mechanistic level
is exercise beneficial for human health does not seem that
obvious to the general scientific community, although there is
extensive literature at a descriptive level documenting the
precise benefits of exercise for many aspects of human health.

If, peeling those layers even further, we then consider the
notion that gene selection during the eons of human evolution
was likely influenced by physical activity to support human
health, we would suspect the reaction would be one of great
skepticism. Therefore, the major objectives of this review are
1) to amalgamate the presently known information, parts of which have
been separately developed from previous investigators
(5, 12–16, 21, 39, 40), that support the above notion of
an evolutionarily derived need for undertaking regular physical
activity to maintain normality of specific metabolic functions,
and 2) to present a hypothesis that the combination of continuous
food abundance and a sedentary lifestyle results in metabolic
derangements because of the stalling of the evolutionarily
programmed metabolic cycles that were selected to support
cycles of feast and famine and of physical activity and
rest.

We contend that achieving such an understanding of
potential gene selection will provide further avenues for fruitful
research into dissecting the cellular and molecular mechanisms
of physical inactivity-mediated chronic diseases."

Very well put (and a very excellent review).

Wayne S. Hill

December 19th, 2003, 03:54 AM

Elzinator wrote:

> Allow me to paste in the introduction of a very recent
> review authored by one of my favorite reserchers in
> molecular/cellular biology of exericse, Dr. Frank Booth (who
> up until a few years ago, was in Houston) and a co-author:
>
> "On a superficial level, many would consider it intuitive to
> make the statement that exercise in general is a good thing.
> However, when the layers of the exercise onion are peeled,
> the answer to the question of how exactly at the mechanistic
> level is exercise beneficial for human health does not seem
> that obvious to the general scientific community, although
> there is extensive literature at a descriptive level
> documenting the precise benefits of exercise for many
> aspects of human health.
>
> If, peeling those layers even further, we then consider the
> notion that gene selection during the eons of human
> evolution was likely influenced by physical activity to
> support human health, we would suspect the reaction would be
> one of great skepticism. Therefore, the major objectives of
> this review are 1) to amalgamate the presently known
> information, parts of which have been separately developed
> from previous investigators (5, 12–16, 21, 39, 40), that
> support the above notion of an evolutionarily derived need
> for undertaking regular physical activity to maintain
> normality of specific metabolic functions, and 2) to present
> a hypothesis that the combination of continuous food
> abundance and a sedentary lifestyle results in metabolic
> derangements because of the stalling of the evolutionarily
> programmed metabolic cycles that were selected to support
> cycles of feast and famine and of physical activity and
> rest.
>
> We contend that achieving such an understanding of
> potential gene selection will provide further avenues for
> fruitful research into dissecting the cellular and molecular
> mechanisms of physical inactivity-mediated chronic
> diseases."
>
> Very well put (and a very excellent review).

Sounds great.

--
-Wayne

Lyle McDonald

December 19th, 2003, 04:44 AM

Elzinator wrote:
>
> "OmegaZero2003" > wrote in message >...
> > "Lyle McDonald" > wrote in message
> > ...
> > > After all of these studies and 30+ years of research, the basic
> > > conclusion is that all diets work, as long as people follow them. And
> > > unless they are totally retarded, they all generate about teh same
> > > weight/fat loss (and for the majority of dieters, small differences in
> > > LBM retention are an irrelevancy; that only matters for athletes and
> > > bodybuilders and tha'ts a tiny percentage of the dieting public).
> > >
> > > Meaning this: pick the dietary approach (which is going to depend on
> > > personal food preferences, activity, etc) that YOU CAN BEST STICK TO. I
> > > have been saying this for years.
> >
> > Oh I agree with this 100%.
> >
> > But it is interesting to look at the mechanisms and theories.
>
> Dude, mechanisms rool. (Lyle only likes endpoints ;)

I am interested in mechanisms as long as they lead to applicable endpoints.
Most of the molecular/gene level stuff does not.

Lyle

OmegaZero2003

December 19th, 2003, 06:17 AM

"Elzinator" > wrote in message
om...
> Lyle McDonald > wrote in message
>...
> > OmegaZero2003 wrote:
>
> > > > Meaning this: pick the dietary approach (which is going to depend on
> > > > personal food preferences, activity, etc) that YOU CAN BEST STICK
TO. I
> > > > have been saying this for years.
> > >
> > > Oh I agree with this 100%.
> > >
> > > But it is interesting to look at the mechanisms and theories.
> >
> > No doubt. But the more you look, the more you find it comes down, more
> > or less to the above.
> >
> > I mean, fundamentally, weight loss is a function of
> >
> > eat less (or eat differently so that you automatically eat less)
> > exercise (or not)
> > repeat
> > forever
> >
> > most of the mechanistic stuff has to do with determining the details of
> > those 4 steps.
>
> Which has more relavence for pathophysiologies and age-related issues
> than the general populace. I agree that mechanistic knowledge is not
> as important for the general populace, and, as you mention later in
> your post, it is easy to attain weight loss (and maintain it) by
> adjusting the two components: diet and exericse. However, age-related
> changes in gene expression and metabolism alter the effects of both
> diet and exericse. Pathophysiologies are often associated with genetic
> mutations and resulting congenital or acquired phenotypes in which the
> effects of diet and exercise may be dissimilar with normal
> individuals.
>
> After the symposium that I attended today on lipodystrophy, the
> multifactorial nature of these pathophysiologies was very apparent;
> not one treatment or therapy will result in equal response in all
> individuals.

This is very similar to the issues facing cancer researchers.

Three very different mechanisms/theories using separate processes all
interacting to produce the endpoint.

>
> This is why pursuing mechanistic studies in diet and exercise and
> weight regulation is imperative. And why I find it so fascinating and
> challenging.
>
> > What to eat and does it even matter what the composition of the diet is?
> > Given a few requirements (which I stated previously), the differences
> > are minor approaching 4/5th of **** all (they certainly aren't that
> > important for your average obese individual; a few pounds either way may
> > be huge for an athlete or bodybuilder). So all diets basically work as
> > long as you reduce calories. One issue is whether or not the diet is
> > going to be strictly controlled or you're allowing ad-lib intakes. If
> > the latter, you need to pick a diet that spontaneously makes folks
> > reduce food intake. Both low-fat and low-carb approaches have studies
> > to back them (reducing fat tends to reduce calories in the short-term
> > because of the high energy density, in that carbs typically make up 50%
> > or more of the daily diet, reducing/removing them tends to reduce
> > calories as well). High-fiber is key and protein is turning out to be
> > the big player as it decreases hunger/appetite the most. A high fiber,
> > high protein, low GI carb, and low to moderate fat diet would probably
> > lead to the greatest spontaneous reduction in caloric intake.
> >
> > Exercise. What type, how much, how often? Studies are showing that
> > exercise has a bigger role in preventing weight regain (but it takes a
> > lot) than in causing weight or fat loss per se. Of course, most
> > exercise studies use pretty paltry intervenions. Of course, the average
> > person won't do/can't handle intense exercise, at least not at first.
>
> Exercise also plays a large role in other traits, such as
> cardioprotection and aiding the immune system. Reduction of diabetes
> and CVD risk, ETC. What we don't know is what exercise prescription to
> assign for each of these, or all for that matter. I suspect that it is
> a combinatin of resistance and aerobic training. Each confers benefits
> the other may not.
>
>
> > On and on it goes. One of these days I'll write a real diet book and
> > adress all of the above issues in the anal retentive detail I'm known
for.
>
> Uh, yeah....
>
> Allow me to paste in the introduction of a very recent review authored
> by one of my favorite reserchers in molecular/cellular biology of
> exericse, Dr. Frank Booth (who up until a few years ago, was in
> Houston) and a co-author:
>
> "On a superficial level, many would consider it intuitive to
> make the statement that exercise in general is a good thing.
> However, when the layers of the exercise onion are peeled, the
> answer to the question of how exactly at the mechanistic level
> is exercise beneficial for human health does not seem that
> obvious to the general scientific community, although there is
> extensive literature at a descriptive level documenting the
> precise benefits of exercise for many aspects of human health.
>
> If, peeling those layers even further, we then consider the
> notion that gene selection during the eons of human evolution
> was likely influenced by physical activity to support human
> health, we would suspect the reaction would be one of great
> skepticism.

Hmmm - the selection-for mechanisms have been theorized to include a way to
reward both curiosity and activity given the nature of the nature most of
homo sapiens' ancestors faced. Even the theory of neuronal group selection
is based on (appropriate) activation upon perturbation (sensory modalities,
motor skills etc.)

..> Therefore, the major objectives of this review are
> 1) to amalgamate the presently known information, parts of which have
> been separately developed from previous investigators
> (5, 12-16, 21, 39, 40), that support the above notion of
> an evolutionarily derived need for undertaking regular physical
> activity to maintain normality of specific metabolic functions,
> and 2) to present a hypothesis that the combination of continuous
> food abundance and a sedentary lifestyle results in metabolic
> derangements because of the stalling of the evolutionarily

Deranged - now that's somethin I can identify with...

> programmed metabolic cycles that were selected to support
> cycles of feast and famine and of physical activity and
> rest.
>
> We contend that achieving such an understanding of
> potential gene selection will provide further avenues for fruitful
> research into dissecting the cellular and molecular mechanisms
> of physical inactivity-mediated chronic diseases."
>
> Very well put (and a very excellent review).

Beemie

December 19th, 2003, 10:47 PM

I went to fitday.com after not going for 2 months or so, and was pleased to
find my weight had moved from the severly overweight to the moderate! only
19 more lbs to go yipeeeeeeee! I guess I haven't done that site enough
to feel fast in noting all the food for the day, etc find it alot of
work, do you ? Does it keep taps on the foods from day to day? I look
up everything , everyday, thats time consuming

Elzinator

December 20th, 2003, 01:08 AM

"OmegaZero2003" > wrote in message >...
> "Elzinator" > wrote in message
> om...

