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Prof. Heikki Hyötyniemi
AS-74.4192 Elementary Cybernetics
Lecture 1: Introduction
Helsinki University of Technology, 23.1.2009
(v.2009.04.10, cleaned from a rough machine translation to only about line 100 yet! marked with #)
[0:00 / 1]
Well, let's begin then.
Welcome to this lecture on Elementary Cybernetics.
I am glad that so many had enrolled to the course -- and also others seem to have come -- and the other thing I am pleased about is that we got Petri Lievonen as an assistant for the course.
All in all, I have a good feeling about this course.
This course has been gradually developing, since 2005, and now we could probably say that this is beginning to be in some way ready.
This spring the idea is to record these lectures, because -- one does not really know whether -- will the course be given next year and so on.
The aim is to get the material available online.
[1:08 / 2]
And -- if we then move forward -- this is now a sort of introductory lecture,
[1:15 / 3]
and the introductions begin with this, the ancient Greeks, in the traditional way.
And now we have -- here in ancient Greece -- had a person of this sort as Heraclitus, who astonishingly well was able to put into words, these ideas, which are related to this modern cybernetics too.
You may have heard of that, "everything flows", "Panta Rhei!" -expression.
It means that nothing will remain unchanged.
That you cannot step into the same stream twice -- that if for the second time you come there, then the water has flowed away and there is some new water in its place but yet for some reason, the water, or stream, as a whole, is unchanged.
And, indeed, all is changing.
In the water the flowing material is continuously moving, but yet the whole in some way remains unchanged.
On the other hand, in a complex system there are a lot of all sorts of tensions, which keep the entity together.
These tensions, or the invisible tensions, the managing of which is the key.
Or that is the path to understanding the overall behavior of the whole.
And, indeed, wisdom is understanding how different things are driven by other things.
It is this kind of decentralized governance idea.
[3:12 / 4]
If we put those aphorisms into verbal form, better, then really this fact, that although people, for example, change in a company, and even if cells are dying and born in a body, still as a whole, the operations of the company or the functioning of these organisms or organs, remain unchanged.
The most surprising is, in fact, that these are in some way in balance -- these cells, these people, these companies -- and from this balance, or balance caused by these tensions and counter-tensions arises differentiation and diversity -- and self-organizing.
Indeed, there is no central control, but all the components in turn require as if their own place in the entirety, and it leads to that each push each other out, and the whole, however, seems as if it were sensible, intelligently functioning, and there really is some kind of self-regulation, and self-organization.
Well, considering that already 2500 years ago, these ideas were discussed, surprisingly little has been achieved in this field.
Modern science is not so well able to answer these questions, or unable to even formulate these issues.
Quite many nod approvingly, so perhaps I will not start justifying what this claim is based on, but one could also well argue against this particular claim.
We will return to these counter arguments in a moment.
And, indeed, now we at least -- you who are our department students -- so you might think that such as our concepts of it, because that way, why is it that there are issues like as if attraktoreita stable, in these systems.
What is their nature, and from where it arises.
It is precisely this issue be discussed further in this course.
Herakleitoksen after a lot of philosophy, but pretty much focused on Plato and Socrates after these life problems.
Platonkin went on the really interesting is just that they remain ideas, there for this to change the underlying reality, and, therefore, Plato focused on those ideas -- and in fact thought that this changing reality is too difficult to understand at all.
But the existing tools, it is perhaps not impossible that they could be sensibly addressed.
[6:52 / 5]
Well yeah, now this is a picture of this sort -- I just had a look Heraclitus, now there is tuommoinen Sugar-Conny watching these studies.
But this is far from justified membrane that cybernetics, specifically, can be on issues like the term as Constructivism and constructivist learning.
It involves the fact that everything is interconnected, and specifically relates to all of the former, the base to which it is built it new.
My background, my pohjani is now in the Neural Networks.
It leads to the fact that we will be those models, which are dealing with -- we will lead in the framework of Neural Networks.
[7:48 / 6]
But the second thing, and even more important, is that if you want to learn these things, or take on things here, so even more, it implies that what is in your own career.
Will be seen that the cybernetics of key issues have any feedback or interaction.
In other words, each system affects another, and second, it seems back to the original.
Similarly, the learning process is a kind of educational process in the reverse side.
In that regard, it would be really quite interesting, at this stage, to know that what you pohjanne is what your image of it is that on which it comes to build.
What is cybernetics, and what are the complex systems.
Another issue is that what your impression is that what you -- do you think that this what you pohjanne on top can be built.
Or, in practice, why are you involved in this course.
What would you like to hear, and what do you hear the rim.
