Science, math and English 12th
始まるよ😊
Whenever there is a chance of expressing myself in English, I’m worried about its content, though it’s all right as long as I do what I want to express.
I’ve expressed, being based on the book, 面白くて眠れなくなる地学, right now, but it will be end until summer was over, at least. After that which topic, should I choose?
Without having basic knowledge at all, my thought is full of curiosity, so there are lots of things to express.
Roughly speaking, I’m not good at science, especially I’m not a math person, so I’m afraid I tend to avoid to handle math here, so I’m going to deal with math positively. But when being into something else, I am apt to forget it.
In addition, I don’t know how to show an equation with nth root here. I find it inconvenient. I have to improve my skill on the pc.
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【We’ve heard the breath from the math】
《The ability on turning it into something abstract and…》
There are two of things which have in common. Without being confused with the part which we can see, whether or not we can look for the thing which have in common behind the two of them.
The one who is able to do is good at math as well. You may have not click with it, but I’m going to show you various examples, so please bear it in mind.
The author said like that, and to my surprise, he is the professor of Tokyo university.
When thinking, turning something into something abstract, what is …
【We’ve heard the breath from the math】
《…and turning it into something simple》
What is in the brain of the one who thinks like that? All of you may have thought the author who is the researcher of Tokyo university always thinks something complicated extremely, but I don’t. When starting to think, its image is something red, something fluffy.
Even if being a splendid scholar, even if being engaged in a hard equation when having an idea, the basic thing in its brain is something so simple that even a student in junior school can express itself.
Let’s suppose starting from one and the goal …
【We’ve heard the breath form the math】
…and the goal is 10, as to the idea of the step from one to three when calculating, it’s not so complicated. Modifying an equation of which level is junior high school or high school at best, and I guess it’s rough concept.
The thing which I think is very simple, to put it the other way around, if going well with a simple thing, we can understand even if a complicated thing in which various elements are mixed, for going well with the simple things is helpful for us. Trying to understand something complicated, we can do nothing, so turning it into simple
【We’ve heard the breath from the math】
《A mathematician isn’t deceived easily. Why?》
The author said the mathematician isn’t deceived easily before, not being deceived easily is one of merits in math.
For example, when watching TV, a specialist said the export would expand by the end of this year, when looking at it say something in the future, what do you think? When getting the information whether or not accepting as it was.
Mathematicians are cautious, so lots of them say it’s something shady, there is something sketchy behind it, for it has something to do with math, they understand….
【We’ve heard the breath from the math】
《A mathematician isn’t deceived easily. Why?》
…they understand the thing behind it, so they see the thing which someone tries to deceive.
When expecting something in the future, needless to say, we can’t see its goal, but as expecting the invisible goal, we have to consider various possibilities. Though being able to understand the first situation, what is the next? It’s different, according to the assumption.
The author said the expectation was the most important in math, but no one can expect the next thing nor it’s absolutely without being the God.
【We’ve heard the breath from the math】
《A mathematician isn’t deceived easily. Why?》
As a result, if it’s x… or if it’s y…, the excuse of the if continues, though it ratifies like if it’s y, in addition it’s z is, 2 is formed. Or it’s y and furthermore it’s w, 3 is formed.
For example, let’s suppose we see the average temperature on the earth would rise by four degrees in 2100 on TV or on news. Needless to say, the assumption is included in the prediction.
The change on the climate on the earth is done various interactions like atmosphere, the sea, and the surface on the land. Taking it…
【We’ve heard the breath from the math】
《A mathematician isn’t deceived easily. Why?》
Taking it into account the prediction on the change of the temperature in the earth is done, but in fact there are lots of things which we can’t understand. For example, the earth is covered with clouds. How much the clouds reflect the heat or light from the sun, how much they convey the heat or light to the earth. The ration between two has never been clear.
Forming the equation and predicting in the uncertain situation, so researchers have to assume in varied ways, and their opinions are varied…
【We’ve heard the breath from the math】
《A mathematician isn’t deceived easily. Why?》
…and their opinions are varied according to the researchers, but the chaos which isn’t solved by mathematics is involved in the weather. It’s tiresome for the math, if the chaos is related, no one can predict exactly.
