#NFTsummer A few weeks ago, we interviewed Xixi Huang (AW#17) in Mandarin and as the AppWorks Fellow who helps us out on the blockchain side, Xixi has a lot of ideas that are worth sharing to a bigger audience. Here's his interview in English:
西西 (Xixi) 黃士晉 is an AppWorks #17 alumni and co-founder of Rydeit. His mission is to bring the applications of blockchain to everyday life because he believes that blockchain can make the world a more fair and better place. As an AppWorks Fellow, he is responsible for guiding founders to think about blockchain and providing insights on blockchain-related investment deals. Before AppWorks, he led his previous team to build more than 10 dapps, including famous games in Taiwan such as 柚子打魚 and Shrimp.Finance. Within a month of launching these games, they had amassed over NT$ 100M (~US$ 3.5M) in transactions. His favorite pastime is traveling with his grandma, and his ultimate goal is to persuade her to buy Bitcoin!
Check out what Xixi has to say about blockchain and NFTs.
#NFTevolution
I started to learn how to write smart contracts in 2016, and learned the entire logic of ERC-20 for tokens and ERC-721 for NFTs. While I was learning about NFTs, I realized that the combination of NFTs with video games was very fitting. In video games, the treasure and equipment you collect becomes virtual assets as NFTs. And the process of using smart contracts to exchange items was very efficient on the blockchain.
At the end of 2018, I designed and created a zombie video game, integrating the concept of playing and drawing cards and packs. Within a pack were 3 NFTs with zombies on them. As a player, the more cards with zombies you collect, the higher your score, and the more tokens you can ultimately earn. From this game, I got connected to other game manufacturers and publishers who were also interested in creating virtual game assets through NFTs. We all had the same idea -- NFTs can bring more meaning and value to the players.
However at the time, many people in the market still believed that tokens and games were riddled with fraud. Since the lifecycle of video games can be short, many traditional gaming companies in the end didn’t find it worthwhile to learn how to integrate NFTs or blockchain into their games.
While the nature of NFTs hasn’t changed, the market has evolved. People’s curiosities are growing, more applications are being developed, and more creators are cropping up. I think now is the right time to start talking to companies about how to integrate NFTs or blockchain into their businesses or games.
#NFTplayground
I think there are many opportunities to start a business these days, and people who want to start one should think about coming to blockchain. Not only is there a huge opportunity but the possibilities are endless. And within blockchain, NFTs currently offer the biggest opportunity. However, it can also pose a new challenge to the team’s endurance, because while easy to obtain traction and users with NFTs, the challenge lies in retaining them.
Similar to other blockchain applications in the past few years, when a new concept is invented, it’ll be flushed with many early users. However, because the surrounding infrastructure wasn’t in place, it was difficult for founders to make valuable extensions or applications. And many of these users don’t actually care about these blockchain products and they are only trying to leverage the ecosystem to make a quick buck. Once they earn all that they can, they will move on to another project.
Right now working on NFTs, you can collect a lot of data in a short amount of time and also make some income to keep you afloat. Founders should seize this opportunity to understand these users, then modify and optimize both their products and mentality to retain them.
Since there’s no geographical restriction on blockchain, I would encourage founders to look beyond your country and region in expanding your NFT products. Also, since blockchain is closely related to finance, if you don’t have a good pricing strategy (or token economics) for your NFT products, the prices might fluctuate greatly. You need to be prepared and remind your users of the risks, otherwise you’ll ultimately get scolded!!
#NFTera
This year, I finally consider myself an official NFT collector. I pay special attention to NFTs with contemporary significance, such as Hashmasks. It signals to the public that NFTs are not just for collecting but that game mechanics can also be applied to interact with users. If we look back ten years from now I’m confident to say that the project that really brought the NFT wave in 2021 would be Hashmasks.
In addition to veteran projects like Hashmasks, other collections I care a lot about are related to Metaverse, such as The Sandbox. I believe that the world will become more and more decentralized and virtual. It is very likely that the next generation will be immersed in a virtual world like Ready Player One, so I am also very optimistic about NFTs in digital worlds like The Sandbox.
