Friday, November 28, 2008

The Best of All Possible Worlds

Some weeks ago, I wrote about the Variational Principle. In a nutshell, it tells us that systems optimize the value of a certain function. In physics that function is the “action”. The way one finds the optimal configuration is to make small changes, called “variations”, and to see how the system reacts to it. If the situation gets less optimal under all changes, you've found a solution.

On this general level, it isn't hard to see the parallels: Trying to optimize situations is something we do every day. On a personal level (fastest way to the restroom), on a group level (best place for dinner), on a national level (unemployment rate) or on a global level (child mortality rate). Optimizing can mean maximizing or minimizing.

The mathematical formulation of the variational principle was inspired by Leibnitz' conjecture that we live in “The Best of All Possible Worlds”. Here, I want to elaborate on the analogy between social and natural systems, and just bounce some thoughts off you.

One should keep in mind that in physics the variations do not “really” take place. They are imagined tries to find the optimal situation, but the optimal solution is then the one which just “is”. Instead, I will here talk about an optimization that takes place over time, where the process of trial and improvement is real.

A Landscape of Possible Worlds

We ask of the systems that govern our lives is that they fulfil a certain task, and help us to work towards a goal. Our economic system is a good example. Its goal is to distribute goods, free capital to allow future investments, and connect traders - all to spur progress. Our political systems have too many tasks to count, but just to name a few: They allow us to live with maximal freedom for everybody without violating anybody else's rights, and they balance long-term with short-term interests. The academic system too has a task, that is to identify valuable research and to build a body of knowledge that helps us to understand nature and actively shape our future.

In most cases however, these systems were not specifically designed and set up for a certain task, they just emerge out of need or out of opportunity and represent cases of spontaneous self-organization. Nevertheless, it is useful to think of a system as having the task of optimizing something desirable, such as minimizing poverty or maximizing the usefulness of education.


For all the possible states the system could be in, consider there is some quantity expressing how good the status of the system is. We will refer to the value of this quantity over the set of possible states as a “landscape” of possibilities (see figure above). In the social context, performance of a system is most often hard to define, and equally hard to measure. However, it might not be necessary to quantify such a function, as long as there are means to evaluate how different states of the system compare to each other. All one really needs to know is whether one situation is “better” than some other, according to some criteria.

It requires effort to bring the system into a more optimal state, since it goes together with an increase of order and decrease of randomness. It also takes constant effort to keep the system in an ordered state. On a fundamental level, many of these efforts are connected to energy supply.

Primary Goals and Secondary Criteria

The essential ingredient to the optimization is now evaluating the system under small changes, to keep the improvements and to toss the worsening. This means the system needs to have means to evaluate how well it is performing. For this evaluation it is first necessary to understand the primary goal of a system, meaning to know what is to be optimized. It can happen easily that during certain phases, aiming for the primary goal goes along with optimizing secondary, derived criteria.

I have previously written about this distinction between primary goals and secondary criteria here and here. It seems to be very common that aiming to optimize secondary criteria instead of primary goals deviates a system from its original task. Bank managers aiming at high bonuses for example might under certain circumstances indeed correlate with an optimal functioning of our financial system, but this correlation is not guaranteed to hold and can lead the system far away from optimizing its primary goal. Similarly, publishing papers is certainly an important ingredient of scientific research and to some extend correlated with research activity and progress. However, the number of publications is a derived secondary criteria that does not generally have to be identical with valuable research. And keeping lobbies happy is a secondary criteria not generally correlated with the primary goal of the political system.


In all these cases, the dominance of secondary goals arises from them being easier to evaluate on an individual level, they thus represent personal incentives. On the long run, pursuing them can lead to a mismatch between the individuals following their micro-interests and the desired macro-behavior of the system, which is to optimize achieving its primary goal. If secondary criteria are used, it is thus necessary to readjust them appropriately so the feedback they provide works indeed towards the primary goal.

Local versus Global Optima

However, when optimizing one has to keep in mind that taking small steps and choosing the direction upwards will lead you to a mountain top, but this will not generally be the top of the highest mountain. A mountain top would be a “local optimum” whereas the highest mountain would be the “global optimum” (see figure below). Improving a local optimum by small changes implies going through a valley.

Yes, this is the same old story with the mountain climbers and valley crossers. Sometimes it has to get worse before it can get better.


Alternatively, one can make a big and courageous change to “tunnel” through a valley. This requires however very precise knowledge about the landscape, otherwise you might end up in a volcano crater lake or something.

