Science,English,and math 4th

【Estimating on Fermi and something approximate】

《Estimating a scale of market on jeans》

The author, ...so the scale of market on jeans is equal to about 0.6% on the GDP, and is equal to a thousand of Ochiai who is a professional Japanese baseball player. By the way how about the whole world?

An annual salary of Ochiai was three hundred million and both the author and his friend love baseball.

His friend, Mmmm...the whole world? There is a cultural sphere where no one puts on jeans, so the number of jeans they buy a year become less. One to ten people buy a pair or two pairs jeans a year?

• 共感2

【Estimation on Fermi and something approximate】

《Estimating a scale of market on jeans》

The author, If one of ten people buy two pair of jeans a year, as the whole population in the world is about sixty billion, so multiply sixty billion by zero.point five by five thousand is equal to six trillion. So the scale of market on jeans in the whole world is six trillion.

The conversation was done in 2000. The author said he found interesting that the estimated value on the scale of market both in Japan and the whole world on jeans was led from a conversation nonchalantly, so he remembers it.

• 共感2

【Estimation on Fermi and something approximate】

《Estimating a scale of market on jeans》

By the way the scale of market on jeans in Japan was about a hundred billion, and six trillion in the world in 2020

As to the scale of the domestic market is less half than the one which the author and his friend calculated, but the scale of market in the world is six trillion.

The author said he read an article on a magazine and the article said that a tendency of being away from putting on jeans among the youth has gone ahead. Some of jeans shop of which sales have dropped to half twenty years ago.

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【Estimation on Fermi and something approximate】

《Estimating a scale of market on jeans》

The author said the three hundred billion isn’t beside the point. First of all this kind of presumption is all right unless it had a wrong number of digits.

The scale of market on the whole world is exactly right, but the whole population in the world is about 7.5 billion at present, so it must have been more then. In either case, it’s not beside the point.

《A father of nuclear power and estimation on Fermi》

Estimating approximate value like the conversation is called the estimation on Fermi.

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【Estimation on Fermi and something approximate】

《A father of nuclear power and estimation on Fermi》

A question like how many manholes are there in Tokyo prefecture? has been prepared in an entrance exam for various companies recently, as a result, the estimation on Fermi seems to be indispensable skill when trying to get a job for new graduates.

There was no phrase of estimation on Fermi twenty years ago when the author was a student, but students who chose a course of science and math carried out it from long ago, estimating approximate value.

When making an experiment, they...

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【An estimation on Fermi and something approximate】

《A father of nuclear power and estimation on Fermi》

When making an experiment, they formulate a hypothesis in the beginning. The hypothesis is an opinion which is set up temporarily so as to express a natural phenomenon. After the hypothesis is recognized officially by the experiment, it will be a new law or new theory then.

How much can we get a value from the experiment? We need to estimate it beforehand. Otherwise, we don’t know an experimental instrument to prepare for. How much precise does the experimental tool need? We need to know.

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【An estimation on Fermi and something approximate】

《A father of nuclear power and an estimation on Fermi》

Furthermore, if estimating in advance, when getting value which was unusual, which means that the value was more different than we expected, we can guess it has possibility of making a mistake when making an experiment.

The origin of the assumption on Fermi is Enrico Fermi who is well known for a father of nuclear power. He received a Nobel prize for physics. He got a remarkable results as theoretical physicist and experimental physicist, and was a master of estimating approximate value

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【An estimation on Fermi and something approximate】

《A father of nuclear power and estimation on Fermi》

Fermi had an episode like the next.

When a bomb exploded, he dropped a sheet of tissue paper, then the tissue paper whirled in the air by the blast. Fermi watched the orbit of the tissue paper and estimate of the amount of the gunpowder on the bomb roughly.

He went to Chicago University for a lecture, and he prepared for a question to freshmen like the next. Its famous.

How many piano tuners are there in Chicago?

Why did Fermi prepare for the question to the freshmen who adopted...

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【An estimation on Fermi and something approximate】

《A father of nuclear power and an estimation on Fermi》

If living through in the world of physics, an ability on estimating something unknown is very important. The question was the message from Fermi to the freshmen.

The target here isn’t always mean that reaching the right value, which means the right number of the piano tuners, for if wanting to grasp the exact number on the piano tuner in Chicago, they have only to phone to a committee on the piano tuners, though it isn’t clear whether there is the committee like that, but therefore ..

