Is Logic Universal?

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Exebeche
 
Reply Fri 28 Aug, 2009 05:29 pm
@BrightNoon,
BrightNoon;86139 wrote:

'..sweat and save, building for a shallow grave!' (in the immortal words of Mr. Morrison) ..if you catch my meaning.

Interesting poetry. I wonder if Jim Morrison wrote these romantic lines by himself. If anyone told me that it's William Blake it would believe it right away.


BrightNoon;86139 wrote:

I find it amusing that determinism is currently the minority, eccentric opinion.

Funny because in Germany i have the feeling i talk to determinists most of the time. If you live in the U.S. i guess the same trend will take place over here.

BrightNoon;86139 wrote:

Whose 'slightest uncertainty' is this? I'm sure you're not suggesting that the universe itself is uncertain what to do, as that would be an absurd personification.


It's more or less a word thing. I just chose the term that Heisenberg used. Well, actually i'm not sure if that's his word, because the german word 'Unschaerfe' is something that does not include an observers perspective as oppose to 'uncertainty'. The problem is, it's hard to tell at what time these physicists created a theory, meaning in which country they were and which language they used originally.

BrightNoon;86139 wrote:

The fact that we are unable to predict what a modeling computer will generate is not proof that this end result is non-determined. Once, we could not predict when the full moon comes out; was it not determined then? If by 'random' or 'chaotic,' you mean only 'unpredictable' then you are quite correct in saying that the result of a modeling computer is random. In that case, it is still determined. If, on the other hand, you mean by 'chaotic' or 'random' that the result is not determined (i.e. that the scenario generated is not the result of a certain set of factors, however absurdly complex and inscrutable those factors may be) then you must believe that events can occur without causes: i.e. magic.


It is extremely important to keep in mind that Chaos theory never ever doubted causality.
Sometimes people say Chaos was something like the 'absolute absence of any rules'. That's essentially wrong.
Causality is a major principle of the universe and by nothing reduced in Chaos.
This has lead to the expression of deterministic chaos.
Complete absence of rules -> perfect chaos has not been observed in this universe and my personal opinion is that it could only be observed in a stage like before or around the big bang.
What we observe is, that systems can be more or less determined.
I guess the Boltzmann equationwhich is the function that describes entropy, can be used as a measure for evaluating how determined a system is.
What is meant by deterministic chaos is:
When you observe chaotic systems you first realize that they appear extremely undetermined. Nonetheless, the more you observe the more you realize that there are still patterns. Rules behind the chaos. This is what manifests in the fascinating symmetry of fractals.
No matter if you observe a linear or a non linear system you will always have observation points in your graphical display. For example you have a graph that displays 'foot above zero' and 'seconds'
For a falling stone you will have a graph that looks parabolic when you connect the observed points. The points are very easy to connect, especially if you increase the number of observations (e.g. pictures) that you make.
In a non linear system however nothing seems like an obvious connection. You can predict the appearance of a point only with a certain probability.
Your observations look totally random first, but the more observations you make, the more you realize these shapes showing that your next point cannot be predicted but is much more likely to appear in a particular area (that looks like a fractal).
These graphical descriptons are mostly very abstract because the graphs are not as simple as a graph that describes a process in time and space. They mostly have many (mathematical) dimensions - phase space.
The least abstract observation of such that i can think of at the moment would probably be what we call an 'electron cloud'.
(Although it's kind of ridiculous to say an electron cloud was not very abstract.)
 
Exebeche
 
Reply Sat 29 Aug, 2009 01:12 pm
@Zetetic11235,
Zetetic11235;86114 wrote:
The distinction is that the brain does not necessarily map to a Turing machine. Gretel does not have to follow the instructions given to her and any input data is only tangentially related to her actions.

