HIJRAH 1430 Ramadhan 07?
FREEDAY, August 28, 2009
UP DILIMAN CAMPUS
I shall rewrite the posting "MUTUALLY EXCLUSIVE & JOINTLY EXHAUSTIVE" because it is more about PHILO OF RELIGION rather than LOGIC. I shall probably delete this last 2 postings of mine... The more fitting title should have been "LOGIC DIAGRAMS". I am reminded of MARTIN GARDNER'S book of the same title which introduced me to the matter. I read this book when I was a college freshman. I remember very well that section of the UP MAIN LIB. The PHILO books were all found in front at the left side of what is now the Reference section. Other excellent books on Literature etcetc were found at the middle & back part. I devoured all the good ones - THE COMPLETE WORKS of H.G. WELLS, COMPLETE SHERLOCK HOLMES, SCI-FI, NIETZSCHE, etcetc ... I was an ELECTRICAL ENGINEERING major then. One of my engineeering classmates who saw the books I had been borrowing warned me to stop reading these & other pocketbooks... He knew better... Guess what? I failed to finish my original course - precisely because I was studying - different subjects!! Who told you studying hard cannot lead to failure/flunking?
LOGIC DIAGRAMS:
Euler Circles & Venn Diagrams
One may claim that these spatial representations of logical notions are some of the very first
CONCEPTUAL MAPS. Conceptual maps are another important topic I wanted to tackle in this BLOG but I shall just insert URLs of excellent websites devoted to this topic. And good book titles too. Conceptual mapping has been associated with such writers as TONY BUZAN et al but actually these things are as old as the MEDIEVAL period.
I have always considered PATTERN & ORDERLINESS as hallmarks of a RATIONAL MIND; that intelligent people practice ORDERED/ORGANIZED/SYSTEMATIC thinking. [BUT I once had a very intelligent MAGNA CUM LAUDE engineering graduate teacher who taught very well but had terrible handwriting & was very topsy-turvy/disorganized! I guess to every rule there is an exception!] Educators have determined that drawing diagrams & patterned maps help in thinking. Apparently, the brain imitates the map & reorganizes itself. BUT, again, the brain actually does not seem to be organized when it comes to storing ideas in memory - It seems that
there is no single spot or area in which all our ideas are stored, clumped together. Like in a computer diskette wherein the data are NOT stored in ordered, contiguous areas but are scattered all over the disk sectors. (DEFRAGMENTING one's hard drive tries to join together
these fragmented data, thus saving space & time.)
Compare a field or garden wherein the plants/trees are scattered randomly with another one wherein these are patterned as in rows and columns, circular hedges etc See the difference? Yet patterns do not seem to be common in NATURE. When we find such patterns in the outside world we automatically assume there is a pattern-maker, a designer, that human beings must have created these... Is NATURE DISORDERLY & ARE HUMANS DESIGNERS/PATTERN-MAKERS?
Circles, Squares, Triangles...
CONSPIRATORIAL GEOMETRY...
JUST DELETED IN THIS EXACT SPOT THREE IMAGES of CIRCLE & TWO EQUILATERAL TRIANGLES WHICH TURNED OUT DISORDERED!... I CANNOT MASTER THIS BLOGGER ENTRY FORM. MY TXT FILE ENDS UP DISORDERED...
-SQUARING THE CIRCLE
-RULER & COMPASSS GEOMETRIC CONSTRUCTIONS
-HOW TO DRAW A PERFECT PENTAGRAM STAR, PENTAGON
-GEOMETRIC ORIGAMI PAPER FOLDINGS
-THE NUMBER pi
-THE NUMBER e
-THE GOLDEN PROPORTION/RATIO
BUT THESE ARE ALL ABOUT GEOMETRY & MATHEMATICS...
I am writing only about LOGIC...
