Mathcad and some secrets of literature (by Valery Ochkov)

(Russian text)

Example 1. Height of Poirot

Example 2. Height of Nicholas Fandorin

Example 3. Height of the Turgenevs Gerassim.

Example 4. Weight of Alex Vronskey

Example 5. Ruble rate at the end of XIX century

Example 6. We calculate money

There is special kind of aesthetes feeling pleasure in upgrading a technical text by citations from literature. It is an extract from the book Mathcad 8 Pro for students and engineers. But literature can ennnoble not only technical text but the literature can set the problems solving in Mathcad with attraction units of measure.

Example 1. Height of Poirot

In the roman of Aghata Christie we read: First of all, his height in my opinion was not more than five feet and five inches. Only one operator solves the riddle of the height of the famous detective in Mathcad:

5 ft + 5 in = 165 cm (This and other values of the height are approximated to integer units)

Certainly we can return that this simple problem can be solved without Mathcad. We have to take only a calculator and an encyclopedia for solving this problem. But the great value of Mathcad is that, it units (integrates) both calculator[1], and reference book by physical value, and many other things[2].

Example 2. Height of Nicholas Fandorin

Here is one more example about feet and inches. In roman of one Russian writer Boris Akunin we read For example, we take height of Nicholas. He has the height of six feet and six inches and it is rather tall person, I think. Nicholas looks down on overwhelming majority. But if we express his height in meters and we have got one meter and ninety- nine centimeters. It is just a little less than two meters. Mathcad prompt that the author of the roman is cunning a little he adds the hero one centimeter:

6 ft + 6 in = 198 cm

This is common example of a conflict between form and content. The author decides this case in form favor. On the other hand the height of two meters gives interesting number 666 the number wild[3] when we express the height in English units of measure:

gr := 0.1 in 6 ft + 6 in + 6 gr = 200 cm

There is no place for this number and all the more speculation around it in scientific and technical literature and in this book too. But If we turn our attention to the history of development of units of measure, then we have to establish a fact that happy, mystical numbers: 3, 7, 12, 40 and other were supposed as a basis many years ago.

Three arshines are in one sazhen, seven inches are in one span, 12 lines are in one inch, and 40 pounds are in one pood A force of superstitions is the main reason why we do not meet anywhere number 6 and all the more 13 (baker's dozen) as a connecting factors. Great French Revolution at the crossroads of XVIII and XIX centuries brought in the tenfold system. At that the Revolution had not for only practical objects connecting with comfort recounts, but it threw out heritage of cursed the past (mysticism and superstitions) from natural science and science and engineering.

But now days the attitude to cursed the past has become more tolerant. The system SI expects to exclude off-system units and all the more dated units from the calculations. It results in that a man, who reads some novels of last century, can not state the value of either measurements, that he meets in books.

Example 3. Height of the Turgenevs Gerassim.

I.S.Turgenev left more difficult puzzle about his heros height. The second indention of the famous story begins next words: The yard-keeper was the most remarkable person from all her servants. The height of this man was twelve vershoks. He was Hercules, and deaf-and-dumb by birth.

vershok[4] := 4.445 in (1.75 inch[5] nevertheless we have a look at a reference book)

12 vershok[6] = 53.36 cm

Gerassim according to the calculation was not the Hercules, but the dwarf. His height was a little more, than a meter and a half. What is the matter!?

The first hypothesis is when Turgenev described Gerassim he did not have in mind common vershoks, but some special ones. There is sazhen and there is broad sazhen (broad shoulders!). There is metric ton, but there is long ton, short ton. There is statute mile and there is nautical mile and so on. But search[7] of mysterious long vershoks is finished bad luck. Verhsoks were vershoks: 1.75 inches, a quarter of a span, one-sixteenth of arshine, and one forty-eighth of sazhen and so on.

More probable hypothesis is the next one. It connects with principle of passing over in silence. Point is that that the height of adult man as rule manage between 2 and 3 arshines:

arshine := 16 vershok (Vershoks have been determined above)

2 arshine = 142.24 cm

3 arshin = 213.36 cm

Two arshines are the steersman of eight in boar racing, but three arshines (sazhen) is a good basketball-player with limit of mans height. We read Master and Margaret by Bulgakov (http://lib.ru/BULGAKOW/master.txt): Suddenly hot air has condensed around of him and strange man has appeared in front of him. On his little head there is a jockey peaked cap and he had a flimsy jacket... His height was one sazhen, but he was narrow in shoulders, very thin. But the main thing that was striking right away, it was his face very sly one. N.V. Gogol wrote in Dead souls (http://www.online.ru/sp/eel/russian/Gogol.Nikolai/mertvye1.rhtml) But courier is already here and stands: his height is three arshines, and his hand is a natural hand of a coachman.

