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Prof. Heikki Hyötyniemi
AS-74.4192 Elementary Cybernetics
Lecture 3: Towards Modeling of Emergence
Helsinki University of Technology, 6.2.2009
(v.2009.04.10, only a rough machine translation, not cleaned yet!)
[0:00 / 1]
Welcome once again -- the subject this time is emergens.
Courage to take the bull by the horns, because without it, that we somehow extract emergens idea, we can not do complex systems mallitusta.
[0:22 / 2]
Here is a little bit the problem that we have something like leased Wonderland here -- that if you ask Irvikissalta "In which direction should go?", So Irvikissa ask "What you would like to do?"
And if the answer is "I do not now I really know", then Irvikissa says, "Well then, is exactly the same what you do" -- to which direction to go, so anything from then is there.
This Escher image files quite well with this situation, if the source of some of the stairs rise up, stand up in agreement, then suddenly huomataankin the others being the bottom of the stairs, and it will continue -- and typically happens in such a manner that will be back to square one -- makes a kind of a cycle there.
Well, the lecture time is right to try to find a coherent way forward, that we start piling up understanding of the old consensus on.
The target would be that even if we have a very holistic problem, so the tools to deal with it would be reduktionistisia -- because the only tools we have, are reduktionistisia.
Initially, we could look down on the top of this mallittamisprosessia general, the manner in which these complex processes has traditionally been approached.
Shortly same repetition than last time we visited.
[2:03 / 3]
A typical approach is this -- the basis of facing up ponnistaen.
There are some -- for example -- simple components, which are known, simple models.
It comes to them then to gather together -- as if the construction of brick houses, and hope that when enough bricks are together, it houses about emergoituu.
A typical example is the growth of this sort in the models.
Let's go even move Exponential Growth, and when you will notice that it is not sufficient, then perhaps take one of the logistic model, or Monodin model, according to.
It will be then such models.
This publication is an example of one of the bacterial model in which the behavior of the substrate is mallitettu, and then the formation of acid, and alcohol consumption.
But the problem in these cases is that, even when this has been the basic building out, so you have a countless number of free parameters which must be affixed.
You must be a large amount of data, so that you could draw the parameters.
If you have so many experiments of a complex system that all of its parameters, you get tied up, as you already very much familiar with the system behavior.
You, not so much about the model no longer any joy is not even.
This is like a fiddler's paradise that it is easy to invent new, such as the nonlinear terms, for this area, and always can make a new publication from then.
The problem, of course, is that the models are very difficult to analyze because they are highly nonlinear, typically.
Could almost say that they are hardly even useable.
[4:35 / 4]
Here is a concrete example of how this assumption as if the hazardous impact on the underlying situation.
Suppose that we want to model the grass, and hares interaction.
Construction of such a model ruoholle that it is just this sort pure integrator here -- that the grass is growing all the time.
Here is one of constant growth factor, which causes it to weed all the time will be.
And then here on this model hares.
This is connected back to a positive cycle -- means that the more hares, the stronger they will grow.
And the more there are hares, so the more you eat the grass.
It is considered simulate this, but states that this model of behavior is absolutely absurd.
Here it leaves the grass enough to stand up in this way, quite correctly, but the hares exponential growth is so strong, that this scale -- we have tens of thousands of them -- will notice that this growth ekspontentiaalinen eat all the grass and even in the way that the linear model leads to a negative ground biomass.
Well, this clearly must be corrected in some way.
[6:02 / 5]
Added to it just this sort Monodin term for it.
Which means that the growth reduction on the basis if we have the food there is not enough.
Now, we see that after the behavior starts to recall already -- in some way -- a meaningful population behavior.
There will be a cycle of this sort.
The problem is that now that the grass be still doing the zero level.
So, the grass biomass is sometimes zero.
That we should certainly be corrected, so that it is credible.
[6:50 / 6]
Put there a restriction of this sort -- that is the grass will be up to zero by means of.
Well, it happens then it means that the grass will decrease to zero, the hares and the number is set to a constant value.
But this is still physically insane, because this Monodin model does not take into account the fact that if indeed the food goes to zero, so this model suggests that the number of hares remains constant thereafter.
[7:25 / 7]
It does not fit here, or we can extend this model by taking to the logistic model of the.
We note that this is beginning to behave more rationally, ie the amount of grass here is set to one of the rational.
And even this number of hares in this set may have one.
Is seen that all the time and others are still quite poskellaan, or should we start now the parameters to match the findings of.
In short, this is an endless task, this model of Tuning in this way, if we go forward basis, to encourage -- in the way it is traditionally, insinöörimäisesti approach.
[8:18 / 8]
Bring recent example was very simple, but when you take a sufficiently large model, it is gonna show you credible.
And on issues like models are used quite a lot further.
Take the example of the Forrester model, which is based on, for example, this time written for the Club of Rome report.
This Forrester block model to emulate, it was found that by 2000, we have all messed up the world -- all the raw materials is at an end, oil is at an end, and it is a kind of catastrophe may have been the world.
It was built in this model the world exactly the way it is in that I have just made.
In other words, states that, for example, natural resources -- they are always eaten, this natural resource stock decreases, and the number of people grows, and so on.
But the problem with issues like hand-coded models are typically the fact that they pretty much models are exactly what they were built mallittamaan.
As long as the results are not what we expected, so as long tweaked the model forward.
The end result is typically that the models can not be so much more to tell than what the model builder the default starting point has been.
Since the models are so complicated, there are so many free parameters, that -- it always will agree to any pre-assumption, quite frankly.
The worst, of course, is that the qualitative behavior depends on the parameters.
If any of the feedback factor is too big, so the model becomes unstable, for example, while a smaller parameter negative feedback stabilizes the system.
So, have the other kinds of approaches?
[10:47 / 9]
The target would be an ambitious goal would be to find methods to approach the problems head on -- rather than the source then the basis of physical models of collecting, building models, so it tries to reach the behavior of movement.
So, starting with the chaos here, and the aim is to reach your order, elikä model.
When I just went in another direction -- that is based on a simple model, but was chaos.
[11:30 / 10]
Here is a simple example of how the principle may be to think that this sort of this holistic approach, or a systemic approach, could be surprisingly effective.
An example of this sort is a refrigerator case.
Well, just an invented example -- think that the 1000-watt refrigerator with an efficiency of 30%, is connected to a network, but forgotten in the fridge door open.
This refrigerator has a room which has been isolated from their environment.
How the temperature of the room you need, when this refrigerator presumably puskee all the time from the cold room?
