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Six Degrees of Separation

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Posted 12 November 2008 20:34

set_zero:  What is the mathematical memory for the sixth degree equaling the separation of the foot print for this earth.

Anotherwards, does anyone know exactly what this means or have an opinion as to its understanding?

Posted 12 November 2008 21:33

blue eclipse:  The six degrees of separation refers to a state of mathematics that tries to put a pattern to the likeliness of people being linked together only separated by knowing or being acquainted with one particular person on the planet with at least six people between person 1 and person 7. 

There are conflicting theories about the validity of this attempt to find a pattern, some refute the likely hood that only six people separate you from any other person... but strangely enough it only takes one or two people to make a link to someone else on the planet. It's been my experience that you just never know who the people you know might know. It's a Wild World ain't it?

 Posted 12 November 2008 21:58

jeronncase:  Someone tried this before and it didn't fare too well.....hopefully this time it'll get more response.

http://forum.jamesblunt.com/viewtopic.php?t=1600

Posted 13 November 2008 01:49

set_zero:  Does anyone believe that this may be connected to;

Deja Vu..............................

Coincidence........................

if so...................................

if not..................................

for added thought, are there opinions on either one of these subjects?

Posted 13 November 2008 02:16

Faith70: Aside from being a mathematical theory, how is it possible to accurately test this?
Maybe if we took a sample of the human population worldwide, and from the moment of birth every person that the child is/was acquainted with is recorded. Then, say by age 30 the database of names is compared to the other people in the sample...I dunno...that's not going to work either!
Obviously I'm a girl who likes scientific evidence.
It's like the question posed several months back on a thread (I think it was about 'regret'). It questioned whether you would be the same person if you went back and changed some situations because you felt 'regret' about it.
Some said 'definitely not because the sum of all your actions and experiences makes you who you are today, and if those experiences were different, then you would be too" (i agree) and some said "yes you could possibly be exactly the same and in the same circumstance because who's to say that fate wouldn't bring you to the same place' (i agree)
I guess my point is...how can any of these theories be tested?
I love the concept there being 6 degrees of separation, and that there is no such thing as a coincidence, but...I wish we could prove it!
The idea of being connected to everyone else on the planet gives me warm fuzzies...actually that could be from lack of sleep (I thought there was a spider on my arm earlier. DELUSIONAL!)
Here's another conundrum...(excuse spelling..to tired to care)...
Is there any such thing as mental telepathy?
I'd normally be skeptical but I keep having these strange experiences with it.
My newborn son (now 10 ish weeks old) wakes when I start to think of him at night when I'm between being awake and asleep.
It happened with my daughter too when she was born (not anymore). 
In hospital, I'd wake and my milk would let down but he was in the 'special care nursery' (nowhere near). I'd be annoyed with myself for waking up for no good reason when I needed rest. Next thing I knew, my baby would be brought in to me for a feed! It happened over and over and still does. WHAT THA?

Posted 13 November 2008 02:26

blue eclipse:  I don't think it's possible to rule out precognition or telepathy. As for the regrets issue- there is something to be said for your experiences becoming the sum of your personality to a certain extent- but I can honestly say there are certain experiences I could have done with out and been all the better for it. There are some things that happen I think because they were 'destined' to occur. Others are produced from a long line of random coincidence. But there is that variable that no one ever accounts for- free will and choice. Do we ever truly have the control to make a 'choice' contradictory to what may have been intended otherwise?

Posted 13 November 2008 18:08

set_zero:  

Ever heard of 

Cognitive Activism: New Way of Knowing

I saw this on CL (craigslist) in SF Bay Area under Groups, posted after this thread was started.


so is this coincidence? or not? and in addition to that what is it exactly?

Zero

Posted 13 November 2008 18:28

blue eclipse:  i am going to extend this hypothesis- by asking these questions:

IF you rely on intuition to guide your everyday decisions and rarely depend heavily on 'logic and rationalization " are you depending on the powers that be- 'god' - the inner 'guide(9)' that leads you to fulfill your 'destiny'? 

Are you countering the guiding predestined path you are intended to follow when you use pure logic and "rationalize' your choices by discounting the 'spiritual" aspects that would lead your life in a direction that does both you and all of humanity less harm and possibly enables you to be the 'vessel' that 'god' would use to counter act the evil that other people let loose on the world when they use excuses to rationalism their choices for denying personal and spiritual responsibility for their actions and choices?