But -- does not happen here in the context of a lecture here through these -- not to visit you -- you might not be in favor of present, yet, but a return to the lecture diaries context.
In other words, the objective should be that you esittäytyisitte there, to each other, and for me.
This lecture diary practice there is some -- probably -- to you the guest, if you are our students, ie it is considered a moment.
[9:55 / 7]
Well yeah, this is very much of this sort a noble thing to that.
The target should be that you can be -- that you would be some kind of kernels of ideas, some kind of attraktoreita remember who rupeaisivat grow some kind of ideas then.
[10:18 / 8]
Let's go now to this very traditional cybernetics, and it is considered that what has traditionally been.
The goal is neutral on the fact that what is at stake.
Cybernetics-term actions to public debate, or science, Norbert Wiener, in this book about 60 years ago.
He wondered whether that on issues like all kinds of systems have common features -- are relevant to general systems and control characteristics.
This was a very influential book or idea in the course.
But -- in a particular way, and just kyberneettisessä mind -- things have gone forward, it is konstruoitunut new structures on top of old.
Wiener in the world was very different -- in that way that did not have control theory exists.
One of the Wiener, this thinking had resulted in its own way of this control technology, control theory on a charge.
The other was artificial then forward the expenditure, and so forth.
In this sixty-year period, all these sectors -- have gone a lot further.
And perhaps now begin to be time to consider whether that -- what they all are able to erityistieteet together to say the truth.
Here again, this picture a little left as a picture-riddles.
But if you go browsing of old papers related to these, as you note that Alan Turing was involved.
He considered the mares Seepran raidoitusta.
How is it possible that the rise of this sort as if organized in the order, even if it does not värittymistä any guide.
After all, he said yes, that really it raidoitus not interested in him, but it is there for the horse tracks in the rear which is the most interesting thing.
[13:22 / 9]
No indeed systems, control, communication -- or data -- they are generally the cybernetics common background.
In that sense you could say that in some way that cybernetics is the lowest common denominator in all of this faculty affairs.
So, this automation side, then on that side of the telecommunications systems and the construction side.
In that sense, this fits well -- if you are our faculty students -- suits of this sort, knowledge, or issues like the wider angle, you osaamispakkiinne.
[14:21 / 10]
Then go to these delusions to.
Or, one might say that cybernetics is so attractive -- and on the other hand, this artificial intelligence is such an attractive idea, and the understanding of systems is so important --
As a long time ago, had all sorts, on issues like -- even when not yet had the science world as mares intense than at present, so even had issues like ismejä, and others, and cybernetics was one of the first ismeistä 60th century, which was financed by a great deal of research -- and in particular artificial half funded a great deal of research -- but then discovered that nothing very useful not failed to deliver, and finance disappeared suddenly.
Then it rose again a new generation of researchers to contribute -- this interest, in that sometimes the 80s -- and it has dominated, these research areas a certain kind of cyclicality, and it is one indication that this is a very evolutiivinen and kyberneettinen tutkimuksenala itself, this cybernetics.
The other hand, in the United States cybernetics was a very popular term at the time, but also the Soviet Union, since that Marxism-Leninism along with cybernetics or control science was considered the second tukijalaksi planned economy based -- that is through cybernetics can be centrally controlled society the best possible end-state.
But there was a certain kind of misunderstanding, even in the case.
Maybe now would take the matter afresh in the sense that it can be -- or, depending on the fact that you have studied, for example, the 70's, and where you studied, so this may affect your views on cybernetics.
If you like fresh students so you do not necessarily have anything false, and you can leave a clean slate.
Just Briefly -- those who have been in the 70's school -- so why is this eastern optimism did not, so it was thought specifically that could be centrally controlled things.
In exactly the same way as our traditional control theory, still think that way.
However, in nature, Herakleitoksen ideas of all is decentralized -- there is no centralized control, but in systems when communicating with each other and turn to play, compete, whether it consists of control -- and organisoituminen.
[18:11 / 11]
You could probably imagine, that this matter is again becoming a hot, or the surface -- a long cold season, or a long stagnation.
Because -- do not go to this story through -- but a glance to tell that this is how one systemiikan and cybernetics conference was sent to random number, in practice -- create a paper, presentation or publication, and it had gone through.
Quite obviously this cybernetics, the issue has now once again a kind of attractive.
[19:07 / 12]
Well, more specifically in mind -- you who have visited your school at a later date, so you probably have also cybernetics become something like the image, because today a lot of talk these kyberneettisistä organisms or kyborgeista.
A certain way, these are also part of this package of cybernetics, but they are very far away from such kyberneettisistä organisms, yet.
