📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

開源報報精彩內容回顧

內容摘要

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✅ 你所不知道的 Javascript 開源電子書
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✅ 一個輕量級的 JavaScript 實用工具，用於建立 Markdown + LaTeX 文件
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✅ 手繪風格的 react 圖表程式庫
✅ 用於簡單的客戶端/ 伺服器端 GraphQL 快取 Npm 套件
✅ 用於基於 React 框架（Gatsby 和 Next.js ）的網站編輯工具套件
✅ 將你的 Raspberry Pi 變成一個內建 DNS 解析的廣告阻隔伺服器
✅ Kubernetes Cluster 檢查器最佳實踐
✅ 一份可縮短 Flutter 初學者和到開發出容易維護，乾淨程式碼 Flutter 專案差距的教學指南
✅ 資料科學的就業建議
✅ 適合機器學習和資料科學的乾淨程式碼概念
✅ 附有 Jupyter notebook 的金融模型演算法收集
✅ VS Code 中做及時的 GraphQL API 的開發
✅ 為 OpenPGP 初學者準備的加密套件。 它被設計成透過瀏覽器或可獨立執行的執行程式
✅ Redis 桌面管理程式

https://softnshare.com/opensource-news-005-machine-learning-cleancode/

分享好文，中學生要學電腦嗎？
作者：創新工場CTO、人工智慧工程院執行院長 王詠剛

文章来自半轻人微信公众号（ban-qing-ren）
………………………………

朋友的孩子高中剛畢業，已拿到美國頂尖大學（非電腦專業）的錄取通知。疫情影響，不知何時才能去學校報到。孩子想抓緊學習一下程式設計，為大學打好基礎。這孩子找我聊了一個多小時，從如何學程式設計，聊到非電腦專業和電腦專業的路徑差異，又聊到如何從不同角度認識電腦與程式設計。聊得比較寬泛，不知是否對這孩子有用。

回想我自己的高中時代：那時雖迷戀程式設計，卻完全沒有懂行的人指導。在我們那個四線城市的廠礦中學裡，開設電腦興趣課的老師知道的資訊還沒我多。我高一時跑到北京中關村逛街，卻完全沒意識到中國第一代頂尖程式師當時就在我身邊的低矮辦公樓裡寫代碼（這話說得並不準確，比如求伯君那年就主要是在珠海做開發），鼎鼎大名的UCDOS、WPS、CCED就出自他們之手……我在當時街邊的一家書店（位置似乎就在今天的鼎好大廈對面）買到了許多種印刷品質極低劣的電腦圖書。用今天的標準看，那就是一批盜版影印或未授權翻譯的國外圖書。可那批書竟成了我高中時代最寶貴的程式設計知識來源。

顯然，我在高中時根本就是野路子學電腦。現在後悔也沒用，當時我的眼界或能觸及的資源就那麼多。如果能穿越回30年前，我該對喜歡程式設計的自己說些什麼呢？這些年，我與世界上最好的一批程式師合作過，也參與過世界上最有價值的軟體系統研發——我所積累的一些粗淺經驗裡，有哪些可以分享給一個愛程式設計的中學生？

【問題1】中學生要不要學電腦？

當然要！

每個中學生都要學。只不過——建議大部分中學生使用“休閒模式”，小部分（不超過10%）中學生使用“探險模式”。

啊？兩個模式？那我該進入哪個模式？⟹請跳轉至【問題2】

【問題2】選哪個模式？

你癡迷電腦嗎？比如，你玩遊戲時會特別想知道這遊戲背後的代碼是如何編寫的嗎？再比如，就算老師家長不同意你學電腦，甚至當著你的面把電腦砸了，你也要堅持學電腦嗎？如果是，恭喜你進入“探險模式”⟹請跳轉至【問題200】

你對數學有興趣嗎？比如，你看到街邊建築的曲線，就會在腦子裡琢磨曲線對應的函數或方程嗎？每當手裡攥著幾粒骰子，你就會不由自主地計算概率嗎？如果是，歡迎進入“探險模式”⟹請跳轉至【問題200】；當然，如果有些猶豫，也可以先進入“休閒模式”⟹請跳轉至【問題100】