Posted 13 November 2008 18:48



set_zero:  Intuition means;

1. direct perception of truth, fact, etc., independent of any reasoning process; immediate apprehension. 
2. a fact, truth, etc., perceived in this way. 
3. a keen and quick insight. 
4. the quality or ability of having such direct perception or quick insight. 
5. Philosophy. a. an immediate cognition of an object not inferred or determined by a previous cognition of the same object. 
b. any object or truth so discerned. 
c. pure, untaught, noninferential knowledge. 

Logic means;

1. the science that investigates the principles governing correct or reliable inference. 
2. a particular method of reasoning or argumentation: We were unable to follow his logic. 
3. the system or principles of reasoning applicable to any branch of knowledge or study. 
4. reason or sound judgment, as in utterances or actions: There wasn't much logic in her move. 
5. convincing forcefulness; inexorable truth or persuasiveness: the irresistible logic of the facts. 
6. Computers. logic circuit. 

Rationalisation means;

1. (psychiatry) a defense mechanism by which your true motivation is concealed by explaining your actions and feelings in a way that is not threatening [syn: rationalization] 
2. the cognitive process of making something seem consistent with or based on reason [syn: rationalization] 
3. (mathematics) the simplification of an expression or equation by eliminating radicals without changing the value of the expression or the roots of the equation [syn: rationalization] 
4. the organization of a business according to scientific principles of management in order to increase efficiency [syn: rationalization] 
5. systematic organization; the act of organizing something according to a system or a rationale [syn: systematization 

Power means;

1. ability to do or act; capability of doing or accomplishing something. 
2. political or national strength: the balance of power in Europe. 
3. great or marked ability to do or act; strength; might; force. 
4. the possession of control or command over others; authority; ascendancy: power over men's minds. 
5. political ascendancy or control in the government of a country, state, etc.: They attained power by overthrowing the legal government. 
6. legal ability, capacity, or authority: the power of attorney. 
7. delegated authority; authority granted to a person or persons in a particular office or capacity: the powers of the president. 
8. a document or written statement conferring legal authority. 
9. a person or thing that possesses or exercises authority or influence. 
10. a state or nation having international authority or influence: The great powers held an international conference. 
11. a military or naval force: The Spanish Armada was a mighty power. 
12. Often, powers. a deity; divinity: the heavenly powers. 
13. powers, Theology. an order of angels. Compare angel (def. 1). 
14. Dialect. a large number or amount: There's a power of good eatin' at the church social. 
15. Physics. a. work done or energy transferred per unit of time. Symbol: P 
b. the time rate of doing work. 

16. mechanical energy as distinguished from hand labor: a loom driven by power. 
17. a particular form of mechanical or physical energy: hydroelectric power. 
18. energy, force, or momentum: The door slammed shut, seemingly under its own power. 
19. Mathematics. a. the product obtained by multiplying a quantity by itself one or more times: The third power of 2 is 8. 
b. (of a number x) a number whose logarithm is a times the logarithm of x (and is called the ath power of x). Symbolically, y =xa is a number that satisfies the equation log y = a log x. 
c. the exponent of an expression, as a in xa. 
d. cardinal number (def. 2). 

Destiny means;

1. something that is to happen or has happened to a particular person or thing; lot or fortune. 
2. the predetermined, usually inevitable or irresistible, course of events. 
3. the power or agency that determines the course of events. 
4. (initial capital letter) this power personified or represented as a goddess. 
5. the Destinies, the Fates. 

Then the answer must be Yes for Me, I chose to counter the predestined path that any other intended for this one to follow, for zero means this and this is me;

1. the figure or symbol 0, which in the Arabic notation for numbers stands for the absence of quantity; cipher. 
2. the origin of any kind of measurement; line or point from which all divisions of a scale, as a thermometer, are measured in either a positive or a negative direction. 
3. a mathematical value intermediate between positive and negative values. 
4. naught; nothing. 
5. the lowest point or degree. 
6. Linguistics. the absence of a linguistic element, as a phoneme or morpheme, in a position in which one previously existed or might by analogy be expected to exist, often represented by the symbol 0̷: Inflectional endings were reduced to zero. The alternate of the plural morpheme in “sheep” is zero. 
7. Ordnance. a sight setting for both elevation and windage on any particular range causing a projectile to strike the center of the target on a normal day, under favorable light conditions, with no wind blowing. 
8. Mathematics. a. the identity element of a group in which the operation is addition. 
b. (of a function, esp. of a function of a complex variable) a point at which a given function, usually a function of a complex variable, has the value zero; a root. 

