Name: シュールな数字（最初の本を書くこと） - Numberphile (Surreal Numbers (writing the first book) - Numberphile)
Uploaded: 2021-01-14T10:14:04.000Z
Duration: 14 min 6 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

過去形

I had this hotel room for a week. On the sixth day I finished it.

On the seventh day I rested; and on the seventh day

I tried to write a letter to my secretary

to tell her how I wanted  this to be typed up

It was gone; the muse was gone. I would start writing and all of a sudden

It was flowing for six days and then it stopped

and so I think it's an inspiration that I can't just turn on and turn off, either

Well, I understand you've been considering

and probably the greatest kind of numbers,

The name actually came to me in the middle of the night; I have no idea...

I have a vague recollection that I saw, at one point,

a French paper that talked about 'nombres sur ordinaux'

I don't pronounce it well, but sort of sur- ordinal numbers

I've never been able to track down that paper and I don't know if I heard about it

before or after I thought of the name "surreal" but you'll see that it's

a great name after you understand  what surreal numbers are.

John Conway invented the concept, and his first description of it was

Not only big and small,  but *inside* and everything.

So people know what the real numbers are, and I call them surreal because

there are infinitely many surreal numbers  between any two real numbers.

[off-camera] I thought the numbers between  all the other numbers already existed, so...?

-Yes, that's what almost everybody  thought except Conway

I happened to be visiting Calgary in Canada at the same day that

John Conway was up there, and we had lunch together and he had recently discovered

this concept, which we're going to describe. During our lunch

he wrote out on a napkin all the rules of...

a definition of surreal numbers. I was enchanted by this idea. Of course I

had lots of other stuff to do, but I kept the napkin--I took it home with me.

The basic idea: you have a new way to describe all numbers: you build up all

numbers starting from nothing, and actually nothing is kind of the

But then you can use 0 to describe another number which turns out to be 1.

And you can use 0 and 1 to make two other numbers, one of which is 2 and

one of which is 1/2. And you can continue creating more and more numbers.

It's something like the creation of a universe. Here we're creating a

universe of numbers. But the numbers that you get are always... the denominator is

You don't get everything... you'll never get 1/3 throughout the first

part of this process, but you keep on creating numbers until you go to

infinity. Then a big bang occurs and all of a sudden you get all the real numbers.

The next day after that then you create infinity plus 1 and infinity minus 1

You also have 1 over infinity which is a number that's bigger than 0

but it's less than any positive real number. That's why I started calling them

surreal, because there's a number like  pi plus one over infinity

This is between pi and  every real number that's greater than pi

And also we keep on going and keep on creating,  so at some point we get

1/2 of infinity, and we get square root of infinity, and we get infinity to the infinity.

All these numbers that we get we can add, subtract, multiply, and divide them

So it goes way beyond any kind of numbers that people ever conceived of before

[off-camera] These sound like tiny slivers that we're dropping into gaps that we didn't even know were there.

-We got the tiny slivers and we also have  the reciprocal, 1 over a tiny sliver,

which is a gigantic thing, larger than we've ever...

people ever thought of before. So that's why Conway called them "All numbers

great and small"  One night in the middle of the night I said, "Hey, I bet

why don't I call them surreal numbers?" But the the main inspiration that I had was,

this is so cool, I think maybe I ought to  write a book for high school students

that would teach them what surreal numbers are." There was a need for a book

that shows how mathematical research is done, and how you take some simple

laws and create gigantic universes  out of simple laws.

And the process of discovering is something that's usually not

You just are taught the facts,  but you don't get to see the thrill of

developing these facts. I woke my wife up.

We were on sabbatical year in Norway and I...

Well maybe I didn't wake her up till the morning, but anyway I had the idea in

the middle of night and I couldn't go to sleep and I said "Wait a minute,

a book like this ought to be written." I was already years behind on books

that I'd promise to write, and I'm still not done writing... that was 50 years ago

Jill, I decided I have to write another book, but it's only gonna take me a week.

She said, well you know that's actually kind of a nice idea...

...time in your life when you can do this, here we are in sabbatical and so we

worked it out that a few weeks later  I would rent a hotel room and

downtown Oslo and spend a week writing this book. She would come visit

me a couple times that week, because we always wondered what it would be like to

have an affair in a hotel room! So that was the plan, and it actually worked out

so marvelously, it was probably the greatest week of my life.

I started out every morning having a big Norwegian breakfast.

My hotel was very near where Ibsen used to live so I could get some of his

There were a group of 50 American students and I could listen to what they

were saying, because I had decided to write this book in dialogue

Alice and Bill. Might as well show you the book. Here's the book and you can see Alice

and Bill here.  My wife did the illustrations.

[reading] How two ex-students turned on to pure mathematics

If you look on the web you find out that that there's a bimodal distribution of

there are those who are looking for beautiful mathematics and those people

are rating it at five, and then there are people who are looking for a novel and

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シュールな数字（最初の本を書くこと） - Numberphile (Surreal Numbers (writing the first book) - Numberphile)

concept

vague

sustainable

describe