When Nash theory brings into play some love

  By Alma Dzib Goodin

Daniel is a Russian physicist ready to conquer the world with his ideas, but in the midst of publications filled with Greek letters and numbers, he has failed to atract a beautiful girl’s love of the lab at the other side of the campus. That girl that walks around with the sweetest smile and when she meets Daniel in the cafeteria, smiles even more broadly, knowing that he is a foreigner so she does not want to say something wrong... that girl who ... does she make him sweat?... perhaps so much that he has even asked her name...

 

Town was suffering the third winter storm of the season that evening, so Daniel went into the library, hiding as it was his habit to expect bad things to pass, it was his refuge for everything and everyone. 

He had been studying game theory during a while, especially from Nash’s perspective, and he was determined to publish an article about this topic, applying a proposal from economic and biological models. Although there is a lot of articles written on the subject, he wanted to innovate, he wanted to find something that no one else had seen, however he had to find  that something, there was no doubt he was going to find it there, or perhaps here... maybe in this journal... maybe...

He began to move from one side to another around 300 magazines on the table when one of them slid...... when he bent down to lift it without paying attention to the environment, he saw a hand taking his magazine. He was ready to shout do not touch my magazine, when his eyes followed a hand, and then an arm and then a shoulder... he came up to the neck and two brown eyes met with his blue eyes.

The smile was expanded as always... but this time she modulated carefully her words:

-Hey!, I found this!... What are reading?, she said.

-I'm reading Nash’s theory... He said as doubting whether those words came from his voice or if he was listening to through his headphones, he took them off to be able to distinguish between his voice and the music he was hearing, and they fell to the floor.

She hurried to help him to lift them up and while she did it put attention into the magazines on the table and reached to read one of them: game theory and their applications in biological models...

When she concluded reading, she gave him the headphones and then she stretched out her hand: 

-My name is Kathleen, Kat... I study nanotechnology applied to biological models, and try to explain evolutionary patterns... I see that you understand math... my advisor says that my proposal has no future... perhaps you can help me?... huh?, what do I say?, I’m sure you are very busy...

When she dropped his hand, he took it back and he said almost in a whisper:

-My name is Daniel... Dan... and yes!, in fact I want to design a model of application with game theory to economic and evolutionary models, although this  has been done before... I want to find a specific area that allows me to innovate a bit.

She moved a chair beside her and then more magazines fell, but this time he rose and offered her his chair,  he began cleaned the table a little and decided to talk about what he knew and loved so much with her... 

- Please,  sit down Kat, I think  I can explain you from mathematics how species have evolvied, however, remember that maths are only models that represent the reality.

-The science is that, isn't it? Kat, said smiling.

-Yes, yes... it is true... just explain the reality...

- What I know about game theory, is that studies the sharing of profits and therefore decision making among the players, if an entity can understand that it can win or lose during an exchange, it makes decisions based on its experience. I believe the same applies to biological models, as if we believe that species should take into account information from the environment and predators to survive, then they must apply decision-making on environmental responses.

Daniel further opened the eyes and arched eyebrows...

 -Exactly!, that's the idea... Game theory is much related to economic theory, where a zero-sum game is a mathematical representation of a situation in which a participant gains or loses profits and utility is exactly balanced by the gain or loss of the participant, as opposed to a non-zero sum game where both profits and losses are added to a situation in which players interact. To sum game zero resolves le with the Minimax theorem that is closely related to the theory of the Nash equilibrium.

-     I couldn’t understand that, could you explain it to me?, but used simple words, please.

-    It is a conceptual solution to the non-cooperative games that include two or more players, in which it is assumed that it is possible to know the balance of strategies of each player  since has something to gain by changing if strategy during the game.

-    It sounds complicated...

-    It is not, in fact it can be ridiculously simple: maybe if we try to understand biological systems... look, we will assume that you have a bee and a butterfly trying to obtain pollen from two flowers... do you work with biological systems at this level?, or perhaps... microbes, bacteria... 

-    Sounds like a cute example with bees and butterflies, please explain this and then maybe we can apply to spores...

-    Daniel looked at her very happy... well... I’ll explain it with butterflies... There are two flowers and one butterfly and one bee are trying to obtain the maximum pollen, if Butterfly makes it first movement, it can take all the pollen and thus the bee lost, and if the bee makes a first movement, butterfly lost, but both want to profit, so it is important to take a decision on the action and you can see it in simple way with a picture like this:

	Bee takes pollen from a flower	Bee tries to take two flower
The butterfly takes pollen from a flower	Maximum common benefit	Bee gains and butterfly loses
Butterfly tries to take the pollen from two flowers	Butterfly gains and bee loses	Maximum common prejudice

- Crap!, it sounds so easy that even I can understand that, but surely there are a lot of numbers and things involved as I can see in your magazines.