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【An estimation on Fermi and something approximate】

《A father of nuclear power and the estimation on Fermi》

...and the important thing for us is even if it’s unknown value, whether or not we can ask an approximate value with our data logically which we have already.

The author expressed a procedure on the estimation of Fermi, adopting the number of piano tuner in Chicago.

1『Formulating a hypothesis』

Framing a hypothesis that a demand and supply on the piano tuner is well balanced in Chicago and thinking over the number on the piano tuners who are indispensable in Chicago so as to tune...

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《A father of nuclear power and the estimation on Fermi》

1『Formulating a hypothesis』

...and thinking over the number of the piano tuners who are indispensable so as to tune all the pianos in Chicago.

2 『Dividing a matter into several elements』

What is a necessary data and an amount of presumption we need so as to think over the question?

The population in Chicago.

The number of people in a single household.

A ration of the household which has the piano in the whole Chicago.

A number of times on tuning the piano for a year.

A number of times on a single piano tuner who does his own....

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《A father of nuclear weapon and the estimation on Fermi》

2『Dividing a matter into several elements』

A number of times on the single piano tuner who does his own job for a year.

3『Making use of data which we’ve already known』

The indispensable data which we estimate the number of piano tuners in Chicago is the population in Chicago. Its population is about three million, though the number isn’t familiar with us, it seems to be common knowledge for the students who go to the Chicago University.

4『Calculating the amount of presumption on each element』

Amount of presumption on the number...

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《A father of nuclear weapon and the estimation on Fermi》

『Taking advantage of data which we’ve already known』

Amount of presumption, 1, the number of the people in a single household.

How many households in a big city of which population is about three million? Needless to say, a household is one and the other is four and another is ten, but we set up the average number on the single household is three.

Amount of presumption 2, the ration on the household which possesses the piano.

How many households do they have the piano in the whole Chicago?

Though the situation may have been...

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《A father of nuclear weapon and the estimation on Fermi》

『Making use of the data which we’ve already known』

Amount of presumption 2, the ration on the households which possesses the piano.

The situation may have been different between Japan and America, but please think over how many children they learned the piano in the class when you were in elementary school.

If the class is coeducational and made up with forty children, there are lots of cases that four or five children who learned to play the piano in the class, the author said, though the elementary school which the author went...

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《A father of nuclear weapon and the estimation on Fermi》

3『Calculating the presumption number on the each element』

Presumption number 2, the ration on the household which possesses the piano.

...though the school which the author went to wasn’t coeducational, so the one who learned to piano was a few in the class.

So we set up that the households which possesses the piano make up for 10% in the class.

When being in junior high school or being in high school, lots of people seemed to stop learning to play the piano, so we should exclude the piano which no one played, for it doesn’t have...

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《A father of nuclear weapon and the estimation on Fermi》

『Calculating the amount of presumption on each element 』

The amount of presumption 2, the ration on the households which possesses the piano.

... for the piano doesn’t have any chance of being tuned, so the number of the piano seems to be a little more, but except for the households, there are pianos in school, a public hall, so it’s all right.

The amount of presumption 3, the number of times on a single piano which is tuned a year.

A piano is usually necessary to be tuned once a year.

The amount of presumption 4, the number of ...

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《A father of nuclear weapon and the estimation on Femir》

4『Calculating the amount of presumption on each element』

Amount of presumption, 4, the number of times on a single piano tuner who does its own job a year.

Thinking over the number of times on the piano for the single piano tuner tunes a year. How many of the piano are tuned?

Tuning the piano is a hard labor and takes a lots of time. Even if the piano tuner works harder, it can tune three pianos a day at most.

If the piano tuner is on a five-day week, and it works 250 days a year, 3×250＝750, so the number of the piano which the...

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《A father of nuclear weapon and the estimation on Fermi》

4『Calculating the amount of presumption on each element』

...so the number of piano which the single piano tuner can tune a year 750.

5『A conclusion』

As being based on those things, we can estimate the number of the piano tuners in Chicago.

The population on Chicago is 3 million, and the number of the people who made up with the single household is three, 300÷3＝100, so the number of households in Chicago is a million.

The number of the pianos in Chicago is 10% of the households, so 100÷10＝10, so the number of pianos are a hundred...