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jamaal_the_jobless@yahoo.com
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Thursday, August 27, 2009
Monday, August 17, 2009
POST 6 MUTUALLY EXCLUSIVE & JOINTLY EXHAUSTIVE
UPLOADED ON
HIJRAH 1430 Sha'ban 25
Monday, August 17, 2009
UP DILIMAN CAMPUS
GEOMETRY & MATHEMATICS OF RELIGION
PART 1 OF 2
Geometrical/Mathematical Tool for aiding one's thinking about concepts
WARNING: GROSSLY OVERSIMPLIFIED
Consider the three circles intersecting at their centers... I will not go into the geometry of the plane figures but those who studied high school geometry know that a lot of theorems can be derived from such a configuration... I will use the circles a la Venn Diagram or Euler Circle... I shall try to categorize & classify human beings according to their professed religions & simplify the case to just the three major ABRAHAMIC faiths: Judaism, Islam & Christianity... [PORTION DELETED]
Now consider the mathematical model of the intersecting circles wherein masses of human beings are represented as plane areas This is an extremely simplified model because other individuals or groups of human beings are not represented - where are the ATHEISTS or AGNOSTICS, the HINDUS, the BUDDHISTS, the CONFUCIANS the ANIMISTS, the NEW AGERS, the WICCANS, the DEVIL-WORSHIPPERS etcetcetc... But this is precisely one purpose of (mathematical) modeling, to simplify a problem so that a pattern may be discerned... Of course the modeller should be aware of the limitations of the model she is using... And what conclusions are justified or may be derived from the limited model... In real science, + or - approximations and margins for error are provided... SCIENCE WAS, IS AND ALWAYS WILL BE A "THEORY" AS IN AN UNFINISHED ENDEAVOR...
The three circles divide the plane into seven(7) contiguous (close together) sectors. These sectors are similar because the image has some symmetry... We let the plane represent the human beings who adopt/profess even NOMINALLY (just in name or in public documents though they never follow the religion's commandments, injunctions or teachings... So all Christians are found within the circle of CHRISTIANS, all Muslims are within the ISLAM circle & the Jews are found within the JEW circle.
OH BY THE WAY NOT ALL THINKING INDIVIDUALS AGREE WITH SUCH MATHEMATICAL MODELLING OF HUMAN BEINGS (ONE OF THEM IS LYNDON LAROUCHE WHO CRITICIZES THE WAY THINKERS SINCE NEWTON INCLUDING SUCH FIGURES AS JOHN VON NEUMAN ETCETC HAVE GROSSLY OVERSIMPLIFIED HUMAN BEINGS... The crucial element, the HUMAN FACTOR, the HUMANITY of the INDIVIDUAL HUMAN is not presented... Nevertheless, one can see the possible practical uses of such models
in crowd study, crowd control, handling masses of people, mass classification etctetc MARXISTS I think adopt such broad generalizations with their conceptions of CLASS, PROLETARIAT , etctetc Of course the PHILOSOPHY OF MARXISM IS DIALECTICAL MATERIALISM...
OF COURSE, I AM AWARE THAT I MYSELF CAN BE TREATED AS A MERE POINT IN THIS GEOMETRIC MODEL BUT MY EXISTENTIAL-RELIGIOUS POSITION CAN COMPLETELY
GO AGAINST THIS POINT OF VIEW... I CAN CLAIM I HAVE MY OWN CIRCLE OF ONE POINT & IT DOES NOT AT ALL APPEAR IN THE MODEL!... This is one nice thing about ISLAM that I like: it does not destroy one's INDIVIDUALITY... Even if one goes to pray with the JAMAAH still after that one can pray alone by oneself... Even the PROPHET practiced such silent aloneness (not loneliness - one may be alone but one is not necessarily lonely & one may be in a crowd of laughing humans & yet one is sadly alone!!!) THus, there are SUFIs and other
interpreters of ISLAM who believe there is an HIDDEN ESOTERIC side to the QuR'AN & the DEEN etcetctetc
PART 2 OF 2
HIJRAH 1430 Sha'ban 24
Sunday, August 16, 2009 GC
At Home
Continuation
=========================================
"MUTUALLY-EXCLUSIVE & JOINTLY-EXHAUSTIVE"
=========================================
THE CIRCLE OF THREE RELIGIONS [ANOTHER JAMAAL ORIGINAL TADAAHHHH!!!]
