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.
89-405: The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz . He noted that the butterfly effect is derived from the 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
178-400: 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
267-423: 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
356-614: A 55% stake in Triumph-Adler. Included in the deal was Royal Typewriter. Sales continued to climb and by 1982 sales in North America of Royal and Triumph-Adler totaled over $ 600 million. In April 1986, Olivetti , the Italian typewriter/computer manufacturer, announced plans to purchase Triumph-Adler and Royal from Volkswagen. For nearly two decades Royal was a part of the Olivetti family. By
445-656: A cheaper model. Royal McBee sold and serviced early computers RPC-4000 and RPC-9000. Royal McBee partnered with General Precision in the Royal Precision Electronic Computer Company, which sold and serviced the LGP-30 (in 1956) and LGP-21 (in 1963) single-user desk computers manufactured by the Librascope division of General Precision. Royal McBee was based in Port Chester, New York . The RPC-4000
534-451: A finite number of iterations x n {\displaystyle x_{n}} maps into a periodic sequence . But almost all θ {\displaystyle \theta } are irrational, and, for irrational θ {\displaystyle \theta } , x n {\displaystyle x_{n}} never repeats itself – it is non-periodic. This solution equation clearly demonstrates
623-478: 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: Recently, a short video has been created to present Lorenz's perspective on predictability limit. A recent study refers to the two-week predictability limit, initially calculated in the 1960s with the Mintz-Arakawa model's five-day doubling time, as
712-505: A floor capacity of 250,000 square feet (23,000 m ) and cost $ 350,000 to build. In 1908, Royal began manufacturing there and in time, Royal and cross town competitor, Underwood Typewriter Company , would make Hartford the “Typewriter Capital of the World”. In 1911, Royal introduced the Royal 5 typewriter, which also utilized the "flatbed" design. Royal's first model utilizing the "upright" design
801-441: 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
890-604: 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
979-645: A private American company again. As of 2019, Royal is still introducing new typewriters under the Royal brand name. On 1 November 2021, Royal Consumer Information Products, Inc. (for the Americas) and the Czechia-based Moravia Consulting spol. s r.o. (for all other markets) became the licensees of HP Development Company, L.P. to continue the development, production, distribution, marketing and support of HP-branded calculators . In March 2024, Royal Consumer Information Products underwent
SECTION 10
#17331251350641068-425: 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 ,
1157-509: A reasonable degree of accuracy. However, the recognition of chaos has led to improvements in weather forecasting , as now forecasters recognize that measurements are imperfect and thus run many simulations starting from slightly different conditions, called ensemble forecasting . Of the seminal significance of Lorenz's work, Kerry Emanuel , a prominent meteorologist and climate scientist at MIT, has stated: "By showing that certain deterministic systems have formal predictability limits, Ed put
1246-459: 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
1335-403: A role in producing a butterfly effect, which is characterized by brief but significant exponential growth resulting from a small disturbance. The first kind of butterfly effect (BE1), 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
1424-449: A sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather that the machine began to predict was completely different from the previous calculation. The culprit: a rounded decimal number on the computer printout. The computer worked with 6-digit precision, but
1513-400: 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
1602-597: A significant organizational change. The company has now officially split into two distinct entities: Royal Consumer Information Products, Inc. - This entity will focus on continuing the core operations and services of the original company within the United States and other international markets. Royal Consumer Information Products de Mexico (www.royallatam.com) - This entity will handle the company's operations and services specifically within Mexico Central America,
1691-515: A significantly different outcome. The idea that small causes may have large effects in weather was earlier acknowledged by the French mathematician and physicist Henri Poincaré . The 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
1780-533: 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
1869-476: 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
SECTION 20
#17331251350641958-427: 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
2047-495: A symposium, named MIT on Chaos and Climate, in honor of the 100th anniversary of the birth of Lorenz and Charney . The two-day event featured presentations from world-renowned experts on the many scientific contributions that the two pioneers made on the fields of numerical weather prediction , physical oceanography , atmospheric dynamics , and experimental fluid dynamics , as well as the personal legacy they left behind of integrity, optimism, and collaboration. A video produced for