即便你對電腦和數學興趣不大，家長、老師還是強烈建議你學電腦嗎？就算你一百個沒時間一千個不願意，家長、老師還是會逼著你學電腦嗎？如果是，建議你主動進入“休閒模式”並向家長、老師彙報說“我已經按照前谷歌資深軟體工程師的專業建議在認真學程式設計了”⟹請跳轉至【問題100】

其他情況，一律進入“休閒模式”。⟹請跳轉至【問題100】

【問題100】休閒模式 | 主要學什麼？

“休閒模式”將電腦視為我們生活、工作中的必備工具，主要學習如何聰明、高效、優雅地使用計算設備。這裡說的計算設備，包括所有形式的電腦、手機、遊戲機、智慧家電以及未來一定會進入生活的自動駕駛汽車。

什麼什麼？你已經會用電腦、會玩手機、會打遊戲了？別著急，慢慢往下看。

【問題101】休閒模式 | 我會用搜尋引擎嗎？

我知道你會用百度搜習題答案。但，習題答案不是知識。你會用搜尋引擎來搜索和梳理知識嗎？請試著用電腦和你喜歡的搜尋引擎來解決如下兩個問題：

（1）圓周率𝜋的計算方法有多少種？每種不同的計算方法分別是由什麼人在什麼時代提出的？借助電腦，今天人們可以將圓周率𝜋計算到小數點後多少位？將圓周率𝜋計算到小數點這麼多位元，一次大概需要花掉多少度電？

（2）全球大約有多少個廁所？在發展程度不同的國家，分別有多少比例的人可以享用安裝了抽水馬桶的衛生廁所？為什麼比爾·蓋茨曾大力推動一個設計新型馬桶的研發專案？比爾·蓋茨的公益組織在這個專案上大約花費了多少資金，最終收到了多大的效果？

如果你沒法快速得到上述問題的全部答案，那就給自己設一個小目標：一個月內，學會用搜尋引擎系統地獲取、梳理一組知識點的全部技巧。

【問題102】休閒模式 | 接下來學什麼？

建議學好典型的工具軟體。比如，我知道你會用Office了，但用Office和用Office是很不一樣的。對生活、學習、工作來說，學好、學透一個工具軟體比鑽研程式設計技巧更實用。

 你會用Excel來管理班級公益基金的預算和實際收支情況嗎？
 你會用Excel做出過去20年裡全球大學排名的演變趨勢圖嗎？
 你會用Word排版一篇中學生論文嗎？論文中的圖表和最後的參考文獻部分該如何排版？
 你會用Word編排一份班級刊物，包含封面、扉頁、目錄、插圖頁、附錄、封底等部分，可以在列印後直接裝訂成冊嗎？
 PowerPoint呢？你有沒有研究過蘋果公司發佈會上那些幻燈片的設計？當約伯斯（多年以前）或蒂姆·庫克站在幻燈片前的時候，他們的演講思路是如何與幻燈片完美結合的？

還有哦，別忘了學學如何為數碼照片做後期，如何用電腦或手機剪視頻，如何為剪輯好的視頻配字幕，如何將照片、音樂、視頻等素材結合起來，做出一段吸引人的快手/抖音短視頻。

最後，抽空玩玩那些設計精妙的遊戲吧，比如《紀念碑穀》、《塞爾達傳說：曠野之息》之類；同時，遠離那些滿屏廣告，或者一心騙你在遊戲裡充值花錢的垃圾。

【問題103】休閒模式 | 不學學知識嗎？

當然要學知識。下面每種實用的電腦知識都夠大家學一陣子了。

（1）色彩知識：你知道同一張數碼照片在不同品牌的手機螢幕上、不同的電腦螢幕上、不同的智慧電視上顯示時，為什麼經常有較大色差嗎？你知道有一些色彩只適合螢幕顯示，不適合列印輸出嗎？你知道軟體工具裡常用的RGB、HSL之類的色彩空間都是什麼意思嗎？如何在設計PowerPoint幻燈片時選擇一組和諧美觀的色彩？

（2）字體知識：你知道什麼是襯線字體，什麼是無襯線字體嗎？你知道網頁中常用的英文字體都有哪些嗎？你知道商務演講時最適用于幻燈片的英文字體有哪些嗎？你知道電腦和手機常用的黑體、宋體、仿宋體、楷體等中文字體分別適合哪些實際應用場合嗎？你會將不同字體混排成一個美觀的頁面嗎？

