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Saturday, March 26, 2011

Artificial Intelligence and Humanity I

This post was based and inspired on the writings of Brian Christian


Turing test

The objective of the Turing test, created by Alan Turing in the year 1950, consists in evaluating during small conversations, if computers could imitate humans. The test incited the creation of Chatterbots such as ELIZA, launched on 1966. Later on the Loebner prize was created, offering a monetary award for the first chatterbot that could pass the test, this competition still takes place once a year.

The classic Turing test consists in one room with judges that make questions for 5 minutes to computers or to humans that are in a second room. After conversations take place judges reveal which chats they think they had with chatterbots and which with humans. The chatterbot that is considered the best is the one that fools the higher percentage of judges. Turing believed that the test would have been passed by the year 2000; far from his prediction a new record that was able to deceive only 30% of the judges was recently achieved.

Controversy

The principal question Turing wanted to solve with this test end up generating lots of controversy because it derivated mainly in three others "Can machines think?", "Are machines intelligent?", "Do machines have a conscience?" Lots of arguments where stated in favor and against them (including the ones that follow), but no unanimous conclusion was reached:

  • How we could tell if a machine was intelligent. After all, mankind has tried to define intelligence for ages and had made little progress except to decide that whatever it is, we've got it.
  • How do you know if the machine actually understands what it is doing, seeing, or saying? A particularly strange side effect of being a conscious being is that you can never truly know that someone other than you is conscious.
  • Not until a machine can write a sonnet or compose a concerto because of thoughts and emotions felt, and not by the chance fall of symbols, could we agree that machine equals brain-that is not only to write it but know that it had written. Neither until they can feel an emotion (Jefferson).
  • Computers can’t originate anything we explicitly tell them to do (Lovelace).
My preferred theory concludes that machines can't think; I argue that thinking cannot be separated from feelings (Damasio) and that it also includes an intuitive component.
Questions and thoughts
  • Do things have an essence, and if so is it possible to describe it? (Like Plato did in the Allegory of the Cave)?
  • What makes something to be something? We guide ourselves mostly by external appearances and actions. But indeed I think the evaluation would be more accurate if we compare that something internal structure and organization.
  • Can we extend the meaning of consciousness? By adding an exception to inanimate objects that does not include the act of thinking, emotions, intuition or any other aspect of the brain, in this case being conscious would mean only to have knowledge of their own existence.
  • Our brains consider that a certain entity is or is not something often by doing lots of assumptions. Instead we could assign a degree of credibility of what we think the entity is.

30 comments:

Janet K said...

The Turing test is about the same as saying, "If it walks like a duck and if it quacks like a duck, then it probably is a duck." If you cannot tell a machine from a human in how they answer questions then there is something, some ability, that they share. We can call that something whatever we want. If we refuse to call it 'intelligence' then that is probably because we have other reasons for not wanting to have a common vocabulary for machines and humans. Of course, a machine will never be exactly the same as a human but that doesn't mean that they can never share the word 'intelligence'. There are probably many ways to solve problems with different strengths and weaknesses. Machines do not have to have intelligence that works like ours to be intelligent.

Charles Gramlich said...

I agree that thinking has an intuitive element. I'm not sure there is 'always' an emotional element though. Have to give it some "thought." :)

Paul Andrew Russell said...

I think it all depends on how you define 'intelligence'. If it is just a matter of solving mathematical equations, remembering dates in history or having massive amounts of data to call upon, then you could say computers possess 'intelligence' to some degree.

If you are talking about true intelligence, the ability to solve problems that are neither mathematical nor academic, let's say for instance the ability to weigh up and find a way out of a potentially dangerous situation, then I do't believe computers will ever have that degree of intelligence. We humans use so much more than intellect to survive and prosper. We have an emotional component that machines will never possess.

We can think 'outside the box' in ways computers can not conceive of. A computer program will never be able to replicate that ability, simply because it is based on an emotional intuition that can not be programmed in to a computer.

Computers are machines. They may well be able to 'fool' us in answering questions. They may well be able to process and use information faster than we could ever dream of. In the end though, they are machines, just machines.

We have life, that spark that is inexplicable and impossible to duplicate. We have the survival instinct and the ability to reproduce. We don't 'build' other people, we procreate. We are each unique. That can't be said of a computer.

Life isn't a few lines of code or indeed a billion lines of code.

Pull the plug on a computer and it's useless. How intelligent is that? Can't plug itself back in can it?