[19:47 / 13]
Here now is a film of this sort that I wanted to now, however, although this is, the engineers time to strange appearance.
This is the one film that I had to do when my wife, who is a nurse, I tried to explain that what is studied.
One could say that the control engineer is not highly trained doctors, who know the mechanisms, and are able to inject the right-back coupling, or the right guidance, if a connection is broken, or in any way does not work -- for example, if the sugar values are too high, so is able to adjust the insulin.
A sad story in itself, the control technology -- or the doctors' point of view, or a whole -- for example, surgery may be successful even if the patient dies.
Then again the general systeemiteoreetikko approaching things in a whole, does not approach things in detail, like this doctor, but the problem is simply that when it comes to over-build general theories, it is not anything useful, however, may be achieved.
It is gonna remind you -- if comparing the medicine -- so, it begins to homeopathy, almost -- that the theories are fine, but do they have theories then, however, in practice, change of this sort of systemic effect.
Namely, this is somewhat surprising in itself, so that homeopathy works, just kyberneettisessä mind -- that if we get this man to believe in healing, so in half the improvement has been achieved -- and in some ways this is the nurse is just this way, any way to make this kyberneetikon swing, that his ideas, or know-how is based on the medicine, yes, but he can take account also of the whole -- and, suddenly, he will be able to get the patient's happy, and happy.
[22:13 / 14]
Well, here now is the fragmented membranes.
This film is for those who have begun studying the knowledge automation technologies, major in or a material.
This course was meant to be like this the end -- the whole of this major of the summary rate.
Well now that this -- we changed this tutorial, and this is no longer practical for anyone no longer mandatory, so here it is now also a little väljennetty these targets -- in other words, this is in some way moved here from pure engineering thinking more like a general systemic thinking in reverse.
If you look at the current and future engineers in a period -- in this automation, system, control the area -- we could say that all the simple things, easy adjustments have already been taken, and what you are going to do that is difficult issues -- such as the large units for adjustment.
Or, since these large units are not adjustable -- such as social or economic life -- the goal is that, at least at some level understand the systems that osaisitte prepare for the future, maybe more when you know how today.
Here the Multivariate Regression Methods course is a place for these complex systems of mathematical methods for accurately through.
Preference is that you have something like the vision, understanding the fact that what the mathematical tools to be used.
That you have some experience of these multi-variable methods.
This course has a couple of drill work, or training session will take place where these mathematical methods through, yes, but now it does not give as pintaraapauksen to these methods.
[24:50 / 15]
This course will focus on one particular aspect -- the narrow sections, which can be classified into cybernetics.
This cybernetics research is part of kompleksisuusteorioita, and the most yleisimmillään looks natural patterns.
We will not go through all the cybernetics of this region -- not to mention those kompleksisuusteorian regions -- different methods or results, but we will focus on one particular aspect.
The reason is that its part of the "we can build a reasonably practical package for these issues.
That is the way that we can go quite a fundamental physical mechanism can be achieved up, emergent levels, then, and one can generalize these ideas to other platforms, this particular theory of the structure.
[26:16 / 16]
Pretty much these luennotkin based on the theory that is built in practice, 2000-first century, until, that is to say, this is the time it fresh in mind.
[26:33 / 17]
Quite large part of the theory is this, together with the report which is found in the course through the pages, and a few printed versions are in the laboratory also available if anyone wants one.
So, just this neokybernetiikka is such osaleikkaus cybernetics of all the area in which to build a coherent whole, and which can be mathematically get caught on.
[27:12 / 18]
This is now just found it that certain way, the mathematical side is a necessary background in order to reach higher up in here.
Because here in mathematical side defines the concepts of what is used at a later date.
These are all the complexity, chaos, cybernetics, artificial intelligence, things are just infamous, in the sense that the concepts are very much and people will understand these terms in different things.
The course runs through more or less consistent with these concepts and used them to turn up in one way -- and consistent with the definition of the concepts of mathematics.
[28:04 / 19]
Here is a cybernetics of this study, our home institution.
It can be found there -- or it can be found in the course pages.
[28:20 / 20]
There are also applications in sight,
[28:25 / 21]
and a demonstration of this sort available -- you can then visit the course website through experimenting with that it looks -- but that knows anything alaolevasta theory -- so what, how kyberneettisen these theories, how they practice, then will look like.
[28:44 / 22]
This is now yet again, this really the same thing.
Cybernetics cybernetics -- that is how it is formed on issues like science attraktoreita inside.
In a sense on issues like research areas, which include a number of interested researchers, and different methods that are living their own lives -- for example, control engineering, artificial intelligence, systems technology.
