Shadowing-Übung: Every Giant Number Explained - Englisch Sprechen Lernen mit Video
Übungsmodus wählen
Jeder Modus öffnet einen Übungsraum im Vollbild.
194 Sätze
Wenn Sätze zu kurz oder zu lang sind, klicke auf Edit, um sie anzupassen.
1
If you wrote one digit on every atom in the observable universe,
2
you'd run out of atoms before you finished writing one of the numbers in this video.
3
And that number isn't even the biggest one here.
4
But let's start small.
5
A million, a billion, a trillion.
6
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.
7
A million seconds is a little over 11 days.
8
A billion seconds is almost 32 years.
9
And a trillion seconds is about 32 ,000 years.
10
That's six times longer than humans have had writing.
11
32 ,000 years ago, the world was in an ice age and people were hunting mammoths.
12
So counting with words gets awkward fast.
13
A million is a one followed by six zeros.
14
Short version, ten to the sixth.
15
A billion is ten to the ninth.
16
A trillion, ten to the twelfth.
17
Every three zeros get a new word.
18
Quadrillion, quintillion, all the way up to a decillion, ten to the thirty -third.
19
The words run out soon.
20
The numbers don't. In 1920,
21
the American mathematician Edward Kasner asked his nine -year -old nephew what to call a one followed by a hundred zeros.
22
The boy, whose name was Milton, said, A Google.
23
A Google is ten to the hundredth.
24
It's easy to write down.
25
It's one line.
26
But what can you count with it?
27
Atoms In the entire observable universe, in all the stars, planets and gas clouds, there are about 10 to the 80th.
28
That's less than a Google.
29
Not a little less, a hundred quintillion times less.
30
Imagine every atom in the universe turned out to be a whole universe full of atoms.
31
Now you'd have more than a Google.
32
But in our real universe, there just aren't that many things.
33
There are that many possibilities, though.
34
In 1950, Claude Shannon estimated how many different chess games there could be.
35
He got about 10 to the 120th, more than a Google.
36
Combinations grow much faster than stuff.
37
By the way, one company's name is a misspelling of Google, and its servers still live at the domain 1E100,
38
which is how programmers write a Google.
39
Milton came up with the next word too.
40
A Googleplex, he said, is a one followed by writing zeros until you get tired.
41
Casno pointed out that different people get tired at different times, so he made it precise.
42
A Googleplex is a one followed by a Google zeros, ten to the power of a Google.
43
And this is where the paper runs out.
44
To write a Googleplex, you need to write a Google zeros.
45
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,
46
and you need 10 to the 100th zeros.
47
If you printed a million zeros per book, you'd need 10 to the 94th books.
48
That's more books than there are atoms in the universe.
49
Carl Sagan made this point in Cosmos back in 1980.
50
There isn't room for a Googleplex in the known universe.
51
But numbers like this do show up in physics.
52
If the universe is infinite, then somewhere out there is an exact copy of Earth, and an exact copy of you watching this video.
53
The physicist Max Tegmark estimated how far away, roughly 10 to the 10 to the 28th miles.
54
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.
55
And a Googleplex is bigger still, much bigger.
56
The Googleplex was invented as a joke, but once an even bigger number was needed for real.
57
Prime numbers divide only by themselves and 1, 2, 3, 5, 7, 11.
58
The further you go, the rarer they get.
59
Gauss came up with a formula that roughly tells you how many primes there are below any number.
60
People checked it for billions, for trillions, for numbers with 19 zeros.
61
And every time, the formula came out a little too high.
62
Every single time.
63
You'd think it would always be that way.
64
But in 1914, John Littlewood proved it isn't.
65
Somewhere far out, the formula starts missing in the other direction, and it flips back and forth infinitely many times.
66
Where exactly, he didn't say.
67
In 1933, his student Stanley Skews found a limit.
68
The first flip has to happen before 10 to the 10 to the 10 to the 34th.
69
Three stories of exponents.
70
G. H.
71
Hardy called it the largest number that had ever served any definite purpose in mathematics.
72
Today we know the first flip happens much earlier, somewhere around 10 to the 316th.
73
But the exact spot still hasn't been found.
74
And that's the lesson.
75
A pattern can hold for every number we can reach and still be false.
76
To go further, we need a new way of writing.
77
and it's built like a ladder.
78
Adding three to itself three times is multiplication.
79
Multiplying three by itself three times is a power, and if you raise three to a power and then raise three to that result,
80
you get a tower of powers.
81
In 1976, Donald Newth suggested arrows for this.
82
One arrow is an ordinary power.
83
Three arrow three is 27.
