His article "Hyozi ability, can flapping butterfly wings in Brazil cause a tornado in Texas?" was the opening shot for a scientific revolution that affected physics, biology and even the social sciences
Edward Lorenz, a meteorologist at MIT who tried to explain why it is so difficult to build good weather forecasts and thereby created a scientific revolution known as chaos theory, died on April 16 of cancer at his home in Cambridge, Massachusetts. He was 90 years old when he died.
Lorenz was the first to identify what is today called chaotic behavior in a mathematical model of weather forecasting. In the early XNUMXs, Lorenz realized that small differences in dynamic systems such as the atmosphere - or in a model of the atmosphere - could cause large and unexpected differences between the predicted results and what actually occurred.
The observations finally led him to formulate what was later called the butterfly effect, which was created in an academic study he published in 1972 under the title: "Hyuzi ability, can flapping butterfly wings in Brazil cause a tornado in Texas?"
These early insights of Lorenz mark the beginning of a field of research that influenced not only mathematics but almost every branch of science - biology, physics and even social sciences. In meteorology, the idea led to the conclusion that it would be impossible to predict weather for a period of more than two to three weeks with a reasonable degree of accuracy. There were scientists who said that the 20th century will be remembered for three scientific revolutions - relativity, quantum theory and chaos.
"By showing that certain deterministic systems have formal prediction limits, Ed drove the last nail in the coffin of the Cartesian universe and created the third scientific revolution of the 20th century, following relativity and quantum theory," said Kerry Emanuel, professor of atmospheric sciences at MIT . "He was also a perfect gentleman, although his intelligence, integrity and humility set high standards for future generations." said Emmanuel.
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I thought that the "butterfly effect" was discovered and described in 1961...
16/4/1989-2008..what will I say and what will I say...maybe one day..for those who don't know chaos will arise from what it is. Terrible. But there is the butterfly effect for a huge resonance..and there is a rising from the dead - in the same body that knows how to be born from it. There is no shaman, magician , a bewitched sorcerer, a good Jew, who is not obliged to kill his soul in order to be reborn into his true spirit - the higher self for which he breathes, lives and works.
Well, there is no connection. The world is indeed very strange .. and many in its wonders .. believe me.
We will note this as a chaotic emission required for the purpose of documentation.
Hugin: Who is like you Michael... who.
Fibonacci:
And all these things are not related to chaos.
It is true that they deal with certain types of mathematical systems that are special (not general!) cases of chaotic systems, but they would deal with them even if the word chaos had not been invented
Michael
There is a whole collection of transformations and theorems and equations and functions, etc. that individually define this mathematical space called according to the inclination of the heart of the various partners in the development of this collection of tools. The examples are really irrelevant, I admit that I didn't put in much effort because the emphasis was on this mathematical theory or technique as a whole. There are some typical creatures you can read about on Wikipedia, surely there is enough evasiveness or on math websites.
Creatures such as strange attractors with partial dimensions that were called fractals by a man named Mandelbrot. There is a collection of functions that can be used to create different families of these and more, see there.
Fibonacci - know what? I will not insist on such a mathematical theorem and will be satisfied even with a physical law with a similar formulation.
Fibonacci:
I think you are wrong and your examples show it very well.
Riemann's geometry consists of axioms, theorems and proofs.
Chaos is not like that.
Are you able to point me to a mathematical theorem that asserts a claim along the lines of "assuming that system X is chaotic, then by necessity such and such exists in it"?
To Ben-Ner in your answer to Michael
Not everyone knows these mathematical concepts, so things look similar to them. With your permission I will add to your words.
Chaos theory is indeed a complete mathematical theory within the world of mathematics. And it includes transformation methods and various computational methods through which a very wide variety of natural phenomena can be easily represented. Phenomena that were considered completely foreign precisely due to their seemingly random nature. Chaos theory when it appeared constituted a kind of fishing net in which various types of "fish" were caught. Starting with blood vessel mapping and topographical maps for Tikshore weather and much more. This mapping ability that made it possible to connect and generalize different fields stems from this mathematical theory.
