Euler Diagram

This article is about Eulerian circles of set theory and logic. For the geometric Euler circle, see Nine-point circle.

An Euler diagram illustrating that the set of "animals with four legs" is a subset of "animals", but the set of "minerals" is disjoint (has no members in common) with "animals".

An Euler diagram is a diagrammatic means of representing sets and their relationships. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783). They are closely related to Venn diagrams.

Venn 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 by other curriculum fields such as reading.^[1]

Contents 1 Overview 2 History 3 Example: Euler- to Venn-diagram and Karnaugh map 4 Gallery 5 Footnotes 6 References 7 External links

Overview

Euler diagrams consist of simple closed curves (usually circles) in the plane that depict sets. The sizes or shapes of the curves are not important: the significance of the diagram is in how they overlap. The spatial relationships between the regions bounded by each curve (overlap, containment or neither) corresponds to set-theoretic relationships (intersection, subset and disjointness).
Each Euler curve divides the plane into two regions or "zones": the interior, which symbolically represents the elements of the set, and the exterior, which represents all elements that are not members of the set. Curves whose interior zones do not intersect represent disjoint sets. Two curves whose interior zones intersect represent sets that have common elements; the zone inside both curves represents the set of elements common to both sets (the intersection of the sets). A curve that is contained completely within the interior zone of another represents a subset of it.

Examples of small Venn diagrams (on left) with shaded regions representing empty sets, showing how they can be easily transformed into equivalent Euler diagrams (right).

Venn diagrams are a more restrictive form of Euler diagrams. A Venn diagram must contain all the possible zones of overlap between its curves, representing all combinations of inclusion/exclusion of its constituent sets, but in an Euler diagram some zones might be missing. When the number of sets grows beyond 3, or even with three sets, but under the allowance of more than two curves passing at the same point, we start seeing the appearance of multiple mathematically unique Venn diagrams. Venn diagrams represent the relationships between n sets, with 2ⁿ zones, Euler diagrams may not have all zones. (An example is given below in the History section; in the top-right illustration the O and I diagrams are merely rotated; Venn stated that this difficulty in part led him to develop his diagrams).

In a logical setting, one can use model theoretic semantics to interpret Euler diagrams, within a universe of discourse. In the examples above, the Euler diagram depicts that the sets Animal and Mineral are disjoint since the corresponding curves are disjoint, and also that the set Four Legs is a subset of the set of Animals. The Venn diagram, which uses the same categories of Animal, Mineral, and Four Legs, does not encapsulate these relationships. Traditionally the emptiness of a set in Venn diagrams is depicted by shading in the region. Euler diagrams represent emptiness either by shading or by the use of a missing region.
Often a set of well-formedness conditions are imposed; these are topological or geometric constraints imposed on the structure of the diagram. For example, connectedness of zones might be enforced, or concurrency of curves or multiple points might be banned, as might tangential intersection of curves. In the diagram to the right, examples of small Venn diagrams are transformed into Euler diagrams by sequences of transformations; some of the intermediate diagrams have concurrency of curves. However, this sort of transformation of a Venn diagram with shading into an Euler diagram without shading is not always possible. There are examples of Euler diagrams with 9 sets that are not drawable using simple closed curves without the creation of unwanted zones since they would have to have non-planar dual graphs.
 

History

 

Photo of page from Hamilton's 1860 "Lectures" page 180. (Click on it, up to two times, to enlarge). The symbolism A, E, I, and O refer to the four forms of the syllogism. The small text to the left says: "The first employment of circular diagrams in logic improperly ascribed to Euler. To be found in Christian Weise."

On the right is a photo of page 74 from Couturat 1914 wherein he labels the 8 regions of the Venn diagram. The modern name for these "regions" is minterms. These are shown on the left with the variables x, y and z per Venn's drawing. The symbolism is as follows: logical AND ( & ) is represented by arithmetic multiplication, and the logical NOT ( ~ )is represented by " ' " after the variable, e.g. the region x'y'z is read as "NOT x AND NOT y AND z" i.e. ~x & ~y & z.

Both the Veitch and Karnaugh diagrams show all the minterms, but the Veitch is not particularly useful for reduction of formulas. Observe the strong resemblance between the Venn and Karnaugh diagrams; the colors and the variables x, y, and z are per Venn's example.

As shown in the illustration to the right, Sir William Hamilton in his posthumously published Lectures on Metaphysics and Logic (1858–60) asserts that the original use of circles to "sensualize ... the abstractions of Logic" (p. 180) was not Leonhard Paul Euler (1707–1783) but rather Christian Weise (?–1708) in his Nucleus Logicoe Weisianoe that appeared in 1712 posthumously. He references Euler's Letters to a German Princess on different Matters of Physics and Philosophy¹" [¹Partie ii., Lettre XXXV., ed. Cournot. – ED.]^[2]
In Hamilton's illustration the four forms of the syllogism as symbolized by the drawings A, E, I and O are:^[3]

• A: The Universal Affirmative, Example: "All metals are elements".
• E: The Universal Negative, Example: "No metals are compound substances".
• I: The Particular Affirmative, Example: "Some metals are brittle".
• O: The Particular Negative, Example: "Some metals are not brittle".

In his 1881 Symbolic Logic Chapter V "Diagrammatic Representation", John Venn (1834–1923) comments on the remarkable prevalence of the Euler diagram:

"...of the first sixty logical treatises, published during the last century or so, which were consulted for this purpose:-somewhat at random, as they happened to be most accessible :-it appeared that thirty four appealed to the aid of diagrams, nearly all of these making use of the Eulerian Scheme." (Footnote 1 page 100)

Composite of two pages 115–116 from Venn 1881 showing his example of how to convert a syllogism of three parts into his type of diagram. Venn calls the circles "Eulerian circles" (cf Sandifer 2003, Venn 1881:114 etc) in the "Eulerian scheme" (Venn 1881:100) of "old-fashioned Eulerian diagrams" (Venn 1881:113).

But nevertheless, he contended "the inapplicability of this scheme for the purposes of a really general Logic" (page 100) and in a footnote observed that "it fits in but badly even with the four propositions of the common Logic [the four forms of the syllogism] to which it is normally applied" (page 101). Venn ends his chapter with the observation that will be made in the examples below – that their use is based on practice and intuition, not on a strict algorithmic practice:

“In fact ... those diagrams not only do not fit in with the ordinary scheme of propositions which they are employed to illustrate, but do not seem to have any recognized scheme of propositions to which they could be consistently affiliated.” (pp. 124–125)

Finally, in his Chapter XX HISTORIC NOTES Venn gets to a crucial criticism (italicized in the quote below); observe in Hamilton's illustration that the O (Particular Negative) and I (Particular Affirmative) are simply rotated:

"We now come to Euler's well-known circles which were first described in his Lettres a une Princesse d'Allemagne (Letters 102–105). The weak point about these consists in the fact that they only illustrate in strictness the actual relations of classes to one another, rather than the imperfect knowledge of these relations which we may possess, or wish to convey, by means of the proposition. Accordingly they will not fit in with the propositions of common logic, but demand the constitution of a new group of appropriate elementary propositions.... This defect must have been noticed from the first in the case of the particular affirmative and negative, for the same diagram is commonly employed to stand for them both, which it does indifferently well". (italics added: page 424)