The possibilities are endless when it comes to NFTs. Right now, few NFTs are connected with our daily lives. For example, I bought a Hashmask. If I want to show it in my apartment, I might still need to print it out. In the future, how will we connect NFTs to the physical world? I believe they can be applied in many ways, including frames, wallets, cars, house deeds, leases, etc. These products in daily life can be combined with NFTs. We just haven’t opened our imagination yet. It’s hard to imagine that only 20 years ago we were having a hard time believing in the power of the internet.
The development of science and technology not only relies on infrastructure, but also the user's learning curve. The world needs to talk about blockchain more, so that everyone will gradually become familiar with it and it’ll continue to evolve.
If you're a founder working in blockchain or NFTs, welcome to apply to AppWorks >> https://bit.ly/3w0WyIl
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📜 [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
endless talk meaning 在 Red Hong Yi Facebook 的最佳貼文
An incredibly beautiful, sad, brave, wise, inspiring post by Facebook COO Sheryl Sandberg. Early this year, I read her book 'Lean In', a book encouraging women to achieve their dreams and ambitions, and was so grateful it was written for such a time as this. I especially loved her chapter about David being so supportive of her. I'm still stunned by all that's happened to them.
Here's to beating the heck out of Option B.
Today is the end of sheloshim for my beloved husband—the first thirty days. Judaism calls for a period of intense mourning known as shiva that lasts seven days after a loved one is buried. After shiva, most normal activities can be resumed, but it is the end of sheloshim that marks the completion of religious mourning for a spouse.
A childhood friend of mine who is now a rabbi recently told me that the most powerful one-line prayer he has ever read is: “Let me not die while I am still alive.” I would have never understood that prayer before losing Dave. Now I do.
I think when tragedy occurs, it presents a choice. You can give in to the void, the emptiness that fills your heart, your lungs, constricts your ability to think or even breathe. Or you can try to find meaning. These past thirty days, I have spent many of my moments lost in that void. And I know that many future moments will be consumed by the vast emptiness as well.
But when I can, I want to choose life and meaning.
And this is why I am writing: to mark the end of sheloshim and to give back some of what others have given to me. While the experience of grief is profoundly personal, the bravery of those who have shared their own experiences has helped pull me through. Some who opened their hearts were my closest friends. Others were total strangers who have shared wisdom and advice publicly. So I am sharing what I have learned in the hope that it helps someone else. In the hope that there can be some meaning from this tragedy.
I have lived thirty years in these thirty days. I am thirty years sadder. I feel like I am thirty years wiser.
I have gained a more profound understanding of what it is to be a mother, both through the depth of the agony I feel when my children scream and cry and from the connection my mother has to my pain. She has tried to fill the empty space in my bed, holding me each night until I cry myself to sleep. She has fought to hold back her own tears to make room for mine. She has explained to me that the anguish I am feeling is both my own and my children’s, and I understood that she was right as I saw the pain in her own eyes.
I have learned that I never really knew what to say to others in need. I think I got this all wrong before; I tried to assure people that it would be okay, thinking that hope was the most comforting thing I could offer. A friend of mine with late-stage cancer told me that the worst thing people could say to him was “It is going to be okay.” That voice in his head would scream, How do you know it is going to be okay? Do you not understand that I might die? I learned this past month what he was trying to teach me. Real empathy is sometimes not insisting that it will be okay but acknowledging that it is not. When people say to me, “You and your children will find happiness again,” my heart tells me, Yes, I believe that, but I know I will never feel pure joy again. Those who have said, “You will find a new normal, but it will never be as good” comfort me more because they know and speak the truth. Even a simple “How are you?”—almost always asked with the best of intentions—is better replaced with “How are you today?” When I am asked “How are you?” I stop myself from shouting, My husband died a month ago, how do you think I am? When I hear “How are you today?” I realize the person knows that the best I can do right now is to get through each day.
I have learned some practical stuff that matters. Although we now know that Dave died immediately, I didn’t know that in the ambulance. The trip to the hospital was unbearably slow. I still hate every car that did not move to the side, every person who cared more about arriving at their destination a few minutes earlier than making room for us to pass. I have noticed this while driving in many countries and cities. Let’s all move out of the way. Someone’s parent or partner or child might depend on it.
