Name: 彩色的科拉茨猜想--數字愛好者。 (Collatz Conjecture in Color - Numberphile)
Uploaded: 2021-01-14T10:14:02.000Z
Duration: 6 min 18 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

-It definitely looks like something from the sea, like...

Okay well it's interesting mathematical seaweed,

and I can explain exactly how we made that image,

because to me that image is one of the most mind-blowing pictures,

So it is - and we're going to get there - the Collatz Conjecture.

I know you've done videos on the Collatz Conjecture,

When you take a number and we can do two things to this number depending on its parity,

If it's even, we're going to divide by two,

and if it's odd, we're going to multiply by three, so triple it, and add one.

-Which will then make it even. -Which will then make it even.

and then we know what we do even numbers, that we divide them by two.

Okay it's even, so divide that by 2, goes to 20.

Uh-oh, odd, multiply by 3, 15, add 1, 16.

The conjecture made by Collatz is that every number that you choose

So some of them are going to go all over the place,

but eventually everything's going to 1 as a conjecture,

which is, we think is true but we can't prove it

and one of the reasons why the conjecture is one of the most famous unsolved problems in math

is that we appear to be nowhere close to a solution, nowhere close at all.

People believe that whole new bits of math need to be invented before we can do this,

and is one of the few things that is so simple to state, yet still so complicated.

It's got the sort of mythical status now among advanced mathematicians,

and what I want to do is show how Edmund Harriss, who is a mathematician who I work with,

has created this amazing image that illustrates what's going on with Collatz

and when he first showed it to me, I was like blown away.

I've started at 13 and then a line like that.

Actually already what people do is you've built this big tree,

because eventually things are going to have to get to one.

So if they get to one they're going to have to come from two,

then they're going to have to come down from four,

What you see with the tree is that you've got all these branches coming down like this,

they're done to try and maximize the sort of logic of how it's done,

so the distance will be the same, they'll be done so it like kind of looks good on the page,

and it looks like something in a math textbook.

But actually what Edmund has done is to make it so it's...

but so that you get more of an insight about why this whole problem is interesting.

either we are going to go up to an odd number or an even number.

If we're getting to an even number, it's going to slightly go off in that direction.

If it's going to an odd number it's going slightly in that direction.

-Clockwise or anti-clockwise.       -Yeah anti-clockwise for odd, and clockwise for even.

And then you get - the tree becomes this.

This is something already... startling to look a bit interesting.

And then obviously we're not that interested in the individual numbers,

we're interested in sort of the overall feel.

and sort of he just looked at the lines between them, how the lines relate,

and sort of thickens the lines to make them look like branches,

and then carried it on until he includes every number less than 10, 000.

divided by 2 or multiply by 3, add 1, and then divided by 2.

Who would have thought that you would get this thing here?

Brady you were saying it looks like something definitely floating at the bottom of the sea.

you've got the nature of the growth, that you've also got the windiness of the waves.

And to think that something so natural looking, something so organic,

something so complicated, comes from something so simple,

this to me is the best way to explain the kind of complicated nature of the Collatz Conjecture,

because what it's doing is you're looking and you're thinking,

and you think, oh now I understand why no one's got a clue.

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