Is there any suggestions ...? Warms or cools?
[I would suggest that the warming up. ]
Yes, this is the first level on issues like systemic thinking that it is -- because the refrigerator, however, is this sort of heat engine, as a whole, it produces more heat than cold.
But, to be used in favor of the overall system -- or the whole of this systemic approach -- we need to look at the entire room with insulation system, which will be 1000-watt output in the heat.
Actually, this is the whole problem-solving.
Quite indifferent to that because what the 1000-watt output in a room is made -- however, there always will be 1000 watts, which is a moment.
Ie the room warms up in 1000-watt power level, in the same way regardless of the efficiency of the refrigerator, or the other.
As a strong performance can in principle be achieved if we have a simplified, merely to the system.
A sad thing of course is -- last time it was found -- that kyberneettiset these systems do not in any way to simple systems.
For example, cropping systems and insulation hypothesis is never true.
Tyypillisestihän is assumed that these must be open systems, so that this entropian accumulation can be explained.
We have to kind of a compromise to find these approaches range from -- therefore, in the very basis of the departing, and then this totally off on to examine the approach to -- be some way to get, to find something like the link between them.
[14:44 / 11]
One approach is to karkeistaminen, or could speak granularisoinnista.
Take a complex system, and it comes -- more or less -- hand-picked from the avainsuureita.
Suppose that the complex system behavior can be described by a small number of key variables.
Well, this is perhaps a sufficiently intuitive example, that if you have a person even if, as some of the key features that a person can get one connected to the painting.
Those who are more 70-century lived, so will know immediately that this is Kekkonen.
Although this is very far karkeistettu.
[15:45 / 12]
This karkeistamisessa is always a risk that if you go too far to go too simple descriptions, so it is no longer responsible, is no longer capable of any level to describe the real world.
This statue is Urho Kekkonen statue, which is over there Kajaanin cemetery, or church land, and it is the artist's vision for this -- that the screw cap image Kekkosta best.
Maybe this is a political vision.
But really, that in general terms, the idea of Holism -- or holistic mallituksessa idea -- would be to get more than what is, in parts alone.
But if this is being done incorrectly, this approach, then the hole is actually bigger than what would be desirable.
So, we left with only -- abstained.
[17:02 / 13]
Well, to get connected to these lower-level models -- that is, the only models we can build our tools, and then this senior-level holistic thinking, or tämmönen holistic intuition, so that proves to be, we must at some level to answer the question that what is emergens.
Because of complex systems always describe this emergens concept.
Complex system is typically semmoinen that there emergoituu any behavior, which is the basic component not.
And if you really want to, an ambitious approach to this complex system mallitusongelmaa, so we must at some level to take a position on this, that what is emergens.
So, you could -- in a lecture day in books -- to consider that what you think is emergens, and how you are approached to the problem.
Here are the final lecture deals with the root of this problem that how we approached it, and how these approaches follow a specific approach in which the name is neokybernetiikka.
But -- you have to remember that this is only one approach to these matters, and if you develop a different kind of approach, so you can rename it to another name.
These are very much still open, these questions.
[18:52 / 14]
Complex systems research is not really anything beforehand Poker.
In this way, that you can choose the approach that the concepts, methods and application areas, the time freely, and is, at least for the moment, it is interesting to study, because, as the last time it was found, so this tutkimuksenala attract just such a very emergent-minded people.
You have quite a lot of freedom there.
But, really, so that we have something concrete to achieve, so this course will focus on just this neokybernetiikkaan now.
So, going into detail, and see what follows from premises, and then when it comes to these starting points to build the system, so can be considered what kind of on top in the visible characteristics, emergente properties then it is.
Now, defining the approaches and concepts, and certainly worth noting that originally, these things were not so straightforward -- this is all mares iterative, and it later can be interpreted that these may be summarized in these basic ideas jonkunlaiseksi set of ideas.
But intuition was originally the driving force.
[20:45 / 15]
This is really very much on issues like conflicting intuition in relation to these complex systems, as stated last time.
And now indeed chosen a line, and try to justify why that is one line, or why it is then a line is selected.
Even last time, it was found that a very large number of kompleksisuustutkijoista focus on this form of surface -- or on issues like fraktaalitutkijat are pretty much satisfied with the fact that if a formula to produce something Fractals and complex behavior, ignore a very large extent on how this formula could tul-in environment, how one gene could semmoista function to implement, for example.
Wolfram These mussels are examples of this approach, too.
And if you read emergens-names book, so there is a comparison of this sort, that the complex system of the brain, are surprisingly well-the same shape as the Hamburg city map was during the Middle Ages.
Did not this have at one -- two complex systems -- a link now ...?
In a sense it is a certain way, yes the link, because they are these the local players here -- neurons, or people -- who will start form on issues like installations, and as if this increase of this sort so in some sense -- they have a common underlying explanation.
But instead of examining this result, the mares inflation outcome, it is fruitful to start to examine what functions these people, and what do these brain cells is here -- and why they are, after all, to some evolution have been proven stable structures.
Prefer to explore these deep structures than surface structures.
[23:19 / 16]
Now determined that this course on issues like these deep structures are precisely those characters emergente.
Does not of itself to be a very revolutionary statement, but it comes to integrate these concepts together -- that is, however, that might be necessary to take a position on that what are the deep structures, and what are the emergent dress, as defined, only that they are now -- to use both terms, but they point to the same matter.
Come on now just concrete -- trying to model, or at least considered as examples of emergent behavior of the concrete, to get some kind of intuition that is what we are, the more common they all have.
We certainly have examples of very specific emergent phenomena,
[24:32 / 17]
and this next slide illustrates the one area in emergens various levels.
Here is a short, gas mallitusta various abstraktiotasoilla, or a range of karkeistuksen levels.
Just at the lowest level, everything -- including the gas particles -- can be modeled alkeishiukkasten, quantum mechanical tools.
It is the lowest level here.
There exist stochastic, random new laws -- if we can kind of too much talk about even then.
And if you want something a great number of gas models, this kvanttitaso or alkeishiukkasten level is not very useful, because we will have a tremendous amount of Schrödinger equations, which we should in some way to simplify.
This simplification is, frankly, been going on -- we can rely on these results.
It can be concluded that it is observed that the sufficient level karkeistuksen, these atoms and the behavior of atoms -- that is their interaction kvarkkien thanks -- both those atoms can be the ideal gas model to look as if the self-biljardipalloina.
