Lewis Carroll The Story of Knots
NoduleVIIMinor expenses
- Aunt Mathematilda!
- What, honey?
— Could you write down the expenses right away? If you don’t write them down now, I will certainly forget.
- At least wait until the cab stops. I can’t write when it’s shaking like that!
- Well, aunt, please! Otherwise I'll really forget.
There were pleading notes in Clara’s voice, which the aunt could not resist. Taking out her notebook with a sigh - several small ivory tablets - she prepared to enter into it the amounts that Clara had just spent at the pastry shop. Auntie paid for everything, of course, but the poor girl knew very well that sooner or later Mad Mathematilda would demand from her a detailed account of every penny spent, and so now, with poorly concealed impatience, she waited for her aunt to find among her tablets the one entitled “ Minor expenses."
“Here she is,” said the aunt at last. – The last entry refers to yesterday’s breakfast. One glass of lemonade (Why can’t you drink plain water like me?), three sandwiches (There’s no trace of mustard in them. I just told the girl behind the counter that’s what she said, and she just lifted her chin in response. Amazing audacity!) and seven biscuits. Togo 1 shilling and 2 pence. So what did you order today?
“One glass of lemonade...” Clara began to list, but then the cab suddenly stopped, and a porter with excellent manners standing at the entrance to the station helped the confused girl get out of the carriage before she could finish the sentence.
Auntie immediately slammed her notebook shut.
“Business comes first,” she said. – Pleasures (and money for small expenses, no matter what you say, is just one of the varieties of pleasures) can wait.
And Mad Mathematilda began to pay the cabman, give detailed and extensive orders regarding the luggage, not paying any attention to the pleas of the unfortunate niece to write down the rest of the expenses for breakfast.
“My dear, you really should develop your memory so that it becomes more capacious,” was the only saying with which the aunt deigned to console her niece. - Are the tablets of your memory not wide enough to contain the cost of one single breakfast?
- Of course, not enough! And not half as wide as they should be! – came the indignant answer.
The words were quite appropriate in meaning, but the voice that spoke them was not Clara’s, and the aunt and niece turned in surprise to see who it was who had suddenly intervened in their conversation.
A plump old woman was fussing at the door, helping the cabman retrieve her exact copy from the depths of the carriage. Deciding which of the two old ladies was plumper and more good-natured was not so easy.
“I’m telling you, this door isn’t half as wide as it should be!” - the old woman repeated when her sister was finally taken out of the cab (with the joint efforts of the cabman and the old woman, the niece flew out of the place of her involuntary captivity, like a cork from a blowgun).
- Isn't it true, girl? – she turned to Clara for support, trying in vain to frown menacingly.
“Some passengers are too wide for a cab,” grumbled the driver.
- Don't make me angry! - exclaimed the old woman, overcome by what must have been an attack of rage. “One more word and I will prosecute you for violating the law on non-touching of persons.”
The cabman touched his hat and walked away smiling.
“To put a presumptuous rude person in his place, my dear, it’s best to refer to some law, even if it’s a bad one,” the old woman remarked confidentially, turning to Clara. “You saw how he immediately chickened out when I mentioned the law on personal inviolability.” Even though I have no idea what this means, it still sounds cool, right?
“I feel somehow uneasy about this law,” Clara objected somewhat vaguely.
“Of course,” exclaimed the old woman. “They drove us crazy, didn’t they, sister?”
“I’ve never been so furious in my life!” – the fatter sister confirmed, smiling radiantly.
Only now did Clara learn about the old sisters whom she met in the art gallery. Taking her aunt aside, she hurriedly whispered in her ear:
“I first met them at the Royal Academy of Fine Arts. They were so kind to me, and today they were having breakfast at the next table. They tried to help me find the painting I was looking for. I think they are very cute old ladies!
- So you're saying these are your friends? – Mad Mathematilda asked. - Well, they make a good impression. You can talk to them while I buy the tickets. Just try to watch your speech and arrange your thoughts in a stricter chronological order!
Soon all four of them - two sisters and an aunt and niece - were sitting on the same bench and, while waiting for the train, were having a casual conversation, as if they had known each other for a long time.
- What a wonderful coincidence! - exclaimed the one of the sisters who was smaller and more talkative (it was her knowledge of jurisprudence that put the cabman to flight). “Not only are we waiting for the same train at the same station - which is quite curious in itself - but we are waiting on the same day and at the same hour! This especially amazes me!!
She glanced at her fatter, quieter sister, whose main purpose in life was to maintain the unity of family opinion. The sister immediately responded humbly:
- Me too, sister!
“These coincidences are not independent,” Mad Mathematilda began, but Clara risked interrupting her.