We image a scene of last century[8]. New group of prisoners put into prison. First warder measures their height, but the next one (clerk) enters these numbers in the minutes. In the room where this procedure takes place, short phrases: Five, Three and a half, Four and a quarter and so on are sounded : Five, Three and a half, Four and a quarter and so on. Counting out in vershoks is not dated from floor (the first failure to mention) (zero is an absolute scale of a measure[9]), but it is dated from two arshines (the second failure to mention is a relative scale of measure[10]). Turghenev threw out two arshines from the story. That is not only because to say for short, but for the fast and correct information transfer. The base of compromise between demands of exactness and quickness is the principle of a failure to mention.

According to previously mentioned hypothesis it is not difficult to calculate height of Gherasim:

2 arshin + 12 vershok = 196 cm

This is normal athletic height!

Finishing with the units of length and passing to another dimensionalities, we disclose the secret about span of native country.

I ask a house-manager:

How many sazhens are there in this flat?

Three sazhens, he says.

I ask what fool built this flat? <> He built too big kitchen blessing it is not necessary to pay for.

That is right, he says. Move in this flat and pay for three useful sazhens, but the kitchen you may use for nothing.

M.Zoshenko Useful square

The secret of span of native country is that we pass over in silence about linearity of this span. We can give any amount of spans of native country, but it does not decrease.

span := 7 in sazhen := 12 span 3 sazhen2 := 13.7 m2

Now we ask How many meters are there in this room? We have in mind its square, but not length or width.

One of a hero by A.Raykin from the play Great force of dramatic art measured width and length of the room by the bottle of vodka. Then he tried to calculate its square in square liters. Square (square meters, square spans, square sazhens and so on) can be measured in liters. For this we have to raise liters to the 2/3 power:

m2 := 100 liter2/3
span2 := 3.161284 liter2/3
sazhen2 := 455.225 liter2/3

Example 4. Weight of Alex Vronskey

In The film Anna Karenina (in the same roman by L.N.Tolstoy author has not found it see http://www.online.ru/sp/rel/russian/Tolstoy.Lev/annak.rhtml) Alex Vronskey says that his weight was standard. That is four and a half (preparations for skipping were held, where weight of a horseman was very important). It is asked what weight of the main hero of the most famous and the greatest ladies novel was.

If in old Russian height was measured in arshines (or rather in vershoks see above), then weight was measured in poods. Russian pood equaled 16.38 kg (40 pounds). Hence we can easily appreciate weight of Vronskey: 4.5*16.38 = 74 kg. It is rather much for jockey! As we can read in the roman Vronskey was short person. Another hypothesis is next. Vronskey had in mind English pound (slug, this unit is built-in in Mathcad), but not Russian one. Vronskey had English teacher who certainly had an eye on his weight. Hence his teacher put him into English scales. In this case weight of Vronskey equaled 4.5 slug = 66 kg. It looks as if it is true. Certainly we can not forget about two six. It is almost the number wild (see above). Alex Vronskey ruined the horse during skipping and he nearly was lost himself. Apart after these events the heroine of the roman had some problems. Anna Karenina had a talk with her husband and so on

Example 5. Ruble rate at the end of XIX century

So we can come to know the particulars of units of length and mass (weight), when we find them in different books. But monetary units are another story. It is rather difficult but not hopeless.

We often meet in literature theme of pecuniary calculations[11]. At that some authors left some puzzles for a reader. The earlier a book was written the more difficult the solution of this puzzle: old Forsite[12] added to testament some note and left for his niece Irene fifteen thousand pound sterlings, but once by mistake he gave to cabman instead of shilling one quid. And here is a dialogue from the roman Dead souls:

Barin, You have not paid for some vodka... an old woman said.

Ah, well, well, mother! Listen son-in low! Please pay. I have penniless.

How much do you need? The son-in-low asked.

It is nothing, I need only twenty-kopeck coin, the old woman said.

It is lie, it is lie. It is enough if you give only half a ruble.

