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Talk:Binary operation

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There's also binary function. Merge them? -- JanHidders

I'm not sure they really mean the same thing. A binary operation is usually an algebraic operation, and is often denoted more like a*b than f(a,b). Probably the article ought to explain this. Also, if I had written the binary operation article from scratch I would have only allowed it to cover functions of the form f : S x S -> S, rather than the general f : S x T -> U. I didn't like to change the original too much, but perhaps it should be changed. In any case it would be a good idea to cross-link binary function and binary operation.

Zundark, 2001-08-08

I agree, binary operations are S x S -> S. This article simply describes functions with two arguments. I think it should be changed, and the popular infix notation a*b for *(a,b) should be mentioned. --AxelBoldt

Oh, you guys don't consider the vector scalar product (V * V -> R) or scaling of vectors (R * V -> V) or matrices ( R * M -> M ), etc to be binary operations? --Buz Cory

Perhaps we should ask "what would Eric Weisstein" have done?" :-) But he doesn't seem to be sure either. There is

http://www.google.com/search?q=cache:LSEQ3bRAKkI:br.crashed.net/~akrowne/crc/math/b/b211.htm+binary+operator+eric+weisstein&hl=en

and there is

http://www.google.com/search?q=cache:FjdWL0BZpB4:www.math.pku.edu.cn/library/encyclopedia/contents/BinaryOperator.html+binary+operator+eric+weisstein&hl=en

which doesn't explicitly require the input domains to be the same. I know that in my own field (computer science) the term is used for any operator that needs two arguments. Perhaps it should be someting like this: -- JanHidders
 * 1) begin with S x S -> S definition
 * 2) something about the notation
 * 3) a remark that sometimes also S x T -> U is possible, with Buz' examples and ref. to binary function

Maybe we should distinguish between a binary operation on a set (S x S->S) and a binary operation as such (S x T->U)? I don't know. --AxelBoldt

I think you are onto something, Axel. Binary operation on a set requires closure for the result, and the elements chosen must also be from the set, so (S x S ->S) makes more sense. WMORRIS

My textbook doesn't agree with the definition used on this article. I guess it is rather a convention or terminology problem than a real issue. It defines a binary operation as "f:AxA -> B". Where closure isn't required. The definition of a Group includes the requirement for closure of course, again, conflicting with the Group article. This is the convention in Israel, I guess.. -- Rotem Dan 14:20 13 Jul 2003 (UTC)
 * Well, from further research, it is actually quite unique to my university. Popular definition in most universities in Israel is f:AxA -> A --Rotem Dan 09:00 26 Jul 2003 (UTC)

At present, there seems to be a compromise between the 'Only operations on a set' and 'General binary functions' alternatives; there is an added section covering some of the 'other' binary operations. However, it does not solve the issue. First of all, I wonder if there hasn't been a confusion between 'scalar product', mentioned as an example supra, and 'scalar multiplication', which now is given as an example in the article. In classical terminology, 'scalar product' is a function $$V \times V \rightarrow R$$ (where V is a vector space over the scalars R, in this context mostly the real numbers); while 'multiplication with scalars' is a function $$R \times V \rightarrow V$$. Some (but far from all) modern textbooks instead use the terms 'dot product' and 'scalar multiplication', respectively. In my opinion, both functions are legitimate candidates for the term 'binary operation'.

Actually, the restriction to the two singly enumerated instances in the present article are not only in conflict with some literature, but with a number of Wikipedia items in the category 'Binary operation'; e.g., Commutative_operation and Outer_product.

Therefore, if no one protests, I think we should change the item, noting that the term is used in different senses in different contexts, sometimes very broadly, including in the Wikipedia notes. If any one does protest, I suggest that he or she briefs through all the items in the category, and lists those that should be omitted or rewritten, if we are to retain the present restricted definition. JoergenB 13:44, 27 August 2006 (UTC)

I would like to see a discussion of the extension of a binary operator to finite sequences through repeated application. For example, the addition operator can be extended to the sum operation, the multiplication operator to the product operation, etc. In general, any binary operator (+) with a left identity can be extended to an operation on finite sequences whose value on the empty sequence is the left identity and whose value on a sequence {a[i]:0 <= i < k+1} of length k + 1 is Sk (+) a[k], where Sk is the value of the operation on the leading subsequence (prefix) {a[i]:0 <= i < k} of length k.

Moreover, what I would really like to see is the generic name for this new operation, which is what I was looking for when I came to this page. I've found the terms "bulk action", "iterated binary operation", and "prefix operation" through google, but haven't seen any clear evidence that any of these terms is in common usage. NoJoy 18:36, 28 October 2005 (UTC)

I don't think "iterated binary operation" would belong in a page about binary operations since it requires a unique left identitity and in the prototypical cases of sum and product notation requires associativity. However a link to such a page would be appropriate if someone who knows enough about it is willing to write it. TooMuchMath 01:50, 13 February 2006 (UTC)

OK, I bit the bullet and added a new page myself. It probably needs help. NoJoy 19:05, 8 June 2006 (UTC)

 * I think you're describing "folding". This is a common notion in functional programming languages, used for recursing (iterating) over data types such as sequences and trees. The only description I can find in Wikipedia is the article Catamorphism, which is the same concept disguised by category theory. However, there should be plenty of stuff on the web if you search for "fold" and "unfold". --Malcohol 10:40, 30 August 2006 (UTC)
 * Oh! I just found your article Iterated_binary_operation which does link to Fold (higher-order function).--Malcohol 10:44, 30 August 2006 (UTC)

--No mention of blob-- The symbol? —Preceding unsigned comment added by 88.106.125.175 (talk) 21:35, 26 February 2008 (UTC)

Closure
It is very tough to determine whether or not closure is necessary in a binary operation from this article. The first paragraph leads one to believe that closure is not required, but then the more precise definition that follows leads one to believe closure is required. Then the article flips back and describes situations where closure is not required. I think the real issue is that the term has been overloaded such that it means slightly different things in different contexts, but this should somehow be made more clear. Mickeyg13 (talk) 17:15, 9 May 2011 (UTC)

 * The subject of closure is discussed in the above section of this Talk page. The current article defines "binary operation on a set" rather than "binary operation".  It would be best to point out in the article that the phrase "on a set" is an important distincion.

 * The article defines "external binary operation" and this may give readers the impression that an "external binary operation" is a more general mathematical object that a "binary operation". Tashiro (talk) 17:55, 22 January 2015 (UTC)

Commutivity
Is the line: "If the operation is commutative, ab = ba, then the value depends only on the multiset a,b,c." Meant to have (a,b),c, where a and b must be together. For it to not matter where c comes in terms of a and b, i.e between a and b, then wouldn't it also require associativity, where it doesn't matter if you do a and b first, or b and c? The next line states it depends only on the multiset a,b,c if it is both associative and commutative. — Preceding unsigned comment added by 149.171.197.62 (talk • contribs)

 * I fixed it, intended formatting changed the meaning.--Patrick (talk) 07:24, 8 August 2011 (UTC)

Mistake?
The article says "More precisely, a binary operation on a set S is a binary relation that maps elements of the Cartesian product S × S to S"

Isn't a binary operation supposed to be a function? This isn't even mentioned in the article. Instead it says it is a binary relation, wich is not a function so should be wrong. — Preceding unsigned comment added by 186.58.23.226 (talk) 16:07, 28 March 2012 (UTC)

 * You are right. This is now fixed. Bill Cherowitzo (talk) 04:47, 30 September 2012 (UTC)

The article opens with:

 * a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

Isn't this a special case of a binary operation? Surely a binary operation is a special case of an operation? Recalling the definition of an operation: an operation is an action or procedure which produces a new value from zero or more input values. Thus a binary operation is surely defined as follows:

 * a binary operation is an action or procedure which produces a new value from two input values

I actually favour a revision to operation too: an operation is a calculation from zero or more input values to an output value. This enables a binary operation to be defined as: a binary operation is calculation from two input values to an output value. — Preceding unsigned comment added by 80.215.158.122 (talk) 12:08, 2 September 2015 (UTC)

