Science,English, and math 9th

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【Exponential function】

《The form on grand piano is related to exponential function》

The lower the octave is, the longer the string by repeating being double. We call the relation exponential function in math, so the exponential function is hidden in the grand piano.

There are 7 octave in the grand piano actually, so when 7 octave is lower, the length on the string is the 7th power of 2, it’s 128 times, so the longest string is over 6 meters.

But changing the weight and tension on the string of the low tone in actual grand piano, so the grand piano is got creative so as to prevent….

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…so the grand piano is got creative so as to prevent the string from being long so much.

【Differential 微分】

《If looking at the burst shot by strobe, we can understand the essence on differential》

The photo is the swing on golf with certain interval by strobe. We can understand lots of things the situation on the swing from the photo.

For example, when swinging up the club, the interval on the head of club is almost fixed, so we can understand the club was swung up with the fixed speed, though I’m afraid the photo is hard to see.

When swinging down the club, the interval on the head…

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【Differential】

…the interval on the head became larger gradually, and was the biggest the moment when the club hit the ball.

It means that the moment when hitting the ball, the head on the club reached the fastest speed. In fact, the essence on differential in math appears here. What does it mean?

《Differential is a way of researching a change》

If looking at the interval on the head taken by the burst shot, we can understand the way of changing the position of the head, that is to say, we can grasp the speed on the head of the club.

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【Differential】

《Differential is a way of researching a change》

The burst shot is filled with information on the way of changing the position of the head of the club.

On the other hand, the differential is a mathematical way of changing function, inclination on tangent接線 and its speed.

As to the word on tangent, it’s too hard to understand for me, so I can’t express it very much. I’m sorry for it.

The differential resembles the burst shot on the function, but there is absolute difference between the burst shot and differential in math. What’s that?

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【Differential】

《Differential is a way of researching a change》

The burst shot catches a small amount of time with an interval, on the other hand, the differential does the amount of change on infinite small interval. Catching the amount of change on infinite small interval has been possible by calculating accurately in mathematical way. It’s the differential done by Newton and Leibniz.

【Integral】

《Integral is an ultimate addition. After dividing minutely infinitely, adding them》

It’s integral which we learn the differential as set in math in high school.

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【Integral】

《Integral is ultimate addition. After dividing minutely infinitely, adding them》

We call the differential and integral calculus.

The differential is paying attention to the amount of change with small interval infinitely. What kind of way of thinking on the integral?

《How do we find the value on the cubic volume of zucchini?》

We can find the value of area of a circle with the equation of radius × radius × π. As to the cubic volume on a cylinder is the area on bottom multiplied by the height. How do we find the value on the cubic volume on a zucchini?

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【Integral】

《Integral is an ultimate addition, After dividing minutely infinitively, adding them》

The part which was cut is a circle and slender. It’s the shape on the zucchini. It resembles a cylinder, but its thickness is different here and there, so we can’t regard it as the cylinder, so cutting it in round slice. The picture on 405 shows it.

The upper one in the picture is the zucchini which was cut in round slice with ten parts and measures the radius on the place where it was cut and regards it as cylinder. When adding all of the cubic volume, we can find the whole volume on…

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【Integral】

…we can find the whole cubic volume on the zucchini.

《After cutting minutely, adding them》

But if adopting the way, there is difference between the actual shape on the zucchini which has a curve and the upper one on the picture of 405, so making the width on the place which was cut small and increasing the number on the round slice to twenty, or fifty, the difference on the shape of the actual zucchini becomes smaller.

In addition, if making the width on the part which is cut smaller infinitively, we can measure the cubic volume of which shape has the curve precisely.

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【Integral】

《Dividing minutely and adding them》

The way of calculating after dividing minutely infinitively and adding them becomes possible. It’s the integral.

Archimedes who is a mathematician in Ancient Greece and Kepler who is an astronomer and discovered the law on the planetary motion got the idea of dividing minutely and adding them.

And it’s Newton and Leibniz who improved the idea and combined the differential with the integral and completed as a pair.

【Useful math】

Artificial intelligence and information technology has changed our society little by little at present.

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【Useful math】

Those technology which handle enormous data and is close to is useful math. I’m going to start the last chapter including essence in math of which importance heightens from now on.

【The law on large number】

《The more expanding the area we research, the more the data approaches the average》

Even a poor gun will hit the target with a number of shots.