84
Two arrows make a tower.
85
3 double arrow 3 is 3 to the 3 to the 3.
86
That's 3 to the 27th.
87
7 ,625 ,000 ,000 ,000 ,000 and change.
88
Not scary yet, but add one more story to the tower.
89
3 to the power of that number.
90
The result has more than 3 .5 trillion digits.
91
Now 3 arrows.
92
3 triple arrow.
93
3 is a tower of 3's more than 7 .5 trillion stories tall.
94
Not that many digits.
95
that many stories.
96
For comparison, a Googleplex fits in a tower of just four tens and skews his number in a tower of five.
97
Four stories of tens and the number already has more digits than there are atoms in the universe.
98
Each new arrow repeats the previous one as many times as the last step produced,
99
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.
App herunterladen
Alles, was du zum fließenden Sprechen brauchst
KI-AussprachebewertungJeder Satz bewertet
IPA-TrainingJeden Laut meistern
WortschatzBaue deinen Wortschatz auf
VokabelspielSpielend lernen
FOR YOU
Empfohlenes Video
C16
104 Sätze
How real are the real numbers, really?
Daily ConversationUniversity Students
C15
56 Sätze
Gemini 4 Argon explained in 5min..
Daily ConversationUniversity Students
C14
33 Sätze
Brainf**k in 100 Seconds
American AccentDaily ConversationUniversity Students
C11
107 Sätze
What If You Lit a Match on Jupiter, Would The Planet Explode?
Daily ConversationUniversity Students
C11
65 Sätze
How do microSD Cards Store 2 TB in such a TINY space?
American AccentDaily ConversationUniversity StudentsWorking Adults
![[Practice Problems] Regular Expressions (Regex) - Visually Explained](https://img.youtube.com/vi/AawczswiGI0/mqdefault.jpg)
C11
61 Sätze
[Practice Problems] Regular Expressions (Regex) - Visually Explained
Daily ConversationUniversity Students
C13
246 Sätze
$15 Trillion Money-Making Machine | How BlackRock Became Too Powerful to Ignore
Daily ConversationUniversity StudentsWorking Adults
C181 Sätze
Mathematician Collapses All Functions to One Weird Formula
Daily ConversationUniversity StudentsWorking Adults
C11
234 Sätze
Every Processing Unit Explained in 20 Minutes
Daily ConversationUniversity Students
C11
498 Sätze
Give me 31 minutes, I will make PyTorch click forever
Daily ConversationUniversity Students
C13
298 Sätze
GENERAL CHEMISTRY explained in 19 Minutes
Daily ConversationUniversity Students
C11
207 Sätze
Go’s Big Mistake
Daily ConversationUniversity StudentsWorking Adults
Wortschatz und Sprechhinweise zu dieser Lektion
Diese Sprechübung basiert auf dem Video „Every Giant Number Explained“. Diese Wörter kommen am häufigsten vor: universe, arrow, Google, atom, colour. Dieses Video enthält 194 Sätze und 1954 Wörter zum Nachsprechen. Der gesprochene Teil dauert 12:13. Der Sprecher spricht in natürlichem Tempo, etwa 160 Wörter pro Minute, ähnlich wie im Alltagsgespräch. Nur 81 % der Wörter gehören zu den 3.000 häufigsten im Englischen, der Wortschatz ist also anspruchsvoll.
Wichtiger Wortschatz in diesem Video
15 lernenswerte Wörter aus dem Video, mit Aussprache und Bedeutung:
| Wort | Aussprache | Bedeutung |
|---|---|---|
| arrow Substantiv | /ˈæɹəʊ/ | Pfeil |
| atom Substantiv | /ˈætəm/ | Atom |
| digit Substantiv | /ˈdɪd͡ʒɪt/ | Ziffer, Stelle |
| infinity Substantiv | /ɪnˈfɪnɪti/ | Unendlichkeit |
| formula Substantiv | /ˈfɔː.mjʊ.lə/ | Formel |
| ordinary Adjektiv | /ˈɔɹdɪnɛɹi/ | gewöhnlich, normal |
| flip Verb | /flɪp/ | umdrehen, wenden |
| dimension Substantiv | /daɪˈmɛn.ʃən/ | Dimension |
| cube Substantiv | /kjub/ | Kubus, Würfel |
| connect Verb | /kəˈnɛkt/ | verbinden |
| roughly Adverb | /ˈɹʌf.li/ | grob |
| symbol Substantiv | /ˈsɪmbəl/ | Symbol, Zeichen |
| triple Adjektiv | /ˈtɹɪp.əl/ | dreifach |
| estimate Substantiv | /ˈɛs.tɪ.mət/ | Schätzung, Abschätzung |
| enormous Adjektiv | /ɪˈnɔː.məs/ | enorm, riesig |
Phrasal Verbs, die du hören wirst
| Wort | Aussprache | Bedeutung |
|---|---|---|
| come up with Verb | ausdenken | |
| run out Verb | ausgehen | |
| write down Verb | aufschreiben | |
| come out Verb | /ˌkʌm ˈaʊt/ | herauskommen |
| point out Verb | hinweisen |
Sätze zum Wiederholen
Kurze, vollständige Sätze aus dem Video, die du im Alltag wiederverwenden kannst:
- You'd think it would always be that way.