Merge with Binary relation?
These two articles appear to cover the same subject, but neither so much as reference or link to the other. I'm inclined to suggest that they be merged together. Thoughts/questions/concerns? --Ipatrol (talk) 17:46, 26 November 2018 (UTC)
 * These are completely different things: a binary operation takes two elements and returns a third one, generally in the same set. The basic examples are addition (+) and multiplication (×). A binary relation takes also two elements, but returns true or false, which mean related and unrelated. Basic examples are =, ≠, <, ≤, ... There are absolutely no reason for a merge. On the contrary, a merge would be confusing for most readers. D.Lazard (talk) 18:43, 26 November 2018 (UTC)
 * I agree with D.Lazard, the only thing in common with these articles is the word "binary". The reason there are no links between these articles is that there are no connections. --Bill Cherowitzo (talk) 20:10, 26 November 2018 (UTC)
 * I agree with D.Lazard and Bill Cherowitzo. From a computer-science point of view, a binary relation could be considered as a special case of a binary operation, with result type . However, in mathematics (in particular in 1st-order predicate logic), operations and relations are usually considered completely different things. - Jochen Burghardt (talk) 21:01, 26 November 2018 (UTC)
 * Well binary operations could be considered a kind of binary relation. Specifically, they are subsets of $$(R \times S) \times T$$. The introduction assumes $$R = S = T$$, and for "external binary operations" relaxes that to just $$R = S$$. However, I understand your point that they describe different things. I would then propose the article be extended or rewritten to be similar in layout to Binary relations, containing a short listing of all the symmetry properties that a binary operation can have, like the associative property, commutative property, distributive property, and so forth. Thoughts? --Ipatrol (talk) 18:17, 28 November 2018 (UTC)
 * No, binary operations cannot be considered as binary relations, as they are ternary relations (relation between their two arguments and their result). However WP articles should be written to be accessible to the largest possible audience, and must proceed by increasing degree of technicality (see WP:TECHNICAL). For this point of view, Binary operation is much better than Binary relation, although the former may be improved. For example, the lead of Binary relation contains many terms that are known only by people having a very good mathematical knowledge, such as Cartesian product (in the first sentence), or power set. Also, the most elementary relations (equality and inequalities) are presented after the divisibility relation (much more technical), and the example of inequalities between numbers are not clearly presented (only their generalizations to various areas are explicitly mentioned). In the body, the properties that are used in all mathematics (for example reflexivity, transitivity, symmetry and anti-symmetry) are defined after or between much more technical properties that are known and used only by specialists of relations and graphs. So, if an article deserves to be rewritten, this is Binary relation, not Binary operation. D.Lazard (talk) 19:13, 28 November 2018 (UTC)
 * I think both articles could stand to be rewritten, although some of your critiques of Binary relation I feel are inapplicable as those terms are linked to articles which define them. I think a short listing of commonly-named symmetry properties would be a useful addition to this article, as they help connect to a variety of algebraic structures, and I cannot find any such listing on Wikipedia either as an article, category, or infobox. --Ipatrol (talk) 20:54, 3 December 2018 (UTC)

Is it f: A × A → A, f: A × A → B or f: A × B → C?
The article is rather vague about it. Could one explain it somehow better, like "usually binary operation means f: A × A → A, while f: A × B → C is called binary function, but sometimes binary operation means f: A × B → C, while f: A × A → A is called internal binary operation" (I am not sure that this is true)? There is certainly an inconsistency between Operation (mathematics), where f: A × A → B is called a binary operation, and Binary function, where f: A × A → A is called a binary operation. Wikisaurus (talk) 22:37, 6 May 2020 (UTC)
 * This is not a WP inconsistency. This an inconsistency of the common mathematics terminology. This is rather common for mathematical concepts that need not to be formally defined, because one considers only specific example, without considering the whole class of objects. Nevertheless, I have edited the article for making clear that both terminologies are used. D.Lazard (talk) 03:41, 7 May 2020 (UTC)

title: Talk:Binary operation


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Butterfly effect

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

The term is closely associated with the work of mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972. He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.

The idea that small causes may have large effects in weather was earlier acknowledged by French mathematician and physicist Henri Poincaré. American mathematician and philosopher Norbert Wiener also contributed to this theory. Lorenz's work placed the concept of instability of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.

The butterfly effect concept has since been used outside the context of weather science as a broad term for any situation where a small change is supposed to be the cause of larger consequences.

History
In The Vocation of Man (1800), Johann Gottlieb Fichte says "you could not remove a single grain of sand from its place without thereby ... changing something throughout all parts of the immeasurable whole".

Chaos theory and the sensitive dependence on initial conditions were described in numerous forms of literature. This is evidenced by the case of the three-body problem by Poincaré in 1890. He later proposed that such phenomena could be common, for example, in meteorology.

In 1898, Jacques Hadamard noted general divergence of trajectories in spaces of negative curvature. Pierre Duhem discussed the possible general significance of this in 1908.

In 1950, Alan Turing noted: "The displacement of a single electron by a billionth of a centimetre at one moment might make the difference between a man being killed by an avalanche a year later, or escaping."

The idea that the death of one butterfly could eventually have a far-reaching ripple effect on subsequent historical events made its earliest known appearance in "A Sound of Thunder", a 1952 short story by Ray Bradbury. "A Sound of Thunder" features time travel.

More precisely, though, almost the exact idea and the exact phrasing —of a tiny insect's wing affecting the entire atmosphere's winds— was published in a children's book which became extremely successful and well-known globally in 1962, the year before Lorenz published: "'...whatever we do affects everything and everyone else, if even in the tiniest way. Why, when a housefly flaps his wings, a breeze goes round the world.'

-- The Princess of Pure Reason"

In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.

Lorenz wrote: "At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last [decimal] place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution."

In 1963, Lorenz published a theoretical study of this effect in a highly cited, seminal paper called Deterministic Nonperiodic Flow (the calculations were performed on a Royal McBee LGP-30 computer). Elsewhere he stated: "One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls."

Following proposals from colleagues, in later speeches and papers, Lorenz used the more poetic butterfly. According to Lorenz, when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly's wings in Brazil set off a tornado in Texas? as a title. Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.

The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate, or even prevent the occurrence of a tornado in another location. The butterfly does not power or directly create the tornado, but the term is intended to imply that the flap of the butterfly's wings can cause the tornado: in the sense that the flap of the wings is a part of the initial conditions of an interconnected complex web; one set of conditions leads to a tornado, while the other set of conditions doesn't. The flapping wing represents a small change in the initial condition of the system, which cascades to large-scale alterations of events (compare: domino effect). Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different—but it's also equally possible that the set of conditions without the butterfly flapping its wings is the set that leads to a tornado.

The butterfly effect presents an obvious challenge to prediction, since initial conditions for a system such as the weather can never be known to complete accuracy. This problem motivated the development of ensemble forecasting, in which a number of forecasts are made from perturbed initial conditions.

Some scientists have since argued that the weather system is not as sensitive to initial conditions as previously believed. David Orrell argues that the major contributor to weather forecast error is model error, with sensitivity to initial conditions playing a relatively small role. Stephen Wolfram also notes that the Lorenz equations are highly simplified and do not contain terms that represent viscous effects; he believes that these terms would tend to damp out small perturbations. Recent studies using generalized Lorenz models that included additional dissipative terms and nonlinearity suggested that a larger heating parameter is required for the onset of chaos.

While the "butterfly effect" is often explained as being synonymous with sensitive dependence on initial conditions of the kind described by Lorenz in his 1963 paper (and previously observed by Poincaré), the butterfly metaphor was originally applied to work he published in 1969 which took the idea a step further. Lorenz proposed a mathematical model for how tiny motions in the atmosphere scale up to affect larger systems. He found that the systems in that model could only be predicted up to a specific point in the future, and beyond that, reducing the error in the initial conditions would not increase the predictability (as long as the error is not zero). This demonstrated that a deterministic system could be "observationally indistinguishable" from a non-deterministic one in terms of predictability. Recent re-examinations of this paper suggest that it offered a significant challenge to the idea that our universe is deterministic, comparable to the challenges offered by quantum physics.

In the book entitled The Essence of Chaos published in 1993, Lorenz defined butterfly effect as: "The phenomenon that a small alteration in the state of a dynamical system will cause subsequent states to differ greatly from the states that would have followed without the alteration." This feature is the same as sensitive dependence of solutions on initial conditions (SDIC) in. In the same book, Lorenz applied the activity of skiing and developed an idealized skiing model for revealing the sensitivity of time-varying paths to initial positions. A predictability horizon is determined before the onset of SDIC.

Illustrations

 * {|class="wikitable" width=100%

! colspan=3|The butterfly effect in the Lorenz attractor
 * colspan="2" style="text-align:center;" | time 0 ≤ t ≤ 30 (larger)
 * style="text-align:center;" | z coordinate (larger)
 * colspan="2" style="text-align:center;"|TwoLorenzOrbits.jpg
 * style="text-align:center;"|LorenzCoordinatesSmall.jpg
 * colspan=3 | These figures show two segments of the three-dimensional evolution of two trajectories (one in blue, and the other in yellow) for the same period of time in the Lorenz attractor starting at two initial points that differ by only 10−5 in the x-coordinate. Initially, the two trajectories seem coincident, as indicated by the small difference between the z coordinate of the blue and yellow trajectories, but for t > 23 the difference is as large as the value of the trajectory. The final position of the cones indicates that the two trajectories are no longer coincident at t = 30.
 * style="text-align:center;" colspan="3" | An animation of the Lorenz attractor shows the continuous evolution.
 * }
 * colspan=3 | These figures show two segments of the three-dimensional evolution of two trajectories (one in blue, and the other in yellow) for the same period of time in the Lorenz attractor starting at two initial points that differ by only 10−5 in the x-coordinate. Initially, the two trajectories seem coincident, as indicated by the small difference between the z coordinate of the blue and yellow trajectories, but for t > 23 the difference is as large as the value of the trajectory. The final position of the cones indicates that the two trajectories are no longer coincident at t = 30.
 * style="text-align:center;" colspan="3" | An animation of the Lorenz attractor shows the continuous evolution.
 * }
 * }

Theory and mathematical definition
Recurrence, the approximate return of a system toward its initial conditions, together with sensitive dependence on initial conditions, are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range (approximately a week in the case of weather) since it is impossible to measure the starting atmospheric conditions completely accurately.