-    I don’t understand it if I see it that way, but let me give you another example to see if I understood... Kat and Dan can learn from each other, and they both make decisions ... then if I do a matrix would be this:

	Kat speaks with Dan	Kat does not speak with Dan
Dan speaks with Kat	Maximum common benefit	Kat goes home
Dan does not speak with Kat	Dan finishes his readings	Maximum common prejudice

-    Yes, more or less like that, but both must have the same level of profit, in this case the gain is different, you would have gone home and I would have read 2 or 3 magazines. 

-I want to study chaotic fluctuations in phenotypic frequency, specifically in those cases where it is necessary the adequacy of a heterozygote based on the measure of a recessive parent the next generation, which I think, is the measure of the adequacy of the homozygotes and heterozygotes would therefore have a destructive effect on the homozygotes and themselves, although to a lesser extent about themselves. This because if a behavior is associated with a low to reply to the environment and high fertility fitness gets a chaotic fluctuation.

Daniel's eyes were opened so much that his glasses were on ready to falling, when he could finally talk, began to mambling few words and then coughed a little to clarify his own ideas...

-Kat... I think that no doubt we both can gain from this talk, there are at least two possible explanations, even it would be possible to make predictions... I can apply my mathematical theories to everything you said,  however, the truth is  I did not understand a half of what you just said, but we can sit down and explain every thing with pears and apples, but I believe that we both would receive profits from all this and it is possible to balance our profits no doubt...

-  I want to know if it is possible to find patterns of adaptation and survival in living populations.

-    Have you ever read about the life of Conway game?

-     Yes, I do!, actually… that what gave me this idea, but I don't understand enough about math,  mmmm but I think that what you just explained and Conway model can help me a lot, now all are algorithms to create stable patterns, as the analysis of the databases, everything is math is our everyday lives, everything is about looking for patterns!.

-   Yes it is, yes... of course... I think you just increase our chances of achieving our dreams...Yes... can I invite a coffee?, I only need to ... collect all these magazines... and... I think it’s not snowing anymore... I can take you in my car, or do you have a car?

-    Let me help you with this… No, I do not have a car, only my bike, but I can leave it on campus, and I come tomorrow on the bus. Climatic variables, increases the probability of accidents as drivers change their behavior patterns...

-    Yes, it is true... well... we can put your bike in my car... I have a porta-bike that I use on weekends... well... only when there is no snow, because as you say... There are changes of patterns in the drivers... Yes... ohm... then if you put your bike in my car, can I take you home?... after coffee, of course...

-    Let me think... If I say yes, then we both get gains, then I should not take the bus tomorrow, and you know where to find me... but in such a case, there will be probably other decisions that each player goes, isn't it?

-    Yes, Yes... the pattern can be exponential... sure!

-    Yes, I figured that... can it become a chaotic fluctuation... the pattern could meet different conditions and therefore... change... evolve...

-    Yes, yes... it's true... yes...

-   Cool!, it seems that mathematics are not so complex!

-    No, no... they are not... they can explain many things and as you say... we apply them more and more everyday... I worked applying all this to economic models and I an algorithm to Google, so it seems that it can read your mind when you type something...

-    Amazing!... have you explained biological models?

-    No, but... apparently... I'm about to do it... If you allow it to me!.

Brain and educational virtual environments

                                       Por Alma Dzib Goodin

The interaction between brain and cultural tools started practically since  Homo Sapiens apparecenced on the planet, because this is a main characteristic of his evolution. 

 

Unlike the Neanderthals, and many other species of hominids, Homo Sapiens developed tools, based on cognitive skills of design and its development, gave to the specie a particular capacity to use them to respond to the needs in the cultural environment that allow a surviving opportunity and developing of new skills.

These tools were designed specifically to solve problems, which of course had impact on the brain, so there is a symbiotic relationship between a designer brain and a learner brain and the use of tools, in this sense, It can be tools such as fire, that exacerbated the sensory systems, while the use of sticks and stones benefited the use of thumb, while others developed movement as walking and the observation of the environment, all that eventually open the door to reading, writing and mathematics that gave rise to science.

Whole brain is a wonder of responsiveness to the environment, generating neural connections able to go beyond, literally, including the Moon and Mars, to benefit not only the human specie, but others, under the knowledge that those who do not adapt and respond to the environment, disappear from the face of the Earth, just as it did with its predecessors the Neanderthals and many other creatures.

It's so thousands of years after a first Homo Sapiens has used a stone to ward off a predator, the digital age opens steps, fast if we think that 30 years ago there was notablets, and breaks in the cultural, economic and educational environment, but in contrast to those who claim that this damages the brain, some others, from an evolutionary point of view, look it just like another step in human evolution.