> > > most of the mechanistic stuff has to do with determining the details of
> > > those 4 steps.
> >
> > Which has more relavence for pathophysiologies and age-related issues
> > than the general populace. I agree that mechanistic knowledge is not
> > as important for the general populace, and, as you mention later in
> > your post, it is easy to attain weight loss (and maintain it) by
> > adjusting the two components: diet and exericse. However, age-related
> > changes in gene expression and metabolism alter the effects of both
> > diet and exericse. Pathophysiologies are often associated with genetic
> > mutations and resulting congenital or acquired phenotypes in which the
> > effects of diet and exercise may be dissimilar with normal
> > individuals.
> >
> > After the symposium that I attended today on lipodystrophy, the
> > multifactorial nature of these pathophysiologies was very apparent;
> > not one treatment or therapy will result in equal response in all
> > individuals.
>
> 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. If you look at some of the signaling models (e.g. on Science
Signaling Knowledge Gateway website), they look like a street map of
NYC. I would like to see interactive models on the website (SKG is
attempting to do that).

However, they are only as good as our existing technology and data.
More is continually added, and the models change. As one visiting
scientist commented, models only allow us to predict responses. The
same can be said for a generalized response to dietary interventions.

> .> Therefore, the major objectives of this review are
> > 1) to amalgamate the presently known information, parts of which have
> > been separately developed from previous investigators
> > (5, 12-16, 21, 39, 40), that support the above notion of
> > an evolutionarily derived need for undertaking regular physical
> > activity to maintain normality of specific metabolic functions,
> > and 2) to present a hypothesis that the combination of continuous
> > food abundance and a sedentary lifestyle results in metabolic
> > derangements because of the stalling of the evolutionarily
>
> Deranged - now that's somethin I can identify with...

You and me both. Outliers, I say!

Wayne S. Hill

December 20th, 2003, 01:25 AM

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. 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.

--
-Wayne

Elzinator

December 20th, 2003, 04:20 AM

"OmegaZero2003" > wrote in message news:
> "Elzinator" wrote in message...

> > "On a superficial level, many would consider it intuitive to
> > make the statement that exercise in general is a good thing.
> > However, when the layers of the exercise onion are peeled, the
> > answer to the question of how exactly at the mechanistic level
> > is exercise beneficial for human health does not seem that
> > obvious to the general scientific community, although there is
> > extensive literature at a descriptive level documenting the
> > precise benefits of exercise for many aspects of human health.
> >
> > If, peeling those layers even further, we then consider the
> > notion that gene selection during the eons of human evolution
> > was likely influenced by physical activity to support human
> > health, we would suspect the reaction would be one of great
> > skepticism.
>
> Hmmm - the selection-for mechanisms have been theorized to include a way to
> reward both curiosity and activity given the nature of the nature most of
> homo sapiens' ancestors faced. Even the theory of neuronal group selection
> is based on (appropriate) activation upon perturbation (sensory modalities,
> motor skills etc.)

I forgot to mention in my previous response that, if you are
interested, I have a few very good papers (pdfs)on evolutionary
biology (and evo-devo) that would be applicable to this topic. Not so
much directed in general. The other thread got me going on this
(evobio) again (a hobby of mine :) A buddy in Austin and I talk this
stuff for hours.

Booth's recent paper extends the basics of evolutoinary biology to the
context of diet and activity. Booth rocks.

Elzinator

December 20th, 2003, 05:29 AM

On 20 Dec 2003 00:25:22 GMT, "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. 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.

Very true, but that's part of the challenge.
I'm trying to talk someone (computational systems geek) into modeling
bodyweight homeostasis.

He's reluctant.

It's not enough to just live. You've got to have something to live for.

Proton Soup

December 20th, 2003, 07:44 AM

On 19 Dec 2003 16:08:11 -0800, (Elzinator)
wrote:

>Biological systems are more complex than most realize: feedback loops,
>negative and positive regulators, redundant and overlapping pathways,
>etc. If you look at some of the signaling models (e.g. on Science
>Signaling Knowledge Gateway website), they look like a street map of
>NYC. I would like to see interactive models on the website (SKG is
>attempting to do that).

You got a URL for that SSKG? I've got a little more than a passive
interest in the subject. When I's in school, I did get to take a
couple of quarters of physiology (and learned it wasn't for me - not
the best student). We used a textbook by Guyton, but not a good one.
We were told that the older editions had a lot of feedback diagrams in
it, which I would have loved to see, given that my interest at the
time was control systems. But because of complaints from bio-geeks,
they removed all trace of system diagrams. Best I can remember, the
only positive feedback system was one used during childbirth, where
the head pressing down on the cervix causes more contractions, which
increases pressure, yadayadayada...

>However, they are only as good as our existing technology and data.
>More is continually added, and the models change. As one visiting
>scientist commented, models only allow us to predict responses. The
>same can be said for a generalized response to dietary interventions.

Ja, people don't like being controlled. But there are certainly
plenty of times that they are, like with patients, or soldiers.

---
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

December 20th, 2003, 07:48 AM

On 20 Dec 2003 00:25:22 GMT, "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. 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.

Yeah, but that is true for all real systems. Overdrive an amplifier,
you'll get clipping. Underdrive a hydroelectric facility, the dam
will overflow. Some are even nonlinear within their useful range, but
we can deal with that, too.

---
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

December 20th, 2003, 07:52 AM

On Fri, 19 Dec 2003 23:29:22 -0500, Elzinator >
wrote:

>On 20 Dec 2003 00:25:22 GMT, "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. 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.
>
>Very true, but that's part of the challenge.
> I'm trying to talk someone (computational systems geek) into modeling
>bodyweight homeostasis.
>
>He's reluctant.

Well, he probably realizes that it's one of those projects that would
never end.

---
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

Elzinator

December 20th, 2003, 04:49 PM

On Sat, 20 Dec 2003 00:52:19 -0600, Proton Soup >
wrote:

>On Fri, 19 Dec 2003 23:29:22 -0500, Elzinator >
>wrote:
>
>>On 20 Dec 2003 00:25:22 GMT, "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. 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.
>>
>>Very true, but that's part of the challenge.
>> I'm trying to talk someone (computational systems geek) into modeling
>>bodyweight homeostasis.
>>
>>He's reluctant.
>
>Well, he probably realizes that it's one of those projects that would
>never end.

We did discuss the limiting factors of accessible and current
information. Of course, models should be flexible to allow for change.
That's the key.

It's not enough to just live. You've got to have something to live for.

Wayne S. Hill

December 20th, 2003, 04:55 PM

Elzinator 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. 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.
>
> Very true, but that's part of the challenge.
> I'm trying to talk someone (computational systems geek)
> into modeling bodyweight homeostasis.
>
> He's reluctant.

When you say he's a computational systems geek, is he into
dynamic modeling? See, this is an area where you're more
likely to have luck if you're into system dynamics and control
(like a coworker of mine). The problem there is that a
controls person would either

a) think it was straightforward and not really appreciate what
he/she was up against (and thereby be ill-prepared for the
task and quickly conclude it was hopeless), or
b) know instantly what a monumental task it is. This is the
person you're looking for: someone who resists the task with
every fiber of his/her being. 8-)

This is not to say that it isn't worth doing, or attempting at
least parts of it, or that a great deal wouldn't be learned in
the process. By comparing actual known behaviors to
simulations, you can discover that certain mechanisms are
missing or improperly represented. Solving succeeding layers
of this onion would improve knowledge.

--
-Wayne

Wayne S. Hill

December 20th, 2003, 05:02 PM

Proton Soup 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. 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.
>
> Yeah, but that is true for all real systems. Overdrive an
> amplifier, you'll get clipping. Underdrive a hydroelectric
> facility, the dam will overflow. Some are even nonlinear
> within their useful range, but we can deal with that, too.

No argument, although few engineering systems rely on
nonlinearity to the extent that biological systems do. For
example, I doubt it's very enlightening to linearize a
biological system around some operating point, because normal
operation involves full-scale perturbations.

--
-Wayne

OmegaZero2003

December 20th, 2003, 09:48 PM

"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

Wayne S. Hill

December 21st, 2003, 12:27 AM

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

OmegaZero2003

December 21st, 2003, 01:40 AM

"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

Wayne S. Hill

December 21st, 2003, 05:29 AM

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

OmegaZero2003

December 21st, 2003, 07:11 AM

"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

OmegaZero2003

December 21st, 2003, 07:29 AM

Proton Soup

December 21st, 2003, 07:50 AM

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

Wayne S. Hill

December 21st, 2003, 04:53 PM

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

Wayne S. Hill

December 21st, 2003, 06:06 PM

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

Wayne S. Hill

December 21st, 2003, 06:25 PM

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!

'ang on there, when we refer to linearity in such systems,
we're referring to linearity of the dynamics, i.e.,

x-dot = A * x + b

This omits simple algebraic behaviors (because x-dot = 0).

> - Hamiltonian oscillators and like systems. (the
> direction field specifically)

Not of great interest in biological systems, except as a
backdrop.

> - continuous-time systems like electrical networks, many
> mechanical systems

Aside from the fact that linearity is an approximation in all
such systems, they all have their nonlinear limits. The
nonlinearity is whatever it is that keeps the systems
operating in their linear range.

> - any discrete system with a transfer
> function whose input, response and output functions depend
> on one variable

Huh? The most common form of discrete systems is the
iteration (strobing based on time or state) of a continuous
system. A single-variable system would be of a form

x-dot = f(x)

Here, f can be (generally is) a nonlinear function of x, so
the system will show nonlinear behavior, both continuously and
discretely.

> - any systems preserving homogeneity (output
> proportional to input) and superposition (a way of combining
> linear functions such that the result is a linear function)

In other words, linear systems.

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

Not in their dynamics. This is the classic engineer's mistake
of characterizing in statistical terms what is not understood.
When you delve into the NLD of such systems, you gain true
insight into what makes them work. I can give examples.

> 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.

That is an approximation that people sometimes find useful to
make. That doesn't make it so, especially when you take the
system outside of the limited context in which you placed it
for convenience.

--
-Wayne

OmegaZero2003

December 21st, 2003, 09:25 PM

"Wayne S. Hill" > wrote in message
...
> 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.