2136-419: 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
2225-532: A wide range of basic sciences and brought about one of the most dramatic changes in mankind's view of nature since Sir Isaac Newton," according to the committee that awarded him the 1991 Kyoto Prize for basic sciences in the field of earth and planetary sciences. Lorenz was born in 1917 in West Hartford, Connecticut . He acquired an early love of science from both sides of his family. His father, Edward Henry Lorenz (1882-1956), majored in mechanical engineering at
2314-561: Is an American technology company founded in January 1904 as a manufacturer of typewriters . Royal’s product line has evolved to include cash registers, shredders, personal digital assistants (PDAs)/electronic organizers, postal scales, weather stations, and a wide range of original and compatible/remanufactured imaging supplies supporting printers, faxes, and copiers. The company is headquartered in Hartford, Connecticut . The Royal Typewriter Company
2403-472: 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." The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in
2492-456: 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
2581-755: 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 {\displaystyle f^{t}} , then f t {\displaystyle 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 ) < δ {\displaystyle 0<d(x,y)<\delta } and such that for some positive parameter
2670-463: Is often somewhat wrong." 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. In Palmer et al., a new type of butterfly effect is introduced, highlighting the potential impact of small-scale processes on finite predictability within
2759-455: Is the computer on which Mel Kaye performed a legendary programming task in machine code, as told by Ed Nather in the hacker epic The Story of Mel . A Royal typewriter is a large story element in Stephen King 's novel Misery . 60 Minutes correspondent Morley Safer was known to write all of his scripts on a Royal typewriter. A Royal typewriter with a Prestige Elite typeface
Butterfly effect - Misplaced Pages Continue
2848-608: The Massachusetts Institute of Technology , and his maternal grandfather, Lewis M. Norton , developed the first course in chemical engineering at MIT in 1888. Meanwhile, his mother, Grace Peloubet Norton (1887-1943), instilled in Lorenz a deep interest in games, particularly chess. Later in life, Lorenz lived in Cambridge, Massachusetts with his wife, Jane Loban (1919–2001), and their three children, Nancy, Cheryl, and Edward. He
2937-637: The Swedish Academy of Sciences , considered to be nearly equal to a Nobel Prize . He was also awarded the Kyoto Prize for basic sciences in the field of earth and planetary sciences in 1991, the Buys Ballot Award in 2004, and the Tomassoni Award in 2008. In 2018, a short documentary was made about Lorenz's immense scientific legacy on everything from how we predict weather to our understanding of
3026-614: The United States Army Air Forces during World War II , leading him to pursue graduate studies in meteorology at the Massachusetts Institute of Technology . He earned both a master's and doctoral degree in meteorology from MIT in 1943 and 1948. His doctoral dissertation, titled "A Method of Applying the Hydrodynamic and Thermodynamic Equations to Atmospheric Models" and performed under advisor James Murdoch Austin , described an application of fluid dynamical equations to
3115-513: The logistic map : which, unlike most chaotic maps, has a closed-form solution : where the initial condition parameter θ {\displaystyle \theta } is given by θ = 1 π sin − 1 ( x 0 1 / 2 ) {\displaystyle \theta ={\tfrac {1}{\pi }}\sin ^{-1}(x_{0}^{1/2})} . For rational θ {\displaystyle \theta } , after
3204-480: The "Predictability Limit Hypothesis." Inspired by Moore's Law, this term acknowledges the collaborative contributions of Lorenz, Mintz, and Arakawa under Charney's leadership. The hypothesis supports the investigation into extended-range predictions using both partial differential equation (PDE)-based physics methods and Artificial Intelligence (AI) techniques. By revealing coexisting chaotic and non-chaotic attractors within Lorenz models, Shen and his colleagues proposed
3293-641: 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
3382-405: The 1970s and 1980s, the typewriter market matured under the market dominance of large companies from Britain, Europe and the United States. Before the advent of daisywheel and electronic machines — Royal as well as the other major manufacturers faced strong competition from typewriters from Asia, including Brother Industries and Silver Seiko Ltd. of Japan. In September 2004, Royal became
3471-563: The Caribbean, and Latin America. This strategic split was designed to enhance Royal's operational efficiency and better serve diverse markets. Both entities remain committed to delivering the high-quality products and services you have come to expect. During the 1980s, Royal also produced consumer daisy wheel printers like the Royal LetterMaster and Royal OfficeMaster 2000, the former being