So, from this sort deterministic model, in which the atoms behave like each other törmäilevät balls.
This is achieved Newton's mechanics, which dominated the world of gases.
This is significantly better -- if you have a large number of atoms, or the ideal gas particles, so it is much more intuitive, user-friendly and more useful, all in all, this model, as this kvanttitason model, or alkeishiukkasmalli.
But then, if you have millions of millions of particles, is beginning to be quite impossible to monitor all of collisions, and we are forced to live with it, that examines this issue in some way statistically.
But it proves indeed that the macroscopic phenomena in terms, as if these emergent greats -- such as temperature and pressure -- are extremely well enough to describe the gas space.
We do not need to know the individual molecules or particles of the behavior, when we know only that everything that we can head to measure the reverse -- that is the temperature and pressure -- they have a range of statistical functions of these particles.
We know, for example, that temperature is directly proportional to the particles of the average kinetic energy, which in turn is directly proportional to the speed squared average.
But then when it comes to large volumes of gas -- in the way that the particles they no longer have access to the same probability in all parts of the tank, for example.
And if you have this sort macroscopic large tank, so environmental impact of the reservoir begins to be different in different.
It follows that, for example, temperature differences -- there gas -- will start to become significant, the different items.
It is the beginning -- is that we should start to take into account the convection, and large quantities of gas are concerned, different turbulent phenomena.
So, this just a temperature and pressure of the model -- the assumption that we must stop these quantities, the same throughout the volume -- it is no longer true.
We will have to look at every point separately.
And then it starts to come of this sort are a statistical model, because the turbulence, for example, can not properly deal with any other than the statistical model.
And if you go from here -- mind that we are fully turbulent, ie hahmoton gas mass, so one could imagine that we will no longer be able to do anything concrete, since these statistical mallitkin a very fluid results, but it proves that when you go down again at a higher level, so This fully mixed, fully turbulenttinen gas tank, it begins to behave as ideaalisekoitin -- ie it can be assumed that every point the cartridge is the same as if -- or when it is fully mixed with the same concentration, the same temperature at which point gas.
Reach to the fact that we can once again start mallittamaan centralized system components, ie, a single concentration or lämpötilamuuttujalla.
Again we have this sort deterministic model.
Well, now we are at that level, that these models, we have issues like the gas tank design, but when we want to model something to an industrial plant where there are dozens of issues like the gas tank, or tanks, so huomataankin that if you approach the problem in just this way the traditional sense -- that is built for each of the shell's own model, what we can do, assuming the ideal confused why -- so when these will be hundreds of these ideaalisekoitinmalleja, then one hundred, this variable is a whole design begins once again be semmoinen that it is unable to control -- no longer possible to say that which of these variables are really important, and what kinds of behaviors, this variable 100 entity then receives a time when there is a different way, connected to the tanks with each other.
It is precisely in these modern automation systems is a problem that even when all the components can be models for a very precise, its overall system robustisuusominaisuuksia or qualitative features do not really possible to say, without any simulation or otherwise.
This would be a challenge, these engineers who will be our future.
So, all those below the basic components are in control, but that the manner in which the entity is managed and understood, so it should be -- it would be the next big challenge.
Similarly, those who are not in our area, so the challenge there -- and, in principle, although understood in a man's behavior, so the entire range of human behavior can not be further from the lead, but it is another of this sort emergenti behavior.
It can be assumed that if this line with developments in this continuing, so the level of stochastic deterministic monitors, and again this determinististä stochastic.
So, one of the statistical mares can be expected to need.
This is really an example on issues like the system where these emergent phenomena following one another -- in other words, it is not in any way -- even if they are truly emergente, these levels are in the way that does not agree to return the lower-level variables, or the behavior of the upper-level phenomena -- it is much convenient to use the upper level of the parameters and laws of the return to the lowest level of quantum mechanics -- so this is, however, semmoinen concrete system in which we can in principle to restore the upper-level definitions -- or upper-level definitions will revert to the lower-level phenomena, and it can be a little more detail here now to consider that how these systems as if they are the new features emergoituvat.
First, if I start from here-floor level, or go one level to another, so that the aikaskaalat grow.
At the lowest level is a very fast phenomena, and they slow down what will be higher.
The other hand, the lowest level is a huge amount of alkeishiukkasia, and it is reduced all the time when you will be higher up, or the number of variables is reduced, ie a certain way just makes this abstraction -- a large number of variables is forgotten, and only some kind of cumulative variables are ignored.
Held to be the mind.
[34:42 / 18]
This is justified, why the hell is a kind of logical that the stochastic and deterministic level following each other.
One might think that if there are two levels of determinististä a row, then they kind of collapse on top -- that is, we could be the upper-level variables deterministiä dealt with low-level deterministic variables among equally well.
Similarly, if two stochastic level would be a row, then it should be the same stochastic model adaptable to all.
Making this sort are bold generalization, kind of, that is when I just found that aikaskaalat will always only be longer, so we think that this emergens comes a stage when time at a lower level, goes to infinity -- that is to say there are an infinite number of time steps, or an infinite number of particles törmäilemässä.
So the one hand, an infinite number, and infinite time -- we think that with sufficient accuracy, if they have something statistically meaningful behavior, the so-stationary situation is reached -- that this gonna poukkoilemaan the term of this sort than stationaarisuus and so forth.
The other hand, it is also ergodisuudesta, if anyone is interested in mathematical matters, because in this way, combined with a series average and time average, ie the view that all the particles are also identical to each other, ie to go and the time-axis of the space variable-axis to infinity, and the same sort of behavior is found.
So, what happens when the time-axis are eliminated?
[36:59 / 19]
Here's intuition of this sort now in use, that is in some sense infinite and emergens are with each other married on the agenda.
If we make on issues like the formula, that is integrated into something even if it is, minus the endless to this moment, so if it receives a vak-a practical value -- means that if this is statistically meaningful, stationary, the signal -- so we wait for some value out of this clause.
This E-operator -- this will be now, if you think the expectation operator, so will be very much wrong to use this, this course, or it might be wiser at this stage to nominate the E-operator emergens operator, jolloinka do not have this problem, but nevertheless pretty much just this expectation is at stake.
In practice, then have to be some way approksimoimaan this infinity -- is assumed that a smaller set of data already achieved this stationaarisuusominaisuus, or if there is stationaarista data as a lower amount of data may be sufficient as an infinite amount.
This approach -- although this is extremely simple -- it is just the good side, that this is mathematically extremely compact and simple, and unique, if you define that emergens is this -- and loosening up a bit, saying that poor emergens is this -- then we have tools to move forward.