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《A father of nuclear weapon and the estimation on Fermi》

5『Conclusion』

...so the whole number of the piano in Chicago is a hundred thousand.

The number of times on the piano which is tuned a year is once a year, 100.000×1＝10, so the tuning on the piano is done a hundred thousand times a year in Chicago.

The number of the times on the piano tuner who can do tune three times a day and it works is 250 days a year on the condition that it adopts the five-day week, 3×250＝750. 100.000÷750＝133...so we can estimate the number of the piano tuners in Chicago is 133.

But the author said it’s his...

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《A father of nuclear power and the estimation on Fermi》

5『Conclusion』

But the author said it’s his own estimation, so it doesn’t alway mean that the number of 133 alone is the right answer.

If the data which we’ve already known is combined with the amount of presumption appropriately, even if it’s not 133, its estimation seems to be right.

《The estimation on Fermi isn’t beside the point so much》

If trying in various ways, we can improve the way on Fermi estimation, so the author suggested we estimate numbers around us, for example, the number of cars which are sold a year, the amount...

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【An estimation on Fermi and something approximate】

《The estimation on Fermi isn’t beside the point so much》

...for example, the number of cars which are bought a year, the amount of domestic consumption on wine, or distance in which a soccer player ran in a match

To tell the truth, if trying to estimate the value on Fermi in related to those things, its value isn’t beside the point from the true value.

It seems to be strange, but it means mixing each of element mutually. It hardly happens that all of the amount of presumption on each element is too much or to less.

A knack on the...

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【An estimation on Fermi and something approximate】

《The estimation on Fermi isn’t beside the point so much》

A knack on the estimation of Fermi is dividing the question as minutely as possible.

The bigger the amount of presumption is, the more there is a risk that the amount of estimation is beside the point from the true value.

The author said he recommended that if the one who reads this sentence is weak at numbers, and has wanted to be good at numbers, it should challenge at the estimation on Fermi.

It seems to be harder a little, but the calculation which we adopt is simple, and we...

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【An estimation on Fermi and something approximate】

《The estimation on Fermi isn’t beside the point so much》

...and we can try it with the way of easygoing and it’s all right as long as we don’t have the wrong number of digits.

Besides, if getting used to it a little more, we can estimate a thing which we have little knowledge pretty close, so we have fun.

The author says he will be happy if the one who read his book learns to like math because of the challenge.

【The number which comes to the head most frequently】

《What is the law on Benford》

There have been varied numbers around us.

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【A number which comes to the head most frequently】

《What is the law on Benford?》

When reading a newspaper, a book or contents on the internet, the number always appears in front of us. Needless to say, a business performance, a telephone number, an address, a population, and a price on stock are expressed with some numbers.

Of course all the values are made up with a combinations of numbers. As to the number on the head, it means a number of the highest digit, it’s limited from 1 to 9.

By the way what is the number at the head of value in every conceivable kind of numbers?

Some people...

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【A number which comes to the head most frequently】

《What is the law on Benford?》

Some people thought as a variety of number appears each of them has the same probability.

Others thought that it’s irregular, and it depends on, so It’s different according to its time and place, so we can’t foresee it.

But the way of appearing the number in the head is regular conspicuously. The author said he was going to show us here it from now on.

In fact it turns out that a ration on the way of appearing the number isn’t equal. The one which appears in the head the most frequently is 1, and the....

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【A number which comes to a head most frequently】

《What’s the law on Benford?》

...and a ration of the value which starts from 1 accounts for about 30%.

If each of numbers from 1 to 9 appears equally, its probability is it’s one-ninth, and one-ninth≒11%, so 30% is high ration. As it’s the head number 0 is excluded.

The larger the number of the head is, the less its ration of which the number appears there was.

The ration of the value which starts from 9 makes up for no more than 20% in the whole number. We call it the law on Benford.

There is a graph and a list in the book. Numerical...

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【The number which comes to a head most frequently】

《What is the law on Benford?》

A ration on the numerical value of which head is one from three is over 60% in the whole number, according to the graph and the list.

It was Frank Benford who showed the law for the first time in 1938. He was an American physicist. It is said he collected samples which was over twenty thousand like an amount of molecule, a population or a number which appears at articles in newspaper, and reached the conclusion.