Most often, one chooses a combination of both, a first large change followed by corrective adjustments.

Feedback

For the optimization to work well, there are thus two ingredients needed: variation and evaluation of the variation. Optimization within the system requires the possibility to evaluate the status relative to that of earlier states, and the ability to react to the outcome of this evaluation. The feedback should be such that the system evolves towards an optimum with regard to the primary goal.

Now there are systems in which the evaluation of its performance and the feedback on the system works better, and in others were it works worse. A free market economy for example is a system that detects very promptly consumers satisfaction (evaluation), and is very flexible in its immediate reaction (variation). A planned economy in contrast is very rigid, and if the predictions of the plan are anything off the actual reality, it easily fails to achieve its primary goal. This does not necessarily have to be the case, but given that social systems are very complex and one does not well know what the landscape looks like, predictions are enormously hard if not impossible, and such plans are very likely to fail due to lacking evaluation and variation.

Similarly, governing by monarchy can work to everybodies' satisfaction in case the monarch happens to know well what keeps the people happy and works towards this goal. It is however very unlikely, since the system lacks evaluation and a feedback mechanism that works towards the goal of achieving happiness for the people. A political system that allows for feedback of citizens' happiness has better chances of improving them. Socializing the means of productions on the other hand does not exclude the possibility to evaluating the system's performance, but the reaction to this evaluation is considerably damped due to lacking personal incentives.

In realistic social systems, the system can be pushed out of its limits of applicability in which case it breaks completely down and has to be rebuilt or replaced. For example chopping the king's head off.

Finding an optimal solution also might not be the only thing one is looking for. Given that realistic social systems are subject to statistical fluctuations, the stability of the state is also an important factor of its desirability. If a solution is unstable, it means that a small change can create an even larger change, and drives the system farther and farther away from the optimal situation. This is a so-called positive feedback, though the adjective sounds misleading. A negative feedback instead would want to work against the attempt to make changes.

Keep in mind that it takes effort to keep the system in a well-working state. A positive feedback would for example be one that does not allow anymore to invest this effort, upon which the system retreats to a less optimal state, which means it can invest even less effort and falls into an even less optimal state, etc all down into the valley were the situation is stable again. Dwindling energy supply that corrupts infrastructure and political stability could be such a case.

Evolving Backgrounds

An additional complication for social systems is that the background one is optimizing in, the landscape, depends on the history of the system itself. Take for example the case in which a major change to improve the political system has been suggested. One took a courageous step, followed by some small adjustment, but the situation turned out to be less optimal than initially. Then returning to the previous state might no longer be possible because the systems' configuration has meanwhile changed. Thus, what previously might have been a locally optimal state might have gone completely lost.

Something else that frequently happens is that mistakes dampen the courage to try changes. One can interpret this loss of courage as deepening the valleys between optima because more people will be unhappy under change. Trying to pass a resolution today might not be the same as passing it next year, even if the content does not change whatsoever. On the other hand, conservatism might increase stability - at least unless the background evolves under you and the optimum you might have been in moves elsewhere. This conflict between the resisting change to achieve stability and the need to adjust to the evolving background is a major tension in our social systems which also reflects in the political spectrum.

Bottomline

This might not be “The Best of All Possible Worlds”, but if we set up appropriately the systems that govern our lives we have a chance to make this world a little better.

25 comments:

Uncle Al said...

Multiply optimize locally or in one shot globally. Local efforts need coupling. Global efforts need accurate timely information.

Lossy coupled, modestly efficient local optimizations tesselating the space damp errors, corruption, and frank stupidity in real time. Government has tightly coupled positive feedback (sycophancy) phase-lagged versus reality, e.g., FEMA in New Orleans.

Washington globally optimizes mandated charity, retirement, healthcare, education, environment, Homeland Severity, and finance. The results are always disasters.

Plato said...

Much to think about here Bee. Not just for people of the US.

If one did not recognize some "basic fundamentals" about the economy, then it will slide past awareness that the "current system" will/shall remain valid for them.

Someone should take a look?:)

Best,

Bee said...

Looking isn't quite sufficient. Yes, the system needs a complete overhaul, not a superficial fix.

Plato said...

I know Bee. Not just Bee.

Social activism does not often reveal the intention, but is often considered as providing "negative feedback( I need to understand this better under your example)," to the circumstance without having people "looking first" and then judging. We need "all the information."

Economic policies do need to be looked at under the current situation to ask "what the influx of printed money" shall do for the current economy?