These make up their own tutkijayhteisöjänsä, then.
Certain way, this is a attraktori to attract certain kinds of people puoleensa ago.
This is a little bit loosely called, but that intuitiviisesti perhaps you can try to understand.
The problem there is then that these attraktorit are indeed cyclical issues like structures here -- that every now and find the same things again.
In particular, in that side of Neural Networks and Artificial Intelligence study the same things -- they return to again and again.
And -- no, for example, this course will take place through the structure of neurons from just the 40-chapter neuronihavainnoista.
But hopefully at some point reach to this is in one of these different research areas, and find this sort as if attraktori whose name would then -- well, sort of, these kompleksisuusteoriat are now this sort comprehensive package which includes all the information, categorically, that we hope, we found a compact tutkimuksenala capable say -- or to bring together all those different paradigm.
[30:54 / 23]
The other hand, we can identify all the dynamic processes, such as in the previous film, but this has now been shared things on issues like network.
This is now something like the description of how the various issues related to each other, how they relate to each other -- it consists of this sort a huge syherö you can go over there to see the original pages.
We are the difficult things to do.
[31:33 / 24]
The appearance of the course is such that it is twelve times in the lecture and the two exercises, and one or two, these seminar presentations.
We need to talk a little more, that should any participant in a seminar presentation, or whether it just extra points -- but it is a very important part of this rate that is seen that way in your own areas of expertise, perhaps to some of these ideas apply.
Return to this, the organization of seminars later -- however, these lectures will be here on Friday, at the same time.
And one thing which is even with your shoulders, these are the lecture notes.
In order for this to be interactive and really kyberneettinen learning event -- something I have learned to teaching methods -- so I would hope that täyttäisitte, or would you, diary of mares.
We had last year, this same practice already, and it was kind of a good time -- people just sent their reflections to these matters, and it saw that things might start selventyä the course progresses -- that is, these are the questions which were raised, they found some kind of intuitive or concrete solutions.
This is a very important part of the course, but it is really the last time in that sense is not successful, that they are pretty much the feedback was the e-mail form, and they returned assistant -- they pretty much stayed there then, that they do not, no one had time to respond.
[33:48 / 25]
Now, however, be on issues like weblog format these things.
You need to go over there at the book by yourself in, then you have a username, and you can you your own account then write a reflection, and others can comment on them.
[Do you want to give more ... ]
From there, really -- go look at the page there -- so then you can see that what is at stake.
[34:25 / 26]
Lectures, the content is then this sort -- that you will see from there, verkostakin -- one could say that the first half will focus on these theories and models.
All the time goes beyond it, these neokyberneettisiin designs -- start to like these complex systems in general modeling.
Leads to very concrete models, which will then be applied here later -- and on the other hand, since the models are very practical, so it proves that we can also have different interpretations of the issues -- for example, we have issues like analogioita.
If you read us our courses so you know that the analogy is in principle a very powerful method to understand things or broaden their skills well to different regions -- we know that under the principles remain the same then we know that they are in some way inherited from one area to another.
[35:41 / 27]
Let's go a little more concrete on these reviews.
This is a particular way of systemic theory in this job.
And to that end we have to understand that what is systemic.
But nothing very concrete, we can not really say in this context, because if some way rajaamme this system concept as it leaves out a number of systems which are different point of view it may be to think about systems.
Actually, the only guide in this matter is that -- precisely this sort kyberneettinen starting point -- in other words, what you at this time, opened up the system, so it is meaningful to the system, including the examination.
For example, you understand that a rabbit -- it is semmoinen living entity which loikkii over there -- so it has its own system.
We will come back to this intuitive definition, the weakness of a moment.
If the system is defined in some way, then the model is the system's performance, in some concrete form.
If the system can be defined as the time loosely, so the key problem is that how we get the model built.
If we can not make it something concrete description, even in words, its function, so it is too vague so that we could examine it.
If we get the design-time, preferably even a mathematical model, then we are much more advanced.
Admittedly, we have time to be modest in this respect because they are all models which are mathematically managed to write, in a certain way already been controlled, and subjected to a control design.
Now we should try to get it even a step higher up.
I just said that the intuitive sense, a rabbit is a [system], but not really kyberneettisessä sense it does not, then, however, [the system].
[38:30 / 28]
Because if you think that the hares be characterized by the fact that it is bouncing there, and it is a living entity, then the life itself can not be defined that is how life is now in the rabbit, a million years, for example, or permanently, in the way that it is a rabbit should be attraktori which should include something jänismäisyyttä one million years, or forever.
Since it is a rabbit dies.
In particular, if it is not an environment that supports its jänismäisyyttä, then it will die very quickly.