(Sandifer 2003 reports that Euler makes such observations too; Euler reports that his figure 45 (a simple intersection of two circles) has 4 different interpretations). Whatever the case, armed with these observations and criticisms, Venn then demonstrates (pp. 100–125) how he derived what has become known as his Venn diagrams from the "old-fashioned Euler diagrams". In particular he gives an example, shown on the left.
By 1914 Louis Couturat (1868–1914) had labeled the terms as shown on the drawing on the right. Moreover, he had labeled the exterior region (shown as a'b'c') as well. He succinctly explains how to use the diagram – one must strike out the regions that are to vanish:

"VENN'S method is translated in geometrical diagrams which represent all the constituents, so that, in order to obtain the result, we need only strike out (by shading) those which are made to vanish by the data of the problem." (italics added p. 73)

Given the Venn's assignments, then, the unshaded areas inside the circles can be summed to yield the following equation for Venn's example:

"No Y is Z and ALL X is Y: therefore No X is Z" has the equation x'yz' + xyz' + x'y'z for the unshaded area inside the circles (but note that this is not entirely correct; see the next paragraph).

In Venn the 0th term, x'y'z', i.e. the background surrounding the circles, does not appear. Nowhere is it discussed or labeled, but Couturat corrects this in his drawing. The correct equation must include this unshaded area shown in boldface:

"No Y is Z and ALL X is Y: therefore No X is Z" has the equation x'yz' + xyz' + x'y'z + x'y'z' .

In modern usage the Venn diagram includes a "box" that surrounds all the circles; this is called the universe of discourse or the domain of discourse.
Couturat now observes that, in a direct algorithmic (formal, systematic) manner, one cannot derive reduced Boolean equations, nor does it show how to arrive at the conclusion "No X is Z". Couturat concluded that the process "has ... serious inconveniences as a method for solving logical problems":

"It does not show how the data are exhibited by canceling certain constituents, nor does it show how to combine the remaining constituents so as to obtain the consequences sought. In short, it serves only to exhibit one single step in the argument, namely the equation of the problem; it dispenses neither with the previous steps, i. e., "throwing of the problem into an equation" and the transformation of the premises, nor with the subsequent steps, i. e., the combinations that lead to the various consequences. Hence it is of very little use, inasmuch as the constituents can be represented by algebraic symbols quite as well as by plane regions, and are much easier to deal with in this form."(p. 75)

Thus the matter would rest until 1952 when Maurice Karnaugh (1924– ) would adapt and expand a method proposed by Edward W. Veitch; this work would rely on the truth table method precisely defined in Emil Post's 1921 PhD thesis "Introduction to a general theory of elementary propositions" and the application of propositional logic to switching logic by (among others) Claude Shannon, George Stibitz, and Alan Turing.^[4] For example, in chapter "Boolean Algebra" Hill and Peterson (1968, 1964) present sections 4.5ff "Set Theory as an Example of Boolean Algebra" and in it they present the Venn diagram with shading and all. They give examples of Venn diagrams to solve example switching-circuit problems, but end up with this statement:

"For more than three variables, the basic illustrative form of the Venn diagram is inadequate. Extensions are possible, however, the most convenient of which is the Karnaugh map, to be discussed in Chapter 6." (p. 64)

In Chapter 6, section 6.4 "Karnaugh Map Representation of Boolean Functions" they begin with:

"The Karnaugh map¹ [¹Karnaugh 1953] is one of the most powerful tools in the repertory of the logic designer. ... A Karnaugh map may be regarded either as a pictorial form of a truth table or as an extension of the Venn diagram." (pp. 103–104)

The history of Karnaugh's development of his "chart" or "map" method is obscure. Karnaugh in his 1953 referenced Veitch 1951, Veitch referenced Claude E. Shannon 1938 (essentially Shannon's Master's thesis at M.I.T.), and Shannon in turn referenced, among other authors of logic texts, Couturat 1914. In Veitch's method the variables are arranged in a rectangle or square; as described in Karnaugh map, Karnaugh in his method changed the order of the variables to correspond to what has become known as (the vertices of) a hypercube.

Example: Euler- to Venn-diagram and Karnaugh map

This example shows the Euler and Venn diagrams and Karnaugh map deriving and verifying the deduction "No X's are Z's". In the illustration and table the following logical symbols are used:

1 can be read as "true", 0 as "false"

~ for NOT and abbreviated to ' when illustrating the minterms e.g. x' =_defined NOT x,

+ for Boolean OR (from Boolean algebra: 0+0=0, 0+1 = 1+0 = 1, 1+1=1)

& (logical AND) between propositions; in the mintems AND is omitted in a manner similar to arithmetic multiplication: e.g. x'y'z =_defined ~x & ~y & z (From Boolean algebra: 0*0=0, 0*1 = 1*0=0, 1*1 = 1, where * is shown for clarity)

→ (logical IMPLICATION): read as IF ... THEN ..., or " IMPLIES ", P → Q =_defined NOT P OR Q

Before it can be presented in a Venn diagram or Karnaugh Map, the Euler diagram's syllogism "No Y is Z, All X is Y" must first be reworded into the more formal language of the propositional calculus: " 'It is not the case that: Y AND Z' AND 'If an X then a Y' ". Once the propositions are reduced to symbols and a propositional formula ( ~(y & z) & (x → y) ), one can construct the formula's truth table; from this table the Venn and/or the Karnaugh map are readily produced. By use of the adjacency of "1"s in the Karnaugh map (indicated by the grey ovals around terms 0 and 1 and around terms 2 and 6) one can "reduce" the example's Boolean equation i.e. (x'y'z' + x'y'z) + (x'yz' + xyz') to just two terms: x'y' + yz'. But the means for deducing the notion that "No X is Z", and just how the reduction relates to this deduction, is not forthcoming from this example.

Given a proposed conclusion such as "No X is a Z", one can test whether or not it is a correct deduction by use of a truth table. The easiest method is put the starting formula on the left (abbreviate it as "P") and put the (possible) deduction on the right (abbreviate it as "Q") and connect the two with logical implication i.e. P → Q, read as IF P THEN Q. If the evaluation of the truth table produces all 1's under the implication-sign (→, the so-called major connective) then P → Q is a tautology. Given this fact, one can "detach" the formula on the right (abbreviated as "Q") in the manner described below the truth table.
Given the example above, the formula for the Euler and Venn diagrams is:

"No Y's are Z's" and "All X's are Y's": ( ~(y & z) & (x → y) ) =_defined P

And the proposed deduction is:

"No X's are Z's": ( ~ (x & z) ) =_defined Q

So now the formula to be evaluated can be abbreviated to:

( ~(y & z) & (x → y) ) → ( ~ (x & z) ): P → Q

IF ( "No Y's are Z's" and "All X's are Y's" ) THEN ( "No X's are Z's" )

The Truth Table demonstrates that the formula ( ~(y & z) & (x → y) ) → ( ~ (x & z) ) is a tautology as shown by all 1's in yellow column..

