I pray you have assured peace, total serenity, and are at complete ease.
The central question that will be addressed is: What is the nature of Wisdom and Intuition? What is the difference between Knowledge and Wisdom?
Semantics: are Knowledge and Wisdom similar or different?
I am led to believe that a Doe can mean a female antelope or deer.
In contrast, St. Anne and St. Hannah refer to the same venerated female.
(The latter exemplifies that different words may in essence represent the same entity.)
Knowledge. Wisdom. (Intuition.)
When we encounter different words or the same words in different contexts, which become difficult for us to clearly differentiate between their meaning and unanimously agree upon, we must ask:
Are they Doe-Doe-words or Anne-Hannah-words?
(There are other derivatives of the above, e.g. Jesus and 'Isa; which originally and in essence represented the same entity ("Anne-word"). However, in time, they were regarded differently by the people who used the respective languages to refer to him. Whereas Jesus died on the cross for millions of people, 'Isa was raised to heaven and was not killed for millions of others ("doe-word").)
How can we differentiate accurately and in a meaningful manner between the concepts of knowledge and wisdom (and what role does intuition play - or does it play any at all)? [not to mention logic or reason] Are Knowledge and Wisdom Anne-Hannah words or do they represent individually distinct concepts?
Why ask the question: what is the difference between Knowledge and Wisdom?
The pleasing nature of this question is the nested implications: in differentiating between the above words, do we use knowledge (logic), or wisdom (or intuition)?
There are many answers - more than all of human history's lifetimes combined could be spent and yet there will be more answers to seek. Hence it is imperative to ask the right questions. Besides the existential and survival questions, the question "what is the difference between knowledge and wisdom" is one of the most important we will encounter. You may suspect that your question is an intriguing and consequential one when the question you are asking, and the method you use to answer it, are congruent with the answer and can be used to better understand other phenomena (be they other questions or other answers).
Enough of abstract. A few shocking examples may clarify and prevent you from clicking the mouse away from this site.
Nested / Fractals / Symmetry
1. A pentagon with alternate corners connected to each other and iterated will produce successively smaller pentagons. And its 5 lines of symmetry will remain intact.
[look at the picture: en.wikipedia.org/wiki/Reiterative]
Certain iterative equations, fractals, produce patterns that we perceive as pleasing to observe.
2. How can approximating the area of a circle teach us about understanding infinity and differentiating between logic and intuition?
(axiom: calculating area of isosceles triangles before the discovery of "pi".) Draw a circle radius r. Within it draw 4 isosceles triangles and area of 4 triangles = 2(r^2). (circle will have a greater area). Now draw 8 which will give a better approximation... and continue... you will see a pattern which you will trust will continue no matter how many times you make smaller and smaller triangles... continue with patience and you will see that the area of circle can be approximated by a converging but never-ending nested root equation ..which goes on until infinity... whose limit is what we know simply as the Greek letter "pi".
[see second equation down: mathworld.wolfram.com/NestedRadical.html]
The above facts used to approximate "pi" assume two angles of an isosceles triangle are equal; intuitive to accept if we trust symmetry. Logically proven by Euclid. Without the logical proofs, there would be no certainty nor consistency and everything else would fall apart. And trust in the pattern of the nested roots is intuitive, the smaller the triangles and the more the number of triangles, the closer the approximation to the area of a circle... but to logically prove it without a doubt is more difficult. ("intuitive" is used loosely in the above sentence.)
Logic as a check for intuition
I am led to believe that a Doe can mean a female antelope or deer.
In contrast, St. Anne and St. Hannah refer to the same venerated female.
(The latter exemplifies that different words may in essence represent the same entity.)
Knowledge. Wisdom. (Intuition.)
When we encounter different words or the same words in different contexts, which become difficult for us to clearly differentiate between their meaning and unanimously agree upon, we must ask:
Are they Doe-Doe-words or Anne-Hannah-words?