Continuing my grade school diagram of the three major ABRAHAMIC faiths... One who identifies himself with only one or just two or all three of the three major world religions may view human beings as being classified or falling into one of three areas of the seven (7) sectors in the diagram. Three sectors are colored and the other four I simply label with the letters "A", "B" & "C" and the center sector with the numeral "1". If the three circles represent all human beings belonging
to the three religions of ISLAM, JUDAISM & CHRISTIANITY, then we may consider the RED sector as those individuals who are exclusively JEWS, the BLUE sector as "pure" CHRISTANS & the GREEN as exclusively MUSLIMS. There are no half-cooked, half-breeds, 50-50, so-so in these sectors. [ALWAYS REMEMBER or NEVER FORGET: this is just a model & overly-simplified...] Now, what or who are those found/located/represented in sectors A, B & C? And those in the middle sector 1? I would say that those in sectors A would form the intersection of JEWS & CHRISTIANS, meaning those whose father might be a JEW & mother a CHRISTIAN & professes either religion [But I think one can be a real Jew only if one's mother is a JEWESS...?] These can also be the sector of the ALLIANCE of JEWS & CHRISTIANS (Those who believe JEWS & CHRISTIANS are not antagonistic to each other & may even be allied...) Similarly
sector B would be those JEWS & MUSLIMS who are allied or do not consider the other as enemy & sector C would form the sector of MUSLIM-CHRISTIAN alliance... There is a saying that "your enemies enemy is your ally" or something similar but I don't fully agree with this...
Anyway, the point in this exercise is the diagram shows us that there is the possibility (We are not claiming that indeed "there actually exists" out there in the real world) of alliances between MUSLIMS & CHRISTIANS, JEWS & MUSLIMS, & CHRISTIAN & JEWS. IF (Those who are not familiar with COUNTERFACTUALS may research/read a little in popular books on Philosophy or the Internet.) - IF the colored sectors represent "purists" who reject the "unpure" then we may say that the colored sectors represent mutually exclusive sectors of MUSLIMS, CHRISTIANS & JEWS... And the intersecting sectors would be the less antagonistic as in accomodating sectors of each RELIGION... Sector A may represent the MUSLIM-JEW ALLIANCE AGAINST CHRISTIANS, sector B may represent the CHRISTIAN-JEW ALLIANCE AGAINST MUSLIMS, and sector C may be the MUSLIM-CHRISTIAN ALLIANCE AGAINST JEWS! And the central sector would be the universalists as in those who find all three religions as all acceptable & NOT EXCLUSIVIST. Does this mean that those in sector 1 are AGAINST the PURISTS in all three religions? Or does this mean that sector 1 represents those who can go along peacefully with any member of any of the three religions?... I PREFER TO VIEW SECTOR 1 AS THE TRUE MUSLIM WHO IS ALSO THE TRUE CHRISTIAN & THE TRUE JEW... THE TRUE MUSLIM IS NON-DIFFERENT FROM THE TRUE CHRISTIAN & THE TRUE JEW.
DEAR READER, What do your think?
Exercise (in futility:) or Homework:
How about well-known or popular individual personalities whom we have come to identify with this or that religion like the present Roman Catholic Pope Benedict or Pope John Paul II or Usamah Binladin or Saudi King Abdullah or ex-Pres. George Bush or Pres. Obama or Yasser Arafat or Ayatullah Khomeini or ETCETCETCETCETCETC...
WHERE WILL YOU LOCATE EACH PERSONALITY? WHAT DOES IT MEAN FOR THEM TO BE LOCATED WITHIN THAT SECTOR OF OUR GEOMETRIC MODEL?
If Mr. X hates Jews & believes in an alliance of Muslims & Christians against the third party, then Mr. X would fall in sector C. But is this interpretation correct or true?
WHAT IS THE TRUE?