Square #	Venn, Karnaugh region		x	y	z		(~	(y	&	z)	&	(x	→	y))	→	(~	(x	&	z))
0	x'y'z'		0	0	0		1	0	0	0	1	0	1	0	1	1	0	0	0
1	x'y'z		0	0	1		1	0	0	1	1	0	1	0	1	1	0	0	1
2	x'yz'		0	1	0		1	1	0	0	1	0	1	1	1	1	0	0	0
3	x'yz		0	1	1		0	1	1	1	0	0	1	1	1	1	0	0	1
4	xy'z'		1	0	0		1	0	0	0	0	1	0	0	1	1	1	0	0
5	xy'z		1	0	1		1	0	0	1	0	1	0	0	1	0	1	1	1
6	xyz'		1	1	0		1	1	0	0	1	1	1	1	1	1	1	0	0
7	xyz		1	1	1		0	1	1	1	0	1	1	1	1	0	1	1	1

At this point the above implication P → Q (i.e. ~(y & z) & (x → y) ) → ~(x & z) ) is still a formula, and the deduction – the "detachment" of Q out of P → Q – has not occurred. But given the demonstration that P → Q is tautology, the stage is now set for the use of the procedure of modus ponens to "detach" Q: "No X's are Z's" and dispense with the terms on the left.^[5]
Modus ponens (or "the fundamental rule of inference"^[6]) is often written as follows: The two terms on the left, "P → Q" and "P", are called premises (by convention linked by a comma), the symbol ⊢ means "yields" (in the sense of logical deduction), and the term on the right is called the conclusion:

P → Q, P ⊢ Q

For the modus ponens to succeed, both premises P → Q and P must be true. Because, as demonstrated above the premise P → Q is a tautology, "truth" is always the case no matter how x, y and z are valued, but "truth" will only be the case for P in those circumstances when P evaluates as "true" (e.g. rows 0 OR 1 OR 2 OR 6: x'y'z' + x'y'z + x'yz' + xyz' = x'y' + yz').^[7]

P → Q , P ⊢ Q

i.e.: ( ~(y & z) & (x → y) ) → ( ~ (x & z) ) , ( ~(y & z) & (x → y) ) ⊢ ( ~ (x & z) )

i.e.: IF "No Y's are Z's" and "All X's are Y's" THEN "No X's are Z's", "No Y's are Z's" and "All X's are Y's" ⊢ "No X's are Z's"

One is now free to "detach" the conclusion "No X's are Z's", perhaps to use it in a subsequent deduction (or as a topic of conversation).
The use of tautological implication means that other possible deductions exist besides "No X's are Z's"; the criterion for a successful deduction is that the 1's under the sub-major connective on the right include all the 1's under the sub-major connective on the left (the major connective being the implication that results in the tautology). For example, in the truth table, on the right side of the implication (→, the major connective symbol) the bold-face column under the sub-major connective symbol " ~ " has the all the same 1s that appear in the bold-faced column under the left-side sub-major connective & (rows 0, 1, 2 and 6), plus two more (rows 3 and 4).

Gallery

• 

  A Venn diagram shows all possible intersections.
• 

  Euler diagram visualizing a real situation, the relationships between various supranational European organisations.
• 

  Euler diagram visualizing a real situation, the relationships between various supranational African organisations.
• 

  Humorous diagram comparing Euler and Venn diagrams.
• 

  Euler diagram of types of triangles, assuming isosceles triangles have at least 2 equal sides.
• 

  Euler diagram of terminology of the British Isles.

Footnotes

1. ^ Strategies for Reading Comprehension Venn Diagrams
2. ^ By the time these lectures of Hamilton were published, Hamilton too had died. His editors (symbolized by ED.), responsible for most of the footnoting, were the logicians Henry Longueville Mansel and John Veitch.
3. ^ Hamilton 1860:179. The examples are from Jevons 1881:71ff.
4. ^ See footnote at George Stibitz.
5. ^ This is a sophisticated concept. Russell and Whitehead (2nd edition 1927) in their Principia Mathematica describe it this way: "The trust in inference is the belief that if the two former assertions [the premises P, P→Q ] are not in error, the final assertion is not in error . . . An inference is the dropping of a true premiss [sic]; it is the dissolution of an implication" (p. 9). Further discussion of this appears in "Primitive Ideas and Propositions" as the first of their "primitive propositions" (axioms): *1.1 Anything implied by a true elementary proposition is true" (p. 94). In a footnote the authors refer the reader back to Russell's 1903 Principles of Mathematics §38.
6. ^ cf Reichenbach 1947:64
7. ^ Reichenbach discusses the fact that the implication P → Q need not be a tautology (a so-called "tautological implication"). Even "simple" implication (connective or adjunctive) will work, but only for those rows of the truth table that evaluate as true, cf Reichenbach 1947:64–66.

References

By date of publishing:

• Sir William Hamilton 1860 Lectures on Metaphysics and Logic edited by Henry Longueville Mansel and John Veitch, William Blackwood and Sons, Edinburgh and London.
• W. Stanley Jevons 1880 Elemetnary Lessons in Logic: Deductive and Inductive. With Copious Questions and Examples, and a Vocabulary of Logical Terms, M. A. MacMillan and Co., London and New York.
• John Venn 1881 Symbolic Logic, MacMillan and Co., London.
• Alfred North Whitehead and Bertrand Russell 1913 1st edition, 1927 2nd edition Principia Mathematica to *56 Cambridge At The University Press (1962 edition), UK, no ISBN.
• Louis Couturat 1914 The Algebra of Logic: Authorized English Translation by Lydia Gillingham Robinson with a Preface by Philip E. B. Jourdain, The Open Court Publishing Company, Chicago and London.
• Emil Post 1921 "Introduction to a general theory of elementary propositions" reprinted with commentary by Jean van Heijenoort in Jean van Heijenoort, editor 1967 From Frege to Gödel: A Sourcebook of Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA, ISBN 0-674-42449-8 (pbk.)
• Claude E. Shannon 1938 "A Symbolic Analysis of Relay and Switching Circuits", Transactions American Institute of Electrical Engineers vol 57, pp. 471–495. Derived from Claude Elwood Shannon: Collected Papers edited by N.J.A. Solane and Aaron D. Wyner, IEEE Press, New York.
• Hans Reichenbach 1947 Elements of Symbolic Logic republished 1980 by Dover Publications, Inc., NY, ISBN 0-486-24004-5.
• Edward W. Veitch 1952 "A Chart Method for Simplifying Truth Functions", Transactions of the 1952 ACM Annual Meeting, ACM Annual Conference/Annual Meeting "Pittsburgh", ACM, NY, pp. 127–133.
• Maurice Karnaugh November 1953 The Map Method for Synthesis of Combinational Logic Circuits, AIEE Committee on Technical Operations for presentation at the AIEE summer General Meeting, Atlantic City, N. J., June 15–19, 1953, pp. 593–599.
• Frederich J. Hill and Gerald R. Peterson 1968, 1974 Introduction to Switching Theory and Logical Design, John Wiley & Sons NY, ISBN 0-71-39882-9.
• Ed Sandifer 2003 How Euler Did It, http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2003%20Venn%20Diagrams.pdf

External links

Wikimedia Commons has media related to: Euler diagrams

• Euler Diagrams. Brighton, UK (2004).What are Euler Diagrams?
• Visualisation with Euler diagrams project

Where is LHC Headed?