If the surrounding system is not something to eat, another ecosystem, or an entire ecosystem, as the hare does not make it good.
In that sense, we can not properly define the issues like kyberneettisen system boundaries.
Because the system is an important part in a particular way but also of its environment.
Not to mention the entire jänispopulaatiosta -- that is needed throughout the rabbit population, so that this jänismäisyys could survive, their environment, a million years.
And another problem is that the system kyberneettiset systems seem equivalent, or be contradictory -- in the sense that when we are accustomed to the Entropia grow naturally -- in any meaningful systems, Entropia will increase, or closed, systems -- the so-kyberneettiset these systems are such that the complexity seems to increase, ie the intuitive level, the order increases and decreases Entropia.
Why is this -- What are the causes of issues like countercurrent flows entropiassa, entropian reproduction.
This is a little similar as the time was that planetary motion, ie the interpretation that they are dominated by some loft lunar phenomena, and the gods will lead these planets.
On the surface phenomena were alisia lunar phenomena, and they had their own natural laws.
Today, thought the time naturally, that all right -- kyberneettiset systems are something other than physical systems, and they do not need either one of entropiaperiaate action.
Of course now, this avoids a conflict because of the view that kyberneettiset systems are open systems -- the environment, however, Entropia will increase, even if the system is reduced Entropia, but -- and this is in some way, inadequate explanation.
[41:38 / 29]
This -- indeed, this has now been found that this is not -- this can not be a good traditional systems theory, this cybernetics, as the systemic theory of the traditional stone-feet -- that is the concepts, such as the system's boundaries, and inputit output -- they are losing relevance in a particular way -- not really is nothing else left than this -- just the idea of systemic, and that these traditional tools are pretty powerless.
Eli -- This is the traditional system's theoretical model, the general form -- that is inputit and is systemic, which is affected -- and then it can be measured, the y-measurements through.
So -- in fact, this limit is changeable, because the whole system is the environment with the married, and these kausaalinuolet certain way to lose meaning, because it is systemic, the rabbit is a part of the package, and change the system or the environment, the entire ecosystem -- or at least in rabbit populations in is a sufficiently strong factor that it is not -- this kausaalinuoli not a one-way at all, but it is precisely semmoinen pankausaalinen relational -- that is, at any time, the environmental impact to the system so the system is interactive with the outside world.
[43:25 / 30]
Another little more philosophical problem is that if we kognitiokoneistomme is kyberneettinen machinery -- to this returns to the later -- so, how it could understand the things that are as complex as it in fact -- that others kyberneettisiä machinery.
Can the brain to study things that are as structurally complex as the brain itself?
You may consider this just a lecture logbook.
Because, precisely, the idea is that they return to later -- or at least you can go back to those ideas later.
So, you put this up, these to your intuition, and a return to those perhaps constructive intuition developed in the course at the end.
[44:28 / 31]
Well, just because this case is cybernetics, a time long, challenging, so we have to kyberneettisesti mallittamaan kyberneettisiä systems.
For example, if we try to understand the self-cybernetics, so we have to understand that kyberneetikot are kyberneettisinä agents built the system, and therefore -- no, quite briefly, that Gregory Bateson decided on issues like the conclusion that we have big things to do, but things have turned out very difficult, and it is why cybernetics has proved difficult, so the reasons are kyberneettisiä.
[45:30 / 32]
Now go, harpataan, single category of concrete things, but still remain a certain way philosophies on.
Eli goes to Wittgenstein.
[45:48 / 33]
His central theory varhaiskaudelta -- was this, that what you can not express, so it you can not even imagine that thinking is such a language based on that if you do not have concepts, and ways to construct the concepts of connectivity, so you can not really do anything.
This is just a fact in itself, but what Wittgenstein did not take into account, perhaps, was the fact that the language of mathematics is a single class stronger than the natural language.
Or perhaps to say that mathematics is nature's natural language.
But still -- is it valid, that even if we use math, so we must understand this tool, it is mathematics, so that we can understand the concepts of what we have to put in place.
Well, why math is so strong?
[36:59 / 34]
Associated these few points here.
The key thing is that when a human time perception and time of changes in perception is difficult, so math is a tool that -- differential calculus, and others -- that allow it to be dealt with on a consistent basis.
Here are just thrown into the throwing of this sort -- for example, as simple as speed, is ultimately not a physical phenomenon -- semmoinen that would measure the speed from one, directly.
But it is necessary to mathematically define the way that it is a status change, between a given.
You have to be carried out two measurements system, and then dividing the change during the term -- then you get speed.
So, since there are only a mathematical definition for this speed.
