@TrustlessState @ArthurB @danrobinson Now, we get to pairings. Described in additive notation, pairings let you "multiply" two elliptic curve points *by each other* (the result is not a curve point, but a different thing called a "GT element")
A * B = X
(3A) * B = A * (3B) = X⚬X⚬X
(A + C) * B = A * B ⚬ C * B

@TrustlessState @ArthurB @danrobinson 现在，我们开始配对。用加法表示法描述，配对让您“乘”两个椭圆曲线点*彼此*（结果不是曲线点，而是称为“GT 元素”的不同事物）
A * B = X
(3A) * B = A * (3B) = X⚬X⚬X
(A C) * B = A * B ⚬ C * B

@TrustlessState @ArthurB @danrobinson But people "born and raised" in elliptic curve land are more likely to prefer additive notation, because it's more convenient.
Eg. in Schnorr signatures:
Sign: s = r - x * e
Verify: R = G * s + X * e
In additive notation, it's easier to see the "symmetry" between the two eqs.

@TrustlessState @ArthurB @danrobinson 但是在椭圆曲线领域“出生和长大”的人更有可能更喜欢加法符号，因为它更方便。
例如。在 Schnorr 签名中：
符号：s = r - x * e
验证：R = G * s X * e
在加法表示法中，更容易看到两个方程之间的“对称性”。

@TrustlessState @ArthurB @danrobinson "Traditional cryptographers" often tend to prefer multiplicative notation, in part because in forms of cryptography that were popular before elliptic curves, the equivalent to ⚬ literally was multiplication. RSA, for example, uses multiplication and exponentiation.

@TrustlessState @ArthurB @danrobinson “传统密码学家”通常更喜欢乘法符号，部分原因是在椭圆曲线之前流行的密码学形式中，相当于 ⚬ 字面意思是乘法。例如，RSA 使用乘法和求幂。

@TrustlessState @ArthurB @danrobinson "Additive notation" means using the "⚬ = addition, repeated ⚬ = multiplication" metaphor for elliptic curve points.
"Multiplicative notation" means using the "⚬ = multiplication, repeated ⚬ = exponentiation" metaphor.

@TrustlessState @ArthurB @danrobinson “加法表示法”意味着对椭圆曲线点使用“⚬ = 加法，重复 ⚬ = 乘法”隐喻。
“乘法符号”是指使用“⚬ = 乘法，重复 ⚬ = 取幂”的比喻。

@TrustlessState @ArthurB @danrobinson The reason why "⚬ = addition, repeated ⚬ = multiplication" and "⚬ = multiplication, repeated ⚬ = exponentiation" are both valid metaphors is because when we work with numbers, * is repeated +, and ^ is repeated *.
2 * 4 = 2 + 2 + 2 + 2
2 ^ 4 = 2 * 2 * 2 * 2

@TrustlessState @ArthurB @danrobinson “⚬ = 加法，重复 ⚬ = 乘法”和“⚬ = 乘法，重复 ⚬ = 取幂”都是有效的隐喻，因为当我们处理数字时，* 重复，^ 重复*。
2 * 4 = 2 2 2 2
2 ^ 4 = 2 * 2 * 2 * 2

@TrustlessState @ArthurB @danrobinson For example, the standard way to convert a private key `k` into the corresponding public key `K` is to agree on a standardized generator point `G`, and apply the operation to it `k` times:
K = G⚬G⚬G ... G [with `k` G's]

@TrustlessState @ArthurB @danrobinson 例如，将私钥`k`转换为对应的公钥`K`的标准方法是约定一个标准化的生成点`G`，并对其应用`k`次操作：
K = G⚬G⚬G ... G [带 `k` G's]

@TrustlessState @ArthurB @danrobinson There is an operation A⚬B -> C on elliptic curve points, and we often do it to the same point many times: A⚬A⚬A ... ⚬A -> D
There are 2 ways to talk about this:
1. ⚬ = "addition", repeating it = "multiplication"
2. ⚬ = "multiplication", repeating it = "exponentiation"

@TrustlessState @ArthurB @danrobinson 有一个操作A⚬B -

@danrobinson The chad take is to use additive notation even for the GT group.

@danrobinson 乍得采取的是即使对于 GT 组也使用加法表示法。

@Nowooski "God, brought to you by Samsung" https://t.co/6pHpLTUpm1

@Nowooski “上帝，三星带给你的” https://t.co/6pHpLTUpm1

@sama Internet opened a new low hanging fruit era and most of the low hanging fruits have now been picked?

@sama Internet开启了一个新的低挂水果时代，现在大部分低挂水果都被摘了？

@0xstark @davidgerard I've had feedback to my drafts that was significant enough that it caused me to rethink the topic and rewrite the entire post. Any of the frequently appearing "special thanks" names has done that at least once.

@0xstark @davidgerard 我收到了对草稿的反馈，这些反馈非常重要，以至于我重新思考了这个话题并重写了整篇文章。任何经常出现的“特别感谢”的名字都至少做过一次。

@RJMacReadyBTC dude ur ability to hold coins and get rich and shitpost about it on twitter depends on elliptic curve math, show some respect

@RJMacReadyBTC 伙计，你持有硬币和致富的能力以及在推特上发布关于它的狗屎取决于椭圆曲线数学，表示尊重

Thread by @davidgerard, criticizing @VitalikButerin. https://twitter.com/davidgerar...

@davidgerard 的主题，批评 @VitalikButerin。 https://twitter.com/davidgerar...

The thing you do with lots of elliptic curve points and lots of scalars

你用很多椭圆曲线点和很多标量做的事情

What kind of layer 3s make sense?
https://vitalik.ca/general/202...

什么样的第 3 层有意义？
https://vitalik.ca/general/202...

RT: the merge being uneventful means the engineers are absolutely fucking elite

RT：合并的顺利意味着工程师绝对是他妈的精英

RT: Congratulations to the Ethereum Team, @VitalikButerin and everyone who worked on the merge to proof of stake last night! This move will reduce worldwide electricity consumption by more than .2%!

RT：祝贺以太坊团队、@VitalikButerin 以及昨晚为权益证明合并工作的所有人！此举将使全球电力消耗减少 0.2% 以上！

RT: It's my honor today to announce the launch of a collaborative book project with my hero, @audreyt, "Plurality: Technology for Collaborative Diversity and Democracy": https://www.plurality.net/. As you will read if you click through, this will be a unique project, mirroring in the

RT：今天我很荣幸地宣布与我的英雄@audreyt 启动一个合作图书项目，“多元化：协作多样性和民主的技术”：https://www.plurality.net/。如您点击后将看到的，这将是一个独特的项目，在

@robinhanson Often, there is a natural alliance for the first half of the journey (unseating or at least building arguments against the existing order) but not for the second half (building the new one). The misalignments that will arise in the second half are often obscured in the first.

@robinhanson 通常，在旅程的前半部分（取消或至少建立反对现有秩序的论据）会自然联盟，但在后半部分（建立新秩序）则不会。下半场出现的偏差往往在上半场被掩盖。

RT: Can't say enough about all of the builders, researchers, coordinators and more that made this all happen.
It's an absolutely incredible feat to transition a globally used blockchain to PoS without most end users even noticing or having to do anything.
Truly incredible. Cheers.

RT：关于所有使这一切发生的建设者、研究人员、协调员等等，说得再多也不为过。
在大多数最终用户甚至没有注意到或不必做任何事情的情况下，将全球使用的区块链转换为 PoS 绝对是一项令人难以置信的壮举。
真是不可思议。干杯。