The author said he was going to express on the chaos later.
What the author wants to say is without taking the assumption into account, and accepting the conclusion is dangerous, for it may have been deceived or the condition changes on the way and the conclusion frequent changes altogether.
【We’ve heard the breadth from the math】
《How much can we trust the eyewitness report?》
The author said he was going to think of a few things which make us see by using the math, and he would give a quiz to the students from then, the question on the probability. There are lots of people who are poor at the probability, and the author himself said he’s researched with the probability, but he didn’t like it very much. Counting the case of the number is something troublesome.
What is the talk which the author started from then? The one on the trial of the hit-and-run case which is well…
【We’ve heard the breath from the math】
《A mathematician isn’t deceived easily. Why?》
The talk on the trial of the hit-and-run case which is well known and interesting. The author said to think of the author as the witness and of the students as the judge.
『Question』
A case of hit-and-run happened. The eyewitness said a taxi ran over someone. There are two of taxi companies in the town, the company of A and B, and the color of the taxi on the A is blue, and the one of the taxi on the B is white. The eyewitness said he saw the white taxi at the crash site.
As the eyewitness appeared, so…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
…so the true culprit must have been someone in the B company, we usually think like that, but is it true? Can you decide someone in the B company is the culprit with the eyewitness report alone?
The author asked the students and continued.
It’s impossible, isn’t it? Even if there is the eyewitness, the question is whether or not we can trust the person who was the eyewitness. Let’s suppose it’s settled. There seem to be other things will be problematic. What are those?
The author asked and the students…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
…and the students answered the probability of mistaking the culprit for someone other, and the author continued.
In fact, the visuality was poor at the crush scene, as there is the probability of mistaking the culprit for someone other, so the probability of seeing someone in the company of B dropped to 80%. At the same time there is the probability of failing to see exactly, 20%.
But it’s accurate with the probability of 80%, so the culprit is someone in the company of B, don’t you? But there is…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
But there is something which you don’t notice. What do you think it is? We’re apt to forget it no matter what, but it’s the precondition first of all, and it’s the most important things. What’s it?
How many cars do they run in the town with regard to both of the company of the A and the B?
Even if we can understand there is the probability of 80% of mistaking, there is the probability of seeing the taxi before it.
When saying it saw the car of the B company, all the taxies belonged to the B company. How…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
How is the problem then?
If the taxi belonged to the B company was no more than one, and the rest of the them belonged to A, how is the problem? If taking all those condition into account, the meaning of watching the one in the B company is different.
Without considering it at all, judging with the information at hand alone is dangerous. Grasping the number of all the taxis belong to each of two companies running around the whole town and we have to correct the condition.
When researching the number …
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
When researching the number of the taxis on the two of companies, it turned out that the B company accounted for 15%, and A made up for 85%.
All the conditions are met. If you are the chief judge, which do you think the true culprit, the one belonged to A company or B company? Please think of it for three minutes.
Do you have a kind of idea which company the true culprit on the run-and-hit the case, A or B? If saying the answer alone, the probability that the true culprit belonged to the A company is high
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
Even if the eyewitness said it saw the taxi belonged to the B company, the culprit is the car belong to the A company with the mathematical point of view. Please lead to the answer. Why is the A?
The student said like the next.
When watching the B and testified it was B correctly, and when watching the A and and testified it was the B by mistake. As long as calculating the probability of two of them, it’s all right, isn’t it?
As to the former one, the probability of seeing the B is fifteen hundredth…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
…and the probability that the testimony is right is eighty hundredths, when multiplying each of probabilities, it’s twelve hundredths.
As to the latter thing is like the next. When seeing the taxi belonged to A, the eyewitness made a mistake in the testimony, the probability of seeming the A is eighty five hundredths, considering the number of its taxies and the probability of making a mistake is twenty hundredths. If multiplying each of the probability is seventeen hundredths.
The author said like the…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
The author said like the next.