“It’s not shaking here,” she said pleadingly. - Maybe we can write down the expenses?
The ivory tablets were again brought to light.
- So, what did we order? - asked the aunt.
— A glass of lemonade, one sandwich, one biscuit. Oh, what should I do? – Clara suddenly exclaimed with despair in her voice.
- Do you have a toothache? – the aunt asked calmly, writing down the menu Clara named. Both sisters immediately opened their bags and took out two different painkillers (each box was written: “The Best”).
- No! – Clara said dejectedly. “I just can’t remember how much I spent on breakfast.”
“Try to figure it out if you don’t remember,” suggested the aunt. – You know what you ordered for breakfast yesterday. And here is a record of what you ordered the day before yesterday - on the first day when we went to the pastry shop for breakfast: one glass of lemonade, four sandwiches, ten biscuits. Total 1 shilling and 5 pence.
With these words, the aunt handed her tablets to Clara. With these words, the aunt handed her tablets to Clara. Through her tears, Clara didn’t even immediately notice that she was holding the signs upside down.
The two sisters listened with the deepest interest to the conversation between their aunt and niece. Seeing that Clara was very upset, the youngest of the sisters affectionately put her hand on her shoulder.
“You know, baby,” she said soothingly, “my sister and I are in the same predicament!” Well, just exactly the same! Really, sister?
“Completely and absolutely the same...” the plumper old woman began, but the scale of the proposal she had in mind was too grandiose, and her smaller sister had no time to wait for her to finish.
“The thing is, baby,” continued the youngest of the sisters, “today you and your aunt had breakfast, and we ordered two glasses of lemonade, three sandwiches and five biscuits, but neither of us has the slightest idea how much we paid.” Really, sister?
“Completely and absolutely...” muttered the second old woman, obviously believing that she was exactly one sentence behind, and considering it necessary to fulfill an already undertaken obligation before taking on a new one. But then the first old woman interrupted her again, and the second old woman, having suffered a crushing fiasco in the conversation, fell silent.
“Will you count for us how much we paid?” – the first old woman asked Clara.
- I hope you haven’t forgotten your arithmetic? – Auntie asked with slight concern. Clara absentmindedly sorted through the signs, trying in vain to gather her thoughts. Her head was empty. The face quickly lost its meaningful expression.
There was a sullen silence.
,Lewis Carroll
HISTORY WITH KNODES
To my favorite student
My friend! You already know
Subtraction and compounding,
Multiplication and division
Just to everyone's surprise.
So go for it! Let the glory echo
Your successes are thundering.
You will become, even if you look modest,
More famous than Euclid!
OVER THE MOUNTAINS AND OVER THE VALLEYS
Evil gnome, lead them up and down the mountains.
The gloomy shadows of the night had already begun to replace the ruddy glow of sunset when two travelers appeared in the distance, quickly - at a speed of 6 miles per hour - descending along the mountainside densely strewn with boulders. The young traveler jumped from stone to stone with the agility of a deer. The older traveler, with difficulty moving his tired legs, could barely keep up with him, bending under the weight of armor and chain mail - the usual clothing of tourists in those places.
As always happens in such cases, the young knight was the first to break the silence.
We're going well! - he exclaimed. - We climbed the mountain much more slowly!
“We’re going really well,” his companion responded with a groan, “and we were climbing the mountain at a speed of 3 miles per hour.
Can you tell me how fast we are going on level ground? - asked the young knight. He was not good at arithmetic and tended to leave considerations of this kind to his companion.
At a speed of 4 miles per hour,” another knight answered wearily and added, with the love of metaphors characteristic of old age: “Exactly 4 miles per hour, not an ounce more and not a farthing less!”
“We left the hotel at exactly 3 o’clock in the afternoon,” the young man noted thoughtfully, “and, of course, we will be late for dinner.” The owner may not leave us anything!
“He’ll even scold us for being late,” the old man picked up sadly, “but he’ll get a fitting rebuff!”
Bravo! Let's give him some pepper! - the young man exclaimed with a cheerful laugh. “But I’m afraid we won’t have a good time at all if we decide to ask him for even something sweet.”
We’ll be in time for the third course,” sighed the older knight, who didn’t understand the jokes and was somewhat annoyed by the frivolity of his young friend that was inappropriate from his point of view.
How much?! How many?! - the young man exclaimed impatiently, never missing an opportunity to expand his knowledge.
The old man was silent.
Only a groan that escaped from the young man’s lips was his answer. The courageous face distorted by suffering and the deep wrinkles that furrowed the young man’s wide forehead testified to the depth of the arithmetic agony into which the randomly asked question plunged the poor fellow.