The speakers are: Michael Peskin (author of the famous QFT textbook) Nima Arkani-Hamed, Riccardo Rattazzi, Gavin Salam, Matt Strassler and Raman Sundrum (or Randall-Sundrum fame).

Illusions of Grandeur?

Illusions of Gravity

Three spatial dimensions are visible all around us--up/down, left/right, forward/backward. Add time to the mix, and the result is a four-dimensional blending of space and time known as spacetime. Thus, we live in a four-dimensional universe. Or do we?

Amazingly, some new theories of physics predict that one of the three dimensions of space could be a kind of an illusion--that in actuality all the particles and fields that make up reality are moving about in a two-dimensional realm like the Flatland of Edwin A. Abbott. Gravity, too, would be part of the illusion: a force that is not present in the two-dimensional world but that materializes along with the emergence of the illusory third dimension.

UC Berkeley's Raphael Bousso presents a friendly introduction to the ideas behind the holographic principle, which may be very important in the hunt for a theory of quantum gravity. Series: "Lawrence Berkeley National Laboratory Summer Lecture Series" [3/2006] [Science] [Show ID: 11140]

This is just a recoup of what had been transpiring since 2005. We have a pretty good picture of the ways such distinctions are held for perspective so that we may look inside the black hole? The labels of this blog entry help with this refreshing.

See Also:

• Graviton in a Can?  

• CFT and the Tomato Soup Can 

•  A Conformal Field Theory Approach?

Questions on the History of Mathematics

Arthur Miller
Einstein and Schrödinger never fully accepted the highly abstract nature of Heisenberg's quantum mechanics, says Miller. They agreed with Galileo's assertion that "the book of nature is written in mathematics", but they also realized the power of using visual imagery to represent mathematical symbols.

For most people I am sure it is of little interest that such an abstract language could have ever amounted to anything,since we might have been circumscribed to the natural living that is required that we could do without it. But really,  can we?

 Paul Dirac 

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

So of course one appreciates those who start the conversation to help raise the questions in ones own mind. Might it be a shared response to something existing deeper in our society that it would warrant descriptions that we might be lacking in. Ways in which to describe something about nature. There is something definitely to be said about the geometer that can visualize the spaces within which they are working. It has to make sense. It has to describe something? Why then not just plain English(whatever language you choose)

String theory's mathematical tools were designed to unlock the most profound secrets of the cosmos, but they could have a far less esoteric purpose: to tease out the properties of some of the most complex yet useful types of material here on Earth.What Good are Mathematics in the Real World?

Do you know how many mathematical expressions are needed in order to describe the theory?

 The language of physics is mathematics. In order to study physics seriously, one needs to learn mathematics that took generations of brilliant people centuries to work out. Algebra, for example, was cutting-edge mathematics when it was being developed in Baghdad in the 9th century. But today it's just the first step along the journey.Guide to math needed to study physics

Conversations on Mind, Matter, and Mathematics

How mathematics arose from cognitive realizations. Ex. Newton and Calculus. The branches of mathematics. Who are it's developers and what did they develop and why?

 It may be as important as the history in relation to how one may perceive the history and development of mathematics. These were important insights into the way one might of asked how did emergence exist if such things could have been imagined in the mind of the beholder. To attempt to describe nature in the way that one might do by invention? So are these mathematical things discovered or are they invented? Why the history is important?

 This is the basis of the question of what already exists in terms of information has always existed and we are only getting a preview of a much more complicated system. It does not have to be a question of what a MBT exemplifies in itself, but raises the questions about what already exists, exists as part of what always existed. Where do ideas and mathematics come from?

This is a foundation stance that is taken right throughout science? If it exists in the universe, it exists in you? How does one connect?

See Also:

WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION? 

See Also: Some Educational links to look at then.

•  Wolfram\alpha
-What is Wolfram\Alpha
• Khan Academy

The Birth of String Theory

• Edited by: Andrea Cappelli, Istituto Nazionale di Fisica Nucleare (INFN), Florence
• Edited by: Elena Castellani, Università degli Studi di Firenze, Italy
• Edited by: Filippo Colomo, Istituto Nazionale di Fisica Nucleare (INFN), Florence
• Edited by: Paolo Di Vecchia, Niels Bohr Institutet, Copenhagen and Nordita, Stockholm

A Path With a Heart

"All paths lead nowhere,so it is important to choose a path that has heart."
-- Carlos Castenada

Update: I am re-posting this article from 2006. I wanted to highlight this post in relation to the idea of intent. What it means to me.  I wanted as well to show the need for, to be enable conventionality into our own lives. If one cannot find such meaning,  does one find them self as if tossed on the waves of some chaotic life living by rote?

Yes, I find it important that this idea of "a tonal"  leaves the impression in my mind and others of the closeness with which sincerity is expressed through our own feelings and the need for such convictions.

If we understand the the anticipated future is part of our living our lives then it should come as no shock that we are the architects of the time we have in living our lives as we do. That the probable futures and probable pasts come from taking a position in life regardless of the idea that not only is it causal toward our projections, but it also within the scope of our reason that we can live or lives as true as possible.



What happens to a culture raised in the early years that we might have felt that we were getting the messages from someone who understood something greater then ourselves. The baby boomers were all part of the process. I was part of the process in that I wanted to explore unconventional thinking.

While I have move forward to the principles of scientific standards today in my explorations I have to say this was indeed part of my past too. So what has come of the points about sophistical questions about our existence?

Shall we stay so blinded then to what could have transpire in our lives to have the myths transported from our own generations past to  be carried forward to another today to have missed the understandings of the times then?





Some of the older folk probably have read the many books of Carlos Castaneda, like I have? Drawn into a strange world of thinking, it challenged my thought processes.  Most of it I was not accustom too. Did Carlos Castaneda actually exist? Was he some fictional character created, to tell the stories?

Anything is one of a million paths. Therefore you must always keep in mind that a path is only a path; if you feel you should not follow it, you must not stay with it under any conditions. To have such clarity you must lead a disciplined life. Only then will you know that any path is only a path and there is no affront, to oneself or to others, in dropping it if that is what your heart tells you to do. But your decision to keep on the path or to leave it must be free of fear or ambition. I warn you. Look at every path closely and deliberately. Try it as many times as you think necessary.

