[Guille]

Mohan,

I’ve taken a time to reply to this thread cause I had many thoughts coming out every day. I really want to congratulate you for such a great idea that this thread is, for it has contributed to my wisdom in many aspects.

First, I want to comment some things about your posts. From them we can make the Three Axiomatic Laws of Problems (TALP):

1.A problem must have a solution.
2.We do not know a solution to a problem if it really is a problem still.
3.A problem which does not have a solution is either a fallacy or paradox, and;
a) If it is a fallacy, it is not a real (natural) problem
b) If it is a paradox, the solution is already given (not as solution, but as escape). (I want to note that I got this from Withoutme’s replies to Subversion’s ‘solution’ of Russell’s paradox).

You also introduce the idea of limits, and we must talk about abilities. In my latest entry in my journal, I logically derive that our actions and thoughts are expressive, they show our abilities, and our hopes and fears are impressive, they show our limitations. We can therefore give a philosophic/cultural definition of problems and solution:
A Problem; is the demonstration of our hopes and fears, of our wills and ways (I must note that this second form of expressing the idea comes from a post by AntonioLao).
A Solution; is the demonstration of our actions and thoughts, of our abilities and decisions (this second form of expressing it, I will explain further in this reply).

Now I want to comment about analysis. We don’t always have to make solutions to problems in abstraction. We can make them in analogy, as I proposed with my Anun theory. But I think you misunderstood the theme. The discussion between abstraction and analogy isn’t about the object, but the subject. I mean, instead of changing how things are looked, we change who we look at them. Analysis is a broad term, and there are many types of analysis. Both abstraction and analogy use analysis, but they are not substitutes to it, they are part of a different conceptual area. I would say that analysis is the predisposition to abstraction or to analogy. I mean, there is a paper that is analysis, and the pencil to write or paint, that is, to abstract or analogue. And this physical analogy is great, because abstraction is governed by pre-concept rules whiles analogy is independent, intuition, applied on each case in a particular way. Thus, painting is much more free than writing. Something important that we must note, is that for abstraction, the analysis must always be open, that is, have no particular shape or texture as a paper. Whereas for analogy, the analysis must be appropriate for each particular type of painting, that is, the texture and shape of the paper must be adequate for each analogy. The inconvenience is that we must develop a theoretical framework by which we can develop the methods which format the analysis in accordance to the analogy. This is a very complex idea, and we must work on it both of us, I belief. Maybe Lloyd can help us on this. For the moment, I want to clear up that analogy is precisely about not finding a true solution, but an adequate solution, in opposition to abstraction. The role of analogy, thus, is not to be the path to search for truth (for this is the role of the analysis), but to be the tool to the search for truth, independently of what the truth is.

About the TOE I must note that if it is really a problem, we must use all this critical thinking to achieve the knowledge. Whereas if the TOE is a paradox, it gives the solution by itself, and that is, the solution if the TOE is a paradox is everything itself, and thus, any conception or theory about everything, about the meaning of the word, from the point of view of mathematical logic, or religion, or art, or philosophy, or experimental science…

Now, I want to unite harmonygirl’s contribution with Robert Fritzius’ contribution. The first said that a problem may have more than one solution, and the second said that a solution may solve more than one problem. Uniting these, and with a bit of logic, we can derive the first of the Three Original Laws of Problems (TOLP):

1.The number of possible (true) solutions for a problem is directly proportional to the number of problems solved by each of the solutions.

Stated in another way: If you have a solution to a problem to which there are many other true solutions, your solution solves other problems apart from this one. I must note that the inverse form also exist: if our solution solves many problems, we know that the are other solutions for these problems. This is also easy to understand if we substitute problem-solution with effect-cause. In history, the more effects which are affected by a cause, then we know that each of those effects has more other causes. We do have to keep in mind that this law assumes that the ‘power’ or ‘solvability’ of say, two solutions, is equal, and if one solves many problems, it is giving smaller parts of it’s ‘solvability’ to each problem than the solution which is solving few problems. That is why the solution which applies less of it’s solvability can’t occupy all the ‘solvational space’ of a problem. Do understand too that the more problems that a solution solves, the less hard or energy tacking each problem is.