The probability of seeing the A is higher than seeing the B, but we can’t lead the correct answer yet, and it is hard a little from here. Leading the two of the probability of seeing the taxi of B company alone doesn’t lead the correct answer. The one which we want to know is the probability that the B is the true culprit actually.
When seeing the B we have to lead the probability that the B is the culprit truly. It’s all right we have to do the next calculations.
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
Adding the probability of seeing the B and testifying it’s the B correctly to the one of seeing A and making a mistake it was the B, and dividing the one when seeing the B and saying it was the B correctly with the addition of the two of the probabilities like the photo.
When calculating it, it’s twelve twenty ninths, 41%, in short, the probability that the culprit is B is 41%, so the probability on the A is the culprit is 59%.
When saying the B is the culprit, the culprit becomes A at once with the…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
…the culprit is the A at once with the mathematical point of view.
The student said like the next.
The eyewitness account is overturned. Surely, if knowing the mathematical way of thinking, the way of looking things seems to be careful too much.
The author said like the next
When taking a healthy food products, we can lose weight like that, there is the advertisement saying like that. We learn not to be deceived by the advertisement like that as long as being aware of the mathematical way of thinking.
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
Because the advertisement may have chosen the one who loses its weight easily. We learn to notice the assumption hidden in the background.
Following the mathematical theory and we can turn over the thing which we think it’s right like the hit-and-run case. When the intuition on a person was in the wrong, the math can correct it.
The hit-and-run case is the one which is taken in the mathematical way of thinking, the Bayesian estimation. This time we know the number of the taxies on driving around the …
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
This time we’ve known already the number of taxies belonged to the two of companies driving around the town, and we can lead each of the probabilities. But actually we don’t know the condition precedent 前提条件. There are the cases a lot.
Then taking a look at the taxi several times, and presuming the condition precedent. It’s the Bayesian estimation.
For example, let’s suppose that there are blue balls and red ones in a big bag. In the way of thinking on the probability in the past, there are eight red…
【We’ve heard the breath from the math】
《How much can we trust the eyewitness report?》
…there are red eight balls and two blue ones in the bag. And what probability is choosing the red ones? We think like that in the probability in the past. The number on the blue ball and the red one is called the prior probability.
In the case of the Bayesian estimation, we don’t know how many there are balls in the bag, nor what rate of the each of balls.
In short, in the situation we don’t know the prior probability, we’re not sure whether it’s blue or red, we choose actually, and presume the prior….
【We’ve heard the breath from the math】
…and presume the prior probability from the information we got. Assuming what we don’t know and repeat doing the trial and error and find out the correct answer.
When following the cause and effect in reverse order, it’s the formula on the Bayesian estimation which playing an active role. When exposing a phenomenon in the background, the Bayesian estimation is the weapon on the math which is active more than anything.
《Being able to hear the breath from the equation》
When expressing a phenomenon with the equation, mathematicians and physicist make …
【We’ve heard the breath from the math】
《Being able to hear the breath from the equation》
…scientists and physicists make much of an imagination. An equation seems to be inorganic signs, but it’s different for researchers. The author said when seeing the equation, including himself, they are aware that what the equation shows, knowing as if they heard the breath from the equation and saw the scene in the equation.
If having an image like that, the way of studying math learns to be different. The author said he hoped the students grasp its image as much as possible at the end of this lecture.
【We’ve heard the breath from the math】
《Being able to hear the breath from the equation》
The author suggested we do a mental imagery training on the equation actually. He said he wanted to think the phenomenon on the surface that the water sways with the students , and saying the students to imagine shaking a cup in the water.
When swaying the surface of the water, if being asked to solve the surface on the water, can you do it?
The student asked, does it mean expressing the surface on the water with the equation?
The author answered yes, and continued.
At first we image what kind of…
【We’ve heard the breath from the math】
《Being able to hear the breath form the equation》
At first we imagine what kind of the surface of the water is made. When shaking, a big vibration occurs, and the surface on the water shakes up down. Waves purged from around, and round wave is also made, gathering and disappearing on after another.
And if being asked to solve it with the equation, we’ll be in difficulty, but we can solve it. What should we do? Changing the moving image into the equation.
