Luyện nói tiếng Anh bằng Shadowing qua video: Every Giant Number Explained

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194 câu

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If you wrote one digit on every atom in the observable universe,

Nếu bạn viết một chữ số lên mỗi nguyên tử trong vũ trụ có thể quan sát được,

you'd run out of atoms before you finished writing one of the numbers in this video.

bạn sẽ dùng hết toàn bộ các nguyên tử trước khi kịp viết xong một trong những con số xuất hiện trong video này.

And that number isn't even the biggest one here.

Và con số đó thậm chí còn không phải là con số lớn nhất ở đây.

But let's start small.

Nhưng hãy bắt đầu từ những điều nhỏ bé thôi.

A million, a billion, a trillion.

Một triệu, một tỷ, một nghìn tỷ.

They sound like neighbours, but each one is a thousand times bigger than the last, and the easiest way to feel that is in seconds.

Chúng nghe có vẻ như là những người hàng xóm, nhưng mỗi thiên thể lại lớn gấp hàng nghìn lần thiên thể đứng trước nó, và cách dễ nhất để cảm nhận được điều đó chỉ mất vài giây.

A million seconds is a little over 11 days.

Một triệu giây dài hơn mười một ngày một chút.

A billion seconds is almost 32 years.

Một tỷ giây gần bằng 32 năm.

And a trillion seconds is about 32 ,000 years.

Và một nghìn tỷ giây tương đương khoảng 32.000 năm.

That's six times longer than humans have had writing.

Đó dài gấp sáu lần thời gian loài người có chữ viết.

32 ,000 years ago, the world was in an ice age and people were hunting mammoths.

32.000 năm trước, thế giới đang trong thời kỳ băng hà và con người đang săn bắn voi ma mút.

So counting with words gets awkward fast.

Vì vậy, việc đếm bằng từ ngữ nhanh chóng trở nên rất khó xử lý.

A million is a one followed by six zeros.

Một triệu là số một theo sau là sáu số không.

Short version, ten to the sixth.

Phiên bản ngắn, mười lũy thừa sáu.

A billion is ten to the ninth.

Một tỷ là mười lũy thừa chín.

A trillion, ten to the twelfth.

Một nghìn tỷ, mười lũy thừa mười hai.

Every three zeros get a new word.

Cứ mỗi ba số không thì lại có một từ mới.

Quadrillion, quintillion, all the way up to a decillion, ten to the thirty -third.

Quadrillion, quintillion, cứ thế tăng dần lên đến decillion, tức là mười lũy thừa ba mươi ba.

The words run out soon.

The numbers don't. In 1920,

the American mathematician Edward Kasner asked his nine -year -old nephew what to call a one followed by a hundred zeros.

The boy, whose name was Milton, said, A Google.

A Google is ten to the hundredth.

It's easy to write down.

It's one line.

But what can you count with it?

Atoms In the entire observable universe, in all the stars, planets and gas clouds, there are about 10 to the 80th.

That's less than a Google.

Not a little less, a hundred quintillion times less.

Imagine every atom in the universe turned out to be a whole universe full of atoms.

Now you'd have more than a Google.

But in our real universe, there just aren't that many things.

There are that many possibilities, though.

In 1950, Claude Shannon estimated how many different chess games there could be.

He got about 10 to the 120th, more than a Google.

Combinations grow much faster than stuff.

By the way, one company's name is a misspelling of Google, and its servers still live at the domain 1E100,

which is how programmers write a Google.

Milton came up with the next word too.

A Googleplex, he said, is a one followed by writing zeros until you get tired.

Casno pointed out that different people get tired at different times, so he made it precise.

A Googleplex is a one followed by a Google zeros, ten to the power of a Google.

And this is where the paper runs out.

To write a Googleplex, you need to write a Google zeros.

Even if you put one zero on every atom in the universe, you wouldn't have enough atoms there are only 10 to the 80th of them,

and you need 10 to the 100th zeros.

If you printed a million zeros per book, you'd need 10 to the 94th books.

That's more books than there are atoms in the universe.

Carl Sagan made this point in Cosmos back in 1980.

There isn't room for a Googleplex in the known universe.

But numbers like this do show up in physics.

If the universe is infinite, then somewhere out there is an exact copy of Earth, and an exact copy of you watching this video.

The physicist Max Tegmark estimated how far away, roughly 10 to the 10 to the 28th miles.

And at that size, it doesn't matter whether you say miles, feet or inches, the difference gets lost somewhere in the last digits of the exponent.