Barin, it is not quite enough, the old woman said. But she took money with gratitude and ran to open the door. She was not out of pocket, because she asked four times as much, than vodka cost.

On the face of it this situation is paradoxical one 50 kopecks are more than 20 kopecks. But in comments by this roman we read: Half a ruble is half a ruble by banknote. The old woman asked silver twenty-kopeck coin that equaled eighty kopecks by banknote. Hence it is easy to understand, that vodka cost five silver kopecks or twenty kopecks by banknote. And he paid two and a half times as much, but not four. We can also suppose that only twenty-kopeck coin and half a ruble are silver, the same way we can suppose that they are banknote. Other hypothesis is next one. The sly woman (other people do not get this job), trying to earn money and insuring against to reproach her with honesty, said right sum but she did not say whether she had wanted banknote or silver.

Now days such situations we meet very often. One authors friend has told such story. It was at school. Parents came to see their childrens teachers. The question about cleaning class was discussed: charwoman had retired on a pension and the class had to be cleaned by pupils or parents had to pay money (three thousand) and engage somebody. At the end of the meeting parents decided that their children would clean the class themselves. It happened because of one rather well dressed man. It was a father of one pupil. Authors friend went home with the father in a car. The car was great. It was jeep. This man turned out a very rich man. On the way to home the father continued to be shocked with the meeting. He said that sometimes he did not earn three thousand in a month. But the father thought that he had to pay three thousand dollars, but the teacher asked to pay each of us three thousand rubles (old rubles that equaled half a dollar. It was in 1997).

Reading Player F.M.Dostoevsky[13] all time we meet rubles, florins, guilders, francs and pounds. Heroes of the roman always used these monetary units[14]. Regular questions emerge. How much money did they win playing roulette? How much money did they loose? What rate of exchange took place in the second part of the XIX century? It is not difficult to find seven quotations[15] from the electronic version of this roman (see footnote). In these quotations there is the solution of this problem.

Quotation 1

You get them immediately, the general replied, turning red in his face. He searched in his bureau, looked into the book and turned out that he owed me about one hundred twenty rubles.

How can we calculate?, he is telling, it is necessary to convert money to thalers. Here they are one hundred thalers the rest will not lose

And later

You should receive in addition these four golden coins and three florins for local calculation.

Quotation 2

Polina became angry, when I gave her only seven hundred guilders.

And then

Listen to me and remember: take these seven hundred florins and go to play. Play roulette and win as much as possible. At any price I need money now.

Quotation 3

I began with that I took out five golden coins i.e. fifty guilders and staked on beads.

Quotation 4

Well, she has won twelve thousand florins! More than twelve thousand we have not calculated gold! It is nearly thirteen with gold. How much is it in our opinion? It is six thousand, is not it?

I said that it is more than seven thousand. But nowadays rate is that that it is nearly eight.

Quotation 5

Oui, madame, he politely confirm, any single stake can not more than four thousand florins, He added.

I staked as much as possible (four thousand guilders) but I lost.

Quotation 6

She had to get exactly four hundred twenty golden coins, that was four thousand florins and twenty golden coins.

Quotation 7

Polina, here is five thousand florins it is nearly fifty thousand francs.

This problem (system of algebraic equations) in M Mathcad is solved very simple: we have (Given) the system (quotations, translating into mathematics language), and we have to find its solution (Find).

Given:

120 rubles=100 thalers+4 golden coins+3 florins

700 guilders=700 florins

5 golden coins=50 guilders

13000 florins=8000 rubles

4000 florins=4000 guilders

420 golden coins=4000 florins+20 golden coins

25000 florins=50000 francs

Find (thalers, golden coins, florins, guilders, and francs)

From the solution we can see that at the second part of XIX century one guilder cost 61 kopecks, one thaler one and a half of guilder (florin), but one golden coin was ten times as much than one guilder. So, general paid his teacher 117 rubles 73 kopecks[16] (about 120 rubles see quotation 1), but grandmother[17] play roulette and won 7930 rubles (it is nearly eight see quotation 4).

In the roman Player there are three stories love, financial and playing ones. They connect each other very closely.

Love story.

In the generals home the teacher (a young man who tell this story) lives. Polina and the teacher love each other rather strange love[18]. Polinas stepfather (general) is enamoured of adventuress m-ll Blanch, who in her turn and in her time will gain the general. Mr. Astley loves Polina and so on.

Financial story.

