## 字幕列表 影片播放

• What am I ever going to need this?

我怎麼會需要這個呢？

• I'm looking at your screen shot and I think the answer is never you are never gonna need this.

我在看你的螢幕截圖，我想答案是永遠不會，你永遠不會需要這個。

• I'm Professor Moon Duchin comma mathematician today, I'm here to answer any and all math questions on twitter.

我是今天的月亮杜欽教授逗號數學家，我在這裡回答微博上所有的數學問題。

• This is math support at records, fluorescent says what is an algorithm?

這就是數學支持的記錄，熒光說什麼是算法？

• Keep hearing this word?

一直聽到這個詞？

• Hmm the way you spelled algorithm like it has rhythm in it.

嗯，你拼寫算法的方式好像有節奏感。

• I like it.

我喜歡它。

• I'm going to keep it a mathematician.

我打算保持它是一個數學家。

• What we mean by algorithm is just any clear set of rules of procedure for doing something.

我們所說的算法只是指做某事的任何一套明確的程序規則。

• The word comes from ninth century Baghdad where al who worries me?

這個詞來自於九世紀的巴格達，在那裡誰讓我擔心呢？

• His name became algorithm but he also gave us the word that became algebra.

他的名字變成了算法，但他也給了我們一個詞，變成了代數。

• He was just interested in building up the science of manipulating what we would think of as equations.

他只是對建立操縱我們所認為的方程式的科學感興趣。

• Usually when people say algorithm, they made something more computerese.

通常情況下，當人們說算法時，他們做出了更多的計算機化的東西。

• Right?

對嗎？

• So usually when we have a computer program we think of the underlying set of instructions as an algorithm given some inputs.

是以，通常當我們有一個計算機程序時，我們認為底層的指令集是一個給定一些輸入的算法。

• It's going to tell you kind of how to make a decision.

它要告訴你那種如何做出決定的方法。

• If an algorithm is just like a precise procedure for doing something, then an example is a procedure that's so precise that a computer can do it at llama Lord 10 91 asks how bofa did the Mayans developed the concept of zero?

如果算法就像做某事的精確程序，那麼一個例子就是一個非常精確的程序，以至於計算機可以在llama Lord 10 91問：瑪雅人是如何博發娛樂官網手機版零的概念？

• Everybody's got a zero in the sense that everybody's got the concept of nothing.

每個人都有一個零，在這個意義上，每個人都有無的概念。

• The math concept of zero is kind of the idea that nothing is a number.

零的數學概念有點像沒有東西是數字的想法。

• The heart of it is how do different cultures incorporate zero as a number.

它的核心是不同的文化如何將零作為一個數字。

• I don't know much about the mayan example particularly but you can see different cultures wrestling with.

我不太瞭解瑪雅人的例子，特別是，但你可以看到不同的文化在進行搏鬥。

• Is it a number?

它是一個數字嗎？

• What makes it number three Math is decided kind of collectively is that it is useful to think about it as a number because you can do arithmetic to it.

是什麼讓它成為數字三 數學是決定性的一種集體，是把它作為一個數字來考慮是有用的，因為你可以對它做算術。

• So it deserves to be called the number at jess peacock says how can math be misused or abused because the reputation of math is just being like plain, right or wrong and also being really hard.

所以它應該被稱為數字，在Jess Peacock說，數學怎麼會被誤用或濫用，因為數學的名聲只是像普通的，對或錯，也真的很難。

• It gives mathematicians a certain kind of authority and you can definitely see that being abused and this is true more and more now that data science is kind of taking over the world but the flip side of that is that math is being used and used well about five years ago I got obsessed with redistricting and gerrymandering and trying to think about how you could use math models to better and fairer redistricting.

它給了數學家某種權威，你絕對可以看到這種權威被濫用，現在數據科學正在接管世界，這一點越來越真實，但其反面是，數學正在被使用和使用得很好，大約五年前，我迷上了重新劃分選區和劃分選區，並試圖思考如何使用數學模型來更好和更公平地重新劃分。

• Ancient ancient math was being used.

正在使用古代的古老數學。

• You just close your eyes and do random redistricting.

