Fairness alternatives to selling below market clearing prices (or community sentiment, or fun)
When a seller has a limited supply of an item in high (or uncertain and possibly high) demand, they frequently set a price far below what "the market will bear." As a result, the item sells out quickly, with lucky buyers being those who tried to buy first. This has happened in the Ethereum ecosystem, particularly with NFT sales and token sales/ICOs. But this phenomenon is much older; concerts and restaurants frequently make similar choices, resulting in fast sell-outs or long lines.
Why do sellers do this? Economists have long wondered. A seller should sell at the market-clearing price if the amount buyers are willing to buy exactly equals the amount the seller has to sell. If the seller is unsure of the market-clearing price, they should sell at auction and let the market decide. So, if you want to sell something below market value, don't do it. It will hurt your sales and it will hurt your customers. The competitions created by non-price-based allocation mechanisms can sometimes have negative externalities that harm third parties, as we will see.
However, the prevalence of below-market-clearing pricing suggests that sellers do it for good reason. And indeed, as decades of research into this topic has shown, there often are. So, is it possible to achieve the same goals with less unfairness, inefficiency, and harm?
Selling at below market-clearing prices has large inefficiencies and negative externalities
An item that is sold at market value or at an auction allows someone who really wants it to pay the high price or bid high in the auction. So, if a seller sells an item below market value, some people will get it and others won't. But the mechanism deciding who gets the item isn't random, and it's not always well correlated with participant desire. It's not always about being the fastest at clicking buttons. Sometimes it means waking up at 2 a.m. (but 11 p.m. or even 2 p.m. elsewhere). Sometimes it's just a "auction by other means" that's more chaotic, less efficient, and has far more negative externalities.
There are many examples of this in the Ethereum ecosystem. Let's start with the 2017 ICO craze. For example, an ICO project would set the price of the token and a hard maximum for how many tokens they are willing to sell, and the sale would start automatically at some point in time. The sale ends when the cap is reached.
So what? In practice, these sales often ended in 30 seconds or less. Everyone would start sending transactions in as soon as (or just before) the sale started, offering higher and higher fees to encourage miners to include their transaction first. Instead of the token seller receiving revenue, miners receive it, and the sale prices out all other applications on-chain.
The most expensive transaction in the BAT sale set a fee of 580,000 gwei, paying a fee of $6,600 to get included in the sale.
Many ICOs after that tried various strategies to avoid these gas price auctions; one ICO notably had a smart contract that checked the transaction's gasprice and rejected it if it exceeded 50 gwei. But that didn't solve the issue. Buyers hoping to game the system sent many transactions hoping one would get through. An auction by another name, clogging the chain even more.
ICOs have recently lost popularity, but NFTs and NFT sales have risen in popularity. But the NFT space didn't learn from 2017; they do fixed-quantity sales just like ICOs (eg. see the mint function on lines 97-108 of this contract here). So what?
That's not the worst; some NFT sales have caused gas price spikes of up to 2000 gwei.
High gas prices from users fighting to get in first by sending higher and higher transaction fees. An auction renamed, pricing out all other applications on-chain for 15 minutes.
So why do sellers sometimes sell below market price?
Selling below market value is nothing new, and many articles, papers, and podcasts have written (and sometimes bitterly complained) about the unwillingness to use auctions or set prices to market-clearing levels.
Many of the arguments are the same for both blockchain (NFTs and ICOs) and non-blockchain examples (popular restaurants and concerts). Fairness and the desire not to exclude the poor, lose fans or create tension by being perceived as greedy are major concerns. The 1986 paper by Kahneman, Knetsch, and Thaler explains how fairness and greed can influence these decisions. I recall that the desire to avoid perceptions of greed was also a major factor in discouraging the use of auction-like mechanisms in 2017.
Aside from fairness concerns, there is the argument that selling out and long lines create a sense of popularity and prestige, making the product more appealing to others. Long lines should have the same effect as high prices in a rational actor model, but this is not the case in reality. This applies to ICOs and NFTs as well as restaurants. Aside from increasing marketing value, some people find the game of grabbing a limited set of opportunities first before everyone else is quite entertaining.
But there are some blockchain-specific factors. One argument for selling ICO tokens below market value (and one that persuaded the OmiseGo team to adopt their capped sale strategy) is community dynamics. The first rule of community sentiment management is to encourage price increases. People are happy if they are "in the green." If the price drops below what the community members paid, they are unhappy and start calling you a scammer, possibly causing a social media cascade where everyone calls you a scammer.
This effect can only be avoided by pricing low enough that post-launch market prices will almost certainly be higher. But how do you do this without creating a rush for the gates that leads to an auction?
Interesting solutions
It's 2021. We have a blockchain. The blockchain is home to a powerful decentralized finance ecosystem, as well as a rapidly expanding set of non-financial tools. The blockchain also allows us to reset social norms. Where decades of economists yelling about "efficiency" failed, blockchains may be able to legitimize new uses of mechanism design. If we could use our more advanced tools to create an approach that more directly solves the problems, with fewer side effects, wouldn't that be better than fiddling with a coarse-grained one-dimensional strategy space of selling at market price versus below market price?