Have you read his book?

>
> >> 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),

It does not ahve to; the form and whether it is local or non-local are
orthogonal.

> the global behaviors of threshold and saturation
> phenomena are common themes in biological systems.

Sure.

My point is that there are linear 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.

This makes little sense. It is the complexity of a system that determines
the breadth and depth of a system_state tree.

>
> > 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 complex system, or a dynamical system need not exhibit emergent phenomena.
The systems that do exhibt emergent phenomena however, are usually complex
dynamical sytems.

> A mass of nitrogen molecules is a
> counter example: it never does anything "emergent",

That is what I said just above.

> 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.

That something varies smoothly (not descrete steps I presume you mean), does
not mean it does not have distinguisable states!!!!!! That is what
intergation and differentiation are all about.

Not only that but ther are clever theories purporting to show:

a) everything is quatal/descrete to the finest level of description
b) everything is analog/no_quantal_states to the finest level of
description.

Both positions are far from established given our level of instrumentality.

> 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.

Or VV!! Chaotic systems far from equilibrium. See Prigogine.

>
> >>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).

Well - I think it is mostly true as I said. But my original point is that
there are linear systems (hell - that is what LP is for!!).

But - in that case...

I think we should have been discussing the (a)/(b) dichotomy I mentioned
above. Whether nature is discontinuoous or continuous.

Instead!

;^)

> 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.

Well -err - not necessarily. The computational capability of brain or any
subset depends on how yu think it characterizes, or *represents*
information!!

IFF it is based on the go/no-go neuronal firing model, and IFF one
establishes as a premise that such is representative of 1 "bit" of
information (which is problematic itself, since the binary system is one of
*represenation* of higher-order/more-complex information represenation
schemes - that is, it is a mapping itself!!!), then one can estimate the
computational extent of that group of neurons (assuming further that one can
charaterize the NN architecture (its connection scheme) in sufficient
detail.

A little bit goes a long way - haha!

>
> >> 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.

More than likely! I like to waves hands and draw on boards!!

>
> > 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.

Or goes crazy! (Becomes chaotic) There are examples of systems that
persist in their output without switching. This kind of system exists on an
organismic level and in vary large systems - like socail systems and
economics.

It all depends on the feedback mechanisms (FF/FB) and *where* in the input
stream the FB occurs, and *whether* that point in the input stream has the
capability to clamp or switch its input-processing algorithm.

>
> > 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.

I don't see as strong a link as you do evidently. There are far more
important aspects that affect robustness and effectiveness of a system than
saturation and threshold.

I guess it depends on how you have learned to view system sciences, control
systems, and biological systems etc.

>
> > 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.

Yo can clamp well-before a saturation level!

>
> > 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?

Huh? Between what and what?

>
> > 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.

Weiner's book does. ANd if you learn about how control systems are
engineered to deal with "profound non-linearities", then you will see what
is important and what is not (from a control standpoint that is.)

The books/people that do provide the "insight" however include another I
mentioned - Alwyn Scott's work.

>
> --
> -Wayne

OmegaZero2003

December 21st, 2003, 09:26 PM

"Proton Soup" > wrote in message
...
> 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.

My original point to the OP on the topic was a retort to the statement that
*all* systems are nonlinear.

That is not true.

>
> >- 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

OmegaZero2003

December 21st, 2003, 09:30 PM

"Wayne S. Hill" > wrote in message
...
> 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.

Welcome to Tautology 101!

Again, I have provided several examples of systems that are chraterizable as
linear. Proton pointedd out one spcific one above.

I provided several categories of linear systems.

My original retort to your original sttement that *all* systems are
non-linear stands: it is not true that all systems are non-linear.

It is very easy to show how a hypothesis that begins: " All..." is false.
I need only provide one counter example.

>
> --
> -Wayne

Proton Soup

December 21st, 2003, 09:58 PM

On Sun, 21 Dec 2003 20:26:26 GMT, "OmegaZero2003"
> wrote:

>"Proton Soup" > wrote in message
...
>> 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.
>
>My original point to the OP on the topic was a retort to the statement that
>*all* systems are nonlinear.
>
>That is not true.

Then how about one example of a real physical system that is linear?
I realize that something digital like a NOT gate may be linear, but it
is still an abstraction. It's physical manifestation is something
different. Linearity is just an idealization, a tool that we use.
Even the mechanical systems mentioned are all nonlinear. A system
using masses and dampers and springs can be pieced together to form
mechanical analogues of RLC electrical circuits, but all those systems
are only linear within a threshold.

Sure, there are linear systems, but they're all in our heads.

---
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

Wayne S. Hill

December 21st, 2003, 10:05 PM

OmegaZero2003 wrote:

> "Wayne S. Hill" > wrote...
>> OmegaZero2003 wrote:
>> >
>> > 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.
>
> Have you read his book?

I haven't read it, but have discussed this at length with
someone who has read it, attended Wolfram's lectures, and
discussed it with Wolfram.

>> 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),
>
> It does not ahve to; the form and whether it is local or
> non-local are orthogonal.

Heh: we're definitely talking past each other.

> My point is that there are linear systems.

Yawn.

> This makes little sense. It is the complexity of a system
> that determines the breadth and depth of a system_state
> tree.

Again, we're talking past each other.

> A complex system, or a dynamical system need not exhibit
> emergent phenomena. The systems that do exhibt emergent
> phenomena however, are usually complex dynamical sytems.

I don't know if I've mentioned this in this thread, but the
term "emergent" is not accepted by the bulk of NLD researchers
(mathematicians or physicists).

> That something varies smoothly (not descrete steps I presume
> you mean), does not mean it does not have distinguisable
> states!!!!!! That is what intergation and differentiation
> are all about.

Once again, we're talking past one another.

> Or VV!! Chaotic systems far from equilibrium. See
> Prigogine.

Yeah, yeah.

>> > 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).
>
> Well - I think it is mostly true as I said. But my original
> point is that there are linear systems (hell - that is what
> LP is for!!).
>
> But - in that case...
>
> I think we should have been discussing the (a)/(b) dichotomy
> I mentioned above. Whether nature is discontinuoous or
> continuous.

Ack!

>> 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.
>
> Well -err - not necessarily. The computational capability
> of brain or any subset depends on how yu think it
> characterizes, or *represents* information!!

But a tiny NN is very simple, and it's quite clear how it
stores information. If the neuron activation function were
linear, it would only be able to store y=Ax+b, which contains
very little information.

>> 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.
>
> Or goes crazy! (Becomes chaotic)

See, I make a living working on systems that are chaotic, so I
don't view them as crazy. For example, the human brain NEEDS
to be chaotic to be functional. Limit cycles are the abnormal
dynamics of brains (epilepsy, etc.).

> I don't see as strong a link as you do evidently. There are
> far more important aspects that affect robustness and
> effectiveness of a system than saturation and threshold.

I wasn't trying to imply that threshold and saturation are
fundamental to robustness of dynamics of nonlinear systems,
but instead that it's fairly easy for self-organizing (e.g.,
biological) systems that have these characteristics to develop
robust dynamics.

>> > 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.
>
> Yo can clamp well-before a saturation level!

Clamping is functionally a sudden saturation.

Yeesh, enough already!

--
-Wayne

Wayne S. Hill

December 21st, 2003, 10:06 PM

OmegaZero2003 wrote:

> My original point to the OP on the topic was a retort to the
> statement that *all* systems are nonlinear.
>
> That is not true.

Nonsense. The OP never said any such thing. 8-p

--
-Wayne

OmegaZero2003

December 21st, 2003, 10:35 PM

"Wayne S. Hill" > wrote in message
...
> 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!
>
> 'ang on there, when we refer to linearity in such systems,
> we're referring to linearity of the dynamics, i.e.,
>
> x-dot = A * x + b

'ang on there yourself!!! Do you know WHAT characterizes a linear system
mathematically? Do you know the difference between an additive versus a
multiplicative factor? Well there is your answer!

In case you have not understood - will will take it slowly at first. Atend:
here is help for you:

"The response of a [ linear ] system to a sum of inputs is the sum of the
responses to each individual input separately.

These two nice properties allow a whole range of tools to be applicable in
designing linear systems and predicting their behavior. Some more examples
of linear systems in real life:

a) Frequency filters -- circuits which only pass low frequencies and reject
high, or vice-versa.

b) Delays are linear. Echos from faraway canyons are linear. Shout twice as
loud, get an echo twice as loud. Two people shouting at the same time comes
back as two people echoing at the same time.

c) Many different kinds of economic systems -- looking at the apple juice
production (output) vs. the apple crop yield, for example.

d) Limiting cases of non-linear systems for small inputs: Even if the
system's response may not satisfy the equation above exactly, it often will
well enough for small enough inputs. In this case, even if the number of
apples bought by consumers, say, is inversely proportional to the price of
apples, you can still model small changes around a reference price with
linear systems (but beware when the inputs get large!).
(http://van.hep.uiuc.edu/van/qa/section/Everything_Else/Math/20020319233837.
htm)

Note that the last item (d) talks about linearization/signal
decomposition/approximation_techniques of/for non-linear systems, which I am
NOT talking about. We are talking about bona fide LINEAR systems fulfilling
all the mathematical/theoretical properties that decades of science has
determined qualifies a system as "Linear" *by definition*!!!!

I am also not talking about trivial examples of what is a linear system in
toto (including extreme), but is subclassed to non-interesting behavior
(like an amp NOT in saturation mode).

>
> This omits simple algebraic behaviors (because x-dot = 0).
>
> > - Hamiltonian oscillators and like systems. (the
> > direction field specifically)
>
> Not of great interest in biological systems, except as a
> backdrop.

We were not restricting the discussion to biological systems.

My original retort to the OP's statement: "All systems are non-linear" was
to say:

That is not true.

It is easy to falsify hypotheses of the form: "All...(x) are (y)" in the
sense that only one counter-example need be provided.

FYI, a special class of linear control systems known as singularly perturbed
control systems, uses the Hamiltonian approach ( recursive) approach based
on t exact pure-slow and pure-fast decoupling of optimal control problems.

