Heads or tails?
A person must think probabilistically. Just because our world is so arranged that each event occurs with a varying degree of probability. And this "reinforced concrete" fact must always be taken into account.
Notice that this does not completely overlap with the dialectical thinking. The difference is that the dialectic describes any situation as a set of multidirectional factors (which, of course, affects the probability of a particular outcome). Then the situation is the essence of the synthesis of these factors at this particular moment.
Probability is a mathematical concept. A classic example is tossing a coin. An “eagle” can fall out, or a “tails” one. Since there are only two sides to the coin, the probability of the “eagle” falling out is 1/2 or 0.5.
There are several very important moments that are included in the notion of “probabilistic thinking”, which can be demonstrated with a coin example.
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Initially, two fundamentally different options : a) when the probability of the entire sequence of events or elements of the system affects the result; b) when what was before the next event is unimportant.
Consider the first option (remember, when the probability of the entire sequence of events or the behavior of the elements of the system affects the result).
What is the probability of falling "eagle" 2 times in a row? That's right, 0.5 * 0.5 = 0.25. Those. 2 times less than the probability of the "eagle" falling out in a single attempt.
This is a very important point that you need to learn to see and understand in any system. Suppose we take a large passenger plane. There are many thousands of parts and mechanisms. Some of them are crucial - i.e. such, failure or failure of which will lead to disaster. Assume that such parts 1000 pieces. The probability of failure of each part separately is quite low. Already because they were designed and manufactured by professionals. Assume that the reliability of every part of 1000 is 0.999. Note that this is very high reliability!
But the outcome of the flight (the reliability of the aircraft as a whole) is affected by all 1000 parts! Therefore, the reliability of the aircraft as a whole will be assessed as 0.999 to the power of 1000. This value is equal to 0.375 in my calculator. What does such a figure mean in life? The plane will fall with a probability of 1-0.368 = 0.632, i.e. more than half the time [thanks to NIN colleague for the amendment]. Would you agree to fly under such conditions? .. (I note in parentheses that special methods have long been developed to improve the reliability of technical systems.)
But this is a piece of iron. Now imagine that you are building a chain of transactions with 5 counterparties. At the same time, each participant you trust (otherwise why get involved in a frankly dubious adventure?) By 80%. Then the probability of successful completion of the transaction 0.8 to the 5th degree is 0.328, i.e. slightly above 30%. Are you ready to risk your money on such conditions?
Now option number 2 , when the probability of the entire sequence of events or the behavior of elements of the system does not affect the result of the next attempt.
Let's say you tossed a coin 10 times - and all “tenes” fell ten times. Well, what does not happen in life, right ?! You quit the 11th time. Question: What is the likelihood that the "tails" will fall again?
The correct answer (to which I myself did not think of in my own time, honestly, I confess) - 0.5! Although I really want to say 0.5 to 11 degrees, i.e. 0,00049.
The fact is that the coin “does not know” how it fell in previous “times”. For her, in each individual attempt there are only 2 options, and the probability of each is 0.5.
In life, it is very important to be able to see such situations that “work” according to such an “independent” mechanism — and distinguish them from “dependent ones” (ie, those in which the probability accumulates).
Please note that the error (difference) in the estimates in this example is 1000 times. Those. we were so modestly mistaken by 3 orders of magnitude. It is even incorrect to use the term “mistaken” - we are simply not aware of what is called. This is about the importance of distinguishing the types of situations in life.
Concluding the conversation about these two different options, it can be mentioned that in terms of philosophy, this means that there is between the events in the first case, and in the second case there is no causal relationship.
In fact, in the first case, the condition for performing the task is all the outcomes of coin flips. For example, if “tails” fell out in the second attempt, then the result of “5 eagles in a row” cannot be achieved, right? In the second case, the outcomes of previous attempts do not affect the outcome of any subsequent ones.
Consideration of unlikely events and boundary conditions
There is another aspect of the theme “Eagle or tails?” Notebooks sometimes joke that there are 2 more possible options:
Is it possible Yes, it is possible. On the edge of a coin can fall on Earth. And it can hang (not fall, ie, not fix any of the possible states) in space, where there is no weight.
In each situation (including life) there is a main question. In a situation with a coin falling on an edge, this is: what is the probability that such an outcome will be?
Here you can stop and make 100 or 1000 coin flips. I am not joking, this is a very important moment. After all, it’s about the fact that for concrete thinking you need practical experience. So you can try on your own experience to achieve a situation so that the coin becomes an edge ...
