Red and green lines. Seven red lines in green
(Conference room)
- Colleagues, - says the head of Nedozaytseva Morkovyeva, - our organization faces a large-scale task. We received a project for implementation, in which we need to draw several red lines. Are you ready to take on this task?
“Of course,” says Nedozaytsev, the head of Sidoryakhin. He is a director, and is always ready to take on a problem that someone from the team will have to bear. However, he immediately clarifies:
- Can we do it?
Petrov's boss Sidoryakhin nods hastily:
- Yes of course. Here we have Petrov, he is our best specialist in the field of drawing red lines. We specially invited him to the meeting so that he could express his competent opinion.
“Very nice,” says Morkovyeva. “Well, you all know me. And this is Lenochka, she is a design specialist in our organization.
Specialist Lenochka blushes and smiles shyly. She recently graduated from economics, and has the same attitude to design as a platypus to the design of airships.
— So, — says Morkoveva. We need to draw seven red lines. All of them must be strictly perpendicular, and in addition, some need to be drawn in green, and some more - transparent. Do you think it's real?
“No,” says Petrov.
“Let's not rush into an answer, Petrov,” says Sidoryahin. “The task has been set, and it must be solved. You are a professional, Petrov. Don't give us a reason to think you're not a professional.
“You see,” Petrov explains, “the term “red line” implies that the color of the line is red. Drawing a red line in green is not exactly impossible, but very close to impossible...
- Petrov, what does "impossible" mean? asks Sidoryahin.
I'm just describing the situation. Perhaps there are people who are colorblind, for whom the color of the line really will not matter, but I'm not sure that the target audience of your project consists exclusively of such people.
- That is, in principle, it is possible, do we understand you correctly, Petrov? asks Morkoveva.
Petrov realizes that he went too far with imagery.
“Let’s put it simply,” he says. - The line, as such, can be drawn with absolutely any color. But to get a red line, you should use only red.
Petrov, please don't confuse us. You just said it was possible.
Petrov silently curses his talkativeness.
No, you misunderstood me. I just wanted to say that in some extremely rare situations, the color of the line will not matter, but even then - the line will still not be red. You see, it will not be red! She will be green. And you need red.
There is a short silence, in which the quiet, tense buzzing of synapses is clearly audible.
“But what if,” Nedozaytsev says, struck by the idea, “draw them in blue?”
“It won’t work anyway,” Petrov shakes his head. - If you draw in blue, you get blue lines.
Again silence. This time he is interrupted by Petrov himself.
“And I still don’t understand… What did you mean when you talked about lines of transparent color?”
Morkovyeva looks at him condescendingly, like a kind teacher at a lagging student.
- Well, how can I explain it to you? .. Petrov, don't you know what "transparent" is?
- And what is the “red line”, I hope you don’t need to explain either?
- No, it's not necessary.
- Here you go. You draw red lines for us with a transparent color.
Petrov pauses for a second, considering the situation.
- And what should the result look like, please, describe please? How do you imagine that?
- Well, uh, Petro-o-ov! Sidorakhin says. - Well, let's not ... What do we have, a kindergarten? Who is the red line specialist here, Morkovyeva or you?
“I’m just trying to clarify the details of the assignment for myself…”
“Well, what’s incomprehensible here? ..” Nedozaytsev interjects into the conversation. Do you know what the red line is?
- Yes, but...
- And what is "transparent", is it clear to you too?
“Of course, but…
"So what do you have to explain?" Petrov, well, let's not stoop to unproductive disputes. The task is set, the task is clear and precise. If you have specific questions, please ask.
“You are a professional,” Sidoryakhin adds.
“Okay,” Petrov surrenders. - God be with him, with color. But do you have something else with perpendicularity there? ..
“Yes,” Morkovyeva readily confirms. “Seven lines, all strictly perpendicular.
- Perpendicular to what? Petrov clarifies.
Morkovyeva starts looking through her papers.
"Uh-uh," she finally says. — Well, sort of… Everything. Between themselves. Well, or whatever… I don't know. I thought it was you who knew what perpendicular lines were - finally she was found.
“Yes, of course he knows,” Sidoryakhin waves his hands. Are we professionals here or not?
Two lines can be perpendicular, explains Petrov patiently. “All seven cannot be perpendicular to each other at the same time. This is geometry, 6th grade.
Morkovyeva shakes her head, driving away the looming ghost of a long-forgotten school education. Nedozaytsev slams his palm on the table:
- Petrov, let's do without this: "6th grade, 6th grade." Let's be mutually polite. Let's not make hints and slide down to insults. Let's maintain a constructive dialogue. Here same not idiots gathered.
“I think so too,” says Sidoryakhin.
Petrov pulls a piece of paper towards him.
“Okay,” he says. Let me draw for you. Here is the line. So?
Morkoveva nods her head in the affirmative.
— Draw another one… — says Petrov. Is it perpendicular to the first one?
Yes, it is perpendicular.
- Well, you see! - happily exclaims Morkoveva.
“Wait, that's not all. Now draw the third one... Is it perpendicular to the first line?..
Thoughtful silence. Without waiting for an answer, Petrov answers himself:
— Yes, it is perpendicular to the first line. But it does not intersect with the second line. They are parallel to the second line.
There is silence. Then Morkovyeva gets up from her seat and, rounding the table, enters Petrov from the rear, looking over his shoulder.
“Well…” she says hesitantly. - Maybe yes.
“That's the point,” says Petrov, trying to consolidate the success achieved. - As long as there are two lines, they can be perpendicular. As soon as there are more...
- Can I have a pen? asks Morkoveva.
Petrov hands over the pen. Morkovyeva carefully draws a few uncertain lines.
- And if so?..
Petrov sighs.
It's called a triangle. No, these are not perpendicular lines. Plus, there are three of them, not seven.
Morkoveva purses her lips.
- Why are they blue? Nedozaytsev suddenly asks.
“Yes, by the way,” Sidoryakhin supports. — I wanted to ask myself.
Petrov blinks several times, looking at the drawing.
“My pen is blue,” he finally says. I'm just to show...