Another interesting special class of linear systems::

"Linear systems with non-rational transfer functions (In this project linear
systems described by partial differential equations having non-rational
transfer functions are studied. The aim of this project is to analyse the
dynamic behaviour and properties of linear input-output systems with
non-rational transfer functions (such as flexible robot arms and heat
processes) in the frequensy domain. For some classes of such systems it is
possible to develop the overall transfer function in analytical form by the
transmission matrix method. The interaction between different parts of the
system (including the way they are coupled to each other) can then be
analysed.
The transmission matrix method has been succesfully applied to multi-link
flexible robot arms and to buckling of multi-segment columns. Another
application concerns the stability of heat processes described by parabolic
partial differential equations. Based on the transmission matrix method a
Nyquist stability test was developed for sandwich-layered materials with
linear inner heat source." (M. Vajta DISC Project 1999)

for a linear system characterized using N first-order linear homogeneous
differential equations with constant coefficient can be found at: (with a
little more detailed math):
http://www.mathpages.com/home/kmath440/kmath440.htm

I leave it to the reader to come up with only three biological systems that
are so charaterized (this is an easy quiz to see if you understand what a
linear system is).

You can also look up sparse linear systems for funzies!

>
> > - continuous-time systems like electrical networks, many
> > mechanical systems
>
> Aside from the fact that linearity is an approximation in all
> such systems, they all have their nonlinear limits. The
> nonlinearity is whatever it is that keeps the systems
> operating in their linear range.
>
> > - any discrete system with a transfer
> > function whose input, response and output functions depend
> > on one variable
>
> Huh?

I think you have to learn the meaning of linear. Note that I am NOT talking
about linearisation of non-linear systems (which seems to be talked about in
this thread instead of the major contentions about what exists.)!!! I am not
talking about signal decomposition to acheive a linear treatment (what you
called piecewise).

Here is some help. Note that he points out some examples in the text.

"Signals, Linear Systems, and Convolution

Professor David Heeger

Characterizing the complete input-output properties of a system by
exhaustive measurement is

usually impossible. Instead, we must find some way of making a finite number
of measurements

that allow us to infer how the system will respond to other inputs that we
have not yet measured.

We can only do this for certain kinds of systems with certain properties. If
we have the right kind

of system, we can save a lot of time and energy by using the appropriate
theory about the system's

responsiveness. Linear systems theory is a good time-saving theory for
linear systems which obey

certain rules. Not all systems are linear, but many important ones are. When
a system qualifies as

a linear system, it is possible to use the responses to a small set of
inputs to predict the response to

any possible input. This can save the scientist enormous amounts of work,
and makes it possible

to characterize the system completely."

Please note the statement: "Not all systems are linear, but many important
ones are."

And now for a little math:

"Linear Systems

A system or transform maps an input signal x(t) into an output signal y(t):

y(t) = T[x(t)];

where T denotes the transform, a function from input signals to output
signals.

Systems come in a wide variety of types. One important class is known as
linear systems. To

see whether a system is linear, we need to test whether it obeys certain
rules that all linear systems

obey. The two basic tests of linearity are homogeneity and additivity.

4

Homogeneity. As we increase the strength of the input to a linear system,
say we double it,

then we predict that the output function will also be doubled. For example,
if the current injected

to a passive neural membrane is doubled, the resulting membrane potential
fluctuations will double

as well. This is called the scalar rule or sometimes the homogeneity of
linear systems.

Additivity. Suppose we we measure how the membrane potential fluctuates over
time in

response to a complicated time-series of injected current x1(t). Next, we
present a second (different)

complicated time-series x2(t). The second stimulus also generates
fluctuations in the membrane

potential which we measure and write down. Then, we present the sum of the
two currents

x1(t) + x2(t) and see what happens. Since the system is linear, the measured
membrane potential

fluctuations will be just the sum of the fluctuations to each of the two
currents presented separately.

Superposition. Systems that satisfy both homogeneity and additivity are
considered to be

linear systems. These two rules, taken together, are often referred to as
the principle of superposition.

Mathematically, the principle of superposition is expressed as:

T(
x1 + x2) =
T(x1) + T(x2) (2)

Homogeneity is a special case in which one of the signals is absent.
Additivity is a special case in

which
= = 1.

Shift-invariance. Suppose that we inject a pulse of current and measure the
membrane potential

fluctuations. Then we stimulate again with a similar pulse at a different
point in time, and

again we measure the membrane potential fluctuations. If we haven't damaged
the membrane with

the first impulse then we should expect that the response to the second
pulse will be the same as

the response to the first pulse. The only difference between them will be
that the second pulse has

occurred later in time, that is, it is shifted in time. When the responses
to the identical stimulus

presented shifted in time are the same, except for the corresponding shift
in time, then we have

a special kind of linear system called a shift-invariant linear system. Just
as not all systems are

linear, not all linear systems are shift-invariant.

In mathematical language, a system T is shift-invariant if and only if:

y(t) = T[x(t)] implies y(t

"

That is pretty much what I told the OP. Not ALL systems are non-linear.

Period, End of story.

QED and all that.

Gabel, Robert A. and Roberts, Richard A., 1973, Signals and Linear Systems,
New York: John Wiley & Sons, 415 pp.

Gaskill, Jack D., 1978, Linear Systems, Fourier Transforms, and Optics, New
York: John Wiley & Sons, 554 pp.

Lathi, B. P., 1992, Linear Systems and Signals, Carmichael, California:
Berkeley-Cambridge Press, 656 pp.

Lewis, Laurel J., Reynolds, Donald K., Bergseth, F. Robert, Alexandro, Jr.,
Frank J., 1969, Linear Systems Analysis, New York: McGraw-Hill Book Company,
489 pp.

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

>

The most common form of discrete systems is the
> iteration (strobing based on time or state) of a continuous
> system. A single-variable system would be of a form
>
> x-dot = f(x)
>
> Here, f can be (generally is) a nonlinear function of x, so
> the system will show nonlinear behavior, both continuously and
> discretely.

>
> > - any systems preserving homogeneity (output
> > proportional to input) and superposition (a way of combining
> > linear functions such that the result is a linear function)
>
> In other words, linear systems.

And there are lots of those!

Do yourself a favor and merely google "linear system", read what you care
to, then come back. I do not believe you do not get this.

I can give you a good start:

Linear System Theory and Design
by Chi-Tsong Chen

Read Chapter 2!

>
> > Even non-deterministic systems can be modeled using
> > statistics for linear dynamics.
>
> Not in their dynamics.

You do not know what you are talking about.

>This is the classic engineer's mistake
> of characterizing in statistical terms what is not understood.
> When you delve into the NLD of such systems, you gain true
> insight into what makes them work. I can give examples.

I have more examples in my head than you can provide. I worked on this for
20 years.

>
> > 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.
>
> That is an approximation that people sometimes find useful to
> make. That doesn't make it so, especially when you take the
> system outside of the limited context in which you placed it
> for convenience.

There are systems that are approximated as linear; that is called
*linearization* and there is a gamut of math to deal with how to do that
properly!

But there are many systems that are inherently and demonstrably linear.

>
> --
> -Wayne

OmegaZero2003

December 21st, 2003, 10:51 PM

"Proton Soup" > wrote in message
...
> On Sun, 21 Dec 2003 20:26:26 GMT, "OmegaZero2003"
> > wrote:
>
> >"Proton Soup" > wrote in message
> ...
> >> 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.
> >
> >My original point to the OP on the topic was a retort to the statement
that
> >*all* systems are nonlinear.
> >
> >That is not true.
>
> Then how about one example of a real physical system that is linear?
> I realize that something digital like a NOT gate may be linear, but it
> is still an abstraction. It's physical manifestation is something
> different. Linearity is just an idealization, a tool that we use.
> Even the mechanical systems mentioned are all nonlinear. A system
> using masses and dampers and springs can be pieced together to form
> mechanical analogues of RLC electrical circuits, but all those systems
> are only linear within a threshold.

See my recent post. There are examples there.

I think you have to understand the *mathematical definition* of a linear
system to understand anything further. I provided that edication in that
recent post.

There are many systems that neet that definition. I am not talking about
approximation techniques, subclassing a system into non-extreme behavior
ranges, or linearization techniques.

>
> Sure, there are linear systems, but they're all in our heads.

And sometimes not even there
>
> ---
> 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

OmegaZero2003

December 21st, 2003, 10:55 PM

"Wayne S. Hill" > wrote in message
...
> OmegaZero2003 wrote:
>
> > My original point to the OP on the topic was a retort to the
> > statement that *all* systems are nonlinear.
> >
> > That is not true.
>
> Nonsense. The OP never said any such thing. 8-p
>
> --
> -Wayne

Here is the context; I see you were pointing to biological systems.

"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. 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."

See where you said they (biological) are all non-linear?

There are biological systems that are linear.

OmegaZero2003

December 21st, 2003, 11:05 PM

"Wayne S. Hill" > wrote in message
...
> OmegaZero2003 wrote:
>
> > "Wayne S. Hill" > wrote...
> >> OmegaZero2003 wrote:
> >> >
> >> > 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.
> >
> > Have you read his book?
>
> I haven't read it, but have discussed this at length with
> someone who has read it, attended Wolfram's lectures, and
> discussed it with Wolfram.
>
> >> 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),
> >
> > It does not ahve to; the form and whether it is local or
> > non-local are orthogonal.
>
> Heh: we're definitely talking past each other.
>
> > My point is that there are linear systems.
>
> Yawn.
>
> > This makes little sense. It is the complexity of a system
> > that determines the breadth and depth of a system_state
> > tree.
>
> Again, we're talking past each other.
>
> > A complex system, or a dynamical system need not exhibit
> > emergent phenomena. The systems that do exhibt emergent
> > phenomena however, are usually complex dynamical sytems.
>
> I don't know if I've mentioned this in this thread, but the
> term "emergent" is not accepted by the bulk of NLD researchers
> (mathematicians or physicists).