It’s a proverb that even if shooting at random, when doing it so much, it happens to hit on the mark. If you look at it from the other side, hitting on the mark once only isn’t sure whether or not the one who shot the gun …

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【The law on large number】

《The more expanding the area we research, the more the data approaches the average》

…hitting on the mark once only isn’t sure whether or not the one who hit on the mark is a master on the gun. We need to research the accuracy rate on hitting so as to judge the skill on the gun when shooting the gun so much.

《If the area we research and it becomes smaller, its results differ》

Making use of computer and putting ten thousand of dots in the big circle at random. The picture in the 410 shows it. When looking at the picture, the concentrated points are in some …

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【The law on large number】

《The more the data we research, the more the data approaches the average》

…the concentrated points are in some areas, the sparse points are in others.

In this way, even if the arrangement at random, if researching in the small area alone, the number on the points are sparse, so its result is forced to be uneven.

On the other hand, if expanding the area we research, the sparse value becomes small, and the value approaches its average. We call it the law on large number in math which handles probability.

The area on the small dot is the thousandth to the…

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【The law on large number】

《The more expanding area we research, the more the data approached the average》

The area on small dot is ten thousand. There are green circles which thousandth to the big circle which includes all the dots, so ten dots could have been included in the green circles in average, but actual number is uneven.

On the other hand, there is little sparse and the number of dots approaches the average in orange circle of which size is hundredth of the big circle.

【Normal distribution】

《If gathering so much unevenness always appears. What character in the evenness?》

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【Normal distribution】

《If gathering so much, unevenness always appears. What character is in the unevenness?》

The ones who learn statistics at university in the U.S.A are in the picture. They line up according to each height. The ones who raise the pink plate are ladies and the ones who do the blue plate are gentlemen. Both of men and women line up, according to the height.

There are lots of people who line in the center lines, but when going to both the left and right line, the number of people decrease gradually. The whole shape of the people who gather there is like a mountain.

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【Normal distribution】

《If gathering so much, unevenness always appears. What character is in the unevenness?》

Lots of data gather in the center of the mountain, and when going to both left and right side, the data decrease as if it were a mountain. We call the way of unevenness like that normal distribution in statistics.

The value in the center of the mountain becomes the average, and the data crowded around the average. If the number on the data is so many, even if being apart from the average, other data exists. The normal distribution shows us it.

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【Normal distribution】

Various data like the height on the people and points on achievement tests show us they are included in the normal distribution.

《There are some data which aren’t included in the normal distribution》

But we need to be careful that all the unevenness isn’t included in the normal distribution.

For example, if dividing people with annual income, its distribution is different from the normal distribution. The ones who are below the average value are the most part.

《What is the normal distribution?》

The shape on the curve of the normal distribution is decided…

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【Normal distribution】

《What is the normal distribution?》

The shape on the normal distribution is decided to the value on the standard deviation 標準偏差. What is the standard deviation? It means how much the data are scattered around the average.

Even if the average is the same, there are often some ways of scattering the data from the average, so even if the two of data on the average is the same, the way of scattering the data is different.

We have to understand the deviation so as to grasp the standard deviation which is difference from the average.

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《What’s the normal distribution?》

How much is each data different from the average? Is the difference big or small? The deviation shows us it.

For example, let’s suppose there was an exam and it’s average was 60, and the one’s point was 50 and the other 80, and the deviation on the data of two of them is like the next.

The one is 50−60＝−10, it means the one is smaller than the average by 10 points.

The other is 80−60＝20, it means the other is bigger than the average by 20 points.

As a result, the standard deviation is difference from the standard average.

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【What’s the normal distribution?】

If we know the standard deviation, we understand the place on each of date in the whole data. When the standard deviation is big, it means there are lots of data which are different from, so the data are scattering.

On the other hand, the standard deviation is small, there aren’t plenty of data which are different from, so the data aren’t scattering.

When being aware of the standard deviation, we change the way of understanding the data. For example, when the average on an exam was 60, my grade on it was 50, then if there was only information on…

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【What’s the standard deviation?】

…then if there is the information on its own grade and average alone, I may have thought, 50 is so so, though it’s lower than the average, for I did my best.

On the other hand, if the standard deviation is 5, my way of understanding the grade on the test changes extremely, for then lots of people are included 60±5, so plenty of people got from 65 to 55 grade on the test, so the 50 wasn’t very good. As a result, I’d be depressed.