（3）網路知識：你知道5G是什麼嗎？你知道5G和4G在通信頻寬、通信距離上的具體區別嗎？你知道什麼是路由器，什麼是防火牆嗎？你知道如何配置路由器，如何配置防火牆嗎？微信或QQ聊天時，對方發的文字、語音或視頻是如何傳送到你的手機上的？

（4）應用知識：淘寶中搜索得到的商品資訊是從哪裡來的？商品是按什麼方式排序的？為什麼購物APP經常會推薦給你一些曾經買過、看過的商品？你知道如何為自己建立個人網站嗎？你知道如何管理微信公眾號嗎？

（5）安全知識：你知道網路上的釣魚攻擊是怎麼回事兒嗎？你知道什麼是電腦漏洞嗎？你知道駭客為什麼想把一大批受攻擊的電腦變成可以遠端操控的傀儡機嗎？你知道為什麼現在很多手機APP都要通過短信發送驗證碼嗎？如果驗證碼被壞人截獲，你會面臨哪些風險？

這裡只是舉例。實用的電腦知識還有很多。大家可以自己發掘。

【問題104】休閒模式 | 我需要學程式設計嗎？

可以學，但不是必須。即便學，也只需要根據自己的需要，學那些最能幫你解決現實問題的部分。

【問題105】休閒模式 | 我該學什麼程式設計語言？

在“休閒模式”裡，電腦就是工具，程式設計也是工具，夠用就好。學什麼程式設計語言，完全看你想要電腦幫你做什麼。

• 如果你想對資料處理有更多自主權，那不妨學學Python；
• 如果你想做簡單的交互演示程式，那就先把JavaScript學起來；
• 如果你想更好、更快地寫論文，那不妨學學LaTeX（什麼什麼，LaTeX不是程式設計語言？你太小看LaTeX了）；
• 如果你想學做簡單的手機APP，那麼，Android手機就學Java，蘋果手機就學Swift好了；
• 如果你只想知道程式設計是怎麼回事，那……從Python或JavaScript開始就行。其實，跟五六歲的小朋友一起學學Scratch圖形程式設計也不錯。

【問題106】休閒模式 | 我需要學人工智慧嗎？

在“休閒模式”裡，最需要學的不是“人工智慧的實現原理”，而是“什麼是人工智慧”，以及“人工智慧能做什麼，不能做什麼”。

• 在手機上試一試，人工智慧做語音辨識時能做到什麼水準？哪些話容易識別，哪些話不容易識別？
• 打開機器翻譯軟體，試一試哪些資訊翻譯得好，哪些資訊翻譯得不好？
• 手機上的拍照軟體一般都有人臉識別功能。試一試人臉識別在什麼場景下做得好，什麼場景下做得不好？
• 找一部講人工智慧的科幻電影，用自己的判斷解讀一下，電影裡哪些技術有可能成為現實，哪些技術存在邏輯矛盾。

【問題107】休閒模式 | 推薦什麼參考書、參考文獻？

書不重要，豆瓣評分7分以上的電腦應用、程式設計甚至科普類圖書都可以拿來翻翻。

直接在知乎裡搜索你想瞭解或學習的知識點可能更有效率。

如果你意猶未盡，覺得自己剛活動開筋骨，還想挑戰更高層次，歡迎進入“探險模式”。⟹請跳轉至【問題200】

否則，“休閒模式”到此結束。⟹請離開此問答

【問題200】探險模式 | 主要學什麼？

“探險模式”需要有挑戰精神。電腦科學的世界技術演進快，脈絡複雜，要想在探索時不迷路，你得通過有順序、有系統地學習電腦知識，慢慢構建出一張可以在未來幫你走得更遠的思維地圖來。

在“探險模式”裡，電腦就不止是一件能快速計算的工具了。電腦更像是我們大腦的一種延伸。這既包括認知能力的延伸，也包括認知邏輯的延伸。隨著學習深入，大家會逐漸體會到電腦所具有的多維度能力：

 電腦是一種可以表示不同類型資訊（數、符號、文字、語音、圖像、視頻、虛擬空間、抽象邏輯）的“資訊管理機”；
 同時，電腦也是一種可以連續執行指令以完成特定的資訊處理任務的“指令處理機”；
 同時，電腦還是一種可以在知識與邏輯層面完成特定推理任務的“知識推理機”；
 同時，電腦也是一種可以從人類給定的資料或自我生成的資料中總結規律，建立模型，自主完成某些決策的“智慧學習機”。

