### Про ёжика в тумане, зазнайство, языки программирования и вериги

Sep. 21st, 2017 09:49 pm

# Beware of mathematicians!

yesterday part

The last exercise does not add anything new to the understanding of the nature of mathematics but it is important for further description of the confrontation between mathematicians and computers.

Let's take the line segment between dots "0" and "1" and summon the tabletop rational demon. This is the green demon who has a magical ruler that can exactly measure the distance between two mathematical points and a magical cutter that cuts a line segment at exact mathematical point. The width of the cut is exactly 0 in any measurement units but you can imagine that the demon leaves a thin green mark on the paper surface in the place of the cut.

The rational demon sets the exact positions for points "0" and "1", measures with his ruler the distance between them and cuts this segment into two halves. He has produced the number "1/2". We usually write it as "0.5".

Now he divides distance between "0" and "1" into three exactly equal segments and cuts the numbers "1/3" and "2/3".

Let's stop and look at the number "1/3". This is a perfectly simple rational number. But if we try to use the decimal representation, we get a strange construction "0.33333333333333…"

Ellipsis "…" means that this sequence is infinite.

By the way, behind "0.5" also lies an infinite sequence. Unfortunately mathematics teachers rarely mention this.

Kids are told that
"125" is "1*100 + 2*10 + 5",
"20403" is "2*10000 + 4*100 + 3" and
"0.27" is "2*0.1 + 7*0.01".

This is correct but describes this mathematical concept from the everyday point of view.

Mathematical decimal number is a sum like "… a5*105 + a4*104 + a3*103 + a2*102 + a1*101 + a0*100 + a-1*10-1 + a-2*10-2 + a-3*10-3 + a-4*10-4 …"

102 = 100
100 = 1
10-3 = 0.001

a4, a-2 and other a's represent some integers between 0 and 9.

Ellipsis "…" at the start and at the end say that this sequence indefinitely continues at left to greater and greater positive powers of ten and at right it indefinitely continues to smaller and smaller negative powers of ten.

Our number "0.5" is the sequence "…0000000000000.5000000000…" and it simply happens that it has only one a-1 not equal zero. We write a zero for a0 to denote the place of the decimal point and we leave out all other zeros because they do not add anything to the sum. The shortened representation ".5" is also widely used.

(A side note: please use the word "zero" for "0" because software developers may use the words "null" and "nil" to represent an empty set "∅". The decimal point in the decimal point format is not the point "0" on your line. Many countries define the comma "," instead of the point "." as the default decimal mark. )

Note, we cannot leave out the intermediate zeros, if the number is not exactly "0.5" but has for instance "1" at the far right place for a-100. This small difference has no meaning for any practical purpose but for mathematics this are different numbers.

You can remember your first demon and say that each three seconds he clarifies next decimal digit in the position of your first dot in some coordinate system. At some iteration he would separate points "0.5" and "0.50000…0001" and draw them as different dots.

If we have two numbers: "1" and "1 + 1*10-10", the first number is included in the set of natural numbers "N", in the set of integer numbers "Z" and in the set of rational numbers "Q" but second belongs only to rational numbers.

This means some mathematical operations defined on the set of natural numbers can use the "exact 1" but the usage of the "nearly exact 1" is not permitted. Despite of the fact that you do not have any possibility to distinguish them as points on your line.

Now your rational demon takes a flask with green mixture, drinks a sip and divides himself into four smaller demons. Each of them stands on a line section (this are (0:1/3), (1/3:1/2), (1/2:2/3), (2/3:1)), each takes a ruler, divides his section into some equal subsections, then drinks a sip of the green mixture and divides himself further.

Note, the rational demon could divide not only the section between "0" and "1" but also a section between "1" and "2", or between "7.5" and "10.82", or between "-0.34" and "-5.672". It is simple to prove that there is no such section between two rational numbers that cannot be divided by the rational demon. This means any section on the line contains indefinite number of rational numbers.

We again have stumbled on infinity. However rational demon is not able to reach all points on the line. The unreachable points represent irrational numbers such as π or 111/2. Irrational numbers cannot be represented as a fraction of natural numbers, any power of ten is a natural number, and this means that the decimal representation contains an indefinite sequence of digits after decimal point. Unlike the decimal representation of "1/3" the tail of this sequence does not repeat itself.

Mathematics says that any point on your mathematical line may be represented as a real number which is included in the set "R" and the set "R" consist of rational numbers "Q" and irrational numbers "I". Between any two different real numbers is indefinite number of real numbers, this means indefinite number of rational numbers and indefinite number of irrational numbers. ("∞ + ∞ = ∞" We are permitted to add them but it is not permitted to say that one infinity is greater than the other infinity.)

Now we have everything we need to blame mathematicians for trying to write software.

Next chunk will follow next week.

