關於 essentially meaning ，我們在網路上蒐集到這些相關的討論、資訊與評價

Back for more! After getting complete blood and urine tests at BodyConscious Bkk with an hour long consultation each about what supplements and lifestyle changes we need to move closer towards optimal health, Byron and I received another round of acupuncture and sound healing. Ahhhhh so peaceful 🥰🥰🥰

This was after Byron’s Shockwave Therapy to specifically target his chronic shoulder pain due to old neck injury. ( He broke his neck pole vaulting at age 18) Look at the size of the needles in his head! 😱 But apparently they acted as a strong pain relief and he was flying high on endorphins afterwards with a big goofy grin on his face 😂 He will need to do these weekly to treat the years of lack of mobility due to fused vertebra and metal pin in his neck but so far it seems to be doing something. Will let you know how it goes!

As for me, I was given a special Gut Health Massage for my digestive issues and emotional blockages. Based on the same technique as Chi Nei Tsang, which helps release stress and promotes healing by using techniques of massage directly over the navel and surrounding abdominal area where stress, tension and negative emotions accumulate and congest. Apparently I’m storing a fair amount of stress and anxiety said the therapist as she kneaded and rolled around my gut. Gives a whole new meaning to having a “knot in your belly” 😅 Immediately after I felt a deep sense of ease and was able to breathe more deeply (which is essentially the key to release of stress and negative emotions)

We will be receiving our personalized supplement and vitamin packs soon and I’ll be back to share more!

#wellnessjourney #bodyconsciousbkk #guthealthmassage #chineitsang #shockwavetherapy #acupuncture #soundhealing

📜 [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

Not Impressed by the Reputations of Men

“God had given me a clear revelation to go and confer with the other apostles concerning the message of grace I was preaching to the non-Jewish people. I spoke privately with those who were viewed as senior leaders of the church. I wanted to make certain that my labor and ministry for the Messiah had not been based on a false understanding of the gospel...Even the most honored and esteemed among the brothers were not able to add anything to my message. Who they are before men makes no difference to me, for God is not impressed by the reputations of men.” (Galatians‬ ‭2:2, 6‬ ‭TPT‬‬)

I love the apostle Paul’s mindset. He was not ‘starstruck’ by Peter, James, and John.

Whereas others would have been intimidated by the fame and reputation of the apostles in Jerusalem, Paul wasn’t.

He was led by God to go and meet them, and the only reason he wanted to speak with them was to confirm that he was preaching the correct Gospel.

Paul valued praise from God, not the praises of men.

If God is not impressed by the reputations of men, then as His children we shouldn’t be impressed too.

There is no need to feel intimidated when speaking to someone with a glorified title.

“When he went into the house of one of the rulers of the Pharisees on a Sabbath to eat bread, they were watching him.” (Luke‬ ‭14:1‬ ‭WEB‬‬)

Jesus went to a party where the most respected Pharisees were, and He still spoke straightforwardly, without mincing His words. He was not afraid to speak the truth, even if it offended reputable men.

“He spoke a parable to those who were invited, when he noticed how they chose the best seats, and said to them, “When you are invited by anyone to a marriage feast, don’t sit in the best seat, since perhaps someone more honorable than you might be invited by him, and he who invited both of you would come and tell you, ‘Make room for this person.’ Then you would begin, with shame, to take the lowest place. But when you are invited, go and sit in the lowest place, so that when he who invited you comes, he may tell you, ‘Friend, move up higher.’ Then you will be honored in the presence of all who sit at the table with you. For everyone who exalts himself will be humbled, and whoever humbles himself will be exalted.” He also said to the one who had invited him, “When you make a dinner or a supper, don’t call your friends, nor your brothers, nor your kinsmen, nor rich neighbors, or perhaps they might also return the favor, and pay you back. But when you make a feast, ask the poor, the maimed, the lame, or the blind; and you will be blessed, because they don’t have the resources to repay you. For you will be repaid in the resurrection of the righteous.”” (Luke‬ ‭14:7-14‬ ‭WEB‬‬)

Jesus’ words above are essentially meaning that the guests at the party were pretentious hypocrites, all trying to curry favor with the rich and famous. Think about how offensive these words would be to most people at the party.

We are a new creation in Christ in contrast to the children of Adam. We are the new and improved version 2.0. Children of Adam are transgressors, whereas children of God are royal priests and heirs of His estate.