When the general retired one spending came to light. It was about 30 thousand rubles. One Frenchman saved the situation of the general. He gave necessary sum of money on the security of the property. But this property did not belong to one general, but it belonged to his children and his stepdaughter Polina, too. This Frenchman was tutor of Polina.Though the general with all his family would go abroad (fashionable and rich German health resort[19]), where he would continue to contract debts. The general hoped for the inheritance of rich widow Polinas grand. This inheritance wanted to get both m-ll Blanch, and the Frenchman and so on.

Playing story.

Instead of telegram informing about death of grandma (la baboulinka), grandma came yourself. She won 7930 rubles (see quotation 4), and then lost, playing roulette (damned zero[20]) about one hundred thousand rubles. It was a half of her fortune. She borrowed money about three thousand francs and went home to Moscow. With help of the general Polina played roulette bond her diamonds and seven hundred guilders (seven hundred rubles, not guilders. By the way it was the generals annual salary.). She dreamed to win fifty thousand francs and got her property out of pawn. m-ll Blanch had played roulette too. It was not good. The general played roulette and won eighty thousand francs. Money got m-ll Blanch (see above love story).

The theme of play is very closed to people who work with computer. For example we take the play Sapper. This play was thought out for quick and simple medium for mastering the mouse. But a lot of money money this play (money is time) took away. You always promise yourself that it was the last game, that we stop playing and that you finally begin working, and delete this file at all. But... You do not do your work, spoil your sight, but you continue playing... And the main thing that new victory does not satisfy. Pleasure (passion) in something else, it was skilfully described in the roman Player by Dostoevsky. Here she is! It is happiness! he said (Dead soul, we have spoken about it above), beginning to dream. That is happiness! That is happiness! I feel trembling! Here is that damned nine. I have lost everything with this nine! I have felt that it lets down, but I am thinking: The devil take it! Let me down, damned nine! Aim (win) is nothing but movement (play) is everything!

Example 6. We calculate money

Good example of calculating money we can find in one of the plays by Molier (http://biblioteka.agava.ru/meschanin_vo_dvor-1.htm).

Dorante. I intend to square accounts with you. Lets calculate together how much I owe you? <> Do you remember how much you lend me?

Mr. Zhurden. Yes, in my opinion I do. I have made a note. Here it is my note. At first time I gave you two hundred luiders.

Dorante. That is right.

Mr. Zhurden. Then I gave you one hundred and twenty.

Dorante. Good.

Mr. Zhurden. Then One hundred forty.

Dorante. You are right.

Mr. Zhurden. So it is four hundred and sixty luiders or five thousand sixty livres[21].

Dorante. Calculate is correct. I owe five thousand sixty livres.

Mr. Zhurden. You owe one thousand eight hundred thirty two livres your supplier.

Dorante. That is correct.

Mr. Zhurden. You owe two thousand seven hundred livres your tailor.

Dorante. Exactly.

Mr. Zhurden. You owe four thousand three hundred seventy nine livres, twelve sou and eight denier your shopkeeper.

Dorante. Very good. Twelve sou eight denier the calculation is right.

Mr. Zhurden. And one more thousand seven hundred forty eight livres seven sou and four denier your servant.

Dorante. Everything is right. How much do I owe altogether?

Mr. Zhurden. You owe fifteen thousand eight hundred livres.

Dorante. Result is right. Fifteen thousand eight hundred livres. Give me please two hundred pistoles and add them to common sum: finally we get eighteen thousand francs. I shall give them back the nearest future.

Here is the solution in Mathcad. We see that one livre equals 20 sou, but one sou equals 12 denier.



[1] Super-calculator can do not only common mathematics operations, Mathcad can calculate integrals and differentials, work with vectors and matrix, and do some analytic conversions (character mathematics).

[2] Many other things are a reference book of the main mathematical and physical formulas and constants, browser Internet, teaching system and many others.

[3] Our churchmen have seen this number in stroke-codes, which it is planed to mark some documents of Russian people.

[4] verh - top

[5] It is easy to remember: span is seven inches, but vershok is a quarter of a span. D. Harms said: My telephone is32-08. It easy to remember: 32 teeth and 8 fingers!

[6] We should to write here 12 vershoks. But vershok and vershoks is the same things in Russian language, but it is different things in Mathcad.

[7] It does not take place only in reference book, but in Internet too.

[8] Author put a mistake of 2000-Th year. If some reader become familiar with this article in 2001-th year, he will decide that this scene took place in 20-th century but not in 19-th one.