There has been some intuitively correct features already evident in this definition -- that is if you have a tree in woodland, or by one, even if the noise sample, which is quite different from all other samples, and it is a single sample in the way that there are no other issues like samples -- in the way that it is not statistically significant -- so the waiting value of, we get this completely disappear in this one tree.
Elikä it does not affect our models samme its forest model from guarantee.
The individual particles, or individual samples of the time do not mean anything.
Only that, if one of the behaviors have something long-term correlations, someone else -- or if it is, if it is semmoista repetitive, and also visible in the past, and hopefully in the future, because we build models for this now nollahetkelle, and we hope that knowing the past will tell something in the future.
In this sense, we should indeed expect that the system is stationary and the statistical properties are preserved, in the future.
[40:36 / 20]
This is of this sort since the new film, what does the old kalvoseteissä been -- I want to little problems connected to this, whether it is really just a emergens averaging?
It is, however, this emergens core, in some way.
Take, for example, it is this, that the manner in which the gas temperature is comparable to those below the particles, or their properties, we could say that really defines the temperature of the average kinetic energy, in the shell, ie the average kinetic energy, it is proportional to the mean square speed, ie does not need aware of the particulate flow directions and does not change, only its scalar speed, and its square, and in light of all of these mean, it is directly proportional to temperature.
So, in this sense, the temperature is low due emergenti feature, or feature semmoinen they then have the individual particles is.
But it is now when I start to approach these genuinely interesting complex systems -- so it is kind of a little semmoinen newer approach to this issue is that we want to link to this emergens the particles the interaction also -- not a single particle properties, but the two little mutual connections, connections, and its expectation value.
The simplest, if we have an i-particle and the j-particle, and they have a feature x, so we want to calculate the expectation value of the properties of particles results.
They are familiar with these mathematical things will notice immediately that, when this and this kind of combined, so get to the end of the day are interested in the system variables covariance.
So back to the then next time.
Here's the good thing about that, as it does this will find the so-linearity trying to maintain in these models, as far as possible.
Although this is a nonlinear function of this correlation, so they can be further analyzed, or they could build a model, linea Aris terms.
It will be seen next time, how it succeeds.
[43:35 / 21]
This is yet more on issues like cross-intuition.
Traditionally, models are to the individual players and individual time points and is now explicitly do not want individuals Designs.
This is, of course, it is a bad side, that at least in principle, we can not, then build -- can not be predicted with a single käyttäytyjän, or a single operator's behavior.
This is the time to understand in itself, after all, these players have the free will.
But a large number of can then find some of the laws.
It is what is the good thing about this approach is that quite a lot of fundamental issues like what the problems of complex systems, which have teeth, or what caused debates on issues like, so they can be overridden, the same way.
For example, quite a lot has been discussed in the theory of evolution that is it now the selfish gene is that really is the operator who is in favor of models, or whether it is this individual, which contain these genes jyllävät, so whether it is the individual, which is in favor of models.
Following this review, the only rational review of the level is really the populations where these genes are pretty.
In other words, the starting point of this sort as soon as the assumption here.
And the other thing is that -- for example, such a profound time for Darwin's starting point for this -- that it is interested only in whether the best, that is, the best survive and reproduce, so this framework is about the entire population, after all, a very large number in the population will continue its genealogy , not only of the best.
Or, say in the way that, if only it would continue the best relationship, so it would die out very quickly throughout the population.
In other words, precisely the population -- or biological strength comes from diversity, that there are differences involved.
These basic Darwiniaaninen theory -- this is not really able to effectively tackle at all, because it -- so tightly connected to the winner, it is a theory.
Just another area to take this for example, that in the NP-hard problems, which are, in principle, be solved by non-polynomiaalisessa time, so much time is devoted time to find the best possible solution, but we think that nature is quite the same situation -- it is one of optimization problem, and it tries to find the best for the solution but did not find it.
It enters into any of the suboptimaaliseen situation, which is pretty good, which is reasonably good, but does not typically have quite the absolute best.
When rupeamme build kyberneettisiä these models, so it is not the best solution to the model, but rather it is a set of models, each of these osamalleista reflects in its own way a good solution, which in some way is able to respond to environmental challenges in their own way.
Then, these models for more than an attempt to build a compact model.
Eli kyberneettiset models are very much the model templates.
[47:47 / 22]
Again, this sort have the opposite intuition here.
There are two options when it comes to complex systems modeling.
Well, that Simon, in the complexity of the architectural book specifically on this issue in the way that there are two choices: either rupeamme to look at these characters, or processes.
And now we have already found that rupeamme to look at these characters, but these processes are probably very interesting, because when rupeamme these characters to look at these systems, we as säätöteoreettisilla or methods, so I will come back to these processes in themselves -- as if through the back and later -- and after all that process philosophy is very close to what this will do.
But, however, that the source directly into circulation for some processes, so it is not really the point of departure, as the time many of the other study, has been detected.
Ie -- no, for example, artificial intelligence will bring a book, what I read at the time, so that at the outset, it is noted that all these artificial methods of interpretation of issues like the process framework, as if the intelligent agent framework, which means that the light completely in this way with an appropriate sense.
[49:42 / 23]
Here is a little motivation for why it is so strongly had the surface.
Justification is, of course, this computer, because all of what the computer is doing on issues like algoritmisia processes, it is easy to take from this sort of comparison.
On the other hand, those of chaos theory, all things are issues like procedural.
And -- no, these are a lot of arguments.
[50:23 / 24]
But now, however, this course seeks to this natural approach the complexity of these are actually the characters in mind.
This is now attempted to tie together these processes and outline.
It is considered a little while for this file.
So, here are two axes, first of this sort dimensionaalisen complexity axis, and then the structural complexity of the shaft.
Pretty much one could say that this structural complexity, it includes epälineaarisuutta, and on issues like struktuuraalisesti complex things -- if you think that the linear system is here, it is semmoinen simple, perfectly well-known structural and behavior, then what more complex epälineaarisuuksia on, so the longer it is here in the structural complexity axis.
It can be argued that the original habitat is structurally very complex, and built physical models, they are structurally complex, where they can find epälineaarisuudet and encode, but compared to the wild -- in other words, this physical model, it is dimensionaalisesti simple, because there is only a few variables, we pursue this whole natural complexity to connect.
Eli abstrahoimme terribly much of this natural complexity out of a lot of variables out of -- get this close to zero here, ie there is only a few variables to this model is built.