This question is one that only a very old man asks. Does this path have a heart? All paths are the same: they lead nowhere. They are paths going through the bush, or into the bush. In my own life I could say I have traversed long long paths, but I am not anywhere. Does this path have a heart? If it does, the path is good; if it doesn't, it is of no use. Both paths lead nowhere; but one has a heart, the other doesn't. One makes for a joyful journey; as long as you follow it, you are one with it. The other will make you curse your life. One makes you strong; the other weakens you.

Before you embark on any path ask the question: Does this path have a heart? If the answer is no, you will know it, and then you must choose another path. The trouble is nobody asks the question; and when a man finally realizes that he has taken a path without a heart, the path is ready to kill him. At that point very few men can stop to deliberate, and leave the path. A path without a heart is never enjoyable. You have to work hard even to take it. On the other hand, a path with heart is easy; it does not make you work at liking it.

I have told you that to choose a path you must be free from fear and ambition. The desire to learn is not ambition. It is our lot as men to want to know.

The path without a heart will turn against men and destroy them. It does not take much to die, and to seek death is to seek nothing.

Well I am not going to tell you what to think. I am just going to show some of the things that attracted my attention and brought me to some of the views I have garnered around what the heart actually meant. The lesson was given by a person who told me the story of the picture of the scale weighting the feather, was to be a important one in my recognition of something profound and true. Possibly, to those who understood the message as well?

That was part of my lesson of learning. That a path with a heart was something better then no path at all.

Experimental philosophy

Experimental philosophy is an emerging field of philosophical inquiry^{[1][2][3][4][5]} that makes use of empirical data—often gathered through surveys which probe the intuitions of ordinary people—in order to inform research on philosophical questions.^[6][7] This use of empirical data is widely seen as opposed to a philosophical methodology that relies mainly on a priori justification, sometimes called "armchair" philosophy by experimental philosophers.^[8][9][10] Experimental philosophy initially began by focusing on philosophical questions related to intentional action, the putative conflict between free will and determinism, and causal vs. descriptive theories of linguistic reference.^[11] However, experimental philosophy has continued to expand to new areas of research.

Disagreement about what experimental philosophy can accomplish is widespread. One claim is that the empirical data gathered by experimental philosophers can have an indirect effect on philosophical questions by allowing for a better understanding of the underlying psychological processes which lead to philosophical intuitions.^[12] Others claim that experimental philosophers are engaged in conceptual analysis, but taking advantage of the rigor of quantitative research to aid in that project.^[13][14] Finally, some work in experimental philosophy can be seen as undercutting the traditional methods and presuppositions of analytic philosophy.^[15] Several philosophers have offered criticisms of experimental philosophy.

Contents   1 History 2 Areas of Research 2.1 Consciousness 2.2 Cultural diversity 2.3 Determinism and moral responsibility 2.4 Epistemology 2.5 Intentional action 3 Criticisms 4 References and further reading 5 References 6 External links

 

History

 

Though in early modern philosophy, natural philosophy was sometimes referred to as "experimental philosophy",^[16] the field associated with the current sense of the term dates its origins around 2000 when a small number of students experimented with the idea of fusing philosophy to the experimental rigor of psychology.
While the philosophical movement Experimental Philosophy began around 2000, the use of empirical methods in philosophy far predates the emergence of the recent academic field. Current experimental philosophers claim that the movement is actually a return to the methodology used by many ancient philosophers.^[10][12] Further, other philosophers like David Hume, René Descartes and John Locke are often held up as early models of philosophers who appealed to empirical methodology.^[5][16]

Areas of Research

 

Consciousness

 

The questions of what consciousness is, and what conditions are necessary for conscious thought have been the topic of a long-standing philosophical debate. Experimental philosophers have approached this question by trying to get a better grasp on how exactly people ordinarily understand consciousness. For instance, work by Joshua Knobe and Jesse Prinz (2008) suggests that people may have two different ways of understanding minds generally, and Justin Sytsma and Edouard Machery (2009) have written about the proper methodology for studying folk intuitions about consciousness. Bryce Huebner, Michael Bruno, and Hagop Sarkissian (2010)^[17] have further argued that the way Westerners understand consciousness differs systematically from the way that East Asians understand consciousness, while Adam Arico (2010)^[18] has offered some evidence for thinking that ordinary ascriptions of consciousness are sensitive to framing effects (such as the presence or absence of contextual information). Some of this work has been featured in the Online Consciousness Conference.

Other experimental philosophers have approached the topic of consciousness by trying to uncover the cognitive processes that guide everyday attributions of conscious states. Adam Arico, Brian Fiala, Rob Goldberg, and Shaun Nichols,^[19] for instance, propose a cognitive model of mental state attribution (the AGENCY model), whereby an entity's displaying certain relatively simple features (e.g., eyes, distinctive motions, interactive behavior) triggers a disposition to attribute conscious states to that entity. Additionally, Bryce Huebner^[20] has argued that ascriptions of mental states rely on two divergent strategies: one sensitive to considerations of an entity's behavior being goal-directed; the other sensitive to considerations of personhood.

Cultural diversity

 

Following the work of Richard Nisbett, which showed that there were differences in a wide range of cognitive tasks between Westerners and East Asians, Jonathan Weinberg, Shaun Nichols and Stephen Stich (2001) compared epistemic intuitions of Western college students and East Asian college students. The students were presented with a number of cases, including some Gettier cases, and asked to judge whether a person in the case really knew some fact or merely believed it. They found that the East Asian subjects were more likely to judge that the subjects really knew.^[21] Later Edouard Machery, Ron Mallon, Nichols and Stich performed a similar experiment concerning intuitions about the reference of proper names, using cases from Saul Kripke's Naming and Necessity (1980). Again, they found significant cultural differences. Each group of authors argued that these cultural variances undermined the philosophical project of using intuitions to create theories of knowledge or reference.^[22] However, subsequent studies were unable to replicate Weinberg et al.'s (2001) results for other Gettier cases, with cross-cultural difference appearing only when the Gettier case involved different models of American cars.^[23]

Determinism and moral responsibility

 

One area of philosophical inquiry has been concerned with whether or not a person can be morally responsible if their actions are entirely determined, e.g., by the laws of Newtonian physics. One side of the debate, the proponents of which are called ‘incompatibilists,’ argue that there is no way for people to be morally responsible for immoral acts if they could not have done otherwise. The other side of the debate argues instead that people can be morally responsible for their immoral actions even when they could not have done otherwise. People who hold this view are often referred to as ‘compatibilists.’ It was generally claimed that non-philosophers were naturally incompatibilist,^[24] that is they think that if you couldn’t have done anything else, then you are not morally responsible for your action. Experimental philosophers have addressed this question by presenting people with hypothetical situations in which it is clear that a person’s actions are completely determined. Then the person does something morally wrong, and people are asked if that person is morally responsible for what she or he did. Using this technique Nichols and Knobe (2007) found that "people's responses to questions about moral responsibility can vary dramatically depending on the way in which the question is formulated"^[25] and argue that "people tend to have compatiblist intuitions when they think about the problem in a more concrete, emotional way but that they tend to have incompatiblist intuitions when they think about the problem in a more abstract, cognitive way".^[26]