Even the wealthiest unbeliever is only like a piece of firewood, due to be thrown in the unquenchable fires of Hell when he dies.

As for speaking to fellow believers, God’s word says that we are one in Christ and that titles don’t matter—we are all of equal standing. We are all saved by one Lord, born-again of the same Spirit, and none of us earned this salvation—it’s all by grace through faith.

“For you are all children of God, through faith in Christ Jesus. For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free man, there is neither male nor female; for you are all one in Christ Jesus.” (Galatians‬ ‭3:26-28‬ ‭WEB‬‬)

Don’t get me wrong, Paul respected the office of apostle which Peter, James, and John held. These positions are given by God. Paul also teaches us to respect the governing bodies and submit to them for the Lord’s sake.

We should also respect our leaders in church for the sake of the offices that they hold since they are ordained by God. Give them proper honor for the sake of the office. Submit to those who have the authority over us, as this authority was given by God.

However, we don’t need to fear reputable men. You don’t have to shrink back, feeling like you are somehow less important, less worthy, or less loved. God loves you even as (as much as) He loves Jesus—that’s how important you are to Him!

If people abuse their office of authority and mistreat you, they themselves will be accountability for it before Jesus. Maybe their eternal rewards will be given to you instead, to restore you for the injustice.

“Jesus answered, “You would have no power at all against me, unless it were given to you from above. Therefore he who delivered me to you has greater sin.”” (John‬ ‭19:11‬ ‭WEB‬‬)

No one can harm you when God is protecting you. Men have no power of their own. Therefore, be bold and have confidence in Christ. Straighten your shoulders and back, and raise your chin up. Be set free from the fear of reputations of men!

I shared more about the time when Jesus went to that Pharisee’s party in my book “Messiah’s Miracles: The Power of Having Faith in Jesus Christ”. Did you know that He healed a man with dropsy there? There is a spectacular lesson in it. See God’s Grace and love towards you in all the 37 recorded miracles of Jesus Christ, and let faith arise for your own supernatural breakthroughs: https://bit.ly/messiahs-miracles

2018方丈和尚果東法師新春祝福 平安無事(英文)
For 2018 Dharma Drum Mountain has chosen “peace and freedom from troubles” as the theme of the year. The abbot president of DDM urges people to cultivate a harmonious heart at peace, with happiness in mind free from troubles. In hoping for a peaceful and happy new year, let us all learn to fulfill our duties and take responsibility, then all tasks, big or small, are good tasks; if we can cultivate merit and wisdom, then all practices, major or minor, are Buddhist practices; if we can take up and let go freely, then all happenings, serious or insignificant, are essentially nothing at all. We should again start from the mind to practice the Dharma, in order to gradually realize the true meaning of peace and freedom from troubles.

コーラ （Regular Coke & Diet Coke）とメントス（Mentos）で夏の理科の実験！

用意するものは
コーラ （Regular Coke & Diet Coke）とメントス（Mentos）

コツは
☆ Mentosを全て一気に入れる（コレが意外に難しい！）
☆ 常温のCokeを使う

【この動画に出てくる例文】

★ What happens when you mix Coke and Mentos?
★ Let's see what happens!
★ Trial and error
★ Let's find out!
★ Why does this happen?
★ This happens.
★ It's your turn to try!
★ Was it higher?

☆ 解説と和訳 ☆

A bottle of Coke is full of bubbles.
コーラのボトル内には泡がいっぱいある。
When you drop any sort of object into a bottle of Coke, bubbles form on the surface of the object. This is called “nucleation”.
コーラのボトルの中に何らかの物質を入れると、その表面に泡が形成される。これは「核形成（または核生成）」と呼ばれる。
The surface of a Mentos is very rough, meaning it’s made up of lots of tiny craters like the moon.
メントスの表面はボコボコしている。つまり、その表面は月のように多くの小さなクレーターでできている。
These tiny pits create a large surface area and essentially provide many more “nucleation sites”.
これらの小さなくぼみにより表面積が拡大され、結果、「核形成の場」が倍増される。
When all of the gas (CO2) is released, it forces Coke up and out of the bottle.
全てのガス（二酸化炭素）が〈泡から〉放出され、〈それが圧力となり〉ボトルからコーラが吹き上げる。
（注）〈 〉は補足。

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