As the wave changes and the surface on the water swells, and let’s suppose the part which swells…
【We’ve heard the breath from the math】
…and let’s suppose the part on the surface of the water which swells is X.
The water on the surface changes by the minutes and when expressing the change with the equation, we use the differential.
The differential is the process of dividing a thing minutely, if using it at will, it’s very enjoyable. As it’s the most powerful weapon working well on, the author said he was going to talk on it in detail. The author said like that.
To tell the truth, I can’t understand the differential very well, so I hope I can understand as well.
【We’ve heard the breath form the math】
《Differential, we can see the future with the slow-motion 》
The differential has been found its base by Newton in the 17th century, after that Leibniz has completed. Which did they find first, Newton or Leibniz? The conflict occurred from then, but after Leibniz expressed the differential with the sign of d, the differential spread over the world all at once, and technical skill making use of the differential developed remarkably from then, the technique solving various phenomenon with the differential was established for the first time.
There are…
【We’ve heard the breath from the math】
《Differential, we can see the future with the slow-motion》
There are varied ways of using in the differential, what is the most marvelous? We can predict the future with the differential. There were lots of things we could understand with the hunch alone or without trying in an experiment until then we couldn’t understand., but we learn to be able to predict so precisely.
Needless to say, we can’t use the differential everything. When it’s related to the psychology on a person, or the phenomenon which changes non-contagiously or suddenly, it doesn’t…
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ふとした疑問、普段気になっていたことなどをみんなで話そう❗
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ハグは世界を救う0レス 4HIT 初心者さん (20代 ♀)
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できないからじゃなくて迷惑だからよって指摘5レス 93HIT おしゃべり好きさん
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両替のはなし6レス 118HIT おしゃべり好きさん
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ずっと友達いないんだけど1レス 72HIT 匿名さん
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私のこと見えるよね…?
明日から秋まで幸せですね。 勉強から離れたい<(_ _)&…(相談したいさん0)
182レス 1850HIT 相談したいさん -
ハグは世界を救う0レス 4HIT 初心者さん (20代 ♀)
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山尾志桜里氏の公認取消しについて
だから、有権者がズレていると言っている。 「みんなが右を向いているか…(寡黙な人さん0)
10レス 128HIT 寡黙な人さん -
できないからじゃなくて迷惑だからよって指摘
ちょっと話が見えないので確認ですが… 会社の先輩から注意された。…(通りすがりさん3)
5レス 93HIT おしゃべり好きさん -
深田萌絵を守る会
日本のお米は無農薬で品質の高い品です。 これを諸外国へ売りさばき日本…(職場の小言さん0)
2レス 51HIT 職場の小言さん (♂)
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主は40代ですが20レス 341HIT 聞いてほしいさん (40代 ♀)
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aikoにそっくりすぎる人の悪口、暴言1レス 89HIT 職場の小言さん
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好きで好きでどうしょうもないと思っていたのに…8レス 124HIT 恋愛好きさん (40代 ♀)
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持病がある方、市販薬を買う時薬剤師に相談しますか？8レス 120HIT OLさん (30代 ♀)
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主は40代ですが
悪いけど…。 それはマウントではなく、主さんが40代にもなって幼…(匿名さん10)
20レス 341HIT 聞いてほしいさん (40代 ♀) -
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今の若い世代が羨ましい。人生やり直したい。
>歌手になりたいと曲作ったり劇団に入ったりなんかしてましたが、今…(匿名さん5)
6レス 252HIT 匿名さん (♀) -
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aikoにそっくりすぎる人の悪口、暴言
https://mikle.jp/viewthread/4146664…(匿名さん1)
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バリウムと胃カメラ
でも呼吸が浅くなるからちゃんと見てくれる医者じゃないと低酸素とかなんと…(社会人さん0)
6レス 119HIT 社会人さん -
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好きで好きでどうしょうもないと思っていたのに…
そうなんですね。いいですね😊(恋愛好きさん0)
8レス 124HIT 恋愛好きさん (40代 ♀)
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