(There are other derivatives of the above, e.g. Jesus and 'Isa; which originally and in essence represented the same entity ("Anne-word"). However, in time, they were regarded differently by the people who used the respective languages to refer to him. Whereas Jesus died on the cross for millions of people, 'Isa was raised to heaven and was not killed for millions of others ("doe-word").)
How can we differentiate accurately and in a meaningful manner between the concepts of knowledge and wisdom (and what role does intuition play - or does it play any at all)? [not to mention logic or reason] Are Knowledge and Wisdom Anne-Hannah words or do they represent individually distinct concepts?
Why ask the question: what is the difference between Knowledge and Wisdom?
The pleasing nature of this question is the nested implications: in differentiating between the above words, do we use knowledge (logic), or wisdom (or intuition)?
There are many answers - more than all of human history's lifetimes combined could be spent and yet there will be more answers to seek. Hence it is imperative to ask the right questions. Besides the existential and survival questions, the question "what is the difference between knowledge and wisdom" is one of the most important we will encounter. You may suspect that your question is an intriguing and consequential one when the question you are asking, and the method you use to answer it, are congruent with the answer and can be used to better understand other phenomena (be they other questions or other answers).
Enough of abstract. A few shocking examples may clarify and prevent you from clicking the mouse away from this site.
Nested / Fractals / Symmetry
1. A pentagon with alternate corners connected to each other and iterated will produce successively smaller pentagons. And its 5 lines of symmetry will remain intact.
[look at the picture: en.wikipedia.org/wiki/Reiterative]
Certain iterative equations, fractals, produce patterns that we perceive as pleasing to observe.
2. How can approximating the area of a circle teach us about understanding infinity and differentiating between logic and intuition?
(axiom: calculating area of isosceles triangles before the discovery of "pi".) Draw a circle radius r. Within it draw 4 isosceles triangles and area of 4 triangles = 2(r^2). (circle will have a greater area). Now draw 8 which will give a better approximation... and continue... you will see a pattern which you will trust will continue no matter how many times you make smaller and smaller triangles... continue with patience and you will see that the area of circle can be approximated by a converging but never-ending nested root equation ..which goes on until infinity... whose limit is what we know simply as the Greek letter "pi".
[see second equation down: mathworld.wolfram.com/NestedRadical.html]
The above facts used to approximate "pi" assume two angles of an isosceles triangle are equal; intuitive to accept if we trust symmetry. Logically proven by Euclid. Without the logical proofs, there would be no certainty nor consistency and everything else would fall apart. And trust in the pattern of the nested roots is intuitive, the smaller the triangles and the more the number of triangles, the closer the approximation to the area of a circle... but to logically prove it without a doubt is more difficult. ("intuitive" is used loosely in the above sentence.)
Logic as a check for intuition
A pre-requisite for discussing knowledge and wisdom is the precise understanding of their little siblings: logic and intuition respectively.
Once logic has proven the theorem, we can present it to our intuition so that it may devour it and internalise it. Future calculations are eased. Every time we use this fact we have saved a lot of time and redundant calculations. Logic has got us started, and intuition has now taken over. If we fall into trouble, we must recognise and be able to go back to utilise logic in order not to over-rely on intuition.
It can further be proven that there exists more numbers between zero and 1 than all the natural numbers counted to infinity (1,2,3,4,5...infinitely). Thus there are different levels of infinite. As you begin to start to count all real numbers from 0 to 1 - just when you think you have found the smallest number (0.00000000000000000000000000000000000000001) to begin counting, you find and even smaller one
(0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001) and your starting point is never within reach (aleph-one). Whereas when counting all natural numbers from 1 up to infinity you begin: 1, 2, 3, 4, 5, 6, 7, .... and you have at least begun your journey (aleph-zero).
Now the proof that aleph-one (0 to 1) is larger than aleph-naught (1,2,3 to infinity) is a serious one in mathematical set-theory. We have used infinity in a lose manner to illustrate the concept. But if you cannot begin to count aleph-one then surely it must be "larger" than aleph-naught... I have appealed to your intuition to grasp and accept it. However, having used many unfamiliar terms (real, rational, natural numbers, infinity) you may accept this is true - but you will never be sure without seeing the logic behind it (see Cantour for the logic).