Now I want to go onto mkrkpatrick’s posts. You say in your first post
that a problem that has no solutin is a fact. Well, if we unite this with the third TALP, we must agree with the statement that ‘paradoxes are facts’ and therefore they are given in nature. This is ok for me, for I believe all true paradoxes are given in nature (we shall not forget Pascal’s statement ‘contradiction is not a sing of falsity, nor is the lack of contradiction a sing of truth’). Also, you give us in your post the second TOLP, just that missing a part of it. You say that anything can be a problem, depending on the situation and the subject, and therefore we can say that ‘Problems are relative and subjective’. This is completely true, we can see that science for example tackles problems in relation to the needs of society (for example, biologists investigated super-fast about AIDS to give a solution, because it was affecting society). Now, but we must remember that a problem is an entity, which needs and asks for an identity (which is the solution). Therefore, here is the second TOLP law:

2.A problem is an absolute entity of it’s own (only depending on it’s solution, which is the identity), and yet it is relative and subjective. (I must note that this conception of a problem being absolute and relative I derived from two sources: Antonio’s description of nothing as absolute (0) and relative (1/infinity) at the same time, and Yasuhiko Genku Kimura’s article ‘Beauty as a Path of Peace’ available in http://www.twilightclub.org/articles/pathofpeace.html).

Finally, the third main point that Michael gives us is ‘too much analysis leads to paralysis’. This proofs the statement that ‘decisions are made by feelings’. For all of what rational thought is, is analysis, and we never can go forward with it. Not even math escapes: when we create mathematical developments we are using logic, yes, but when we decide what to create, or how to go about it, etz, it’s all from our emotions and believes. I will discuss this further now, in my reply to Lloyd.

The modern world treats the metaphysical problems with entities: mind-body, choice-chance, thought-feeling… And the posmodern world has abandoned that because it was creating things to destroy them later. Now, I don’t believe it is apropiate to abandon metaphysics, but to develop a new form of thinking. Not a new metaphysics, and not a non-metaphysical; a new form of thinking which can do what metaphysics did but without being metaphysics. Part of it, is, for example, treating dualities are parts of the same thing. Good and evil (as Leibniz did), body and mind (as Sloterdijk writes), culture and nature, and finally, thought-feeling. Rationality and impressions; logic and emotions. Lloyd, you divide completelly these aspects, wrongly. All our decisions, the actual process which ‘decision’ represents in the mind, is that of feeling. We might analyse problems, investgiate about them, etz, but all decisions we make, from discussing in this thread, to breathing, to finding a solution to a mathematical conjecture, it is always done by the sub-consciousness, instinctive, sensational, feelingly, imaginative, emotional, intuitional part of the brain, of the mind. Reason and emotions are strongly related.

I'll write the third TOLP in my next reply, where I will explain a few more things about the nature of the problem.

[AntonioLao]

When searching the web, remembering Steven Weinberg (co-founder of electroweak theory) having once said about working and getting certain solution to the wrong problem, four of the hits are the following links: http://www.cs.utexas.edu/~vl/notes/weinberg.html and http://www.astro.uni-bonn.de/~willerd/weinberg.html and http://www.physicstoday.org/vol-58/iss-11/p31.html and http://nobelprize.org/physics/laureates/1979/weinberg-lecture.pdf

[Guille]

What does the 'solution to the wrong problem' mean? Is it that even problems which are not real problems (that is, they are either fallacial problems or paradoxical problems) have solutions?