He seemed to gather various kinds of sample. For example, loss on HP, or a black body.

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【The number which comes to a head most frequently】

《What is the law on Benford?》

As to the loss on HP, HP is heat pump and it’s an instrument which collects heat and the loss on HP means that the energy on the instrument is lost.

The black body is a material which never reflects the light.

To my sorrow, I don’t know anything on physics, and as to the two of them, it’s just that I’ve expressed as the book says.

Average value on the samples which were over twenty thousand were close to the value on the theory of Benford.

When paying attention one by one, some distribution on numbers ...

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【The number which comes to a head most frequently】

《What is the law on Benford?》

If paying attention one by one, the distribution on numbers like the area of a river’s basin, numbers which appear at articles in newspaper, a pressure, a design, and address are close to the values on the theory.

On the other hand, physical constant 物理定数, the amount of molecule, and the amount of atom, they have a bigger margin of error comparatively 誤差.

By the way when having read until now, I’m afraid you aren’t satisfied with my expression, but the ground on Benford is from now on. Please just a moment.

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【The number which comes to a head most frequently】

《Germs increases in w way of exceptional function 指数関数》

Some of numbers correspond to the values on theory, but others don’t. Why?

Let’s think over a reason intuitively why the law on Benford stands up.

For example, some number becomes double within the set time in natural world like germs increase. It’s not unusual.

If it becomes a double in a year, when there is a hundred, it becomes two hundred in the next year. After two years, four hundred. After three years, eight hundred, and after four years, one thousand six hundred.

This way...

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主さん。外語や英文科の専門学校など、各種学校を、きっと卒業でもされたんですか？ 前々から、知っている。

すっごーい。

すげえ(感嘆)

• << 234 スレ主です。 レスしているのは、私の兄です。応援して下さり、ありがとうございます。 英語のお勉強、頑張って下さいね。

• 共感1

>> 231 主さーん！

私アラフォーのおとななんだけど、
法政大学在学が、始まりました。
卒業をしたいんだ。かならず。


その後、専門学校を複数どうしても卒業がしたいし、
仕事ができないから、旦那、家族、血縁が、おかねをだします！

だから、恩返しとしても、
また、その後、大学院の博士課程迄、修了をしたいんだ。頑張りますので、主さんが、昔っから、私の励みなんだよね！

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【The number which comes to a head most frequently】

《Germs increase in a way of exceptional function》

This way of increasing is called an increase of exceptional function.

In this case, it takes a year to increase from 100 to 200, and then its head of the number remains 1 until the next year.

On the other hand, if the head number is 5, for example when the number increases from 500 to 600, it’s no more than three months, but it doesn’t always mean that I’ve calculate if for myself, but the book said so, it takes three months.

In the same way, if increasing from 1000 to 2000, it takes...

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>> 231 主さん。外語や英文科の専門学校など、各種学校を、きっと卒業でもされたんですか？ 前々から、知っている。 すっごーい。 すげえ(… スレ主です。

レスしているのは、私の兄です。応援して下さり、ありがとうございます。

英語のお勉強、頑張って下さいね。

• << 237 パソコン アクセス、ワード、エクセル、ビジネスマナーも、今の大学の経済学部も、みんな一斉アルバイト、派遣などは、しないで、そっちを頑張りますので宜しくお願い致します。

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＞＞231

To the person who responded 231

Thank you for your message and congratulation on being a student in Hosei University. To be exact, I’m not ぬし,for instead my sister built thread for me.

It’s just that I’m interested in English, so I’ve started to study English at the age of 45. I’ve never been to any university, for my school record wasn’t so good.

It seems that you will be in difficulty for the time being from now on, but lots of people around expect you. Please good luck.

I’m not sure whether or not my English so wonderful as to encourage you, but I’m going to do my best.