I don't know the answer. I suspect responsible people with science degrees do have the answer "having looked at the underlying reality" of the way we do things?

Apply your skills as you would want any event to be considered from a scientific perspective.

What would be your conclusion then? That we could take it and find the same thing "repeatable" once you provide the method?

Best,

Bee said...

Hi Plato,

No, I don't think it would become repeatable. There is a German song called "1000 and One Night" which nicely documents sudden threshold effects without apparent external cause. I think our possibilities to predict a system's evolution are thus very limited. It depends on the timescales. Very short and very long term behaviour might be easier to grasp than the intermediate one (similarly to the weather forecast/climate evolution). However, the important point is not the predictability but the way the system reacts to the possibly unpredictable. The relevant point is to set up the system such that it remains within its range of functionality during this evolution with high probability, even if the exact evolution is unknown.

There will however always be cases that can spoil this attempt, much like you can get hit by a meteroid tomorrow. Risk of a sudden unexpected breakdown can certainly never be excluded, but one could at least try to exclude the expected breakdowns. Best,

B.

Phil Warnell said...

Hi Bee,

I must say that as Plato reminds you have left much to consider here. To be honest I will have to look at this more carefully to have any great deal of it sinks in. Just as of now from at best only an instinctive level this type of described system is bound to be chaotic in nature and as such tiny differences can lead to large changes. I realize you imagine that feedback might be somehow built into the model to be utilized, which I find intriguing as there has been some evidence lately that even evolution may contain, in part, such a mechanism running parallel and together within the classic Darwinian process.

It also leaves me mindful of Isaac Asimov's famous Foundation Trilogy where a scientist named Hari Seldon developed a branch of mathematics called psychohisory to enable him to not only foresee the overall future yet also to mold it to benefit civilization’s progress and security.

The tricky part being it was so sensitive that if those being affected were to learn that such a thing existed and being incorporated it would destroy the ability of control it had. What was done is a remote planet, populated by a dedicated (and forever isolated) group of scientists was founded and kept to be a secret to enable the plan to be executed.

As the first book of the series was written in 1951 I was always astounded how close this resembled Chaos Theory , fathered first by Edward Lorentz in 1961, some ten years after resultant of computing how weather patterns diverged ( Butterfly Effect ). Later it was championed and further expanded by Benoit Mandelbrot and others.

What this whole thing holds as being unique is that it remained undetected until the advent of computers. It has since had me often fancifully wonder if Asimov’s vision could be finally realized with the perfection of quantum computing. Oh by the way, would you be willing to volunteer to spend your life on that planet which Asimov imagined would also be a required element?

Best,

Phil
P.S. This should not be taken as having what so ever any connection with the battle poor Stefan has been dealing with which is raging in another thread. Then again perhaps the papers in question have been so prolifically produced by a computer whom we are not as yet aware as being created.

Plato said...

I may have been confusing negative feedback with positive.

You can do the math on how many billion?:) What is the value of the "excessive reserve?"

This is the beginning of the deposit expansion process. In the first stage of the process, total loans and deposits of the banks rise by an amount equal to the excess reserves existing before any loans were made (90 percent of the initial deposit increase). At the end of Stage 1, deposits have risen a total of $19,000 (the initial $10,000 provided by the Federal Reserve's action plus the $9,000 in deposits created by Stage 1 banks). See illustration 4. However, only $900 (10 percent of $9000) of excess reserves have been absorbed by the additional deposit growth at Stage 1 banks. See illustration 5.

How many billion and who profits from "the interest?" It's a question. Not to forget to mention about the "devaluation of the dollar."

If there are changes in Paulson's position from the original intent, and it had been decided that the banks were to disseminate this money throughout the population as borrowed money, who was to benefit? Why was there a change?

Best,

Plato said...

The following must be held in context of Lincoln's Greenback.

CURRENCY, BANKING, AND THE MONEY TRUST

Yes, these money lenders began early to acquire control. They have never let it go. They started in Europe long, long ago, and just as soon as there was anything doing over here they were on hand. Alexander Hamilton was one of their supporters. I shall not review his acts, but shall refer to a few later things emanating directly from the banks. The English money lenders have co-operated with those of our country, and in 1862 an agent, quietly and under a sort of confidential seal, distributed among the aristocrats and the wealthy class a circular. It was called the Hazard Circular and related in a way to the Civil War. It read :

Quotation “B”

“Slavery is likely to be abolished by the war power and all chattel slavery abolished. This I and my European friends are in favor of, for slavery is but the owning of labor and carries with it the care of the laborers while the European plan, led on by England, is that capital shall control labor by controlling wages. The great debt that capitalists will see to it is made out of the war, must be used as a means to control the volume of money. To accomplish this the bonds must be used as a banking basis. We are now waiting for the Secretary of the Treasury to make this recommendation to Congress. It will not do to allow the greenback, as it is called, to circulate as money any length of time, as we cannot control that. But we can control the bonds and through them the bank issues.”

