“Science is the belief in the ignorance of experts”?

There have been a lot of attempts by the various press reporters to get some kind of a capsule of this talk; I prepared it only a little time ago, so it was impossible; but I can see them all rushing out now to write some sort of headline which says: "The Professor called the President of NSTA a toad."

Under these circumstances of the difficulty of the subject, and my dislike of philosophical exposition, I will present it in a very unusual way. I am just going to tell you how I learned what science is.

That's a little bit childish. I learned it as a child. I have had it in my blood from the beginning. And I would like to tell you how it got in. This sounds as though I am trying to tell you how to teach, but that is not my intention. I'm going to tell you what science is like by how I learned what science is like.

Pretty much, yes. How it got into his way of thinking, his mindset. 思考方式?

When I was very young--the earliest story I know--when I still ate in a high chair, my father would play a game with me after dinner.

He had brought a whole lot of old rectangular bathroom floor tiles from some place in Long Island City. We sat them up on end, one next to the other, and I was allowed to push the end one and watch the whole thing go down. So far, so good.

Next, the game improved. The tiles were different colors. I must put one white, two blues, one white, two blues, and another white and then two blues--I may want to put another blue, but it must be a white. You recognize already the usual insidious cleverness; first delight him in play, and then slowly inject material of educational value.

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up--that is, if you go over each time the same amount when you go up a row, you make a straight line--a deep principle of analytic geometry! It went on. I was rather amazed. I didn't realize the female mind was capable of understanding analytic geometry.

FBM wrote:

Pretty much, yes. How it got into his way of thinking, his mindset. 思考方式?

Thanks.
The Chinese phrase is expressed by you accurately.I've put "way of thinking"into Google Translator and found the result is different. So it seems that you may have written the four Chinese characters yourself.
I now wrote the following Chinese. Can you understand it? If you can, please translate it into English and let me see whether you would have done it well.
费因曼是二十世纪与爱因斯坦并驾齐驱的最伟大的物理学家之一。

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When I was very young--the earliest story I know--when I still ate in a high chair, my father would play a game with me after dinner.

He had brought a whole lot of old rectangular bathroom floor tiles from some place in Long Island City. We sat them up on end, one next to the other, and I was allowed to push the end one and watch the whole thing go down. So far, so good.

Looks like that the floor titles are made of wood/plastic? But for bathroom, ceramic tiles are best IMO.

The speaker went on:

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Next, the game improved. The tiles were different colors. I must put one white, two blues, one white, two blues, and another white and then two blues--I may want to put another blue, but it must be a white. You recognize already the usual insidious cleverness; first delight him in play, and then slowly inject material of educational value.

Failed to get a clear picture of "the usual insidious cleverness." It appears that the clever idea in the speaker's mind was that he had an impulse to put another blue tile on the two blue tiles; yet the rule is: he must put a white on two blue tiles. So "the insidious cleverness" showed up itself in his brain, which he had no clue how it occurred - that is why it is insidious.
Am I on the right track?

The speaker went on:

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I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up--that is, if you go over each time the same amount when you go up a row, you make a straight line--a deep principle of analytic geometry! It went on. I was rather amazed. I didn't realize the female mind was capable of understanding analytic geometry.

Failed to get "for each row you go up" clearly. If you make a line on a paper, we make it from top to bottom of the paper. So for each row we go down, not up.
(But for weaving, you go up each row, yes)

oristarA wrote:

The speaker went on:

Quote:

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up--that is, if you go over each time the same amount when you go up a row, you make a straight line--a deep principle of analytic geometry! It went on. I was rather amazed. I didn't realize the female mind was capable of understanding analytic geometry.

Failed to get "for each row you go up" clearly. If you make a line on a paper, we make it from top to bottom of the paper. So for each row we go down, not up.
(But for weaving, you go up each row, yes)

Think instead about graph paper, not a blank white sheet. Columns are vertical, rows are horizontal.