Thus you can check your intuitive understanding by using logic. Both are a method and form of understanding.
Using Logic and Intuition to differentiate between Knowledge and Wisdom.
Now to differentiate between knowledge and wisdom and intuition, we must use a combination of them to understand, differentiate, and then express their differences. It may seem a futile endeavour: circulatory, nested and unenlightening. The outcome, however, is as beautiful and significant as the elegance of "pi" or "e" which is found in nature, difficult to logically arrive at, yet important in every aspect of nature and our environment. With the only difference that in our case, we begin with the condensed concepts of "knowledge" and "wisdom" and wish to elaborate and arrive at the never-ending nested roots.
Just to reiterate the importance of intuition and wisdom, which seems to have been neglected, or even denied in the modern era: as I am not a mathematician, read from a mathematician how intuition guides much of logical deduction and proofs and should be highly-regarded:
Poincaré on intuition in Mathematics:
http://www.gap-system.org/~history/Extras/Poincare_Intuition.html
Knowledge as an organised body of Logic
* a compilation of rational facts and logical arguments make up knowledge about a certain topic.
* wisdom is the integration of several bodies of related or un-related knowledge into a holistic understanding which can far exceed the sum of logical combinations of the bodies of knowledge. Wisdom is often viewed as running in parallel to knowledge. Whereas this is usually the case, wisdom can also encompass knowledge and more. Wisdom is what is produced in the character and mannerisms and understanding of a person (sage) with an observant, humble, intuitive, and different look and wonder at a common phenomenon. Is it not intriguing that a beautiful "celestial" body with perfect curves such as the circle, has inherent within it an "ugly/messy" irrational number: pi? The intrigue of this makes pi inherently wonderous and pleasing. (alternative example: e and its role in radioactive decay. )
Logic deciphers the action potentials, current, ions fluxes in a single cardiac myocyte. Logic can, theoretically, combine millions of cells and integrate their action potentials in time and space to produce an overall cardiac activity trace and this can then be interpreted within the produced body of knowledge to interpret the trace... this is that of the ECG. But ask a doctor why you get ST depression and then elevation in the ECG of a patient underdoing a heart attack and you might be surprised: rarely are they aware that there even is a scientific explanation. Partly due to lack of knowledge of elementary physics and electronics, but also due to the difficulty in integrating all myocyte depolarisations and repolarisations which are spatially and temporally out of phase. Despite theoretically possible to logically deduce, in practice the "statistical" behaviour of depolarisations and errors in measurement make it very improbable. However, a single 3 or 12-lead ECG trace can summarise all the events and be interpreted correctly most of the time with minimal training.
In this example, the doctor-interpreted ECG is wisdom applied to logic (W--> --> L), myocyte action potentials are individual knots of thread of logic. The combined action potentials of all myocytes is a body of knowledge.
Intuition as a process, a function, and a transformation
* intuition is a function, a process, a transformation. If understood and used skill-fully, it can be applied to fast-track us from logic to knowledge, and from knowledge to wisdom. With incorrect evaluation of empirical data and experience, intuition may be altered and can mis-guide. (can it be argued that this is not true intuition? fa idha wajhaka li deene 7anifa, fatara-allaha fitrata naasa 'alayha. la tabdeela le khalqi-allah...)
logic often paves the way for intuition.
* if intuition is done away with entirely, wisdom will not survive; but knowledge may.
The smaller scale is logic, indispensable as certainty, culminating at an appropriate zoom-out to knowledge. At the larger scale is wisdom, which can exceed beyond the logical addition of vast bodies of knowledge and guide when logic is over-whelmed by too many variables and yet ever-so delicate in helping us make even the smallest of decisions. Intuition, helping us adjust the lens focus and zoom in or out to the desired scale: logic, knowledge, wisdom.