Just a few thoughts from a rambling mind, Mariana. lol

Mariana Soffer said...

Janet K:
I liked the example of the duck, it is really original, dough it is not exactly what he says, it is pretty similar. He states: if machines can talk/think like humans then they can think (only living creatures where suppose to be able to do it, including humans).

Turing wants to prove machines are intelligent but mainly that they can think.

I agree that humans like to be unique and have unique abilities.

Regarding your final sentence I think that for example you can start with the fact that people's intelligence work in different ways, they work differently, nevertheless there is no doubt that they are all intelligent.
The problem with defining machines as intelligent involves:
1. That there is not a clear definition of intelligence.
2. The fact of knowing humans are intelligent because intelligence is defined as a skill we have.
3. That computers are not by definition intelligent.

Thanks a lot for your valuable comment Janet.

Mariana Soffer said...

Paul Andrew Russell:
I agree the problem is in the lack of clear definition, which is probably because we do not know how the brain works, neither how to measure it.

I completely agree with your third paragraph, indeed if you do not mind, I might borrow it because it is well written and it will help me express what I want.

When You say that computers are just machines and that we have a life that involves many things, I would add that we have needs and desires (which is what we driven by), but computer's don't.

I do not understand what you mean about pulling the plug, if we die it is also the end, besides once we are turned off there is no way to turn us on again. Feel free to explain this if you want.

I liked your ramblings, they are really "Intelligent" and your visit is a pleasure.

Janet K said...

Actually I disagree with the Turing test in general. It seems to imply that animals (who do not talk) do not have intelligence. But most people will accept that dogs, dolphins, elephants, chimps, parrots, octopuses etc. are at least somewhat intelligent yet they would not pass a Turing test. And computers that don't pass the test can do many things faster and more accurately then humans (math for example). Each animal and machine has different amounts and different types of intelligence. Anything that can solve problems has some amount of some kind of intelligence. Its a personal preference - I prefer to give intelligence a wide meaning. The Turing test only measures how closely a machine can mimic a human. I think I could imagine a machine with a big enough memory that could pass the test by having a stored answer for more or less everything, but would have hardly any of what we would recognize as intelligence if we knew how it actually worked. So the test is both too hard and too easy. It will fail things we feel are intelligent and pass things we feel are not intelligent - poor test.

Mariana Soffer said...

JanetK:
Thanks for continuing sharing your thoughts. What you begin with reminds me on something I reacently read that said that in the past humans used to compare themselves to animals but now they do compare themselves with machines (I think it is interesting to reflect about this).
I think it is very important not to forget that there are very kinds of intelligence.
And I completelly agree with what you say about machines storing every possible answer, that is not inteligence at all, it is just memorizing, storing knowledge.
It reminds me about the famous "achievement" of AI, when it beat the chess championship Kasparov. I, myself did program chess algorithms, and I do not think that when deep blue won it meat that the machine was a more intelligent chess player than Kasparov, it just meant that it could do the following, which is how games generally are played by computers:
We need an algorithm to help us decide what move to make. The idea is this:
1. How do I know what my best move is? Simple! The best move is
the one that, after you make the best countermove, leaves me in the best shape.
2. Well, but how do I know what your best countermove is? Simple!
It’s the one that, after my best reply, leaves you in the best shape.
(And how do we know what my best reply is? Simple! See step one!)
You’re starting to get the sense that this is a rather circular definition.
Or not circular, exactly, but what computer scientists call recursive. A function that calls itself.
This creates a tree of all the posibilities derived for all the moves (at least as many as the machine has space for), which lets a machine look many moves ahead than the human being.
There is no intelligence applied by the computer while playing the game, it just follows a simple and repetitive strategy,that a human being programmed it to perform.
For more details about this check:
http://www.ocf.berkeley.edu/~yosenl/extras/alphabeta/alphabeta.html
or
http://en.wikipedia.org/wiki/Game_tree

Hope you found this interesting Janet, feel free to ask me if there is something you do not understand.

Take Care

Janet K said...

I was once a programmer so have no problem with recursive calls and trees. And I suppose that Deep Blue has added rules-of-thumb logic on how to compare positions, and libraries of standard openings and end plays. I think it probably had ways to judge when to give up on a tree branch. etc. Is this very different to how most people play (not necessarily masters)? Personally, my trees may be shallow and sparse and I only know a few openings but there is no magic - I do approximately what a good computer program would do but I am not as good or as fast at it. I win sometimes.
The reason that people think that chess is hard and takes intelligence but that walking is easy and doesn't, is that chess is done largely consciously (using our tiny working memory) and walking is done largely unconsciously (not limited by working memory). So we have a computer that can beat a chess master but can't move the pieces by itself.
That which person has no idea how to do, often appears very easy to them when they see others doing it.