... I hope you have already poured enough and we can continue. I suspect that even in 1000 attempts the coin has never stood on the edge. Although by hand, acting very carefully and carefully, we can put it in this position, right? Those. some finite probability exists.
For the purposes of our conversation, the main conclusion from this exercise is two things:
• in most cases, when one event has a probability 10 or more times higher than another event, the second alternative can be excluded from consideration (usually a difference of an order of magnitude and more is called “quality”);
• At the same time, it is important to remember that we are always dealing with probabilistic processes. And what we excluded at the stage of analysis of this or that option is not because it is impossible in principle, but because it is unlikely, and the possible “price” of such an outcome is not prohibitively large for us. If at stake life or condition - then you need to think once more, and whether you can neglect even such a small probability of a negative outcome ...
It is important to clearly be aware of what and what kind of analysis you are doing, to be adequate and professional.
A little more about taking into account the boundary conditions
An example of a coin hanging in the air indicates the importance of taking into account the conditions in which a particular process takes place. It is always necessary to clearly clarify as a separate item the boundary conditions of the problem that you are offered to solve (act, work). By the way, the classic example of such a situation is Alexander the Great and the Gordian knot. As you know, he did not untie him, he just cut him. At the same time, it does not matter whether the conditions were set or not, since Both options are equally useful to think about: a) you can take advantage of the uncertainty of the boundary conditions, or b) you can consciously go beyond the boundaries of the specified conditions, since - remaining in them - the task is not solved.
Further, there is a phrase: "With him, I would not go to the exploration." What is its essence in terms of probability? In it, on the basis of observing the behavior of this person, a certain forecast is made about his possible actions under the extreme conditions of the intelligence operation (ie, about the likelihood of an outcome in other boundary conditions).
And the logic is this: if there are alarming moments in the behavior of this individual in everyday life, how will he behave when his “fried rooster bites” ?!
The conclusion is simple: if you fundamentally change the conditions for conducting one or another experience, then you should be prepared for the fact that the results obtained in the initial conditions will be frankly unreliable. Those. the probability distribution of outcomes will change dramatically.
It is very important to clearly understand the boundary conditions of the problem.
On the differences between a priori and a posteriori estimates
From the probabilistic nature of most events, the fundamental difference between the so-called. a priori and a posteriori assessment. Those. evaluation before and after the event.
Before the flight, you can a priori declare that it will definitely be successful? It is possible, but it will be absolutely incorrect, because the ultimate probability of adverse outcome always exists. But after the flight, you can say something like, "Yes, I did not doubt it, because the probability of failure was negligible! .."
The biggest difference in such assessments is the psychological difference. You will easily understand this when you remember your condition before the flight and after the plane touched the wheels of the earth.
This is, in fact, a very unbanal conclusion, although at first glance it may seem that way. You will easily understand its importance if you remember how people, having learned to do something (for example, photographing), then say with deliberate negligence: “Easy! ..” So, this is the a posteriori assessment and at the same time the person has already “forgotten” ”That there was no guarantee of such an outcome, there was only a possibility. And for a person who has not yet learned this, it looks like a mockery, and it is completely incomprehensible and even more offensive from this. It is also offensive because it is absolutely not a fact that in his case the factors will converge in the desired configuration and he will also make this qualitative leap. Thousands are photographed, and few are photographers.
It is important to remember that what is a posteriori for you is a priori for others. They look at this task from the other side, they still do not know about it what you know ...
Instead of conclusion
The manifestation of "probabilistic thinking" in your head should be a numerical estimate of the probability of an event. Those. you should think, for example, like this: “an assessment of the probability of an unfavorable outcome of 0.1, and this is already serious and unacceptable for me.” But not "perhaps, this will not happen."
I have touched only a small part of what I call probabilistic thinking. This is a large area, which is desirable to learn, realize and acquire the necessary automatic skills (including the implementation of all types of assessment).
The main thing, for the sake of which I decided to write this small essay, is to remind you that the state of uncertainty (and probability, as a measure of uncertainty) is an essential condition, an attribute of human existence, our life. It is formally possible to increase certainty, and this should be done. Unfortunately, almost always such attempts are associated either with an unreasonably high expenditure of energy, or lack of time. The most important processes in our life are fundamentally vague, due to their exceptional complexity and multifactor character. As a result, our most significant decisions are always made in conditions of a lack of information, when the probability of success is not at all as great as we would like to think. And we have no choice but to try to learn to treat this situation calmly and to be quite effective in such conditions.
PS In order not to end on a pathos-instructive note, let me remind you of a classic anecdote about “probabilistic thinking” in inept performance:
- What is the probability that tomorrow will end the world?