Applied to space-time, quantum and relativity; what we have in physics currently is the logical forms and knowledge. We have seen how brief glimpses of a trained minds wisdom can revolutionize others' understanding: the Schrodinger-wave equation and Einstein's special theory of relativity thought experiment. A further wisdomous intuition (of quantum and cosmological proportions) is required to combine the lingering theories from their current nested infinite square roots to a congruent understanding. The closest candidate to such an understanding is that of Nottale:
(read the short preface):
http://books.google.co.uk/books?hl=en&lr&id=FxpBouT_Fo8C&oi=fnd&pg=PR5&dq=space-time+fractal&ots=ZhJXOczeGc&sig=Q16cjFGPmb62fPPsrGBa1EbbTsU&fb_source=message#v=onepage&q&f=false
I pray you have knowledge which brings assured peace, wisdom which brings total serenity, and immaculate intuition that ensures in every decision you are at complete ease.
May peace engulf your entire existence, and mine.
Once logic has proven the theorem, we can present it to our intuition so that it may devour it and internalise it. Future calculations are eased. Every time we use this fact we have saved a lot of time and redundant calculations. Logic has got us started, and intuition has now taken over. If we fall into trouble, we must recognise and be able to go back to utilise logic in order not to over-rely on intuition.
Intuition is our perceived car speed, and logic is the check (i.e. the dashboard number) telling us how fast we are going.
Infinity (in the English language) is a loose concept (whereas in mathematical language it is a precise concept). pi represents an infinity as alluded to above. square root of 2 also represents an infinity of some sorts: it cannot be represented in fraction or finite decimals - technically referred to as an irrational number. Yet we can convince ourselves that there exists one "number" between one and two when multiplied by itself it yields precisely the number 2. This is represented by square root of 2 - which is nothing more than mathematical language: the shorthand of the above long form. (If we have an incorrect understanding of numbers as natural counting numbers; our intuition would be corrupted and we couldn't envisage a sq.root of 2. But with the understanding that natural numbers may only be a smaller subset of a larger group of numbers including the existence of that sq.root of 2 - despite our initial lack of understanding of its existence. We can get to know and understand sq. root of 2 by conversing with it in mathematics: i.e. using it in our mathematical language to see how it behaves and if the language it speaks reflects that which we observe in the real world).
Infinity (in the English language) is a loose concept (whereas in mathematical language it is a precise concept). pi represents an infinity as alluded to above. square root of 2 also represents an infinity of some sorts: it cannot be represented in fraction or finite decimals - technically referred to as an irrational number. Yet we can convince ourselves that there exists one "number" between one and two when multiplied by itself it yields precisely the number 2. This is represented by square root of 2 - which is nothing more than mathematical language: the shorthand of the above long form. (If we have an incorrect understanding of numbers as natural counting numbers; our intuition would be corrupted and we couldn't envisage a sq.root of 2. But with the understanding that natural numbers may only be a smaller subset of a larger group of numbers including the existence of that sq.root of 2 - despite our initial lack of understanding of its existence. We can get to know and understand sq. root of 2 by conversing with it in mathematics: i.e. using it in our mathematical language to see how it behaves and if the language it speaks reflects that which we observe in the real world).
(Intuition may be considered to fail alone when it comes to imaginary numbers, but wisdom when applied to logic (W--> --> L) might suggest why not consider a number when multiplied by itself would yield negative 1. It is experience, and not logic or intuition, that finds it hard not to reject this concept. Wisdom inherently is creative and trusts in intangible and unseen numbers and forces).
It can further be proven that there exists more numbers between zero and 1 than all the natural numbers counted to infinity (1,2,3,4,5...infinitely). Thus there are different levels of infinite. As you begin to start to count all real numbers from 0 to 1 - just when you think you have found the smallest number (0.00000000000000000000000000000000000000001) to begin counting, you find and even smaller one
(0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001) and your starting point is never within reach (aleph-one). Whereas when counting all natural numbers from 1 up to infinity you begin: 1, 2, 3, 4, 5, 6, 7, .... and you have at least begun your journey (aleph-zero).