Begin with the goals. We'll try to cover ICOs, NFTs, and conference tickets (really a type of NFT) all at the same time.
1. Fairness: don't completely exclude low-income people from participation; give them a chance. The goal of token sales is to avoid high initial wealth concentration and have a larger and more diverse initial token holder community.
2. Don’t create races: Avoid situations where many people rush to do the same thing and only a few get in (this is the type of situation that leads to the horrible auctions-by-another-name that we saw above).
3. Don't require precise market knowledge: the mechanism should work even if the seller has no idea how much demand exists.
4. Fun: The process of participating in the sale should be fun and game-like, but not frustrating.
5. Give buyers positive expected returns: in the case of a token (or an NFT), buyers should expect price increases rather than decreases. This requires selling below market value.
Let's start with (1). From Ethereum's perspective, there is a simple solution. Use a tool designed for the job: proof of personhood protocols! Here's one quick idea:
Mechanism 1 Each participant (verified by ID) can buy up to ‘’X’’ tokens at price P, with the option to buy more at an auction.
With the per-person mechanism, buyers can get positive expected returns for the portion sold through the per-person mechanism, and the auction part does not require sellers to understand demand levels. Is it race-free? The number of participants buying through the per-person pool appears to be high. But what if the per-person pool isn't big enough to accommodate everyone?
Make the per-person allocation amount dynamic.
Mechanism 2 Each participant can deposit up to X tokens into a smart contract to declare interest. Last but not least, each buyer receives min(X, N / buyers) tokens, where N is the total sold through the per-person pool (some other amount can also be sold by auction). The buyer gets their deposit back if it exceeds the amount needed to buy their allocation.
No longer is there a race condition based on the number of buyers per person. No matter how high the demand, it's always better to join sooner rather than later.
Here's another idea if you like clever game mechanics with fancy quadratic formulas.
Mechanism 3 Each participant can buy X units at a price P X 2 up to a maximum of C tokens per buyer. C starts low and gradually increases until enough units are sold.
The quantity allocated to each buyer is theoretically optimal, though post-sale transfers will degrade this optimality over time. Mechanisms 2 and 3 appear to meet all of the above objectives. They're not perfect, but they're good starting points.
One more issue. For fixed and limited supply NFTs, the equilibrium purchased quantity per participant may be fractional (in mechanism 2, number of buyers > N, and in mechanism 3, setting C = 1 may already lead to over-subscription). With fractional sales, you can offer lottery tickets: if there are N items available, you have a chance of N/number of buyers of getting the item, otherwise you get a refund. For a conference, groups could bundle their lottery tickets to guarantee a win or a loss. The certainty of getting the item can be auctioned.
The bottom tier of "sponsorships" can be used to sell conference tickets at market rate. You may end up with a sponsor board full of people's faces, but is that okay? After all, John Lilic was on EthCC's sponsor board!
Simply put, if you want to be reliably fair to people, you need an input that explicitly measures people. Authentication protocols do this (and if desired can be combined with zero knowledge proofs to ensure privacy). So we should combine the efficiency of market and auction-based pricing with the equality of proof of personhood mechanics.
Answers to possible questions
Q: Won't people who don't care about your project buy the item and immediately resell it?
A: Not at first. Meta-games take time to appear in practice. If they do, making them untradeable for a while may help mitigate the damage. Using your face to claim that your previous account was hacked and that your identity, including everything in it, should be moved to another account works because proof-of-personhood identities are untradeable.
Q: What if I want to make my item available to a specific community?
A: Instead of ID, use proof of participation tokens linked to community events. Another option, also serving egalitarian and gamification purposes, is to encrypt items within publicly available puzzle solutions.
Q: How do we know they'll accept? Strange new mechanisms have previously been resisted.
A: Having economists write screeds about how they "should" accept a new mechanism that they find strange is difficult (or even "equity"). However, abrupt changes in context effectively reset people's expectations. So the blockchain space is the best place to try this. You could wait for the "metaverse", but it's possible that the best version will run on Ethereum anyway, so start now.
More on Web3 & Crypto
Ben
3 years ago
The Real Value of Carbon Credit (Climate Coin Investment)
Disclaimer : This is not financial advice for any investment.
TL;DR
You might not have realized it, but as we move toward net zero carbon emissions, the globe is already at war.
According to the Paris Agreement of COP26, 64% of nations have already declared net zero, and the issue of carbon reduction has already become so important for businesses that it affects their ability to survive. Furthermore, the time when carbon emission standards will be defined and controlled on an individual basis is becoming closer.
Since 2017, the market for carbon credits has experienced extraordinary expansion as a result of widespread talks about carbon credits. The carbon credit market is predicted to expand much more once net zero is implemented and carbon emission rules inevitably tighten.