- 50%, because either it comes, or it does not ...
Notice that this does not completely overlap with the dialectical thinking. The difference is that the dialectic describes any situation as a set of multidirectional factors (which, of course, affects the probability of a particular outcome). Then the situation is the essence of the synthesis of these factors at this particular moment.
Probability is a mathematical concept. A classic example is tossing a coin. An “eagle” can fall out, or a “tails” one. Since there are only two sides to the coin, the probability of the “eagle” falling out is 1/2 or 0.5.
There are several very important moments that are included in the notion of “probabilistic thinking”, which can be demonstrated with a coin example.
')
Initially, two fundamentally different options : a) when the probability of the entire sequence of events or elements of the system affects the result; b) when what was before the next event is unimportant.
Consider the first option (remember, when the probability of the entire sequence of events or the behavior of the elements of the system affects the result).
What is the probability of falling "eagle" 2 times in a row? That's right, 0.5 * 0.5 = 0.25. Those. 2 times less than the probability of the "eagle" falling out in a single attempt.
This is a very important point that you need to learn to see and understand in any system. Suppose we take a large passenger plane. There are many thousands of parts and mechanisms. Some of them are crucial - i.e. such, failure or failure of which will lead to disaster. Assume that such parts 1000 pieces. The probability of failure of each part separately is quite low. Already because they were designed and manufactured by professionals. Assume that the reliability of every part of 1000 is 0.999. Note that this is very high reliability!
But the outcome of the flight (the reliability of the aircraft as a whole) is affected by all 1000 parts! Therefore, the reliability of the aircraft as a whole will be assessed as 0.999 to the power of 1000. This value is equal to 0.375 in my calculator. What does such a figure mean in life? The plane will fall with a probability of 1-0.368 = 0.632, i.e. more than half the time [thanks to NIN colleague for the amendment]. Would you agree to fly under such conditions? .. (I note in parentheses that special methods have long been developed to improve the reliability of technical systems.)
But this is a piece of iron. Now imagine that you are building a chain of transactions with 5 counterparties. At the same time, each participant you trust (otherwise why get involved in a frankly dubious adventure?) By 80%. Then the probability of successful completion of the transaction 0.8 to the 5th degree is 0.328, i.e. slightly above 30%. Are you ready to risk your money on such conditions?
Now option number 2 , when the probability of the entire sequence of events or the behavior of elements of the system does not affect the result of the next attempt.
Let's say you tossed a coin 10 times - and all “tenes” fell ten times. Well, what does not happen in life, right ?! You quit the 11th time. Question: What is the likelihood that the "tails" will fall again?
The correct answer (to which I myself did not think of in my own time, honestly, I confess) - 0.5! Although I really want to say 0.5 to 11 degrees, i.e. 0,00049.
The fact is that the coin “does not know” how it fell in previous “times”. For her, in each individual attempt there are only 2 options, and the probability of each is 0.5.
In life, it is very important to be able to see such situations that “work” according to such an “independent” mechanism — and distinguish them from “dependent ones” (ie, those in which the probability accumulates).
Please note that the error (difference) in the estimates in this example is 1000 times. Those. we were so modestly mistaken by 3 orders of magnitude. It is even incorrect to use the term “mistaken” - we are simply not aware of what is called. This is about the importance of distinguishing the types of situations in life.
Concluding the conversation about these two different options, it can be mentioned that in terms of philosophy, this means that there is between the events in the first case, and in the second case there is no causal relationship.
In fact, in the first case, the condition for performing the task is all the outcomes of coin flips. For example, if “tails” fell out in the second attempt, then the result of “5 eagles in a row” cannot be achieved, right? In the second case, the outcomes of previous attempts do not affect the outcome of any subsequent ones.
Consideration of unlikely events and boundary conditions
There is another aspect of the theme “Eagle or tails?” Notebooks sometimes joke that there are 2 more possible options:
- the coin falls on the edge;
- the coin hangs in the air.
Is it possible Yes, it is possible. On the edge of a coin can fall on Earth. And it can hang (not fall, ie, not fix any of the possible states) in space, where there is no weight.
In each situation (including life) there is a main question. In a situation with a coin falling on an edge, this is: what is the probability that such an outcome will be?
Here you can stop and make 100 or 1000 coin flips. I am not joking, this is a very important moment. After all, it’s about the fact that for concrete thinking you need practical experience. So you can try on your own experience to achieve a situation so that the coin becomes an edge ...
... I hope you have already poured enough and we can continue. I suspect that even in 1000 attempts the coin has never stood on the edge. Although by hand, acting very carefully and carefully, we can put it in this position, right? Those. some finite probability exists.
