What is a bifurcation point?
Another cross-post from my main technical blog .
In fact, you probably already know all this, but in order not to overload future articles, I just need a reference to the explanation. So I will ask the purists not to worry and let me explain to those who still do not know, maybe not very precisely, but simply “on the fingers”, what are bifurcation points and what they eat with. <O: p> < o: p>
Let's start? So, all of you probably heard the problem Buridanova ass. A donkey stands near two absolutely identical piles of hay at exactly the same distance from the donkey to the right and left. Question: how can a donkey choose one of them? The answer mentioned Buridan was that the donkey would die of hunger. <O: p> </ o: p>
Now let's take a look at this picture in the imagination. Here is a donkey. Here is the hay. A donkey unable to choose a handful and dozed off by an intellectual effort. A single photon broke through the half-closed donkey's eyelid and flew into the cone on the retina of the donkey's eye, exciting the optic nerve. The nerve transmitted a signal to the neuron in the donkey's brain, and the donkey had a delightful (or terrible, does not matter) dream that caused the donkey to turn around in a dream. When the donkey woke up, heaps already appeared at different distances and in general he saw only one before the muzzle, which he ate. It is likely that later he turned around and ate another, but for our conversation it does not matter. And what matters is that a completely microscopic phenomenon (in this example, at the quantum level, a single photon) in this situation led to a change in the macroworld — it determined which pile of hay was eaten first. <O: p> </ o: p>
')
This is the bifurcation point. The bifurcation point is the state of the system when a very small impact leads to global changes. In the spirit of, "the flap of a butterfly's wing led to a hurricane in California." By the way, the “butterfly effect” is just about the bifurcation points. <O: p> </ o: p>
The donkey between two equal piles of hay is a bifurcation point. The knight at the crossroads is a bifurcation point. Romulus and Rem, peering into the sky in anticipation of the sign on which hill to build the city, is the bifurcation point. The spacecraft flying exactly in the center of gravity between the Earth and the Moon and not having enough speed to escape from both is at the bifurcation point. He will become either a satellite of the Earth or a satellite of the Moon. Which of them depends on microscopic influences like the solar wind or micrometeorite that hit the satellite. <O: p> </ o: p>
Bifurcation points are not only in nature. They are full, for example, in economics and politics. In the stock or forex market, support or resistance levels are bifurcation points. The security or currency reached them will fall down or go up depending on very minor factors. The trust of consumers very often passes bifurcation points, in which one good or bad news is enough to maintain the status quo or lead to an outcome to a competitor in biblical proportions. August 91st was the bifurcation point for the USSR, into which, one must admit, they tried to drive him for several years from 1985. Presidential elections in the United States in 2000 were the point of bifurcation. Do not take the Supreme Court to vote for the Americans, we would live in a very different world now. <O: p> </ o: p>
There are situations where bifurcation points are abundant and frequent. For example, in the flow of gases and liquids. That is why we still do not know how to predict the weather. Say, the storm resolutely moves ashore, and then suddenly turns 90 degrees and goes into the ocean, why? The butterfly flapped its wings in Shanghai ... By the way, it’s not for nothing that currencies and securities have such quality as “liquidity”, the situation with bifurcation points on the stock exchanges is not so far from the situations in aero-hydrodynamics. <O: p> </ o: p>
I hope I managed to explain this concept, since I will have to refer to it in upcoming articles. On that while I finish.
Well, and finally, the usual informal part. Today I climbed again on that favorite trail and took a photo of the town of Issaqua in the late autumn:
And finally, I was going to scan a napkin with a drawing on career themes in the corporate world, which I painted explaining the subject to one acquaintance (in fact, it was assumed that an exhausted little man crawls out of the arch on the right, who had just achieved the blissful goal - promotion ... and looks at the arch in front of him with amazement, but there was not enough time in the conversation, I just had to say it verbally):
In fact, you probably already know all this, but in order not to overload future articles, I just need a reference to the explanation. So I will ask the purists not to worry and let me explain to those who still do not know, maybe not very precisely, but simply “on the fingers”, what are bifurcation points and what they eat with. <O: p> < o: p>
Let's start? So, all of you probably heard the problem Buridanova ass. A donkey stands near two absolutely identical piles of hay at exactly the same distance from the donkey to the right and left. Question: how can a donkey choose one of them? The answer mentioned Buridan was that the donkey would die of hunger. <O: p> </ o: p>
Now let's take a look at this picture in the imagination. Here is a donkey. Here is the hay. A donkey unable to choose a handful and dozed off by an intellectual effort. A single photon broke through the half-closed donkey's eyelid and flew into the cone on the retina of the donkey's eye, exciting the optic nerve. The nerve transmitted a signal to the neuron in the donkey's brain, and the donkey had a delightful (or terrible, does not matter) dream that caused the donkey to turn around in a dream. When the donkey woke up, heaps already appeared at different distances and in general he saw only one before the muzzle, which he ate. It is likely that later he turned around and ate another, but for our conversation it does not matter. And what matters is that a completely microscopic phenomenon (in this example, at the quantum level, a single photon) in this situation led to a change in the macroworld — it determined which pile of hay was eaten first. <O: p> </ o: p>
')
This is the bifurcation point. The bifurcation point is the state of the system when a very small impact leads to global changes. In the spirit of, "the flap of a butterfly's wing led to a hurricane in California." By the way, the “butterfly effect” is just about the bifurcation points. <O: p> </ o: p>
The donkey between two equal piles of hay is a bifurcation point. The knight at the crossroads is a bifurcation point. Romulus and Rem, peering into the sky in anticipation of the sign on which hill to build the city, is the bifurcation point. The spacecraft flying exactly in the center of gravity between the Earth and the Moon and not having enough speed to escape from both is at the bifurcation point. He will become either a satellite of the Earth or a satellite of the Moon. Which of them depends on microscopic influences like the solar wind or micrometeorite that hit the satellite. <O: p> </ o: p>
Bifurcation points are not only in nature. They are full, for example, in economics and politics. In the stock or forex market, support or resistance levels are bifurcation points. The security or currency reached them will fall down or go up depending on very minor factors. The trust of consumers very often passes bifurcation points, in which one good or bad news is enough to maintain the status quo or lead to an outcome to a competitor in biblical proportions. August 91st was the bifurcation point for the USSR, into which, one must admit, they tried to drive him for several years from 1985. Presidential elections in the United States in 2000 were the point of bifurcation. Do not take the Supreme Court to vote for the Americans, we would live in a very different world now. <O: p> </ o: p>
There are situations where bifurcation points are abundant and frequent. For example, in the flow of gases and liquids. That is why we still do not know how to predict the weather. Say, the storm resolutely moves ashore, and then suddenly turns 90 degrees and goes into the ocean, why? The butterfly flapped its wings in Shanghai ... By the way, it’s not for nothing that currencies and securities have such quality as “liquidity”, the situation with bifurcation points on the stock exchanges is not so far from the situations in aero-hydrodynamics. <O: p> </ o: p>
I hope I managed to explain this concept, since I will have to refer to it in upcoming articles. On that while I finish.
Well, and finally, the usual informal part. Today I climbed again on that favorite trail and took a photo of the town of Issaqua in the late autumn:
And finally, I was going to scan a napkin with a drawing on career themes in the corporate world, which I painted explaining the subject to one acquaintance (in fact, it was assumed that an exhausted little man crawls out of the arch on the right, who had just achieved the blissful goal - promotion ... and looks at the arch in front of him with amazement, but there was not enough time in the conversation, I just had to say it verbally):
Source: https://habr.com/ru/post/16369/
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