And a Googleplex is bigger still, much bigger.

The Googleplex was invented as a joke, but once an even bigger number was needed for real.

Prime numbers divide only by themselves and 1, 2, 3, 5, 7, 11.

The further you go, the rarer they get.

Gauss came up with a formula that roughly tells you how many primes there are below any number.

People checked it for billions, for trillions, for numbers with 19 zeros.

And every time, the formula came out a little too high.

Every single time.

You'd think it would always be that way.

But in 1914, John Littlewood proved it isn't.

Somewhere far out, the formula starts missing in the other direction, and it flips back and forth infinitely many times.

Where exactly, he didn't say.

In 1933, his student Stanley Skews found a limit.

The first flip has to happen before 10 to the 10 to the 10 to the 34th.

Three stories of exponents.

G. H.

Hardy called it the largest number that had ever served any definite purpose in mathematics.

Today we know the first flip happens much earlier, somewhere around 10 to the 316th.

But the exact spot still hasn't been found.

And that's the lesson.

A pattern can hold for every number we can reach and still be false.

To go further, we need a new way of writing.

and it's built like a ladder.

Adding three to itself three times is multiplication.

Multiplying three by itself three times is a power, and if you raise three to a power and then raise three to that result,

you get a tower of powers.

In 1976, Donald Newth suggested arrows for this.

One arrow is an ordinary power.

Three arrow three is 27.

Two arrows make a tower.

3 double arrow 3 is 3 to the 3 to the 3.

That's 3 to the 27th.

7 ,625 ,000 ,000 ,000 ,000 and change.

Not scary yet, but add one more story to the tower.

3 to the power of that number.

The result has more than 3 .5 trillion digits.

Now 3 arrows.

3 triple arrow.

3 is a tower of 3's more than 7 .5 trillion stories tall.

Not that many digits.

that many stories.

For comparison, a Googleplex fits in a tower of just four tens and skews his number in a tower of five.

Four stories of tens and the number already has more digits than there are atoms in the universe.

Each new arrow repeats the previous one as many times as the last step produced,

and these are the arrows you need to describe the next number.

100

Take a cube and connect every corner to every other corner.

101

Colour each line red or blue.

102

Now look for four corners that lie in one plane with all six lines between them the same colour.

103

With an ordinary cube, you can colour the lines so that no such four exist.

104

But what about a cube in more dimensions?

105

From which dimension on is there always such a group of four, no matter how you colour?

106

In 1971, Ronald Graham and Bruce Rothschild proved that such a dimension exists.

107

And in 1977, Martin Gardner wrote about a number

108

Graham had found as an upper bound for the answer.

109

Three years later, it was in the Guinness Book of World Records as the largest number ever used in a serious proof.

110

Here's how it's built.

111

Take three, four arrows, three.

112

That's step one, and it's already monstrously bigger than anything so far.

113

In step two, there are as many arrows between the threes as step one produced.

114

In step 3, as many as step 2.

115

And so on, 64 times.

116

Physicists say a region the size of your head can hold only a limited amount of information.

117

Cram in more, and that region becomes a black hole.

118

The digits of Graham's number won't fit in your head.

119

They won't fit in the whole universe.

120

And yet we know how it ends.

121

Its last digits are 2464195387.

122

And the actual answer to the problem?

123

Today we know it's at least 13.

124

The answer might be a small number.

125

Only the bound was enormous.

126

Graham's number came from a problem.

127

The next one comes from a game you can play on a sheet of paper.

128

You draw trees.

129

Dots connected by lines, with no loops.

130

Each dot can be one of several colours.

131

The first tree can have at most one dot.

132

The second, at most two.

133

The third, at most three.

134

And so on.

135

The main rule?

136

No earlier tree may fit inside a later one with the same colours and the same branching.

137

As soon as you can't draw a new tree, the game is over.

138

In 1960, Joseph Kruskal proved a theorem that means this game always ends, no matter how many colours you use.

139

With one colour, the game lasts one move.

140

With two colours, three moves.

141

And for three colours, the logician Harvey Friedman called the length of the longest possible game tree of three.

142

It's finite.

143

The game really does end.

144

But next to tree of three, Graham's number is practically zero.

145

Friedman showed that if you try to prove this game ends using modest arithmetic,

146

the proof itself would be longer than anything you could write down in the universe.

147

Three colours and simple rules.

148

And the result is a number that makes all of Knuth's arrows look like toys.