Hello! Ben here from Nonce Classic. Nonce Classic has recently confirmed the tremendous growth potential of the carbon credit market in the midst of a major trend towards the global goal of net zero (carbon emissions caused by humans — carbon reduction by humans = 0 ). Moreover, we too believed that the questions and issues the carbon credit market suffered from the last 30–40yrs could be perfectly answered through crypto technology and that is why we have added a carbon credit crypto project to the Nonce Classic portfolio. There have been many teams out there that have tried to solve environmental problems through crypto but very few that have measurable experience working in the carbon credit scene. Thus we have put in our efforts to find projects that are not crypto projects created for the sake of issuing tokens but projects that pragmatically use crypto technology to combat climate change by solving problems of the current carbon credit market. In that process, we came to hear of Climate Coin, a veritable carbon credit crypto project, and us Nonce Classic as an accelerator, have begun contributing to its growth and invested in its tokens. Starting with this article, we plan to publish a series of articles explaining why the carbon credit market is bullish, why we invested in Climate Coin, and what kind of project Climate Coin is specifically. In this first article let us understand the carbon credit market and look into its growth potential! Let’s begin :)
The Unavoidable Entry of the Net Zero Era
Net zero means... Human carbon emissions are balanced by carbon reduction efforts. A non-environmentalist may find it hard to accept that net zero is attainable by 2050. Global cooperation to save the earth is happening faster than we imagine.
In the Paris Agreement of COP26, concluded in Glasgow, UK on Oct. 31, 2021, nations pledged to reduce worldwide yearly greenhouse gas emissions by more than 50% by 2030 and attain net zero by 2050. Governments throughout the world have pledged net zero at the national level and are holding each other accountable by submitting Nationally Determined Contributions (NDC) every five years to assess implementation. 127 of 198 nations have declared net zero.
Each country's 1.5-degree reduction plans have led to carbon reduction obligations for companies. In places with the strictest environmental regulations, like the EU, companies often face bankruptcy because the cost of buying carbon credits to meet their carbon allowances exceeds their operating profits. In this day and age, minimizing carbon emissions and securing carbon credits are crucial.
Recent SEC actions on climate change may increase companies' concerns about reducing emissions. The SEC required all U.S. stock market companies to disclose their annual greenhouse gas emissions and climate change impact on March 21, 2022. The SEC prepared the proposed regulation through in-depth analysis and stakeholder input since last year. Three out of four SEC members agreed that it should pass without major changes. If the regulation passes, it will affect not only US companies, but also countless companies around the world, directly or indirectly.
Even companies not listed on the U.S. stock market will be affected and, in most cases, required to disclose emissions. Companies listed on the U.S. stock market with significant greenhouse gas emissions or specific targets are subject to stricter emission standards (Scope 3) and disclosure obligations, which will magnify investigations into all related companies. Greenhouse gas emissions can be calculated three ways. Scope 1 measures carbon emissions from a company's facilities and transportation. Scope 2 measures carbon emissions from energy purchases. Scope 3 covers all indirect emissions from a company's value chains.
The SEC's proposed carbon emission disclosure mandate and regulations are one example of how carbon credit policies can cross borders and affect all parties. As such incidents will continue throughout the implementation of net zero, even companies that are not immediately obligated to disclose their carbon emissions must be prepared to respond to changes in carbon emission laws and policies.
Carbon reduction obligations will soon become individual. Individual consumption has increased dramatically with improved quality of life and convenience, despite national and corporate efforts to reduce carbon emissions. Since consumption is directly related to carbon emissions, increasing consumption increases carbon emissions. Countries around the world have agreed that to achieve net zero, carbon emissions must be reduced on an individual level. Solutions to individual carbon reduction are being actively discussed and studied under the term Personal Carbon Trading (PCT).
PCT is a system that allows individuals to trade carbon emission quotas in the form of carbon credits. Individuals who emit more carbon than their allotment can buy carbon credits from those who emit less. European cities with well-established carbon credit markets are preparing for net zero by conducting early carbon reduction prototype projects. The era of checking product labels for carbon footprints, choosing low-emissions transportation, and worrying about hot shower emissions is closer than we think.
The Market for Carbon Credits Is Expanding Fearfully
Compliance and voluntary carbon markets make up the carbon credit market.
A Compliance Market enforces carbon emission allowances for actors. Companies in industries that previously emitted a lot of carbon are included in the mandatory carbon market, and each government receives carbon credits each year. If a company's emissions are less than the assigned cap and it has extra carbon credits, it can sell them to other companies that have larger emissions and require them (Cap and Trade). The annual number of free emission permits provided to companies is designed to decline, therefore companies' desire for carbon credits will increase. The compliance market's yearly trading volume will exceed $261B in 2020, five times its 2017 level.