Well, then when it is sufficiently complex model, we do not really no other way but to simulate it -- mathematical methods can not so much epälineaarisuudesta at all to say -- we can simulate it, when we get here in the structural axis of complexity, a simpler, a little bit, but we dimensionaalisen complexity axis low -- origosta farther away, because we have to fiksata all initial states and others -- so that we can simulate the system so all the free parameters must be committed.
They aimed to make in the way that they are the best match of this natural system here.
Once it has been driving this model, as pursued in the mix of different situations -- we get a large amount of data, which is typically always the same shape, and it can be treated with a uniform methodology, ie it is structurally simple, this data.
Typically, it is dimensionaalisesti complicated -- there are a lot of the data.
At best, it can be argued that if we can find data about characters, we can simplify it, reduce the variables, and on the other hand, this structure reduces.
This is the goal, we can find that on issues like the character design.
What do these figures now mean, as we come back to it later, but the idea is that this character model is the one who is able to keep sisässään the other hand, this physical model of behavior that the natural behavior.
Since the data is what we get here, and what mallitamme here once we get this character model -- so it may come directly from nature, these measurements are of nature.
This is of this sort, no at the next -- or the moment will be finding that this is in some ways Kantilaista modeling.
In the sense that we fiksaamaan something in advance -- we are in this case, fiksaamaan this, that the shape of characters to pick from here, but the figure inside the structure is then more or less unambiguous, that how this is a future here the data are interpreted, that the type of characters to be found there.
So, those old philosophers are still valid, yes.
It is not only the human perception mechanism, but also in our machinery of these -- when we want it to automatically mallittamaan something, so the same problems as humans will have been -- that is to do complex data mallittamaan we must have something to which the structure rupeamme to build this model -- that is now these figures will be the basic structure of those on our key components.
[55:44 / 25]
This is another of these cross-intuition -- that is traditionally thought that when the model is built, so we want to simplify, to uniquely identify a single one like a complex system model, and as if looking for the truth of that -- ie the system behavior, without any interference or non-interactions, seeks to find the core of it.
But now -- first, we see or know that all our systems are always truly interact with the environment -- we want more models of the process of interaction with the environment, than the individual system.
Because of its isolated system alone is not interesting -- it is a rabbit, for example, it will die out -- rather than the hare populations modify their environment and the environment is interacting with.
Ie, instead of something Seeking the truth in what the data will never be able to get -- this is yet more to this philosophy to the cross that we must be satisfied with something, tämmöisiin shadows of reality, if you sought the truth -- instead of its relevance if we pick, so it is there in the data shown , ie we can see the data of variables between the interaction effects of the very basis of the data.
It can be assumed that all of what is interesting, it is apparent, ie it must be able to pick up the correct variables in the system behavior, in which case all interest is ultimately to be in the data.
This is the starting point, therefore, that pretty much -- or no does not mention any of the truth, speaks only of relevance mallituksesta, so avoid these philosophical bridge hole.
[58:09 / 26]
If muistelette these planes in the model where the past still had issues like ideaalisekoittimet here, so now may be approaching the issue of the level of characters -- that we come back next time and practice, says that we can approach it mallitusta tämmöisten statistical multivariate methods, and then in certain environments, we can, when it is appropriate , the so-called harvakoodautuneita features found there, so we can even rename them -- we get back tämmöisten funktionaalisuuksien, or symbolic concepts at a level up.
But it pays to remember that although you are now training exercises will deal with this pääkomponenttianalyysia and so on, so next time, at its next session will be to find that instead that we now should be of this sort toolbox what we like -- the force of natural behavior, so will be to detect that this is a multi-variable analytics -- specifically pääkomponenttianalyysi and harvakoodaus -- it emergoituu then the system itself.
Eli is not so, that we should now be a tool box, which is a requirement to be reconciled with nature, and nature were forced then to act on these pre-assumptions.
Here is our statement that we now have a case of this sort Kantilaistyyppinen compromise here.
This now let this sort, only an apostrophe.
If someone has these Kant pure irrational criticisms come across somewhere, so to say that this is true in some sense it is comparable to the -- that we need someone kind teoriaohjautuneisuutta in this case, on the other hand, the theory must then make room for this data.
[1:00:31 / 27]
Well, this was found already that in order for this expected value operator, giving something sensible, we need the data, or their datojen kovariaation, stationaarista be in the way that the dependence on the past relations and future dependency relations are assumed to remain the same.
Well, so this stationaarisuus could be valid, so the system must be stable in the broad sense.
Does not mean stability in the way that it should always fiksautua to a certain point, but it must be stable in such a way that it will be able to answer -- that if the environment becomes even though the disturbances ...
... that is the attempt to balance the dynamic disorder is affected.
It is noted that only if it is sufficiently stable conditions, so this sort of a emergenti kind of phenomenon is able to then emergoitumaan -- because typically these emergent phenomena are very sensitive, so if you would be too drastic conditions, so it was never there emergoituisi.
Well, those returning to myöhemmnin.
It may of course ask whether it is wise to confine stable systems, and, indeed, this course does not focus on all mathematically possible systems or means of mathematical models of potential, but only physically meaningful.
It may be noted that all the physically meaningful models are at some level stable, because if they would be unstable, so they would have exploded a long time ago -- they do not exist anymore.
- Or it can be argued that some processes have been an explosion, but their impact is then spread throughout the universe in the way that we see only with the explosion of the outcome here.
In that sense, is not a transient phenomenon, necessary or useful to model, because we have no data about the behavior, we see only the end result.
Another possible outcome is that it does not explode, but going into extinction, this sort unstable behavior -- just as much we can not be models out of dead animals -- is what is interesting is the one who is able to survive until now, it can perhaps give something really an indication of how our systems could survive.
[1:03:35 / 28]
Such a return to later, but certainly worth remembering that this sort of static and dynamic balance are very different things.
On the contrary they seem quite the same, and typically when you think that balance is not sufficiently strong frame of reference mallitettaessa complex systems, as merely to think about issues like static balance weights.
Instead, the dynamic balance between the apparently stable under the surface happens all the time.
It is precisely the dynamic equilibrium is a balance of tension -- it is interesting that all the time is as if ready to collapse, unless there is something about the effects of consolidation.
In this now as if the extension of this dynamic equilibrium concept, ie it can be argued that this sort termodynaaminen death is, then -- is achieved at the stage when the all-time figures are derivative zeros.