149

Every number so far can be computed.

150

Slowly, longer than the life of the universe, but by the rules.

151

And then there are numbers that can't be computed at all.

152

Take the simplest computer, a Turing machine.

153

It's an endless tape of cells and a head that reads a symbol, writes a new one, and moves, following a table of rules.

154

Back in 1936, Turing proved that there's no way to tell in advance, for every program, whether it will ever stop or run forever.

155

In 1962, Tibor Rado came up with a game called The Busy Beaver.

156

Take all machines with a given number of rules and run them on a blank tape.

157

Among the ones that stop, find the one that runs the longest.

158

With one rule, one step.

159

With two, six.

160

With three, twenty -one one, with four a hundred

161

and seven with five forty seven million one hundred seventy six thousand eight hundred seventy steps

162

that was only proven in july 2024

163

and it was done mostly by amateurs working together online with six rules in 2025 someone found a machine

164

that runs longer than two triple arrow five this function grows faster than any function

165

that can be computed sooner or later it overtakes the arrows, graham and tree.

166

And for a machine with 215 rules, the answer can no longer be proven with ordinary mathematics.

167

That was shown in October 2026.

168

There's one last step.

169

In 2007, at MIT, two philosophers held a duel.

170

Who can name the bigger number?

171

Agustin Rayo won like this.

172

Take every number that can be described in the language of logic with no more than a Google symbols.

173

Rayo's number is the smallest number bigger than all of them.

174

A million seconds, the atoms in the universe, a Google, a Googleplex, Skews,

175

the Arrows, Graham, Tree of Three, the Beaver, Rayo.

176

It feels like we've gone very far.

177

But here's the strange part.

178

Whichever of these numbers you pick, there are infinitely many numbers bigger than it, and only finitely many smaller.

179

So almost all whole numbers are bigger than Rayo's number.

180

We haven't gone far at all.

181

We're standing at the very start of the number line.

182

So is the biggest number infinity?

183

No. Infinity isn't the last number in line.

184

It answers a different question.

185

Not which number, but how many numbers there are in total.

186

And that question has a ladder too.

187

Georg Cantor showed that infinities come in different sizes.

188

There are infinitely many whole numbers, but there are even more points on a line.

189

And above that infinity, there's another one, and so on, forever.

190

And any number in this video, even Rayo's number, is no better than one when you put it next to infinity.

191

Enormous, but finite.

192

We started with the idea that the universe doesn't have enough atoms to write down one number.

193

Now it's clear the problem isn't the universe.

194

Numbers simply grow faster than any place you could write them down.

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104 câu

Từ vựng và ghi chú luyện nói cho bài học này

Bài luyện nói này dựa trên video “Every Giant Number Explained”. Những từ được nhắc lại nhiều nhất trong bài: universe, arrow, Google, atom, colour. Video này có 194 câu và 1954 từ để luyện shadowing. Phần lời nói dài 12:13. Người nói nói với tốc độ tự nhiên, khoảng 160 từ mỗi phút, gần với hội thoại hằng ngày. Chỉ 81% số từ nằm trong 3.000 từ tiếng Anh thông dụng nhất, nên từ vựng khá khó.

Từ vựng quan trọng trong video

15 từ đáng học trong video, kèm phiên âm và nghĩa:

Từ	Phiên âm	Nghĩa
arrow danh từ	/ˈæɹəʊ/	mũi tên, tên
atom danh từ	/ˈætəm/	nguyên tử
digit danh từ	/ˈdɪd͡ʒɪt/	chữ số
infinity danh từ	/ɪnˈfɪnɪti/	vô cực
formula danh từ	/ˈfɔː.mjʊ.lə/	công thức
cube danh từ	/kjub/	hình lập phương
connect động từ	/kəˈnɛkt/	nối
symbol danh từ	/ˈsɪmbəl/	ký hiệu, biểu tượng
triple tính từ	/ˈtɹɪp.əl/	ba lần
estimate danh từ	/ˈɛs.tɪ.mət/	ước lượng
enormous tính từ	/ɪˈnɔː.məs/	khổng lồ
mathematics danh từ	/mæθ(.ə)ˈmæt.ɪks/	toán học
ladder danh từ	/ˈlæd.ɚ/	thang
lesson danh từ	/ˈlɛs.ən/	bài, bài học
cloud danh từ	/ˈklaʊ̯d/	mây

Cụm động từ bạn sẽ nghe

Từ	Nghĩa
run out động từ	hết
write down động từ	viết ra, ghi xuống

Những câu đáng luyện lại

Các câu ngắn, trọn ý trong video mà bạn có thể dùng lại khi giao tiếp hằng ngày:

You'd think it would always be that way.
It feels like we've gone very far.
We haven't gone far at all.