In the Voluntary Market, carbon reduction is voluntary and carbon credits are sold for personal reasons or to build market participants' eco-friendly reputations. Even if not in the compliance market, it is typical for a corporation to be obliged to offset its carbon emissions by acquiring voluntary carbon credits. When a company seeks government or company investment, it may be denied because it is not net zero. If a significant shareholder declares net zero, the companies below it must execute it. As the world moves toward ESG management, becoming an eco-friendly company is no longer a strategic choice to gain a competitive edge, but an important precaution to not fall behind. Due to this eco-friendly trend, the annual market volume of voluntary emission credits will approach $1B by November 2021. The voluntary credit market is anticipated to reach $5B to $50B by 2030. (TSCVM 2021 Report)
In conclusion
This article analyzed how net zero, a target promised by countries around the world to combat climate change, has brought governmental, corporate, and human changes. We discussed how these shifts will become more obvious as we approach net zero, and how the carbon credit market would increase exponentially in response. In the following piece, let's analyze the hurdles impeding the carbon credit market's growth, how the project we invested in tries to tackle these issues, and why we chose Climate Coin. Wait! Jim Skea, co-chair of the IPCC working group, said,
“It’s now or never, if we want to limit global warming to 1.5°C” — Jim Skea
Join nonceClassic’s community:
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Mail us : general@nonceclassic.org
TheRedKnight
3 years ago
Say goodbye to Ponzi yields - A new era of decentralized perpetual
Decentralized perpetual may be the next crypto market boom; with tons of perpetual popping up, let's look at two protocols that offer organic, non-inflationary yields.
Decentralized derivatives exchanges' market share has increased tenfold in a year, but it's still 2% of CEXs'. DEXs have a long way to go before they can compete with centralized exchanges in speed, liquidity, user experience, and composability.
I'll cover gains.trade and GMX protocol in Polygon, Avalanche, and Arbitrum. Both protocols support leveraged perpetual crypto, stock, and Forex trading.
Why these protocols?
Decentralized GMX Gains protocol
Organic yield: path to sustainability
I've never trusted Defi's non-organic yields. Example: XYZ protocol. 20–75% of tokens may be set aside as farming rewards to provide liquidity, according to tokenomics.
Say you provide ETH-USDC liquidity. They advertise a 50% APR reward for this pair, 10% from trading fees and 40% from farming rewards. Only 10% is real, the rest is "Ponzi." The "real" reward is in protocol tokens.
Why keep this token? Governance voting or staking rewards are promoted services.
Most liquidity providers expect compensation for unused tokens. Basic psychological principles then? — Profit.
Nobody wants governance tokens. How many out of 100 care about the protocol's direction and will vote?
Staking increases your token's value. Currently, they're mostly non-liquid. If the protocol is compromised, you can't withdraw funds. Most people are sceptical of staking because of this.
"Free tokens," lack of use cases, and skepticism lead to tokens moving south. No farming reward protocols have lasted.
It may have shown strength in a bull market, but what about a bear market?
What is decentralized perpetual?
A perpetual contract is a type of futures contract that doesn't expire. So one can hold a position forever.
You can buy/sell any leveraged instruments (Long-Short) without expiration.
In centralized exchanges like Binance and coinbase, fees and revenue (liquidation) go to the exchanges, not users.
Users can provide liquidity that traders can use to leverage trade, and the revenue goes to liquidity providers.
Gains.trade and GMX protocol are perpetual trading platforms with a non-inflationary organic yield for liquidity providers.
GMX protocol
GMX is an Arbitrum and Avax protocol that rewards in ETH and Avax. GLP uses a fast oracle to borrow the "true price" from other trading venues, unlike a traditional AMM.
GLP and GMX are protocol tokens. GLP is used for leveraged trading, swapping, etc.
GLP is a basket of tokens, including ETH, BTC, AVAX, stablecoins, and UNI, LINK, and Stablecoins.
GLP composition on arbitrum
GLP composition on Avalanche
GLP token rebalances based on usage, providing liquidity without loss.
Protocol "runs" on Staking GLP. Depending on their chain, the protocol will reward users with ETH or AVAX. Current rewards are 22 percent (15.71 percent in ETH and the rest in escrowed GMX) and 21 percent (15.72 percent in AVAX and the rest in escrowed GMX). escGMX and ETH/AVAX percentages fluctuate.
Where is the yield coming from?
Swap fees, perpetual interest, and liquidations generate yield. 70% of fees go to GLP stakers, 30% to GMX. Organic yields aren't paid in inflationary farm tokens.
Escrowed GMX is vested GMX that unlocks in 365 days. To fully unlock GMX, you must farm the Escrowed GMX token for 365 days. That means less selling pressure for the GMX token.
GMX's status
These are the fees in Arbitrum in the past 11 months by GMX.
GMX works like a casino, which increases fees. Most fees come from Margin trading, which means most traders lose money; this money goes to the casino, or GLP stakers.
Strategies
My personal strategy is to DCA into GLP when markets hit bottom and stake it; GLP will be less volatile with extra staking rewards.
GLP YoY return vs. naked buying
Let's say I invested $10,000 in BTC, AVAX, and ETH in January.
BTC price: 47665$
ETH price: 3760$
AVAX price: $145
Current prices
BTC $21,000 (Down 56 percent )
ETH $1233 (Down 67.2 percent )
AVAX $20.36 (Down 85.95 percent )
Your $10,000 investment is now worth around $3,000.
How about GLP? My initial investment is 50% stables and 50% other assets ( Assuming the coverage ratio for stables is 50 percent at that time)
Without GLP staking yield, your value is $6500.
Let's assume the average APR for GLP staking is 23%, or $1500. So 8000$ total. It's 50% safer than holding naked assets in a bear market.
In a bull market, naked assets are preferable to GLP.