你只要閉上眼睛，隨機進行重新劃分。

• You're not going to get something that's very good for minorities And now that's become much clearer because of these mathematical models and when you know that you can fix it.

你不會得到對少數民族非常好的東西。現在，由於這些數學模型，這一點變得更加清晰，當你知道你可以修復它。

• And I think that's an example of math being used to kind of move the needle in a direction.

我想這是一個用數學的例子，可以把針朝一個方向移動。

• That's pretty good at chris ex chris explain news that is hard to say analytic valley girl.

這是相當好的在克里斯前克里斯解釋的新聞，很難說分析的山谷女孩。

• I honestly have no idea what math research looks like and all I'm envisioning is a dude with a mid atlantic accent narrating over footage of guys in lab coats looking at shapes and like a number four on a whiteboard.

老實說，我不知道數學研究是什麼樣子的，我所設想的是一個帶著大西洋中部口音的傢伙，在穿著白大褂的人在白板上看形狀和像數字4的畫面上進行敘述。

• There's this fatal error at the center of your account.

在你的賬戶中心有這個致命的錯誤。

• The white board, like no mathematicians are fairly united on this point of disdaining whiteboards together.

白板，就像沒有數學家在一起不屑於白板這一點上相當一致。

• So we really like these beautiful things called chalkboards and we especially like this beautiful fetish object, japanese chalk and then when you write, it's really smooth.

所以我們真的很喜歡這些美麗的東西，叫做黑板，我們特別喜歡這種美麗的戀物，日本的粉筆，然後當你寫的時候，它真的很光滑。

• The things that are fun about this, like the colors are really vivid and also it erases well which matters.

這個東西很有趣，比如顏色真的很鮮豔，而且它的擦除效果也很好，這很重要。

• You just feel that much smarter when you're using good chalk.

當你使用好的粉筆時，你就會覺得自己更聰明瞭。

• One thing I would say about math research that probably is a little known is how collaborative it is.

關於數學研究，我想說的一件事可能是鮮為人知的，那就是它的合作性。

• Typical math papers have multiple authors and we're just working together all the time.

典型的數學論文有多個作者，我們只是一直在一起工作。

• It's kind of fun to look back at the paper correspondence of mathematicians from like 100 years ago who are actually putting all this like cool math into letters and sending them back and forth.

回顧一下100年前的數學家們的紙質信件是很有趣的，他們實際上是把所有這些像是很酷的數學放在信件中，然後來回發送。

• We've done this really good job of packaging math to teach it and so that it looks like it's all done and clean and neat but math research is like messy and creative and original and new and you're trying to figure out how things work and how to put them together in new ways.

我們已經做了非常好的工作，把數學包裝起來教給大家，這樣看起來就像全部完成了，乾淨整潔，但數學研究就像混亂的、創造性的、原始的、新的，你要努力弄清楚事情是如何運作的，如何以新的方式把它們放在一起。

• It looks nothing like the math in school, which is sort of a much polished up after the fact finished product version of something that's actually like out there and messy and weird.

它看起來與學校裡的數學完全不同，那是一種事後拋光的成品版本，實際上就像外面的東西，混亂而奇怪。

• So Dylan john kemp says serious question, that sounds like it's not a serious question for mathematicians, scientists and engineers.

所以迪倫-約翰-坎普說的是嚴肅的問題，這聽起來好像不是數學家、科學家和工程師的嚴肅問題。

• Do people use imaginary numbers to build real things?

人們是否使用虛數來建造真實的東西？

• Yes, they do.

是的，他們這樣做。

• You can't do much without them.

沒有他們，你就做不了什麼。

• In particular, equation solving requires these things.

特別是，方程解法需要這些東西。

• They got called imaginary at some point because just people didn't know what to do with them.

他們在某些時候被稱為虛構的，因為只是人們不知道該如何對待他們。

• There were these concepts that you needed to be able to handle and manipulate but people didn't know whether they count as numbers.

有這些概念，你需要能夠處理和操作，但人們不知道它們是否算作數字。

• No pun intended.

沒有雙關的意思。

• Here's the usual number line that you're comfortable with.