3560-540: The Lorenz 1969 model. Additionally, the identification of ill-conditioned aspects of the Lorenz 1969 model points to a practical form of finite predictability. These two distinct mechanisms suggesting finite predictability in the Lorenz 1969 model are collectively referred to as the third kind of butterfly effect. The authors in have considered Palmer et al.'s suggestions and have aimed to present their perspective without raising specific contentions. The third kind of butterfly effect with finite predictability, as discussed in,
3649-619: The MIT Department of Meteorology and Physical Oceanography merged with the Department of Geology to become the current MIT Department of Earth, Atmospheric and Planetary Sciences, where Lorenz remained a professor before becoming an emeritus professor in 1987. In the late 1940s and early 1950s, Lorenz worked with Victor Starr on the General Circulation Project at MIT to understand the role the weather system played in determining
Butterfly effect - Misplaced Pages Continue
3738-852: The Quiet Deluxe series of portable typewriters, produced from 1939 until 1959 (with a gap during WWII). In 1947, Royal produced, in limited quantity, a gold-plated version of its popular Quiet Deluxe model. Ian Fleming , the British novelist who wrote the James Bond novels, used a gold-plated Quiet Deluxe. Many other writers used a Quiet Deluxe, including Ernest Hemingway , or other models of Royal typewriter, including John Steinbeck . Other typewriter manufacturers utilized Royal's innovations in their typewriters. In 1947, Royal won patent suits against Remington and LC Smith Corona. In February 1950, Royal introduced its first electric typewriter. Lewis C. Myers,
3827-569: The acquisition of Royal McBee. The deal became final in March 1965. Litton would change the name of Royal McBee back to Royal Typewriter and reorganize the company into five divisions: Royal Typewriter, Roytype Consumer Products, Roytype Supplies, McBee Systems, and RMB. October 1966 saw Litton announce plans to acquire the English typewriter producer Imperial, through its Royal Typewriter division. In January 1969, Litton Industries further cemented its hold on
3916-491: 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. Recurrence , the approximate return of a system toward its initial conditions, together with sensitive dependence on initial conditions, are
4005-418: The applicability of BE1 in other areas, such as pandemics or historical events. 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. According to Lighthill (1986), the presence of SDIC (commonly known as the butterfly effect) implies that chaotic systems have
4094-496: 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
4183-490: The book "The Essence of Chaos," in the chapter "Our Chaotic Weather" from 1993, authored by Edward Lorenz and Krzysztof Haman , the authors delved into the challenges of weather forecasting. The work discusses the consequences of chaos in the atmosphere and its impact on weather prediction. They describe a scenario in which meteorologists, in the computer age, generate multiple long-term weather forecasts based on different yet similar initial atmospheric conditions. Differences in
4272-402: 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
4361-423: 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
4450-401: The effect of a butterfly's wings creating 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
4539-674: The energetics of the general circulation of the atmosphere. From this work, in 1967, Lorenz published a landmark paper, titled "The Nature and Theory of the General Circulation of the Atmosphere," on atmospheric circulation from an energetic perspective, which advanced the concept of available potential energy . In the 1950s, Lorenz became interested in and started work on numerical weather prediction , which relied on computers to forecast weather by processing observational data on such things as temperature, pressure, and wind. This interest
SECTION 50
#17331251350644628-593: The event highlights the indelible mark made by Charney and Lorenz on MIT and the field of meteorology as a whole. Lorenz published many books and articles, a selection of which can be found below. A more complete list can be found on the Lorenz Center website: link Archived 2019-04-05 at the Wayback Machine Royal McBee Royal Consumer Information Products, Inc. (formerly The Royal Typewriter Company )
4717-414: The film No Time for Sergeants (1958) , when Will Stockdale ( Andy Griffith ) visits U.S. Air Force psychiatrist Maj. Royal B. Demming ( James Millhollin ), a Royal typewriter is prominently displayed in his office. In the opening title sequence of the television series Kolchak: The Night Stalker , the main character, Carl Kolchak (portrayed by actor Darren McGavin ), is seen writing up a news story on
4806-438: The first nationwide radio hook-up. "The Daily News" of New York estimated that 20 million fans from coast to coast listened to the broadcast. Royal's introduction of its portable line of typewriters was an immediate success and launched the company to become the world's #1 selling typewriter brand. On October 9, 1926, the " Hartford Daily Courant " reported that Royal had just produced its one millionth typewriter. To promote