Short farming using GLP
Simple GLP short farming.
You use a stable asset as collateral to borrow AVAX. Sell it and buy GLP. Even if GLP rises, it won't rise as fast as AVAX, so we can get yields.
Let's do the maths
You deposit $10,000 USDT in Aave and borrow Avax. Say you borrow $8,000; you sell it, buy GLP, and risk 20%.
After a year, ETH, AVAX, and BTC rise 20%. GLP is $8800. $800 vanishes. 20% yields $1600. You're profitable. Shorting Avax costs $1600. (Assumptions-ETH, AVAX, BTC move the same, GLP yield is 20%. GLP has a 50:50 stablecoin/others ratio. Aave won't liquidate
In naked Avax shorting, Avax falls 20% in a year. You'll make $1600. If you buy GLP and stake it using the sold Avax and BTC, ETH and Avax go down by 20% - your profit is 20%, but with the yield, your total gain is $2400.
Issues with GMX
GMX's historical funding rates are always net positive, so long always pays short. This makes long-term shorts less appealing.
Oracle price discovery isn't enough. This limitation doesn't affect Bitcoin and ETH, but it affects less liquid assets. Traders can buy and sell less liquid assets at a lower price than their actual cost as long as GMX exists.
As users must provide GLP liquidity, adding more assets to GMX will be difficult. Next iteration will have synthetic assets.
Gains Protocol
Best leveraged trading platform. Smart contract-based decentralized protocol. 46 crypto pairs can be leveraged 5–150x and 10 Forex pairs 5–1000x. $10 DAI @ 150x (min collateral x leverage pos size is $1500 DAI). No funding fees, no KYC, trade DAI from your wallet, keep funds.
DAI single-sided staking and the GNS-DAI pool are important parts of Gains trading. GNS-DAI stakers get 90% of trading fees and 100% swap fees. 10 percent of trading fees go to DAI stakers, which is currently 14 percent!
Trade volume
When a trader opens a trade, the leverage and profit are pulled from the DAI pool. If he loses, the protocol yield goes to the stakers.
If the trader's win rate is high and the DAI pool slowly depletes, the GNS token is minted and sold to refill DAI. Trader losses are used to burn GNS tokens. 25%+ of GNS is burned, making it deflationary.
Due to high leverage and volatility of crypto assets, most traders lose money and the protocol always wins, keeping GNS deflationary.
Gains uses a unique decentralized oracle for price feeds, which is better for leverage trading platforms. Let me explain.
Gains uses chainlink price oracles, not its own price feeds. Chainlink oracles only query centralized exchanges for price feeds every minute, which is unsuitable for high-precision trading.
Gains created a custom oracle that queries the eight chainlink nodes for the current price and, on average, for trade confirmation. This model eliminates every-second inquiries, which waste gas but are more efficient than chainlink's per-minute price.
This price oracle helps Gains open and close trades instantly, eliminate scam wicks, etc.
Other benefits include:
Stop-loss guarantee (open positions updated)
No scam wicks
Spot-pricing
Highest possible leverage
Fixed-spreads. During high volatility, a broker can increase the spread, which can hit your stop loss without the price moving.
Trade directly from your wallet and keep your funds.
>90% loss before liquidation (Some platforms liquidate as little as -50 percent)
KYC-free
Directly trade from wallet; keep funds safe
Further improvements
GNS-DAI liquidity providers fear the impermanent loss, so the protocol is migrating to its own liquidity and single staking GNS vaults. This allows users to stake GNS without permanent loss and obtain 90% DAI trading fees by staking. This starts in August.
Their upcoming improvements can be found here.
Gains constantly add new features and change pairs. It's an interesting protocol.
Conclusion
Next bull run, watch decentralized perpetual protocols. Effective tokenomics and non-inflationary yields may attract traders and liquidity providers. But still, there is a long way for them to develop, and I don't see them tackling the centralized exchanges any time soon until they fix their inherent problems and improve fast enough.
Read the full post here.
Vitalik
3 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3
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Tim Denning
3 years ago
Bills are paid by your 9 to 5. 6 through 12 help you build money.
40 years pass. After 14 years of retirement, you die. Am I the only one who sees the problem?
I’m the Jedi master of escaping the rat race.
Not to impress. I know this works since I've tried it. Quitting a job to make money online is worse than Kim Kardashian's internet-burning advice.
Let me help you rethink the move from a career to online income to f*ck you money.
To understand why a job is a joke, do some life math.
Without a solid why, nothing makes sense.
The retirement age is 65. Our processed food consumption could shorten our 79-year average lifespan.
You spend 40 years working.
After 14 years of retirement, you die.
Am I alone in seeing the problem?
Life is too short to work a job forever, especially since most people hate theirs. After-hours skills are vital.
Money equals unrestricted power, f*ck you.
F*ck you money is the answer.
Jack Raines said it first. He says we can do anything with the money. Jack, a young rebel straight out of college, can travel and try new foods.
F*ck you money signifies not checking your bank account before buying.
F*ck you” money is pure, unadulterated freedom with no strings attached.
Jack claims you're rich when you rarely think about money.