Now the proof that aleph-one (0 to 1) is larger than aleph-naught (1,2,3 to infinity) is a serious one in mathematical set-theory. We have used infinity in a lose manner to illustrate the concept. But if you cannot begin to count aleph-one then surely it must be "larger" than aleph-naught... I have appealed to your intuition to grasp and accept it. However, having used many unfamiliar terms (real, rational, natural numbers, infinity) you may accept this is true - but you will never be sure without seeing the logic behind it (see Cantour for the logic).
Thus you can check your intuitive understanding by using logic. Both are a method and form of understanding.
Using Logic and Intuition to differentiate between Knowledge and Wisdom.
Now to differentiate between knowledge and wisdom and intuition, we must use a combination of them to understand, differentiate, and then express their differences. It may seem a futile endeavour: circulatory, nested and unenlightening. The outcome, however, is as beautiful and significant as the elegance of "pi" or "e" which is found in nature, difficult to logically arrive at, yet important in every aspect of nature and our environment. With the only difference that in our case, we begin with the condensed concepts of "knowledge" and "wisdom" and wish to elaborate and arrive at the never-ending nested roots.
Just to reiterate the importance of intuition and wisdom, which seems to have been neglected, or even denied in the modern era: as I am not a mathematician, read from a mathematician how intuition guides much of logical deduction and proofs and should be highly-regarded:
Poincaré on intuition in Mathematics:
http://www.gap-system.org/~history/Extras/Poincare_Intuition.html
Knowledge as an organised body of Logic
* a compilation of rational facts and logical arguments make up knowledge about a certain topic.
* if logic is every knot of thread in the hands of a knitter; the resulting jumper is a body of knowledge.
Wisdom as a super-symmetrical transformation of Knowledge
Wisdom as a super-symmetrical transformation of Knowledge
* wisdom is the integration of several bodies of related or un-related knowledge into a holistic understanding which can far exceed the sum of logical combinations of the bodies of knowledge. Wisdom is often viewed as running in parallel to knowledge. Whereas this is usually the case, wisdom can also encompass knowledge and more. Wisdom is what is produced in the character and mannerisms and understanding of a person (sage) with an observant, humble, intuitive, and different look and wonder at a common phenomenon. Is it not intriguing that a beautiful "celestial" body with perfect curves such as the circle, has inherent within it an "ugly/messy" irrational number: pi? The intrigue of this makes pi inherently wonderous and pleasing. (alternative example: e and its role in radioactive decay. )
Logic deciphers the action potentials, current, ions fluxes in a single cardiac myocyte. Logic can, theoretically, combine millions of cells and integrate their action potentials in time and space to produce an overall cardiac activity trace and this can then be interpreted within the produced body of knowledge to interpret the trace... this is that of the ECG. But ask a doctor why you get ST depression and then elevation in the ECG of a patient underdoing a heart attack and you might be surprised: rarely are they aware that there even is a scientific explanation. Partly due to lack of knowledge of elementary physics and electronics, but also due to the difficulty in integrating all myocyte depolarisations and repolarisations which are spatially and temporally out of phase. Despite theoretically possible to logically deduce, in practice the "statistical" behaviour of depolarisations and errors in measurement make it very improbable. However, a single 3 or 12-lead ECG trace can summarise all the events and be interpreted correctly most of the time with minimal training.
In this example, the doctor-interpreted ECG is wisdom applied to logic (W--> --> L), myocyte action potentials are individual knots of thread of logic. The combined action potentials of all myocytes is a body of knowledge.
Intuition as a process, a function, and a transformation
* intuition is a function, a process, a transformation. If understood and used skill-fully, it can be applied to fast-track us from logic to knowledge, and from knowledge to wisdom. With incorrect evaluation of empirical data and experience, intuition may be altered and can mis-guide. (can it be argued that this is not true intuition? fa idha wajhaka li deene 7anifa, fatara-allaha fitrata naasa 'alayha. la tabdeela le khalqi-allah...)
logic often paves the way for intuition.