Epistemology

 

Recent work in experimental epistemology has tested the apparently empirical claims of various epistemological views. For example, research on epistemic contextualism has proceeded by conducting experiments in which ordinary people are presented with vignettes that involve a knowledge ascription.^[27][28][29] Participants are then asked to report on the status of that knowledge ascription. The studies address contextualism by varying the context of the knowledge ascription (for example, how important it is that the agent in the vignette has accurate knowledge). Data gathered thus far show no support for what contextualism says about ordinary use of the term "knows".^[27][28][29] Other work in experimental epistemology includes, among other things, the examination of moral valence on knowledge attributions (the so-called "epistemic side-effect effect")^[30] and judgments about so-called "know-how" as opposed to propositional knowledge.^[31]

Intentional action

 

A prominent topic in experimental philosophy is intentional action. Work by Joshua Knobe has especially been influential.^{[citation needed]} "The Knobe Effect", as it is often called, concerns an asymmetry in our judgments of whether an agent intentionally performed an action. Knobe (2003a) asked people to suppose that the CEO of a corporation is presented with a proposal that would, as a side effect, affect the environment. In one version of the scenario, the effect on the environment will be negative (it will "harm" it), while in another version the effect on the environment will be positive (it will "help" it). In both cases, the CEO opts to pursue the policy and the effect does occur (the environment is harmed or helped by the policy). However, the CEO only adopts the program because he wants to raise profits; he does not care about the effect that the action will have on the environment. Although all features of the scenarios are held constant—except for whether the side effect on the environment will be positive or negative—a majority of people judge that the CEO intentionally hurt the environment in the one case, but did not intentionally help it in the other.^{[citation needed]} Knobe ultimately argues that the effect is a reflection of a feature of the speakers' underlying concept of intentional action: broadly moral considerations affect whether we judge that an action is performed intentionally. However, his exact views have changed in response to further research.^{[citation needed]}

Criticisms

 

Antti Kauppinen (2007) has argued that intuitions will not reflect the content of folk concepts unless they are intuitions of competent concept users who reflect in ideal circumstances and whose judgments reflect the semantics of their concepts rather than pragmatic considerations.^{[citation needed]} Experimental philosophers are aware of these concerns,^[32] and have in some cases explicitly argued against pragmatic explanations of the phenomena they study.^{[citation needed]} In turn, Kauppinen has argued^{[citation needed]} that any satisfactory way of ensuring his three conditions are met would involve dialogue with the subject that would be engaging in traditional philosophy.
Timothy Williamson (2008) has argued that we should not construe philosophical evidence as consisting of intuitions, and that such a conception rests on the "dialectical conception of evidence".^{[citation needed]}

References and further reading

 

• Bengson, J., Moffett, M., & Wright, J.C. (2009). "The Folk on Knowing How". Philosophical Studies, 142(3): 387-401. (link)
• Buckwalter, W. (2010). "Knowledge Isn’t Closed on Saturday: A Study in Ordinary Language", Review of Philosophy and Psychology (formerly European Review of Philosophy), special issue on Psychology and Experimental Philosophy ed. by Edouard Machery, Tania Lombrozo, & Joshua Knobe, 1 (3):395-406. (link)
• Feltz, A. & Zarpentine, C. (2010). "Do You Know More When It Matters Less?" Philosophical Psychology, 23 (5):683–706. (link)
• Kauppinen, A. (2007). "The Rise and Fall of Experimental Philosophy", Philosophical Explorations 10 (2), pp. 95–118. (link)
• Knobe, J. (2003a). "Intentional action and side effects in ordinary language", Analysis 63, pp. 190–193. (link)
• Knobe, J. (2003b). "Intentional action in folk psychology: An experimental investigation", Philosophical Psychology 16, pp. 309–324. (link)
• Knobe, J. (2004a). "Intention, Intentional Action and Moral Considerations", Analysis 64, pp. 181–187.
• Knobe, J. (2004b). "What is Experimental Philosophy?" The Philosophers' Magazine, 28. (link)
• Knobe, J. (2007). "Experimental Philosophy and Philosophical Significance", Philosophical Explorations, 10: 119-122. (link)
• Joshua Michael Knobe; Shaun Nichols (2008). Experimental philosophy. Oxford University Press, USA. ISBN 978-0-19-532326-9.
• Knobe, J. and Jesse Prinz. (2008). "Intuitions about Consciousness: Experimental Studies". Phenomenology and Cognitive Science.(link)
• Kripke, S. (1980). Naming and Necessity. Harvard University Press.
• Machery, E., Mallon, R., Nichols, S., & Stich, S. (2004). "Semantics, Cross-Cultural Style". Cognition 92, pp. B1-B12.
• May, J., Sinnott-Armstrong, W., Hull, J.G. & Zimmerman, A. (2010). "Practical Interests, Relevant Alternatives, and Knowledge Attributions: An Empirical Study", Review of Philosophy and Psychology (formerly European Review of Philosophy), special issue on Psychology and Experimental Philosophy ed. by Edouard Machery, Tania Lombrozo, & Joshua Knobe, Vol. 1, No. 2, pp. 265–273. (link)
• Nichols, S. (2002). "How Psychopaths Threaten Moral Rationalism: Is It Irrational to Be Amoral?" The Monist 85, pp. 285–304.
• Nichols, S. (2004). "After Objectivity: An Empirical Study of Moral Judgment". Philosophical Psychology 17, pp. 5–28.
• Nichols, S. and Folds-Bennett, T. (2003). "Are Children Moral Objectivists? Children's Judgments about Moral and Response-Dependent Properties". Cognition 90, pp. B23-32.
• Nichols, S. & Knobe, J. (2007). Moral Responsibility and Determinism: The Cognitive Science of Folk Intuitions. Nous, 41, 663-685. (link)
• Sandis, C. (2010). "The Experimental Turn and Ordinary Language". Essays in Philosophy Vol. 11: Iss. 2, 181-196. (link)
• Schaffer, J. & Knobe, J. (forthcoming). "Contrastive Knowledge Surveyed". Nous. (link)
• Sytsma, J. & Machery, E. (2009). "How to Study Folk Intuitions about Consciousness". Philosophical Psychology. (link)
• Weinberg, J., Nichols, S., & Stich, S. (2001). "Normativity and Epistemic Intuitions". Philosophical Topics 29, pp. 429–460.
• Williamson, T. (2008). The Philosophy of Philosophy. Wiley-Blackwell.
• Spicer, F. (2009). "The X-philes: Review of Experimental Philosophy, edited by Knobe and Nichols". The Philosophers' Magazine (44): 107. Retrieved 2009-01-08. (link)

References

 