So, something like a contradiction -- in the rupeamme focus on these non-static balance weights -- both of these systems neokyberneettiset gonna focus on these dynamic tasapainohin, and gonna change them, a static equilibrium, and then when it is as if the end kaluttu, this first-time figure of static equilibrium, so aletaankin focus another single figure in the balance, and so forth.
The end result is a sudden, the fact that I should like to thermodynamic equilibrium, where the extreme far this goes kyberneettistä Chain -- ie this can be a very profound analysis, then, finally, returning to it after a while just briefly.
Well, so that these issues like balance the search process would be possible to the local players, so we have to interpret them jonkunlaisina diffuusioprosesseina, that is spoken in generalized diffuusioprosesseista future.
We can pretty much those we like the standard models.
But this generalization here, means that they are also -- those variables may be a way, even on issues like information variables, not just the physical variables, concentrations, or the other.
And they can be multi-dimensional diffuusioprosesseja.
[1:06:32 / 29]
Well once again the cross-intuition.
Of this sort -- and this is semmoinen familiar image that comes with when teaching about these kompleksisuusteorioihin.
It states that it is first of Poker on issues like systems which are not interesting, then, is a little more complex systems periodisia who like to return to the same space, and then there are issues like chaotic systems.
These chaotic systems, they are -- to them we do not, they can not too much to say, they are epäkiinnostavia, but also on issues like periodiset systems, they can we fully know, and they are not in the sense of interest -- these complex systems are a kind of extremely narrow interface in this epäkiinnostavien and epäkiinnostavien between.
It is a little bit of this sort of doubtful, or semmoinen vague place that is what this chaos interface here -- that is how we succeed, how complex the system stays in this interesting region.
This is just the basic fundamental problem in that kompleksisuusteoriassa that this is a very unstable kind of place -- that complex systems place -- ie nearly all of the approaches pullahtavat either side of chaos, or else tämmöisten simple systems side.
How can natural systems will remain as if this automatically, all the time on this interface?
Well, will find that this is a certain kind of attraktori here, and as you kyberneettiset systems are developing, so that the interface moves further chaos in there side.
These classics, such as the Schrödinger, "What Is Life" book, it assumes that all of life or living systems, they are characterized by this that they are as far removed from the balance -- they are very unstable, and in that way -- and it is this intuition, that are very far from equilibrium, so one might almost say that this intuition is false, that Schrödinger was thinking mares static equilibrium, because otherwise he would not have been able to argue that the dynamic equilibrium is death, but the ability to stay in this dynamic balance in this chaos and order at the border , so it is rather characteristic of life.
The second is that Prigogine which assumes that what dissipatiivisempi, the more the system consumes energy, the environment, for example, its lively it is, and that is what the balance further away it is, the more lively.
They all lit up, quite a different point of view.
[1:10:12 / 30]
Well, here now is this sort oriental symbol -- it deserves this place in such a way that even if this interpretation of the oriental static equilibrium of the balance pretty much -- the thought that the human body -- this sort Oriental medicine seeks to balance -- so it does not think the West just as thoroughly as it should think.
It really is not a static balance, but this oriental balance is of this sort -- of this sort mystical, some kind of dynamic equilibrium, in other words, this is also something to steam -- the second interpretation for this is in the steam -- and the second interpretation is järjestymisperiaate.
It is a very profound idea indeed, this basically balance the oriental idea of what this sort of Western interpretation is not able to formalisoimaan.
But on the other hand, it is not even the oriental philosophy, and it will not be able to formalisoimaan this, that when these issues are approached, as it leads to these, tämmöisiin logical paradox, koaneihin.
[1:11:43 / 31]
Well this is like a nutshell, what has come to be established, or what will face or what will be discussed in the future of this course.
Kyberneettiset These structures have a certain way on issues like stabiilisuusrakenteita, semmoisia attraktoreita root, which in the long term, stable, on issues like dynamic constructs, even if they momentarily appear to be very sensitive to semmoisia, fluid.
Rather than talk of dynamic balance alone, so talk to the Balance balance, ie the single chapter balans.
It is precisely in the sense that kyberneettinen system is a multi-level, and emergens has many levels, and multiple.
Kyberneettinen and model of this sort is relevant spectrum of behavior more.
[1:13:00 / 32]
And, it is a model tämmöisten Oct. alien minima over.
In other words, I just found that these NP problems, they usually try to find -- as the passenger's problem -- to find the best solution, so kyberneettisessä framework seeks to identify any kind of pattern to it that what a picture, or what is common in all reasonably good models that are not there are optimal, but which are close to their optima, and eligible.
Indeed, the fact that models of these different options, so it can be intuitively close this Herakleitoksen the idea that when the models for the river, so never the same models for the river, but the river idea.
[1:14:09 / 33]
This is now true again, the same finding, that the models only physically meaningful systems stable.
It is an extremely small class of all possible mathematical systems.
We can easily justify this.
Where is the state variables of the songs, and think that they are dynamic variables -- in terms of the corresponding mode has been thrown into the complex plane at random -- the so-so that the overall system is stable, each of these randomly thrown poles must hit the left half plane, because if there is one right half plane, the polar, or variable, so it means that the overall system is unstable.
It follows that we can more or less intuitive formula leads in this way that it is 1 / 2 ^ n, is the probability that all the poles at random would be thrown in the left half plane.
How many people got this idea from?
However, this has to be justified by the fact that the mathematical mind, this set of models we look at what is an extremely narrow.
But the extremely narrow range of fit in all the systems of interest, however.
This in itself is not so restrictive that it is limited to stable systems, since it is apparent that these complex systems in themselves are in control systems, ie when they are connected to the environment, which may have been originally unstable -- when they are sufficiently closely connected, so they may achieve it, that the whole environment changes stable, and this is the very nature of these root systems kyberneettisille that originally unstable system will change -- when it changes it kyberneettiseksi system -- becomes stable.
[1:16:30 / 34]
It involves the way it is, that when this kyberneettinen system is received at a lower level signals are stabilized, and pushed in practice, the signal variation of the heat death, so the system rupeaakin focus on what still is left, that is a kind of higher-level equilibrium.
Seeks to focus on stabilizing it.
It follows that in the end we end up on issues like higher single chapter balance, which may appoint a thermodynamic heat death.
To return to the course at the end just to the fact that how this idea of these kyberneettiset systems are thermodynamic entirely consistent.
So, even if kyberneettisissä systems typically order to grow, leading to the legislator, this improves, so if the system takes that system and the whole environment, so the overall system, in this environment + system in the variables stabiloituvat better, ie closer to the inflow of heat death, ie Entropia grows.