ROOMS WITH ALL AMENITIES
Go straight along the crooked alley, and then along the closed square.
“Let’s ask Balbus,” said Hugh.
It's coming! - Lambert agreed.
“He’ll think of something,” said Hugh.
And how! - Lambert exclaimed.
Not another word was said: the two brothers understood each other perfectly.
Balbus was waiting for them at the hotel. The road, according to him, was somewhat tiring, so the two young pupils set off to wander around the resort town in search of a boarding house without their elderly mentor - an inseparable companion of both brothers from early childhood. The brothers nicknamed him Balbus in honor of the hero of one book - a collection of exercises in the Latin language, which they had to study. This collection contained an incredible number of stories about the adventures of the tireless hero - stories in which the lack of reliable facts was more than made up for by a brilliant manner of presentation. Against the story entitled “How Balbus Defeated All His Enemies,” the tutor wrote in the margin: “Valor Crowned with Victory.” He was sincerely confident that such maxims would help his students extract morals from every story. Sometimes these notes were edifying in nature (for example, against the story “How Balbus kidnapped a hefty dragon and what came of it,” the wise mentor wrote in the margins: “Rashness of actions”), sometimes approving (for what, other than approval, sounds in the words “Joint effort as a consequence of mutual understanding”, which adorned the margins of the pages on which the story “How Balbus Helped His Mother-in-Law Convince the Dragon” was told), and sometimes were reduced to a single word (thus, the moral that the venerable mentor of youth extracted from the touching story “How Balbus cut off tail to the dragon and retreated,” resulting in a laconic inscription: “Prudence”).
Lewis Carroll
HISTORY WITH KNODES
To my favorite student
My friend! You already know
Subtraction and compounding,
Multiplication and division
Just to everyone's surprise.
So go for it! Let the glory echo
Your successes are thundering.
You will become, even if you look modest,
More famous than Euclid!
OVER THE MOUNTAINS AND OVER THE VALLEYS
Evil gnome, lead them up and down the mountains.
The gloomy shadows of the night had already begun to replace the ruddy glow of sunset when two travelers appeared in the distance, quickly - at a speed of 6 miles per hour - descending along the mountainside densely strewn with boulders. The young traveler jumped from stone to stone with the agility of a deer. The older traveler, with difficulty moving his tired legs, could barely keep up with him, bending under the weight of armor and chain mail - the usual clothing of tourists in those places.
As always happens in such cases, the young knight was the first to break the silence.
We're going well! - he exclaimed. - We climbed the mountain much more slowly!
“We’re going really well,” his companion responded with a groan, “and we were climbing the mountain at a speed of 3 miles per hour.
Can you tell me how fast we are going on level ground? - asked the young knight. He was not good at arithmetic and tended to leave considerations of this kind to his companion.
At a speed of 4 miles per hour,” another knight answered wearily and added, with the love of metaphors characteristic of old age: “Exactly 4 miles per hour, not an ounce more and not a farthing less!”
“We left the hotel at exactly 3 o’clock in the afternoon,” the young man noted thoughtfully, “and, of course, we will be late for dinner.” The owner may not leave us anything!
“He’ll even scold us for being late,” the old man picked up sadly, “but he’ll get a fitting rebuff!”
Bravo! Let's give him some pepper! - the young man exclaimed with a cheerful laugh. “But I’m afraid we won’t have a good time at all if we decide to ask him for even something sweet.”
We’ll be in time for the third course,” sighed the older knight, who didn’t understand the jokes and was somewhat annoyed by the frivolity of his young friend that was inappropriate from his point of view.
How much?! How many?! - the young man exclaimed impatiently, never missing an opportunity to expand his knowledge.
The old man was silent.
Only a groan that escaped from the young man’s lips was his answer. The courageous face distorted by suffering and the deep wrinkles that furrowed the young man’s wide forehead testified to the depth of the arithmetic agony into which the randomly asked question plunged the poor fellow.
ROOMS WITH ALL AMENITIES
Go straight along the crooked alley, and then along the closed square.
“Let’s ask Balbus,” said Hugh.
It's coming! - Lambert agreed.
“He’ll think of something,” said Hugh.
And how! - Lambert exclaimed.
Not another word was said: the two brothers understood each other perfectly.