J said...

Mariana, it has been shown that there us a strong relation between people who are sytematic thinkers, and their finger ratios.
I know this is off topic, but you have just given another example of how you are very into logic and systems thinking.
Would I be correct in guessing that your ring finger is longer than your index finger?

Mariana Soffer said...

Janet K:
Very interesting, I did not know you use to be a programmer, that is why I explained the chess algorithm in a very simplified way, I know your program also has opening, that the tree can be ininite (repeat itself), so you should take care with the algorithm in those cases, and also that you can not cover all the possible trees, therefore what you should do if find a way to measure/evaluate the board situation for the player in order to choose what is more convinient for it.

It was enlightening your paragraph about why people think some tasks are hard and some are easy. It made me think that when you are conscious of the effort you are making things feel more difficult. But when you are unconscious you are not even able to realize what efforts the tasks involves and even less how hard are those tasks.

Maybe when you start doing something unconsciously is when it stop being difficult for your self because it is already automatied/learned and stored in your non rational parts of your brain, like for example driving, when you stop thinking about the pedals and the lights and do it automatically.

I liked your last paragraph too, it left me thinking actually.

Thanks once again for sharing your reflections.

Mariana Soffer said...

J:
Sorry but I am a bit skeptical about that theory. Do you have any serious articles/papers where I can read about it?
And sorry to disappoint but the rule does not apply to me.

Thanks anyway for your collaboration J

J said...

Oh well, maybe it's not such a solid theory.
I got book by one of the biggest proponents of the theory and there is a lot of interesting research, but there is also academic criticism of the idea out there on the web too.
As is usual, without an intimate grasp of academic research methods it can be hard to tell what is the best theory, or how far it is true.
OK, I will give you a hand, and help you put your finger on better information. The theory may not fit the reality like a glove but if you were to knuckle down, thumb through some papers and grasp the research you may find you have the answers in the palm of your hand. On the other hand you could give it all the finger and ... I may be losing my grip.

The main man for this idea is prof. John Manning, his blog is here, but it's not very well structured.

https://fingerlengthdigitratio.wordpress.com/

OK, will have another read of your blog entry here and see if I have anything real to add to the debate, seeing as you go to the trouble to make a debate.

J said...

OK, now I can add to the debate.
I always find it interesting the assumption of intelligence being property of conscious living people seperate from the dead matter of the universe.
Also the assumption that a human is a free, seperate entity acting upon a dead, passive universe of matter.
If a human is an integral part of the universe of matter then it seems like the intelligence of that human is also an integral part of the universe of matter and a product of it.
It's a questionable assumption, to me, that humans are the authors of their own intelligence rather than the universe itself being the author of human intelligence.
In an analogy, it is like the speakers on a cd player thinking they are the originators of the sound, and forgetting they are part of a whole system.
If we say that human intelligence is at all times a response to environmental queues, then surely the environment is the original source of our intelligent thought, not the brain. The tail does not wag the dog.
If this is so, then all the talk of artificial intelligence involves a mistaken assumption of a lack of intelligence in matter, but I think many thinkers on this subject realise this. What you can say is that human intelligence is a different type or level of intelligence, for sure, I would go along with that. Human intelligence is symbolic, for one thing, when it is conscious.
Then artificial intelligence is also a different type of intelligence once more, but I think artificial is perhaps a misnomer, as it is still an aspect of nature's intelligence.
I don't think the distinction between artificial and natural is well explained or understood by people, or even necessarily true.

Your mention of Plato's cave is interesting, and raising the question of whether we can really know the essence of something, which is a theme still being explored by science which is constantly telling us of ways in which we are not seeing the real world, that there is always something un-knowable which we can deduce but not experience or see - like dark matter, higher dimensions etc etc.

As far as science goes, it tells us that we cannot ever see things as they are because every act of perception takes time. It tells us that we are constantly lagging behind reality (I may be missing out on some science education, of course).

Which begs the question, what is the most immediate experience, what is the smallest time lag between world and conscious perception? Is there anything we can know without a time delay.

But that's me wandering around, you were on the point of Turing and his tests but I don't know more than the basic idea.
I have had a go with Ray Kurzweil's Ramona - a Turing test program, but it is offline at the moment for upgrades I think.