After all, when the systems limits the right way, so the end result is that, in the same manner as that of simple physical systems, including those kyberneettiset systems tend towards entropian maximum.
[1:18:35 / 35]
Well, then this intuition would each like to say that since these are the tensions on issues like models, after all, so pretty well describes the behavior of these issues like transienttitilanteissa elastic system of intuition, a system of mechanical intuition, that is if they poikkeutetaan about balance, so they are a force to return the balance to .
And also for the electrical side analogioita found, ie it proves -- if the two systems are interacting with each other, so that the power between the maximum move and would not have the power to lose, so the impedance between them have agreed with the country.
This may say e-something men, but a return to these later.
[1:19:37 / 36]
Now, suitably covered jyrinää there -- we are coming to the philosophies and very far really over here in science pens.
In other words, so that we can move forward consistently mallituksessa this, we need on issues like really fundamental prinsiipin, which supports us.
If we can agree on issues like -- here it is now named Pallas Athena hypothesis that -- if this is acceptable, we are quite consistent with the path to move forward at a later date.
But what does this mean this hypothesis, so this is a very good idea kontroversiaalinen itself.
But can you think about it in mind that if this is acceptable.
You know, perhaps the Gaia hypothesis, it is a bit similar to him.
Gaia is the god, and that Lovelock and others have raised semmoisen idea that these processes, all klimatologiset and palaeontological, any processes on Earth is, and even volcanic eruptions, and others, they are very easy to wipe all life on Earth out.
But it appears that the earth, or rather the earth mother, Gaia elikä-goddess, elikä the god, has directed all of the processes as a way to behave, however, that they in some way in support of life, and allow ever more complex sits on life here on earth.
That while this Gaia, or the earth goddess is somehow very semmoinen unstable and mentally a little epäbalanssissa one, so it is, however, made it possible for all disasters is life still exists here.
And, now get this Gaia hypothesis that, in fact, that can lead to very effective, very powerful models, on issues like klimatologisille or to the ground handlers ilmiöille, if you think that they are limited to semmoisiin phenomena that allow for life on Earth.
So, may be limited to all of the potential range of behavior, only those behaviors that are not too drastic.
Ie -- no, you can see this in Gaia hypothesis further.
This is a very questionable theory.
And just as questionable theory is then that Pallas Athena hypothesis which relates to the fact that Pallas Athena -- if Gaia was the goddess, as Pallas Athena was the goddess of science.
Well, this Wiegner and Einstein, are in turn, and all the other scientists in turn have in mind at least have said, and wondered how that could be possible that the math is so strong that it is able to tackle natural phenomena, how it is able to explain it.
And precisely Einstein once said that how is it possible that nature at all mallitettavissa.
How is it possible that can be kompressoida so this world kaikenpuolinen complexity so simple that we can truly understand and even mathematical models for it?
This is really a complete mystery.
But this Pallas Athena, the hypothesis now assumes that this goddess to protect us, and science has not yet been exhausted.
That may be -- science progresses further.
If this hypothesis can be accepted, that science has not yet stopped, as if a large scale -- that is not only just semmoisia to fill gaps left, so when we will be very powerful tools available suddenly.
They return to the moment.
This is a bit like a parallel-axiom, there Euklidisessa geometry.
That we can take on issues like -- or we can assume that this is not valid and, for example, non-linearity is an essential part of all nature, all natural mallitusta.
Then we get quite different paths along the different results.
But if we take seriously the Pallas Athena-hypothesis, then we end up very different world in which pretty much dominates the linearity of the phenomena.
Now this is neokybernetiikka explicitly -- based on the idea that, for example, linearity is dominated by --
[1:25:10 / 37]
Well, before you go to the so-linearity into second intuition, which, as follows from that Pallas Athena hypothesis.
A certain kind of determinism.
So if the measure of data -- data is the only thing we can draft, after all, to detect or collect to get -- the so-so science can develop, as its scientific progress must be based on this data collection, after all.
Where there may be some models to build, then it must be more or less unambiguous, that it is how data is to be interpreted.
Because otherwise the risk of just that post-modern ambiguity.
In other words, data can be interpreted in different ways, and it then hajotaan different directions of interpretation.
So that we would be one of the only interpretation, at least in the broad sense, is valid, then it requires that any kind of non-random nature of systems.
So, in a particular way kyberneettisten these systems, they must have a kind of natural mirror images -- to go into detail more specifically -- but not in the way that they more or less uniquely describe the surrounding world.
[1:26:59 / 38]
Another very semmoinen intuitive idea in itself, is that because this system and environment are strongly married to each other, and the environment, it consists of other systems, so these models have to be symmetrical, in a particular way, that what the model tells the surroundings and what it says a systemic, it is more or less mirrors or rotatable.
[1:27:45 / 39]
Well, then this is really the most questionable, or the most striking objections to the hypothesis in this context, it is this lineaarisuusolettamus.
Well okay, we can imagine always that if the system is in balance, so it is somehow säätynyt to a point where it acts as its operating point for the environment, so it can be linearisoida -- but this is a profound idea in itself, this, because we first have to get there linearisointipisteeseen.
No why this lineaarisuusolettamusta now highlights so far -- and will continue to keep this a guideline in the way that, as far as possible, is the linear, pending the establishment of epälineaarisuuksia -- so why is this done?
No justification is that epälineaaristen the category is so broad and so uncharted, and then never find any consistent yhtenäisteoriaa, or semmoista a single class models, which in some way to cover all possible epälineaarisuudet.
Only lineaariteorian side of this is possible.
[1:29:11 / 40]
Well, this is indeed a very fundamental nature of the starting point of these kompleksisuustutkimuksissa that almost the first sentence always states that the complex phenomena, or emergent phenomena, the following epälineaarisuudesta, a lower level.
So, this is a very, very fundamental difference -- although, if we examine the covariance something else and so, after all, it is the variables of income, ie non-linear function, but it can still be modeled linearly.
And -- no, one of reasons is also this, that if we are not interested in those processes, but only in the final quarters, that the outcome of its process of going into balance, dynamic balance, so that balance analysis can be much easier than that of the review process itself.
So, it is a balance -- there may be sufficient linearity of this sort in itself.
[1:30:16 / 41]
Here are few of these konkluusioita.
So, next time will have to apply the one hand, this balance between the search of a stage, on the other hand, lineaarisuustavoitetta in every phase.