Balbus was waiting for them at the hotel. The road, according to him, was somewhat tiring, so the two young pupils set off to wander around the resort town in search of a boarding house without their elderly mentor - an inseparable companion of both brothers from early childhood. The brothers nicknamed him Balbus in honor of the hero of one book - a collection of exercises in the Latin language, which they had to study. This collection contained an incredible number of stories about the adventures of the tireless hero - stories in which the lack of reliable facts was more than made up for by a brilliant manner of presentation. Against the story entitled “How Balbus Defeated All His Enemies,” the tutor wrote in the margin: “Valor Crowned with Victory.” He was sincerely confident that such maxims would help his students extract morals from every story. Sometimes these notes were edifying in nature (for example, against the story “How Balbus kidnapped a hefty dragon and what came of it,” the wise mentor wrote in the margins: “Rashness of actions”), sometimes approving (for what, other than approval, sounds in the words “Joint effort as a consequence of mutual understanding”, which adorned the margins of the pages on which the story “How Balbus Helped His Mother-in-Law Convince the Dragon” was told), and sometimes were reduced to a single word (thus, the moral that the venerable mentor of youth extracted from the touching story “How Balbus cut off tail to the dragon and retreated,” resulting in a laconic inscription: “Prudence”).
The shorter the moral, the more the brothers liked it, because the more space was left in the margins for illustrations. In the last example, they needed all the empty space to properly depict the hero's haste to leave the battlefield.
Returning to the hotel, Lambert and Hugh were unable to tell their mentor anything comforting. The fashionable resort of Little Mendip, where they arrived on the waters, was, as the brothers put it, “teeming with” vacationers. Nevertheless, in one square-shaped square, the brothers managed to notice on the doors of at least four houses cards on which in huge letters it was written: “Rooms for rent with all amenities.”
In any case, we have a large choice,” Hugh, who took on the role of speaker, summed up his observations.
This does not at all follow from what you said,” Balbus objected, rising from the shaky chair on which he was dozing sweetly over the local newspaper. - Only one room can be rented in each house, and we would prefer to rent three bedrooms and one living room in one house, but it still doesn’t hurt to take a look. By the way, I’ll be glad to stretch my legs a little, otherwise there’s simply nowhere to stretch them here.
In response to the last remark, an impartial observer might object that stretching already long legs is a completely unnecessary operation, and that the appearance of the skinny creature who made it would have benefited greatly if his lower limbs had been shorter. But, of course, such a thought could not even occur to the loving pupils. Flanking their mentor, the brothers tried their best to keep up. Balbus rushed down the street with giant strides. As he ran, Hugh kept mumbling a phrase from a letter he had just received from his father abroad. This phrase haunted both him and Lambert.
Lewis Carroll
HISTORY WITH KNODES
To my favorite student
My friend! You already know
Subtraction and compounding,
Multiplication and division
Just to everyone's surprise.
So go for it! Let the glory echo
Your successes are thundering.
You will become, even if you look modest,
More famous than Euclid!
OVER THE MOUNTAINS AND OVER THE VALLEYS
Evil gnome, lead them up and down the mountains.
The gloomy shadows of the night had already begun to replace the ruddy glow of sunset when two travelers appeared in the distance, quickly - at a speed of 6 miles per hour - descending along the mountainside densely strewn with boulders. The young traveler jumped from stone to stone with the agility of a deer. The older traveler, with difficulty moving his tired legs, could barely keep up with him, bending under the weight of armor and chain mail - the usual clothing of tourists in those places.
As always happens in such cases, the young knight was the first to break the silence.
We're going well! - he exclaimed. - We climbed the mountain much more slowly!
“We’re going really well,” his companion responded with a groan, “and we were climbing the mountain at a speed of 3 miles per hour.
Can you tell me how fast we are going on level ground? - asked the young knight. He was not good at arithmetic and tended to leave considerations of this kind to his companion.
At a speed of 4 miles per hour,” another knight answered wearily and added, with the love of metaphors characteristic of old age: “Exactly 4 miles per hour, not an ounce more and not a farthing less!”
“We left the hotel at exactly 3 o’clock in the afternoon,” the young man noted thoughtfully, “and, of course, we will be late for dinner.” The owner may not leave us anything!
“He’ll even scold us for being late,” the old man picked up sadly, “but he’ll get a fitting rebuff!”
Bravo! Let's give him some pepper! - the young man exclaimed with a cheerful laugh. “But I’m afraid we won’t have a good time at all if we decide to ask him for even something sweet.”
We’ll be in time for the third course,” sighed the older knight, who didn’t understand the jokes and was somewhat annoyed by the frivolity of his young friend that was inappropriate from his point of view.
How much?! How many?! - the young man exclaimed impatiently, never missing an opportunity to expand his knowledge.
The old man was silent.
Only a groan that escaped from the young man’s lips was his answer. The courageous face distorted by suffering and the deep wrinkles that furrowed the young man’s wide forehead testified to the depth of the arithmetic agony into which the randomly asked question plunged the poor fellow.
