Mathcad and some secrets of literature (by Valery Ochkov)

Example 2. Height of Nicholas Fandorin

Example 3. Height of the Turgenev’s Gerassim.

Example 4. Weight of Alex Vronskey

Example 5. Ruble rate at the end of XIX century

«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.

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].

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.

I.S.Turgenev
left more difficult puzzle about his hero’s 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 man’s 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 soundedçâó÷àò êîðîòêèå ôðàçû: «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 sazhen^{2} := 13.7 m^{2}

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:

m^{2} := 100 liter^{2/3
}span^{2} := 3.161284 liter^{2/3
}sazhen^{2} := 455.225 liter^{2/3}

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

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 author’s friend has told such
story. It was at school. Parents came to see their children’s 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. Author’s 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.

– 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.

– 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.

*In the general’s home the teacher (a *«young man»*
who tell this story) lives. Polina and the teacher love each other rather*
«strange love[18]». Polina’s 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 Polina’s
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 general’s 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 Íî ñêîëüêî «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!

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. Let’s
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] âåðõ – 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 ÕÕ or ÕÕI century. One thinks about magic of numbers. It is like on a car’s
speedometer all zeros appear after all ten-oared boat. Willy-nilly you will
consider that youÂîëåé-íåâîëåé áóäåøü ñ÷èòàòü, ÷òî «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 ÕÕI century. We shall consider
that this article has been published between ÕÕ and ÕÕI
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 ÕÕ 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