Nature has provided to all species of mechanisms of self preservation, able to respond to the enviroment needs, human beings in particular thanks to the evolution and management of tools designs, which need a reflective thought open the door to a process called brain plasticity that permits the brain adjust to each new need even auto repair  in order to continue providing the ability to solve problems.

Years later computers burst as tool simulating a brain, giving answers and simplifying tasks, through artificial neural networks able to simulate many cognitive tasks, with ever greater precision and elegance.

Simulating the brain activities, new technology has understood that  brain changes, with each learning creates new neural networks, removed those that are not used, sharing, recycling, although unlike their natural model, gadgets are renewed at a very large cost, while never leaving  the goal of perfection as the natural model, that has never achieved because the brain never stops passing, because it can not!, when it is thought that a task is already well learned, comes a change in the environment, or even human creativity opens the door and says: and if do I add this?, and if do I do it this way?.

The brain is constantly using information, so it has specialized its data storage system. While memory is finite, its hability to recover it is prodigious, specially when the stimulus provided as a question or key is correct.

However the maximum capacity of the brain maybe are language, thought and creativity, and  computers can not yet achieve that perfection, as example I can find Siri, the personal Secretary of Apple which is incapable of understanding the inflections of the language, the double meaning or slight changes in modulation.

So at this sense, analyzing the role of technology as a learning tool, as education has been trying during the last decade, wishing an interface between the brain of the natural and the artificial, able to share files with one click, it is not possible since we can not forget a fundamental principle: the natural brain controls and provides information to the artificial brain. 

No matter how incredible is a word processor, still requires the ideas of a writer to convert a blank screen in a worthy article of a Nobel Prize winner, and this will require also the social acceptance of ideas, despite the marketing claim that this or that gadget is an intelligent devices, the user will have the last word against its use and productivity capabilities and troubleshooting.

Brain 2.10 million vs Web 3.0

My brain is renewed, learns, adapts, auto repairs, auto analyses, is capable of determining errors in its performance and start again, searching new paths of answers and even questioning. This is not a simulation of artificial systems, they are perfected processes on the basis of other natural prototypes that have been able to survive despite everything, and we took the best of every one, for example, from reptilian prototype, we obtained emotions, of the mammalian model, we got a selective memory, and attention. The human brain is the evolutionary sum of other prototypes and every day we learn more of its simple capacity to adapt. 

Before a paper sheet, there were human brains communicating. Before the video in HD, there were people telling stories. Before radio stations, there were brains sharing news and art. Before satellites, there were brains sending messages to the rest of the world. Before smart phones, there were intelligent brains who thought them, believed them possible, designing them, tried them, arranged their problems and returned to start, perfecting every detail, adding applications that make our life easier.

A Smartphone can say how to get to a place, but it needs to know the destination.

So we can say technology is an effort to simulate the brain, understanding the infinite plasticity that a natural brain has, therefore this is discarded, becomes obsolete, as well as those areas that are not used, as Darwin observed that any part of our body will atrophy and studies show that the brain also. Saturated information in a chaotic day, or week of exams, after days without sleep, similar to artificial systems after saturating the RAM memory.

The other process that has been copied as an application is the ability to process information, it is true, computers make it faster, but still can not interpret it without the support of their natural example. Although Google has an algorithm to complete words, you need sufficient information to decide what you want or need to search. This same ability to complete  information that the cognitive process has been refined over thousands of years.

Computers and education

The first great tool exploited by education in order to share specific information for the purpose of teaching - learning was the book. This replaced the word, and its most ingenious application was not improved until Jan Amos Comenicus in 17th century put images in textbooks, to help to children learning better.

Three centuries later, the next revolution, changed the books by screens, but is only a another implementation tool at the service of learning to which the brain will adapt, it’s not adding anything new, except some memory and over stimulation, which it had been aside since the man could rest from their predators, creating what is known as attentional problems which actually is the awakening of the consciousness after having spent centuries with face looking to the front and the mystical silence inherited by ecclesiastical education.

There is no mystery in these new tools, brain adapts to them, because they are part of the environment and they are used to solve problems. More adapted people are those who use them in everyday life, the rest of us mortals only employs an average of 12 apps and we know only about 20% of its total functions.

Generation X was born with this technological revolution, they did not have to learn the language of Basic to open and close documents or applications, they did not know the monochrome computer or 5 1/2 floppy disks. They did not fight with point printers. In return, they were born with Windows, not the first version that revolutionized, presenting the information with an easy-to-read structure and the wonderful quality of having icons, icons?, like the images in the books of Jan Amos Comenicus?.

After few prototypes, we add sound to our readings, we added movement and the ability to customize environments, being the last great step removal of buttons and keys, creating interactive displays, on tactil screen.