I totally agree.
The question wether or not the human brain maps to a Turing machine opens a door to a complex discussion, that you are obviously familiar with:
J.R. Searle's chinese room.
However i don't even think that we have to go so far because i also agree with your other statement:

Zetetic11235;86114 wrote:

Besides, following a logical path to a goal is not necessarily equivalent to making a decision.

Exactly.
Following a logical path is only one possible way for the human brain to make a decision.
Actually in these days the number of people decreases who claim that the logical path is the common human way of making a decision.
Humans have a lot of evaluation criteria which are partially contradictive.
That's why many decisions are made more by your stomach (as we say in german) than by your brain.
Still i don't see why making a decision based on logic should not be a decision.

Zetetic11235;86114 wrote:

Question: Are those chess programs based on probabilistic algorithms?

Not that i know of.

Zetetic11235;86114 wrote:

Besides, isn't chess decidable?

I'm not sure about the word decidable.
The way you use it you make it sound absolute like one can use the word 'determined' in an absolute sense.
I don't know if chess is decidable. However you seem to see implications that i don't see..
Even if chess was decidable in an absolute way, like for every move there's a perfect answer, this wouldn't mean that a computer or a person would have acces to this answer.


Zetetic11235;86114 wrote:

but I do know that every computer maps to a Turing machine.
The point is that (unless we are talking about quantum computing) your computer is very much deterministic.

Can a Turing machine calculate non linear processes?
If so i would say the calculation is not determined. However i doubt that it can. From what i know about the Turing machine i don't see how it could manage parallel processing.
I remember having heard that a Turing machine could deal with any computer based calculation however i would have to do some research if i can trust this assumption.
The statement that every computer maps to a Turing machine could also be just not up to date.


Zetetic11235;86114 wrote:

Actually, Chaos theory was a child of astronomy. Henri Poincare discovered the basic irregularities while trying to solve the three body problem.

I never heard of it, but it sounds interesting.
Who deserves the Oscar is not of too much relevance though.
If you look at the internet: There are so many different opinions about who created the internet...
However if you have a link that explains further what you mean i would read it with interest.
 
Zetetic11235
 
Reply Sun 30 Aug, 2009 04:59 pm
@Exebeche,
Exebeche;86648 wrote:

Exactly.
Following a logical path is only one possible way for the human brain to make a decision.
Actually in these days the number of people decreases who claim that the logical path is the common human way of making a decision.
Humans have a lot of evaluation criteria which are partially contradictive.
That's why many decisions are made more by your stomach (as we say in german) than by your brain.
Still i don't see why making a decision based on logic should not be a decision.


My point was that the logical path proceeds from a decision, and each step requires a decision to continue following it. The logical path itself has nothing to do with the decision to follow it. I am curious about what mechanism decision making follows, as it does not appear to be logical, but rather as you say, 'aus dem bauch' (I only know a little German).


Exebeche;86648 wrote:

I'm not sure about the word decidable.
The way you use it you make it sound absolute like one can use the word 'determined' in an absolute sense.
I don't know if chess is decidable. However you seem to see implications that i don't see..
Even if chess was decidable in an absolute way, like for every move there's a perfect answer, this wouldn't mean that a computer or a person would have acces to this answer.

Decidability




Exebeche;86648 wrote:
Can a Turing machine calculate non linear processes?
If so i would say the calculation is not determined. However i doubt that it can. From what i know about the Turing machine i don't see how it could manage parallel processing.
I remember having heard that a Turing machine could deal with any computer based calculation however i would have to do some research if i can trust this assumption.
The statement that every computer maps to a Turing machine could also be just not up to date.

Turing machine - Wikipedia, the free encyclopedia

I can't find much on the modeling of nonlinear processes with software. If you could provide some links for this I would appreciate it. The idea is certainly strange to me, it could certainly be the case that a deterministic automaton could represent a chaotic system. Fractals can certainly do interesting, seemingly unpredictable, things.



Exebeche;86648 wrote:
I never heard of it, but it sounds interesting.
Who deserves the Oscar is not of too much relevance though.
If you look at the internet: There are so many different opinions about who created the internet...
However if you have a link that explains further what you mean i would read it with interest.