“It will turn out the same,” Petrov says confidently.
- Well, how about the same? Nedozaytsev says. How can you be sure if you haven't even tried? You draw red, and we'll see.
“I don’t have a red pen with me,” Petrov admits. But I can totally...
“But why didn’t you prepare,” Sidoryakhin says reproachfully. “We knew there would be a meeting…
“I can tell you with absolute certainty,” Petrov says in despair, “that exactly the same thing will turn out in red.
“You yourself told us last time,” Sidoryakhin retorts, “that you need to draw red lines in red. Here, I even wrote it down for myself. And draw them yourself with a blue pen. What do you think, red lines?
“By the way, yes,” remarks Nedozaytsev. — I also asked you about the color blue. What did you answer me?
Petrov is suddenly saved by Lenochka, who is studying his drawing with interest from her seat.
“I think I understand,” she says. You're not talking about color right now, are you? It's about this one, what do you call it? Perper something?
“Perpendicular lines, yes,” Petrov responds gratefully. - It has nothing to do with the color of the lines.
“That's it, you completely confused me,” says Nedozaytsev, looking from one participant in the meeting to another. "So what's the problem with us?" With color or with perpendicularity?
Morkovyeva makes confused noises and shakes her head. She got confused too.
“Both the one and the other,” Petrov says quietly.
“I can’t understand anything,” says Nedozaytsev, looking at his clasped fingers. - There is a task. All you need is seven red lines. I understand that there would be twenty of them! .. But there are only seven. The task is simple. Our customers want seven perpendicular lines. Right?
Morkoveva nods.
“And Sidoryahin also sees no problem,” says Nedozaytsev. “Am I right, Sidoryahin?.. Well, then. So what is stopping us from completing the task?
“Geometry,” Petrov says with a sigh.
"Well, just ignore her, that's all!" Morkoveva says.
Petrov is silent, collecting his thoughts. Colorful metaphors are born in his brain one after another, which would make it possible to convey to those around him the surrealism of what is happening, but as luck would have it, all of them, clothed in words, begin with an invariably obscene word, completely inappropriate within the framework of a business conversation.
Tired of waiting for an answer, Nedozaytsev says:
- Petrov, you answer simply - can you do it or can't you? I understand that you are a narrow specialist and do not see the big picture. But it's not difficult to draw some seven lines? We have been discussing some nonsense for two hours now, we can’t come to a decision.
“Yes,” says Sidoryahin. - You just criticize and say: “Impossible! Impossible!" You offer us your solution to the problem! And even a fool can criticize, pardon the expression. You are a professional!
Petrov wearily says:
- Fine. Let me draw you two guaranteed perpendicular red lines, and the rest in transparent color. They will be transparent and not visible, but I will draw them. Will that suit you?
“Will that suit us?” Morkovyeva turns to Lenochka. - Yes, it will suit us.
“Only at least a couple more - in green,” Lenochka adds. - And I have another question, can I?
- Can one line be depicted in the form of a kitten?
Petrov is silent for a few seconds, and then asks again:
- Well, in the form of a kitten. Kitten. Our users love animals. It would be great…
“No,” says Petrov.
- And why?
— No, of course I can draw you a cat. I'm not an artist, but I can try. Only it will no longer be a line. It will be a cat. A line and a cat are two different things.
“Kitten,” Morkovyeva clarifies. - Not a cat, but a kitten, so small, cute. Cats they...
“It doesn’t matter,” Petrov shakes his head.
“Not at all, right? ..” Lenochka asks disappointedly.
“Petrov, you could at least listen to the end,” Nedozaytsev says irritably. - You haven't listened to the end, but already say "No".
“I understand the idea,” says Petrov, without looking up from the table. - It is impossible to draw a line in the form of a kitten.
“Well, you don’t have to then,” Lenochka allows. "Won't the bird work too?"
Petrov silently looks up at her and Lenochka understands everything.
“Well, don’t, then,” she repeats again.
Nedozaytsev slams his hand on the table.
- So where did we stop? What are we doing?
“Seven red lines,” says Morkovyeva. — Two in red, and two in green, and the rest transparent. Yes? Did I understand correctly?
“Yes,” Sidoryahin confirms before Petrov can open his mouth.
Nedozaytsev nods in satisfaction.
- That's great ... Well, then, that's it, colleagues? .. Let's part ways? .. Any more questions? ..
“Oh,” Lenochka recalls. We also have a red balloon! Say, can you blow it up?
“Yes, by the way,” says Morkovyeva. Let's discuss this right away, so as not to gather twice.
"Petrov," Nedozaytsev turns to Petrov. - Can we do it?
“And what does the ball have to do with me?” Petrov asks in surprise.
“It’s red,” Lenochka explains.
Petrov is stupidly silent, trembling with his fingertips.
“Petrov,” Nedozaytsev asks nervously. So can you or can't you? It's a simple question.
“Well,” Petrov says cautiously, “in principle, of course, I can, but…
“Good,” Nedozaytsev nods. - Go to them, inflate. Travel allowance, if necessary, we will issue.
- Tomorrow can be? asks Morkoveva.
“Of course,” Nedozaytsev replies. - I think there will be no problems ... Well, now we have everything? .. Excellent. We worked productively ... Thank you all and goodbye!
Petrov blinks several times to return to objective reality, then gets up and slowly walks towards the exit. At the very exit, Lenochka catches up with him.
“Can I ask you more?” - blushing, says Lenochka. - When you inflate the balloon ... can you inflate it in the shape of a kitten? ..
Petrov sighs.
“I can do anything,” he says. - I can absolutely everything. I'm professional.
At a meeting that took place on Tuesday, employee Petrov's brain was taken out. Then it was divided into portions and put on plates. After the procedure, everyone sat down at the table and began to eat it, while showing their approval. And it began:
We received an offer to implement the project. The goal of the project is to present several red lines. This project means a lot to our organization. Are you ready to take on such loads? - An employee of Markovyeva turned to her colleagues.
Of course, Nedozaytsev answered quickly. This was the director, who at any moment can take on the burden of solving a problem of any complexity. After all, one of the employees will have to deal with it. And he continues: After all, can we?
