쉐도잉 연습: Turing & The Halting Problem - Computerphile - 영상으로 영어 말하기 배우기

Today we're going to be talking about a problem in logic, and how in solving that problem,

Alan Turing almost inadvertently invented the modern digital computer.

So we start back at the beginning of the 20th century, where mathematicians had posed this problem.

- Thank you.

In logic, we're interested in finding, do these premises entail this conclusion?

So premises are the bits you start off with in an argument.

They are the bits you know at the beginning or your assumptions.

And the conclusion is the bit you want to establish, the bit that you reason to with your argument.

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?

Is there an automatic way of finding out whether they do or whether they don't. So that's the problem.

It's called the decision problem.

and mathematicians wanted to find out Is there an answer to the decision problem for first order logic?

That's the kind of logic you learn in philosophy or mathematics at university.

So lots of mathematicians were trying to work out, is first order logic decidable?

That is, can we automatically test whether the premises entail the conclusion?

Alan Shuring was one of the first to discover that first order logic isn't decidable.

I To prove this, It's really difficult conceptually,

because you have to be able to show no possible program can give you the answer.

But how do you do that?

How do you show something about every possible program?

You can't run through every program one by one.

But Turing came up with a brilliant solution.

Yeah.

His idea goes something like this.

Suppose we have a program and let's just draw it as a black box.

It's going to take some inputs, and it's going to give us some outputs.

our program is going to solve some problem.

a problem like, do the premises entail the conclusion?

We ask it a question and it will give us an answer: yes, or no?

Now here's another question we can ask: Thank you.

Let's look at all of those possible programs.

And we're just thinking of them as black boxes at the moment.

We might want to know, is this program Given a certain input, gonna give us an answer.

Or is it going to trundle on forever and never give us an answer?

That is, is it going to halt or is it not going to halt eventually?

So think about your computer running.

You want it to give you an answer.

And whether it's a good answer or a bad answer, it's better than no answer.

No answer would mean the computer trundles round forever and ever in a loop.

And you would just never know whether it's going to finish today, tomorrow or never.

So halting is good.

So there's another question we can ask: Given some program and some inputs, will it ever halt?

Now it turns out that our logical problem Do these premises entail this conclusion?

is very similar to this halting problem.

In fact, if we can solve the logical problem, then we can solve the halting problem.

Will this program halt on this input?

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.

That is to tell us whether a given machine with a given input will halt or not.

And here's how we did it.

Let's suppose we've got a machine or a program that solves the problem for us it solves the holding problem.

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.

Yes it will halt or no it won't halt.

Just suppose that's possible.

Call that machine H for the halting problem.

If you give me that machine, I can transform it into a different machine like this.

I stick some extra bits on it so that If it gives me a yes answer, I make it loop forever without ever stopping.

If it gives me a no answer on the other hand, it's gonna halt straight away.

Let's call that big machine the whole thing.

H plus.

Now here's another question we can ask: what happens if I feed the whole machine into itself.

So I'm going to put H plus Thank you in here and H + in here.

So the question I'm now asking is, I'm feeding H + into itself.

So I'm asking the question: Does H + halt?

give an input H+.

And here's where it all goes wrong.

because If H + does halt, We get a yes answer.

But then it loops forever, so it doesn't halt.

On the other hand, if it doesn't halt, We get a no answer, but then it halts.

So if it does halt, then it doesn't halt.

But if it doesn't halt, then it does halt.

Either way, we get a contradiction.

It's a paradox.

And what that shows is we started off assuming that we can solve the problem.

we've ended up with a paradox.

So our assumption was bad.

It turns out there's no possible machine, no possible program that solves the halting problem.

The really clever bit about Turing's idea is it doesn't matter what kind of program or machine it is.

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.

We've proved that no such program is possible.

you Turing, as part of his argument, had to say a little bit about what's going on in these black boxes.

And the idea is that every card represents an instruction in this Turing machine.

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이 영상에는 섀도잉할 문장 81개와 단어 976개가 있습니다. 말하는 구간의 길이는 6:14입니다. 화자는 분당 약 157단어로, 일상 대화에 가까운 자연스러운 속도로 말합니다. 단어의 83%가 영어에서 가장 많이 쓰이는 3,000단어에 속합니다. 나머지는 연습 전에 미리 확인해 두세요.

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영상에 나오는 익혀 둘 만한 단어 14개를 발음, 뜻과 함께 정리했습니다.

단어	발음	뜻
hungry 형용사	/ˈhʌŋ.ɡɹi/	배고프다, 굶주리다
solve 동사	/sɒlv/	해결하다
conclusion 명사	/kənˈkluːʒən/	종결
loop 명사	/luːp/	고리
paradox 명사	/ˈpæ.ɹəˌdɒks/	모순, 자가당착
output 명사	/ˈaʊtpʊt/	출력
discover 동사	/dɪˈskʌvə/	발견하다
automatic 형용사	/ˌɔː.təˈmæt.ɪk/	자동, 자동적
mathematics 명사	/mæθ(.ə)ˈmæt.ɪks/	수학
transform 동사	/tɹænsˈfɔɹm/	변형시키다, 변형하다
algorithm 명사	/ˈælɡəɹɪðm̩/	알고리즘, 알고리듬
invent 동사	/ɪnˈvɛnt/	발명하다
mathematician 명사	/ˌmæθ.(ə.)məˈtɪʃ.ən/	수학자
contradiction 명사	/ˌkɑːntɹəˈdɪkʃən/	모순

주의할 발음

화자는 doesn't, I'm, don't 같은 축약형과 약화된 형태를 25번 사용합니다. 들리는 대로 짧게 발음하세요.

“th” 소리: mathematics /mæθ(.ə)ˈmæt.ɪks/, algorithm /ˈælɡəɹɪðm̩/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/
“sh”와 “zh” 소리: conclusion /kənˈkluːʒən/, assumption /əˈsʌm(p).ʃ(ə)n/, establish /ɪˈstæb.lɪʃ/, instruction /ɪnˈstɹʌkʃən/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/
긴 단어 — 강세 위치에 주의: automatic /ˌɔː.təˈmæt.ɪk/, mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/, decidable [dɪˈsaɪdəbəɫ], conceptually /kənˈsɛp.tjʊə.li/

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자신의 목소리를 녹음해 원본과 비교하고, hungry, solve, conclusion 같은 단어에 특히 주의합니다.

쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법

쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.

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