I have learned how ephemeral everything can feel—and maybe everything is. That whatever rug you are standing on can be pulled right out from under you with absolutely no warning. In the last thirty days, I have heard from too many women who lost a spouse and then had multiple rugs pulled out from under them. Some lack support networks and struggle alone as they face emotional distress and financial insecurity. It seems so wrong to me that we abandon these women and their families when they are in greatest need.
I have learned to ask for help—and I have learned how much help I need. Until now, I have been the older sister, the COO, the doer and the planner. I did not plan this, and when it happened, I was not capable of doing much of anything. Those closest to me took over. They planned. They arranged. They told me where to sit and reminded me to eat. They are still doing so much to support me and my children.
I have learned that resilience can be learned. Adam M. Grant taught me that three things are critical to resilience and that I can work on all three. Personalization—realizing it is not my fault. He told me to ban the word “sorry.” To tell myself over and over, This is not my fault. Permanence—remembering that I won’t feel like this forever. This will get better. Pervasiveness—this does not have to affect every area of my life; the ability to compartmentalize is healthy.
For me, starting the transition back to work has been a savior, a chance to feel useful and connected. But I quickly discovered that even those connections had changed. Many of my co-workers had a look of fear in their eyes as I approached. I knew why—they wanted to help but weren’t sure how. Should I mention it? Should I not mention it? If I mention it, what the hell do I say? I realized that to restore that closeness with my colleagues that has always been so important to me, I needed to let them in. And that meant being more open and vulnerable than I ever wanted to be. I told those I work with most closely that they could ask me their honest questions and I would answer. I also said it was okay for them to talk about how they felt. One colleague admitted she’d been driving by my house frequently, not sure if she should come in. Another said he was paralyzed when I was around, worried he might say the wrong thing. Speaking openly replaced the fear of doing and saying the wrong thing. One of my favorite cartoons of all time has an elephant in a room answering the phone, saying, “It’s the elephant.” Once I addressed the elephant, we were able to kick him out of the room.
At the same time, there are moments when I can’t let people in. I went to Portfolio Night at school where kids show their parents around the classroom to look at their work hung on the walls. So many of the parents—all of whom have been so kind—tried to make eye contact or say something they thought would be comforting. I looked down the entire time so no one could catch my eye for fear of breaking down. I hope they understood.
I have learned gratitude. Real gratitude for the things I took for granted before—like life. As heartbroken as I am, I look at my children each day and rejoice that they are alive. I appreciate every smile, every hug. I no longer take each day for granted. When a friend told me that he hates birthdays and so he was not celebrating his, I looked at him and said through tears, “Celebrate your birthday, goddammit. You are lucky to have each one.” My next birthday will be depressing as hell, but I am determined to celebrate it in my heart more than I have ever celebrated a birthday before.
I am truly grateful to the many who have offered their sympathy. A colleague told me that his wife, whom I have never met, decided to show her support by going back to school to get her degree—something she had been putting off for years. Yes! When the circumstances allow, I believe as much as ever in leaning in. And so many men—from those I know well to those I will likely never know—are honoring Dave’s life by spending more time with their families.
I can’t even express the gratitude I feel to my family and friends who have done so much and reassured me that they will continue to be there. In the brutal moments when I am overtaken by the void, when the months and years stretch out in front of me endless and empty, only their faces pull me out of the isolation and fear. My appreciation for them knows no bounds.
I was talking to one of these friends about a father-child activity that Dave is not here to do. We came up with a plan to fill in for Dave. I cried to him, “But I want Dave. I want option A.” He put his arm around me and said, “Option A is not available. So let’s just kick the shit out of option B.”
Dave, to honor your memory and raise your children as they deserve to be raised, I promise to do all I can to kick the shit out of option B. And even though sheloshim has ended, I still mourn for option A. I will always mourn for option A. As Bono sang, “There is no end to grief . . . and there is no end to love.” I love you, Dave.