A dynamical system displays sensitive dependence on initial conditions if points arbitrarily close together separate over time at an exponential rate. The definition is not topological, but essentially metrical. Lorenz defined sensitive dependence as follows:

The property characterizing an orbit (i.e., a solution) if most other orbits that pass close to it at some point do not remain close to it as time advances.

If M is the state space for the map $$f^t$$, then $$f^t$$ displays sensitive dependence to initial conditions if for any x in M and any δ > 0, there are y in M, with distance $d(., .)$ such that $$0 < d(x, y) < \delta $$ and such that
 * $$d(f^\tau(x), f^\tau(y)) > \mathrm{e}^{a\tau} \, d(x,y)$$

for some positive parameter a. The definition does not require that all points from a neighborhood separate from the base point x, but it requires one positive Lyapunov exponent. In addition to a positive Lyapunov exponent, boundedness is another major feature within chaotic systems.

The simplest mathematical framework exhibiting sensitive dependence on initial conditions is provided by a particular parametrization of the logistic map:
 * $$x_{n+1} = 4 x_n (1-x_n), \quad 0\leq x_0\leq 1,$$

which, unlike most chaotic maps, has a closed-form solution:
 * $$x_{n}=\sin^{2}(2^{n} \theta \pi)$$

where the initial condition parameter $$\theta$$ is given by $$\theta = \tfrac{1}{\pi}\sin^{-1}(x_0^{1/2})$$. For rational $$\theta$$, after a finite number of iterations $$x_n$$ maps into a periodic sequence. But almost all $$\theta$$ are irrational, and, for irrational $$\theta$$, $$x_n$$ never repeats itself – it is non-periodic. This solution equation clearly demonstrates the two key features of chaos – stretching and folding: the factor 2n shows the exponential growth of stretching, which results in sensitive dependence on initial conditions (the butterfly effect), while the squared sine function keeps $$x_n$$ folded within the range [0, 1].

Overview
The butterfly effect is most familiar in terms of weather; it can easily be demonstrated in standard weather prediction models, for example. The climate scientists James Annan and William Connolley explain that chaos is important in the development of weather prediction methods; models are sensitive to initial conditions. They add the caveat: "Of course the existence of an unknown butterfly flapping its wings has no direct bearing on weather forecasts, since it will take far too long for such a small perturbation to grow to a significant size, and we have many more immediate uncertainties to worry about. So the direct impact of this phenomenon on weather prediction is often somewhat wrong."

Differentiating Types of Butterfly Effects
The concept of the butterfly effect encompasses several phenomena. The two kinds of butterfly effects, including the sensitive dependence on initial conditions, and the ability of a tiny perturbation to create an organized circulation at large distances, are not exactly the same. A comparison of the two kinds of butterfly effects and the third kind of butterfly effect   has been documented. In recent studies, it was reported that both meteorological and non-meteorological linear models have shown that instability plays a role in producing a butterfly effect, which is characterized by brief but significant exponential growth resulting from a small disturbance.

Recent Debates on Butterfly Effects
The first kind of butterfly effect, known as SDIC (Sensitive Dependence on Initial Conditions), is widely recognized and demonstrated through idealized chaotic models. However, opinions differ regarding the second kind of butterfly effect, specifically the impact of a butterfly flapping its wings on tornado formation, as indicated in two 2024 articles. For the third kind of butterfly effect, the limited predictability within the Lorenz 1969 model is explained by scale interactions in one article and by system ill-conditioning in another more recent study.

Finite Predictability in Chaotic Systems
According to Lighthill (1986), the presence of SDIC (commonly known as the butterfly effect) implies that chaotic systems have a finite predictability limit. In a literature review, it was found that Lorenz's perspective on the predictability limit can be condensed into the following statement:

 * (A). The Lorenz 1963 model qualitatively revealed the essence of a finite predictability within a chaotic system such as the atmosphere. However, it did not determine a precise limit for the predictability of the atmosphere.
 * (B). In the 1960s, the two-week predictability limit was originally estimated based on a doubling time of five days in real-world models. Since then, this finding has been documented in Charney et al. (1966) and has become a consensus.

Recently, a short video has been created to present Lorenz's perspective on predictability limit.

Revised Perspectives on Chaotic and Non-Chaotic Systems
By revealing coexisting chaotic and non-chaotic attractors within Lorenz models, Shen and his colleagues proposed a revised view that "weather possesses chaos and order", in contrast to the conventional view of "weather is chaotic". As a result, sensitive dependence on initial conditions (SDIC) does not always appear. Namely, SDIC appears when two orbits (i.e., solutions) become the chaotic attractor; it does not appear when two orbits move toward the same point attractor. The above animation for double pendulum motion provides an analogy. For large angles of swing the motion of the pendulum is often chaotic. By comparison, for small angles of swing, motions are non-chaotic. Multistability is defined when a system (e.g., the double pendulum system) contains more than one bounded attractor that depends only on initial conditions. The multistability was illustrated using kayaking in Figure on the right side (i.e., Figure 1 of ) where the appearance of strong currents and a stagnant area suggests instability and local stability, respectively. As a result, when two kayaks move along strong currents, their paths display SDIC. On the other hand, when two kayaks move into a stagnant area, they become trapped, showing no typical SDIC (although a chaotic transient may occur). Such features of SDIC or no SDIC suggest two types of solutions and illustrate the nature of multistability.

By taking into consideration time-varying multistability that is associated with the modulation of large-scale processes (e.g., seasonal forcing) and aggregated feedback of small-scale processes (e.g., convection), the above revised view is refined as follows:

"The atmosphere possesses chaos and order; it includes, as examples, emerging organized systems (such as tornadoes) and time varying forcing from recurrent seasons."

In quantum mechanics
The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics, including atoms in strong fields and the anisotropic Kepler problem. Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments; however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller and John B. Delos and co-workers. The random matrix theory and simulations with quantum computers prove that some versions of the butterfly effect in quantum mechanics do not exist.

Other authors suggest that the butterfly effect can be observed in quantum systems. Zbyszek P. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians. David Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect". Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity. This quantum butterfly effect has been demonstrated experimentally. Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.

In popular culture
The butterfly affect has appeared across mediums such as literature (for instance, A Sound of Thunder), films and television (such as The Simpsons), video games (such as Life Is Strange), AI-driven expansive language models, and more.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Butterfly effect


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Borland

Borland Software Corporation was a computing technology company founded in 1983 by Niels Jensen, Ole Henriksen, Mogens Glad, and Philippe Kahn. Its main business was developing and selling software development and software deployment products. Borland was first headquartered in Scotts Valley, California, then in Cupertino, California, and then in Austin, Texas. In 2009, the company became a full subsidiary of the British firm Micro Focus International plc. In 2023, Micro Focus (including Borland) was acquired by Canadian firm OpenText, which later absorbed Borland's portfolio into its application delivery management division.

The 1980s: Foundations
Borland Ltd. was founded in August 1981 by three Danish citizens – Niels Jensen, Ole Henriksen, and Mogens Glad –  to develop products like Word Index for the CP/M operating system using an off-the-shelf company. However, the response to the company's products at the CP/M-82 show in San Francisco showed that a U.S. company would be needed to reach the American market. They met Philippe Kahn, who had just moved to Silicon Valley and had been a key developer of the Micral.

The three Danes had embarked, at first successfully, on marketing software first from Denmark, and later from Ireland, before running into some challenges when they met Philippe Kahn. Kahn was chairman, president, and CEO of Borland Inc. from its beginning in 1983 until 1995. The company name "Borland" was a creation of Kahn's, taking inspiration from the name of an American Astronaut and then-Eastern Air Lines chairperson Frank Borman. The main shareholders at the incorporation of Borland were Niels Jensen (250,000 shares), Ole Henriksen (160,000), Mogens Glad (100,000), and Kahn (80,000).

Borland International, Inc. era
Borland developed various software development tools. Its first product was Turbo Pascal in 1983, developed by Anders Hejlsberg (who later developed .NET and C# for Microsoft) and before Borland acquired the product which was sold in Scandinavia under the name Compas Pascal. In 1984, Borland launched Sidekick, a time organization, notebook, and calculator utility that was an early terminate-and-stay-resident program (TSR) for MS-DOS compatible operating systems.

By the mid-1980s, the company had an exhibit at the 1985 West Coast Computer Faire along with IBM and AT&T. Bruce Webster reported that "the legend of Turbo Pascal has by now reached mythic proportions, as evidenced by the number of firms that, in marketing meetings, make plans to become 'the next Borland'". After Turbo Pascal and Sidekick, the company launched other applications such as SuperKey and Lightning, all developed in Denmark. While the Danes remained majority shareholders, board members included Kahn, Tim Berry, John Nash, and David Heller. With the assistance of John Nash and David Heller, both British members of the Borland Board, the company was taken public on London's Unlisted Securities Market (USM) in 1986.

Schroders was the lead investment banker. According to the London IPO filings, the management team was Philippe Kahn as president, Spencer Ozawa as VP of Operations, Marie Bourget as CFO, and Spencer Leyton as VP of sales and business development. All software development continued to take place in Denmark and later London as the Danish co-founders moved there. A first US IPO followed in 1989 after Ben Rosen joined the Borland board with Goldman Sachs as the lead banker and a second offering in 1991 with Lazard as the lead banker.