Now, either I have the queerest sense of humor OR I am correct and funny and just like Mr. Blunt on the hunt for the LOVE of my life!! Just borrowing his site for a bit my friends, because I am a strange card, stuck in a deck of Aces and Jacks. Only one other person in or on this earth would like to Deal with me, (that is a pun). 

Poker anyone, bets are set at Zero.

Posted 13 November 2008 18:59

blue eclipse:  lol.. and that is laughter out of a keen sense of the absurdity of how rational and irrational can be the same thing.


-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 

x= -8 
y= 8 

x+y = 0 


LOL!

Posted 13 November 2008 19:05



blue eclipse:  and if you want to delve biologically... 

chromosomes
female- XX (gender sex)
male- XY (gender sex)

http://www.biology-online.org/2/6_sex_chromosomes.htm

Posted 13 November 2008 21:26

set_zero:  Hey Blue,

Will you run the bets for me? Doubt there would be any takers though, most are to caught up in the dream of the unreal. I personally don't think that American T.V. could compare with a trist like this one, so we can do it for the real, in REAL. 

Here and now, we could prove 6 degrees of separation, how? By clocking from the first bet forward. I may be only a shallow test but it would prove all the above one way or another. What do you think? 

By the way, I could feel you laugh at what I wrote and it felt good from here!! I went through a lot of posts on here from you, and I will tell you this, you have something to say and in accordance to the rules and regulations of John Mayer, he says, "Say what you want to say" and you do, don't apologize ever again. 

Sixth degree my dear, hit me back!! 



Trist means;

Trist

Trist\, n. [See Tryst.]

1. Trust. [Obs.] 

2. A post, or station, in hunting. [Obs.] --Chaucer. 

3. A secret meeting, or the place of such meeting; a tryst. See Tryst. [Obs.] 

George Douglas caused a trist to be set between him and the cardinal and four lords; at the which trist he and the cardinal agreed finally. --Letter dated Sept., 1543.



Zero, to the 5th Dimension., 2008/11/13

Posted 13 November 2008 22:02

blue eclipse:  HMM 

1543

numerically 1+5+4+3= 13

1+3= 4

the name of an album by a rock n roll group called "Foreigner' 

four= the number phonetically in Chinese apparently sounds like the word death

Am I playing with a full deck yet? 

You need five cards to play a hand of poker. .. i think Five Card Stud may be just one of the variations. 

A Cardinal of a Christian faith? protestant, catholic or 'other'?

Posted 13 November 2008 22:14

set_zero:  Using Blue's Theory, which in advance I absolutely bet all, we have a 5th card.

2008

numerically 2+0+0+8= 10

1+0=1

Is that a full enough deck? Coincidence? or what? definitely an "other"!

Posted 13 November 2008 22:30

blue eclipse:  interesting

I did not really think about the numerical implications of 2008. or maybe i did but just didn't make the connection consciously. 

today is a 11,13, 2008 day.

1+1+1+3+2+8= 16

1+6= 7

7Even Year Itch- Collective Soul sort of day perhaps? "She Said" 

7 7 7 7

Posted 13 November 2008 22:38

wkdnic:  Was it that night in the Carnival hall at Crompton when the two three degrees tribute acts had a mega scrap and never talkwd to each other again?

read more at http::://http://jamesblunt-s.warnerartists.com/forum/Topic92532-12-1.aspx

Venn diagram

From Wikipedia, the free encyclopedia

Venn diagram showing which uppercase letter glyphs are shared by the Greek, Latin and Russian alphabets

Part of a series on Statistics
Probability theory
Probability axioms
Probability space Sample space Elementary event Event Random variable Probability measure
Complementary event Joint probability Marginal probability Conditional probability
Independence Conditional independence Law of total probability Law of large numbers Bayes' theorem Boole's inequality
Venn diagram Tree diagram
v t e

A Venn diagram (also known as a set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets. They are thus a special case of Euler diagrams, which do not necessarily show all relations. Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships inprobability, logic, statistics, linguistics and computer science.