Only the mathematically you will be able to consistently deal with it.
The other hand, given the natural language of their own tools, such simple concepts, such important concepts -- but the tools of mathematics is much stronger.
Another thing is that the real number in mathematics can be treated naturally.
Certain way, this sort blur is automatically according to the models, where the twists are real.
Continuity of this sort is possible.
Traditionally, when dealing with language issues -- trying to build something cognition model, linguistically filosofoiden -- then it necessarily leads to semmoiseen problem that, for example -- where there is awareness of the fact that awareness is detected or the observation of this process, so who is doing the finding, we need someone homonculus -- no who it is homonculuksen mallitusprosessia dominate, a second, the next -- lead in issues like infinity landing a way that does not get rid of the need, but always new, infinite number of homonculuksia, in order to try to understand, for example, the process of thinking.
Mathematically, we can -- in a particular way on a simplistic -- we can get to this sort of infinite series is converging and suppeneva -- can look at this infinite chain meaningfully.
The key thing is also, of course, this mean that we can examine the mathematics of parallel phenomena naturally.
When linguistically we always injected the queue, as in mathematics using vectors and matriisilaskentaa we can handle arbitrary number of things simultaneously.
[50:25 / 35]
Here now is this really what the syntax will be used -- just such a quick introduction to this issue.
We have the symbols t, symbols x and u and so on and so on, and will be used semmoista interpretation -- that in itself provides a math syntax only for us.
In order to get something achieved by means of mathematics, we must have the interpretation of those things.
And now this, quote marks "semantics", is the fact that in nature or the environment or the real world, this t, it corresponds to the time, and these X and u: take responsibility for the internal space, on the other hand, this corresponds to the state of the environment, this u.
These may be included in history.
This is a systemic theory as such, that even if things are linked in history, so when you have enough korkeadimensioinen tilavektori, so it's past can be encoded by the static tilavektoriin -- this is just such a mathematical system theory of strong results.
This is now of this sort -- if we have the x-vector and the u-vector, so between them, or they may be determined in differential equations, which says that the status changes -- this seems very trivial, whether on issues like using to describe something really interesting things .
But this is the basic mathematical tool box -- its purpose is to demonstrate here is that math is not going to be this course difficult.
We need only a basic understanding of derivaattaoperaattorista and then the basic understanding of matrix -- in practice Lineaarialgebra.
[52:44 / 36]
In this connection, we need understanding of the multi-variable methods or multivariate analysis.
How many people are familiar with this sort expression?
I would like to ask that how many people know, for example, kovarianssimatriisin structure, and definition?
They will run a lot.
And then the other, -- kovarianssimatriisin structure, it consists of a large number of parameters that can be kompressoida so-called property and ominaisvektorien help.
Eigenvalues and ominaisvektorit will be the very key to this course.
They are Lineaarialgebra essential tools.
Well, here is the "cast" of this sort than infomaatio.
We will later find that this clause is in some sense infomaation interpretation.
Eli is a shift from data to information.
[53:58 / 37]
Well yeah, this is the film, which you can also think about -- luentomuistiinpanoissa, lecture, or log book.
In other words, whether in mathematical rules of the game right, or whether they are final.
A certain way mathematics was born of free men in free-time hobby in Greece.
It was not anything to assure that it would be applicable in the wild.
Euklideen geometry, it pyöriteltiin points and direct -- oh well, they came very fast applications, yes.
But nevertheless, the rules of the game itself was completely temmattuja hat.
For example, the starting point for Greeks was that it is available only compass and ruler.
It has been the whole Euclidean geometry to build -- in itself a powerful performance.
But, however, may be questioned whether the modern world -- or is it a natural conclusion that it is only a compass and ruler available and can be used only for finite number of times?
An example of this can say that the ancient Greeks had a major problem in the fact that -- or the main problems that they had been in mathematics, was the fact that what may be an arbitrary angle is divided into three equal parts.
It is indeed an impossible task, these tools -- especially under the condition that this method has to be the "Poker", or Quadrature finite.
Instead, two-angle is very easy to share.
You remember -- do not go down, but still -- it is the arbitrariness angle always done -- harpin and viivottimen help.
And, if joustamme little of these original rules, as a way to allow that the infinite chain of harpin and viivottimen uses are permitted -- and since then we have become, or will be -- will notice that the world broaden surprisingly -- for example, the angle distribution of the three equal parts is suddenly entirely possible.
For example, exactly what can be done in such a way that distributed the first corner in two parts, a half, then divided this part of a half turn, then divided this part of a half, and so on, will continue till infinity.