In response to the director's question, the head of the drawing department, Sidoryakhin, quickly nods his head:
Certainly! We have a smart redline painter. His name is Petrov. He is right now among us. He was invited specifically on this issue to express his opinion.
Here again, Markovyeva takes over the baton, starting to introduce another employee: You know me, of course. But we have a designer among us. Her name is Lenochka.
The girl Lenochka begins to blush and be embarrassed. She recently graduated from economics. And it has nothing to do with design.
So, - Markovyeva continued, - this order is as follows: you need to draw 7 red lines perpendicular to each other. In addition, there should be a few transparent and green lines among them. Is it doable, do you think?
No, - answered the specialist Petrov.
Let's not rush to a conclusion. We have a task before us, and we must solve it!” Sidoryakhin interrupted him. "You're a professional, so don't give us any reason to doubt it."
Understand, red lines should be drawn only in red, but not in green or in any other color. It's just not possible, - explains Petrov.
How can I understand you, Petrov? Why is it impossible? - Sidoryahin asks indignantly.
There is a possibility that some part of the audience of this project will consist of people who suffer from color blindness. It won't matter to them what color the lines are. But I'm not sure that the main part of our project consists of just such people. Petrov answers.
But from your words, we understand that this is possible, right? asks Markoviev.
Here Petrov realizes that he exaggerated a little with the description.
Understand that a line can be depicted in absolutely any color. But to get a red line, you need to use only red colors, he replies.
Are you confusing us? Did you just say otherwise?
Petrov mentally begins to punish himself for his talkativeness.
You misunderstand me. There are cases where the color of the line doesn't matter. But such cases are extremely rare. Do you understand? But even in such situations, the line will not be exactly red. You see, it won't! It will have a different color, but not red. This is what I wanted to explain to you.
There was a pause after Petrov's explanation. It clearly felt tense and nervous atmosphere.
Then suddenly the director comes up with an idea.
What if we draw these lines in blue?
Nothing will come of it,” Petrov replies. Then the lines will be blue.
There is another pause in the conversation, but Petrov decides to interrupt it and asks.
I have a question. You said something about transparent lines. What did you mean?
Markovyeva looked at Petrov like a teacher at a weak student.
What don't you understand? You have no idea about the concept of "transparent"?
Of course I have.
What about the term “red line”?
Here you see. If you all know, so what's the problem? Draw us these red lines with transparent color only.
Here Petrov froze. After considering the situation, he asks a question.
Okay, now you tell me what will be the result? Can you describe it to me?
Petrov, don't forget! You are our red line specialist, not Markovyeva. Let's not have a kindergarten here.
I'm trying to figure out some details of this assignment...
Here director Nedozaytsev interrupts him...
What don't you understand? After all, you know the concept of "red line"?
What about "transparent"?
Of course, but...
So what explanations do you still need? Let's not get into useless arguments. The task is simple and clear. If someone has specific questions, then ask them.
After all, you are a professional, - says Sidoryakhin.
Well, - agrees Petrov, - we figured out the color. What are the other conditions?
According to the assignment, all lines should be perpendicular, - Markovyeva answers.
What are they perpendicular to? Petrov asks.
Here Markovyeva starts reviewing the documents.
How can I tell you? ... Well ... Probably, they are perpendicular to everything and to each other. I understand that you should know, because you are an expert in this matter.
Of course, he knows, - Sidoryakhin butts in. Are we professionals or not?
How is this possible? After all, only two lines can be perpendicular to each other, but not seven. The proof of this rule is in the geometry course for grade 6.
Markovyeva shakes her head, ignoring Petrov's remark. And Nedozaytsev beats the table with his hand:
This is how to understand, Petrov? What does "6th grade" mean? Let's not bring our dialogue to the point of humiliation. We must be polite to each other in order to achieve a result. After all, we are stupid people.
I join your opinion, - says Sidoryakhin.
Petrov takes a sheet of paper and says:
Let's try to draw these lines now, shall we? Let's draw one line. Now another. Is the second line perpendicular to the first?
Yes, it is perpendicular to the first.
Here you go! Markovyeva says happily.
Take your time, I'm not done yet. Here is the third line. Is it perpendicular to the first?
Silence in the room, but Petrov decided to answer himself:
Of course it is perpendicular to the first line, but not the second. The third line is parallel to the second.
There is complete silence in the room. Markovyeva gets up and approaches Petrov from behind. Looks at the drawing over his shoulder and says hesitantly:
Probably yes. You're right.
Therein lies the problem. Only two lines can be perpendicular. But if their numbers increase...
Not having time to finish her story, Petrova interrupts Markoviev and asks for a pen. Uncertainly draws three lines and asks:
Is this option possible?
Taking a deep breath, Petrov replies:
This is a triangle. It has only three lines, not seven. And they are not perpendicular.
Markovyeva thinks, and Nedozaytsev asks a question:
Can you tell me why the lines are blue?
Indeed, why are they blue? - connects to the director Sidoryahin.
So I just showed the drawing with a blue pen, - Petrov answers.
It will be the same, - Petrov confidently answers.
But why? How can you be sure that you haven't tried it yet? You try it and then we'll see.
I did not take a red pen with me,” Petrov said. But I'm sure...
You knew where you were going. Why didn't you prepare? - Sidoryakhin indignantly asks Petrov.
I can tell you with confidence that the same thing will happen with a red pen, - Petrov says disappointedly.
No, Petrov, you yourself told us that the red lines should be depicted exclusively in red, and not in any other color. Here, I even wrote down your words. Do you paint in blue, or do you think it's red?
Exactly, - emphasizes Nedozaytsev. “I also asked you about it. What did you answer me?
Suddenly, Lenochka intervenes in the conversation. She looked at the drawing with interest.
I think I understand what you want to say, - says Lenochka. “It’s not about color now, is it?” And about this perpen-something-there?
Quite right, the perpendicularity of the lines, says Petrov. - In this matter, the color of the lines does not matter.
Now I'm completely confused, - says Nedozaytsev, looking at both employees. "So what's the problem anyway?" With color or lines?