For the purposes of our conversation, the main conclusion from this exercise is two things:
• in most cases, when one event has a probability 10 or more times higher than another event, the second alternative can be excluded from consideration (usually a difference of an order of magnitude and more is called “quality”);
• At the same time, it is important to remember that we are always dealing with probabilistic processes. And what we excluded at the stage of analysis of this or that option is not because it is impossible in principle, but because it is unlikely, and the possible “price” of such an outcome is not prohibitively large for us. If at stake life or condition - then you need to think once more, and whether you can neglect even such a small probability of a negative outcome ...
It is important to clearly be aware of what and what kind of analysis you are doing, to be adequate and professional.
A little more about taking into account the boundary conditions
An example of a coin hanging in the air indicates the importance of taking into account the conditions in which a particular process takes place. It is always necessary to clearly clarify as a separate item the boundary conditions of the problem that you are offered to solve (act, work). By the way, the classic example of such a situation is Alexander the Great and the Gordian knot. As you know, he did not untie him, he just cut him. At the same time, it does not matter whether the conditions were set or not, since Both options are equally useful to think about: a) you can take advantage of the uncertainty of the boundary conditions, or b) you can consciously go beyond the boundaries of the specified conditions, since - remaining in them - the task is not solved.
Further, there is a phrase: "With him, I would not go to the exploration." What is its essence in terms of probability? In it, on the basis of observing the behavior of this person, a certain forecast is made about his possible actions under the extreme conditions of the intelligence operation (ie, about the likelihood of an outcome in other boundary conditions).
And the logic is this: if there are alarming moments in the behavior of this individual in everyday life, how will he behave when his “fried rooster bites” ?!
The conclusion is simple: if you fundamentally change the conditions for conducting one or another experience, then you should be prepared for the fact that the results obtained in the initial conditions will be frankly unreliable. Those. the probability distribution of outcomes will change dramatically.
It is very important to clearly understand the boundary conditions of the problem.
On the differences between a priori and a posteriori estimates
From the probabilistic nature of most events, the fundamental difference between the so-called. a priori and a posteriori assessment. Those. evaluation before and after the event.
Before the flight, you can a priori declare that it will definitely be successful? It is possible, but it will be absolutely incorrect, because the ultimate probability of adverse outcome always exists. But after the flight, you can say something like, "Yes, I did not doubt it, because the probability of failure was negligible! .."
The biggest difference in such assessments is the psychological difference. You will easily understand this when you remember your condition before the flight and after the plane touched the wheels of the earth.
This is, in fact, a very unbanal conclusion, although at first glance it may seem that way. You will easily understand its importance if you remember how people, having learned to do something (for example, photographing), then say with deliberate negligence: “Easy! ..” So, this is the a posteriori assessment and at the same time the person has already “forgotten” ”That there was no guarantee of such an outcome, there was only a possibility. And for a person who has not yet learned this, it looks like a mockery, and it is completely incomprehensible and even more offensive from this. It is also offensive because it is absolutely not a fact that in his case the factors will converge in the desired configuration and he will also make this qualitative leap. Thousands are photographed, and few are photographers.
It is important to remember that what is a posteriori for you is a priori for others. They look at this task from the other side, they still do not know about it what you know ...
Instead of conclusion
The manifestation of "probabilistic thinking" in your head should be a numerical estimate of the probability of an event. Those. you should think, for example, like this: “an assessment of the probability of an unfavorable outcome of 0.1, and this is already serious and unacceptable for me.” But not "perhaps, this will not happen."
I have touched only a small part of what I call probabilistic thinking. This is a large area, which is desirable to learn, realize and acquire the necessary automatic skills (including the implementation of all types of assessment).
The main thing, for the sake of which I decided to write this small essay, is to remind you that the state of uncertainty (and probability, as a measure of uncertainty) is an essential condition, an attribute of human existence, our life. It is formally possible to increase certainty, and this should be done. Unfortunately, almost always such attempts are associated either with an unreasonably high expenditure of energy, or lack of time. The most important processes in our life are fundamentally vague, due to their exceptional complexity and multifactor character. As a result, our most significant decisions are always made in conditions of a lack of information, when the probability of success is not at all as great as we would like to think. And we have no choice but to try to learn to treat this situation calmly and to be quite effective in such conditions.
PS In order not to end on a pathos-instructive note, let me remind you of a classic anecdote about “probabilistic thinking” in inept performance:
- What is the probability that tomorrow will end the world?
- 50%, because either it comes, or it does not ...
Source: https://habr.com/ru/post/370779/
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