This shows how mercenary these usurers are. Rather than assume the care of the slaves, they would control labor with the use of capital. It necessarily followed that when the laborer ceased to be of service because of sickness or old age, he would be of no concern to capital. He could either get well or die without the capitalists being obliged to provide medical attention or bury the dead. Such was the interest that capital had in the result of the Civil War. The people of this country poured out both their treasure and their blood to establish the political and industrial independence of humanity, and the mercenary capitalists turned a trick of finance and converted the enormous sacrifice made by the people during that struggle into a victory for capital, in order that they might enforce upon humanity the industrial slavery that the trusts preferred rather than the chattel slavery which then existed in the Southern States.

Bee said...

Hi Phil,

Neither our political, nor economical, nor social systems are chaotic. They are complex, and hard to understand, they might be in practice impossible to predict, but their behavior is not sensitive to infinitely small changes. One thing that I find funny about this current financial crisis turning economical crisis is how often I've come accross comments blaming psychological quirks and irrationality. This is far from the truth. The truth is that on an individual level everybody who took part was acting rationally - short sighted, but rationally. The problem was just that this behavior did not result in any desirable emergent macroscopic trend (which would not have been hard to predict, but who'd have listened?).

The point you raise about spoiling predictions if people know of the predictions is an interesting one. I was about to elaborate on this issue, but the post already got fairly long. For one, I want to point out again that nothing in my writing talks about predicting a systems behavior. Instead, the aim is to set it up such that it works towards a certain goal, even though one might not be able to predict how so. This isn't the same. It's like manufacturing a car that drives doesn't tell you where to drive. But besides this the issue of spoiling predictability (on an average level) seems to imply that there is an incentive of spoiling it. I don't see this necessarily has to be the case. Best,

B.

Phil Warnell said...

Hi Bee,

I both appreciate and understand your reasoning as to insist that our political, economical or social systems are not by themselves chaotic, yet what of the entities that drive them being namely humans. When a politician (president) or any individual of great power and influence choices a direction what can that be assigned as being, a large change or a small one? I think that the question of scale is somewhat obscure here; for what is a change of mind to be counted as and what are the fundamental aspects of this system?

Best,

Phil

TechNald said...

its the best!!!

Bee said...

Hi Phil,

If you think about it I am sure your will find, as I did, that there is on a personal, as well as on a national (or international!) a large resistance to change of any kind. If a politician can initiate a chance because the time is right and he knows how to use the opportunity, that does not mean he could initiate any change - which would make the system chaotic. It is more that for change to happen, it often needs a trigger, much like a crystallization point. Best,

B.

Phil Warnell said...

Hi Bee,

You can be certain I will consider all what you have said and should be assured that I have not come to any firm conclusions as to what the systems referred to actually are. Further I’m sure you realize my comments relate more as to emphasis this personal uncertainly. First and only for the benefit of some that might read this is to note that a chaotic system is not the same as one formed of and displaying attributes as one being random.

I agree as to what you said that these systems resistant to change being more so because it take’s greater then a single change of mind to invoke them most often then not. What I have found to be the trigger that you refer to quite often is fear. That could be like in the case as with the past U.S. administration, where fear was recognized to be what could be utilized to render an overall change of mind, even to the extent that those who did willingly relinquished some freedoms that were in the past thought to be untouchable.

I would further contend that even Obama himself can attribute to fear being present the primary reason for his being elected. This time however not the fear of an external enemy or ideology, yet rather fear of failure that would bring both personal and collected ruin. Consistent with this you will find many more concerned with identifying an enemy or perpetrator rather then finding solutions.

My question then is to ask what actually is fear in terms of what is real? I would say that fear is not something that is real yet merely an anticipated outcome resultant of recognizing what appears to be a certainty. These kinds of things are only assignable to beings that think, for action elsewhere in nature are never the result of perceived potential yet rather only actual ones. So this still leaves me to wonder to ask if we truly can access these systems as being of the nature you describe? This of course is simply a question and not a statement of knowledge, yet I would maintain that it is one that should not be ignored or even can be if your objectives are to be reached.

