Once upon a time in YouTube history, Mr Beast made a video where he counted all the way from 1 to 100,000.

在YouTube的歷史上，曾經有一次，野獸先生做了一個視頻，他從1一直數到10萬。

The process took him 40 entire hours to finish, which got me thinking, How far could you actually physically count, too?

這個過程他花了整整40個小時才完成，這讓我想到，其實你的體力也能算到什麼程度？

If you just kept on going like if you never stopped and just kept on going on and on and on for an infinite amount of time, where would you end up at the answers to that question?

如果你就這樣一直走下去，就像如果你從來沒有停過，就這樣一直走下去，一直走下去，一直走下去，走到無限長的時間，你最終會在哪裡找到這個問題的答案？

Start simple.

從簡單的開始。

But the numbers eventually get so enormous, so colossal that the math begins to get really, really weird, like breaking the universe and reality itself.

但數字最終變得如此巨大，如此巨大，以至於數學開始變得非常非常奇怪，就像打破了宇宙和現實本身。

Kind of weird.

有點奇怪。

We'll get to that point soon, but let's start out by diving into some number counts that we can actually comprehend first.

我們很快就會說到這一點，但我們先來深入瞭解一些我們能實際理解的數字數。

Once upon a time, 10 years before Mr Beast completed his count to 100 1000 another board crazy man had the idea toe livestream himself, counting not toe 100,000 but to one million.

從前，在 "野獸 "先生完成數到100 1000之前的10年，另一個板瘋子有了自己直播的想法，不是數到10萬，而是數到100萬。

His name is Jeremy Harper, and in preparation for the task he was setting himself, he requested off from work, locked himself in his apartment room, turned on his camera and began counting.

他的名字叫傑里米-哈珀，為了準備給自己設定的任務，他向公司申請了休假，把自己鎖在公寓房間裡，打開相機，開始數數。

He would do nothing but count number after number for 16 hours every day, reserving the remaining eight hours for eating and sleeping.

他什麼都不做，只是每天16個小時一個數字一個數字地數，剩下的8個小時留給吃飯和睡覺。

He was determined to never leave his apartment until he reached the mythical number of one million and ordered all of the food that he needed through delivery services.

他下定決心，在沒有達到100萬這個神話般的數字之前，決不離開自己的公寓，並通過快遞服務訂購了自己所需的所有食物。

He soldiered on day after day until finally, after 89 straight days of counting, one number after another in front of a camera, he finally made it toe one million and earned the Guinness Book of World Records achievement for the highest number ever manually counted to buy a human.

他日復一日地堅持著，直到最後，在鏡頭前連續數了89天，一個數字一個數字地數，他終於做到了100萬，並獲得了有史以來人工數買人類最高數字的金氏世界紀錄成就。

So if you wanted to be, this record accounted to one million and one prepared to spend at least 89 days trying to do it now, obviously that is possible to do.

所以，如果你想成為，這個記錄佔到100萬，一個人準備花至少89天的時間，現在想做，顯然是可以做到的。

But how far could you actually count, too, if you dedicated all of your time towards it?

但是，如果你把所有的時間都用在這上面，你到底也能算得上是什麼？

If county toe one million takes around 89 days.

如果縣城到100萬需要89天左右。

And if you kept up that same pace going on from there, and if you began counting from one at the age of 10 then by the time you hit the age of 79 which happens to be the average life expectancy in the United States, you would probably end up hitting somewhere around 283 million.

如果你保持同樣的速度從那裡開始，如果你在10歲的時候就開始從1開始計算，那麼到了79歲的時候，恰好是美國的平均預期壽命，你可能最終會達到2.83億左右。

And that is, if you did nothing else but count day after day for 16 hours every single day.

那就是，如果你什麼都不做，只是日復一日地數著，每天數16個小時。

Worst of all, 283 million doesn't even really seem like that huge of a number, especially compared to what's coming next.

最糟糕的是，2.83億甚至看起來並不是一個多麼巨大的數字，尤其是與接下來的事情相比。

But in reality, that's probably about as far as a single human being could ever reach counting to during a lifetime.

但實際上，這可能是一個人一生中所能達到的數到的極限了。

But numbers obviously get way, way bigger than 283 million.

但數字顯然會比2.83億大很多，大很多。

In the mad world of math, consider for a moment the difference between one million and one billion.

在瘋狂的數學世界裡，先考慮一下100萬和10億的區別。

At first glance, when you're just looking at the numbers, they don't really seem to be that much different.