Contents

  [hide] 

• 1Example
• 2History
• 3Overview
• 4Extensions to higher numbers of sets
  • 4.1Edwards' Venn diagrams
  • 4.2Other diagrams
• 5Related concepts
• 6See also
• 7Notes
• 8References
• 9Further reading
• 10External links

Example[edit]

Sets A (creatures with two legs) and B (creatures that can fly)

This example involves two sets, A and B, represented here as coloured circles. The yellow circle, set A, represents all living creatures that are two-legged. The blue circle, set B, represents the living creatures that can fly. Each separate type of creature can be imagined as a point somewhere in the diagram. Living creatures that both can fly and have two legs—for example, parrots—are then in both sets, so they correspond to points in the area where the blue and orange circles overlap. That area contains all such and only such living creatures.

Humans and penguins are bipedal, and so are then in the orange circle, but since they cannot fly they appear in the left part of the orange circle, where it does not overlap with the blue circle. Mosquitoes have six legs, and fly, so the point for mosquitoes is in the part of the blue circle that does not overlap with the orange one. Creatures that are not two-legged and cannot fly (for example, whales and spiders) would all be represented by points outside both circles.

The combined area of sets A and B is called the union of A and B, denoted by A ∪ B. The union in this case contains all living creatures that are either two-legged or that can fly (or both).

The area in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B. For example, the intersection of the two sets is not empty, because there are points that represent creatures that are in both the orange and blue circles.

History[edit]

Venn diagrams were introduced in 1880 by John Venn in a paper entitled On the Diagrammatic and Mechanical Representation of Propositions and Reasonings in the "Philosophical Magazine and Journal of Science", about the different ways to represent propositions by diagrams.^[1][2] The use of these types of diagrams in formal logic, according to Ruskey and M. Weston, is "not an easy history to trace, but it is certain that the diagrams that are popularly associated with Venn, in fact, originated much earlier. They are rightly associated with Venn, however, because he comprehensively surveyed and formalized their usage, and was the first to generalize them".^[3]

Venn himself did not use the term "Venn diagram" and referred to his invention as "Eulerian Circles".^[2] For example, in the opening sentence of his 1880 article Venn writes, "Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called 'Eulerian circles,' has met with any general acceptance..."^[1] The first to use the term "Venn diagram" was Clarence Irving Lewis in 1918, in his book "A Survey of Symbolic Logic".^[3]

Venn diagrams are very similar to Euler diagrams, which were invented by Leonhard Euler in the 18th century.^{[note 1]} M. E. Baron has noted that Leibniz (1646–1716) in the 17th century produced similar diagrams before Euler, but much of it was unpublished. She also observes even earlier Euler-like diagrams by Ramon Lull in the 13th Century.^[4]

In the 20th century, Venn diagrams were further developed. D.W. Henderson showed in 1963 that the existence of an n-Venn diagram with n-fold rotational symmetry implied thatn was a prime number.^[5] He also showed that such symmetric Venn diagrams exist when n is 5 or 7. In 2002 Peter Hamburger found symmetric Venn diagrams for n = 11 and in 2003, Griggs, Killian, and Savage showed that symmetric Venn diagrams exist for all other primes. Thus rotationally symmetric Venn diagrams exist if and only if n is a prime number.^[6]

Venn diagrams and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s. Since then, they have also been adopted in the curriculum of other fields such as reading.^[7]

Overview[edit]

See also: Set (mathematics) § Basic operations

Intersection of two sets   Union of two sets   Symmetric difference of two sets  Relative complement of A (left) in B (right)   Absolute complement of A in U

A Venn diagram is constructed with a collection of simple closed curves drawn in a plane. According to Lewis,^[8] the "principle of these diagrams is that classes [or sets] be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram. That is, the diagram initially leaves room for any possible relation of the classes, and the actual or given relation, can then be specified by indicating that some particular region is null or is not-null".^[8]:157

Venn diagrams normally comprise overlapping circles. The interior of the circle symbolically represents the elements of the set, while the exterior represents elements that are not members of the set. For instance, in a two-set Venn diagram, one circle may represent the group of all wooden objects, while another circle may represent the set of all tables. The overlapping area or intersection would then represent the set of all wooden tables. Shapes other than circles can be employed as shown below by Venn's own higher set diagrams. Venn diagrams do not generally contain information on the relative or absolute sizes (cardinality) of sets; i.e. they are schematic diagrams.