Markovyeva shakes her head, thus showing her confused state.
And with that, and with that, - Petrov says quietly.
I don’t understand anything,” says Nedozaytsev, examining his hands and clasped fingers. - We have a task. It consists in the fact that you need to draw only seven red lines. Not twenty, but only seven. After all, it's simple. Customers requested only seven perpendicular lines. So?
Markovyeva nods her head.
So the head of the department also does not see the problem, - continues Nedozaytsev. - Really, Sidoryahin? So what's the problem? What's stopping us from ordering?
Geometry - answers Petrov.
And you try not to pay attention to her! Markoveva says.
Petrov stands silently and collects his thoughts. But there is no way to collect them together. Vivid metaphors appear in his head. With their help, of course, it was possible to convey the essence of what was happening, but alas, they all begin with the word “Fuck!”. Unfortunately, it will be out of place in this conversation.
Petrov, why are you silent? Just answer the question before you - will you complete or not complete the order? I get the impression that you are not a professional in your field. We have been discussing the same issue for two hours and cannot come to a conclusion.
Indeed, - adds Sidoryahin. - So far you have only criticized and said “Impossible!”. Any fool can criticize! Can you suggest us any solution to the problem. Show what a professional you are, sorry for the expression.
Let's try this, - says Petrov, - I will draw two perpendicular lines in red, and the remaining five will be transparent. They won't be visible, but I'll draw them. Will this option work for you?
Lenochka, will this option suit us? - asks Markoviev, - Yes, it will.
And it would be possible to make a couple of lines in green, - says Lenochka. - I have a question, may I?
Yes, Petrov answers.
Is it possible to draw one line in the form of a kitten?
What? Petrov asks after a short pause.
In the form of a kitten. The fact is that our users really like little animals. It would be very...
No, says Petrov.
But why?
Of course, I'm not an artist, but I can try to draw a cat. But it's not a line. It's a cat. These are completely different things.
Markovyeva intervenes in the conversation.
Not a cat, but a small, pretty kitten. Cats they...
There is no difference, says Petrov.
Can't you? – asks disappointed Lenochka.
You didn't even listen to the end, - the irritated director intervenes. - Say "no" right away.
I understood the idea, - says Petrov, lowering his head. – It is not possible to draw a kitten as a line.
No, it’s not like that,” Lenochka says. - Can't you have a bird?
Petrov did not answer, and silently looked up at her. Lenochka understood everything.
No, it’s not like that, Lenochka repeated.
So what have we come to? What are we deciding? asks Nedozaytsev.
It is necessary to depict seven red lines. Of these: two green, two red and three transparent. Am I right?
That's right, - confirms Sidoryahin, even before Petrov tried to open his mouth.
Great, says the director. - That's all? Maybe someone else has questions?
Oh, another question, - Lenochka recalls. - And we have a red balloon! Can you blow it up?
Nedozaytsev turns to Petrov and asks:
Can we do it, Petrov?
Does the ball have anything to do with me? Petrov asks with a surprised face.
But it's red, - says Lenochka.
Petrov sits stupidly silently at the table and twitches his fingertips.
So will you answer the question, Petrov? - nervous Nedozaytsev. - Can you do it or not?
In principle, I can do it, but ... - Petrov says carefully.
Agreed, - said Nedozaytsev. - Go to them and inflate the balloon. If you need travel allowance for this, we will issue it.
Can it be done tomorrow? asks Markoviev.
Of course, there is no problem, - the director answered. - That's it? Amazing. Well done. Everybody's Free. Goodbye!
Petrov sat for a few more seconds to return to reality. He gets up from the table and walks slowly towards the exit. But Lenochka catches up with him and asks:
I have one request for you, - says Lenochka, while blushing. - Can you blow up a balloon in the form of a kitten?
Taking a deep breath, Petrov answers:
I'm a professional! I can do everything! Petrov answered.
Meeting or Seven Red Lines
Petrov came to the meeting on Tuesday. They took out his brain there, put it on saucers and began to eat, smacking his lips and generally expressing all kinds of approval. Petrov's boss, Nedozaytsev, prudently handed out dessert spoons to those present. And it began.
Colleagues, - says Morkovyeva, - our organization faces a large-scale task. We received a project for implementation, in which we need to draw several red lines. Are you ready to take on this task?
Of course, - says Nedozaytsev. He is a director, and is always ready to take on a problem that someone from the team will have to bear. However, he immediately clarifies: - We can do it?
The head of the drawing department, Sidoryakhin, nods hastily:
Yes of course. Here we have Petrov, he is our best specialist in the field of drawing red lines. We specially invited him to the meeting so that he could express his competent opinion.
Very nice, - says Morkoveva. - Well, you all know me. And this is Lenochka, she is a design specialist in our organization.
Lenochka is covered with paint and smiles embarrassedly. She recently graduated from economics, and has the same attitude to design as a platypus to the design of airships.
So, - says Morkoveva. - We need to draw seven red lines. All of them must be strictly perpendicular, and in addition, some need to be drawn in green, and some more - transparent. Do you think it's real?
No, says Petrov.
Let's not rush to answer, Petrov, - says Sidoryahin. - The task is set, and it needs to be solved. You are a professional, Petrov. Don't give us a reason to think you're not a professional.
You see, Petrov explains, the term "red line" implies that the color of the line is red. Drawing a red line in green is not exactly impossible, but very close to impossible...
Petrov, what does "impossible" mean? - asks Sidoryahin.
I'm just describing the situation. Perhaps there are people who are colorblind, for whom the color of the line really will not matter, but I'm not sure that the target audience of your project consists exclusively of such people.
That is, in principle, it is possible, do we understand you correctly, Petrov? - asks Morkoveva.
Petrov realizes that he went too far with imagery.
Let's put it simply, he says. - The line, as such, can be drawn with absolutely any color. But to get a red line, you should use only red.
Petrov, please don't confuse us. You just said it was possible.
Petrov silently curses his talkativeness.
