Name: グラハムの番号 - 番号マニア (Graham's Number - Numberphile)
Uploaded: 2021-01-14T04:45:25.000Z
Duration: 9 min 16 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：

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TONY PADILLA: If you actually tried to picture Graham's

number in your head, then your head would collapse to form a

you couldn't store that much information in your head.

MATT PARKER: People think mathematicians just basically

look at bigger and bigger calculations, and bigger and

But Graham's number I love, because it's the biggest

TONY PADILLA: Well, because there's a sort of maximum

amount of what we call entropy that can be

And the maximum amount of entropy you can store in your

head is related to a black hole the size of your head.

And the entropy of a black hole the size of your head

carries less information than it would take to write out

So the inevitability is if you started to try to write out

Graham's number in your head, then your head would

eventually have so much information that it would

MATT PARKER: If you start with a small number-- and 3 is a

what you can do is you can start adding 3 to itself.

And if you want, you could do lots of these.

TONY PADILLA: OK, and that's 27, so we're happy with that.

The way I would write this down in arrow notation would

Hopefully you're still with me at this stage.

MATT PARKER: If you do 3 to the power of 3 to the power of

3, we would write that as 3 to the power of, to

TONY PADILLA: This means 3 arrow 3 arrow 3.

well, we've already seen that that's 27, so 3 arrow 27.

MATT PARKER: And if you actually work that out, it

comes out to be around about 7.6 trillion.

So the next one, let's say we did 3 to the power of,

Well, that is equivalent to 3 to the double, to the double,

That's 3 to the power of 3, to the power 3, to

And you start from the top and work your way down.

You get a number that is absolutely off the chart.

Now we've got a stack of 3s 7.6 trillion of them high.

And the question is, why would you want to know, right?

And so actually the reason we have arrow notation is to look

The famous, the quintessential never-ending--

well, it does end, it's a finite number--

So in math we do things called combinatorics, where you look

And we look at networks, which mathematicians call graphs,

and you look at different ways of coloring in graphs.

And so mathematicians looked at ways to color in,

You can get cubes in higher dimensions and look at

And they tried to count the number of dimensions--

There's a very famous analogy for how this works.

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グラハムの番号 - 番号マニア (Graham's Number - Numberphile)

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