跟讀練習: Turing & The Halting Problem - Computerphile - 通過影片學習英語口語
選擇練習模式
每種模式都會開啟全屏練習室。
81 句
如果句子過短或過長，請點選 Edit 進行調整。
1
Today we're going to be talking about a problem in logic, and how in solving that problem,
2
Alan Turing almost inadvertently invented the modern digital computer.
3
So we start back at the beginning of the 20th century, where mathematicians had posed this problem.
4
- Thank you.
5
In logic, we're interested in finding, do these premises entail this conclusion?
6
So premises are the bits you start off with in an argument.
7
They are the bits you know at the beginning or your assumptions.
8
And the conclusion is the bit you want to establish, the bit that you reason to with your argument.
9
And we want to know, is there a test that will tell us, yes, for sure, these premises do or don't entail this conclusion?
10
Is there an automatic way of finding out whether they do or whether they don't. So that's the problem.
11
It's called the decision problem.
12
and mathematicians wanted to find out Is there an answer to the decision problem for first order logic?
13
That's the kind of logic you learn in philosophy or mathematics at university.
14
So lots of mathematicians were trying to work out, is first order logic decidable?
15
That is, can we automatically test whether the premises entail the conclusion?
16
Alan Shuring was one of the first to discover that first order logic isn't decidable.
17
I To prove this, It's really difficult conceptually,
18
because you have to be able to show no possible program can give you the answer.
19
But how do you do that?
20
How do you show something about every possible program?
21
You can't run through every program one by one.
22
But Turing came up with a brilliant solution.
23
Yeah.
24
His idea goes something like this.
25
Suppose we have a program and let's just draw it as a black box.
26
It's going to take some inputs, and it's going to give us some outputs.
27
our program is going to solve some problem.
28
a problem like, do the premises entail the conclusion?
29
We ask it a question and it will give us an answer: yes, or no?
30
Now here's another question we can ask: Thank you.
31
Let's look at all of those possible programs.
32
And we're just thinking of them as black boxes at the moment.
33
We might want to know, is this program Given a certain input, gonna give us an answer.
34
Or is it going to trundle on forever and never give us an answer?
35
That is, is it going to halt or is it not going to halt eventually?
36
So think about your computer running.
37
You want it to give you an answer.
38
And whether it's a good answer or a bad answer, it's better than no answer.
39
No answer would mean the computer trundles round forever and ever in a loop.
40
And you would just never know whether it's going to finish today, tomorrow or never.
41
So halting is good.
42
So there's another question we can ask: Given some program and some inputs, will it ever halt?
43
Now it turns out that our logical problem Do these premises entail this conclusion?
44
is very similar to this halting problem.
45
In fact, if we can solve the logical problem, then we can solve the halting problem.
46
Will this program halt on this input?
47
So the clever part of Turing's proof is to show that it's impossible for any machine, however clever it is, to solve the halting problem.
48
That is to tell us whether a given machine with a given input will halt or not.
49
And here's how we did it.
50
Let's suppose we've got a machine or a program that solves the problem for us it solves the holding problem.
51
Don't worry about how it works, let's just think of it as a black box, taking a description of a machine and an input, and giving us an answer.
52
Yes it will halt or no it won't halt.
53
Just suppose that's possible.
54
Call that machine H for the halting problem.
55
If you give me that machine, I can transform it into a different machine like this.
56
I stick some extra bits on it so that If it gives me a yes answer, I make it loop forever without ever stopping.
57
If it gives me a no answer on the other hand, it's gonna halt straight away.
58
Let's call that big machine the whole thing.
59
H plus.
60
Now here's another question we can ask: what happens if I feed the whole machine into itself.
61
So I'm going to put H plus Thank you in here and H + in here.
62
So the question I'm now asking is, I'm feeding H + into itself.
63
So I'm asking the question: Does H + halt?
64
give an input H+.
65
And here's where it all goes wrong.
66
because If H + does halt, We get a yes answer.
67
But then it loops forever, so it doesn't halt.
68
On the other hand, if it doesn't halt, We get a no answer, but then it halts.
69
So if it does halt, then it doesn't halt.
70
But if it doesn't halt, then it does halt.
71
Either way, we get a contradiction.
72
It's a paradox.
73
And what that shows is we started off assuming that we can solve the problem.
74
we've ended up with a paradox.
75
So our assumption was bad.
76
It turns out there's no possible machine, no possible program that solves the halting problem.
77
The really clever bit about Turing's idea is it doesn't matter what kind of program or machine it is.
78
It doesn't matter whether it's An abstract algorithm, whether it's a real computer, a physical computer, it doesn't matter what it is.
79
We've proved that no such program is possible.
80
you Turing, as part of his argument, had to say a little bit about what's going on in these black boxes.
81
And the idea is that every card represents an instruction in this Turing machine.