* if intuition is done away with entirely, wisdom will not survive; but knowledge may.
The smaller scale is logic, indispensable as certainty, culminating at an appropriate zoom-out to knowledge. At the larger scale is wisdom, which can exceed beyond the logical addition of vast bodies of knowledge and guide when logic is over-whelmed by too many variables and yet ever-so delicate in helping us make even the smallest of decisions. Intuition, helping us adjust the lens focus and zoom in or out to the desired scale: logic, knowledge, wisdom.
Applied to space-time, quantum and relativity; what we have in physics currently is the logical forms and knowledge. We have seen how brief glimpses of a trained minds wisdom can revolutionize others' understanding: the Schrodinger-wave equation and Einstein's special theory of relativity thought experiment. A further wisdomous intuition (of quantum and cosmological proportions) is required to combine the lingering theories from their current nested infinite square roots to a congruent understanding. The closest candidate to such an understanding is that of Nottale:
(read the short preface):
http://books.google.co.uk/books?hl=en&lr&id=FxpBouT_Fo8C&oi=fnd&pg=PR5&dq=space-time+fractal&ots=ZhJXOczeGc&sig=Q16cjFGPmb62fPPsrGBa1EbbTsU&fb_source=message#v=onepage&q&f=false
I pray you have knowledge which brings assured peace, wisdom which brings total serenity, and immaculate intuition that ensures in every decision you are at complete ease.
May peace engulf your entire existence, and mine.
What are the neural correlates of logic, and intuition; knowledge and wisdom?
ReplyDeleteIf they are so elementary to our existence and mind, do you have specific brain-modules which deal with them? Just as we have a fusiform face area which processes identities including faces?
Knowledge has previously been defined with some adjustments, as infallibly justified true beliefs. Infallibly justified here is a reference to logic. Most of what we think we know, are merely unjustified beliefs that we have taken for knowledge. when i walk over a bridge: I do not know that it can support me, I think and believe it can as I trust the engineers that built it. If it turns out to fall - then my belief was incorrect. If it turns out to be true, then I cannot retrospectively claim to have known...but merely to have believed, and in that one occasion my belief was true.
ReplyDelete[see discussions on Epistemology by Plato, Russell, Gettier]
Note therefore, that logic is what we use to transfer our knowledge to others. The synapses in our brains must all have certain common characteristics through which logic remains infallible throughout space (Americas or Asia) time (Newton's formulas, given the assumptions, still hold today) gender, race and culture.
When Einstein understood the relative nature of space-time, it was a flash of wisdom. Used in the context of a thought-experiment in his original special relativity paper, logic took over and arrived at conclusions. Out of all the thought-experiments he could have chosen, he chose this specific one which when fed to logic produces the special theory of relativity. Why did he chose and arrange his thought experiment as he did? A larger zoomed-out holistic understanding had already glimpsed the question and the answer and devised the though-experiment. His wisdom had seen the larger picture. he then zoomed right back in and logic took over and sequentially showed with lorentz transforms that space and time are relative. Thus creating a new body of infallible belief - which with further real experiments were shown to be true. True, infallibly justified, belief, and thus special relativity was knowledge. And with training, intuition can learn to do what the mathematical language does without the tiresome calculations.
The concern is that intuition is more variable than logic within the human mind.
Wisdom created the axiom. Logic churned it into organised knowledge (ie science). Intuition was a transformation that allowed Einstein to zoom from the holistic wisdom to the detailed logic.
Rarely do we come across scientist who possess both wisdom and intuition to convert their wisdom (via logic) into knowledge and science for others to understand and accept also.
With only wisdom, a person may arrive at the correct conclusions and decisions, but his lips will be sealed and his tongue-tied: he will have trouble getting others to agree with him.