Reading through what Weinberg says, I think he should restrict himself to be a scientist and don't go onto philosophy, it is far too dense and relative for him (I don't say he's not sufficiently intelligent, I just think his intellgence is not good for philosophy). Philosophy is based on interpretations and science is based on observations. And Weinberg philosophizes within obsevations, within a 'method', and, as he says that each scientist is pre-himself, that is, newton was pre-newtonian, and maxwell was pre-maxwellian, it is also true for philosophers, and descartes, the last philosopher to believe in a method for philosophy (notice the title of one of his main books: Discourse of Method), was pre-cartesian, in the sense that all of who came after him agreed (except Schopenhauer, who was an idiot) there is no such thing as a 'philosophical method' (at least not one which is sort of analogous to the scientific method). Weinberg criticizes Kuhn's magnum opus in absurd ways. He says that Kuhn is wrong when he says that the way to verify the truth in a theory changes with the change of paradigms, when scientific revolutions occur. But this is something that no one can really argue, if not, in what sense did science change from 1905 onwards? In that any proposition defending the idea of ether was neglected, and after the start of QM, any proposition defending the idea of non point-like particles was neglected... So I don't know where Weinberg has background for what he says. He also says that sociologists, philosophers etz, are wrong when they say that scientific paradigms are dependent on many external factors to 'the search for truth', like what society needs, the space-time point we are in, the politico-economical conditions... Of course science depends on those! Science advances in those areas to where there is money, just as many biologists work to solve the problem of certain terrible deseases but not other deseases, because the one they are trying to solve is affecting more people, even though others might be much more dangerous. Also, if there is war, scientists are put to work on war equipment, like Einstein and others in the race to the nuclear bomb. Also, Winberg says that Kuhn is wrong when he says that science doesn't progrees towards something, it just progresses. Well, towards what does science progress, according to Weinberg? Is it a TOE, well then he must be wrong because science is more and more diversed every decade significantly, is it towards an occupation of all problems? well no because there are many problems for the human mind which are already proven to not be for science, and in fact many problems which science tries to solve but it can't (like the true nature of light, of gravity, etz). Summarized, Kuhn was smarter than what Weinberg thinks, and in contrary to him, Kuhn was good for philosophy.

[AntonioLao]

Originally Posted by GUILLE

Kuhn was smarter than what Weinberg thinks, and in contrary to him, Kuhn was good for philosophy.

You are right that Weinberg is a scientist who wants to be a philosopher at a period when his scientific achievement where on its declining phase. So, he turned to philosophy for safe keeping by admitting to the fact that a TOE is not yet in sight at the distant horizon. More about Steven Weinberg on his upcoming birthday for his successful formulation of electroweak theory, please see http://www.sciencewatch.com/interviews/stephen_weinberg1.htm and http://en.wikipedia.org/wiki/Steven_Weinberg and http://www.ph.utexas.edu/~weintech/weinberg.html and http://www.quotationspage.com/quotes/Steven_Weinberg/ and http://almaz.com/nobel/physics/1979c.html and http://online.itp.ucsb.edu/online/kitp25/weinberg/

His Nobel lecture mentioned about his discovery of the correct solution for the wrong problem.

[Lloyd Gillespie]

Originally Posted by <<<GUILLE>>>

Mohan,

[size=3][font=Times New Roman]The modern world treats the metaphysical problems with entities: mind-body, choice-chance, thought-feeling… And the posmodern world has abandoned that because it was creating things to destroy them later. Now, I don’t believe it is apropiate to abandon metaphysics, but to develop a new form of thinking. Not a new metaphysics, and not a non-metaphysical; a new form of thinking which can do what metaphysics did but without being metaphysics. Part of it, is, for example, treating dualities are parts of the same thing. Good and evil (as Leibniz did), body and mind (as Sloterdijk writes), culture and nature, and finally, thought-feeling. Rationality and impressions; logic and emotions. Lloyd, you divide completelly these aspects, wrongly. All our decisions, the actual process which ‘decision’ represents in the mind, is that of feeling. We might analyse problems, investgiate about them, etz, but all decisions we make, from discussing in this thread, to breathing, to finding a solution to a mathematical conjecture, it is always done by the sub-consciousness, instinctive, sensational, feelingly, imaginative, emotional, intuitional part of the brain, of the mind. Reason and emotions are strongly related.

Hi Guille, I'd be more than willing to help with what you are working on. As to your interpretation of my dividing I think you would have to know my mind better, as the unity of the particular and the universal is of utmost importance to me. I only try to separate out the emotional into my own cognizant intuitive perception in order to more clearly see the true issues. I always unite them after. As a matter of fact Aristotle's Nicomachean Ethics of the intuitive reasoning is the most important tool to my thinking processes. As you may know he stated that not only our first principles were intuitive reasoning but also our final philosophical wisdom was also intuitive. The metaphysics of Heraclitus and Aristotle founds many a great thinker, as they were most important to both Hegel and Charles Sanders Peirce. As a matter of fact Hegel said he founded his entire logic on Heraclitus, and if you have studied both Hegel and Aristotle, you will find Aristotle's ethics almost identical to Hegel's logic about first principles and "being." I think these four minds make an excellent foundation to expand any new thinking from.