同頻道
FOR YOU
推薦影片
C11
136 句
Early Computing: Crash Course Computer Science #1
Business EnglishUniversity StudentsWorking Adults
C13
260 句
【TED】優れたリーダーはどうやって行動を促すか/サイモン・シネック （日本語字幕）
Business EnglishDaily ConversationUniversity Students
C13
85 句
AI Will End Philosophy, Physicist Claims
Daily ConversationUniversity StudentsWorking Adults
C12
24 句
you are programmed to doubt yourself
Business EnglishUniversity StudentsWorking Adults
C13
80 句
What is clean code? - Uncle Bob
Business EnglishUniversity StudentsWorking Adults
C18
102 句
World Models explained in 10min..
Business EnglishUniversity StudentsWorking Adults
C12
86 句
The Map of Mathematics
British AccentBusiness EnglishUniversity StudentsWorking Adults
C14
413 句
Exposing The Flaw In Our Phone System
Business EnglishUniversity StudentsWorking Adults
C13
200 句
CAP Theorem in System Design Interviews
Business EnglishInterview EnglishUniversity Students
C1465
25 句
The Human Economy in the Age of AI | Ben Pascut | TEDx
IELTS PrepBusiness EnglishUniversity Students
C15
54 句
The Science of Thinking
Business EnglishDaily ConversationUniversity Students
C11
146 句
🚫 Java Deadlock Explained: Why Your Code is Stuck 😱 (Beginners Must Watch!)
Daily ConversationUniversity StudentsWorking Adults
本課的詞彙與口語要點
這段影片共有 81 個句子、976 個單詞可供跟讀。 講話部分時長為 6:14。 說話人語速自然，每分鐘約 157 個詞，接近日常對話。 83% 的單詞屬於英語最常用的 3,000 詞，其餘的詞建議在練習前先學一下。
影片中的重點詞彙
影片中 15 個值得學習的單詞，附發音和釋義：
| 單詞 | 發音 | 釋義 |
|---|---|---|
| hungry 形容詞 | /ˈhʌŋ.ɡɹi/ | 飢餓 /飢餓, 餓 /餓 |
| solve 動詞 | /sɒlv/ | 解決 /解決 |
| input 名詞 | /ˈɪnpʊt/ | 輸入 /輸入 |
| conclusion 名詞 | /kənˈkluːʒən/ | 結束 /結束 |
| premise 名詞 | /ˈpɹɛm.ɪs/ | 前提 |
| loop 名詞 | /luːp/ | 圈, 環 /環 |
| assumption 名詞 | /əˈsʌm(p).ʃ(ə)n/ | 假設 /假設 |
| paradox 名詞 | /ˈpæ.ɹəˌdɒks/ | 悖論 /悖論, 矛盾 |
| establish 動詞 | /ɪˈstæb.lɪʃ/ | 確定 /確定 |
| output 名詞 | /ˈaʊtpʊt/ | 輸出 /輸出 |
| discover 動詞 | /dɪˈskʌvə/ | 發現 /發現, 發覺 /發覺 |
| automatic 形容詞 | /ˌɔː.təˈmæt.ɪk/ | 自動的 /自動的 |
| mathematics 名詞 | /mæθ(.ə)ˈmæt.ɪks/ | 數學 /數學, 算學 /算學 |
| abstract 名詞 | /ˈæbˌstɹækt/ | 摘要 |
| instruction 名詞 | /ɪnˈstɹʌkʃən/ | 教導 /教導 |
影片中出現的短語動詞
| 單詞 | 發音 | 釋義 |
|---|---|---|
| find out 動詞 | 找出, 查明 | |
| turn out 動詞 | 原來 /原來 | |
| come up with 動詞 | 想出, 提出 | |
| work out 動詞 | /ˌwɝk ˈaʊt/ | 計算 /計算, 算出 |
需要注意的發音
說話人用了 25 次縮略和弱讀形式，例如 doesn't, I'm, don't。請按聽到的簡短形式來說。
- “th” 音: mathematics /mæθ(.ə)ˈmæt.ɪks/, algorithm /ˈælɡəɹɪðm̩/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/
- “sh” 和 “zh” 音: conclusion /kənˈkluːʒən/, assumption /əˈsʌm(p).ʃ(ə)n/, establish /ɪˈstæb.lɪʃ/, instruction /ɪnˈstɹʌkʃən/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/
- 長單詞——注意重音位置: automatic /ˌɔː.təˈmæt.ɪk/, mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/, decidable [dɪˈsaɪdəbəɫ], conceptually /kənˈsɛp.tjʊə.li/
如何用這段影片練習
- 先完整聽一遍影片，不要開口，記下不認識的單詞。
- 先用 0.75 倍速逐句跟讀，熟練之後再回到正常速度。
- 錄下自己的聲音並與原聲對比，特別注意 hungry, solve, input 這類單詞。
什麼是跟讀法？
跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。