In 1985, Borland acquired Analytica and its Reflex database product. The engineering team of Analytica, managed by Brad Silverberg and including Reflex co-founder Adam Bosworth, became the core of Borland's engineering team in the US. Brad Silverberg was VP of engineering until he left in early 1990 to head up the Personal Systems division at Microsoft. Adam Bosworth initiated and headed up the Quattro project until moving to Microsoft later in 1990 to take over the project which eventually became Access.

In 1987, Borland purchased Wizard Systems and incorporated portions of the Wizard C technology into Turbo C. Bob Jervis, the author of Wizard C became a Borland employee. Turbo C was released on May 18, 1987. This drove a wedge between Borland and Niels Jensen and the other members of his team who had been working on a brand-new series of compilers at their London development centre. They reached an agreement and spun off a company named Jensen & Partners International (JPI), later TopSpeed. JPI first launched an MS-DOS compiler named JPI Modula-2, which later became TopSpeed Modula-2, and followed up with TopSpeed C, TopSpeed C++, and TopSpeed Pascal compilers for both the MS-DOS and OS/2 operating systems. The TopSpeed compiler technology still exists as the underlying technology of the Clarion 4GL programming language, a Windows development tool.

In September 1987, Borland purchased Ansa-Software, including their Paradox (version 2.0) database management tool. Richard Schwartz, a cofounder of Ansa, became Borland's CTO and Ben Rosen joined the Borland board.

The Quattro Pro spreadsheet was launched in 1989. Lotus Development, under the leadership of Jim Manzi, sued Borland for copyright infringement (see Look and feel). The litigation, Lotus Dev. Corp. v. Borland Int'l, Inc., brought forward Borland's open standards position as opposed to Lotus' closed approach. Borland, under Kahn's leadership, took a position of principle and announced that they would defend against Lotus' legal position and "fight for programmer's rights". After a decision in favour of Borland by the First Circuit Court of Appeals, the case went to the United States Supreme Court. Because Justice John Paul Stevens had recused himself, only eight justices heard the case, and concluded in a 4–4 tie. As a result, the First Circuit Court decision remained standing but did not bind any other court and set no national precedent.

Additionally, Borland's approach towards software piracy and intellectual property (IP) included its "Borland no-nonsense license agreement"; allowing the developer/user to utilize its products "just like a book". The user was allowed to make multiple copies of a program, as long as it was the only copy in use at any point in time.

The 1990s: Rise and change
In September 1991, Borland purchased Ashton-Tate, bringing the dBASE and InterBase databases to the house, in an all-stock transaction. However, competition with Microsoft was fierce. Microsoft launched the competing database Microsoft Access and bought the dBASE clone FoxPro in 1992, undercutting Borland's prices. During the early 1990s, Borland's implementation of C and C++ outsold Microsoft's. Borland survived as a company, but no longer dominated the software tools that it once had. It went through a radical transition in products, financing, and staff, and became a very different company from the one which challenged Microsoft and Lotus in the early 1990s.

The internal problems that arose with the Ashton-Tate merger were a large part of the downfall. Ashton-Tate's product portfolio proved to be weak, with no provision for evolution into the GUI environment of Windows. Almost all product lines were discontinued. The consolidation of duplicate support and development offices was costly and disruptive. Worst of all, the highest revenue earner of the combined company was dBASE with no Windows version ready. Borland had an internal project to clone dBASE which was intended to run on Windows and was part of the strategy of the acquisition, but by late 1992 this was abandoned due to technical flaws and the company had to constitute a replacement team (the ObjectVision team, redeployed) headed by Bill Turpin to redo the job.

Borland lacked the financial strength to project its marketing and move internal resources off other products to shore up the dBASE/W effort. Layoffs occurred in 1993 to keep the company afloat, the third instance of this in five years. By the time dBASE for Windows eventually shipped, the developer community had moved on to other products such as Clipper or FoxBase, and dBASE never regained a significant share of Ashton-Tate's former market. This happened against the backdrop of the rise in Microsoft's combined Office product marketing.

A change in market conditions also contributed to Borland's fall from prominence. In the 1980s, companies had few people who understood the growing personal computer phenomenon and so most technical people were given free rein to purchase whatever software they thought they needed. Borland had done an excellent job marketing to those with a highly technical bent. By the mid-1990s, however, companies were beginning to ask what the return was on the investment they had made in this loosely controlled PC software buying spree. Company executives were starting to ask questions that were hard for technically-minded staff to answer, and so corporate standards began to be created. This required new kinds of marketing and support materials from software vendors, but Borland remained focused on the technical side of its products.

In 1993 Borland explored ties with WordPerfect as a possible way to form a suite of programs to rival Microsoft's nascent integration strategy. WordPerfect itself was struggling with a late and troubled transition to Windows. The eventual joint company effort, named Borland Office for Windows (a combination of the WordPerfect word processor, Quattro Pro spreadsheet, and Paradox database) was introduced at the 1993 Comdex computer show. Borland Office never made significant inroads against Microsoft Office. WordPerfect was then bought by Novell. In October 1994, Borland sold Quattro Pro and rights to sell up to a million copies of Paradox to Novell for $140 million in cash, repositioning the company on its core software development tools and the Interbase database engine and shifting toward client-server scenarios in corporate applications. This later proved a good foundation for the shift to web development tools.

Philippe Kahn and the Borland board disagreed on how to focus the company, and Kahn resigned as chairman, CEO and president, after 12 years, in January 1995. Kahn remained on the board until November 7, 1996. Borland named Gary Wetsel as CEO, but he resigned in July 1996. William F. Miller was interim CEO until September of that year, when Whitney G. Lynn (the current Chairman at mergers & acquisitions company XRP Healthcare) became interim president and CEO (along with other executive changes), followed by a succession of CEOs including Dale Fuller and Tod Nielsen.

The Delphi 1 rapid application development (RAD) environment was launched in 1995, under the leadership of Anders Hejlsberg.

In 1996 Borland acquired Open Environment Corporation, a Cambridge-based company founded by John J. Donovan.

On November 25, 1996, Del Yocam was hired as Borland CEO and chairman.

In 1997, Borland sold Paradox to Corel, but retained all development rights for the core BDE. In November 1997, Borland acquired Visigenic, a middleware company that was focused on implementations of CORBA.

Inprise Corporation era
In April 1998, Borland International, Inc. announced it had become Inprise Corporation.

For several years, before and during the Inprise name, Borland suffered from serious financial losses and poor public image. When the name was changed to Inprise, many thought Borland had gone out of business. In March 1999, dBASE was sold to KSoft, Inc. which was soon renamed dBASE Inc. (In 2004 dBASE Inc. was renamed to DataBased Intelligence, Inc.).

In 1999, Dale L. Fuller replaced Yocam. At this time Fuller's title was "interim president and CEO". The "interim" was dropped in December 2000. Keith Gottfried served in senior executive positions with the company from 2000 to 2004.

A proposed merger between Inprise and Corel was announced in February 2000, aimed at producing Linux-based products. The plan was abandoned when Corel's shares fell and it became clear that there was no strategic fit.

InterBase 6.0 was made available as open-source software in July 2000.

In November 2000, Inprise Corporation announced the company intended to officially change its name to Borland Software Corporation. The legal name of the company would continue to be Inprise Corporation until the completion of the renaming process during the first quarter of 2001. Once the name change was completed, the company would also expect to change its Nasdaq market symbol from "INPR" to "BORL".

Borland Software Corporation era
On January 2, 2001, Borland Software Corporation announced it had completed its name change from Inprise Corporation. Effective at the opening of trading on Nasdaq, the company's Nasdaq market symbol would also be changed from "INPR" to "BORL".

Under the Borland name and a new management team headed by president and CEO Dale L. Fuller, a now-smaller and profitable Borland refocused on Delphi and created a version of Delphi and C++Builder for Linux, both under the name Kylix. This brought Borland's expertise in integrated development environments to the Linux platform for the first time. Kylix was launched in 2001.

Plans to spin off the InterBase division as a separate company were abandoned after Borland and the people who were to run the new company could not agree on terms for the separation. Borland stopped open-source releases of InterBase and has developed and sold new versions at a fast pace.

In 2001, Delphi 6 became the first integrated development environment to support web services. All of the company's development platforms now support web services.

C#Builder was released in 2003 as a native C# development tool, competing with Visual Studio .NET. By the 2005 release, C#Builder, Delphi for Win32, and Delphi for .NET were combined into one IDE named "Borland Developer Studio", though it was still popularly known as "Delphi". In late 2002 Borland purchased design tool vendor TogetherSoft and tool publisher Starbase, makers of the StarTeam configuration management tool and the CaliberRM requirements management tool (eventually, CaliberRM was renamed as "Caliber" ). The latest releases of JBuilder and Delphi integrate these tools to give developers a broader set of tools for development.

Former CEO Dale Fuller quit in July 2005, but remained on the board of directors. Former COO Scott Arnold took the title of interim president and chief executive officer until November 8, 2005, when it was announced that Tod Nielsen would take over as CEO effective November 9, 2005. Nielsen remained with the company until January 2009, when he accepted the position of chief operating officer at VMware; CFO Erik Prusch then took over as acting president and CEO.