J said...

More, Mariana....
I saw Ray Kurzweil's Transcendent Man film lately, and in it there is a scene in which he is watching the ocean and thinking about the computation that the ocean is doing.
An intriguing idea, and one I have been wondering about for a while.

Is ordinary matter already doing computation?

And here is an interviewer actually asking the question I would want to ask Kurzweil. It's also relevent to your blog topic.

http://www.youtube.com/watch?v=EkGUEaZtIK4

I guess that these topics are already very well discussed by enthusiasts but I am not in those groups.

Mariana Soffer said...

j:thank you very much for the explanation and for passing me the reference, but let me tell you that I did not like the website very much, it did not look serious, dough the content might be. I also feel honored rhat you like to debate with me. I am almost done with my next post, so you willl soon have a chance to discuss it.
Regarding the finger theory, my first thought was that it was a myth. But I am skepticall by default. Nevertheless I do belive that humans have patterns that repeat along the same kind of individuals, and that the phisical traits can be produced by a cerain combination of genes. Nevertheless In order to give you a serious reply about what I think I will need to read the papers and check if I consider their analysis serious enough, the information they work with valid and large enough to be able to agree or disagree with the conclusions reached in them.

Mariana Soffer said...

J:
Glad you are back.
I do rhink that intelligence is also a property that other living beings have, such as monkeys.
Regardig what you said about humans being separated entities from non living entities, I thought that it would be interesting to provide different meanings to consciousness and self-awarness in this too kind of existing things.For example one of the things I thought Is why can't rocks be self-aware that they are rocks, they do not need to have intelligence for that.It is true that intelligence is acquired among other things from the universe of matter.

You think it is questionable the belief that humans are in part authors of their own intelligence.I do think this relates tp the famous debate about nature versus nurture, check it out.

What I think about the analogy and its previous thought is that a large number of factors and their interactions define human intelligence. Like innate qualities, life experiences, training the mind in different skills (either when you are an adult but also when you where a kid that was influenced by their parents (dough you might not remember this) in developing certain skills and also ignoring others.

Since I have serious doubts about the definition of intelligence I can`t provide a serious philosophical answer Although my intuition tells me that inanimate objects such as rocks do not think.

I do not agree that human intelligence is always symbolic when we are conscious.I do believe that intelligence can also involve perception and intuition which are not necessarily translated to symbols nevertheless they can affect our
conscious process of thought. providing an emotional component
to it.

I do believe that artificial refers to entities or processes that where created or altered by human being, while natural
refers to entities or proccesses that naturally evolved.

I believe we can never completely know something,we can understand it from different perspectives or dimensions but not by all of them at the same time.

Regarding what you say that we can never see things while their are happening, but later, it is a true principle of physics.It is pretty interesting to reflect about it. one of my reflections includes considering if the present really exists.

Let me tell you that I am not a big fan of Kurzwail, I do not agree with his thoughts about the future of artificial intelligence, the singularity and the global brain.I recommend you to start reading other authors that speak about AI although they are rather old I would start with Marving Minsky and Douglas Hofstadter.

Very interesting reflection J, you made me thought a lot.

Mariana Soffer said...

J
I am glad that you got to know this guy, it has interesting thoughts and ideas but I am not
a big fan of "the singularity". His idea about how IN the future Artificial intelligence will modify the world and also the way human beings live and behave.

Thanks for sending the link, I watched it twice, I think it is a great introduction to how he things for
the people that are new to him and to AI. I also ended up thinking about the behaviour of the ocean iin mathematical terms.
That idea reminded me to fractals (iI do not know if you have an idea about it, if not search it in wikipedia^) their mathematical formulas and the many ways that they can be visualized. There is a very simple formula for creating a fractal that visuallly is equal to a certain tree leaf. It seems strange at least to me how can a very simple math calculation can draw almost perfectly a living organism. In this case a leaf.

I woudnt say that matter is doing computation I will interpret this fact as one of the examples of patterns that repeat in different areas and disciplines.

I recomend you to read about the subjects I mentioned that I did not like from him. At least check:
http://en.wikipedia.org/wiki/The_Singularity_Is_Near

http://en.wikipedia.org/wiki/Transhumanism

and

http://en.wikipedia.org/wiki/Technological_singularity

You can also read his blog and some articles he published.

If you want let me know what is your personal opinion about these theories.

Take Care
M

J said...