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＞＞231

231にレスした方へ。

メッセージありがとう、そして法政大学在学おめでとう御座います。正確に言えば、主は自分ではなく、妹が自分のためにスレを立ててくれました。

英語に興味があったので、45歳から英語の勉強を始めました。学校の成績は良くなかったので、大学には行けなかった。お恥ずかしい。

これから暫くは大変ですね、でもあなたの周りの大勢の人があなたに期待しているんですね、頑張って下さい。

あなたを励ませるかどうかは分からないけど、自分も英語の勉強を頑張ります。

• << 238 有り難うございます。 頭が私すごーく悪いため、 仕事、家事手伝いが不可能となりました。実はIQ76しかないんです。 (詳しくは私のスレで！ せんか慎重派さんのハンドルネームです。) だから、学校に行く以外、ないのです。 こういうとりえがなんもない。 スタイルも163センチ、75キロ以上の学習障害、発達障害の、中学校にてあまりに低いIQだから、大人になり自力で生きる力がありません。 進学校進学 専門学校 短大、大学ましてや院。 高校生アルバイトや、大学からの正社員の仕事もみんな不可。担任にボーダーのIQを心配され、親が呼び出された三者面談がありました。親は教室や公共交通機関の中でも、声にあげておいおい泣き伏し、家庭に帰宅ののち、すっごい剣幕でおこられ、生むんじゃなかった、元気ないからよ。シャキッとしなさい。見た目も。同時にお父さん、おばあちゃん、お姉ちゃんにも。15才の時のはなしです。私は地頭がとてもよくないから、一生懸命学歴を手にして、いじめられたり、囃し立てられたり、下に見られ、もうなめられたりしたくはないから、 長々、ヒトのスレ内にすみませんでした。

• 共感3

>> 234 スレ主です。 レスしているのは、私の兄です。応援して下さり、ありがとうございます。 英語のお勉強、頑張って下さいね。 パソコン
アクセス、ワード、エクセル、ビジネスマナーも、今の大学の経済学部も、みんな一斉アルバイト、派遣などは、しないで、そっちを頑張りますので宜しくお願い致します。

• 共感1

>> 236 ＞＞231 231にレスした方へ。 メッセージありがとう、そして法政大学在学おめでとう御座います。正確に言えば、主は自分ではなく… 有り難うございます。

頭が私すごーく悪いため、
仕事、家事手伝いが不可能となりました。実はIQ76しかないんです。
(詳しくは私のスレで！
せんか慎重派さんのハンドルネームです。)

だから、学校に行く以外、ないのです。
こういうとりえがなんもない。
スタイルも163センチ、75キロ以上の学習障害、発達障害の、中学校にてあまりに低いIQだから、大人になり自力で生きる力がありません。

進学校進学

専門学校
短大、大学ましてや院。

高校生アルバイトや、大学からの正社員の仕事もみんな不可。担任にボーダーのIQを心配され、親が呼び出された三者面談がありました。親は教室や公共交通機関の中でも、声にあげておいおい泣き伏し、家庭に帰宅ののち、すっごい剣幕でおこられ、生むんじゃなかった、元気ないからよ。シャキッとしなさい。見た目も。同時にお父さん、おばあちゃん、お姉ちゃんにも。15才の時のはなしです。私は地頭がとてもよくないから、一生懸命学歴を手にして、いじめられたり、囃し立てられたり、下に見られ、もうなめられたりしたくはないから、


長々、ヒトのスレ内にすみませんでした。

• 共感1

【The number which comes to a head most frequently】

《Germs increase in a way of exceptional function》

In the same way, when increasing from 1000 to 2000, it takes a year, but when doing from 5000 to 6000, it takes no more than three months.

In other case, as to the change on increase of exceptional function, the period when the head number is 1 above all longer than any other period in other numbers come.

《Even if its unit changes, is it the same nature?》

Even if it doesn’t change in a way of exceptional function, the law on Benford is applied to some cases. They are the ones in which...

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＞＞236,238

To the person who responded 236,238

Thank you for your message. I’m wondering if it is mortifying for you until now.

236, 238 にレスしてくれた方へ。

メッセージ有難う御座います。今まで悔しい思いをしてこられたのだろうと思います。

I used to express it in English but do in Japanese for the first time here, at ミクル. I’m sure I’m suffering from what is called Asperger Syndrome.

英語では言った事があるけど、日本語ではここ、ミクルでは初めてです。自分はアスペルガーだと思います。

I’m afraid you have been distressed by your situation and will be in difficulty from now on, but I’m also on the same boat and we shouldn’t be daunted.

あなたは、今まで辛い思いをしてこられ、これからも大変だと思います。でも、自分も同じです。挫けちゃいけない。

• 共感2

>> 240 とりあえず、私の仕事。
学生をする。卒業資格をつけること。

中退はしません。

有り難うございます、かなりヤル気みなぎりましたからー🖤。

• << 259 だだ、いじめられないように、 気を付けて中断しないように、 細心の注意を払います。

• 共感1

＞＞241

Good luck and please do your best.