In early 2007 Borland announced new branding for its focus around open application life-cycle management. In April 2007 Borland announced that it would relocate its headquarters and development facilities to Austin, Texas. It also had development centers in Singapore, Santa Ana, California, and Linz, Austria.

On May 6, 2009, the company announced it was to be acquired by Micro Focus for $75 million. The transaction was approved by Borland shareholders on July 22, 2009, with Micro Focus acquiring the company for $1.50 per share. Following Micro Focus shareholder approval and the required corporate filings, the transaction was completed in late July 2009. Borland was estimated to have 750 employees at the time.

On April 5, 2015, Micro Focus announced the completion of integrating the Attachmate Group of companies that was merged on November 20, 2014. During the integration period, the affected companies were merged into one organization. In the announced reorganization, Borland products would be part of the Micro Focus portfolio.

Subsidiaries

 * Leaders: In October 2005, Borland acquired Leaders, to add its IT management and governance suite, named Tempo, to the Borland product line.
 * CodeGear: On February 8, 2006, Borland announced the divestiture of their IDE division, including Delphi, JBuilder, and InterBase. At the same time, they announced the planned acquisition of Segue Software, a maker of software test and quality tools, to concentrate on application life-cycle management (ALM). On March 20, 2006, Borland announced its acquisition of Gauntlet Systems, a provider of technology that screens software under development for quality and security. On November 14, 2006, Borland announced its decision to separate the developer tools group into a wholly-owned subsidiary. The newly formed operation, CodeGear, was responsible for four IDE product lines. On May 7, 2008, Borland announced the sale of the CodeGear division to Embarcadero Technologies for an expected US$23 million price and US$7 million in CodeGear accounts receivables retained by Borland.

Recent
The products acquired from Segue Software include Silk Central, Silk Performer, and Silk Test. The Silk line was first announced in 1997. Other programs are:

• Borland AppServer

• Borland Caliber DefineIT

• Borland CaliberRM

• Borland Enterprise Server

• Borland Enterprise Studio, for C++, Mobile and Java

• Borland Gauntlet

• StarTeam

• Borland Tempo

• Borland Together for Eclipse

• Visibroker

Historical products
• Borland C++

• Borland Delphi

• Brief (text editor)

• C++Builder, C++BuilderX

• C#Builder

• CodeWright

• Entera (acquired from OEC)

• Eureka: The Solver (numerical solver for mathematical systems of equations)

• IntraBuilder

• JBuilder

• Kylix

• ObjectVision

• Turbo Assembler

• Turbo BASIC (now PowerBASIC)

• Turbo C

• Turbo C++

• Turbo Debugger

• Turbo Delphi

• Turbo Pascal

• Turbo Pascal Database Toolbox

• Turbo Pascal Editor Toolbox

• Turbo Pascal Graphix Toolbox

• Turbo Pascal Numerical Methods Toolbox

• Turbo Pascal Tutor

• Turbo Profiler

• Turbo Prolog (now Visual Prolog)

• dBase

• InterBase

• Borland Paradox

• Sidekick

• Sidekick Plus

• SuperKey

• Turbo Lightning (TSR spell checker)

• Borland Eureka the Solver

• Borland Reflex

• Quattro

• Quattro Pro

• Sprint

• Turbo GameWorks (Turbo Pascal source and executables for bridge, Gomoku, and chess)

• Word Wizard (Requires Turbo Lightning)

Unreleased software

 * Turbo Modula-2: Later sold by TopSpeed as TopSpeed Modula-2.

Marketing

 * CB Magazine: It is an official magazine by Borland Japan. The magazine was republished on April 3, 1997.

Renaming to Inprise Corporation
Along with renaming from Borland International, Inc. to Inprise Corporation, the company refocused its efforts on targeting enterprise applications development. Borland hired a marketing firm Lexicon Branding to come up with a new name for the company. Yocam explained that the new name, Inprise, was meant to evoke "integrating the enterprise". The idea was to integrate Borland's tools, Delphi, C++Builder, and JBuilder with enterprise environment software, including Visigenic's implementations of CORBA, Visibroker for C++ and Java, and the new product, Application Server.

Frank Borland
Frank Borland is a mascot character for Borland products. According to Philippe Kahn, the mascot first appeared in advertisements and the cover of Borland Sidekick 1.0 manual, which was in 1984 during Borland International, Inc. era. Frank Borland also appeared in Turbo Tutor - A Turbo Pascal Tutorial, Borland JBuilder 2.

A live action version of Frank Borland was made after Micro Focus plc had acquired Borland Software Corporation. This version was created by True Agency Limited. An introductory film was also made about the mascot.

title: Borland


text:
Talk:Buckminster Fuller

Practical achievements
Sort these, not all are his: Practical achievements Fuller introduced a number of concepts, and helped develop others. Certainly, a number of his projects were not successful in terms of commitment from industry or acceptance by most of the public. However, more than 500,000 geodesic domes have been built around the world and many are in use. According to the Buckminster Fuller Institute, the largest geodesic-dome structures are:
 * Seagaia Ocean Dome: Miyazaki, Japan, 216 m (710 ft).
 * Multi-Purpose Arena: Nagoya, Japan, 187 m (614 ft).
 * Tacoma Dome: Tacoma, Washington, USA, 162 m (530 ft).
 * Superior Dome: Northern Michigan Univ. Marquette, Michigan, USA, 160 m (525 ft).
 * Walkup Skydome: Northern Arizona Univ. Flagstaff, Arizona, USA, 153 m (502 ft).
 * Poliedro de Caracas: Caracas, Venezuela, 145 m (475 ft).
 * Round Valley High School Stadium: Springerville-Eagar, Arizona, USA, 134 m (440 ft).
 * Former Spruce Goose Hangar: Long Beach, California, USA, 126 m (415 ft).
 * Formosa Plastics Storage Facility: Mai Liao, Taiwan, 123 m (402 ft).
 * Union Tank Car Maintenance Facility: Baton Rouge, Louisiana USA, 117 m (384 ft), destroyed in November 2007.
 * Lehigh Portland Cement Storage Facility: Union Bridge, Maryland USA, 114 m (374 ft).
 * The Eden Project, Cornwall, United Kingdom

Other notable domes include:
 * Spaceship Earth at Disney World's Epcot Center in Florida, 80.8-meters (265 ft) wide (Spaceship Earth is actually a self-supporting geodesic sphere, the only one currently in existence.)
 * The former USA Pavilion at Expo 67 in Montréal - 76 meters wide (250 ft) - became the Montreal Biosphère, an environmental museum on Île Sainte-Hèlène.  In 1967, the US government selected the Dome structure, but did not retain the world vision exposition concept proposed by Buckminster Fuller: A giant Planet Earth Globe within the Dome with a multimedia presentation that would have demonstrated how we could make the world work for all of humanity within 10 years if we switched from "Killingry to Livingry".
 * The Gold Dome in Oklahoma City, formerly a bank and now a multicultural society and business center.
 * Downtown Vancouver, British Columbia, is a geodesic sphere hosting the Telus World of Science, a science centre (formerly called Science World), that was originally the Expo Centre built for Expo 86.
 * The dome over a shopping center in downtown Ankara, Turkey, 109.7-meter (360 ft) tall
 * The dome enclosing a civic center in Stockholm, Sweden, 85.3-meter (280 ft) high.
 * The world's largest aluminum dome formerly housed the “Spruce Goose” airplane in Long Beach Harbor, California, USA.

However, contrary to Fuller's hopes, domes are not an everyday sight in most places. In practice, most of the smaller owner-built geodesic structures had disadvantages (see geodesic domes), including their unconventional appearance.

A spin-off of Fuller's dome-design conceptualization was the Buckminster Ball, which was the official FIFA approved design for footballs (association football), from their introduction at the 1970 World Cup until recently. The design was a truncated icosahedron – essentially a "Geodesic Sphere", consisting of 12 pentagonal and 20 hexagonal panels. This was used continuously for 34 years until replaced by the 14-panel Teamgeist for the 2006 World Cup.

Fuller was followed (historically) by other designers and architects, such as Sir Norman Foster and Steve Baer, willing to explore the possibilities of new geometries in the design of buildings, not based on conventional rectangles.

First paragraph of Biography
Not really sure if this should go in the talk page, but the first paragraph of the biography is not cited. I didn't want to delete it, but it has some trivia-like statements that could easily be inventions of a creative Wikipedia editor. — Preceding unsigned comment added by 75.83.207.60 (talk) 06:25, 6 August 2012 (UTC) Ieashu (talk) 19:10, 21 June 2013 (UTC)

Use of Language and Neologisms
I have removed the sentence 'Fuller considered information 'negative-entropic' from the biography section. The content is true, but it needs elaboration. I have changed the section heading 'Neologisms' to 'Use of Language and Neologisms' because I feel it is important to describe and give examples of Fuller's writing style. The new text is certainly not perfect and neither is the referencing. There are quotes which I feel are very helpful to the reader and it would be gret if there was a way to link to those quotes. Thanks to all for editing / sharing. - Dobtoronto, October 31st 2006

Under the heading Geodesic Dome, the section "... non-believers, Fuller hung from the structure’s framework several students who had helped him build it." should be re-written. The implication is that he hung students, literally, which obviously isn't true. —Preceding unsigned comment added by 216.104.73.235 (talk) 23:32, 18 August 2010 (UTC)

Commemorative stamp
I found this picture of Buckmintser Fuller. (http://img.timeinc.net/time/magazine/archive/covers/1964/1101640110_400.jpg) Is this usable?
 * That's the Time magazine version of his commemorative stamp. A link to info about the stamp is in the external links but I would like to see a mention of the stamp with a thumbnail at the tail of the bio. It's the decent thing to do. • Q^#o • 17:02, 25 June 2009 (UTC)

Poet? Architect?
Fuller is described in the article's intro as "an American visionary, designer, architect, poet, author, and inventor." I admire him as a great man, but:

I have never read his poetry, though given the voluminous and often turgid prose that he wrote and published, I wonder if the poetry he wrote warrants his being described as a "poet"?