乍一看，當你只看數字的時候，它們似乎並沒有太大的區別。

But one billion is, in fact, a vastly larger number than one million.

但十億，其實是一個比百萬大得多的數字。

If you take both numbers in terms of seconds, you would discover that one million seconds is approximately the same as 12 days.

如果把這兩個數字都以秒為組織、部門，你會發現，100萬秒大約等於12天。

That maybe seems like a decently long time until you switch over toe one billion seconds and discover that's the same as 30 entire years worth of time.

這也許看起來像一個體面的時間很長，直到你切換到十億秒，發現這相當於30年的時間。

And comparing one trillion seconds makes even one billion looked like a puny number because one trillion seconds is almost the same as 30,000 years.

而比較一萬億秒，連十億都顯得像個小數，因為一萬億秒幾乎等於三萬年。

One million seconds ago was less than two weeks ago.

一百萬秒前還不到兩週。

One billion seconds ago was back when the Soviet Union still existed and one trillion seconds ago the Neanderthals had only recently gone extinct.

十億秒前是蘇聯還存在的時候，一萬億秒前尼安德特人才剛剛滅絕。

Each increase in the order of magnitude from one million to one billion and one trillion dramatically increases the scale of the number that you're talking about.

從一百萬到十億、一萬億，每增加一個數量級，都會大大增加你所說的數字規模。

And they just keep getting bigger and bigger After you hit the trillions.

當你達到數萬億的時候，它們就會越來越大。

You just keep going up through quadrillion quintillion, cept illion and so on and so on, all the way until you eventually reach a Google, which is the same as 10 to the 1/100 power or a one with 100 zeros written after it.

你就通過quadrillion quintillion，cept illion等等一直往上走，一直到最後到達一個Google，也就是10到1/100的冪或者後面寫著100個0的一個。

Which, for the record, looks like this a Google is an absolutely enormous number, and it's almost possible for our human brains to truly comprehend it to try and put it into some perspective.

其中，鄭重聲明，看起來這一個谷歌絕對是一個巨大的數字，我們人類的大腦幾乎可以真正理解它，嘗試著把它放到一些角度。

10 to the 80th Power is a vastly smaller number than a Google is, but that is already roughly equal to the number of every single individual Adam that exists in the entire observable universe.

10到80的力量是一個比谷歌小得多的數字，但這已經大致相當於整個可觀測宇宙中存在的每一個個體亞當的數量。

To put it all into even more perspective, consider for a moment the difference in mass between a single simple electron and the entire observable universe.

為了讓這一切變得更有意義，請考慮一下一個簡單的電子和整個可觀測宇宙之間的品質差異。

With around two trillion Galaxies, the mass of the electron is 10 to the negative 30th power kilograms, while the mass of the observable universe is 10 to the 60th power kilograms.

約有兩萬億個銀河系，電子的品質是10的負30次方公斤，而可觀測宇宙的品質是10的60次方公斤。

The difference in mass between the two is only 10 to the 90th power, which is only the same as 0.0 zero 0001% of a Google.

兩者的品質相差只有10的90次方，只相當於谷歌的0.0零點01%。

This means that at the scale of a Google, the mass of an electron and the mass of the entire universe are effectively identical to blow your mind, even mawr, with just how big of a number of Google is, imagine the size of the entire observable universe.

這意味著，在谷歌的規模下，一個電子的品質和整個宇宙的品質實際上是相同的，讓你大吃一驚，甚至是茅塞頓開，谷歌的數字有多大，想象一下整個可觀測宇宙的大小。

It's 93 billion light years across, meaning that it takes light 93 billion entire years just to travel from one side over to the other.

它的直徑是930億光年，也就是說，光從一邊走到另一邊需要930億年。

It's unbelievably huge, but imagine filling up this entire space from top to bottom and from side to side completely 100% with sand.

這是不可思議的巨大，但想象一下，把這整個空間從上到下，從邊到邊完全100%用沙子填滿。

Imagine being able to fly at the speed of light and flying through nothing but endless sand in every direction for tens of billions of years in whatever direction you choose to fly in.

想象一下，能夠以光速飛行，無論你選擇哪個方向飛行，都能在各個方向上飛上幾百億年，除了無盡的沙子，什麼都沒有。

It doesn't matter.

這不重要

It would all seem essentially endless to you.

在你看來，這一切基本上都是無止境的。

But now imagine counting out every single individual grain of sand in that entire universe filled to the brim with sand.