1. ^ Lackman, Jon. The X-Philes Philosophy meets the real world, Slate, March 2, 2006.
2. ^ Appiah, Anthony. The New New Philosophy, New York Times, December 9, 2007.
3. ^ Appiah, Anthony. The 'Next Big Thing' in Ideas, National Public Radio, January 3, 2008.
4. ^ Shea, Christopher. Against Intuition, Chronicle of Higher Education, October 3, 2008.
5. ^ ^{a b} Edmonds, David and Warburton, Nigel. Philosophy’s great experiment, Prospect, March 1, 2009
6. ^ The Experimental Philosophy Page.
7. ^ Prinz, J. Experimental Philosophy, YouTube September 17, 2007.
8. ^ Knobe, Joshua. What is Experimental Philosophy?. The Philosophers' Magazine, (28) 2004.
9. ^ Knobe, Joshua. Experimental Philosophy, Philosophy Compass (2) 2007.
10. ^ ^{a b} Knobe, Joshua. Experimental Philosophy and Philosophical Significance, Philosophical Explorations (10) 2007.
11. ^ Knobe, Joshua. What is Experimental Philosophy? The Philosophers' Magazine (28) 2004.
12. ^ ^{a b} Knobe, Joshua and Nichols, Shaun. An Experimental Philosophy Manifesto, in Knobe & Nichols (eds.) Experimental Philosophy, §2.1. 2008.
13. ^ Lutz, Sebastian. Ideal Language Philosophy and Experiments on Intuitions. Studia Philosophica Estonica 2.2. Special issue: S. Häggqvist and D. Cohnitz (eds.), The Role of Intuitions in Philosophical Methodology, pp. 117–139. 2009
14. ^ Sytsma, Justin. The proper province of philosophy: Conceptual analysis and empirical investigation. Review of Philosophy and Psychology 1(3). Special issue: E. Machery, T. Lombrozo, and J. Knobe (eds.), Psychology and Experimental Philosophy (Part II), pp. 427–445. 2010.
15. ^ Machery, Edouard. What are Experimental Philosophers Doing?. Experimental Philosophy (blog), July 30, 2007.
16. ^ ^{a b} Peter Anstey, "Is x-phi old hat?", Early Modern Experimental Philosophy Blog, 30 August 2010.
17. ^ Huebner, B., Bruno, M., and Sarkissian, H. 2010. "What Does the Nation of China Think about Phenomenal States?", Review of Philosophy and Psychology, 1(2): 225-243.
18. ^ Arico, A. 2010. "Folk Psychology, Consciousness, and Context Effects", Review of Philosophy and Psychology, 1(3): 371-393.
19. ^ Arico, A., Fiala, B., Goldberg, R., and Nichols, S. forthcoming. Mind & Language.
20. ^ Huebner, B. 2010. "Commonsense Concepts of Phenomenal Consciousness: Does Anyone Care about Functional Zombies?" Phenomenology and the Cognitive Sciences, 9 (1): 133-155.
21. ^ Weinberg, J., Nichols, S., & Stich, S. (2001). Normativity and Epistemic Intuitions. Philosophical Topics 29, pp. 429–460.
22. ^ Machery, E., Mallon, R., Nichols, S., & Stich, S. (2004). Semantics, Cross-Cultural Style. Cognition 92, pp. B1-B12.
23. ^ Nagel, J. (forthcoming). "Intuitions and Experiments: A Defense of the Case Method in Epistemology". Philosophy and Phenomenological Research.
24. ^ Nahmias,E., Morris, S., Nadelhoffer, T. & Turner, J. Surveying Freedom: Folk Intuitions about Free Will and Moral Responsibility. Philosophical Psychology (18) 2005 p.563
25. ^ Nichols, Shaun; Knobe, Joshua (2007). "Moral Responsibility and Determinism: The Cognitive Science of Folk Intuitions". Noûs 41 (4): 663–685. (PDF p.2)
26. ^ Phillips, Jonathan, ed. (15 August 2010). "X-Phi Page". Yale. (§Papers on Experimental Philosophy and Metaphilosophy)
27. ^ ^{a b} Phelan,M. Evidence that Stakes Don't Matter for Evidence
28. ^ ^{a b} Feltz, A. & Zarpentine, C. Do You Know More When It Matters Less? Philosophical Psychology.
29. ^ ^{a b} May, J., Sinnott-Armstrong, W., Hull, J. & Zimmerman, A. (2010) Practical Interests, Relevant Alternatives, and Knowledge Attributions: An Empirical Study. Review of Philosophy and Psychology^{[dead link]}
30. ^ Beebe, J. & Buckwalter,W. The Epistemic Side-Effect Effect Mind & Language.
31. ^ Bengson, J., Moffett, M., & Wright, J.C. The Folk on Knowing How, Philosophical Studies, 142(3): 387-401.
32. ^ Sinnott-Armstrong, W. Abstract + Concrete = Paradox, 'in Knobe & Nichols (eds.) Experimental Philosophy, (209-230), 2008.

External links

 

• The Experimental Philosophy Page
• The Experimental Philosophy Blog - with several prominent contemporary philosophers as contributors.
  • (As of July 2009, The Experimental Philosophy Page and Blog list around 120 different contributors who are actively involved with research in experimental philosophy.)
• 'Yale's Experimental Philosophy Lab (EPL)
• Experimental Philosophy Society (XPS)
• Arizona's Experimental Philosophy Lab
• Indiana's Experimental Epistemology Lab
• Schreiner's Behavioral Philosophy Lab
• Bristol's Experimental Philosophy Page
• Buffalo's Experimental Epistemology Research Group (EERG)
• Metro Experimental Research Group (MERG)
• Experimental Philosophy on PhilPapers (Edited by Mark Phelan).
• Xphilosophy YouTube Channel
• Early Modern Experimental Philosophy Blog (University of Otago, New Zealand)

Being Able to See

How does one turn on the internal vision when we use our eyes to look at the day to day happenings with eyes wide open?

What made this interesting for me was the fact that sensory examination could have been used physically by people by no fault of their own under the auspice ofSynesthesia.. This is an examination where the internal wiring causes overlaps in sensory perceptions. So anyway the idea here is that we look at what intentionality means here in the progress toward science and examination of what we can gain in understanding a way in being able to see differently.

Experimental research

In recent years, there has been a large amount of work done on the concept of intentional action in experimental philosophy.^[1] This work has aimed at illuminating and understanding the factors which influence people's judgments of whether an action was done intentionally. For instance, research has shown that unintended side effects are often considered to be done intentionally if the side effect is considered bad and the person acting knew the side effect would occur before acting. Yet when the side effect is considered good, people generally don't think it was done intentionally, even if the person knew it would occur before acting. The most well-known example involves a chairman who implements a new business program for the sole purpose to make money but ends up affecting the environment in the process. If he implements his business plan and in the process he ends up helping the environment, then people generally say he unintentionally helped the environment; if he implements his business plan and in the process he ends up harming the environment, then people generally say he intentionally harmed the environment. The important point is that in both cases his only goal was to make money.^[2] While there have been many explanations proposed for why the "side-effect effect" occurs, researchers on this topic have not yet reached a consensus.

So we understand that there is a physiological effect to how perception can be altered by understanding the effect of  Synesthesia? Such alteration can be given to the idea that if we change the way we see experimental processes as in sound application what comparative analogy can be safe? Can we say that it would be acceptable to science?