Cool to hear from you Mariana, I will have a look at those things and come back. Espero que estés bien.

J said...

Mariana says...

"Regarding the finger theory, my first thought was that it was a myth. But I am skepticall by default."

My impression is that the relationship of testosterone to finger length is robust, physiology and embryology are intensely studied sciences.

The relationship with personality and the brain is probably not so easy to establish.

My own interest is that I have a very low finger ratio.

"Regarding what you said about humans being separated entities from non living entities, I thought that it would be interesting to provide different meanings to consciousness and self-awarness in this too kind of existing things.For example one of the things I thought Is why can't rocks be self-aware that they are rocks, they do not need to have intelligence for that."

Simon and Garfunkel sang a great song about what it's like to be a rock. *joke*.

I really don't know about the self awareness of a rock. To consider the possibility would mean a trip into religious mysticism.

"It is true that intelligence is acquired among other things from the universe of matter."

Yes, some say it's only about matter, some disagree. It's a very strange thing, it's also strange that we, as matter, can be conscious or unconscious - yet our matter doesn't change from one to the other.
Very little changes in our matter between waking and sleeping (although there are some changes).
So consciousness seems also to involve a process by which matter is organised, what it is doing, unless there is a mysterious factor X that has not been discovered by science.

Perhaps Kurzweil is right, that matter is simply unconscious because it is waiting to be woken up.

"You think it is questionable the belief that humans are in part authors of their own intelligence.I do think this relates tp the famous debate about nature versus nurture, check it out."

Yes it does.

"Since I have serious doubts about the definition of intelligence I can`t provide a serious philosophical answer Although my intuition tells me that inanimate objects such as rocks do not think."

Me too.

" I do not agree that human intelligence is always symbolic when we are conscious.I do believe that intelligence can also involve perception and intuition which are not necessarily translated to symbols nevertheless they can affect our
conscious process of thought. providing an emotional component
to it."

Yes.

"I do believe that artificial refers to entities or processes that where created or altered by human being, while natural refers to entities or proccesses that naturally evolved."

In a very ordinary way artificial simply means human made, just as some things are made by animals.
There is an extra philosophical twist that I think is often involved when people use the word artificial, they seperate the world of humans from the world of nature as if they are two different things.

So some will say, "look at what humanity is doing to the world", and others will say that the world's artificial problems are just natural, as we are made by nature.

"I believe we
can never completely know something,we can understand it from different perspectives or dimensions but not by all of them at the same time."

Yes.

"Regarding what you say that we can never see things while their are happening, but later, it is a true principle of physics.It is pretty interesting to reflect about it. one of my reflections includes considering if the present really exists."

That's what I am wondering.
v=d/t puts us in the past. Strange that so few seem to think how profound this is, yet it is so very simple!

This could be a difficult and isolating thing to think of emotionally, maybe that's why people don't want to. We are all be at the ass end of reality!

J said...

"Let me tell you that I am not a big fan of Kurzwail, I do not agree with his thoughts about the future of artificial intelligence, the singularity and the global brain.I recommend you to start reading other authors that speak about AI although they are rather old I would start with Marving Minsky and Douglas Hofstadter."

I agree that I could read others thoughts and not just Kurzweil - he is only one person. I've heard of Minsky, he's quite famous, but never really read anything. I have tried to read Hofstadter but found him to be difficult, I would really have to concentrate and work at it.

" That idea reminded me to fractals (iI do not know if you have an idea about it, if not search it in wikipedia^) their mathematical formulas and the many ways that they can be visualized. There is a very simple formula for creating a fractal that visuallly is equal to a certain tree leaf. It seems strange at least to me how can a very simple math calculation can draw almost perfectly a living organism. In this case a leaf."

I know the very basics of fractals, the re-iteration of simlpe algorithms or equations.

"I wouldn't say that matter is doing computation I will interpret this fact as one of the examples of patterns that repeat in different areas and disciplines."

I don't know what you mean.

"I recomend you to read about the subjects I mentioned that I did not like from him. At least check: [lots of Kurzweil]

You can also read his blog and some articles he published."

I do, I get the weekly newsletter.
I've watched (perhaps too many) Kurzweil films, read his books.

"If you want let me know what is your personal opinion about these theories."