No, you misunderstood me. I just wanted to say that in some extremely rare situations, the color of the line will not matter, but even then - the line will still not be red. You see, it will not be red! She will be green. And you need red.
There is a short silence, in which the quiet, tense buzzing of synapses is clearly audible.
And what if, - Nedozaytsev says, inspired by the idea, - draw them in blue?
It still won't work, - Petrov shakes his head. - If you draw in blue, you get blue lines.
Again silence. This time he is interrupted by Petrov himself.
And I still don't get it... What did you mean when you talked about transparent color lines?
Morkovyeva looks at him condescendingly, like a kind teacher at a lagging student.
Well, how can I explain it to you? .. Petrov, don't you know what "transparent" is?
And what is the “red line”, I hope you don’t need to explain either?
No, don't.
Here you go. You draw red lines for us with a transparent color.
Petrov pauses for a second, considering the situation.
And what should the result look like, please, describe please? How do you imagine that?
Well-u-u, Petro-o-ov! - says Sidoryahin. - Well, let's not ... What do we have, a kindergarten? Who is the red line specialist here, Morkovyeva or you?
I'm just trying to clarify the details of the task for myself...
Well, what’s incomprehensible here? .. - Nedozaytsev intervenes in the conversation. - Do you know what the red line is?
And what is "transparent", is it clear to you too?
Of course, but...
So what do you have to explain? Petrov, well, let's not stoop to unproductive disputes. The task is set, the task is clear and precise. If you have specific questions, please ask.
You are a professional, - adds Sidoryakhin.
Okay, - surrenders Petrov. - God be with him, with the color. But do you have something else with perpendicularity there? ..
Yes, - readily confirms Morkovyeva. - Seven lines, all strictly perpendicular.
Perpendicular to what? - specifies Petrov.
Morkovyeva starts looking through her papers.
Uh-uh, she finally says. - Well, sort of... Everything. Between themselves. Well, or whatever… I don't know. I thought it was you who knew what perpendicular lines were - finally she was found.
Yes, of course he knows, - Sidoryakhin waves his hands. Are we professionals here or not?
Two lines can be perpendicular, - Petrov patiently explains. - All seven cannot be perpendicular to each other at the same time. This is geometry, 6th grade.
Morkovyeva shakes her head, driving away the looming ghost of a long-forgotten school education. Nedozaytsev slams his palm on the table:
Petrov, let's do without this: "6th grade, 6th grade." Let's be mutually polite. Let's not make hints and slide down to insults. Let's maintain a constructive dialogue. Here same not idiots gathered.
I also think so, - says Sidoryakhin.
Petrov pulls a piece of paper towards him.
Okay, he says. Let me draw for you. Here is the line. So?
Morkoveva nods her head in the affirmative.
We draw another ... - says Petrov. - Is it perpendicular to the first one?
Yes, it is perpendicular.
Well, you see! - joyfully exclaims Morkoveva.
Wait, that's not all. Now draw the third one... Is it perpendicular to the first line?..
Thoughtful silence. Without waiting for an answer, Petrov answers himself:
Yes, it is perpendicular to the first line. But it does not intersect with the second line. They are parallel to the second line.
There is silence. Then Morkovyeva gets up from her seat and, rounding the table, enters Petrov from the rear, looking over his shoulder.
Well…” she says uncertainly. - Maybe yes.
That's the point, - says Petrov, trying to consolidate the success achieved. - As long as there are two lines, they can be perpendicular. As soon as there are more...
Can I have a pen? - asks Morkoveva.
Petrov hands over the pen. Morkovyeva carefully draws a few uncertain lines.
And if so?..
Petrov sighs.
It's called a triangle. No, these are not perpendicular lines. Plus, there are three of them, not seven.
Morkoveva purses her lips.
Why are they blue? - suddenly asks Nedozaytsev.
Yes, by the way, - supports Sidoryahin. - I wanted to ask myself.
Petrov blinks several times, looking at the drawing.
My pen is blue, he finally says. I'm just to show...
It will turn out the same, - Petrov says confidently.
Well, how is the same? - says Nedozaytsev. - How can you be sure if you haven't even tried? You draw red, and we'll see.
I don’t have a red pen with me,” Petrov admits. But I can totally...
Why didn’t you prepare, ”Sidoryakhin says reproachfully. We knew there would be a meeting...
I can tell you with absolute certainty, - Petrov says in despair, - that exactly the same thing will turn out in red.
You yourself told us last time, - Sidoryakhin retorts, - that you need to draw red lines in red. Here, I even wrote it down for myself. And draw them yourself with a blue pen. What do you think, red lines?
By the way, yes, - notes Nedozaytsev. - I also asked you about the blue color. What did you answer me?
Petrov is suddenly saved by Lenochka, who is studying his drawing with interest from her seat.
I think I understand,” she says. - You're not talking about color now, are you? It's about this one, what do you call it? Perper something?
The perpendicularity of the lines, yes, - Petrov responds gratefully. - It has nothing to do with the color of the lines.
That's it, you completely confused me, - says Nedozaytsev, looking from one meeting participant to another. - So what's the problem with us? With color or with perpendicularity?
Morkovyeva makes confused noises and shakes her head. She got confused too.
Both with that, and with another, - quietly speaks Petrov.
I can’t understand anything,” says Nedozaytsev, looking at his fingers clasped in the castle. - There is a task. All you need is seven red lines. I understand that there would be twenty of them! .. But there are only seven. The task is simple. Our customers want seven perpendicular lines. Right?
Morkoveva nods.
And Sidoryahin also sees no problem, says Nedozaytsev. - Am I right, Sidoryahin?.. Well. So what is stopping us from completing the task?
Geometry, - Petrov says with a sigh.
Well, you just ignore her, that's all! - says Morkoveva.
Petrov is silent, collecting his thoughts. Colorful metaphors are born in his brain one after another, which would make it possible to convey to those around him the surrealism of what is happening, but as luck would have it, all of them, clothed in words, invariably begin with the word “Fuck!”, Completely inappropriate within the framework of a business conversation.