It very quickly konvergoituu to a specific section of this round-trip puolitus angles, and can be proved, geometric series, that it is indeed the sum of the series is one third the original angle.
This first lecture will specifically consider whether the mathematics ready.
But on the other hand will also end up to the fact that this course will be used only in the manufacture math, which is very well developed.
Does not need any machines in the cell, or other tools.
[57:30 / 38]
In essence it is a strong tool that will help us korkeaulotteisen understanding the data, it is pääkomponenttianalyysi and so forth.
But I want to emphasize that this is not the tool semmoinen what the source of the application as if the traditional engineering sense -- that we would have a tool box which is now forcing we apply in one application -- but I would like to stress explicitly that this pääkomponenttiominaisuus emergoituu these kyberneettisistä models automatically.
It is just a fortunate coincidence that we have the root of this sort a strong tool box ready for them to understand the models.
[58:21 / 39]
Well insinöörimäinen introductory multivariate methods are also available on that network -- that we have a fall course that deals with these methods.
But a brief introduction to get to this course in these matters -- that if you have not had something similar rate so it does not crash things.
[58:45 / 40]
However, what might -- or what is a very important thing, whenever I start a data-based analysis to make -- and a certain way it would be good if you had ever used the methods they are -- you would have found that when pushing rubbish into the rubbish is also out -- that even if matemaatinen machinery is very strong, and it is precisely these pääkomponenttianalyysit are extremely powerful methods, so you must have good data, so that you get something meaningful done.
For example, if there is something entirely -- or has bad data, too little -- so can be quite incomprehensible, or imaginative designs which have no power of prophecy -- that they do not have yleistettävyyttä, they can not be generalized to the data of the population.
For example, here is the analysis that auringonpilkut has given period korreloinut those Republican eve thigh amount.
This could build a model then if you would like to -- but it probably would not be very useful model.
[1:00:02 / 41]
When you compare these global data-based methods, the so-kyberneettisissä these systems have yet semmoinen additional problem is that typically they are in any way -- live, and in some way at a low level of intelligent systems.
This now is a little exaggeration in saying that they will flee to measure drive -- that if someone pistät meter there and it will shirk away from.
But the answer is yes about the -- the results can be interpreted that way.
They are very strong -- if we talk about while technical terms -- they have a very strong puskurointiominaisuus, first.
You are doing what you want them, so for example, the cell space for you very easily can be changed -- it is a very solid all the environment changes.
And, therefore, a data-based analysis is complicated.
Even if you do some of the input-changes, so space is not likely to change very much.
Although multi-variable analysis can be achieved better results than if the measurement of only one variable then the system from within.
And the other thing is this, that proves that when looking at a sufficiently complex system, even something of economic life, so has the force of this sort havaitsijailmiö -- actually quite the same as what is valid kvanttifysiikassa.
That if you measure something you system, even if you want someone to measure the demand and supply in one market, so it can be measured only by introducing a product, and once you have the product on the market, measured in demand, so the market has changed, the original market is not really no longer -- after you have brought this product to market.
[1:01:58 / 42]
This is then again semmoisille people who are mathematically-oriented, so now, even at this stage, I would say that this is some of these terminologioita simplified -- for example, when we talk about korrelaatiomatriiseista and the correlation, so they are pretty much just inland revenue, that is not normalized and not keskiarvoisteta, typically, and so forth.
[1:02:33 / 43]
Well, I took this, now that this "four-Kakkonen" now work on the yet.
After all, it is "proven", or at least said that 42 is the solution to all these problems, we -- that is life, the universe and everything, the problems.
So, this is the Douglas Adams book, in which this claim is found.
A certain way can be considered the fact that this is how it is -- just to formulate the question that way, so yes, it will always form at the root of the answer is simple.
But, the key The point would be to find them now -- justiin interpretations of how this four-two to be interpreted.
And how the issues should be set.
[1:03:48 / 44]
In other words, if we have a sufficiently strong point of reference of this sort, or a conceptual apparatus, or if there is a sufficiently large number of variables and degrees of freedom available, so we typically always found a good explanation.
The more variables so typically the better explanation can be found.
This Douglas Adams himself claims that the four had two full hat temmattu figure to him.
But when this is pyöritelty enough, it has been found that a certain frame of reference four two answers all the questions -- that is life, the universe, everything -- because if it is interpreted as an ASCII code, the four two, so it corresponds to the star -- ascii codes.
And we know that -- if you feel that work is kuolinilmoituksia -- so that means the star is born -- in practice of life, on the other hand, the star now refers to the universe.
And in particular it is responsible for all this star, because of computer technology, this Kleenen the star corresponds to an arbitrary number of absolutely any issue.