I would not agreee with that. it may (certainly is I will say) be the case
that what is characterized *as* emergent* is not agreed to.

There is a difference.

That there is a definition/theory of emergence is indisputable. That such
has been defined with mathematical characterizations of systems is also
true.

What usually is confused or, better, *conflated* by those whom you may be
speaking, is "emergence" and "synergistic phenomena".

>
> > That something varies smoothly (not descrete steps I presume
> > you mean), does not mean it does not have distinguisable
> > states!!!!!! That is what intergation and differentiation
> > are all about.
>
> Once again, we're talking past one another.
>
> > Or VV!! Chaotic systems far from equilibrium. See
> > Prigogine.
>
> Yeah, yeah.
>
> >> > 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).
> >
> > Well - I think it is mostly true as I said. But my original
> > point is that there are linear systems (hell - that is what
> > LP is for!!).
> >
> > But - in that case...
> >
> > I think we should have been discussing the (a)/(b) dichotomy
> > I mentioned above. Whether nature is discontinuoous or
> > continuous.
>
> Ack!
>
> >> 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.
> >
> > Well -err - not necessarily. The computational capability
> > of brain or any subset depends on how yu think it
> > characterizes, or *represents* information!!
>
> But a tiny NN is very simple, and it's quite clear how it
> stores information.

No is isn't!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

It isn't clear at all how brain *represents* information. This is one of
the biggest challenges facing neuroscience; how to span the gap between the
psychological phenomena/overt behavior (verbal behavior etc.) and the NCCs
(the neural correlates of consciousness)!!!!!!!!!!!!

And all those silly extrapolations of how much the brain can compute if the
brain can compute all day (based on such simplistic notions as you seem to
think are veridical), have been shown to be silly!

See Chalmer's page on such at:
http://www.u.arizona.edu/~chalmers/biblio.html

BTW, I have read ALL of those papers. This is my life's work.

> If the neuron activation function were
> linear, it would only be able to store y=Ax+b, which contains
> very little information.
>
> >> 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.
> >
> > Or goes crazy! (Becomes chaotic)
>
> See, I make a living working on systems that are chaotic, so I
> don't view them as crazy.

I was using the term loosely.

> For example, the human brain NEEDS
> to be chaotic to be functional. Limit cycles are the abnormal
> dynamics of brains (epilepsy, etc.).

I agree.

>
> > I don't see as strong a link as you do evidently. There are
> > far more important aspects that affect robustness and
> > effectiveness of a system than saturation and threshold.
>
> I wasn't trying to imply that threshold and saturation are
> fundamental to robustness of dynamics of nonlinear systems,
> but instead that it's fairly easy for self-organizing (e.g.,
> biological) systems that have these characteristics to develop
> robust dynamics.

Hmmm - OK - let me think about that.

>
> >> > 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.
> >
> > Yo can clamp well-before a saturation level!
>
> Clamping is functionally a sudden saturation.

No! Not theoretically or practically.

Control systems are clamped at a setpoint that assures continued, NORMAL
operation, in the vast majority of cases.

>
> Yeesh, enough already!
>
> --
> -Wayne

OmegaZero2003

December 21st, 2003, 11:09 PM

"OmegaZero2003" > wrote in message
s.com...
>
> "Wayne S. Hill" > wrote in message
> ...
> > OmegaZero2003 wrote:
> >
> > > "Wayne S. Hill" > wrote...
> > >> OmegaZero2003 wrote:
> > >> >
> > >> > 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.
> > >
> > > Have you read his book?
> >
> > I haven't read it, but have discussed this at length with
> > someone who has read it, attended Wolfram's lectures, and
> > discussed it with Wolfram.
> >
> > >> 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),
> > >
> > > It does not ahve to; the form and whether it is local or
> > > non-local are orthogonal.
> >
> > Heh: we're definitely talking past each other.
> >
> > > My point is that there are linear systems.
> >
> > Yawn.
> >
> > > This makes little sense. It is the complexity of a system
> > > that determines the breadth and depth of a system_state
> > > tree.
> >
> > Again, we're talking past each other.
> >
> > > A complex system, or a dynamical system need not exhibit
> > > emergent phenomena. The systems that do exhibt emergent
> > > phenomena however, are usually complex dynamical sytems.
> >
> > I don't know if I've mentioned this in this thread, but the
> > term "emergent" is not accepted by the bulk of NLD researchers
> > (mathematicians or physicists).
>
>
> I would not agreee with that. it may (certainly is I will say) be the case
> that what is characterized *as* emergent* is not agreed to.
>
> There is a difference.
>
> That there is a definition/theory of emergence is indisputable. That such
> has been defined with mathematical characterizations of systems is also
> true.
>
> What usually is confused or, better, *conflated* by those whom you may be
> speaking, is "emergence" and "synergistic phenomena".
>
>
>
> >
> > > That something varies smoothly (not descrete steps I presume
> > > you mean), does not mean it does not have distinguisable
> > > states!!!!!! That is what intergation and differentiation
> > > are all about.
> >
> > Once again, we're talking past one another.
> >
> > > Or VV!! Chaotic systems far from equilibrium. See
> > > Prigogine.
> >
> > Yeah, yeah.
> >
> > >> > 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).
> > >
> > > Well - I think it is mostly true as I said. But my original
> > > point is that there are linear systems (hell - that is what
> > > LP is for!!).
> > >
> > > But - in that case...
> > >
> > > I think we should have been discussing the (a)/(b) dichotomy
> > > I mentioned above. Whether nature is discontinuoous or
> > > continuous.
> >
> > Ack!
> >
> > >> 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.
> > >
> > > Well -err - not necessarily. The computational capability
> > > of brain or any subset depends on how yu think it
> > > characterizes, or *represents* information!!
> >
> > But a tiny NN is very simple, and it's quite clear how it
> > stores information.
>
> No is isn't!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>
> It isn't clear at all how brain *represents* information. This is one of
> the biggest challenges facing neuroscience; how to span the gap between
the
> psychological phenomena/overt behavior (verbal behavior etc.) and the NCCs
> (the neural correlates of consciousness)!!!!!!!!!!!!
>
> And all those silly extrapolations of how much the brain can compute if
the
> brain can compute all day (based on such simplistic notions as you seem to
> think are veridical), have been shown to be silly!
>
> See Chalmer's page on such at:
> http://www.u.arizona.edu/~chalmers/biblio.html
>
> BTW, I have read ALL of those papers. This is my life's work.

Since I know you are not gonna wade through 2000 papers, here is the part
that pertains:

http://www.u.arizona.edu/~chalmers/biblio/4.html#4.2

What is key is *how* the brain represents information and that is a subject
of *intense* debate and research!!!

>
>
> > If the neuron activation function were
> > linear, it would only be able to store y=Ax+b, which contains
> > very little information.
> >
> > >> 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.
> > >
> > > Or goes crazy! (Becomes chaotic)
> >
> > See, I make a living working on systems that are chaotic, so I
> > don't view them as crazy.
>
> I was using the term loosely.
>
> > For example, the human brain NEEDS
> > to be chaotic to be functional. Limit cycles are the abnormal
> > dynamics of brains (epilepsy, etc.).
>
> I agree.
>
>
>
> >
> > > I don't see as strong a link as you do evidently. There are
> > > far more important aspects that affect robustness and
> > > effectiveness of a system than saturation and threshold.
> >
> > I wasn't trying to imply that threshold and saturation are
> > fundamental to robustness of dynamics of nonlinear systems,
> > but instead that it's fairly easy for self-organizing (e.g.,
> > biological) systems that have these characteristics to develop
> > robust dynamics.
>
>
> Hmmm - OK - let me think about that.
>
> >
> > >> > 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.
> > >
> > > Yo can clamp well-before a saturation level!
> >
> > Clamping is functionally a sudden saturation.
>
> No! Not theoretically or practically.
>
> Control systems are clamped at a setpoint that assures continued, NORMAL
> operation, in the vast majority of cases.
>
> >
> > Yeesh, enough already!
> >
> > --
> > -Wayne
>
>

Wayne S. Hill

December 21st, 2003, 11:11 PM

OmegaZero2003 wrote:

> "Wayne S. Hill" > wrote...
>> OmegaZero2003 wrote:
>>
>> > My original point to the OP on the topic was a retort to
>> > the statement that *all* systems are nonlinear.
>> >
>> > That is not true.
>>
>> Nonsense. The OP never said any such thing. 8-p
>
> Here is the context; I see you were pointing to biological
> systems.

I wasn't the OP.

--
-Wayne

OmegaZero2003

December 21st, 2003, 11:20 PM

"Wayne S. Hill" > wrote in message
...
> OmegaZero2003 wrote:
>
> > "Wayne S. Hill" > wrote...
> >> OmegaZero2003 wrote:
> >>
> >> > My original point to the OP on the topic was a retort to
> >> > the statement that *all* systems are nonlinear.
> >> >
> >> > That is not true.
> >>
> >> Nonsense. The OP never said any such thing. 8-p
> >
> > Here is the context; I see you were pointing to biological
> > systems.
>
> I wasn't the OP.

OK - nevermind.

I thought it was you that said that about biological systems?

>
> --
> -Wayne

OmegaZero2003

December 21st, 2003, 11:43 PM

"Ignoramus32303" > wrote in message
...
> Some systems are linear, within some limits, and within a certain
> accuracy.
>
> There is no perfect linear system.

What is "perfect"?

Fist - ther is a rigorouus *mathematical* defintion of what it takes for a
system to be characterized as linear by definition.

You need to find out what that is (I gave a lot of info/refs for you to do
so easily).

> Most systems that we talk about as
> linear, fail at being linear as you increase the input, the failure
> and non-linearity growing with the input.

Many do; not all.

> Sometimes, to become
> sufficiently non-linear, the input has to grow to unreasonable levels,

Yeah - like an (audio) amp being turned way up to saturation whenre you hear
screeches in the output.

> reasonable defined as what we experience in real life.

Well - some audio systems are inadvertently turned up too loud!

>
> I believe that I have given a fairly accurate summary that should be
> supported by consensus.