Avoid confusion.
This doesn't imply you can buy a Lamborghini. It indicates your costs, income, lifestyle, and bank account are balanced.
Jack established an online portfolio while working for UPS in Atlanta, Georgia. So he gained boundless power.
The portion that many erroneously believe
Yes, you need internet abilities to make money, but they're not different from 9-5 talents.
Sahil Lavingia, Gumroad's creator, explains.
A job is a way to get paid to learn.
Mistreat your boss 9-5. Drain his skills. Defuse him. Love and leave him (eventually).
Find another employment if yours is hazardous. Pick an easy job. Make sure nothing sneaks into your 6-12 time slot.
The dumb game that makes you a sheep
A 9-5 job requires many job interviews throughout life.
You email your résumé to employers and apply for jobs through advertisements. This game makes you a sheep.
You're competing globally. Work-from-home makes the competition tougher. If you're not the cheapest, employers won't hire you.
After-hours online talents (say, 6 pm-12 pm) change the game. This graphic explains it better:
Online talents boost after-hours opportunities.
You go from wanting to be picked to picking yourself. More chances equal more money. Your f*ck you fund gets the extra cash.
A novel method of learning is essential.
College costs six figures and takes a lifetime to repay.
Informal learning is distinct. 6-12pm:
Observe the carefully controlled Twitter newsfeed.
Make use of Teachable and Gumroad's online courses.
Watch instructional YouTube videos
Look through the top Substack newsletters.
Informal learning is more effective because it's not obvious. It's fun to follow your curiosity and hobbies.
The majority of people lack one attitude. It's simple to learn.
One big impediment stands in the way of f*ck you money and time independence. So often.
Too many people plan after 6-12 hours. Dreaming. Big-thinkers. Strategically. They fill their calendar with meetings.
This is after-hours masturb*tion.
Sahil Bloom reminded me that a bias towards action will determine if this approach works for you.
The key isn't knowing what to do from 6-12 a.m. Trust yourself and develop abilities as you go. It's for building the parachute after you jump.
Sounds risky. We've eliminated the risk by finishing this process after hours while you work 9-5.
With no risk, you can have an I-don't-care attitude and still be successful.
When you choose to move forward, this occurs.
Once you try 9-5/6-12, you'll tell someone.
It's bad.
Few of us hang out with problem-solvers.
It's how much of society operates. So they make reasons so they can feel better about not giving you money.
Matthew Kobach told me chasing f*ck you money is easier with like-minded folks.
Without f*ck you money friends, loneliness will take over and you'll think you've messed up when you just need to keep going.
Steal this easy guideline
Let's act. No more fluffing and caressing.
1. Learn
If you detest your 9-5 talents or don't think they'll work online, get new ones. If you're skilled enough, continue.
Easlo recommends these skills:
Designer for Figma
Designer Canva
bubble creators
editor in Photoshop
Automation consultant for Zapier
Designer of Webflow
video editor Adobe
Ghostwriter for Twitter
Idea consultant
Artist in Blender Studio
2. Develop the ability
Every night from 6-12, apply the skill.
Practicing ghostwriting? Write someone's tweets for free. Do someone's website copy to learn copywriting. Get a website to the top of Google for a keyword to understand SEO.
Free practice is crucial. Your 9-5 pays the money, so work for free.
3. Take off stealthily like a badass
Another mistake. Sell to few. Don't be the best. Don't claim expertise.
Sell your new expertise to others behind you.
Two ways:
Using a digital good
By providing a service,
Point 1 also includes digital service examples. Digital products include eBooks, communities, courses, ad-supported podcasts, and templates. It's easy. Your 9-5 job involves one of these.
Take ideas from work.
Why? They'll steal your time for profit.
4. Iterate while feeling awful
First-time launches always fail. You'll feel terrible. Okay. Remember your 9-5?
Find improvements. Ask free and paying consumers what worked.
Multiple relaunches, each 1% better.
5. Discover more
Never stop learning. Improve your skill. Add a relevant skill. Learn copywriting if you write online.
After-hours students earn the most.
6. Continue
Repetition is key.
7. Make this one small change.
Consistently. The 6-12 momentum won't make you rich in 30 days; that's success p*rn.
Consistency helps wage slaves become f*ck you money. Most people can't switch between the two.
Putting everything together
It's easy. You're probably already doing some.
This formula explains why, how, and what to do. It's a 5th-grade-friendly blueprint. Good.
Reduce financial risk with your 9-to-5. Replace Netflix with 6-12 money-making talents.
Life is short; do whatever you want. Today.
Tim Denning
2 years ago
One of the biggest publishers in the world offered me a book deal, but I don't feel deserving of it.
My ego is so huge it won't fit through the door.
I don't know how I feel about it. I should be excited. Many of you have this exact dream to publish a book with a well-known book publisher and get a juicy advance.
Let me dissect how I'm thinking about it to help you.
How it happened
An email comes in. A generic "can we put a backlink on your website and get a freebie" email.
Almost deleted it.
Then I noticed the logo. It seemed shady. I found the URL. Check. I searched the employee's LinkedIn. Legit. I avoided middlemen. Check.