SPECIAL BONUS PROBLEM:
USING THE SAME MODEL ANALYZE THE MAJOR RELIGIONS OF THE WORLD
INCLUDING HINDUISM, BUDDHISM, SHINTOISM, CONFUCIANISM, CONFUSIONISM ETC ETC TO BE SUBMITTED "PASA" ASAP
HIJRAH 1430 Sha'ban 25
Monday, August 17, 2009
UP DILIMAN CAMPUS
GEOMETRY & MATHEMATICS OF RELIGION
PART 1 OF 2
Geometrical/Mathematical Tool for aiding one's thinking about concepts
WARNING: GROSSLY OVERSIMPLIFIED
Consider the three circles intersecting at their centers... I will not go into the geometry of the plane figures but those who studied high school geometry know that a lot of theorems can be derived from such a configuration... I will use the circles a la Venn Diagram or Euler Circle... I shall try to categorize & classify human beings according to their professed religions & simplify the case to just the three major ABRAHAMIC faiths: Judaism, Islam & Christianity... [PORTION DELETED]
Now consider the mathematical model of the intersecting circles wherein masses of human beings are represented as plane areas This is an extremely simplified model because other individuals or groups of human beings are not represented - where are the ATHEISTS or AGNOSTICS, the HINDUS, the BUDDHISTS, the CONFUCIANS the ANIMISTS, the NEW AGERS, the WICCANS, the DEVIL-WORSHIPPERS etcetcetc... But this is precisely one purpose of (mathematical) modeling, to simplify a problem so that a pattern may be discerned... Of course the modeller should be aware of the limitations of the model she is using... And what conclusions are justified or may be derived from the limited model... In real science, + or - approximations and margins for error are provided... SCIENCE WAS, IS AND ALWAYS WILL BE A "THEORY" AS IN AN UNFINISHED ENDEAVOR...
The three circles divide the plane into seven(7) contiguous (close together) sectors. These sectors are similar because the image has some symmetry... We let the plane represent the human beings who adopt/profess even NOMINALLY (just in name or in public documents though they never follow the religion's commandments, injunctions or teachings... So all Christians are found within the circle of CHRISTIANS, all Muslims are within the ISLAM circle & the Jews are found within the JEW circle.
OH BY THE WAY NOT ALL THINKING INDIVIDUALS AGREE WITH SUCH MATHEMATICAL MODELLING OF HUMAN BEINGS (ONE OF THEM IS LYNDON LAROUCHE WHO CRITICIZES THE WAY THINKERS SINCE NEWTON INCLUDING SUCH FIGURES AS JOHN VON NEUMAN ETCETC HAVE GROSSLY OVERSIMPLIFIED HUMAN BEINGS... The crucial element, the HUMAN FACTOR, the HUMANITY of the INDIVIDUAL HUMAN is not presented... Nevertheless, one can see the possible practical uses of such models
in crowd study, crowd control, handling masses of people, mass classification etctetc MARXISTS I think adopt such broad generalizations with their conceptions of CLASS, PROLETARIAT , etctetc Of course the PHILOSOPHY OF MARXISM IS DIALECTICAL MATERIALISM...
OF COURSE, I AM AWARE THAT I MYSELF CAN BE TREATED AS A MERE POINT IN THIS GEOMETRIC MODEL BUT MY EXISTENTIAL-RELIGIOUS POSITION CAN COMPLETELY
GO AGAINST THIS POINT OF VIEW... I CAN CLAIM I HAVE MY OWN CIRCLE OF ONE POINT & IT DOES NOT AT ALL APPEAR IN THE MODEL!... This is one nice thing about ISLAM that I like: it does not destroy one's INDIVIDUALITY... Even if one goes to pray with the JAMAAH still after that one can pray alone by oneself... Even the PROPHET practiced such silent aloneness (not loneliness - one may be alone but one is not necessarily lonely & one may be in a crowd of laughing humans & yet one is sadly alone!!!) THus, there are SUFIs and other
interpreters of ISLAM who believe there is an HIDDEN ESOTERIC side to the QuR'AN & the DEEN etcetctetc
PART 2 OF 2
HIJRAH 1430 Sha'ban 24
Sunday, August 16, 2009 GC
At Home
Continuation
=========================================
"MUTUALLY-EXCLUSIVE & JOINTLY-EXHAUSTIVE"
=========================================
THE CIRCLE OF THREE RELIGIONS [ANOTHER JAMAAL ORIGINAL TADAAHHHH!!!]