They have a wide range of heuristisia, theoretical and practical arguments -- you can read about that -- but all in all, these starting points to more or less unambiguous suuntaviivaston what direction to go in favor of, or in what direction to go.
[1:30:52 / 42]
Here is one example of what can follow if you have epälineaarisuutta system.
I will run this through quickly -- this is so surprising result, when we have two things in combination, non-linearity and korkeadimensioisuus.
So, in future we will be satisfied korkeadimensioisuuteen and linearity -- because we know that even if the dimension is high, the so-linearity to save us.
It is considered mares, a system that is very close to a linear model, ie it is diskreettiaikainen model in which the next state of s (k +1) is a function of the previous state of s (k).
It is this sort matrix A, which makes lineaarikuvauksen new place, it is just this sort in the non-linearity.
If this is not something that f-seven would be so totally know the quality of how that system behaves, there was a dimension of the problem, huh.
Well, now defined as the non-linearity in this way that it only cut the negative values in the way that if s is positive, or it s the element is positive, then go through the s in.
But if s is negative, the output provides a simple zero.
What do you think is this not a simpler behavior of this system as a linear system, because no variable or the variable element is now able to go negative?
It is only the first kvadraatti, or hyperkvadraatti available for the single-space, and there is a linear model.
Does not seem to narrow the time of this behavior?
However, it proves that this is much more complex behavior than the linear model.
[1:32:53 / 43]
Can be shown that the appropriate A-matrix of choice, brings diskreettiaikainen model capable of simulating any algorithm.
That is the way that the state s is a snapshot of the program, because that way there are the values of variables, and then the program counter.
Take the example of this.
[1:33:20 / 44]
This is a program of this sort, a very simple language described, but that language is a direct translator that is able to reverse the Matlab-code, and on issues like matrix.
So, this is a translation of this phrase here, or in this matrix.
You can see here that the first X in one of the X value and Y has a zero-value, and then the program counter goes into circulation on this -- that if X is even greater than zero, then X is reduced by one, Y, was reared in one , and goes sextuplets, and this is again that, in practice, going all the time 'X' down, so long that X is zero, when pullahdetaan out of the loop, and this program will stop.
But what is this side of on the fact that whenever the X-seven minimized, so is Y was also changed in the way that changed its leader, will be zero.
It follows from the fact that, depending on the x's parity, then Y has an end value, either number one or zero.
So, this is -- one could say that this is a generalized parity function.
If you remember neuraaliverkkoteoriaa, so you know that someone XOR, elikä a kind of parity, just two parameters, has already been quite a test of the problem, and here you can x the value to be any integer, so it always returns the outcome Y in -- either number one or a zero, depending on whether it is an even or odd.
It is just -- this is the standard, this A-matrix, s but keep it sisälläään x: the value of the initial state, and then ohjelmalaskurin here.
And then when it stops the process, enters into the balance, as it always does, then the Y has something other than zero -- or it is zero or unity.
This has now been tested that varied with some of this' X ', and this varied with ohjelmalaskurin value -- because this is just a purely arbitrary, this sort s, the vector can be iteroida this through and to see to it that what it konvergoituu.
[1:35:48 / 45]
Well this is the end result.
See you, that this ohjelmalaskurin value of this axis, and then the initial status, ie the x's value is in this axis.
So, you can see, the classic of this sort parity function is defined only in the integer points, and we can see that if you have a program counter number one initially, and one integer value, then it enters into in the way that it is zero to zero in the inflow, ykkösestä number one, second place to zero, the three number one, and so forth -- ie Y is, or is loppulos, is number one if it is odd that the initial value of x.
But really, we can of this Y's values, Y, by the final values of the draw with the other initial values of Poker in these well-defined values -- in other words, this is this sort generalized parity function here korkeadimensioisessa in space, can not say.
Well, this in itself was the only experiment of this sort,
[1:37:03 / 46]
but it is what this is what the thing is that when it comes to this sort komputationaalinen strength of this mallikehyksellä, then suddenly it is a Pandora's box opened.
In other words, if an arbitrary algorithm can be implemented in this way matrix, so we can take to the so-called universal machine in the form.
Universal Machine is semmoinen, which includes the parameter in the other program codes, by simulating it and return it to the value of what it does inside of a function or algorithm would return.
So, this has to be put into practice now semmoinen a universal machine.
And, it is a universal machine has been used in such a way that that having someone inside the algorithm, and to interpret its results.
This is a little bit complicated, now, but the question is whether
[1:38:17 / 47]
which is also Gödelin epätäydellisyyslauseessa, that is, it proves that if able to do semmoisen the algorithm which is able to say something about that the last film in the system -- from A-matrix -- then it would prove that the overall system -- that is, if you would semmoinen algorithm which is able to say about the system, Will it ever stop at an arbitrary feed or not, so we could submit it to the algorithm, which makes this reasoning, we could give in to this system -- this system works in such a way that if this system itsestänsä says that it is going to stop, so it pistääkin this eternal luuppiin, ie it never stops, and if so semmoinen algorithm which is able to say that it does not stop, it stops abruptly.
This is the pysähtymisteoreemoja, and so forth.
However, the end result is that --
[1:39:32 / 48]
can you report this to look at what it is -- however, it is essential that the system here is semmoinen that although the future systeemiteoreetikot would use most of the time of this analysis, it was never going to be semmoista a method that is able to say all the feeds you, that if this is stable or not, this system, it is a question.
So, some simple non-linearity than what was examined, both when it has a sufficient number of dimension, as if this is more than 300-dimensioinen system -- I mean that we are capable of three hundred to take the dimensions of this universal machine -- so its behavior is qualitatively completely gone -- that nothing will really be able to longer say, this system, since all the algorithms are returned to that pysähtymisongelmaan of this framework.
[1:40:33 / 49]
Well, here is this mallitusstrategia what is implemented on time.
[1:40:41 / 50]
However, here is this idea, in short, that we started as if the circulation of this situation that does not really have to know that what will take the stairs, so now if you are moving these osviittojen in accordance with, then it goes to one of the dark -- we do not know in advance what it will take, but still achieve consistent, according to the forwards.
It is perhaps reasonable to conclude the course watch them again, this film sets, just in the sense that it may bring to mind that the more age than was promised.
And it's all learning, at least kyberneettinen learning, is the root mares iterative learning.
In other words, piled up to the increasing consensus on the new information.
Well, thank you.
[1:41:37 / -]
(v.2009.04.10, only a rough machine translation, not cleaned yet!)