Chaos theory - Wikipedia, the free encyclopedia

I know a bit about the history of the field because I attended a lecture on the subject at my University. It is interesting.
 
Exebeche
 
Reply Mon 31 Aug, 2009 02:28 pm
@Zetetic11235,
Zetetic11235;86992 wrote:
My point was that the logical path proceeds from a decision, and each step requires a decision to continue following it. The logical path itself has nothing to do with the decision to follow it. I am curious about what mechanism decision making follows, as it does not appear to be logical, but rather as you say, 'aus dem bauch' (I only know a little German).


You say the logical path has nothing to do with the decision to follow it, i agree, although i tend to say, making a decision does not equal following a logical path, that sounds less excluding.
I haven't really worked on a definition of the word 'decision' before this thread, however 'aus dem Bauch' Wink i would call a decision:
To make a choice based upon an evaluating system.
For a computer this evaluation will most of the times be based on common logic (although not even this is necessary. Look at games for example, their rules are many times based on their own particular logic. The (basic) logic of programming will always be the common one. However the built up logic can differ a lot. Just like language does. )

Now, Gretel's decision has only points of contact with common logic.
She may calculate the price and then make a completely contradictory decision.
Her evaluating system takes in account very subjective qualities.
How big are the apples (not so subjective)? What colour do they have (highliy intuitive)? How do they taste (very subjective - based on intuition)?
In former times we would have had to admit that this is a kind of evaluating system that can not be analysed by any common logic, however nowadays it's different.
If we look at the way neuronal networks are organized we get a little bit of a picture.
The different neurons have their particular weights, of course there can be billions of real neurons included in such a process.
That makes it understandable why the decision is sometimes hard to find for humans.
There are billions of neurons putting their weight into the -> measurement - and that's what it is with humans, it's not a logical calculation, it's a measurement of neuronal weights.
Our consciousness kind of controls which weights are taken into account, although to be honest, i believe, our consciousness has no idea, that actually our subconscious is the leader who decides what is taken into account.
For example Gretel might not even consider the colour of an apple.
She wonders how they taste and doesn't even realize how her subconscious analyses the colour and surface.
The same when you look at an attractive girl.
When you come to the conclusion that she has an interesting character your subconscious has already checked one thousand aspects of genetical compatibility.

I hope i could add something to your investigation on what a decision is [edit: or how a human decision works]. (?)


Thanks for the links, i will see if i can get something about nonlinear functions.
 
Zetetic11235
 
Reply Tue 1 Sep, 2009 02:17 pm
@Exebeche,
It is very interesting that you bring up size and color. as they fall directly into the domain of ideas that Fuzzy Logic seeks to make more precise. In Fuzzy logic, truth values range over an interval on the Real Number line, usually from [0,1] , so thatif you need to make a gradated decision you can base it on the weight of inclusion in some set like the set of all large apples. This way we do not have to say that 10 centimeters is a large diameter for an apple but then 9.9998 centimeters is not longer large; in essence Fuzzy logic seeks to make precise the notion of 'how large' or 'how thick' something is given reasonable parameters. This could certainly in theory (and I think it has in practice) approximate the more subjective aspects of Gretle's decision making process.

I think that there is something important to consider here, and that is how one takes into account what one does when making a decision. You seem to be trying to make this point as well. It seems that when we make a decision, we often have a set of parameters that just 'come to us', they were not consciously selected from the set of all things that we know, that would take an impractical amount of time. This huge aspect of decision making appears to be largely automatic. I wonder if the neuron weights you mention might define themselves based on past experience so as to index a type of experience and initiate an appropriate response. It would be very useful to figure out the exact mechanics necessary for the sort of response to a problem that humans have. Possibly some result in swarm intelligence will come to prove itself as a good model for this sort of process.
 
 

 
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