【Vector】

《Vector is amount which is shown by arrows. We can understand the flow on wind quite obvious》

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【Vector】

《Vector is the amount which is shown by arrows. We can recognize the flow on the wind quite obvious》

There have been some instances on calculation shown by photograph or illustration here so far. All of the calculations are shown on numbers, but the subject on the calculation isn’t the number alone. There are lots of arrows in the illustration on the response of 420, and they are the subject on the calculation in math.

We call the arrow vector in math, and the vector expresses the amount. To put it briefly, the vector is the amount which has size and direction.

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【Vector】

On the other hand we call the one which doesn’t have the direction scalar. It’s an ordinary number.

We can do addition and subtraction on the number, likewise we can do the same calculation on the vector. For example, as to the calculation on the vector A ＋ the other vector B, adding the end of the vector A to the vector B, and the arrow of connecting the starting point with the ending point in the whole image is the answer.

《When making a flow visible, the vector is useful》

The vector is useful in our everyday life. For example, there is an illustration in which the…

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【Vector】

…there is an illustration in which the direction and the force on the wind is shown on each place. It’s the right side on the illustration of the 420, though it’s too small to understand. Even if magnifying it, I’m afraid it’s hard. I’m sorry for it.

When looking at the illustration, we can understand the direction and the force on the wind quite obvious. Furthermore, the vector is related a cell phone which is essential to our everyday life.

When exchanging the information, electric wave is used. When the electric wave passes through the space, the electric field and…

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【Vector】

…the electric field and magnetic field change by the minute. Those the electric field and magnetic field are expressed by using the vector. When the electric wave reaches a cell phone, electronics in antenna are influenced and by the electric field and the magnetic field and are forced to be moved. As a result, electric current flows in the antenna, and the electric current changes into information.

By the way, the expression including illustration is over for a while.

I’m going to express the book, science on a candle in the next written by Faraday.

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【Preface】

How far the way from a torch in the primitive age to a candle of paraffin is! How big the difference between two of them!

The way of illuminating at night by people shows us how much their civilization goes ahead.

Bitumen 瀝青 of which shape is liquid burning with dark red flame on a poor unglazed earthenware in a eastern country.

A lamp made by Etruscans. Though it’s elaborate, it couldn’t fulfill its role.

Oil of whale, seal, or bear which fills bad smell rather than light with a hut of Eskimo or the Lapp people.

Tremendous candle made from wax illuminating glittering altar.

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【Preface】

And a line of gas lamp arranged on the street in this country. All of them have each of story. If they can speak, all the lights show us how much they wait on people on the pleasure for them, for the love on families, or the labor, and makes our heart feel warm.

Worshipers on the flame who lived in the time of prehistory, and the ones who used the fire. Hundreds of them have used the fire so far, and no doubt they thought of mystery on the fire.

Probably some hearts without hesitation could have reached near the truth earlier. Please think of the time when the people lived…

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【Preface】

Please think of the time when the people used to live in the helpless ignorance. Please think that the truth is discovered in an instant when a single life continues to the next life.

Chains on the logic has been trained from an atom to a ring. Some of rings were made so rash and so weak that they broke easily and were replaced for the better instrument, but the great phenomenon has been well known at present, and its outline is expressed correctly and skillful painters are about to fill the space.

Children who listen to this lecture carefully will understand on the fire better…

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【Preface】

Children who listen to this lecture carefully will understand on the fire better than Aristotle.

Candles are made so as to illuminate a dark place in the natural world.

A blowpipe and prism are adding knowledge on the crust to us, but we have to light the fire on intelligence at the very beginning. Some of readers on this book will dedicate their lives on accumulation for increasing knowledge. The fire on science has to be flare up. Go ahead the fire.

Faraday used to give a lecture for children, and it was published as book. The preface is from the book. Here we go.

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Faraday is an English, so the book could have been written in English originally,, and it’s so interesting that it was translated into the Japanese, I’m wondering, but I’m going to express it in English…Is what I’m going to do useful? I hope it is.

【First lesson, a single candle, its flame, raw material, structure, movement, or brightness】

As to the situation on a candle, there are plenty of interesting stories when starting from everywhere, and it leads to various fields on science, so I’m forced to surprised at it.

This universe where we live has been controlled by various laws evenly.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

All the various laws which control the universe are related to the phenomena which the candle shows us. What is the candle made of? The one which belongs to the candle is very curious. I’ve had some pieces of wood with me, and they are well known because they burn very much. Look at it, it’s the strange one.