4895-419: The forecast results arise due to the sensitivity of the system to initial conditions. Lorenz's insights on deterministic chaos resonated widely starting in the 1970s and 80s, when it spurred new fields of study in virtually every branch of science, from biology to geology to physics. In meteorology, it led to the conclusion that it may be fundamentally impossible to predict weather beyond two or three weeks with
4984-410: The impact of a butterfly flapping its wings on tornado formation, as indicated in two 2024 articles. In more recent discussions published by Physics Today , it is acknowledged that the second kind of butterfly effect (BE2) has never been rigorously verified using a realistic weather model. While the studies suggest that BE2 is unlikely in the real atmosphere, its invalidity in this context does not negate
5073-531: The last nail in the coffin of the Cartesian universe and fomented what some have called the third scientific revolution of the 20th century, following on the heels of relativity and quantum physics." Late in his career, Lorenz began to be recognized with international accolades for the importance of his work on deterministic chaos. In 1983, along with colleague Henry Stommel , he was awarded the Crafoord Prize from
5162-480: The late 1950s, Lorenz was skeptical of the appropriateness of the linear statistical models in meteorology, as most atmospheric phenomena involved in weather forecasting are non-linear . It was during this time that his discovery of deterministic chaos came about. In 1961, Lorenz was using a simple digital computer, a Royal McBee LGP-30 , to simulate weather patterns by modeling 12 variables, representing things like temperature and wind speed. He wanted to see
5251-462: 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
5340-405: 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
5429-401: 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
SECTION 60
#17331251350645518-498: The plan and Royal McBee was formed. From 1954 to 1964 sales soared from $ 84.7 million to over $ 113 million. Royal McBee was consistently listed as a Fortune 500 company. In December 1957, Royal announced it had just produced its 10 millionth typewriter. Congratulations were received from U.S. Secretary of Commerce Sinclair Weeks and the Governor of Connecticut, Abe Ribicoff. In December 1964, Litton Industries ' stockholders approved
5607-453: 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 ",
5696-427: The practical problem of predicting the motion of storms. Lorenz spent the entirety of his scientific career at the Massachusetts Institute of Technology . In 1948, he joined the MIT Department of Meteorology as a research scientist. In 1955, he became an assistant professor in the department and was promoted to professor in 1962. From 1977 to 1981, Lorenz served as head of the Department of Meteorology at MIT. In 1983,
5785-446: The present state—and in any real system such errors seem inevitable—an acceptable prediction of an instantaneous state in the distant future may well be impossible....In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be nonexistent." His description of the butterfly effect , the idea that small changes can have large consequences, followed in 1969. In
5874-514: The printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term results. Lorenz's discovery, which gave its name to Lorenz attractors , showed that even detailed atmospheric modelling cannot, in general, make precise long-term weather predictions. His work on
5963-412: The properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos . The concept of the butterfly effect 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. In The Vocation of Man (1800), Johann Gottlieb Fichte says "you could not remove
6052-747: 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 . The butterfly effect 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 ), webcomics (such as Homestuck ), AI-driven expansive language models, and more. Edward Norton Lorenz Edward Norton Lorenz (May 23, 1917 – April 16, 2008)
6141-706: The ruggedness of its typewriters, George Edward Smith, president of Royal, bought a Ford-Stout tri-motor airplane in August 1927. This plane, commonly called the Royal Airtruck, dropped over 200 typewriters in crates with parachutes to dealers over the eastern seaboard of the USA on its maiden flight. Royal eventually delivered over 11,000 typewriters this way with only ten being damaged. In January 1941, Edward B. Hess, one of Royal's founders and vice presidents, died in Orlando, Florida . Hess
6230-447: 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
6319-637: The surviving founder of the Royal Typewriter Company, died in Freeport, New York at the age of 84. Worldwide demand caused Royal to open a new factory in Leiden, the Netherlands, to produce typewriters in 1953. In April 1954, the Royal typewriter Company announced its plan to merge with McBee, a leading manufacturer of accounting and statistical machines and supplies. By July, Royal stockholders had approved
6408-414: 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
6497-485: 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
6586-513: The topic, assisted by Ellen Fetter , culminated in the publication of his 1963 paper "Deterministic Nonperiodic Flow" in Journal of the Atmospheric Sciences , and with it, the foundation of chaos theory . He states in that paper: "Two states differing by imperceptible amounts may eventually evolve into two considerably different states ... If, then, there is any error whatever in observing