Mixed feelings. LinkedIn hasn't valued my writing for years. I'm just a guy in an unironed t-shirt whose content they sell advertising against.
They get big dollars. I get $0 and a few likes, plus some email subscribers.
Still, I felt adrenaline for hours.
I texted a few friends to see how they felt. I wrapped them.
Messages like "No shocker. You're entertaining online." I didn't like praises, so I blushed.
The thrill faded after hours. Who knows?
Most authors desire this chance.
"You entitled piece of crap, Denning!"
You may think so. Okay. My job is to stand on the internet and get bananas thrown at me.
I approached writing backwards. More important than a book deal was a social media audience converted to an email list.
Romantic authors think backward. They hope a fantastic book will land them a deal and an audience.
Rarely occurs. So I never pursued it. It's like permission-seeking or the lottery.
Not being a professional writer, I've never written a good book. I post online for fun and to express my opinions.
Writing is therapeutic. I overcome mental illness and rebuilt my life this way. Without blogging, I'd be dead.
I've always dreamed of staying alive and doing something I love, not getting a book contract. Writing is my passion. I'm a winner without a book deal.
Why I was given a book deal
You may assume I received a book contract because of my views or follows. Nope.
They gave me a deal because they like my writing style. I've heard this for eight years.
Several authors agree. One asked me to improve their writer's voice.
Takeaway: highlight your writer's voice.
What if they discover I'm writing incompetently?
An edited book is published. It's edited.
I need to master writing mechanics, thus this concerns me. I need help with commas and sentence construction.
I must learn verb, noun, and adjective. Seriously.
Writing a book may reveal my imposter status to a famous publisher. Imagine the email
"It happened again. He doesn't even know how to spell. He thinks 'less' is the correct word, not 'fewer.' Are you sure we should publish his book?"
Fears stink.
I'm capable of blogging. Even listicles. So what?
Writing for a major publisher feels advanced.
I only blog. I'm good at listicles. Digital media executives have criticized me for this.
It is allegedly clickbait.
Or it is following trends.
Alternately, growth hacking.
Never. I learned copywriting to improve my writing.
Apple, Amazon, and Tesla utilize copywriting to woo customers. Whoever thinks otherwise is the wisest person in the room.
Old-schoolers loathe copywriters.
Their novels sell nothing.
They assume their elitist version of writing is better and that the TikTok generation will invest time in random writing with no subheadings and massive walls of text they can't read on their phones.
I'm terrified of book proposals.
My friend's book proposal suggestion was contradictory and made no sense.
They told him to compose another genre. This book got three Amazon reviews. Is that a good model?
The process disappointed him. I've heard other book proposal horror stories. Tim Ferriss' book "The 4-Hour Workweek" was criticized.
Because he has thick skin, his book came out. He wouldn't be known without that.
I hate book proposals.
An ongoing commitment
Writing a book is time-consuming.
I appreciate time most. I want to focus on my daughter for the next few years. I can't recreate her childhood because of a book.
No idea how parents balance kids' goals.
My silly face in a bookstore. Really?
Genuine thought.
I don't want my face in bookstores. I fear fame. I prefer anonymity.
I want to purchase a property in a bad Australian area, then piss off and play drums. Is bookselling worth it?
Are there even bookstores anymore?
(Except for Ryan Holiday's legendary Painted Porch Bookshop in Texas.)
What's most important about books
Many were duped.
Tweets and TikTok hopscotch vids are their future. Short-form content creates devoted audiences that buy newsletter subscriptions.
Books=depth.
Depth wins (if you can get people to buy your book). Creating a book will strengthen my reader relationships.
It's cheaper than my classes, so more people can benefit from my life lessons.
A deeper justification for writing a book
Mind wandered.
If I write this book, my daughter will follow it. "Look what you can do, love, when you ignore critics."
That's my favorite.
I'll be her best leader and teacher. If her dad can accomplish this, she can too.
My kid can read my book when I'm gone to remember her loving father.
Last paragraph made me cry.
The positive
This book thing might make me sound like Karen.
The upside is... Building in public, like I have with online writing, attracts the right people.
Proof-of-work over proposals, beautiful words, or huge aspirations. If you want a book deal, try writing online instead of the old manner.
Next steps
No idea.
I'm a rural Aussie. Writing a book in the big city is intimidating. Will I do it? Lots to think about. Right now, some level of reflection and gratitude feels most appropriate.
Sometimes when you don't feel worthy, it gives you the greatest lessons. That's how I feel about getting offered this book deal.
Perhaps you can relate.
Shawn Mordecai
3 years ago
The Apple iPhone 14 Pill is Easier to Swallow
Is iPhone's Dynamic Island invention or a marketing ploy?
First of all, why the notch?
When Apple debuted the iPhone X with the notch, some were surprised, confused, and amused by the goof. Let the Brits keep the new meaning of top-notch.
Apple removed the bottom home button to enhance screen space. The tides couldn't overtake part of the top. This section contained sensors, a speaker, a microphone, and cameras for facial recognition. A town resisted Apple's new iPhone design.