ROOMS WITH ALL AMENITIES
Go straight along the crooked alley, and then along the closed square.
“Let’s ask Balbus,” said Hugh.
It's coming! - Lambert agreed.
“He’ll think of something,” said Hugh.
And how! - Lambert exclaimed.
Not another word was said: the two brothers understood each other perfectly.
Balbus was waiting for them at the hotel. The road, according to him, was somewhat tiring, so the two young pupils set off to wander around the resort town in search of a boarding house without their elderly mentor - an inseparable companion of both brothers from early childhood. The brothers nicknamed him Balbus in honor of the hero of one book - a collection of exercises in the Latin language, which they had to study. This collection contained an incredible number of stories about the adventures of the tireless hero - stories in which the lack of reliable facts was more than made up for by a brilliant manner of presentation. Against the story entitled “How Balbus Defeated All His Enemies,” the tutor wrote in the margin: “Valor Crowned with Victory.” He was sincerely confident that such maxims would help his students extract morals from every story. Sometimes these notes were edifying in nature (for example, against the story “How Balbus kidnapped a hefty dragon and what came of it,” the wise mentor wrote in the margins: “Rashness of actions”), sometimes approving (for what, other than approval, sounds in the words “Joint effort as a consequence of mutual understanding”, which adorned the margins of the pages on which the story “How Balbus Helped His Mother-in-Law Convince the Dragon” was told), and sometimes were reduced to a single word (thus, the moral that the venerable mentor of youth extracted from the touching story “How Balbus cut off tail to the dragon and retreated,” resulting in a laconic inscription: “Prudence”).
The shorter the moral, the more the brothers liked it, because the more space was left in the margins for illustrations. In the last example, they needed all the empty space to properly depict the hero's haste to leave the battlefield.
Returning to the hotel, Lambert and Hugh were unable to tell their mentor anything comforting. The fashionable resort of Little Mendip, where they arrived on the waters, was, as the brothers put it, “teeming with” vacationers. Nevertheless, in one square-shaped square, the brothers managed to notice on the doors of at least four houses cards on which in huge letters it was written: “Rooms for rent with all amenities.”
In any case, we have a large choice,” Hugh, who took on the role of speaker, summed up his observations.
This does not at all follow from what you said,” Balbus objected, rising from the shaky chair on which he was dozing sweetly over the local newspaper. - Only one room can be rented in each house, and we would prefer to rent three bedrooms and one living room in one house, but it still doesn’t hurt to take a look. By the way, I’ll be glad to stretch my legs a little, otherwise there’s simply nowhere to stretch them here.
In response to the last remark, an impartial observer might object that stretching already long legs is a completely unnecessary operation, and that the appearance of the skinny creature who made it would have benefited greatly if his lower limbs had been shorter. But, of course, such a thought could not even occur to the loving pupils. Flanking their mentor, the brothers tried their best to keep up. Balbus rushed down the street with giant strides. As he ran, Hugh kept mumbling a phrase from a letter he had just received from his father abroad. This phrase haunted both him and Lambert.
He writes that his friend is the governor... Lambert, what is the name of that place?
Kgovjni,” Lambert suggested.
Oh yes! So here it is. The governor of this very... what's his name?... wants to throw a dinner party in a very close circle and intends to invite his father's brother-in-law, his brother's father-in-law, his father-in-law's brother and his brother-in-law's father. Father wants us to guess how many guests the governor will have.
After some slight confusion, Balbus finally asked:
Doesn't your father write down what size pudding they're going to serve at the dinner party? If the volume of pudding is divided by the volume of the portion that one guest can eat, then the quotient will be exactly equal to...
“No, the letter doesn’t say a word about pudding,” Hugh replied. - And here is the same square area I was talking about.
With these words, the whole trio turned the corner, and the gaze of the panting travelers opened up to a view of the square where rooms were rented “with all amenities.”
Yes she and indeed It's shaped like a square! - Balbus exclaimed with delight, looking around. - Amazing! Fabulous! All sides are equal and even the angles are right!
The boys looked around the square with less enthusiasm.
The first advertisement for a room for rent is on house number 9, noted Lambert, who was alien to poetry; but it was not so easy to make the ecstatic Balbus come down to earth.
Just look! - he shouted in ecstasy. - There are twenty doors along each side! What symmetry! Each side is divided into twenty-one equal parts! Just a miracle!
Should I knock or call? - asked Hugh, looking puzzled at the square copper plate with the laconic inscription “Call too.”
“Both,” replied Balbus. - This, my boy, is the so-called ellipse. Haven't you seen an ellipse before?