Millions of bits of information currently available, it is said that practically you can learn everything you want in a digital system, seriously?, well, first there will be to teach to select relevant information to resolve a question or problem from a good design process that leads to a goal. 

Where was the human brain in the middle of this?, it didn’t go anywhere, continues fulfilling its role that nature gave it, which gave all species the possibility to create specific responses to the environment, continues its process of evolution, similar  as smart devices, since its legacy is literally renew or die. 

When it says that technological age has produced changes in the brain, are right, but refuses the constant motivation to respond to the environment. Even species that depend on genes closed such as bees and birds, have shown that its survival depends on its neurowear, which is the set of neural connections. 

The human brain has managed to overcome what no other species has been able to do, not only has adapted to the environment, has adapted the environment, change it, provided shelter, uses imagination, it’s creative, all this thanks to the use of same tools created by itself, seeking always to make them better, creating new, always imagining other forms, textures and functions. Technology should be seen as an extension of the creative mind, which has no reason to curb the evolutionary legacy. The brain will continue its process of adaptation with technology  no matter what kind of.

Proof of this is that there are groups who have never seen a computer, and yet are capable of creating spaces of identity. The culture is in this sense, their  parachute to support creation of answers, as anthropological and ethological studies show it.

Are there benefits in the use of technology?, this is a constant question, and I would say that the benefit is that now our responses will employ different tools. There are currently three ways to close a door: the movement of an arm, with a button or touching a screen, but should not forget that these three methods are achieving the same goal and all depend on the response of a brain.

A problem seen in educational strategies is the forgetfulness of this capacity, with the tendency to create specific response patterns: thus made things, according to a specific algorithm, but this is going against thousands of years of evolution, brain became creative, became from an Néandertal brain to a Sapiens, but we should not forget that many other species have accompanied the human brain. There are reptiles, viruses and bacteria. How can we think that a tool can affect something that remains and will remain as a prototype?. 

Computers and learning

If it is true that affect the evolutionary process, do computers benefit learning?. If you are based on the idea that learning is part of the ability to respond to the environment, and the environment is surrounded by computers, no doubt the interaction is beneficial, the youngest brains are more easily than those who have habits that make rigid response process adopted. 

If a baby make a mistake, it is said that he or she is learning; If an adult makes a mistake, it is said that it is a failure, I think that if learning is seen from this window, education will continue slowing our creativity and our need to innovate. 

Sometimes I think that when adults can give themselves the opportunity to accept that we are not more than a prototype and that the only force capable of changing our environment is death, begin to create much more adaptive responses, being able to increase the life expectancy of the people. It is true that computers have helped us, but there is no achievement that has not started with an idea, net and absolutely human idea.

Learning at the current time, depends on the recognition of the technological environment provides that human remains as the centre of the process and that humans are able to develop this ability to solve problems, solutions, recognize the chain of events that come with clear, specific goals and above all, successful ways to react.

It is clear that learning never depended only of a tool, i.e., we do not learn only from books or teachers. Humans are the only species that creates artificial learning environments, makes tests infertile and maintains such environments for more than 20 years. For the rest of the species on Earth, behavior modeling is brief and the further consideration is to survive.

Believe that a technological tool will teach, means changing the environment of schools by another, perhaps  funnier, with greater capacity for information, but equally sterile if the apprentice is not able to create adaptive responses. While it is possible to order food online, still cannot get the nutrients in this way, we still require food to physically meet the digestion process.

While there is cybersex, is not able yet to fertilize an egg and create a new life. Humans are tied to the natural demands, for some years longer at least until virtual environments to become real environments for the brain. But if Siri is not yet able to recognize words, I think that the road is still long and windy.

In this sense, education must continue focusing efforts on the student, which has not since part of the process since  the ancient Greece, Because after its break between the Catholic Church and the Anglican education focused on the curriculum, and now more that ever students are bombarded by too much information, which causes them problems not only to understand it, but applicate it.

This is why, regardless of the technology, some believe that we must bet on the development of meta cognitive skills, which enable flexible, same thinking applies in everyday life, science and art, since they create patterns of needs analysis for design patterns of responses, choice and check of possibilities concerning specific goals using any tools available, in order to adapt to the environment, including, of course, technology.

If we think for a moment, despite the wonders that it is possible to achieve thanks to the support of computers, they wouldn't exist without a human mind which thought them, designed them and made them work, and sometimes, put them  all together. We can  marvel  the ability of Apple products, but everything is due to the genius of Steve Jobs and his team with an specific ability to imagine. That is a distinctly human quality, that you don't get when the information flows in avalanche and know that there is only one right answer, on a review of all or nothing.

Hopefully one day education understand the brain mechanisms and apply them, because when that happens, it will begin to teach brains capable of learning. 

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