Ngữ pháp trong video

Những cấu trúc người nói dùng nhiều nhất, kèm đúng cụm từ trong video:

Cấu trúc	Trong video
Câu bị động be + quá khứ phân từ — nhấn vào việc xảy ra, không phải người làm	was invented · been found · can be computed
Thì hiện tại hoàn thành have/has + quá khứ phân từ — việc đã xảy ra nhưng còn liên quan đến hiện tại	have had · hasn't been found · we've gone

Phát âm cần chú ý

Người nói dùng 23 dạng rút gọn, ví dụ isn't, you'd, can't. Hãy nói theo dạng ngắn đúng như bạn nghe.

Âm “th”: mathematics /mæθ(.ə)ˈmæt.ɪks/, sixth /sɪksθ/, thirty /ˈθɝti/, ninth /naɪnθ/, theorem /ˈθiərəm/
Âm “sh” và “zh”: dimension /daɪˈmɛn.ʃən/, sheet /ʃit/, combinations /kɑmbɪˈneɪʃənz/, logician /ləˈd͡ʒɪʃən/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/
Từ dài — đặt trọng âm cho đúng: infinity /ɪnˈfɪnɪti/, ordinary /ˈɔɹdɪnɛɹi/, infinitely /ˈɪnfɪnɪtli/, mathematics /mæθ(.ə)ˈmæt.ɪks/, practically /ˈpɹæk.tɪ.k(ə.)li/

Những âm người Việt thường gặp khó:

Cụm phụ âm cuối — đọc đủ từng âm, đừng nuốt âm cuối: connect /kəˈnɛkt/, mathematics /mæθ(.ə)ˈmæt.ɪks/, bind /ˈbaɪ̯nd/, physics /ˈfɪz.ɪks/, sixth /sɪksθ/
Âm /tʃ/, /dʒ/ và /ʒ/ — tiếng Việt không có, đừng đọc thành “ch” hay “gi”: digit /ˈdɪd͡ʒɪt/, amateur /ˈæ.mə.t͡ʃɚ/, chess /t͡ʃɛs/, whichever /wɪt͡ʃˈɛvɚ/, logician /ləˈd͡ʒɪʃən/
Âm /æ/ — mở miệng rộng hơn âm “e”: arrow /ˈæɹəʊ/, atom /ˈætəm/, graham /ɡɹæm/, mathematics /mæθ(.ə)ˈmæt.ɪks/, ladder /ˈlæd.ɚ/

Cách luyện với video này

Nghe hết video một lần, chưa cần nói, và ghi lại những từ bạn chưa biết.
Bắt đầu ở tốc độ 0,75×, nói đuổi từng câu, rồi quay lại tốc độ bình thường khi đã quen.
Ghi âm giọng mình rồi so với bản gốc, chú ý các từ như arrow, atom, digit.

Phương Pháp Shadowing Là Gì?

Shadowing là kỹ thuật học ngôn ngữ có cơ sở khoa học, ban đầu được phát triển cho chương trình đào tạo phiên dịch viên chuyên nghiệp và được phổ biến rộng rãi bởi nhà đa ngôn ngữ học Dr. Alexander Arguelles. Nguyên lý cốt lõi đơn giản nhưng cực kỳ hiệu quả: bạn nghe tiếng Anh của người bản xứ và lặp lại to ngay lập tức — như một "cái bóng" (shadow) đuổi theo người nói với độ trễ chỉ 1–2 giây. Khác với luyện ngữ pháp hay học từ vựng bị động, Shadowing buộc não bộ và cơ miệng phải đồng thời xử lý và tái tạo ngôn ngữ thực tế. Các nghiên cứu khoa học xác nhận phương pháp này cải thiện đáng kể phát âm, ngữ điệu, nhịp điệu, nối âm, kỹ năng nghe và độ lưu loát khi nói — đặc biệt hiệu quả cho người luyện IELTS Speaking và muốn giao tiếp tiếng Anh tự nhiên như người bản ngữ.

Phương pháp shadowing: đọc hướng dẫn từng bước đầy đủ →

Luyện nói tiếng Anh bằng Shadowing qua video: Every Giant Number Explained

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