Guille, I am really quite emotional, I just disguise it with cognition. Cognition and logic is how I was raised, by both parents. And as you have seen I have a tendency to lean this way when I think and write, however it doesn't mean it is all I think. As Aristotle pointed out life is about giving as much space for the subjective and the objective, the heart and the head, the emotion and the logic. I assure you I do both. But our goal is to unite the subject and object in the universal ideal, and this takes the type of thinking you have been talking about with analogous universality, and what I mentioned about conceptual intentionality. These are a start and as you have mentioned it can be a foundation for a whole new way of thinking or an entirely new metaphysics.

Just think of the analogies of morality alone that can be more clearly understood by making analogous comparisons between nations of the obvious materialisms, representing the conceptual intentionalities of different nations' desires. By this I simply mean how much different nations are willing to spend to protect its women, children and all citizens. These are real analogous comparisons that can be made world wide. Another would be the materialism that represents love, say the most obvious being the Taj-Mahal. Another would by the materialism representing faith, religion, soul whatever you wish to call it or not___but by the many cathedrals built, churches erected, crosses built, services attended, monuments to saints emplaced___these are all representations of analogous comparisons of real emotions of people that are even mathematizable as to comparative analyses of different nations moores. The list is unending for what we can do with real world comparisons as relates to a new world philosophy or just plain old thinking. The direct cognitive observation of such events reveals an entirely new way of looking at nations' and peoples' emotions.

hope I helped,
Lloyd

[Mohan.C]

Guille,
How do you look at paradoxes I didn't entirely grasp your meaning. But I view paradoxes as problems which cannot have a true solution and hence are false. Paradoxes occur only when we try to manipulate a problem (like time travel). But nature itself has only problems, which we need to understand, and has a solution, because nature operates.

[Mohan.C]

When we try to solve a problem should we be aware of it implications on the society?
Or should we solve the problem just because.....its a problem.
Is problem just an headache or is it a kind of door to the solution itself which could be both good or bad.

When we limit, the probabilities reduce. But does this make it any good because someone else may have considered it in a different sense and we may have missed it. But that's the whole point of limits, to get on to a particular solution which will avoid all such confusions. But a person taking different limits will have arrived at a different particular solution.

It's okay in trignometry but in society its a whole different thing. How exactly can we recognize a true solution.

I know it was me who started this thread but all this is confusing me.

[mkirkpatrick]

Originally Posted by Mohan.C

When we try to solve a problem should we be aware of it implications on the society?
Or should we solve the problem just because.....its a problem.
Is problem just an headache or is it a kind of door to the solution itself which could be both good or bad.

When we limit, the probabilities reduce. But does this make it any good because someone else may have considered it in a different sense and we may have missed it. But that's the whole point of limits, to get on to a particular solution which will avoid all such confusions. But a person taking different limits will have arrived at a different particular solution.

It's okay in trignometry but in society its a whole different thing. How exactly can we recognize a true solution.

I know it was me who started this thread but all this is confusing me.

You would re-cognise a true solution in society by intuitive perception,coupled by an inner soulful note of a harmonial tone!
kind regards michael

[Mohan.C]

Originally Posted by <<<GUILLE>>>

Mohan,

I’ve taken a time to reply to this thread cause I had many thoughts coming out every day. I really want to congratulate you for such a great idea that this thread is, for it has contributed to my wisdom in many aspects.

First, I want to comment some things about your posts. From them we can make the Three Axiomatic Laws of Problems (TALP):

1.A problem must have a solution.
2.We do not know a solution to a problem if it really is a problem still.
3.A problem which does not have a solution is either a fallacy or paradox, and;
a) If it is a fallacy, it is not a real (natural) problem
b) If it is a paradox, the solution is already given (not as solution, but as escape). (I want to note that I got this from Withoutme’s replies to Subversion’s ‘solution’ of Russell’s paradox).

You also introduce the idea of limits, and we must talk about abilities. In my latest entry in my journal, I logically derive that our actions and thoughts are expressive, they show our abilities, and our hopes and fears are impressive, they show our limitations. We can therefore give a philosophic/cultural definition of problems and solution:
A Problem; is the demonstration of our hopes and fears, of our wills and ways (I must note that this second form of expressing the idea comes from a post by AntonioLao).
A Solution; is the demonstration of our actions and thoughts, of our abilities and decisions (this second form of expressing it, I will explain further in this reply).