From iPhone X to 13, the notch has gotten smaller. We expected this as technology and engineering progressed, but we hated the notch. Apple approved. They attached it to their other gadgets.
Apple accepted, owned, and ran with the iPhone notch, it has become iconic (or infamous); and that’s intentional.
The Island Where Apple Is
Apple needs to separate itself, but they know how to do it well. The iPhone 14 Pro finally has us oohing and aahing. Life-changing, not just higher pixel density or longer battery.
Dynamic Island turned a visual differentiation into great usefulness, which may not be life-changing. Apple always welcomes the controversy, whether it's $700 for iMac wheels, no charging block with a new phone, or removing the headphone jack.
Apple knows its customers will be loyal, even if they're irritated. Their odd design choices often cause controversy. It's calculated that people blog, review, and criticize Apple's products. We accept what works for them.
While the competition zigs, Apple zags. Sometimes they zag too hard and smash into a wall, but we talk about it anyways, and that’s great publicity for them.
Getting Dependent on the drug
The notch became a crop. Dynamic Island's design is helpful, intuitive, elegant, and useful. It increases iPhone usability, productivity (slightly), and joy. No longer unsightly.
The medication helps with multitasking. It's a compact version of the iPhone's Live Activities lock screen function. Dynamic Island enhances apps and activities with visual effects and animations whether you engage with it or not. As you use the pill, its usefulness lessens. It lowers user notifications and consolidates them with live and permanent feeds, delivering quick app statuses. It uses the black pixels on the iPhone 14's display, which looked like a poor haircut.
The pill may be a gimmick to entice customers to use more Apple products and services. Apps may promote to their users like a live billboard.
Be prepared to get a huge dose of Dynamic Island’s “pill” like you never had before with the notch. It might become so satisfying and addicting to use, that every interaction with it will become habit-forming, and you’re going to forget that it ever existed.
WARNING: A Few Potential Side Effects
Vision blurred Dynamic Island's proximity to the front-facing camera may leave behind grease that blurs photos. Before taking a selfie, wipe the camera clean.
Strained thumb To fully use Dynamic Island, extend your thumb's reach 6.7 inches beyond your typical, comfortable range.
Happiness, contentment The Dynamic Island may enhance Endorphins and Dopamine. Multitasking, interactions, animations, and haptic feedback make you want to use this function again and again.
Motion-sickness Dynamic Island's motions and effects may make some people dizzy. If you can disable animations, you can avoid motion sickness.
I'm not a doctor, therefore they aren't established adverse effects.
Does Dynamic Island Include Multiple Tasks?
Dynamic Islands is a placebo for multitasking. Apple might have compromised on iPhone multitasking. It won't make you super productive, but it's a step up.
iPhone is primarily for personal use, like watching videos, messaging friends, sending money to friends, calling friends about the money you were supposed to send them, taking 50 photos of the same leaf, investing in crypto, driving for Uber because you lost all your money investing in crypto, listening to music and hailing an Uber from a deserted crop field because while you were driving for Uber your passenger stole your car and left you stranded, so you used Apple’s new SOS satellite feature to message your friend, who still didn’t receive their money, to hail you an Uber; now you owe them more money… karma?
We won't be watching videos on iPhones while perusing 10,000-row spreadsheets anytime soon. True multitasking and productivity aren't priorities for Apple's iPhone. Apple doesn't to preserve the iPhone's experience. Like why there's no iPad calculator. Apple doesn't want iPad users to do math, but isn't essential for productivity?
Digressing.
Apple will block certain functions so you must buy and use their gadgets and services, immersing yourself in their ecosystem and dictating how to use their goods.
Dynamic Island is a poor man’s multi-task for iPhone, and that’s fine it works for most iPhone users. For substantial productivity Apple prefers you to get an iPad or a MacBook. That’s part of the reason for restrictive features on certain Apple devices, but sometimes it’s based on principles to preserve the integrity of the product, according to Apple’s definition.
Is Apple using deception?
Dynamic Island may be distracting you from a design decision. The answer is kind of. Elegant distraction
When you pull down a smartphone webpage to refresh it or minimize an app, you get seamless animations. It's not simply because it appears better; it's due to iPhone and smartphone processing speeds. Such limits reduce the system's response to your activity, slowing the experience. Designers and developers use animations and effects to distract us from the time lag (most of the time) and sometimes because it looks cooler and smoother.
Dynamic Island makes apps more useable and interactive. It shows system states visually. Turn signal audio and visual cues, voice assistance, physical and digital haptic feedbacks, heads-up displays, fuel and battery level gauges, and gear shift indicators helped us overcome vehicle design problems.
Dynamic Island is a wonderfully delightful (and temporary) solution to a design “problem” until Apple or other companies can figure out a way to sink the cameras under the smartphone screen.
Apple Has Returned to Being an Innovative & Exciting Company
Now Apple's products are exciting. Next, bring back real Apple events, not pre-recorded demos.
Dynamic Island integrates hardware and software. What will this new tech do? How would this affect device use? Or is it just hype?
Dynamic Island may be an insignificant improvement to the iPhone, but it sure is promising for the future of bridging the human and computer interaction gap.