Tired of waiting for an answer, Nedozaytsev says:
Petrov, you answer simply - can you do it or can't you? I understand that you are a narrow specialist and do not see the big picture. But it's not difficult - to draw some seven lines? We have been discussing some nonsense for two hours now, we can’t come to a decision.
Yes, says Sidoryahin. - You just criticize and say: “Impossible! Impossible!" You offer us your solution to the problem! And even a fool can criticize, pardon the expression. You are a professional!
Petrov wearily says:
Fine. Let me draw you two guaranteed perpendicular red lines, and the rest in transparent color. They will be transparent and not visible, but I will draw them. Will that suit you?
Will it suit us? - Morkovyeva turns to Lenochka. - Yes, it will suit us.
Only at least a couple more - in green, - Lenochka adds. - And I have another question, can I?
Can one line be drawn as a kitten?
Petrov is silent for a few seconds, and then asks again:
Well, like a kitten. Kitten. Our users love animals. It would be great…
No, says Petrov.
And why?
No, of course I can draw you a cat. I'm not an artist, but I can try. Only it will no longer be a line. It will be a cat. Line and cat are different things.
Kitten, - specifies Morkovyeva. - Not a cat, but a kitten, so small, cute. Cats they...
It doesn't matter, Petrov shakes his head.
Not at all, right? .. - Lenochka asks disappointedly.
Petrov, you should at least listen to the end, - Nedozaytsev says irritably. - You haven't listened to the end, but already say "No".
I understood the idea, - without looking up from the table, says Petrov. - It is not possible to draw a line in the form of a kitten.
Well, you don’t need it then, - Lenochka allows. - A bird, too, will not work?
Petrov silently looks up at her and Lenochka understands everything.
Well, you don’t have to then, ”she repeats again.
Nedozaytsev slams his hand on the table.
So where did we stop? What are we doing?
Seven red lines, says Morkovyeva. - Two in red, and two in green, and the rest transparent. Yes? Did I understand correctly?
Yes, Sidoryahin confirms before Petrov can open his mouth.
Nedozaytsev nods in satisfaction.
That's great ... Well, then, that's it, colleagues? .. Let's part ways? .. Any more questions? ..
Oh, Lenochka recalls. - We still have a red balloon! Say, can you blow it up?
Yes, by the way, - says Morkoveva. - Let's also discuss this right away, so as not to gather twice.
Petrov, - Nedozaytsev turns to Petrov. - Can we do it?
And what does the ball have to do with me? Petrov asks in surprise.
It is red, - Lenochka explains.
Petrov is stupidly silent, trembling with his fingertips.
Petrov,” Nedozaytsev asks nervously. So can you or can't you? It's a simple question.
Well, - Petrov says carefully, - in principle, of course, I can, but ...
Good, - Nedozaytsev nods. - Go to them, inflate. Travel allowance, if necessary, we will issue.
Tomorrow can be? - asks Morkoveva.
Of course, - answers Nedozaytsev. - I think there will be no problems ... Well, now we have everything? .. Excellent. We worked productively ... Thank you all and goodbye!
Petrov blinks several times to return to objective reality, then gets up and slowly walks towards the exit. At the very exit, Lenochka catches up with him.
Can I ask you more? - blushing, says Lenochka. - When you inflate the balloon ... can you inflate it in the form of a kitten? ..
Petrov sighs.
I can do anything, he says. - I can absolutely everything. I'm professional.
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Petrov came to the meeting on Tuesday. They took out his brain there, put it on saucers and began to eat, smacking his lips and generally expressing all kinds of approval. Petrov's boss, Nedozaytsev, prudently handed out dessert spoons to those present. And it started.
Colleagues, - says Morkovyeva, - our organization faces a large-scale task. We received a project for implementation, within which we need to draw several red lines. Are you ready to take on this task?
Of course, - says Nedozaytsev. He is a director, and is always ready to take on a problem that someone from the team will have to bear. However, he immediately clarifies: - We can do it?
The head of the drawing department, Sidoryakhin, nods hastily:
Yes, of course. Here we have Petrov, he is our best specialist in the field of drawing red lines. We specially invited him to the meeting so that he expressed his competent opinion.
Very nice, - says Morkoveva. - Well, you all know me. And this is Lenochka, she is a design specialist in our organization.
Lenochka is covered with paint and smiles embarrassedly. She recently graduated from economics, and has the same attitude to design as a platypus to the design of airships.
So, - says Morkoveva. - We need to draw seven red lines. All of them must be strictly perpendicular, and in addition, some need to be drawn in green, and some more - transparent. Do you think this is real?
No, says Petrov.
Let's not rush to answer, Petrov, - says Sidoryakhin. - The task has been set, and it needs to be solved. You are a professional, Petrov. Don't give us a reason to think that you are not a professional.
You see, - explains Petrov, - the term "red line" implies that the color of the line is red. Drawing a red line in green is not impossible, but very close to impossible ...
Petrov, what does "impossible" mean? - asks Sidoryahin.
I'm just describing the situation. Perhaps there are colorblind people for whom the color of the line really will not matter, but I'm not sure that the target audience of your project consists exclusively of such people.
That is, in principle, it is possible, do we understand you correctly, Petrov? - asks Morkoveva.
Petrov realizes that he went too far with imagery.
Let's put it simply, he says. - The line, as such, can be drawn in absolutely any color. But to get a red line, you should use only red.
Petrov, please don't confuse us. You just said it was possible.
Petrov silently curses his talkativeness.
No, you misunderstood me. I just wanted to say that in some extremely rare situations, the color of the line will not matter, but even then - the line will still not be red. You see, it will not be red! She will be green. And you need red.
There is a short silence, in which the quiet, tense buzzing of synapses is clearly audible.
And what if, - inspired by the idea, says Nedozaytsev, - draw them in blue?
It won't work anyway, - Petrov shakes his head. - If you draw in blue, you will get blue lines.
Again silence. This time he is interrupted by Petrov himself.
And I still don't understand... What did you mean when you talked about transparent color lines?
Morkovyeva looks at him condescendingly, like a kind teacher at a lagging student.
Well, how can I explain to you? .. Petrov, don't you know what "transparent" is?