Fairly accurate is not accurate enough, apparently. The devil is in the
details and there are systems that fall within the mathematical definition
that are not "llinearized", subclassed (as with the audio amp), or
approximated.

>
> i

OmegaZero2003

December 22nd, 2003, 12:30 AM

"Ignoramus32303" > wrote in message
...
> In article >,
OmegaZero2003 wrote:
> >
> > "Ignoramus32303" > wrote in message
> > ...
> >> Some systems are linear, within some limits, and within a certain
> >> accuracy.
> >>
> >> There is no perfect linear system.
> >
> > What is "perfect"?
>
> that gives a response exactly proportional to the output, to any
> output.

Good!

I should have mentioned an obvious one: optics!

See:
http://www.wkonline.com/a/Linear_Systems_Fourier_Transforms_and_Optics_04712 92885.htm

>
> > Fist - ther is a rigorouus *mathematical* defintion of what it takes for
a
> > system to be characterized as linear by definition.
> >
> > You need to find out what that is (I gave a lot of info/refs for you to
do
> > so easily).
> >
> >
> >> Most systems that we talk about as
> >> linear, fail at being linear as you increase the input, the failure
> >> and non-linearity growing with the input.
> >
> > Many do; not all.
> >
> >> Sometimes, to become
> >> sufficiently non-linear, the input has to grow to unreasonable levels,
> >
> > Yeah - like an (audio) amp being turned way up to saturation whenre you
hear
> > screeches in the output.
>
> try getting the amp to amplify 1 megawatt of power...
>
> >> reasonable defined as what we experience in real life.
> >
> > Well - some audio systems are inadvertently turned up too loud!
> >
> >>
> >> I believe that I have given a fairly accurate summary that should be
> >> supported by consensus.
> >
> > Fairly accurate is not accurate enough, apparently. The devil is in the
> > details and there are systems that fall within the mathematical
definition
> > that are not "llinearized", subclassed (as with the audio amp), or
> > approximated.
>
> Yes, details are important.
>
> i

Wayne S. Hill

December 22nd, 2003, 12:32 AM

OmegaZero2003 wrote:

> "Wayne S. Hill" > wrote...
>
>> I wasn't the OP.
>
> OK - nevermind.
>
> I thought it was you that said that about biological
> systems?

Yeah, in a follow-up.

--
-Wayne

Wayne S. Hill

December 22nd, 2003, 12:38 AM

OmegaZero2003 wrote:

> "Wayne S. Hill" > wrote...
>
>> But a tiny NN is very simple, and it's quite clear how it
>> stores information.
>
> No is isn't!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

A tiny artificial neural network (which is what I've been
referring to all along)? Sure it is. I'm not talking about
brains here (although a friend of mine has mapped the function
of the sense of smell of a crayfish brain, and he thinks he
knows how it works in detail).

>> Clamping is functionally a sudden saturation.
>
> No! Not theoretically or practically.
>
> Control systems are clamped at a setpoint that assures
> continued, NORMAL operation, in the vast majority of cases.

<sigh>

--
-Wayne

OmegaZero2003

December 22nd, 2003, 12:50 AM

"Wayne S. Hill" > wrote in message
...
> OmegaZero2003 wrote:
>
> > "Wayne S. Hill" > wrote...
> >
> >> But a tiny NN is very simple, and it's quite clear how it
> >> stores information.
> >
> > No is isn't!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>
> A tiny artificial neural network (which is what I've been
> referring to all along)? Sure it is. I'm not talking about
> brains here (although a friend of mine has mapped the function
> of the sense of smell of a crayfish brain, and he thinks he
> knows how it works in detail).

Did you bother to see the papers on computing and representation I
referenced?

I do not care what the neurophsyiological response of a crayfish CNS is;
there ain't any instruments yet that can tell just what processes and
properties in *any* part of a NN exactly *represent* a "piece" of
information - even given what the definition of "information" is (beyond a
difference).

Ask your friend how the smell is represented to the crayfish? What is it
like to be a crayfish smelling a pizza for example?

Do you know what I am talking about when I use the word: "representation"?
It is key.

Otherwise , your friend is seeing Neural Correlates Of Smelling. Those are
correlates and not the representation of the qualia of the smell.

Let me give a quick example. We know how the VC (visual cortex) works in
detail. Trust me on this. Yet, we now next to nothing about what it is that
the NNet (together with its associated environmental context - the
neurochemicals, fields etc. - the soup the neurons are immersed in) does to
*represent*, say, the image of me performing a 1000 pound squat in a meet.
Or the image that Michael Jordan used to visualize himslef in any number of
patterns in which he scored.

The image is the representation and it is an image presented to a conscious
process that is made aware, or is aware, of that *represenation* qua (as)
the real thing!

This is a key issue in cognitive neuroscience - the binding problem is an
associated issue - how do all those things (smell, taste, thoughts etc.)
come together to represent a *whole* to the conscious being?

Much of that issue arises from the unknown manner in which a neural net in
situ (as I qualified above - in the soup), represents that information and
performs "computations" upon it.

In terms of computational neuroscience and ANNs(artificial neural net),
remember that the ANN is a couple orders of magnitude less sophisticated (at
least) (using simple I/O transforms and connection schemes used to build
multi-layer ANNS) than the real thing in situ.

>
> >> Clamping is functionally a sudden saturation.
> >
> > No! Not theoretically or practically.
> >
> > Control systems are clamped at a setpoint that assures
> > continued, NORMAL operation, in the vast majority of cases.
>
> <sigh>
>
> --
> -Wayne

OmegaZero2003

December 22nd, 2003, 01:03 AM

"OmegaZero2003" > wrote in message
s.com...
>
> "Wayne S. Hill" > wrote in message
> ...
> > OmegaZero2003 wrote:
> >
> > > "Wayne S. Hill" > wrote...
> > >
> > >> But a tiny NN is very simple, and it's quite clear how it
> > >> stores information.
> > >
> > > No is isn't!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> >
> > A tiny artificial neural network (which is what I've been
> > referring to all along)? Sure it is. I'm not talking about
> > brains here (although a friend of mine has mapped the function
> > of the sense of smell of a crayfish brain, and he thinks he
> > knows how it works in detail).
>
> Did you bother to see the papers on computing and representation I
> referenced?

Here is the page(s) with live links to the online papers.

http://www.u.arizona.edu/%7Echalmers/online.html

The Consciousness and Physics set and the Consciousness and Artificial
Intellgence set are appropo.

If you merely look through the titles, you will absorb a lot - that is - you
will see that the characterization of any *real* live NN *in situ* involves
a huge amount of parameters and processes, from the neurochemical and field
distributions and desities (and how that afffects signalling ) to
oscillatory effects on processing and on and on.

Lots of progress, but the upshot is that neurosci has not come up with a
theory of how the brain (or parts of the brain) represent "information" such
that it can be cognized/processed/computed by some conscious entity (like a
crayfish).

And if you tell the story that knowing a simple I/O scheme (based on the
go-no_go/thresholding/etc)of the black box model of a neuron (or group of
neurons), then you are missing, oh - perhaps 99% of what is going on!

Signaling, computation and representation are accomplished through a host of
mechansims that no theory has provided adequate explanation for yet.

>
> I do not care what the neurophsyiological response of a crayfish CNS is;
> there ain't any instruments yet that can tell just what processes and
> properties in *any* part of a NN exactly *represent* a "piece" of
> information - even given what the definition of "information" is (beyond a
> difference).
>
> Ask your friend how the smell is represented to the crayfish? What is it
> like to be a crayfish smelling a pizza for example?
>
> Do you know what I am talking about when I use the word: "representation"?
> It is key.
>
> Otherwise , your friend is seeing Neural Correlates Of Smelling. Those
are
> correlates and not the representation of the qualia of the smell.
>
> Let me give a quick example. We know how the VC (visual cortex) works in
> detail. Trust me on this. Yet, we now next to nothing about what it is
that
> the NNet (together with its associated environmental context - the
> neurochemicals, fields etc. - the soup the neurons are immersed in) does
to
> *represent*, say, the image of me performing a 1000 pound squat in a meet.
> Or the image that Michael Jordan used to visualize himslef in any number
of
> patterns in which he scored.
>
> The image is the representation and it is an image presented to a
conscious
> process that is made aware, or is aware, of that *represenation* qua (as)
> the real thing!
>
> This is a key issue in cognitive neuroscience - the binding problem is an
> associated issue - how do all those things (smell, taste, thoughts etc.)
> come together to represent a *whole* to the conscious being?
>
> Much of that issue arises from the unknown manner in which a neural net in
> situ (as I qualified above - in the soup), represents that information and
> performs "computations" upon it.
>
> In terms of computational neuroscience and ANNs(artificial neural net),
> remember that the ANN is a couple orders of magnitude less sophisticated
(at
> least) (using simple I/O transforms and connection schemes used to build
> multi-layer ANNS) than the real thing in situ.
>
>
>
>
>
>
> >
> > >> Clamping is functionally a sudden saturation.
> > >
> > > No! Not theoretically or practically.
> > >
> > > Control systems are clamped at a setpoint that assures
> > > continued, NORMAL operation, in the vast majority of cases.
> >
> > <sigh>
> >
> > --
> > -Wayne
>
>

Proton Soup

December 22nd, 2003, 01:32 AM

On Sun, 21 Dec 2003 21:35:47 GMT, "OmegaZero2003"
> wrote:

>
>"Wayne S. Hill" > wrote in message
...
>> 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!
>>
>> 'ang on there, when we refer to linearity in such systems,
>> we're referring to linearity of the dynamics, i.e.,
>>
>> x-dot = A * x + b
>
>'ang on there yourself!!! Do you know WHAT characterizes a linear system
>mathematically? Do you know the difference between an additive versus a
>multiplicative factor? Well there is your answer!
>
>In case you have not understood - will will take it slowly at first. Atend:
>here is help for you:
>
>"The response of a [ linear ] system to a sum of inputs is the sum of the
>responses to each individual input separately.

All engineers should know what superposition is. Are you trying to be
condescending?