這裡是你所熟悉的通常的數字線。

• 012 and so on real numbers over here and then just give me this number up here and call it I that gives me a building block to get anywhere.

012等等真正的數字在這裡，然後只要給我這個數字在這裡，叫它I，這就給了我一個基石，可以得到任何東西。

• So now I come out here, this will be like three plus two.

所以現在我來到這裡，這就像三加二。

• I so I is now the building block that can get me anywhere in space.

我所以我現在是可以讓我在太空中的任何地方的構件。

• Yes, every bridge and every spaceship and all the rest.

是的，每座橋和每艘飛船以及其他所有的東西。

• Like you better hope someone could handle imaginary numbers well at let Clara Vinny it says hashtag movie errors that bugged me the seventh equation down on the third chalkboard in a beautiful mind was erroneously shown with two extra variables and an incomplete constant boy that requires some zooming, I will say though for me and lots of mathematicians watching the math in movies is a really great sport.

就像你最好希望有人能很好地處理虛數，在讓克拉拉-維尼它說標籤的電影錯誤，讓我感到厭煩的是，在第三塊黑板上的第七個方程下來的美麗心靈被錯誤地顯示為兩個額外的變量和一個不完整的常數男孩，需要一些縮放，我會說，雖然對我和很多數學家來說，看電影中的數學是一項非常偉大的運動。

• So what's going on here is I see a bunch of sums, I see some partial derivatives.

所以這裡發生的事情是我看到了一堆和，我看到了一些部分導數。

• This movie about john nash who is actually famous for a bunch of things in math world.

這部電影是關於約翰-納什的，他實際上是以數學世界中的一堆事情而聞名。

• One of them is like game theory, ideas and economics, but I do not think that's what's on the board here.

其中一個是像博弈論、思想和經濟學，但我認為這不是這裡的問題。

• If I had to guess, I think what he's doing is earlier.

如果讓我猜，我認為他所做的事情更早。

• Very important work of his.

他的非常重要的作品。

• Um this is like Nash embedding theorems I think.

嗯，這就像納什嵌入定理，我想。

• So this is like fancy geometry, you can't tell because it looks like a bunch of sums and squiggles.

所以這就像花式幾何，你看不出來，因為它看起來就像一堆和和的方塊。

• You're missing the part of the board that defines the terms.

你錯過了董事會中定義術語的部分。

• So um do I agree with Jk Vinnie that stuff is missing from the bottom row.

所以，嗯，我同意Jk Vinnie的觀點，即底排的東西是缺失的。

• I don't think that I do.

我不認為我這樣做。

• Sorry Vinnie at a D H S Jag club asks questions without using numbers and without using a search engine.

對不起，Vinnie在D H S Jag俱樂部問問題時沒有使用數字，也沒有使用搜索引擎。

• Do you know how to explain what pi is in words you sort of need pie or something like it to, to talk about any measurements of circles, Everything you want to describe about round things.

你知道如何用語言解釋什麼是圓周率嗎？你需要派或類似的東西來談論任何關於圓的測量，你想描述的所有關於圓的東西。

• You need pie to make it precise circumference, surface area area, volume um anything that relates length to other measurements on circles needs pie, but here's a fun one.

你需要派來使它精確的圓周率，表面積面積，體積嗯任何與長度和其他測量有關的圓圈都需要派，但這裡有一個有趣的問題。

• So what if you took four and you subtracted four thirds and then you added back for fifth and then subtracted 4/7 and so on.

那麼，如果你拿了4，然後減去3分之4，再加回5，再減去4/7，如此反覆。

• So it turns out that if you kept going forever, this actually equals pi, they don't teach you this in school.

是以，事實證明，如果你一直走下去，這實際上等於圓周率，他們在學校沒有教你這個。

• So this is what's called a power series.

所以這就是所謂的冪級數。

• And it's it's pretty much like all the originators of calculus were kind of thinking this way about these like infinite sums.

而這就像微積分的所有創始人都是這樣思考這些像無限大的和。

• So that's another way to think about it.

所以這是另一種思考方式。

• If you are allergic to circles because you're the only one bro why did math?

如果你對圓圈過敏，因為你是唯一的兄弟，為什麼做了數學？

• People have to invent infinity?