There are many examples of mathematical theories in various fields that made it possible to generalize wide-ranging physical concepts under one roof. For example, the geometry of curved spaces and the Riemann tensors that allowed Einstein to represent and map the theory of general relativity. Or the theory of bunches developed by Lei Abel and more and made a decisive contribution to the calculation of the forces and the mapping of the nuclear phenomena in the atom. As we know, the Sundertic quantum theory is one of the most successful theories and is based on mappings using the theory of bunches. And there are many other examples.
To Michael
I understand that you do not distinguish between two concepts
which are similar but different. One concept is the concept of "randomness" and the other - "chaos".
Contrary to your claim, chaos is not a "phenomenon" but a "perception"="a method for analyzing and understanding a chaotic system". A chaotic system is a probabilistic (predictable) system. That is, the prediction is not deterministic but probabilistic, even though the prediction values are within a finite range.
For example, in weather forecasting, despite the chaotic nature of the forecast, it is known that the range of temperature values in the State of Israel will not rise above 330 degrees and will not fall below 260 degrees and generally between 330-170
degrees (k). Of course, in more defined areas of time and place, the prediction will be even more accurate. The fact that any system is chaotic does not mean that the range of predictions is infinite, but that the prediction is probabilistic in a finite range of values.
If in the past the attitude towards a chaotic system was like a completely random system, today the concept of chaos allows to give probabilistic quantitative values for the forecast.
By the way, this is also the answer to the question of how, how and why it happens that "Hapoel Tel Aviv" wins one week against Beitar Y-M 0:3
And a week after that, Jaljulia loses to the local council 1:4.
A. Ben Ner:
In my opinion, you have a mistake in your knowledge of history and a fundamental mistake in understanding the phenomenon of chaos.
In terms of history, they have known for many years about functions that are not stable - those that a small change in their parameters creates a huge change in the phenomenon. That's the whole point, in addition to the fact that there are many parameters that have also always been taken for granted.
You didn't have to say chaos for people to know that they don't know how to calculate the weather in a good way and it's not at all surprising that none of the questions you raised as examples never bothered the scientists. To everyone, the answer to these questions was, as it should have been, "trivial".
So much for history and now for understanding the phenomenon of chaos.
Note that I did not use the phrase "chaos theory" that you used. Why? Because there is no such thing. The phenomenon of chaos does not contribute anything and a half to the prediction of the happenings in nature and is therefore not a theory or theory. "Chaos" is just, as I said, another word in the lexicon, a nice word but not one that contributes anything to understanding.
To Michael and the point that responded before,
I think you are wrong in your comments.
Chaos theory is extremely important for understanding the amazing diversity in the universe. Otherwise, how can you answer the following questions:
Why aren't all stars the same size?
Why aren't all galaxies the same size?
Why not all black holes..?
Etc. etc'..
.
Why not all life according to the Bible - bacteria, viruses of all kinds, insects of all kinds, mammals of all kinds..etc..etc..-
are not equal and the same?
What is the logical mechanism (!) that produces such tremendous variation in nature, whether in the "living" world or in the "inanimate" world?
Did there exist, until the chaos "substrate", any scientific theory that claims to answer these questions? Apparently, until chaos theory came into use, science treated diversity as a given, without making a serious attempt to describe the sources of diversity in nature with scientific-mathematical tools.
So to claim that "chaos" is only a "name" for known phenomena and that "chaos" has no practical scientific use, is a fundamental mistake. Once the principle of "chaos" was understood, it could also be described with scientific and mathematical tools. The uses of these tools are many
most in understanding different distribution mechanisms in nature.
Chaos theory has absolutely no scientific importance.
Forgive me for the heresy, but in my opinion he just gave a name to a phenomenon that had been known for a long time.
Sometimes naming is a constructive thing (this is the whole essence of language as an aid to communication and thinking) but sometimes not.
It is constructive for thought (and this is what is more important) when you can use the name to build more complex terms and thus allow our active memory (which is not able to handle more than 7 plus or minus 2 different concepts at the same time) to be more effective. Otherwise it has no real value.
In my opinion, the term chaos falls more in the realm of worthless tongue-prints than in the realm of useful tongue-prints.
It is true that it became a fashion, but in my opinion, no real insights came out of it.
According to this, it is not possible to predict if it will not be possible to predict the future more precisely.