His big idea about exponential growth is very attractive, and quite easy to understand. It is not a completely new idea but he has a lot to say on it.
However, it is such an easy idea that I have not looked very hard at it, or at the criticisms.
One thing which he has in common with a lot of futurists is his answer to the potential problems of technology. Futurists will say how it may be a problem if 'terrorists' get hold of biotechnology for example.
The flaw in this view is that it has always been governments and corporations doing the damage with these things, not terrorists.
I think top scientists are at the beck and call of top politicians, they know what to say to keep their positions and avoid trouble. This I find a bit creepy and cowardly.


Take Care
M

And you
J

uncle tree said...

Hello, Mariana!

I'm not sure if this will be of help to you or any of your readers, but I feel compelled to quote Carl Jung. Man has to decide right from wrong, and good from evil. Even if one man could hold all the knowledge and history known to man up to this day, he would still need to make a decision based on personal prejudices and preferences which are part and parcel of his inborn temperament; his particular and unique individual nature, which ultimately limits his choices. Thus, he can only speak for himself, and cannot generalize or expound universal moral truths that would amount to a 'good' or a 'better' for any other human being. If a machine had to fight within itself as we do, it would certainly blow a circuit, and end up in a hospital, where it would be diagnosed as having gone haywire.

"The decisive question for man is: Is he related to something infinite or not? That is the telling question of his life. Only if we know that the thing which truly matters is the infinite can we avoid fixing our interests upon futilities, and upon all kinds of goals which are not of real importance. If we understand and feel that here in this life we already have a link with the infinite, desires and attitudes change. In the final analysis, we count for something only because of the essential we embody, and if we do not embody that, life is wasted."

Excerpt from the chapter: On Life After Death.
Carl J. Jung's "Memories, Dreams, Reflections" 1963

Take care, sweet niece!
Luvz & Hugz to you from your 'good' old Uncle Tree ~I-->

Mariana Soffer said...

Uncle Tree:
It is so nice to see you here.
Besides I always like what you say so who cares if it is useful, you always make beautiful conections and have a very ice
writing style.

Interesting Jung quote, dough I am not sure I agree completely, well at least I would not put it in that words "unique individual nature, which ultimately limits our choices", I would said that our unique individual nature,
make us choose our choices in our own unique way (which is limited, but so many things are limited that I do not think that is an interesting thing to say about a particular person). I like to think that is great that
each person has a unique individual nature, which make us all special, and with different things to share with one another.
I will have it if we were all the same, indeed I do not like it when I think some technological/cultural things
make us less unique, uniform us.
But I completely agree about not generalizing, and I loved what you said what would happen to computers if they had a fight with themselves, that is really a subject that is worth thinking about, I would love to explore it.

I really liked you second paragraph, I had to read it a couple of times. I agree with what you say about a man's
relation to infinite. I think it exist one, but sadly many people do not realize. And I also agree with the last sentence of that paragraph, it is so true. Those are such deep thoughts about what it is/means being and our escence. You made me wonder, can anybody really escape it's escence?

Thanks a lot for leaving such interesting quote and things to reflect upon

Love and hugs to you dear uncle

Guillermo said...

How are the judges chosen for the competition? What is the selection criteria?

Mariana Soffer said...

Guillermo:
The main condition the Test calls for is the employment of computer-naïve judges, who know virtually nothing of AI and its claims, and who listen to the hidden entities without prejudice.

There is a lot of controversy about this, for example some people critique that selection method with the following argument:
How does one find judges who are representative of “general educated opinion,” yet who have had no interaction with cleverly programmed computers and no encounter with the notion of “thinking machines”?

ines said...

Did alan Turing invented other fundamental tests related to computers, that where not yet able to be solved?c

Mariana Soffer said...

INES:
I a way he did, dough the problem was proven to be unsolvable, he created the turing machine or halting problem which is a decision problem about properties of computer programs on a fixed Turing-complete model of computation. The problem is to determine, given a program and an input to the program, whether the program will eventually halt when run with that input. In this abstract framework, there are no resource limitations of memory or time on the program's execution; it can take arbitrarily long, and use arbitrarily much storage space, before halting. The question is simply whether the given program will ever halt on a particular input.

For more information about it search it on Wikipedia.

Mariana Soffer said...

J:
I wanted to tell you that I made a mistake and deleted some of the comments from my blog, I can not recover them, I hate that had happend. Nut whaterver there are worst things. But I remember we Had a different, longer and more interesting conversation.

If you know by any chance how to recover deleted comments please let me know.


Take care
M

J said...

That's life, Mariana, it's all just castles in the sand.

J

Mariana Soffer said...

j:
Excelent comment!

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