人們要發明無限大？

• Because it is so convenient.

因為它是如此方便。

• It completes us.

它使我們完整。

• Um Could we do math without infinity?

呃......我們能不能在沒有無限的情況下做數學題？

• The fact that the numbers go on forever.

事實上，這些數字一直在持續。

• 1234 dot dot dot It would be pretty hard to do math without the dot dot dots.

1234點點點 如果沒有點點點，做數學就相當困難了。

• In other words, without the idea of things that go on forever.

換句話說，沒有了事情永遠持續下去的想法。

• We kind of need that but we maybe didn't have to create a symbol for it and creating arithmetic around it and create like a geometry for it where there's like a point of infinity.

我們需要這個，但我們也許沒有必要為它創造一個符號，圍繞它創造算術，為它創造一個幾何學，其中有一個無限的點。

• That was optional.

那是可有可無的。

• But it's pretty at the fill which Alex, what is the sexiest equation?

但它在填充的時候很好看，這亞歷克斯，什麼是最性感的方程式？

• I'm going to show you an identity or a theorem that I love, I just think is really pretty and that I use a lot.

我將向你展示一個我喜歡的身份或定理，我只是認為它非常漂亮，而且我經常使用。

• So this is about surfaces and the geometry of surfaces looks like this.

是以，這是關於曲面的問題，曲面的幾何形狀是這樣的。

• This is called Minsky's product regions theorem.

這被稱為明斯基的產品區域定理。

• So this is a kind of almost equality that we really like in my kind of math, the picture that goes along with this theorem looks something like this.

所以這是一種我們在我的數學中非常喜歡的幾乎是平等的，與這個定理一起的圖片看起來是這樣的。

• You have a surface, you have some curves.

你有一個表面，你有一些曲線。

• This is called a genius to surface.

這被稱為天才的浮現。

• It's like a double inner tube.

這就像一個雙內胎。

• It's sort of like to hollow donuts kind of surgery together in the middle.

這有點像空心甜甜圈，在中間做手術。

• And so this is telling you what happens when you take some curves, like the ones that I've colored here and you squeeze them really thin.

所以這是在告訴你，當你把一些曲線，比如我在這裡畫的那些曲線，把它們擠壓得非常薄，會發生什麼。

• So it's the thin part, 1st Set of Curves.

所以它是薄的部分，第一組曲線。

• And it's telling you that um this looks just like what would happen if you like pinch them all the way off and cut open the surface there.

它告訴你，嗯，這看起來就像如果你把它們全部掐斷並切開那裡的表面會發生什麼。

• You'd get something simpler.

你會得到更簡單的東西。

• And a leftover part that is well understood at Absa says what if Blockchain is just a plot by math majors to convince governments VC funds and billionaires to give money to low level math research?

而在Absa很瞭解的一個遺留部分說，如果區塊鏈只是數學專業的人的一個陰謀，說服政府VC基金和億萬富翁給低水平的數學研究提供資金，那怎麼辦？

• No, and here's how I know we're really bad at telling the world what we're doing.

不，這就是我如何知道我們真的不善於告訴世界我們在做什麼。

• And incidentally getting money for it.

並順便拿錢來買。

• Most people could tell you something about new physics ideas, chemistry, new biology, ideas from say the 20th century.

大多數人可以告訴你一些關於新的物理學思想、化學、新的生物學，比如說20世紀的思想。

• And most people probably think there aren't new things in math right?

而大多數人可能認為數學中沒有新東西吧？

• There are breakthroughs in math all the time.

數學方面一直都有突破性進展。

• One of the breakthrough ideas from the 20th century is turns out there aren't three basic three dimensional geometries.

20世紀的一個突破性想法是，原來並沒有三個基本的三維幾何圖形。

• There are eight flat, like like a piece of paper round like a sphere.

有八個平的，像像一張紙一樣圓的，像一個球體。

• And then the third one looks like a pringle.

然後第三個人看起來像一個普林格。

• It's this hyperbolic geometry or like saddle shape.

它是這種雙曲幾何或像馬鞍的形狀。

• Another one is actually instead of a single Pringle, you passed to a stack of Pringles.