For example, in 1704 Sir Isaac Newton struggled to devise mathematical formulas to equate the vibrational frequency of sound waves with a corresponding wavelength of light. He failed to find his hoped-for translation algorithm, but the idea of correspondence took root, and the first practical application of it appears to be the clavecin oculaire, an instrument that played sound and light simultaneously. It was invented in 1725. Charles Darwin’s grandfather, Erasmus, achieved the same effect with a harpsichord and lanterns in 1790, although many others were built in the intervening years, on the same principle, where by a keyboard controlled mechanical shutters from behind which colored lights shne. By 1810 even Goethe was expounding correspondences between color and other senses in his book, Theory of Color. Pg 53, The Man Who Tasted Shapes, by Richard E. Cytowic, M.D.

 What if you caused intentional blindness in the sense that you isolate the sensory effect of allowing eyes to be deprived of light. Force the condition to effect internalize vision to take place?  So, what happens in isolation? Does the mind then rely on the world constructs that we had had during our lifetimes to say that the whole internal world is then the effect of what we had gained in experience through seeing. How do you the separate the effect of or emotive states from the understanding that our perceptions colored the world of experience and then forced it toward a memory induced fabrication of what we had experienced?

Now you say, how did that happen? Such a fast shift from what is apparent in the looking at the world is to see that we had lost control of the visual capabilities of see reality as it is?  There is this understanding that without intentionality  a ruthless world of our emotive states can take over quite easily as we say that all of reality is clean and perfect without the recognition of what science is to mean.

5 types of ATLAS event shape data

The data is first processed using the vast and all-powerful ATLAS software framework. This allows raw data (streams of ones and zeroes) to be converted step-by-step into ‘objects’ such as silicon detector hits and energy deposits. We can reconstruct particles using these objects. The next step is to convert the information into a file containing two or three columns of numbers known as a "breakpoint file". It can also be used as a "note list". This kind of file can be read by compositional software such as the Composers Desktop Project (CDP) and Csound software used for this project. See: How is Data Converted into Sounds

So while you do experiments it is important to have "intentionality" in regard to your experiments? If this is so then what you had done is prepare for the excursion to what you want to find out? You already had some idea? You want to put controls in the environment?



 How do you separate consciousness from the clean lines of experimentation and reality seeking? You can't? Because without it you were not able to put the controls in that you need too,  in order to find something out. You are part of the vibrations.
 
The very fact that all of the environment is based on the factors of sound would have you believe then that such conversions are possible and that all sounds are envisioned within the context of the world of sound controlled?

I want to force you to be able to see differently. I want to convert the reality of existence of seeing in a vibrational mode. How does this translate then into consciousness and experimentation? What will we be able to find out if we change the constraints on or examinations of reality if we force the mind to see so?

The Ganzfeld effect

The  Ganzfeld effect (from German for “complete field”) is a phenomenon of visual perception caused by staring at an undifferentiated and uniform field of color. The effect is described as the loss of vision as the brain cuts off the unchanging signal from the eyes. The result is "seeing black"^[1] - apparent blindness.

History 

 

In the 1930s, research by psychologist Wolfgang Metzger established that when subjects gazed into a featureless field of vision they consistently hallucinated and their electroencephalograms changed.

The Ganzfeld effect is the result of the brain amplifying neural noise in order to look for the missing visual signals. The noise is interpreted in the higher visual cortex, and gives rise to hallucinations. This is similar to dream production because of the brain's state of sensory deprivation during sleep.

The Ganzfeld effect has been reported since ancient times. The adepts of Pythagoras retreated to pitch black caves to receive wisdom through their visions^[2], known as the prisoner's cinema. Miners trapped by accidents in mines frequently reported hallucinations, visions and seeing ghosts when they were in the pitch dark for days. Arctic explorers seeing nothing but featureless landscape of white snow for a long time also reported hallucinations and an altered state of mind.

The effect is a component of a Ganzfeld experiment, a technique used in the field of parapsychology.
The artist James Turrell (partly inspired by clear blue skies) has created many such "Ganzfelds" throughout his oeuvre.

See also

• Sensory deprivation
• Ganzfeld experiment
• Dark retreat
• Floatation tank
• Hypnagogia

 

References

1. ^ Ramesh B. Ganzfeld Effect.
2. ^ Ustinova, Yulia.Caves and the Ancient Greek Mind: Descending Underground in the Search for Ultimate Truth, Oxford University Press US, 2009. ISBN 0199548560

• Wolfgang Metzger, "Optische Untersuchungen am Ganzfeld." Psychologische Forschung 13 (1930) : 6-29. (the first psychophysiological study with regard to Ganzfelds)

 EGG: Did you reach this conclusion through more traditional media, like painting or sculpture?

JT: I haven't had anything to do with either sculpture or painting. I have done works that look painted or works that have form and look like sculpture. I make these spaces that apprehend light for your perception. In a way, it's like Plato's cave, where we are sitting in the cave looking at the reflection of reality with our backs to reality. I make these spaces where the spaces themselves are perceivers or in some way pre-form perception. It's a little bit like what the eye does. I mean, I look at the eye as the most exposed part of the brain, as something that is already forming perception. I make these rooms that are these camera-like spaces that in some way form light, apprehend it to be something that's physically present.

EGG: What happens when you use space this way?

JT: This results in an art that is not about my seeing, it's about your direct perception of the work. I'm interested in having a light that inhabits space, so that you feel light to be physically present. I mean, light is a substance that is, in fact, a thing, but we don't attribute thing-ness to it. We use light to illuminate other things, something we read, sculpture, paintings. And it gladly does this. But the most interesting thing to find is that light is aware that we are looking at it, so that it behaves differently when we are watching it and when we're not, which imbues it with consciousness. Often people say that they want to touch some of the work I do. Well, that feeling is actually coming from the fact that the eyes are touching, the eyes are feeling. And this happens because the eyes are quite sensitive only in low light, for which we were made. We're actually made for this light of Plato's cave, the light of twilight. See: Interview with James Turrell

psychomanteums

The room is set up to optimize psychological effects such as trance. Its key features are low light or near-darkness, flickering light, and a mirror. The dimness represents a form of visual sensory deprivation, a condition helpful to trance induction, the undifferentiated colour without horizon producing the Ganzfeld effect^[4], a state of apparent "blindness". The Ganzfeld experiment replicates the conditions of a psychomanteum where a state of trance may be induced by a uniform field of vision. In the way of strobe or flashing light, stimulus is provided by indirect, moving light in the psychomanteum. Flickering candles or lamps are sometimes recommended to induce hallucination. It is supposed the indeterminate depth of the mirror’s darkness allows the eyes to relax and become unfocused, a state that reduces alertness.^[2]

Dr. Raymond Moody, author of the 1981 book about near death experiences, Life After Life, included the psychomanteum in his research trialling 300 subjects which he recorded in his 1993 book, Reunions. Moody viewed the room as a therapeutic tool to heal grief and bring insight.^[2]