And what is the "red line", I hope you don't need to explain either?
No, don't.
Here you go. You draw red lines for us with a transparent color.
Petrov freezes for a second, considering the situation.
And how should the result look like, please, describe please? How do you imagine it?
Well-u-u, Petro-o-ov! - says Sidoryahin. - Well, let's not ... Do we have a kindergarten? Who is the red line specialist here, Morkovyeva or you?
I'm just trying to clarify the details of the task for myself ...
Well, what’s incomprehensible here? .. - Nedozaytsev intervenes in the conversation. - Do you know what the red line is?
And what is "transparent", is it clear to you too?
Of course, but...
So what do you have to explain? Petrov, well, let's not stoop to unproductive disputes. The task has been set, the task is clear and precise. If you have specific questions, then ask.
You are a professional, - adds Sidoryahin.
Okay, - surrenders Petrov. - God be with him, with the color. But do you have something else with perpendicularity? ..
Yes, - readily confirms Morkovyeva. - Seven lines, all strictly perpendicular.
Perpendicular to what? - specifies Petrov.
Morkovyeva starts looking through her papers.
Uh-uh, she finally says. - Well, sort of... Everything. Between themselves. Well, or whatever… I don't know. I thought you know what perpendicular lines are - finally she is.
Yes, of course he knows, - Sidoryakhin waves his hands. - Are we professionals here, or are we not professionals? ..
Two lines can be perpendicular, - Petrov patiently explains. - All seven cannot be perpendicular to each other at the same time. This is geometry, 6th grade.
Morkovyeva shakes her head, driving away the looming ghost of a long-forgotten school education. Nedozaytsev slams his palm on the table:
Petrov, let's do without this: "6th grade, 6th grade." Let's be mutually polite. Let's not make hints and slide into insults. Let's have a constructive dialogue. It's not idiots gathered here.
I also think so, - says Sidoryakhin.
Petrov moves a piece of paper towards him.
Okay, he says. - Let me draw for you. Here is the line. So?
Morkovyeva nods her head in the affirmative.
We draw another ... - says Petrov. - Is it perpendicular to the first one?
Yes, it is perpendicular.
Well, you see! - joyfully exclaims Morkovyeva.
Wait, that's not all. Now draw the third one... Is it perpendicular to the first line?..
Thoughtful silence. Without waiting for an answer, Petrov answers himself:
Yes, it is perpendicular to the first line. But it does not intersect with the second line. They are parallel with the second line.
Silence comes. Then Morkovyeva gets up from her seat and, rounding the table, enters Petrov from behind, looking over his shoulder.
Well ... - she says uncertainly. - Probably, yes.
That's the point, - says Petrov, trying to consolidate the success achieved. - As long as there are two lines, they can be perpendicular. As soon as there are more of them ...
Can I have a pen? - asks Morkoviev.
Petrov hands over the pen. Morkovyeva carefully draws a few uncertain lines.
And if so?..
Petrov sighs.
This is called a triangle. No, these are not perpendicular lines. Besides, there are three of them, not seven.
Morkoveva purses her lips.
Why are they blue? - suddenly asks Nedozaytsev.
Yes, by the way, - supports Sidoryahin. - Sam wanted to ask.
Petrov blinks several times, looking at the drawing.
My pen is blue, he finally says. - I'm just to demonstrate...
It will turn out the same, - Petrov says confidently.
Well, how is it the same? - says Nedozaytsev. - How can you be sure if you haven't even tried? You draw red ones, and we'll see.
I don’t have a red pen with me,” Petrov admits. But I can totally...
Why didn’t you prepare, ”Sidoryakhin says reproachfully. - They knew that there would be a meeting ...
I can absolutely tell you for sure, - Petrov says in despair, - that exactly the same thing will turn out in red.
You yourself told us last time, - retorts Sidoryahin, - that you need to draw red lines in red. Here, I even wrote it down for myself. And draw them yourself with a blue pen. What are these, red lines in your opinion?
By the way, yes, - notices Nedozaytsev. - I also asked you about the blue color. What did you answer me?
Petrov is suddenly rescued by Lenochka, who studies his drawing with interest from her seat.
I think I understand, she says. - You are not talking about color now, are you? This is about this one, what do you call it? Perper-something-there?
The perpendicularity of the lines, yes, - Petrov responds gratefully. - It has nothing to do with the color of the lines.
That's it, you completely confused me, - says Nedozaytsev, looking from one participant in the meeting to another. - So what's the problem with us? With color or with perpendicularity?
Morkovyeva makes confused sounds and shakes her head. She also got confused.
Both with that, and with another, - quietly speaks Petrov.
I can’t understand anything, - says Nedozaytsev, looking at his fingers clasped in the castle. - Here is a task. All you need is seven red lines. I understand that there would be twenty of them! .. But there are only seven. The task is simple. Our customers want seven perpendicular lines. Right?
Morkoveva nods.
And Sidoryahin also sees no problem, - says Nedozaytsev. - Am I right, Sidoryahin? .. Well. So what is stopping us from completing the task?
Geometry, - Petrov says with a sigh.
Well, you just don't pay attention to her, that's all! - says Morkoveva.
Petrov is silent, collecting his thoughts. In his brain, colorful metaphors are born one after another that would make it possible to convey to those around him the surrealism of what is happening, but as luck would have it, all of them, clothed in words, invariably begin with the word "Fuck!", Completely inappropriate within the framework of a business conversation.
Tired of waiting for an answer, Nedozaytsev says:
Petrov, you answer simply - can you do it or can't you? I understand that you are a narrow specialist and do not see the big picture. But it's not difficult - to draw some seven lines? We've been discussing some nonsense for two hours now, we can't come to a decision.
Yes, says Sidoryahin. - You just criticize and say: "Impossible! Impossible!" You offer us your solution to the problem! And then a fool can criticize, pardon the expression. You are a professional!
Petrov wearily says:
Fine. Let me draw you two guaranteed perpendicular red lines, and the rest in transparent color. They will be transparent and will not be visible, but I will draw them. Will that suit you?
Will it suit us? - Morkoveva turns to Lenochka. - Yes, it will suit us.