6675-558: The two key features of chaos – stretching and folding: the factor 2 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 {\displaystyle x_{n}} folded within the range [0, 1]. 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
6764-488: 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
6853-639: The typewriter market by purchasing the German typewriter manufacturer, Triumph-Adler . Almost immediately, the U.S. government filed an anti-trust suit against Litton accusing it of creating a monopoly. The FTC ruled in March 1973 that Litton had to divest itself of Triumph-Adler. Litton appealed and, in a rare reversal, the FTC issued a ruling in April 1975 stating that Litton could keep Triumph-Adler. In March 1979, Volkswagen , seeking to diversify, announced its intention to acquire
6942-511: The universe. Lorenz is remembered by colleagues and friends for his quiet demeanor, gentle humility, and love of nature. He was described as "a genius with a soul of an artist" by his close friend and collaborator Jule Charney . In 2011, The Lorenz Center, a climate think tank devoted to fundamental scientific inquiry, was founded at MIT in honor of Lorenz and his pioneering work on chaos theory and climate science . In February 2018, The Edward Lorenz Center and Henry Houghton Fund hosted
7031-628: 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
7120-466: 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 creates 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
7209-619: The words as they are typed. Ryan put up $ 220,000 in exchange for financial control. In March 1906 the first Royal typewriter, the Royal Standard, was sold. The Royal Standard was set apart from its competition by its 'flatbed' design. With demand increasing, Royal purchased 5¼ acres in Hartford, Connecticut, as the new site for its manufacturing facility. Original plans called for the Royal Typewriter Company Building to have
7298-522: Was a prolific inventor and held over 140 patents relating to the typewriter. World War II brought tremendous change to Royal. In order to aid the war effort, Royal converted its manufacturing to war work exclusively. Royal manufactured machine guns, rifles, bullets, propellers, and spare parts for airplane engines. It wouldn't be until September 1945 that Royal started typewriter production full-time again and not until December 1948 that it caught up on its pre-war backlog. Royal's most popular models were in
7387-459: Was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability , as well as the basis for computer-aided atmospheric physics and meteorology . He is best known as the founder of modern chaos theory , a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions . His discovery of deterministic chaos "profoundly influenced
7476-466: Was an avid outdoorsman, who enjoyed hiking, climbing, and cross-country skiing. He kept up with these pursuits until very late in his life. On April 16, 2008, Lorenz died at his home in Cambridge from cancer at the age of 90. Lorenz received a bachelor's degree in mathematics from Dartmouth College in 1938 and a master's degree in mathematics from Harvard in 1940. He worked as a weather forecaster for
7565-486: Was founded by Edward B. Hess and Lewis C. Myers in January 1904 in a machine shop in Brooklyn, New York. The next year, Hess and Myers turned to Thomas Fortune Ryan , to whom they demonstrated a prototype typewriter. Their machine had numerous innovations including a friction-free, ball-bearing, one-track rail to support the weight of the carriage, a new paper feed, a lighter and faster typebar action, and complete visibility of
7654-521: Was one of the items found at Zodiac suspect Arthur Leigh Allen 's apartment, matching the typewriter the Zodiac killer used to write letters sent to the Riverside Police Department. Jessica Fletcher used a Royal typewriter to write her novels. Mason Williams threw a Royal Model X typewriter out of a speeding car driven by Ed Ruscha for their art book Royal Road Test (1967). In
7743-457: Was primarily proposed based on a convergent geometric series, known as Lorenz's and Lilly's formulas. Ongoing discussions are addressing the validity of these two formulas for estimating predictability limits in. 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
7832-634: Was sparked, in part, after a visit to the Institute for Advanced Study in Princeton, New Jersey, where he met Jule Charney , then head of the IAS's Meteorological Research Group and a leading dynamical meteorologist at the time. (Charney would later join Lorenz at MIT in 1957 as a professor of meteorology.) In 1953, Lorenz took over leadership of a project at MIT that ran complex simulations of weather models that he used to evaluate statistical forecasting techniques. By
7921-454: Was the Royal 10, which came out in 1914. Original models had two beveled glass panes on each side. In 1926 Royal introduced the "Roytype" brand name for its line of typewriter ribbons and carbon paper. In order to promote the new portable Royal president G. E. Smith secured the exclusive sponsorship of the September 23, 1926, Dempsey–Tunney championship fight for $ 35,000. This boxing match was
#63936