This is in some way a justification for why 42 is the solution -- or in a compact form in any way give any indication to all these world syleileviin questions.
But -- it is so loaded, semantics, that surely this can only be a joke.
It just that all do not like these things vitseinä.
It is this postmodern world view assumes that -- pretty much based on it -- that all theories are merely a product of mind, constructive, kyberneettisiä models of the world.
And we can build -- at least when a sufficiently complex modeling issues, they have no equivalent in the world directly -- or at least they are the world of phenomena can be interpreted in the framework in such a way that will agree on any theory of explanation.
Everything is only a discourse -- that the scientific community the debate, which consists of the world, and concepts -- in a particular way kyberneettinen great starting point or an idea, but nevertheless -- however futile.
And this course is to find something tangible, something real tools, and it is precisely that the concepts could be defined by the underlying language of mathematics allows.
It lit up then.
No -- I took on issues like this -- this is perhaps a little bad joke in itself, but that they are actually lived in the 70's will remember the ad's "get the house four to two, put rats to low level" -- elikä 4-2 was rat poison name.
A certain way, this will also resolve all all the problems of this rat poison.
[1:07:42 / 45]
Well, in this particular way now pulling back from other people, namely the ancient Finns now at this time.
A certain way, the Finns have had a very profound understanding of the fact that what the world is.
Because of all the world to hahmotettiin -- or at least considered that can be controlled with any other phenomenon of the world where the understanding of its native words, how it was born -- that the current terms, if you manage to emergens, could say.
The Kalevala is the old wisdom of the People, and must -- I would like to emphasize already at this stage that they are alive in the past, sometimes, they were not stupid people, but it seems to us perhaps tyhmältä because we live in a different world.
Sometimes 500 years ago, people were just -- they had more time to think about things, even the researchers.
And in that sense, I do not in any way wish to emphasize that we now understand the issues in greater depth than it was then, but now, at this time we have better tools, the mathematical tools are better than before.
You could come back here, tämmöisiin system native words at the end of the course -- but what precisely what I want to burn you at the end of the course, so is it you would understand this extremely värssyrakenteen.
Here is every eight bits in all of these items in bags -- so why it can be argued that the extreme of reduced syllables they can write to that format in the way that it has another four and then there are two.
We come back to this, that the clause form again.
Actually, what specifically would like to emphasize here is that a certain way math -- or no, math is math, but the modeling world is a natural philosophy, and it is not math, and it is not even science, in the sense that there could be intuition or otherwise -- in a particular way but also a kind of humor is an essential part of the natural philosophical worldview.
Just in the sense that -- this could start a long conversation, and I hope to discuss the subject line, or we can continue there, but this is the fact that today's world, science is a struggle, as has been noted that it does not match really interesting questions -- rather read though horoscopes corresponding topical issues, or some of the homeopathic methodology, as science now, but is so far removed from the human world.
One way to do this closer to the human world -- or to get it closer to the human world -- is to make it more understandable, more intuitive, but the other, to make it more fun.
Because, after all, science, or at least in the natural philosophy, it should be a series of meemien or entity who live in the human community on the human or the idea of definition-in space.
If it is assumed that they are the only scientists who have access to this encrypted wisdom, so to be -- close the gap in a terrible lot of the population, generating innovations.
At least in principle, should not accept the fact that science is ryppyotsaista and only on issues like the clergy understand.
This course goes a little hand -- or do you see the film that they are somewhat intuitive.
I think it specifically, knowing the choice of this course.
If you are our students, so -- this is indicated by L plays this course, in other words, this is a postgraduate course of study -- a particular way at this stage you should have known, or know-how, these basic tools, matematiikoista, and insinöörimäisistä methods, ie you are good models -- if do you have a bowl system in industry, you can build a model, and know how to adjust it, but this course is designed to just open a few of these ossification.
So, all things that can be models, and what is meaningful to understand, they do not have issues like insinöörimäisiä systems.
But, especially in time for many people the world is precisely the engineering world outside, and you have yourself a favor, if you are able to discuss these people.
Here was this really what I wanted on this first attempt to say.
These membranes have a lot of time on each satsiin, that is fifty copies.
They will go through aikalailla a superficial way, but it may be, if -- you may want a little look at them beforehand, because some kind -- or preliminary slides are there, the network offered.
If one thing is particularly interested, they may linger for longer then.
But in principle, the idea is that since you have very different backgrounds, it is a very different film, then, to be something for everyone.
Any one of the film does not say anything, and any of it might give somebody kind of aha-experience, and I wish to comment on these, that if some of the slides are not anyone's opinion, not good they can be left out completely.
[1:15:05 / -]
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