It’s a piece of wood which was taken from the wood of candle. It was taken it from a marsh in Ireland. It has such a lot of wax that it burns very well. The wood is so hard and so durable that…

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The wood is so hard and so durable that the place where a big force is applied is strong, so it’s suitable for the expression by the author. In addition, it burns so much that the people who live in the place where the wood grows so much cut the wood and use as torch there. It burns with the flame as if it were a candle, and illuminates bright light surprisingly then.

Thus we can see an explanation in the wood on the ordinary nature of the candle which is better than anything.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The fuel which is prepared, the way that the fuel is carried away to the place where a chemical reaction is done, and supplying for air, heat, and brightness gradually, regularly to the place where the chemical reaction is done.

Judging from the all the things happened from the small piece of wood, it’s made of natural candle absolutely.

While there is the candle like that, the author said he was forced to talk about ordinary candles which are sold at store. He said he had three kinds of candle.

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【First lesson, a single candle, its flame, raw material, structure, movement and brightness】

One of the candles is the one which we call ひたしロウソク.

There is a cotton thread which is cut in the fixed length, and dipping it in beef fat and taking it out of the beef fat and repeating the work several times until the beef fat of which thickness is the same as the candle sticks to the cotton thread. It’s the 浸しロウソク.

He said he was going to show the candles which he had so as to clear the various nature on the candle. They were very small and very strange. Miners used to adopt in mines long ago.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

In habit long ago, miners had to make the candle by themselves. If comparing them with a big candle, they had been thought it was hard to catch on fire in the explosive gan in mines.

Furthermore, there was a economical reason. The miners made lots of candles from the one pound of beef fat. One pound is some 453.6 gram. Twenty, thirty, forty, and sometimes half dozens of the candles were made from the one pound of the beef fat, but after that the handmade candles were replaced with other safe light.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The next candle which he was going to show was the one which was pulled up from a sunken ship. It had been sunken in the deep sea for a long time and affected by the salty water.

But if looking at it, we see the candle can be preserved. Though the candle was cracked and broke so much, when setting on fire, it burns ordinarily. When being melted by flame, the beef fat regains its own nature at once.

A kind person who made candles gave the author a wonderful sample and raw material on the candle.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The author said he was going to express the sample and raw material on the candle from now on.

The raw material is the fat from a bull. He said he thought it was raw material on the 浸しロウソク in Russia. Someone succeeded in changing the beef fat into a beautiful material. We call it stearin. The white one near the fat beef is the stearin.

As you know, the candle which we use at present isn’t the one which is sticky with the fat beef like the candle made from the beef fat.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

When touching, we find it smooth. Without dirtying anything, being able to remove drops of wax which was melted and to change it into powder.

The author said he was going to express the way of making stearin acid. At first simmering the beef fat and quicklime 生石灰 and making it boil. Then a kind of soap is made. Adding it to sulfuric acid and decomposes the soap, so the lime is removed and the beef fat is left as stearin. At the same time, lots of glycerin is also made.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The glycerine which is as if it were sugar, which is sweet material resembles the sugar is made from the beef fat in chemical reaction like that.

The mixture of the fat beef and stearin include the fat beef which wasn’t decomposed, so if adding pressure to the mixture, lumps which are lined up here is made. When watching them in order, we can see impurities and oil are taken out with the pressure.

At the end of the work, the stearin alone is left, and melting it with heat and putting it into a mold

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

Finally, the white candle which is as if it were snow is completed. The candle which was in the author’s hand was the stearin candle of which material is stearin acid taken from the beef fat.

In the next , the author adopted other candle which was made from whale oil. Refining the oil from sperm whale マッコウクジラ, and the candle was made. There are other candles which is beeswax and refined beeswax, and there is paraffin which is strange thing. The paraffin is a place name in England.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The paraffin is made there and the candle made from paraffin is produced there. In addition, there is a candle made in Japan. His kind friend sent him it. It’s a kind of wax. Paraffin is a kind of formed element on petroleum and white material. All the candles which we see ordinarily are the one made from paraffin.

The author adopted the word of wax, but it’s a general term for chemical compound of fatty acid and alcohol of high quality.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The raw material on the candle which used to be made in Japan long ago is the fruit of ハゼ. Strictly speaking, it’s not wax but a kind of fat.