Now I want to comment about analysis. We don’t always have to make solutions to problems in abstraction. We can make them in analogy, as I proposed with my Anun theory. But I think you misunderstood the theme. The discussion between abstraction and analogy isn’t about the object, but the subject. I mean, instead of changing how things are looked, we change who we look at them. Analysis is a broad term, and there are many types of analysis. Both abstraction and analogy use analysis, but they are not substitutes to it, they are part of a different conceptual area. I would say that analysis is the predisposition to abstraction or to analogy. I mean, there is a paper that is analysis, and the pencil to write or paint, that is, to abstract or analogue. And this physical analogy is great, because abstraction is governed by pre-concept rules whiles analogy is independent, intuition, applied on each case in a particular way. Thus, painting is much more free than writing. Something important that we must note, is that for abstraction, the analysis must always be open, that is, have no particular shape or texture as a paper. Whereas for analogy, the analysis must be appropriate for each particular type of painting, that is, the texture and shape of the paper must be adequate for each analogy. The inconvenience is that we must develop a theoretical framework by which we can develop the methods which format the analysis in accordance to the analogy. This is a very complex idea, and we must work on it both of us, I belief. Maybe Lloyd can help us on this. For the moment, I want to clear up that analogy is precisely about not finding a true solution, but an adequate solution, in opposition to abstraction. The role of analogy, thus, is not to be the path to search for truth (for this is the role of the analysis), but to be the tool to the search for truth, independently of what the truth is.

About the TOE I must note that if it is really a problem, we must use all this critical thinking to achieve the knowledge. Whereas if the TOE is a paradox, it gives the solution by itself, and that is, the solution if the TOE is a paradox is everything itself, and thus, any conception or theory about everything, about the meaning of the word, from the point of view of mathematical logic, or religion, or art, or philosophy, or experimental science…

Now, I want to unite harmonygirl’s contribution with Robert Fritzius’ contribution. The first said that a problem may have more than one solution, and the second said that a solution may solve more than one problem. Uniting these, and with a bit of logic, we can derive the first of the Three Original Laws of Problems (TOLP):

1.The number of possible (true) solutions for a problem is directly proportional to the number of problems solved by each of the solutions.

Stated in another way: If you have a solution to a problem to which there are many other true solutions, your solution solves other problems apart from this one. I must note that the inverse form also exist: if our solution solves many problems, we know that the are other solutions for these problems. This is also easy to understand if we substitute problem-solution with effect-cause. In history, the more effects which are affected by a cause, then we know that each of those effects has more other causes. We do have to keep in mind that this law assumes that the ‘power’ or ‘solvability’ of say, two solutions, is equal, and if one solves many problems, it is giving smaller parts of it’s ‘solvability’ to each problem than the solution which is solving few problems. That is why the solution which applies less of it’s solvability can’t occupy all the ‘solvational space’ of a problem. Do understand too that the more problems that a solution solves, the less hard or energy tacking each problem is.

Now I want to go onto mkrkpatrick’s posts. You say in your first post
that a problem that has no solutin is a fact. Well, if we unite this with the third TALP, we must agree with the statement that ‘paradoxes are facts’ and therefore they are given in nature. This is ok for me, for I believe all true paradoxes are given in nature (we shall not forget Pascal’s statement ‘contradiction is not a sing of falsity, nor is the lack of contradiction a sing of truth’). Also, you give us in your post the second TOLP, just that missing a part of it. You say that anything can be a problem, depending on the situation and the subject, and therefore we can say that ‘Problems are relative and subjective’. This is completely true, we can see that science for example tackles problems in relation to the needs of society (for example, biologists investigated super-fast about AIDS to give a solution, because it was affecting society). Now, but we must remember that a problem is an entity, which needs and asks for an identity (which is the solution). Therefore, here is the second TOLP law:

2.A problem is an absolute entity of it’s own (only depending on it’s solution, which is the identity), and yet it is relative and subjective. (I must note that this conception of a problem being absolute and relative I derived from two sources: Antonio’s description of nothing as absolute (0) and relative (1/infinity) at the same time, and Yasuhiko Genku Kimura’s article ‘Beauty as a Path of Peace’ available in http://www.twilightclub.org/articles/pathofpeace.html).

Finally, the third main point that Michael gives us is ‘too much analysis leads to paralysis’. This proofs the statement that ‘decisions are made by feelings’. For all of what rational thought is, is analysis, and we never can go forward with it. Not even math escapes: when we create mathematical developments we are using logic, yes, but when we decide what to create, or how to go about it, etz, it’s all from our emotions and believes. I will discuss this further now, in my reply to Lloyd.