>These two nice properties allow a whole range of tools to be applicable in
>designing linear systems and predicting their behavior. Some more examples
>of linear systems in real life:
>
>a) Frequency filters -- circuits which only pass low frequencies and reject
>high, or vice-versa.

They only work within a narrowly-bounded input-output range. Too much
signal input and they will break (non-linear).

>b) Delays are linear. Echos from faraway canyons are linear. Shout twice as
>loud, get an echo twice as loud. Two people shouting at the same time comes
>back as two people echoing at the same time.

Two much volume and you will heat the air, changing the transmission
characteristics (speed) of your pressure wave (non-linear).

>c) Many different kinds of economic systems -- looking at the apple juice
>production (output) vs. the apple crop yield, for example.

This too will fail linearity at the extremes of yield. A bumper crop
one year could mean an inability to harvest all the fruit before it
goes bad.

>d) Limiting cases of non-linear systems for small inputs: Even if the
>system's response may not satisfy the equation above exactly, it often will
>well enough for small enough inputs. In this case, even if the number of
>apples bought by consumers, say, is inversely proportional to the price of
>apples, you can still model small changes around a reference price with
>linear systems (but beware when the inputs get large!).
>(http://van.hep.uiuc.edu/van/qa/section/Everything_Else/Math/20020319233837.
>htm)
>
>Note that the last item (d) talks about linearization/signal
>decomposition/approximation_techniques of/for non-linear systems, which I am
>NOT talking about. We are talking about bona fide LINEAR systems fulfilling
>all the mathematical/theoretical properties that decades of science has
>determined qualifies a system as "Linear" *by definition*!!!!

Real systems are always limited on their inputs. Real systems break
down at some point if too much energy enters the system. Linearity is
only a trait of a system over its useful operating range.

>I am also not talking about trivial examples of what is a linear system in
>toto (including extreme), but is subclassed to non-interesting behavior
>(like an amp NOT in saturation mode).

In reality, people who make things that work must take nonlinearity
into account. It's the only way to make reliable systems. You may
not be thinking in toto, but I am, because I have to. We know what
linear is. We also know it doesn't really exist. We try to make
things work as linear as possible, because many useful things exhibit
a limited version of it (like amps and filters).

The definition of linearity for that amp doesn't allow for limiting
the input. If it were truly linear, you wouldn't have to place extra
limits on it. So I think you are coming around to accept the
assertion that linear systems don't really exist. I will admit,
though, they are nice on paper.

>> This omits simple algebraic behaviors (because x-dot = 0).
>>
>> > - Hamiltonian oscillators and like systems. (the
>> > direction field specifically)
>>
>> Not of great interest in biological systems, except as a
>> backdrop.
>
>
>We were not restricting the discussion to biological systems.
>
>My original retort to the OP's statement: "All systems are non-linear" was
>to say:
>
>That is not true.
>
>It is easy to falsify hypotheses of the form: "All...(x) are (y)" in the
>sense that only one counter-example need be provided.
>
>FYI, a special class of linear control systems known as singularly perturbed
>control systems, uses the Hamiltonian approach ( recursive) approach based
>on t exact pure-slow and pure-fast decoupling of optimal control problems.
>
>Another interesting special class of linear systems::
>
>"Linear systems with non-rational transfer functions (In this project linear
>systems described by partial differential equations having non-rational
>transfer functions are studied. The aim of this project is to analyse the
>dynamic behaviour and properties of linear input-output systems with
>non-rational transfer functions (such as flexible robot arms and heat
>processes) in the frequensy domain. For some classes of such systems it is
>possible to develop the overall transfer function in analytical form by the
>transmission matrix method. The interaction between different parts of the
>system (including the way they are coupled to each other) can then be
>analysed.
>The transmission matrix method has been succesfully applied to multi-link
>flexible robot arms and to buckling of multi-segment columns. Another
>application concerns the stability of heat processes described by parabolic
>partial differential equations. Based on the transmission matrix method a
>Nyquist stability test was developed for sandwich-layered materials with
>linear inner heat source." (M. Vajta DISC Project 1999)

Good grief. Robot arms are the last thing in the world that would be
linear. There may be some use of linear mathematics in the control
law, but that's it. Linear math in control algorithms is the norm.

>for a linear system characterized using N first-order linear homogeneous
>differential equations with constant coefficient can be found at: (with a
>little more detailed math):
>http://www.mathpages.com/home/kmath440/kmath440.htm
>
>I leave it to the reader to come up with only three biological systems that
>are so charaterized (this is an easy quiz to see if you understand what a
>linear system is).
>
>You can also look up sparse linear systems for funzies!
>
>
>>
>> > - continuous-time systems like electrical networks, many
>> > mechanical systems
>>
>> Aside from the fact that linearity is an approximation in all
>> such systems, they all have their nonlinear limits. The
>> nonlinearity is whatever it is that keeps the systems
>> operating in their linear range.
>>
>> > - any discrete system with a transfer
>> > function whose input, response and output functions depend
>> > on one variable
>>
>> Huh?
>
>I think you have to learn the meaning of linear. Note that I am NOT talking
>about linearisation of non-linear systems (which seems to be talked about in
>this thread instead of the major contentions about what exists.)!!! I am not
>talking about signal decomposition to acheive a linear treatment (what you
>called piecewise).
>
>
>Here is some help. Note that he points out some examples in the text.
>
>"Signals, Linear Systems, and Convolution
>
>Professor David Heeger
>
>Characterizing the complete input-output properties of a system by
>exhaustive measurement is
>
>usually impossible. Instead, we must find some way of making a finite number
>of measurements
>
>that allow us to infer how the system will respond to other inputs that we
>have not yet measured.
>
>We can only do this for certain kinds of systems with certain properties. If
>we have the right kind
>
>of system, we can save a lot of time and energy by using the appropriate
>theory about the system's
>
>responsiveness. Linear systems theory is a good time-saving theory for
>linear systems which obey
>
>certain rules. Not all systems are linear, but many important ones are. When
>a system qualifies as
>
>a linear system, it is possible to use the responses to a small set of
>inputs to predict the response to
>
>any possible input. This can save the scientist enormous amounts of work,
>and makes it possible
>
>to characterize the system completely."
>
>Please note the statement: "Not all systems are linear, but many important
>ones are."
>
>And now for a little math:
>
>"Linear Systems
>
>A system or transform maps an input signal x(t) into an output signal y(t):
>
>y(t) = T[x(t)];
>
>where T denotes the transform, a function from input signals to output
>signals.
>
>Systems come in a wide variety of types. One important class is known as
>linear systems. To
>
>see whether a system is linear, we need to test whether it obeys certain
>rules that all linear systems
>
>obey. The two basic tests of linearity are homogeneity and additivity.
>
>4
>
>Homogeneity. As we increase the strength of the input to a linear system,
>say we double it,
>
>then we predict that the output function will also be doubled. For example,
>if the current injected
>
>to a passive neural membrane is doubled, the resulting membrane potential
>fluctuations will double
>
>as well. This is called the scalar rule or sometimes the homogeneity of
>linear systems.
>
>Additivity. Suppose we we measure how the membrane potential fluctuates over
>time in
>
>response to a complicated time-series of injected current x1(t). Next, we
>present a second (different)
>
>complicated time-series x2(t). The second stimulus also generates
>fluctuations in the membrane
>
>potential which we measure and write down. Then, we present the sum of the
>two currents
>
>x1(t) + x2(t) and see what happens. Since the system is linear, the measured
>membrane potential
>
>fluctuations will be just the sum of the fluctuations to each of the two
>currents presented separately.
>
>Superposition. Systems that satisfy both homogeneity and additivity are
>considered to be
>
>linear systems. These two rules, taken together, are often referred to as
>the principle of superposition.
>
>Mathematically, the principle of superposition is expressed as:
>
>T(
>x1 + x2) =
>T(x1) + T(x2) (2)
>
>Homogeneity is a special case in which one of the signals is absent.
>Additivity is a special case in
>
>which
>= = 1.
>
>Shift-invariance. Suppose that we inject a pulse of current and measure the
>membrane potential
>
>fluctuations. Then we stimulate again with a similar pulse at a different
>point in time, and
>
>again we measure the membrane potential fluctuations. If we haven't damaged
>the membrane with
>
>the first impulse then we should expect that the response to the second
>pulse will be the same as
>
>the response to the first pulse. The only difference between them will be
>that the second pulse has
>
>occurred later in time, that is, it is shifted in time. When the responses
>to the identical stimulus
>
>presented shifted in time are the same, except for the corresponding shift
>in time, then we have
>
>a special kind of linear system called a shift-invariant linear system. Just
>as not all systems are
>
>linear, not all linear systems are shift-invariant.
>
>In mathematical language, a system T is shift-invariant if and only if:
>
>y(t) = T[x(t)] implies y(t
>
>
>
>"
>
>
>
>That is pretty much what I told the OP. Not ALL systems are non-linear.
>
>Period, End of story.
>
>QED and all that.
>
>
>Gabel, Robert A. and Roberts, Richard A., 1973, Signals and Linear Systems,
>New York: John Wiley & Sons, 415 pp.
>
>Gaskill, Jack D., 1978, Linear Systems, Fourier Transforms, and Optics, New
>York: John Wiley & Sons, 554 pp.
>
>Lathi, B. P., 1992, Linear Systems and Signals, Carmichael, California:
>Berkeley-Cambridge Press, 656 pp.
>
>Lewis, Laurel J., Reynolds, Donald K., Bergseth, F. Robert, Alexandro, Jr.,
>Frank J., 1969, Linear Systems Analysis, New York: McGraw-Hill Book Company,
>489 pp.
>
>Schwarz, Ralph J. and Friedland, Bernard, 1965, Linear Systems, New York:
>McGraw-Hill Book Company, 521 pp
>
>
>
>
>
>
>>
>
> The most common form of discrete systems is the
>> iteration (strobing based on time or state) of a continuous
>> system. A single-variable system would be of a form
>>
>> x-dot = f(x)
>>
>> Here, f can be (generally is) a nonlinear function of x, so
>> the system will show nonlinear behavior, both continuously and
>> discretely.
>
>
>>
>> > - any systems preserving homogeneity (output
>> > proportional to input) and superposition (a way of combining
>> > linear functions such that the result is a linear function)
>>
>> In other words, linear systems.
>
>And there are lots of those!
>
>Do yourself a favor and merely google "linear system", read what you care
>to, then come back. I do not believe you do not get this.
>
>I can give you a good start:
>
>Linear System Theory and Design
>by Chi-Tsong Chen
>
> Read Chapter 2!
>
>>
>> > Even non-deterministic systems can be modeled using
>> > statistics for linear dynamics.
>>
>> Not in their dynamics.
>
>You do not know what you are talking about.
>
>>This is the classic engineer's mistake
>> of characterizing in statistical terms what is not understood.
>> When you delve into the NLD of such systems, you gain true
>> insight into what makes them work. I can give examples.
>
>I have more examples in my head than you can provide. I worked on this for
>20 years.
>
>>
>> > 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.
>>
>> That is an approximation that people sometimes find useful to
>> make. That doesn't make it so, especially when you take the
>> system outside of the limited context in which you placed it
>> for convenience.
>
>There are systems that are approximated as linear; that is called
>*linearization* and there is a gamut of math to deal with how to do that
>properly!
>
>But there are many systems that are inherently and demonstrably linear.
>
>
>>
>> --
>> -Wayne
>