In his friend and student J. Baldwin's book, BuckyWorks, Baldwin cites Fuller as referring to architects as "exterior decorators" and apparently being more comfortable seeing himself as a "designer." What about changing the description of Fuller in the intro to "an American visionary, designer, author, and inventor"? To me that would seem more accurate, though I do feel "philosopher" might be added. Joel Russ 17:39, 20 February 2007 (UTC)

 * Bad poetry is still poetry, y'know. --Gwern (contribs) 19:13 20 February 2007 (GMT)

 * It seems to me that including this idea that Fuller was a poet may serve to belittle his other accomplishments, which were substantial. To illustrate what I mean, lets imagine that someone like Steve Wozniak plays golf and enjoys it (and I have no idea if he does or doesn't, in actuality - this being just an analogy).  If this famous and accomplished person simply dabbles in golf, why refer to him as "a golfer" in the first sentence of an encyclopedia article about him, a sentence that lists his major areas of genius or contribution?Joel Russ 00:30, 13 November 2007 (UTC)

Buckminster Fullerene
No mention whatsoever about buckyballs/ buckminster fullerene. -- Jdedmond 20:35, 24 April 2007 (UTC)

Now it is mentioned in the second paragraph. — Preceding unsigned comment added by 98.150.235.107 (talk) 03:45, 25 March 2012 (UTC)

continuous tension discontinuous compression
His first "continuous tension – discontinuous compression" geodesic dome (full sphere in this case) was constructed at the University of Oregon Architecture School in 1959 with the help of students. (Ref: The Dymaxion World of Buckminster Fuller ISBN 0385018045.) These continuous tension – discontinuous compression structures featured single force compression members (no flexure or bending moments) that did not touch each other and were 'suspended' by the tensional members.

What is meant by continuous tension discontinuous compression should be explained. I'd rewrite this if I had any idea what it was trying to say. Maybe a diagram would help? What does it mean they are suspended, they're not actually attached? How can the compression members not touch? What is attached to what? — Preceding unsigned comment added by 98.150.235.107 (talk) 04:00, 25 March 2012 (UTC)

closest packing of spheres
Their construction is based on extending some basic principles to build simple "tensegrity" structures (tetrahedron, octahedron, and the closest packing of spheres), making them lightweight and stable The parenthetical remark at first seems to be a list of examples of tensegrity structures, then tosses in the bit about "closest packing of spheres". This is confusing, since I doubt that "closest packing of spheres" is an example of a tensegrity structure. I get almost a whiff of what the sentence is intended to convey, maybe that sphere packing is one of the basic principles used.. But since I came here knowing little about Fuller or geodesic domes, I hesitate to swap my wild guess for this incomprehensible sentence. Help me! — Preceding unsigned comment added by 98.150.235.107 (talk) 04:28, 25 March 2012 (UTC)

 * I remember the original Earth Day, in Manhattan. I'd been recruited to tie-dye banners to hang from the tall street lamps on Fifth Avenue. Somebody said that we were right upstairs from the headquarters of "Rat", the underground newspaper where the "mad bomber" sent letters predicting where the next bomb would explode. Then, when the day arrived, Bucky came to Columbia to address about 150 people on the concept of spaceship earth. He had peculiar ideas about the filling of space. He argued that using cubes and cubic units to measure space was illogical. I didn't get it. He proposed using another space-filling solid (with square and triangular faces) as a fundamental unit for conceptualizing volume. On the subject of space-filling spheres, he pointed out that a circle could be surrounded by six congruent circles, and they'd all touch their neighbors, so one layer of spheres is perfect, in a way. If you put an identical layer of spheres on top of it, they'd fall into depressions in the first layer, and that would leave out a minimum of volume outside the spheres, or a maximum within them. But when you attempt to add a third layer, things get interesting, because you can place it so the spheres are directly above the ones on the first layer, or you can place it another way. So there's no unique, perfect way to do it. Either way is perfect. [I used to be "Unfree", but I lost my password.] 172.56.26.91 (talk) 09:32, 3 May 2014 (UTC)

Article is written in the tone of a fan-site
I added the 'fan-site' template because the article reads like something a Buckminster Fuller museum tour guide might say to museum-goers. The article needs to be rewritten with an eye towards sobriety. J.R. Hercules 02:09, 4 May 2007 (UTC)

Why deletion of whole sections??
What was the point of deleting the article's sections on Fuller's Practical Achievements and Major Projects? I moved it to the talk section to ask a question. They are applications of the geodesic dome, and probably should be on that page. If they have to be on this page, can it be a quick paragraph or something? Ieashu (talk) 15:43, 27 June 2013 (UTC) And why (other than the lack of alphabetization or some other system of ordering the titles) was the section on literature about Fuller, his work, and his contributions removed? Joel Russ 14:12, 19 May 2007 (UTC)

I believe there used to be a section about his near suicide, which is crucially important to his next phase in life. This needs to be added back into the wikipedia article. — Preceding unsigned comment added by 208.120.1.64 (talk) 06:51, 10 June 2013 (UTC)

Image
The picture of Fuller provided is not the one most people are familiar with (check Google image search to confirm this). In addition, it was taken before he had done anything interesting. I recommend the picture at http://bfi.org/our_programs/who_is_buckminster_fuller

It's well-known and provided by the Buckminster Fuller Institute. I would change it right now, but I wonder if there might be copyright questions. Sonicsuns 05:07, 17 July 2007 (UTC)

 * You're right that copyright is the problem. The current one is Free, but no license is listed for that image and so we must assume it is proprietary and non-Free. Policy/guideline is that removing Free images in favor of non-Free images is something that just shouldn't happen. --Gwern (contribs) 22:00 17 July 2007 (GMT)

He is hot in that picture tho! —Preceding unsigned comment added by 86.140.165.216 (talk) 17:35, 25 July 2009 (UTC)

Non Sequitors/Strange paragraph about Graham Bell
Taken from the biography secion:

"In 1927 at the age of 32, bankrupt and jobless, living in inferior housing in Chicago, Illinois, Fuller lost his young daughter Alexandra to complications from polio and spinal meningitis. He felt responsible, and this drove him to drink and to the verge of suicide. At the last moment he decided instead to embark on "an experiment, to find what a single individual can contribute to changing the world and benefiting all humanity."

'''Alexander Graham Bell: actual inventor of the geodesic formula, and physical creation. Bell worked with many geodesic forms and creations, and is the man who first discoverd and developed the physical geodesic shape. Fulled has fully succumbed to the great inventors original position. Bell, as scientisits are aware was a man of vast discovery, creation and invention. Fuller developed the common structural form used for houses and such.'''

Fuller accepted a position at a small college in North Carolina, Black Mountain College. There, with the support of a group of professors and students, he began work on the project that would make him famous and revolutionize the field of engineering, the geodesic dome. In 1949, he erected the world’s first geodesic dome..."

Just pointing this out.

neckface 63.70.91.229 20:25, 23 July 2007 (UTC)

Strange Link
The link on the word "worldview" from the line "Fuller was one of the first to propagate a systemic worldview..." in "Philosophy and worldview" links to an article about a radio show. I'd fix it, but i have no idea how and don't want to destroy anything.

Henry Ford link
Hi I don't actually know how to do this, but under the Dymaxion House section, you mention how there is one on display at the Henry Ford Museum. You should probably have a link to that page. 69.141.55.59 22:48, 24 September 2007 (UTC)

Bibliography work and unexplained mass-deletion
I've added a complete bibliography list, based on the 2 sources and.

I see there are 2 sections above (Talk:Buckminster Fuller/Archive 1 and ) commenting on the bibliography, and deleted sections, so I searched the history and found: Hopefully someone can take the time to go through that and re-add whatever is appropriate. Thanks. --Quiddity (talk) 21:32, 14 November 2007 (UTC)
 * this extensive vandalism/deletion that was never fixed.

 * I believe I've restored all the useful things. --Gwern (contribs) 22:22 16 November 2007 (GMT)

Debunked
I removed the reference to the word debunked as a Fuller coinage. This is contradicted by the OED, which assigns the word to W.E. Woodward, 1923, in the book "Bunk," and also by Cassels dictionary http://books.google.com/books?id=YzG9fPXE9AMC&pg=PA41&lpg=PA41&dq=%22William+E+Woodward%22+bunk&source=web&ots=BAKPV1bdA6&sig=CwJOCp_I0pBNbp7Gg-RMMUeG2N4&hl=en - which discusses the word origin in terms of a criticism of Henry Ford, who said, "History is more or less bunk.