How are those candles made? As to the ひたしロウソク, the author said already, so he was going to say the candle on mold.

Let’s suppose that all of those candles were made of raw material which became mold, but everyone may have thought the candle is melted by heat, and if being melted by heat, it can be mold, but it can’t.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

Technical skill on production has progressed and in the device on appropriate way so as to reach to a conclusion which we request is done, but strange to say, a thing which our expectation is betrayed often happens. It doesn’t always mean the candle is made by the mold.

For example, the candle made by the wax isn’t able to be made by the mold, and it’s made by special way. The author said he could express it in a few minutes, but he said he abstained from expressing it, though I want him to do it.

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The wax burns very well, and if changing it into the shape on the candle, when being heated, it melts right away.

Anyway, the author said he was going to express the candle of mold.

There is a case in which lots of mold on the candle is fixed. At first,we have to pass through the core into the molds one by one.

There are cores hanging from the wire. The cores were knitted with cotton thread. When burning, we don’t have to cut the core. The core is bound to the wooden nail at the bottom of the mold

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【First lesson, a single candle, its flame, raw material, structure, movement, and brightness】

The wooden nail has two roles. The first is stretching the core tightly, and the second is stuffing the hole at the bottom and preventing the melted beef fat from leaking.

The preparation is done like that, and the beef fat is heated, melted and poured the mold. The mold is filled with the beef fat.

After the mold is cooled, wiping off the beef fat around the mold, and cutting off the both end of the beef fat as we like in the mold. Thus the candle is made in the mold one by one.

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【What I’ve thought】

Though I’ve been expressed myself in English on the book of science on the candle, I don’t think I find it interesting, so I don’t feel like expressing it any more.

It seems that lots of people admire the book, but the important thing is whether or not I find it interesting. Even if all the people on the earth praise the book, I’m not interested in it, so I’m going to give it up.

Though it’s just that I don’t reach the place where there is something interesting, so I’m sorry for the people who read my English eagerly. I’m going to adopt other topic.

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【Without using electricity, shutting the valve】

Using the muscle on a worm, a valve which controls the flow on the water has been enveloped.

There are lots of implements by making use of muscles on creatures operates, and they have been researched until now, but electric stimulation used to be necessary so as to make the muscle move in the past, but taking out the muscle alone from a worm, giving a chemical substance to the muscle and making the valve open and shut at will. That kind of valve has been developed.

When cutting the worm into round slice and opening the round slice, the sheet…

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【Without using electricity, shutting the valve】

When cutting the worm into round slice and opening the round slice, the sheet of muscle which contracts is completed.

It is said that the sheet made of the muscle contracts stronger and more quickly than the one of other animal, but electrical stimulus of 6 voltage used to be indispensable so as to contract the sheet made of the muscle.

Instead of the electricity, researchers gave acetylcholine which stimulates the muscle to the round slice, then the sheet made of the muscle contracts longer time than by stimulating with the electricity.

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【Without using electricity, shutting valve】

When fixing the sheet made of the muscle to an instrument with a pin and stimulating with the acetylcholine, the contraction was caused, and the contraction made the valve shut, so it prevented stream of water from flowing temporarily.

Strengthening durability and nature on the sheet made of muscle may have be enable to apply for device which is implanted into the body in the future, the researchers say like that.

【Medical science】

《Mechanism in which stress get worse cancer》

It seems that nervous sympathicus functions and it causes to…

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【Medical science】

《Mechanism in which stress gets worse cancer》

…and it causes to increase and spread cancer all over the body.

It is well known when receiving stress, sympathetic nerve which is kind of autonomic nervous system reacts.

There had been the result on study that chronic stress speeds up the progress on the cancer, but it wasn’t clear the relation between the sympathetic nerve and the cancer concretely in the past.

This time researchers have discovered that the autonomic nerve system went into organization on breast cancer with the progress on the breast cancer on the mouse.

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【Medical science】

《Mechanism in which stress gets worse cancer》

And then stimulating the sympathetic nerve, it turns out that cells on cancer increase, or spreading the cancer increased.

On the other hand, if getting rid of the sympathetic nerve from the cell on the cancer, it proves that it’s hard to increase and to spread the cancer.

In addition, as to a person, if density on the sympathetic nerve is high in the cell on the cancer, the cancer recurs easily. It becomes clear.

Main treatment on the cancer at present is an operation, drug therapy, or radiation treatment.

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