“探險模式”的目標就是盡可能準確地認識電腦，掌握有關電腦運行的最基本規律。有了這些基礎。未來在大學期間或工作中，你就能更容易地設計電腦軟硬體系統，或是設計出碳基大腦（人類）與矽基大腦（機器智慧）之間的最佳協作方案。

【問題201】探險模式 | 我的英語水準足夠嗎？

蘋果每年秋季的新品發佈會，不加字幕的話，你能聽懂多少？

 能聽懂大部分：建議在學習電腦的過程中，盡可能使用英文教材、英文文檔。
 能聽懂小部分：建議將原來準備學電腦的時間，分出一部分來學英語。
 只能聽懂“你好”“再見”之類：⟹請離開此問答。然後，把原來準備學電腦的時間用於學英語，六個月後再回來。

【問題202】探險模式 | 我的數學水準足夠嗎？

 如果你是數學和數學應用小能手——較複雜的數學問題總能快速找到核心思路，或快速簡化為簡單問題；很容易就能將抽象概念映射到具體的數學圖形，或將數學問題與相應的現實問題關聯在一起：請繼續探險之旅。
 如果你應付正常數學課程感到吃力：建議將原來準備學電腦的時間，分出一部分來學數學。
 如果你還搞不清楚什麼是方程、函數、集合、概率……：⟹請離開此問答。然後，把原來準備學電腦的時間用於學數學，六個月後再回來。

【問題203】探險模式 | 為什麼強調英語和數學？

（1）統計上說，最好的電腦參考資料大都是英文寫的，最好的電腦課程大都是用英文講的，最新的電腦論文大都是用英文發表的。

（2）函數、方程、坐標系、標量、向量、排列組合、概率這些中學數學裡會初步學習到的數學知識，是電腦科學的基礎。

【問題204】探險模式 | 電腦知識那麼多，正確的學習順序是什麼？

最重要的順序有兩個。建議先從順序一開始，學有餘力時兼顧兩個順序。

順序一：自底向上，即，自底層原理向上層應用拓展的順序。

 電腦原理的基礎知識：
 為什麼每台電腦（包括手機）都有CPU、記憶體和外部設備？
 （馮·諾依曼體系結構的）記憶體中為什麼既可以存儲資料，也可以存儲指令？
 CPU是如何完成一次加法運算的？
 程式設計語言的基礎知識：
 資料類型，值，變數，作用域……
 語句，流程控制語句……
 過程、方法或函數，類，模組，程式，服務……
 編譯系統的基本概念：
 電腦程式是如何被解釋或編譯成目標代碼的？
 演算法和資料結構的基礎知識：
 陣列，向量，鏈表，堆，棧，二叉樹，樹和圖……
 遞迴演算法，排序演算法，二叉樹搜索演算法，圖搜索演算法……
 應用層的基礎知識：
 為什麼電腦需要作業系統？設備驅動程式是做什麼的？
 網路通信的基本原理是什麼？流覽器是怎麼找到並顯示一個網頁的？
 資料庫是做什麼用的？
 虛擬機器是怎麼回事？
 人工智慧系統的基礎知識：
 先熟悉些線性代數、概率和數學優化的基礎知識。
 什麼是機器學習？從簡單的線性回歸中體會機器學習的基本概念、基本思路。
 什麼是神經網路？什麼是深度神經網路？為什麼神經網路可以完成機器學習任務？
 如何使用PyTorch或TensorFlow實現簡單的深度學習功能？

順序二：自頂向下，即，自頂層抽象邏輯向下層具體邏輯拓展的順序。

• 電腦的本質是什麼？
• 什麼是圖靈機？什麼是通用圖靈機？
• 什麼是讀取﹣求值﹣輸出迴圈（Read–eval–print Loop，REPL）？
 如何用自頂向下的方式理解（解析、解釋、編譯）一段程式碼？
• 靜態語言和動態語言的區別？
 如何理解變數與資料類型之間的綁定關係？
• 什麼是函數式程式設計？
 程式設計語言中，函數的本質是什麼？
 函數為什麼可以像一個值一樣被表示、存儲、傳遞和處理？