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go down--that is, if you go over each time the same amount when you go down a row, you make a straight line--a deep principle of analytic geometry! It went on. I was rather amazed. I didn't realize the female mind was capable of understanding analytic geometry.

She went on and said, "Suppose you have another line coming in from the other side, and you want to figure out where they are going to intersect. Suppose on one line you go over two to the right for every one you go up, and the other line goes over three to the right for every one that it goes up, and they start twenty steps apart," etc.--I was flabbergasted. She figured out where the intersection was. It turned out that one girl was explaining to the other how to knit argyle socks. I, therefore, did learn a lesson: The female mind is capable of understanding analytic geometry. Those people who have for years been insisting (in the face of all obvious evidence to the contrary) that the male and female are equally capable of rational thought may have something. The difficulty may just be that we have never yet discovered a way to communicate with the female mind.

When I was learning later in school how to make the decimals for fractions, and how to make 3 1/8, 1 wrote 3.125 and, thinking I recognized a friend, wrote that it equals pi, the ratio of circumference to diameter of a circle. The teacher corrected it to 3.1416.

Does "a friend" here refer to "the equivalent (of 3.125)"?

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Does "a friend" here refer to "the equivalent (of 3.125)"?

Not really. Friend refers to pi (which was his "friend"). He thought 3.125 was pi, because he was eager to see pi. Why eager? Because it was his friend.

I illustrate these things to show an influence. The idea that there is a mystery, that there is a wonder about the number was important to me--not what the number was. Very much later, when I was doing experiments in the laboratory--I mean my own home laboratory, fiddling around--no, excuse me, I didn't do experiments, I never did; I just fiddled around. Gradually, through books and manuals, I began to discover there were formulas applicable to electricity in relating the current and resistance, and so on. One day, looking at the formulas in some book or other, I discovered a formula for the frequency of a resonant circuit, which was f = 1/2 pi LC, where L is the inductance and C the capacitance of the... circle? You laugh, but I was very serious then. Pi was a thing with circles, and here is pi coming out of an electric circuit. Where was the circle? Do those of you who laughed know how that comes about?

In the context below, does "-not what the number was" refer to "what the number was is not important to me (but that there is a wonder about the number was important to me")"?.

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In the context below, does "-not what the number was" refer to "what the number was is not important to me (but that there is a wonder about the number was important to me")"?.

I'm not quite sure what you're saying here, Oris, so I'm not sure how to answer it with a simple yes or no.

As I read it the wonder he has is about WHY he became fascinated with Pi. He wasn't fascinated by the exact value of the number itself (whether it be 3.126, 3.14, or whatever). It was a number that described EVERY circle in some way, and I think he found that part fascinating. It wasn't what the number was, but just the fact that there was such a number.

You follow me?

FBM wrote:

oristarA wrote:

The speaker went on:

Quote:

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up--that is, if you go over each time the same amount when you go up a row, you make a straight line--a deep principle of analytic geometry! It went on. I was rather amazed. I didn't realize the female mind was capable of understanding analytic geometry.

Failed to get "for each row you go up" clearly. If you make a line on a paper, we make it from top to bottom of the paper. So for each row we go down, not up.
(But for weaving, you go up each row, yes)

Think instead about graph paper, not a blank white sheet. Columns are vertical, rows are horizontal.

I searched for graph paper. It impressed me that whether you go up a row or go down you get a straight line altogether if the base line or reference line itself is a straight line:

Quote:

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go down--that is, if you go over each time the same amount when you go down a row, you make a straight line--a deep principle of analytic geometry! It went on. I was rather amazed. I didn't realize the female mind was capable of understanding analytic geometry.

What do you think?

If there are three points (A,B,C) on a vertical (straight) line and if you move over each time from the points the same amount, you get another three points: A1,B1,C1; connecting A1,B1,C1 you get a straight line. Is this what the author tells us?