Only at least a couple more - in green, - Lenochka adds. - And I also have such a question, can I?
Can one line be drawn as a kitten?
Petrov is silent for a few seconds, and then asks again:
Well, in the form of a kitten. Kitten. Our users love animals. It would be great…
No, says Petrov.
And why?
No, of course I can draw a cat for you. I'm not an artist, but I can try. Only it will no longer be a line. It will be a cat. The line and the cat are different things.
Kitten, - specifies Morkovyeva. - Not a cat, but a kitten, so small, cute. Cats they...
It doesn't matter, - Petrov shakes his head.
Not at all, right? .. - Lenochka asks disappointedly.
Petrov, you should at least listen to the end, - Nedozaytsev says irritably. - You didn’t listen to the end, but you already say “No”.
I understood the idea, - without looking up from the table, says Petrov. - It is impossible to draw a line in the form of a kitten.
Well, it’s not necessary then, - Lenochka allows. - A bird, too, will not work?
Petrov silently looks up at her and Lenochka understands everything.
Well, it’s not necessary then, - she repeats again.
Nedozaytsev slams his palm on the table.
So where did we stop? What are we doing?
Seven red lines, says Morkovyeva. - Two in red, and two in green, and the rest in transparent. Yes? Did I understand correctly?
Yes, Sidoryahin confirms before Petrov can open his mouth.
Nedozaytsev nods in satisfaction.
That's great ... Well, then, that's it, colleagues? .. Disperse? .. Any more questions? ..
Oh, - Lenochka remembers. - We still have a red balloon! Tell me, can you inflate it?
Yes, by the way, - says Morkovyeva. - Let's also discuss this right away so that we don't get together twice.
Petrov, - Nedozaytsev turns to Petrov. - Can we do it?
And what does the ball have to do with me? - Petrov asks in surprise.
It is red, - Lenochka explains.
Petrov is stupidly silent, trembling with the tips of his fingers.
Petrov,” Nedozaytsev nervously asks. - So you can or can't? It's a simple question.
Well, - Petrov says carefully, - in principle, of course, I can, but ...
Good, - Nedozaytsev nods. - Go to them, inflate. Travel allowances, if necessary, we will write out.
Is it possible tomorrow? - asks Morkovyeva.
Of course, - Nedozaytsev answers. - I think there will be no problems ... Well, now we have everything? .. Excellent. We worked productively ... Thank you all and goodbye!
Petrov blinks several times to return to objective reality, then gets up and slowly walks towards the exit. At the very exit, Lenochka catches up with him.
Can I ask you more? - blushing, says Lenochka. - When will you inflate the balloon ... Can you inflate it in the form of a kitten? ..
Petrov sighs.
I can do anything, he says. I'm a professional.
To clarify the condition of the problem, I found the original text. The author turned out to be someone Alexei Berezin, a blogger. Everything would be fine, but there is one subtlety. There is one passage in the original text that clearly indicates the author's intent:
“Two lines can be perpendicular,” Petrov patiently explains. - All seven cannot be perpendicular to each other at the same time. This is geometry, 6th grade.
That is, it was supposed to be seven straight lines, but the author used the word "line". On purpose or through thoughtlessness, now it doesn’t matter anymore, the task has lost most of the pathos and inadequacy. It would be forgivable if it were a clumsy translation from English, where line means both "line" and "straight". The line may or may not be straight. But what's done is done.
And this gave rise to many formally correct, but ugly decisions.
I’ll just put a screenshot of the search engine results for the query “seven red lines”. As you can see, the creative quality is not the highest.
We define TK as:
1. Seven straight red lines.
2. All these straight lines are mutually perpendicular
3. These two lines are green.
4. Three are transparent.
5. One of the straight lines in the shape of a cat (any).
I confess that my first thought was to use Lobachevsky's geometry. There are many such solutions. Here, look at what beautiful Scott Williamson offers on a looped ribbon.
And although he uses red paper in his solution, there are still questions about green red. And with transparent red there, too, not everything is as clear as we would like.
In the world familiar to us, only three mutually perpendicular straight lines can be drawn. We need to come up with something that will allow us to hold four more. An obvious assumption would be that it is not necessary to be limited to three dimensions, more can be used. For example, seven. Then in the seven-dimensional space the problem has a simple solution.
A little more difficult with the green color of the red lines. To do this, they must approach the observer with a certain speed sufficient for the occurrence of the Doppler effect. A few formulas...
Let's take a simplified formula for speeds much less than the speed of light, we only need to estimate the order of magnitude.
v=cz
where z is the coefficient calculated by the formula
z = (λ - λ°) / λ
where λ is the wavelength of the visible color, λ° is the wavelength of the original color.
Red will have a wavelength of approximately 700 nm.
Green respectively 500 nm.
It turns out that the speed of approach will be approximately 0.3 of the speed of light. Theoretically quite possible speed. Everything is fine here...
Further assumptions become more. For the next three measurements, in which red (straight) lines are drawn, we assume that they do not interact with electromagnetic radiation in any way. Accordingly, straight red lines in them will be invisible (transparent).
And the most important thing! Let one of the dimensions, which does not interact with electromagnetic radiation in any way, be projected into our three-dimensional world and its projection takes the form of a cat. But, since it is invisible, the cat is also invisible. By analogy with Schrodinger's cat, I propose to call him Morkoveva's cat.
Finally, I would like to arrange all of the above in the form of a continuation of the same story:
“Remembering the last meeting, Petrov has been preparing for this for a long time. For every question and every objection, he now has something to say.
- Colleagues, - Petrov looks at those gathered at the table, smiles and adjusts his glasses, - the task was close to unsolvable, almost on the very border with the impossible.
Nedozaytsev looks at him with enthusiasm, Morkovyeva looks at him skeptically, and Lenochka tries to understand why she is here again. Sidoryahin is absent due to illness.
But I managed to solve it! - says Petrov and looks victorious. The fire of madness shines in his eyes.
Lenochka suddenly hiccups and is cutely embarrassed.
Here! - Petrov solemnly shows the image.