但現在想象一下，在那充滿沙子的整個宇宙中，數出每一粒單獨的沙子。

How long do you think that that might take you?

你覺得這要花多長時間？

Eternity is honestly not a far fetched answer.

永恆說實話，這並不是一個遙不可及的答案。

But after you've finally done it and you've laid to rest the final grain of sand in the entire universe sized sandbox, you would realize that in orderto actually reach a Google grains of sand, you would have to start all over again from grain of sand number one and begin county again from scratch and repeat that whole entire process over again.

但當你終於做到了，你已經將整個宇宙大小的沙盒中的最後一粒沙子安放好之後，你會意識到，為了真正達到谷歌的沙粒，你必須從第一粒沙子開始重新開始，再從頭開始縣，重新重複這整個過程。

Another 100,000 times.

又是十萬次。

Only then, after you've counted every single grain of sand in the universe sized sandbox 100,000 times over again, would you finally arrive at a Google grains of sand?

只有這樣，當你把宇宙大小的沙盒裡的每一粒沙子都數了十萬遍之後，你才會最終得出一個谷歌的沙粒？

But of course, a Google is a puny number when compared with a googol plex, which is simply a Google to the Google.

但當然，與googol plex相比，一個Google是一個微不足道的數字，它只是一個Google的Google。

If power, it was already basically impossible to imagine how Maney grains of Sand a Google would actually be.

如果權力，已經基本無法想象馬尼粒沙一個谷歌到底會有多大的影響力。

So how can you possibly even begin to comprehend the size of a googol plex instead of trying to imagine the size of the number?

所以，你怎麼可能甚至開始理解一個googol plex的大小，而不是試圖想象數字的大小？

Let's just imagine for a moment how long it would actually take to simply write the number out.

我們先想象一下，如果僅僅是把數字寫出來，到底需要多長時間。

A typical 400 page book can be written with 10 to the sixth zeros inside of it across every page.

一般400頁的書，每一頁都可以寫出10個零到6個零裡面的內容。

So if you just continuously wrote 400 page book after 400 page book with nothing but zeros and all of them, you would need to write 10 to the 94th books in order to reach a googol plex zeros.

所以，如果你只是連續寫了一本又一本400頁的書，除了零和所有的零，你需要寫10本到第94本，才能達到googol plex的零。

So to put that into perspective, if each book weighed only 100 g, they're literally isn't enough mass in the entire universe to create that many books because the mass of all of those books would be heavier than the mass of the NT higher universe.

所以，從這個角度來說，如果每本書的重量只有100克，他們從字面上看，整個宇宙沒有足夠的品質來創造那麼多的書，因為所有這些書的品質會比新臺幣高級宇宙的品質更重。

So if you're just running out zeros on paper, it's physically possible to write out a googol plex in full form in our universe, even if you had an infinite amount of time to do it, let alone actually counting to it.

所以，如果你只是在紙上跑出零，在我們的宇宙中，即使你有無限的時間來寫出一個完整的googol plex，在物理上也是可能的，更不用說真正數到它了。

The plank volume is the smallest size that we currently understand in physics.

木板體積是目前我們在物理學中理解的最小尺寸。

It's such a small space, in fact, that you can fit 100 quintillion plank volumes inside of just a proton.

事實上，它的空間非常小，僅僅一個質子就可以在裡面裝下100個質子量。

So if you shrunk your zeros all the way down to the size of the plank volume, how many zeros do you think you could fit then?

那麼如果你把你的零點一直縮小到木板體積的大小，你覺得你能裝多少個零點呢？

Inside of the observable universe?

在可觀測的宇宙內部？

If the entire universe was filled from top to bottom with tiny plank volume size zeroes, this is the natural limit of numerical expression inside of our universe.

如果整個宇宙從上到下都充滿了微小的木板體積大小的零，這就是我們宇宙內部數值表達的自然極限。

The number of the smallest units of measurement that we know of that can fit inside of the biggest thing that we know of.

我們所知道的最小的計量單位的數量，可以裝在我們所知道的最大的東西里面。

Beyond this, it might be literally impossible to contain any more digits and the answer is still pathetically small compared with the size of a googol plex.

除此以外，它可能真的不可能包含更多的數字，而答案與googol plex的大小相比，還是小得可憐。

You can Onley fit 10 to the 185th plank volumes inside of the observable universe.

你可以在可觀測的宇宙裡面安利10到185個板塊的體積。

To truly appreciate just how gargantuan Lee colossal a Google plucks, actually is.