### Трамвай-призрак

Sep. 21st, 2017 10:18 pm

### Другим наука

Sep. 21st, 2017 03:16 pm

### Про ёжика в тумане, зазнайство, языки программирования и вериги

Sep. 21st, 2017 12:16 am

# Beware of mathematicians!

yesterday part

Now please take a pen and draw a straight line that goes through points "1" and "2". Measure the size between your dots and draw the point "0" before "1". It would be nice, if the lengths from "0" to "1" and from "1" to "2" are equal, however this is not important.

Imagine two small mathematical demons standing at the point "0". They are big enough to go forward on top of your line. The black demon holds a flag with "{i : i ∈ N}" on it. He counts natural numbers. The red demon holds a flag with "{2*i : i ∈ N}". He counts only even natural numbers.

They start to go forward and they both make one move each second. The black "i" steps on the point "1", the red "2*i" jumps on the point "2". Then the "i" steps on the point "2". The "2*i" jumps again two times longer.

A mathematics teacher would draw a big circle and label it with "N" then a smaller one within it and label the smaller with something like "N2". The sentence you would hear during this may sound like "The set of even natural numbers is included in the set of natural numbers".

The representation is obvious, the definition is clear. Does this mean that there are two times more natural numbers than even natural numbers? (We use the definition of "N" that excludes the number "0".)

### Бинбанк

Sep. 20th, 2017 10:02 pm
ЦБ объявил о финансовой помощи Бинбанку.
ЦБ может вскоре ввести в Бинбанк временную администрацию и передать его под контроль Фонда консолидации банковского сектора
.

Последнюю неделю занимался договором с ними.
Слали какие-то разногласия к договору, зачем-то меняли местами пункты и писали в них то же самое другими словами.
Вчера разродились протоколом разногласий, предлагали поменять два пункта, в обоих написали про сроки предоставдения докуметов, но разное.
Звоню продажникам, типа что за фигня. Они мечутся, мол "шеф, всё пропало" - завтра у них могут ввести временную администрацию и все расходы запретят.
Пришлось брать ситуацию в свои руки.
Звоню их закупантам, куда-то на Байкал. Прошу определиться, когда же им нужна первичка, за две тысячи километров слышно, как у девушки скрипят мозги и хлопают глаза, невнятно что-то рассказывает, что им нужно время для оплаты, чтобы первичка успела с Байкала приехать в Нск, говорю ОК, давайте просто срок оплаты подправим, у девушки аж отлегло, говорит, давайте.
Подправил протокол их, всем разослал, уж не знаю, успенют ли теперь заключить...

### Про ёжика в тумане, зазнайство, языки программирования и вериги

Sep. 20th, 2017 08:15 am

# Beware of mathematicians!

yesterday part

To discover the second word, please draw the second point.

How many dots did you draw?

1 + 1 = 2

This is the simplest thing about mathematics anybody learns at the primary school.

Now look at your dots. They are different!

We add second dot to the first and get "2". We add first dot to the second and again get "2".

A kid looks into a schoolbook and counts "One apple plus one apple equals two apples". Then it asks "Why can we add them? They are different! Why can we add a good apple and a rotten one and again write '2'? Why can we add one apple and one peach and get '2 fruits'?"

Teachers and parents almost always do not answer this questions. Even in rare cases they know the reasons they think first-graders are too young to know the true. Instead, they label this curious child with "You do not have the mathematical thinking". Most children believe them.

Classmates who have weak imagination do not have interest in questions teacher do not answer and blindly repeat what the elders say. They believe they understand mathematics.

This is terrible.

Mathematics does not add apples to peaches. It does not add apples to apples or dots to dots. It operates with mathematical objects.

Before you transform your dots into "1 + 1" you strip them from all distinguishing features.

The second word that connects our world with mathematics is "abstract".

Please write the number "1" below your first dot and the number "2" below your second dot.

Now your dots represent two objects from the set of natural numbers. Mathematicians usually identify this set with the letter "N".

Are "1" and "2" you have written the same numbers that stand in the equation "1 + 1 = 2"?

No. Numbers you have written under dots are called "ordinal numbers" and numbers you use in your equation are called "cardinal numbers". This means you could use the set of letters and label your dots with "a" and "b". Or you could use the set of words and write "first" and "second". If your only task is to force mathematics to distinguish your dots, all three methods are equivalent.

The next mathematical word for you to memorize is "context".

Things that look the same may have different mathematical meaning. Things that look different may have the same meaning. Mathematicians may use the same term for different concepts and label the same concept with different terms. Anything depends on context.

Note, the set of natural numbers may start with "1" and may include "0" before "1". It is printed in books usually not as "N" but as double-struck capital N "ℕ" however nobody bothers to draw two lines in "N" on paper or on a whiteboard. Even the simplest mathematical abstraction has misleading representations and two different definitions.

Thursday part.

### Кофейности немного в ленту

Sep. 20th, 2017 12:08 pm

### Нах Корею

Sep. 20th, 2017 12:27 pm

### Горизонт планирования

Sep. 20th, 2017 12:19 pm

### Даешь безусловный базовый доход! Здесь и сейчас!

Sep. 19th, 2017 11:20 pm

Безусловный базовый доход - это когда каждому постоянно падает бабло за просто так, по факту существования.
Это, наверно, как коммунизм, который к 1980 в СССР обещали (только зачем-то еще работать заставляли).