Best,

Phil

Plato said...

What are the causes of "inflation or the lack thereof?"

While this might be of a cosmological concern, it is never the less a relevant one when we can attribute understanding to such expansionisms, while in cosmology we are still asking, what are the causes there in?

IT is relevant then from a logical standpoint that one asks what is it that can be created out of nothing and we settle to the idea that there can never really be a nothing. So there always has to be something. So we can move back before any beginning seen in relation to cosmology and ask what is this principal inherent in the "development of the fictitious," to create more nothing?

On the contrary if foundations are anything but sound and what benefits areas of control that it could maintain it over a large population, we would see that an order ensues now. So most certainly.

It is not fear in which one which is to propagate but the misunderstanding of what is flying under our observations and is accept whole heartily.

Then, one is operating under the premise of "wrong information," and further perpetuating ignorance among the masses.

People are smarter then this.

Best,

Neil' said...

Clever - talking about very deep physics and then how the ideas are relevant to political economy. Well, there's an old, "classical economics" that IMHO is just as behind the curve as classical physics is (and yet, like CP "seems to work" in the FAPP sense.)

Bee, try to get Paul Krugman and other big guys and gals interested in this sort of thinking, even Obama's team. I've met one of the latter and could send an email. Really, give it a shot (or maybe I'll just link to this post, or do you have preferences ....)

Bee said...

Hi Neil: I would love to, seriously, but how? Best,

B.

Arun said...

Dear Bee,

Everyone in the current financial crisis may have being acting rationally but shortsightedly is not strictly correct - unless being rational means overlooking one's duty to one's employer (which is not the same as one's boss).

-Arun

Arun said...

On a grimmer note, I would like to know what those dozen men in Mumbai were trying to optimize.

Neil' said...

Bee,

I'll send an email to Melody Barnes (I met during campaign meeting) who is named as Director of the White House Domestic Policy Council for Barack Obama. She's met lots of people and wouldn't remember me much personally, but I can reference the locale and occasion. I can tell her about The Lightcone Institute and the PI. Will CC or BCC you re.

They must hear about a lot of things but there must be some respect for getting input from interdisciplinary outfits.

If you can get a blurb in Discover Magazine, Scientific American etc. it would be helpful. Don't be afraid to write directly to people like Paul Krugman.

Bee said...

Hi Neil:

That's interesting, thanks. I'll be courious to see what comes out of it. I'm not afraid to write to anybody, but I know from years of experience that's not how things work. It's all about who you know, it's all about having the right "connections" and dropping the right names in the right places. Very tiresome. Best,

B.

Bee said...

Dear Arun,

Things get murky if you try to optimize post-mortem. Also, as I mentioned above, on intermediate scales it's hard to tell anything. That is between the very short and the very long time-scales but also between the very micro and the very macro-level. I've always found groups of any kind scary. Best,

B.

Bee said...

Dear Arun,

Regarding the financial crisis, there is unfortunately a rationale behind doing what others do. It has caused so many problems during the history of mankind that one would think we had learned by now it can go disastrously wrong. Best,

B.

Phil Warnell said...

Hi Bee,

I would agree many of the actions were rational, self serving perhaps yet rational never the less. I think the concept Arun is confusing it with is "justifiable" which in this context relates to ethics, which is considered by many to be on a higher plane. I for one don't share that view for I do find there to be a difference between ethical and moral, since the first requires only logical justification and later cannot always be expressed as being so attained. In short I think that reason extends beyond logic or rather what its normally considered as being such.


Best,

Phil

Plato said...

There are two ways to conquer and enslave a nation. One is by the sword. The other is by debt. John Adams 1735-1826

Barack Obama can never admit.:)

Only by some "gravitational inclination then" the ball starts rolling toward the valley, is there "a reason" coming to rest?

No group effort here other then to ask those who "hang together" and might we call them so?

Sure, maybe a crystallization point.

Ya okay. So we only talk about this universe then, and on some other parallel world, what is the description for all life to consider itself. An expression of some symmetrical idealization, not to have this valley come to mean and reveal, that this is our universe. Our world just "is" this way?

Leave it then to more powerful people to persuade all of us of a reasoned world "as it shall be," that is "justifiable now" as it is, and was nurtured to become.

Then, so be it?:)WE are helpless to change anything?

Best,

Michael F. Martin said...

I like the way you're thinking about things.

http://brokensymmetry.typepad.com/broken_symmetry/2008/05/editorial-note.html