In the Fuller archives at http://archives.lib.siu.edu/search.php?creatorid=8 it states "The term debunked is often contradicted to be William Woodward’s invention in 1923, rather than Fuller’s later version in 1927." —Preceding unsigned comment added by 24.20.131.50 (talk) 20:45, 13 May 2008 (UTC)

Fuller in Context, and Bias
There's little discussion in this article about Buckminster Fuller's work in the wider context. For example: what geodesic domes were in use before Fuller, can it be argued he invented them, what influence did this have on architecture, in which contexts, who upon. Who were his critics, what effect did he have on larger society, what is his legacy?

I'm afraid that this whole article reads like - and is - an idolisation of Fuller with zero critical content, a biased point of view and no discussion of his work in the wider context. Fuller (I am told by the article) wanted to change the path of humanity. Well, did he succeed? To what degree? How? Who with? Why?

This article is seems obviously very, very heavily watched and moderated by those in charge of the Buckminster Fuller Institute, and is in essence a de-facto homepage for their institute. It seems like they wish to create an article that's rose tinted and puts Fuller on a pedestal. I think many of us, though, would like to create an article that tells a whole, critical and useful story about Fuller. 78.86.149.141 (talk) 15:14, 3 June 2008 (UTC)

Largest dome

The article claims that a "Fantasy Entertainment Complex" on "Kyosho Isle" in Japan, measuring 216 m, is the world's largest geodesic dome. The island of Kyushu indeed has the world's largest dome (at one point), the now closed Seagaia Ocean Dome, but it's 300x100x38m and, being elongated in shape, is not a pure geodesic dome. Should it be removed from this list, or at least tagged with a disclaimer? Jpatokal (talk) 04:28, 26 February 2010 (UTC)

 * Thank you for making this connection. I have updated the list, which has been moved to Geodesic dome.  --Lasunncty (talk) 12:26, 19 October 2017 (UTC)

Earth II and Climatron
I'm including the topics together because they're both mine and to save space. I would like to add a reference to Fuller's Involvment in the made for TV Earth II, which features the Dymaxion map, in which Fuller was given credit as "Technical Advisor for Earth" (although I expect they meant "Earth II"). Anyway, his influence on the political and social landscape of the show are indelible. I'm just not sure which section of the article it should go in.

Also, I think that the Climatron, in the St. Louis Arboretum, deserves a mention, as a significant dome, and one designed by Fuller himself, and will so add it if noone objects. —Preceding unsigned comment added by 74.243.181.167 (talk) 22:35, 13 June 2010 (UTC)

Is there an intentional gap in the history for World War 2?
The history jumps from 1930's to 1948 with occasional mention on his WW2 service?

Is the omission intentional, or has it been purged by vandals and no one noticed? --194.197.79.18 (talk) 10:24, 22 November 2010 (UTC)

Discussion of dome, cable intercepts, and Bauersfeld
The text introducing the excerpt on cable intercepts makes does not follow. Is this meant to imply he came upon the idea from Bauersfeld from cable intercepts? If so, this implication is not documented and the text makes no sense anyway. I've been bold and removed it for the time being, perhaps someone can make this point more clearly and with a source...? -Reagle (talk) 14:57, 28 June 2011 (UTC)

Geodesic - or Not
Not everything that looks like a dome is necessarily geodesic. Fuller's principles about geodesic lines included specific circles of struts similar to the classical arch for maximum strength. If you look at plans for real Fuller domes, you might be surprised how many different lengths of the struts are used to channel the structural forces in an optimized way. I haven't yet found out about the Bauersfeld dome, and I can't tell about the rotating animation, but I suspect that both are built in a more economic way, with as little as possible different strut lengths. (Also, as I understood it, the concept of "geodesic" only makes sense in relation to gravity, so a ball spinning in space might be rather pointless.) Similarly that Kyushu dome mentioned above could be something else. I don't know about that. The biggest geodesic dome was a railway tank car servicing depot in the southern US IIRC. I'll have to look it up again before I can go into more details. Eden Project is obviously not geodesic: If you trace a line of struts you can't find a single great-circle. I also suspect, that all struts are the same length in any given dome. Don't understand me wrong: I'm not a "Fuller was the biggest genius ever" fanboy, and I also love Eden Project - but I am an engineer, and I'm trying to get the technical details unmuddled. --BjKa (talk) 14:10, 9 January 2013 (UTC)

 * A geodesic is a "straightest" possible path in a curved space; on a sphere, a geodesic is a great circle. Nothing to do with gravity, unless we're talking about general relativity (which describes gravity as a curvature of spacetime). —Tamfang (talk) 07:57, 5 March 2013 (UTC)

Where's the proof of bankruptcy?
The article says he was bankrupt at 32, but where's the proof that he actually filed for bankruptcy protection? This "bankrupt" claim in Wikipedia has found its way all across the Internet and elsewhere, so don't rely on a circular reference. Being extremely poor or nearly bankrupt is likely more accurate. Here is a high quality reference from The New Yorker magazine, June 9, 2008 http://www.newyorker.com/reporting/2008/06/09/080609fa_fact_kolbert: {{Quote| During the First World War, Fuller married Anne Hewlett, the daughter of a prominent architect, and when the war was over he started a business with his father-in-law, manufacturing bricks out of wood shavings. Despite the general prosperity of the period, the company struggled and, in 1927, nearly bankrupt, it was bought out. At just about the same time, Anne gave birth to a daughter. With no job and a new baby to support, Fuller became depressed. I would like to suggest that regular editors here should consider revising the description to "nearly bankrupt" in the absence of proof with a year. 5Q5 (talk) 15:06, 15 February 2013 (UTC)

Whether bankruptcy protection was available or not when Buckminster Fuller was 32 has little to do with his personal financial situation at the time. — Preceding unsigned comment added by 208.120.1.64 (talk) 06:55, 10 June 2013 (UTC)

The book Buckminster Fuller's Universe By Lloyd Steven Sieden claims that Fuller had "no savings to fall back upon" (page 85) after he lost his job with Stockade Building Systems in 1927. Fuller was again "unemployed and with no prospects for supporting himself or his wife". (page 85) "With no steady income the Fuller family was living beyond its means and falling further and further into debt". (page 87). The book doesn't mention him filing for bankruptcy, but it is clear that his financial situation was poor. Stuart mcmillen (talk) 02:34, 28 July 2013 (UTC)
 * Here is a description in his own words --Nowa (talk) 13:30, 28 July 2013 (UTC)

Bucky vision of the Internet
I've always thought Buckminster Fuller's idea of individualized two way TV was about the clearest vision of the internet from the 60's.
 * “...with a few high masts...the entire community could be 'hooked up'...with beam casting you will be able to send individualized messages to each of those houses...it works in both directions....the receiving individual can beam back 'I don't like it'...constant referendum of democracy will be manifest....it is also possible...to send out many different programs simultaneously...children will be able to look up any kind of information they want....The answers to their questions and probing will be the best information that is available up to that minute in history” Education Automation 1962

Does anyone know of any reliable secondary sources that make a similar observation?--Nowa (talk) 15:39, 5 July 2013 (UTC)

 * To me, this suggests the idea of cellphones, more than the Internet. The Internet doesn't depend on towers, but the interconnectivity of cellphones does. [formerly "Unfree"] 172.56.27.67 (talk) 10:01, 3 May 2014 (UTC)

This would go in the Influences section, but I don't know how to source it.
If you look at the Leon Russel record, Leon Russell and the Shelter People, the liner notes say rather cryptically, "Dear Friends: Here are some better words. -- Find out all you can about Buckminster Fuller Love Leon." --75.94.221.254 (talk) 02:55, 29 July 2013 (UTC)

Invention of the Geodesic Dome
Other articles in Wikipedia, including the article on Walther Bauersfeld and the Geodesic dome article itself attribute the invention of the geodesic dome to Bauersfeld, more than twenty years before Buckminster Fuller popularized it. I changed the text to say that Fuller popularized the geodesic dome rather than inventing it based on this. It's likely that Fuller was not aware of Bauersfeld's work and thus reinvented it, though I cannot find any sources that speak either way on this.

Bill (talk) 15:01, 19 November 2013 (UTC)

Saying "Fuller neglected to cite that the self supporting dome had already been built some 26 years prior in his patent applications" implies he was aware of the previous design and chose to keep quiet about it. If that is the case I think it needs a reference to that effect. Otherwise I suggest Buckminster Fuller's entry should be more neutral, simply observing that "Fuller's patent application made no mention of Bauersfeld's self-supporting dome built some 26 years prior" so I've changed the text accordingly. Hope acceptable?