- It feels like we've gone very far.
- We haven't gone far at all.
Grammatik in diesem Video
Die Strukturen, die der Sprecher am häufigsten verwendet, mit den genauen Worten aus dem Video:
| Struktur | Im Video |
|---|---|
| Passiv be + Partizip Perfekt – wichtig ist, was geschieht, nicht wer es tut | was invented · been found · can be computed |
| Present Perfect have/has + Partizip Perfekt – eine vergangene Handlung, die jetzt noch wichtig ist | have had · hasn't been found · we've gone |
Aussprache, auf die du achten solltest
Der Sprecher verwendet 23 Kurzformen und abgeschwächte Formen, zum Beispiel isn't, you'd, can't. Sprich sie in der kurzen Form, so wie du sie hörst.
- Die „th“-Laute: mathematics /mæθ(.ə)ˈmæt.ɪks/, sixth /sɪksθ/, thirty /ˈθɝti/, ninth /naɪnθ/, theorem /ˈθiərəm/
- Die Laute „sh“ und „zh“: dimension /daɪˈmɛn.ʃən/, sheet /ʃit/, combinations /kɑmbɪˈneɪʃənz/, logician /ləˈd͡ʒɪʃən/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/
- Lange Wörter – auf die Betonung achten: infinity /ɪnˈfɪnɪti/, ordinary /ˈɔɹdɪnɛɹi/, infinitely /ˈɪnfɪnɪtli/, mathematics /mæθ(.ə)ˈmæt.ɪks/, practically /ˈpɹæk.tɪ.k(ə.)li/
Laute, die Deutschsprachigen schwerfallen:
- /w/ — mit runden Lippen, nicht wie das deutsche „w“ (/v/): awkward /ˈɔk.wɚd/, whichever /wɪt͡ʃˈɛvɚ/, twelfth /twɛlfθ/ [tʰw̥ɛɫfθ]
- Stimmhafter Auslaut — /b/, /d/, /g/, /z/, /v/ am Wortende nicht verhärten: cube /kjub/, bind /ˈbaɪ̯nd/, cloud /ˈklaʊ̯d/, awkward /ˈɔk.wɚd/, divide /dɪˈvaɪd/
- /æ/ — offener als „ä“: arrow /ˈæɹəʊ/, atom /ˈætəm/, graham /ɡɹæm/, mathematics /mæθ(.ə)ˈmæt.ɪks/, ladder /ˈlæd.ɚ/
So übst du mit diesem Video
- Höre dir das ganze Video einmal an, ohne zu sprechen, und notiere die Wörter, die du nicht kennst.
- Beginne mit 0,75-facher Geschwindigkeit, sprich Satz für Satz nach und wechsle zur normalen Geschwindigkeit, sobald es leichtfällt.
- Nimm dich auf und vergleiche mit dem Original; achte dabei auf Wörter wie arrow, atom, digit.
Was ist die Shadowing-Technik?
Shadowing ist eine wissenschaftlich fundierte Sprachlerntechnik, die ursprünglich für die professionelle Dolmetscherausbildung entwickelt und durch den Polyglotten Dr. Alexander Arguelles populär gemacht wurde. Die Methode ist einfach aber wirkungsvoll: Du hörst englisches Audio von Muttersprachlern und wiederholst es sofort laut — wie ein Schatten, der dem Sprecher mit nur 1–2 Sekunden Verzögerung folgt. Anders als passives Hören oder Grammatikübungen zwingt Shadowing dein Gehirn und deine Mundmuskulatur, gleichzeitig echte Sprachmuster zu verarbeiten und zu reproduzieren. Studien zeigen, dass es Aussprachegenauigkeit, Intonation, Rhythmus, verbundene Sprache, Hörverständnis und Sprechflüssigkeit signifikant verbessert — was es zu einer der effektivsten Methoden für die IELTS Speaking-Vorbereitung und reale englische Kommunikation macht.