頑張れ〜💪

＞＞239

【The number which comes to a head most frequently】

《Even if an unit on measure is changed, is it the same nature?》

This is the case in which the numbers are lined up in order from the 1 like membership number. Then the number which starts from 0 is excluded.

For example, let’s suppose there was a fan club made up with five thousand of members. Then each of membership number of which the head number is either 5,6,7,8,or 9 is extremely less than the each one of which number is 1,2, or 3.

• 共感3

【The number which comes to a head most frequently】

《Even if an unit on measure is changed, is it the same nature?》

There is a list on the book.

When the number of membership is from a thousand to ten thousand, researching the head number of the numbers of membership at a place where is good to count numbers like 1000, 2000, or 3000, to 10000l.

The number of which the head is 1 is more than any other number of membership of each place like 1000, 2000. It has been showed on the list, but to tell the truth, I’m not sure of the way of looking at the list, so I’m not sure of it.

• 共感3

【The number of which head comes most frequently】

《Even if an unit on measure is changed, is it the same nature?》

Except for the number of memberships of which number increases in order, in a case in which the numbers are scattered in some extent with almost the same ways like a population or a length of a river, the same phenomenon occurs, so the law on Benford is applied well.

As to the number of membership, I can understand, but I’m not sure in relation to the population and the length of the river.

A line of numbers which is determined by other rule like a telephone number, and a...

• 共感3

【The number of which head comes most frequently】

《Even if an unit on measure is changed, is it the same nature?》

...and data controlled by normal distribution like the score in the National Center Test for University Admission センター試験 isn’t applied to the law on Benford. The normal distribution is the most important part in statistics. Its shape becomes a temple bell.

In addition, as to a set for numbers of which value is limitless and are showed at random, it isn’t applied to the law on Benford.

However if picking up from some data which isn’t applied to the law on Benford like numbers...

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【The number of which head comes most frequently】

《Even if an unit on measure is changed, is it the same nature?》

But if picking up some data at random from some distributions which aren’t applied to the law on Benford, it proved out that they are applied to the law on Benford.

Even if I can understand the law on Benford means, I can’t grasp why it is until now, except for the numbers of membership.

《A knack on judging injustice with regard to numbers》

How is the law on Benford useful in our society?

Hal Varian who designed a model for advertising which was a source of income at the...

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【The number of which head comes most frequently】

《A knack on judging injustice with regard to numbers》

Hal Varian who designed a model for advertising on source of income in Google at the dawn is said to be a economist who made Google a number one company in the world.

He said if putting the law practical use, we can see a window-dressing settlement 粉飾決算.

Without knowing the law on Benford, the one who tries to disguise an amount of money at an account book in company, it tends to express the numerical value with a distribution of being too much equal head number, on the other hand it’s...

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【The number of which head comes most frequently】

《A knack on judging injustice with regard to numbers》

...on the other hand, it’s apt to express the distribution which leans some places alone too much.

Then the ration in which the value starts from 1 is against the law on Benford, so we can discover it’s a false data.

In fact, the next thing happened actually in the beginning of 1990s.

An instructor in an accounting school gave his students a lesson. He said his students to make sure whether or not each number of biggest digit on earnings and expenses of a company corresponded to the law.

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【The number of which head comes most frequently】

《A knack on judging injustice in regard to numbers》

There was a student whose relative managed a hardware store, and the number on the account book was different from the law on Benford so much, so the student discovered it and it led to the discovery of injustice on the account book.

Except for auditing 会計監査, the law on Benford has been adopted for verification on unfair voting in an election as well at present.

【How to find a way of useful information】

《Digging up unfair usage from a mountain of data》

The author was sure that lots of...

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【How to find a way of useful information】

《Digging up unfair usage from a mountain of data》

The author said he was sure that lots of people have heard of a word, data mining. It has suddenly learned to be used a few years in the past with other phrase, big data.

If translating the data mining word for word, it means mining potential needs from data. It originally started to be used in a studying field called Knowledge Discovery in Database from the latter half in 1990s.

After that the internet has spread over the world due to the IT revolution and knowledge on computer has expanded by...

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