另一個是實際上不是一個單一的普林格，而是傳遞給一疊普林格。

• So like this so we call this H two cross are put these all together and you get a three dimensional geometry and then the last three are nil.

所以像這樣，所以我們把這個叫做H兩個十字是把這些都放在一起，你得到一個三維的幾何體，然後最後三個是零。

• This guy over here sol which is a little bit like nil but it's hard to explain.

這個傢伙在這裡的sol有點像nil，但很難解釋。

• And then the last one which I kid you not is called sl two are twiddle.

然後是最後一個，我開玩笑說，這叫 "兩隻手"。

• Really?

真的嗎？

• That's what it's called.

這就是它的名字。

• Finally it was proved to like the community satisfaction what is now called the geometry?

最後證明，像現在的社會滿意度，也就是所謂的幾何？

• Ization theorem.

Ization定理。

• The idea of how you can build stuff out of those eight kinds of of worlds.

你如何能在這八種世界中建造東西的想法。

• It's just one example of the publicity mathematicians are failing to generate.

這只是數學家們宣傳失敗的一個例子。

• Did we invent Blockchain to like get money for ourselves?

我們發明區塊鏈是為了喜歡為自己撈錢嗎？

• No we did not at Riley?

不，我們沒有在萊利？

• Alonzo is geometric group theory.

阿隆佐是幾何群論。

• Just an ability anthropology.

只是一種能力的人類學。

• And then there's this like my absolute favorite part of this is the laughing crying emoji because Riley is just like cracking herself up here or Riley's I think really saying here has to do with just like how much things commute, right?

然後還有這個像我絕對喜歡的部分是笑著哭的表情符號，因為萊莉就像在這裡破解自己，或者萊莉的我認為真正的說在這裡有做只是像多少東西通勤，對嗎？

• So you're used to A.

所以你已經習慣了A。

• B equals B.

B等於B。

• A.

A.

• That's when things commute.

這時事情就會發生變化。

• And then you can sort of do math where that's not true anymore for like you know A B equals B.

然後你可以做一些數學題，這不再是真的，比如你知道A B等於B。

• A.

A.

• Times a new thing called C.

時代的一個新東西叫C。

• That's just not the math you learned in school.

這不是你在學校學到的數學。

• Like what is this new thing and how do you understand it?

比如這個新東西是什麼，你怎麼理解它？

• Well it turns out this is the math of this model here.

好吧，事實證明這就是這個模型在這裡的數學原理。

• This is a model of what's called nil or nil potent geometry.

這是一個所謂的無或無勢力的幾何模型。

• It's pretty cool as I rotate it.

在我轉動它的時候，它是相當酷的。

• You can probably see that there's some complexity here from some angles.

你可能可以看到，從某些角度看，這裡有一些複雜性。

• It looks one way from some angles.

從某些角度看，它是一個方向。

• You see different kinds of structure.

你看到不同種類的結構。

• This is my favorite.

這是我的最愛。

我喜歡思考這個問題。

• A.

A.

• And B.

而B.

• Are kind of moving horizontally and see is kind of moving up in this model.

在這個模型中，是一種水準的移動，看到的是一種向上的移動。

• So that really shows you something about what Riley's calling geometric group theory.

是以，這真的向你展示了一些關於萊利所謂的幾何群論的東西。

• You start with just like the group theory of how to multiply things.

你從就像如何乘以事物的群論開始。

• And it builds geometry for you like you know it's sort of stringing a bunch of words together and trying to make meaning out of them.

它為你建立了幾何學，就像你知道的那樣，它是把一堆詞串在一起，並試圖從它們中獲得意義。

• And I think that's the joke here.

而我認為這就是這裡的笑話。

• And like all jokes when you try to explain it.

就像所有的笑話一樣，當你試圖解釋它時。

• It sounds desperately unfunny at ruth Townsend Law question for mathematicians, why don't we solve maths problems in a particular order of operations?

在魯斯-湯森德的法律問題上，聽起來令人絕望地感到不快，為什麼我們不按照特定的運算順序來解決數學問題？

• E.

E.

• G.

G.