要真正體會到李巨人一個谷歌的拔取，其實是多麼巨大的。

Try imagining an entire universe beyond our observable universe.

試著想象一個超越我們可觀測宇宙的整個宇宙。

That's a googol plex meters across in every direction.

那是一個從各個方向橫跨數米的googol plex。

There are some models of the universe that estimate to the true size of the entire universe beyond what we can simply observe toe actually be closer in size to this.

有一些宇宙的模型，估計到整個宇宙的真實大小，超出我們可以簡單地觀察到的大小，實際上是更接近這個。

So if that's true, consider this.

所以，如果是真的，可以考慮這樣。

Imagine the volume of space that you occupy, the total number of possible quantum states or arrangements of particles that can occur inside of the space that you take up is vastly, vastly less than a googol plex.

想象一下，你所佔據的空間體積，在你所佔據的空間裡面，可能發生的量子態或粒子排列的總數量，比googol plex要少很多很多。

What this implies is that if the actual size of the full universe is actually closer to a googol plex, cubic meters and volume than sheer random probability almost guarantees that there are going to be exact identical copies of you existing somewhere else far away in the same universe.

這意味著，如果全宇宙的實際大小實際上更接近googol plex，立方米和體積比純粹的隨機概率幾乎可以保證，有將是完全相同的副本你存在的其他地方遠在同一宇宙。

This is because every possible arrangement of matter inside of a human sized space will likely occur many, many times inside of a universe this big, meaning that everything that could possibly exist would exist and would exist multiple times, meaning multiple versions of people who are identical to you, meaning multiple versions who are only slightly different than you, meaning multiple versions of every single human you've ever known in your life.

這是因為在一個人類大小的空間裡面，每一種可能的物質排列方式都可能在這麼大的宇宙裡面出現很多很多次，也就是說一切可能存在的東西都會存在，而且會存在很多次，也就是說有多個版本的人和你是一樣的，也就是說有多個版本的人和你只有一點點的不同，也就是說有多個版本的人是你這輩子認識的每一個人。

Exact copies of every single person you've ever known, heard of, loved or hated all throughout history would still exist somewhere out there, far away.

你所認識的、聽說過的、愛過的、恨過的每一個人的精確拷貝，在歷史上都會存在於遙遠的某個地方。

If the universe actually is this big.

如果宇宙真的有這麼大。

There's almost certainly other versions of you right now doing other things and living their own lives.

幾乎可以肯定，現在還有其他版本的你在做其他事情，過著自己的生活。

And some of them might even be doing something a lot more productive than what you're doing now, like learning more about math and science on brilliance, there are even numbers that air far bigger than a mere googol plex in the realm of mathematics that you can learn all about on brilliant, like this entire section.

而有些人甚至可能在做一些比你現在做的更有成效的事情，比如在輝煌上學習更多的數學和科學知識，在數學領域甚至有一些空氣遠比單純的googol plex大的數字，你可以在輝煌上了解所有的內容，比如這一整節。

That explains the number that makes even a googol plex look tiny called grams number learning.

這就解釋了連googol plex都顯得很小的數字叫克數學習。

New complex things can often feel difficult, scary or more than anything, time consuming, but brilliant makes it all simple.

複雜的新事物往往會讓人覺得困難、可怕，或者更多的是耗費時間，但輝煌讓一切變得簡單。

Take their computer science courses, for example, which start by teaching you how to program a drone by arranging simple instructions, and along the way you'll learn the basic structure of every program that you'll ever write.

以他們的計算機科學課程為例，首先教你如何通過排列簡單的指令對無人機進行編程，在這一過程中，你會了解到你所編寫的每一個程序的基本結構。

Brilliant takes multiple complex subjects just like this and breaks them down into bite size chunks so that understanding a new thing doesn't feel impossible.

Brilliant就這樣把多個複雜的主題，分解成一口一口的小塊，讓理解一個新事物不會覺得不可能。

And every course that brilliant offers has interactive challenges just like this to make learning new things feel interactive and fun.

而輝煌提供的每一門課程都有像這樣的互動挑戰，讓學習新事物的過程充滿互動和樂趣。

Whether you're totally new to a subject or professional who's brushing up on cutting edge topics, brilliant is the place for you to achieve all of your stem learning goals.

無論你是完全陌生的學科，還是正在刷新前沿話題的專業人士，輝煌都是你實現所有乾貨學習目標的地方。