• 什麼是物件導向？
 類的本質是什麼？
 如何用物件導向的方式定義個功能介面？
 如何依據介面實現具體功能？
• 什麼是事件驅動？
 什麼是事件？事件如何分發到接收者？
 如何在事件驅動的環境中理解代碼的狀態和執行順序？

【問題205】探險模式 | 如何提高程式設計水準？

在掌握基本知識體系的基礎上，學好程式設計只有一條路：多程式設計，多參加程式設計比賽，多做程式設計題，多做實驗項目，多找實習機會——其中，能參與真實專案是最有價值的。

【問題206】探險模式 | 該從哪一門程式設計語言學起？

 我個人推薦的程式設計入門語言（可根據情況任選）：
 Python
 Java
 Swift
 C#
 JavaScript / TypeScript
 Ruby
 ……
 可能不適合入門，但適合後續深入學習的語言：
 C
 C++
 Go

 Objective-C
 組合語言
 機器語言（CPU指令集）
 Shell Script
 Lua
 Haskell
 OCaml
 R
 Julia
 Erlang
 MATLAB
 ……

【問題207】探險模式 | 如何選參考書和參考資料？

（1）強烈推薦的參考書和參考資料：

• MIT、Stanford、CMU、UC Berkeley這四所大學中任何一個電腦專業方向使用的教學參考書或參考資料。網上可以查到這些學校電腦專業方向的課程體系，有的學校甚至公開了課程視頻。其中往往會列舉參考書和參考資料連結。
• 維琪百科（英文）上的數學、電腦科學相關條目。
• Github上star數在1000以上的開原始程式碼和開來源文件。

（2）強烈推薦但須小心辨別的參考資料：

 知乎上的數學、電腦科學相關條目。使用時需要格外注意三件事：
 儘量只看高贊答案或高贊文章；
 辨別並避開廣告軟文；
 辨別並避開純抖機靈的故事或段子。
 Stack Overflow上的程式設計問題解答：
 自己動手實驗，辨別解答是否有效。
 CSDN上的程式設計問題解答：
 自己動手實驗，辨別解答是否有效。

（3）其他推薦的參考書和參考資料：

 國內專業作者寫作的專業技術書籍（豆瓣評分7分以上的）。
 大廠（Google、Facebook、Microsoft、Amazon、阿裡、騰訊、百度、頭條等）資深工程師的技術公號、專欄、博客等。

 著名圖書系列：如O’Reilly的動物封面的系列圖書（請注意最新版本和時效性）。
 國內翻譯的著名技術圖書（譯本在豆瓣評分7分以上的）。

（4）儘量避免的參考書和參考資料：

• 已經過時的圖書或參考資料。
• 作者或譯者人數比章節數還多的專業圖書。
• 百度百科上的數學或電腦科學相關資料。

什麼什麼？你這篇問答居然沒有推薦一本具體的圖書？是，沒錯。如果你覺得即便有了上面的線索，自己還是找不到好書好資料，那也許你還是適合“休閒模式”⟹請跳轉至【問題100】

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Makeup by Kylah - Logan 狼人教學

材料:
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Video by Kylah Chan
Edited by 阿尤 Simon


-------------------------------------------------
Makeup Artist | Blogger
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Merry Christmas Everyone~^^
聖誕小精靈常常會在聖誕節的前夕出沒在有小朋友的家中~
小朋友若有乖巧 聖誕老公公才會發禮物唷!!

〔同場加映〕 這次 Ariel要教你用簡易的方式做出(假皮)精靈耳朵和尖尖的鼻子!!!

~記得可以轉成HD收看喔~
如果喜歡這則影片的話~
記得跟朋友【分享】、【訂閱】我或按個【讚】吧!



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👉🏻Ariel.Lin特效x化妝分享頻道
https://www.facebook.com/Arielinfxmakeup/


影片中使用的產品/Products Used:
皮膚蠟 Ben Nye Nose & Scar Wax
液態乳膠 Ben Nye Liquid Latex
植村秀武士刀眉筆 Shu uemura eyebrow pencil
眼影盤 Urban Decay's Naked 2 Palette
超激細抗暈眼線液 Maybelline Hypersharp Liner
唇釉 Giorgio Armani Lip Maestro Chinese Lacquer


Music:
Kevin MacLeod - Dance of the Sugar Plum Fairies
「Creative Commons Attribution」http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100270