Continuing my grade school diagram of the three major ABRAHAMIC faiths... One who identifies himself with only one or just two or all three of the three major world religions may view human beings as being classified or falling into one of three areas of the seven (7) sectors in the diagram. Three sectors are colored and the other four I simply label with the letters "A", "B" & "C" and the center sector with the numeral "1". If the three circles represent all human beings belonging
to the three religions of ISLAM, JUDAISM & CHRISTIANITY, then we may consider the RED sector as those individuals who are exclusively JEWS, the BLUE sector as "pure" CHRISTANS & the GREEN as exclusively MUSLIMS. There are no half-cooked, half-breeds, 50-50, so-so in these sectors. [ALWAYS REMEMBER or NEVER FORGET: this is just a model & overly-simplified...] Now, what or who are those found/located/represented in sectors A, B & C? And those in the middle sector 1? I would say that those in sectors A would form the intersection of JEWS & CHRISTIANS, meaning those whose father might be a JEW & mother a CHRISTIAN & professes either religion [But I think one can be a real Jew only if one's mother is a JEWESS...?] These can also be the sector of the ALLIANCE of JEWS & CHRISTIANS (Those who believe JEWS & CHRISTIANS are not antagonistic to each other & may even be allied...) Similarly
sector B would be those JEWS & MUSLIMS who are allied or do not consider the other as enemy & sector C would form the sector of MUSLIM-CHRISTIAN alliance... There is a saying that "your enemies enemy is your ally" or something similar but I don't fully agree with this...
Anyway, the point in this exercise is the diagram shows us that there is the possibility (We are not claiming that indeed "there actually exists" out there in the real world) of alliances between MUSLIMS & CHRISTIANS, JEWS & MUSLIMS, & CHRISTIAN & JEWS. IF (Those who are not familiar with COUNTERFACTUALS may research/read a little in popular books on Philosophy or the Internet.) - IF the colored sectors represent "purists" who reject the "unpure" then we may say that the colored sectors represent mutually exclusive sectors of MUSLIMS, CHRISTIANS & JEWS... And the intersecting sectors would be the less antagonistic as in accomodating sectors of each RELIGION... Sector A may represent the MUSLIM-JEW ALLIANCE AGAINST CHRISTIANS, sector B may represent the CHRISTIAN-JEW ALLIANCE AGAINST MUSLIMS, and sector C may be the MUSLIM-CHRISTIAN ALLIANCE AGAINST JEWS! And the central sector would be the universalists as in those who find all three religions as all acceptable & NOT EXCLUSIVIST. Does this mean that those in sector 1 are AGAINST the PURISTS in all three religions? Or does this mean that sector 1 represents those who can go along peacefully with any member of any of the three religions?... I PREFER TO VIEW SECTOR 1 AS THE TRUE MUSLIM WHO IS ALSO THE TRUE CHRISTIAN & THE TRUE JEW... THE TRUE MUSLIM IS NON-DIFFERENT FROM THE TRUE CHRISTIAN & THE TRUE JEW.
DEAR READER, What do your think?
Exercise (in futility:) or Homework:
How about well-known or popular individual personalities whom we have come to identify with this or that religion like the present Roman Catholic Pope Benedict or Pope John Paul II or Usamah Binladin or Saudi King Abdullah or ex-Pres. George Bush or Pres. Obama or Yasser Arafat or Ayatullah Khomeini or ETCETCETCETCETCETC...
WHERE WILL YOU LOCATE EACH PERSONALITY? WHAT DOES IT MEAN FOR THEM TO BE LOCATED WITHIN THAT SECTOR OF OUR GEOMETRIC MODEL?
If Mr. X hates Jews & believes in an alliance of Muslims & Christians against the third party, then Mr. X would fall in sector C. But is this interpretation correct or true?
WHAT IS THE TRUE?
SPECIAL BONUS PROBLEM:
USING THE SAME MODEL ANALYZE THE MAJOR RELIGIONS OF THE WORLD
INCLUDING HINDUISM, BUDDHISM, SHINTOISM, CONFUCIANISM, CONFUSIONISM ETC ETC TO BE SUBMITTED "PASA" ASAP
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