Now days there is not common opinion if 2000-th year is or I century. One thinks about magic of numbers. It is like on a cars speedometer all zeros appear after all ten-oared boat. Willy-nilly you will consider that you- , get to new millenium. Other remembers, that there was no zero year. And they consider that there is no reason to suggest year with three zeros in Date, 2000 is the first year of I century. We shall consider that this article has been published between and I centuries. New Millennium is more publicity event, than metrological one. Author felt time (calendar dates), and number 2000 charmed very much. He thought whether I would live completely this year and anything dangerous would not happen with last beat of the chiming clock. One satirist said: The turn of the month! The turn of the quarter! The turn of the year! The turn of the century! The turn of the millenium! Can you image what we shall have in shops?! Only days became deficit. Nevertheless an expectation of something unusual wandered at the end of century.

[9] Relative scale is widely used for measure temperatures, for example. In private life and technics the origin of reheat or cooling power is not absolute thermal zero. If we have in mind Celsius scale, the origin of reheat or cooling power is thawing-ice temperature. When we speak that a pressure in vessel has some value we operate with relative scale of measure. Manometer shows superfluous pressure relative atmospheric one. There is a physical value that is time. For this value there is no absolute scale of measures. Although such attempts were made more than once both from theological (World Creation) and physical (theory of Big explosion) positions.

[10] Height of a man we can measure both from two arshines and floor and from another value.

 

[12] Here one miniature is remembered On a football match: I do not know what does Offside mean?! At first Offside does not have any meaning, but Offside is a man! Old Offside was, young Offside was, and they had some children. There is hole roman about it.

[13] Dostoevsky gives me more than any scientist, more than Gauss! This phrase was found in Internet with help of keyword Dostoevsky by author. In Internet you can find the text of player by the same address http://www.online.ru/sp/eel/russian/Dostoevsky.Fedor/igrok.rhtml.

[14] Ratio of plot lines (amorous, financial, and playing lines see late) can be appraised, leading static analysis of the text. There are about 47 thousand words in this roman. And we meet golden coin 77 times, money (or profits) 67, franc 50, guilder 43, florin 25, banknote 22, ruble 9, thaler 7, pound 4, kopeck 2, love 2, twenty-copeck coin 1 and half-kopeck coin 1.

It is difficult to make a frequency dictionary, using the command Change the word golden coin for the same word. When we do this fictitious global substitution Word gives out the statement about number of substitutions.

[15] We can take fewer quotations, but seven is a nice number that we often meet in the roman Player by Dostoevsky. Here seven quotations from the roman Player are.

Yesterday the general read me instruction for seven hundred rubles in a year. You were there during our conversation. But it did not mean that I would get that money from him.

He had gone away! But he had all my things! I had nothing! That money that you had brought... that money! I do not know how much was it. It seems to me about seven hundred francs I have for the present moment. That is all. But what next? I do not know!

Once I almost had to use my force, as I could not allow him to buy this brooch for seven francs. At any price he wanted to make a present for Blanche.

Stake on zero, on zero! Once more on zero! Stake as much as possible! How much do we have? Do we have seventy golden coins? Do not grudge them; stake by twenty at once.

But I have been attached to red one as I have noticed that it has taken place seven times running.

I did not eat and drink enough during my wok, but in two month I saved up seventy guilders.

Half a year ago her grandmother dead. Do you remember that mad woman? She left only for her seven thousand pounds.

[16] From the novel Player we can get to know that the teacher's annual salary was 700 rubles. From Internet by keyword thaler we have next information: Annual salary of the teacher in 1850 was 400 florins (600 thalers), but in 1870 600 florins (900 thalers). At that time as we have got to know thaler cost 61 kopecks. But at that time in Russia teachers got about two thousand in a year. Reader can draw a conclusion about salary of teacher abroad and in our country at that time and nowadays.

[17] grandmother is the title of staging of the roman Player in Lenkom (www.lenkom.ru). Grandmother was Great Russian artist I.Churikova (www.lenkom.ru/churikova.htm).

[18] Theme of strange love is the most favorite of F.M.Dostoevsky.

[19] Researches of works by Dostoevsky consider that it is Wiesbaden (www.wiesbaden.de).

[20] Zero plays special role as we play roulette as in informatics. It is a way to keep information in binary code.

[21] Livre is a French word