Venn diagrams are similar to Euler diagrams. However, a Venn diagram for n component sets must contain all 2ⁿ hypothetically possible zones that correspond to some combination of inclusion or exclusion in each of the component sets. Euler diagrams contain only the actually possible zones in a given context. In Venn diagrams, a shaded zone may represent an empty zone, whereas in an Euler diagram the corresponding zone is missing from the diagram. For example, if one set represents dairy products and anothercheeses, the Venn diagram contains a zone for cheeses that are not dairy products. Assuming that in the context cheese means some type of dairy product, the Euler diagram has the cheese zone entirely contained within the dairy-product zone—there is no zone for (non-existent) non-dairy cheese. This means that as the number of contours increases, Euler diagrams are typically less visually complex than the equivalent Venn diagram, particularly if the number of non-empty intersections is small.^[9]

The difference between Euler and Venn diagrams can be seen in the following example. Take the three sets:

• 
• 
• 

The Venn and the Euler diagram of those sets are:

• 

  Euler diagram
 
• 

  Venn diagram

Extensions to higher numbers of sets[edit]

Venn diagrams typically represent two or three sets, but there are forms that allow for higher numbers. Shown below, four intersecting spheres form the highest order Venn diagram that has the symmetry of a simplex and can be visually represented. The 16 intersections correspond to the vertices of a tesseract (or the cells of a 16-cell respectively).

For higher numbers of sets, some loss of symmetry in the diagrams is unavoidable. Venn was keen to find "symmetrical figures...elegant in themselves,"^[10] that represented higher numbers of sets, and he devised a four-set diagram using ellipses (see below). He also gave a construction for Venn diagrams for any number of sets, where each successive curve that delimits a set interleaves with previous curves, starting with the three-circle diagram.

• 

  Venn's construction for 4 sets
 
• 

  Venn's construction for 5 sets
 
• 

  Venn's construction for 6 sets
 
• 

  Venn's four-set diagram using ellipses
 
• 

  Non-example: This Euler diagram isnot a Venn diagram for four sets as it has only 13 regions (excluding the outside); there is no region where only the yellow and blue, or only the red and green circles meet.
 
• 

  Five-set Venn diagram using congruent ellipses in a 5-fold rotationally symmetrical arrangement devised byBranko Grünbaum. Labels have been simplified for greater readability; for example, A denotes A ∩ B^c ∩ C^c ∩ D^c∩ E^c, while BCE denotes A^c ∩ B ∩ C∩ D^c ∩ E.
 
• 

  Six-set Venn diagram made of only triangles (interactive version)

Edwards' Venn diagrams[edit]

• 

  Three sets
 
• 

  Four sets
 
• 

  Five sets
 
• 

  Six sets

A. W. F. Edwards constructed a series of Venn diagrams for higher numbers of sets by segmenting the surface of a sphere. For example, three sets can be easily represented by taking three hemispheres of the sphere at right angles (x = 0, y = 0 and z = 0). A fourth set can be added to the representation by taking a curve similar to the seam on a tennis ball, which winds up and down around the equator, and so on. The resulting sets can then be projected back to a plane to give cogwheel diagrams with increasing numbers of teeth, as shown here. These diagrams were devised while designing a stained-glass window in memory of Venn.

Other diagrams[edit]

Edwards' Venn diagrams are topologically equivalent to diagrams devised by Branko Grünbaum, which were based around intersecting polygons with increasing numbers of sides. They are also 2-dimensional representations of hypercubes.

Henry John Stephen Smith devised similar n-set diagrams using sine curves^[11] with the series of equations

Charles Lutwidge Dodgson devised a five-set diagram.

Related concepts[edit]

Venn diagram as a truth table

Venn diagrams correspond to truth tables for the propositions , , etc., in the sense that each region of Venn diagram corresponds to one row of the truth table.^[12][13] Another way of representing sets is with R-Diagrams.