Ныне во всем мире обсуждают, хорошая эта идея или плохая, где на это брать деньги и прочая...
И даже где-то какие-то эксперименты проводят.

Однако вопросы политические-социологические я обсуждать не буду, потому что в них не разбираюсь.

Я просто хочу показать, что вот прямо здесь и сейчас... да-да! в России в 2017 - некоторая часть населения может получать безусловный базовый доход. И это будут не какие-то там копейки а-ля минимальное пособие по безработице (4900 руб. в месяц ЕМНИП). Это будет доход, превышающий среднюю зарплату по стране! Разумеется, с уплатой всех налогов (НДФЛ+ПФ/ФСС/НДС).

Ах, да, никаких дополнительных расходов от государства не понадобится! Напротив, гос.расходы будут уменьшены!

Что, говорите, я совсем свихнулся и несу утопический-фантастический бред?
Давайте посчитаем.

Что-то здесь не так, правда?
А что не так и что со всем этим делать - я предпочту помолчать и послушать умных людей. Потому что ни экономист ни разу.

### Мне кажется, я уже это видел где-то

Sep. 19th, 2017 05:49 pm
Puritanism: The haunting fear that someone, somewhere, may be happy.

Sententiæ: The Citizen and the State, p. 624
https://en.wikiquote.org/wiki/H._L._Mencken

### Про ёжика в тумане, зазнайство, языки программирования и вериги

Sep. 19th, 2017 11:06 am

# Beware of mathematicians!

This post is written in English because it is very important.

## 3. Mathematics is inhuman

First and foremost: I do not have moral rights to critique mathematicians from the point of view of a mathematician. Despite of my past participation in mathematical competitions, excellent marks, advanced courses in tricky topics and finally my external appearance I do not like mathematics.

It would be nice to point here to an article written by a Professor of Mathematics and simply note that I agree with this reputable opinion. Unfortunately all such texts I have seen so far are either not readable or wrong.

The second sin I force upon myself is the childish approach. To impose as a mathematician you must use a humiliatingly complex vocabulary and hide simple thoughts behind complex grammatical constructions. The text below is on the level of middle-schoolers with good imagination. This means many people who claim they are mathematicians or that they have the Mathematical Thinking would be not willing or not able to understand it.

Before I write the last part about dangers that mathematicians introduce into software development I try to describe some tricky aspects of the nature of this science.

You must distinguish between mathematicians and mathematicians. All my descriptions, samples and conclusions are based on knowledge I had received from excellent teachers and marvelous books. I only try to translate this wisdom into simpler words and I hope I would not fail.

The following text is divided into chunks of about 500 words, reading time for each is about 2-3 minutes. The author is not responsible for any mental or moral damage produced by execution of exercises described below.

### Скайлайн

Sep. 19th, 2017 04:37 pm
В выходные стояли исключительные погоды, наверное, уже последние в этом году.
Довольно много гулял.
В воскресенье ближе к вечеру добрался до Нового моста и пофотал открывающиеся оттуда виды на город.
Вот таким видят Барнаул въезжающие в него через Обь по Новому мосту, т.е. те, кто приехал по Чуйскому тракту, неважно с севера или с юга

### Утрободрости пост

Sep. 19th, 2017 09:54 am

### Сдохни!

Sep. 19th, 2017 02:56 am

### Про Cеверную и Южную Кореи

Sep. 18th, 2017 02:12 pm
Читаем с младшим первый том сборника Николая Коляды. Короткие рассказы восьмидесятых годов, зарисовки из советской провинции. Сразу видно, что это вышло из под пера драматурга. Характеры прописаны точными грубыми мазками. Динамично и сочно.

Для ребёнка другой культуры психология людей той эпохи странна и не понятна. Другая логика жизни, другая система ценностей, другая мораль. Иногда на очевидное для советского человека действие сын удивлённо спрашивает "На самом деле?.. А зачем?.. Это он что, своровал?.."

Кстати, понял, почему текст про математику не хотел писаться: страшно. Получается на самом деле какая-то жуть.

Начну со вторника по кусочку выкладывать.

### 99 франков

Sep. 18th, 2017 11:30 am

### Краски осени

Sep. 17th, 2017 11:48 pm
Вид с окна рабочего кабинета как-то уже показывал.
А сейчас посмотрим на другую сторону (северную).
Там у нас город контрастов - сокращающиеся остатки частного сектора и наступающие на него новостройки.
Но пост не об этом, а о том, как заметны уже краски осени.
В прошлом году в начале октября снег выпал (и остался) на совершенно ещё зелёные деревья, так мы и ушли из лета в зиму, а в этом в первой уже половине сентября зазолотило вовсю, к чему это не знаю, надеюсь, от противного, - к долгой красивой осени...
Впрочем, сегодня уже, хоть день и очень тёплый был, по городу, никого не стесняясь, летают синицы...

### Мастер фэншуя

Sep. 17th, 2017 03:19 pm

gapel

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