---
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

OmegaZero2003

December 22nd, 2003, 01:35 AM

"Proton Soup" > wrote in message
...
> On Sun, 21 Dec 2003 21:35:47 GMT, "OmegaZero2003"
> > wrote:
>
> >
> >"Wayne S. Hill" > wrote in message
> ...
> >> 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!
> >>
> >> 'ang on there, when we refer to linearity in such systems,
> >> we're referring to linearity of the dynamics, i.e.,
> >>
> >> x-dot = A * x + b
> >
> >'ang on there yourself!!! Do you know WHAT characterizes a linear system
> >mathematically? Do you know the difference between an additive versus a
> >multiplicative factor? Well there is your answer!
> >
> >In case you have not understood - will will take it slowly at first.
Atend:
> >here is help for you:
> >
> >"The response of a [ linear ] system to a sum of inputs is the sum of the
> >responses to each individual input separately.
>
> All engineers should know what superposition is. Are you trying to be
> condescending?

Who? Me?

Sorry. I was probably a little. It seemed elementary considering the
responses seemed to be intelligent but missed major aspects of this.

Wayne S. Hill

December 22nd, 2003, 02:15 AM

OmegaZero2003 wrote:

> "Proton Soup" wrote...
>
>> All engineers should know what superposition is. Are you
>> trying to be condescending?
>
> Who? Me?
>
> Sorry. I was probably a little. It seemed elementary
> considering the responses seemed to be intelligent but
> missed major aspects of this.

No they didn't. That was a representation in your own wetware.

--
-Wayne

Wayne S. Hill

December 22nd, 2003, 02:37 AM

OmegaZero2003 wrote:

> Did you bother to see the papers on computing and
> representation I referenced?

Nope! 8-)

See, I have a limited capacity for curiosity, and I suspect
we're arguing about subtleties that verge on the meaningless.
At the very least, a lot is being lost in translation.

> I do not care what the neurophsyiological response of a
> crayfish CNS is; there ain't any instruments yet that can
> tell just what processes and properties in *any* part of a
> NN exactly *represent* a "piece" of information - even given
> what the definition of "information" is (beyond a
> difference).

The problem I have with this is that there's a point, with a
very small number of neurons, where this distinction vanishes.
This is the same problem most researchers have with the idea
of "emergence". Beyond a high level of complexity, the
network representation is probably closest to a high-
dimensional hologram. At a low level of complexity, it's
probably pretty much like an ANN. Is the distinction one of
topological significance, or is it really all the same thing?

> In terms of computational neuroscience and ANNs(artificial
> neural net), remember that the ANN is a couple orders of
> magnitude less sophisticated (at least) (using simple I/O
> transforms and connection schemes used to build multi-layer
> ANNS) than the real thing in situ.

I never claimed otherwise: I brought ANN's into the
discussion because of the clear understanding of the roles of
threshold and saturation on their behavior.

--
-Wayne

Tom Morley

December 22nd, 2003, 02:54 AM

OmegaZero2003 wrote:
> "Proton Soup" > wrote in message
> ...
>
>>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.
>
>
> My original point to the OP on the topic was a retort to the statement that
> *all* systems are nonlinear.
>
> That is not true.
>
>
>>>- 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
>
>
>

As several people have pointed out, linear vs. non--linear, per se,
is meaningless. It all depends on the description. Some things are
exactly linear (in the right description.) Sometimes linear is just
local -- but even if local, this can provide quantitative information.
(The example that comes to mind is the tumbling book. Two
directions are stable, one is not. Linear analysis shows this.)

--
Tom Morley | Same roads
| Same rights
| Same rules
AIM: DocTDM

OmegaZero2003

December 22nd, 2003, 06:08 AM

"Tom Morley" > wrote in message
link.net...
>
>
> OmegaZero2003 wrote:
> > "Proton Soup" > wrote in message
> > ...
> >
> >>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.
> >
> >
> > My original point to the OP on the topic was a retort to the statement
that
> > *all* systems are nonlinear.
> >
> > That is not true.
> >
> >
> >>>- 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
> >
> >
> >
>
>
> As several people have pointed out, linear vs. non--linear, per se,
> is meaningless. It all depends on the description. Some things are
> exactly linear (in the right description.).

> Sometimes linear is just
> local -- but even if local, this can provide quantitative information.

Sure - but that is known as a subclassed system. You are only examining it
within a range of I/O/Xfer_function(s). Which is fine as far as it goes,

I was referring to a system that exhibits true linear behavior throughout
all known or extraploated ranges of input.

> (The example that comes to mind is the tumbling book. Two
> directions are stable, one is not. Linear analysis shows this.)

Yes; although the point that was made , as I now understand, was about
biological system, which certainly have more than the bulk of examples of
non-lineear systems.

>
>
> --
> Tom Morley | Same roads
> | Same rights
> | Same rules
> AIM: DocTDM
>

OmegaZero2003

December 22nd, 2003, 06:12 AM

"Wayne S. Hill" > wrote in message
...
> OmegaZero2003 wrote:
>
> > "Proton Soup" wrote...
> >
> >> All engineers should know what superposition is. Are you
> >> trying to be condescending?
> >
> > Who? Me?
> >
> > Sorry. I was probably a little. It seemed elementary
> > considering the responses seemed to be intelligent but
> > missed major aspects of this.
>
> No they didn't. That was a representation in your own wetware.

How do you know I am not an ANN!

You still have not shown how robustness is a function of saturation and/or
thresholding.

Although after thinking about it, in an oblique way, one can make up a story
about it - a mind game ala Einstein. I.e., theoretically, I can imagine
that a system can be thought of as robust if it escapes
deterioration/degradation and/or elimination from the context/environment if
it exhibits saturation/thresholding and that prevents state spaces leading
to elimination.

Coming up with a *real* example of such a charaterization in nature is left
to the reader.

>
> --
> -Wayne

OmegaZero2003

December 22nd, 2003, 06:25 AM

"Wayne S. Hill" > wrote in message
...
> OmegaZero2003 wrote:
>
> > Did you bother to see the papers on computing and
> > representation I referenced?
>
> Nope! 8-)
>
> See, I have a limited capacity for curiosity, and I suspect
> we're arguing about subtleties that verge on the meaningless.
> At the very least, a lot is being lost in translation.
OK.

>
> > I do not care what the neurophsyiological response of a
> > crayfish CNS is; there ain't any instruments yet that can
> > tell just what processes and properties in *any* part of a
> > NN exactly *represent* a "piece" of information - even given
> > what the definition of "information" is (beyond a
> > difference).
>
> The problem I have with this is that there's a point, with a
> very small number of neurons, where this distinction vanishes.

First, I suspect that that type of system is uninteresting.

Second, it probably does not exist as a real system in situ' one can take
away only so much of a system auntil it ceases *being* anything like what
you were trying to show in the first place.

Such is the case with a system whose function is representation (and
transformation/translation/signalling).

Third, that distinction is not a quatitative one - it is qualitative. take
away the neurochemical soup for example, and what you show about information
representation is apt to be misleading at best. *Analysis* (in the form of
reductionism)is not always a good approach when dealing with complexity .

> This is the same problem most researchers have with the idea
> of "emergence". Beyond a high level of complexity, the
> network representation is probably closest to a high-

But that is only the network representation; one of several maps, none of
which is the territory.

And most neuroscience researchers or AI researchers for that matter, so not
have a problem with emergence. It is quite well described and accepted.
Again, a really good book is Alwyn Scott's! I recommend it to any scientist
I speak with (just as I recommend Wolfram's work, and Bucky Fuller's
Synergetics).

> dimensional hologram. At a low level of complexity, it's
> probably pretty much like an ANN. Is the distinction one of
> topological significance, or is it really all the same thing?

I don't follow; I don;t think even a highly-connected network like the brain
has properties at the network level (nodes, connections, vertices etc.) that
are appropriate in a discussion about holographical metaphors.

Now, quantum effects, or other field effects -now we're talking.

>
> > In terms of computational neuroscience and ANNs(artificial
> > neural net), remember that the ANN is a couple orders of
> > magnitude less sophisticated (at least) (using simple I/O
> > transforms and connection schemes used to build multi-layer
> > ANNS) than the real thing in situ.
>
> I never claimed otherwise: I brought ANN's into the
> discussion because of the clear understanding of the roles of
> threshold and saturation on their behavior.

YEs - OK - I understand. But those are man-made systems that, llike I said
above, are so abstracted, or rahter, simplified from the actual NN in the
CNS -in situ with all the attendent functions provided by messenger
molecules, densities , field effects etc., that the analysis has analysed
away any chance of getting a parsimonious, satisfying sanswer to things like
representation in a real brain.

>
> --
> -Wayne