WikiKeith (talk) 16:42, 21 March 2021 (UTC)

No section on the World Game? Plus, just want to say hello
Huge fan of Bucky and want to help to contribute to this article. I am wondering why there is not a section on the World Game. I also want to say hello to the Bucky editing community here too - before I go in an make any edits or changes. Halfman halfthing (talk) 17:04, 28 November 2013 (UTC)
 * I think a world game section would be great. Dive in.--Nowa (talk) 22:00, 29 November 2013 (UTC)
 * Just added a few sentences on the World Game and wikilinked it. I put it under the alternative map projection sub-heading, which I renamed "Dymaxion map and World Game". The two (the map and the World Game) go together, but perhaps each of these developments deserves its own sub-heading?GuineaPigC77 (talk) 07:45, 19 January 2014 (UTC)

Plato
It was Plato, I suppose, who came up with the five perfect solids, all of whose sides, faces, and angles are equal. If I recall correctly, they were the (regular) tetrahedron, cube, octahedron, dodecahedron, and icosa[meaning twenty]hedron. Cubes are made up of squares, dodecahedra of pentagons, and the others of equilateral triangles. Since you see pentagons in the pattern of geodesic domes, it occurs to me that they might be elaborations of dodecahedra, in which each pentagon is divvied up into triangles which bulge out to the shape of a sphere. On the other hand, each vertex of an icosahedron is surrounded by five triangles. (Aside from triangles, squares, and pentagons, you can't use any other regular polygons, of course, because regular hexagons fill the plane, and higher-numbered polygons can't come together.) Any thoughts on the matter? What's the right way of conceptualizing Bucky's geodesic spheres? [--formerly "Unfree"] 208.54.85.208 (talk) 09:54, 3 May 2014 (UTC)

Eye
There was something about one or both of Bucky's eyes that he said helped him learn how to imagine three-dimensional things better than most people. Was he blind in one eye? Severely myopic? 208.54.85.218 (talk) 10:33, 3 May 2014 (UTC)

"Neo"-Futuristic?
A number of points in this article need attention:

 * Why "neo-futuristic"? Why not just "futuristic"?

Frankly, I had not encountered the term "neo-futuristic" before this article. There is a Wiki article titled "neo-futurism", which defines it, in part, as "...an early 21st century movement in the arts, design, and architecture."

Seeing as how Fuller died nearly a quarter century before the advent of the 21st century, it's difficult to see how he could have been a "neo-futurist" according to this definition. One of the two articles needs to be fixed.

 * Since Friedrich Fröbel basically originated the modern concept of kindergarten -- all kingergarten -- what does it mean to say that Fuller attended "Froebelian kindergarten"?  It just means he attended kindergarten, right?  So what?  Millions of other kids did, too.

 * "Later in life Fuller took exception to the term "invention"." In what way?  Why?  did he just not like the word for some reason?  What reason?  Did he propose an alternate?  What was it?

 * "By his own appraisal, he was a non-conforming misfit in the fraternity environment." This statement jumps in like a non-sequitur.  What fraternity?  There is no prior mention of fraternities, or of Fuller having been affiliated with any.  We are told that he "began studying at Harvard" but plenty of people attend Harvard without joining a fraternity.  We are told that he was affiliated with "Adams House," but Adams House is not a fraternity.

 * I also note the article refers to Fuller as a "designer". What kind of designer?  A fashion designer?  Graphic designer?  Automotive designer?  All kinds?  — Preceding unsigned comment added by 74.95.43.249 (talk) 22:46, 5 November 2014 (UTC)

Guinea Pig B
I notice that a quote from 'Guinea Pig B' is used near the top of the article, yet Guinea Pig B is mentioned nowhere else on this page (or anywhere else on WP). I think it would be great if 'Guinea Pig B' was added to the bibliography, or perhaps the quote could say that it was originally from the introduction to Fuller's 'Inventions', which is listed in the bibliography, or maybe, since the reference given for the quote is to 'Inventions' and not to 'Guinea Pig B', perhaps the "Guinea Pig B" could just be removed. Thanks! Doctormatt (talk) 22:28, 4 May 2015 (UTC)

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Ahead of his time
So I updated the 'Best Known Work' section with the title of the work 'Dymaxion Chronofile'. He was recording his life usually every 15 minutes for decades before the web or Facebook existed. Talk about a lot of status updates! Is there a digital copy of it? I think it deserves more attention. Synesthetic (talk) 04:25, 21 March 2017 (UTC)

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Tensegrity controversy
20 years ago I knew a brilliant girl, (Eva, from Montréal) who was HARDCORE into M.C. Escher, optical illusions, patterns, deep math, and Buckminster Fuller. She taught me brief overviews on these and introduced me to tensegrity. She explained that Bucky was showman popularist who accepted accolades yet didn't invent the geodesic dome or tensegrity, nor properly credit those who did. She was a bit bitter about this but still loved Bucky, including his "faults", at least as reported by some (I don't know what biographies or math history books she gleened this from). I'd like to see this mentioned in more detail in the "tensegrity" and "Bucky Fuller" articles. ~  JasonCarswell   (talk)   05:41, 21 August 2018 (UTC)

Buckminster Fuller quote
Years ago, in a documentary, I heard a sustainability quote attributed to Bucky, and every few years I look again on the Internet to try to find it and/or find legit attribution. The quote was something like, "Waste is simply raw materials we haven't found a new use for." Also, if you're a fan of Bucky you may appreciate The House of Tomorrow (2017 film). ~  JasonCarswell   (talk)   05:46, 21 August 2018 (UTC)

Walther Bauersfeld
Several statements are made throughout the article that Walther Bauersfeld held a patent for the geodesic dome prior to Bucky Fuller. At one place in the article it is stated that Bucky Fullers patent is nearly identical to Walther Bauersfeld's patent, and provides the patent number for Bucky's patent, but does not provide the patent number for Bauersfeld's patent or any other supporting reference to the claim. If statements such as these are to be made they deserve and require thorough documentation and the patent number for Bauersfeld's patent should be made known in that context along with Fullers patent. Otherwise it is heresay and tantamount to slander. 2600:1004:B03D:103D:CEFF:A273:C418:8BA6 (talk) 21:04, 24 April 2022 (UTC)

 * @2600:1004:B03D:103D:CEFF:A273:C418:8BA6 correction, the articles says not that the parents are identic, but that Fullers design is the same design as Bauersfeld's design. It reads, "An examination of the geodesic design by Walther Bauersfeld for the Zeiss-Planetarium, built some 28 years prior to Fuller's work, reveals that Fuller's Geodesic Dome patent (U.S. 2,682,235; awarded in 1954) is the same design as Bauersfeld's." 2600:1004:B03D:103D:CEFF:A273:C418:8BA6 (talk) 21:24, 24 April 2022 (UTC)

 * @2600:1004:B03D:103D:CEFF:A273:C418:8BA6 I'm not suggesting that anyone is deliberately slandering Bucky Fuller, but that is how it comes off when such statements are made without thorough, accessible documentation. 2600:1004:B03D:103D:CEFF:A273:C418:8BA6 (talk) 21:26, 24 April 2022 (UTC)

Name
It may be a stupid question, perhaps also a trivial one, but I seem to have missed the information: Is "Buckminster" one of his given names or is it part of the family name? Does anyone know? 2A02:8071:686:3660:CF24:D1FB:DE1E:5470 (talk) 09:29, 11 October 2022 (UTC)

Alec Nevala-Lee Biography
This article would benefit from incorporating the findings in Alec Nevala-Lee's new biography, which uses extensive archival sources to refute a lot of the myths surrounding Fuller. Many of the sources in this article are hagiographic texts that perpetuate fables that Fuller told about himself. I will try to correct a couple of things to begin, but it is a huge project. See also this excellent review of Nevala-Lee's biography by James Gleick: https://www.nybooks.com/articles/2022/11/03/space-age-magus-buckminster-fuller/ Owunsch (talk) 13:08, 20 October 2022 (UTC)

I Seem To Be a Verb authorship disputed
Prior to Fuller's visit to Lewis & Clark College (February 5th, 1979), we were advised NOT to mention 'I Seem to be a Verb'. Fuller was perturbed that the (co) authors listed him as Author on their compilation of his works -- without his permission. So, the book is NOT Fuller's book. Johnedwardmiller (talk) 21:24, 3 February 2024 (UTC)

 * @Johnedwardmiller Are there any published, reliable sources to support that story? —C.Fred (talk) 14:49, 4 February 2024 (UTC)
 * I don't know. I don't seem to have a copy of the memo that was sent by his office in advance of his visit.  Perhaps there is such a copy in the archive at Stanford.  I'll pursue that.  Perhaps the PUBLISHER would have a record of his objection. Unfortunately, they may not have wanted that fact made public. Johnedwardmiller (talk) 20:32, 4 February 2024 (UTC)
 * Page 374 in "Inventor of the Future" by Alec Nevala-Lee backs the notion that Buckminster Fuller himself did not directly collaborate on the writing or creation of the book. It's simply the compilation / remix of Fuller's previous words and sentences, targeted at the younger (Hippie) audience.  Fuller did not "write" this book, nor is he the author. CHAT GPT says: "The inclusion of Buckminster Fuller as a coauthor is more symbolic of his influence rather than direct involvement in the book's writing process." Johnedwardmiller (talk) 06:22, 5 February 2024 (UTC)
 * In the book GUINEA PIG B, published posthumously by Fuller's estate, there is an appendix of "Books By R Buckminster Fuller".  28 books are listed.  "I Seem to be a Verb" is NOT listed, nor mentioned in the book.
 * There have been a thousand articles and books written /about/ Fuller, that quoted Fuller. "I Seem to be a Verb" falls in the latter category, and therefore should not be listed on Wikipedia as a book written /by/ Fuller. (BFI perpetuated this myth.  I intend to follow up with BFI.) Johnedwardmiller (talk) 23:40, 12 February 2024 (UTC)

title: Talk:Buckminster Fuller