The modern world treats the metaphysical problems with entities: mind-body, choice-chance, thought-feeling… And the posmodern world has abandoned that because it was creating things to destroy them later. Now, I don’t believe it is apropiate to abandon metaphysics, but to develop a new form of thinking. Not a new metaphysics, and not a non-metaphysical; a new form of thinking which can do what metaphysics did but without being metaphysics. Part of it, is, for example, treating dualities are parts of the same thing. Good and evil (as Leibniz did), body and mind (as Sloterdijk writes), culture and nature, and finally, thought-feeling. Rationality and impressions; logic and emotions. Lloyd, you divide completelly these aspects, wrongly. All our decisions, the actual process which ‘decision’ represents in the mind, is that of feeling. We might analyse problems, investgiate about them, etz, but all decisions we make, from discussing in this thread, to breathing, to finding a solution to a mathematical conjecture, it is always done by the sub-consciousness, instinctive, sensational, feelingly, imaginative, emotional, intuitional part of the brain, of the mind. Reason and emotions are strongly related.

I'll write the third TOLP in my next reply, where I will explain a few more things about the nature of the problem.

Guille,

Now I will straightaway go to the TALP
on the second TALP: Once you find a solution the problem does not vanish. I exists as a solved problem, in a diferent state, that's all. A problem starts when our brain starts to work. Every problem has a root, a base.And if we find a solution to it then only there shall "no unsolved problems"A solutions within limits can only solve the problems closely associated with it. But not the root problem.

Moving onto your further comments,
You say "Our actions and thoughts are expressive"
---Actions are expressions of thoughts.

And you say "our hopes and fears are impessive , they show our limitations"
---When you hope you fear. There is an anxiey. They show us something irrational. Like, there is nothing to be afraid of, nor is there a need to hope for results.

Now on your ideas on problems or it's more like a definition.
---A problem does not mean we cannot see across it. We can know the implication of the problem even before we have solved it.But a problem is just the limitation to the cause which produces an effect. But until the problem is solved it does not mean we don't know the effect. But there is a probability of many effects. We just don't know what to choose.

And on your idea of a solution.
---A solution is a door through which the true effects of a cause can be analysed. Not the probabilities, but the truth. That's where I meant we need to limit ourselves, to drop the probabilities. A solutions is not a demonstration of our abilities and decisions. If we try to do that our ego will rule us. And take us far from the truth.There is only logic and science.

You say we don't always have to make solutions in abstraction. We can make them in analogy .
---I don't know about that I think we have to make in analogy.

On your next point on analysis, analogy and abstraction.
---you said I had misunderstood, but I had never understood it at all.
But let me make something clear. Analysing requires existing resource. If we go beyond that we are abstract.

Next point on your post.
The first TOLP.
---I don't believe a problem can have more than one solution. But just different ways to come to that solution. Or different forms of the same solution. But there could be the same solution to many problems. In math atleast.

Next you say it is easy if we substiute problem-solution with cause-effect.
---According to me, A problem is a limitation to the cause. And a soluion is the path to the effect.

Next you talk about solvabilty, solvational space etc..
---What do you mean by solvational space?

Next you say paradoxes are facts. And paradoxes already have a solution-escape.
---But facts are not meant to run-away. But to digest, so that we can use them in future references. Paradoxes do not exist in nature they are just human creation due to his being over curious.

"Contradiction is not a sing of falsity,
nor is the lack of contradiction a sing of truth"
---But "contradiction is the prison placed in between the two"

Next you give us the second TOLP.
---I completely agree with that

And finally you give us a beauiful post as a reply to lloyd.
---That was the one of the best parts of the posts.

Finally Guille.--- Nature did not have problems. "Problems are what man encountered in his way to understanding"
So, you better not call them laws

[mkirkpatrick]

Originally Posted by Mohan.C

Yes I guess you ar right. Any problem does not have a single origin but they have many dimensons. So A true solution will have solved all the problems associated with it.

If you had a cup of coffee
that was black and bitter tasting,then a possible solution would be to place
two or three teaspoonfuls of sugar into the cup,the sugar would then become,dis-solved while re-solving your localised problem,residing in your cup?How many dimensions would that involve!



kind regards michael.