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
(Edited)
Hackernoon
3 years ago
👏 Awesome post! When is part 3 coming?
Trent Lapinski
3 years ago
Very complex topic, great explanation
More on Web3 & Crypto
CyberPunkMetalHead
2 years ago
It's all about the ego with Terra 2.0.
UST depegs and LUNA crashes 99.999% in a fraction of the time it takes the Moon to orbit the Earth.
Fat Man, a Terra whistle-blower, promises to expose Do Kwon's dirty secrets and shady deals.
The Terra community has voted to relaunch Terra LUNA on a new blockchain. The Terra 2.0 Pheonix-1 blockchain went live on May 28, 2022, and people were airdropped the new LUNA, now called LUNA, while the old LUNA became LUNA Classic.
Does LUNA deserve another chance? To answer this, or at least start a conversation about the Terra 2.0 chain's advantages and limitations, we must assess its fundamentals, ideology, and long-term vision.
Whatever the result, our analysis must be thorough and ruthless. A failure of this magnitude cannot happen again, so we must magnify every potential breaking point by 10.
Will UST and LUNA holders be compensated in full?
The obvious. First, and arguably most important, is to restore previous UST and LUNA holders' bags.
Terra 2.0 has 1,000,000,000,000 tokens to distribute.
25% of a community pool
Holders of pre-attack LUNA: 35%
10% of aUST holders prior to attack
Holders of LUNA after an attack: 10%
UST holders as of the attack: 20%
Every LUNA and UST holder has been compensated according to the above proposal.
According to self-reported data, the new chain has 210.000.000 tokens and a $1.3bn marketcap. LUNC and UST alone lost $40bn. The new token must fill this gap. Since launch:
LUNA holders collectively own $1b worth of LUNA if we subtract the 25% community pool airdrop from the current market cap and assume airdropped LUNA was never sold.
At the current supply, the chain must grow 40 times to compensate holders. At the current supply, LUNA must reach $240.
LUNA needs a full-on Bull Market to make LUNC and UST holders whole.
Who knows if you'll be whole? From the time you bought to the amount and price, there are too many variables to determine if Terra can cover individual losses.
The above distribution doesn't consider individual cases. Terra didn't solve individual cases. It would have been huge.
What does LUNA offer in terms of value?
UST's marketcap peaked at $18bn, while LUNC's was $41bn. LUNC and UST drove the Terra chain's value.
After it was confirmed (again) that algorithmic stablecoins are bad, Terra 2.0 will no longer support them.
Algorithmic stablecoins contributed greatly to Terra's growth and value proposition. Terra 2.0 has no product without algorithmic stablecoins.
Terra 2.0 has an identity crisis because it has no actual product. It's like Volkswagen faking carbon emission results and then stopping car production.
A project that has already lost the trust of its users and nearly all of its value cannot survive without a clear and in-demand use case.
Do Kwon, how about him?
Oh, the Twitter-caller-poor? Who challenges crypto billionaires to break his LUNA chain? Who dissolved Terra Labs South Korea before depeg? Arrogant guy?
That's not a good image for LUNA, especially when making amends. I think he should step down and let a nicer person be Terra 2.0's frontman.
The verdict
Terra has a terrific community with an arrogant, unlikeable leader. The new LUNA chain must grow 40 times before it can start making up its losses, and even then, not everyone's losses will be covered.
I won't invest in Terra 2.0 or other algorithmic stablecoins in the near future. I won't be near any Do Kwon-related project within 100 miles. My opinion.
Can Terra 2.0 be saved? Comment below.
Robert Kim
3 years ago
Crypto Legislation Might Progress Beyond Talk in 2022
Financial regulators have for years attempted to apply existing laws to the multitude of issues created by digital assets. In 2021, leading federal regulators and members of Congress have begun to call for legislation to address these issues. As a result, 2022 may be the year when federal legislation finally addresses digital asset issues that have been growing since the mining of the first Bitcoin block in 2009.
Digital Asset Regulation in the Absence of Legislation
So far, Congress has left the task of addressing issues created by digital assets to regulatory agencies. Although a Congressional Blockchain Caucus formed in 2016, House and Senate members introduced few bills addressing digital assets until 2018. As of October 2021, Congress has not amended federal laws on financial regulation, which were last significantly revised by the Dodd-Frank Act in 2010, to address digital asset issues.
In the absence of legislation, issues that do not fit well into existing statutes have created problems. An example is the legal status of digital assets, which can be considered to be either securities or commodities, and can even shift from one to the other over time. Years after the SEC’s 2017 report applying the definition of a security to digital tokens, the SEC and the CFTC have yet to clarify the distinction between securities and commodities for the thousands of digital assets in existence.
SEC Chair Gary Gensler has called for Congress to act, stating in August, “We need additional Congressional authorities to prevent transactions, products, and platforms from falling between regulatory cracks.” Gensler has reached out to Sen. Elizabeth Warren (D-Ma.), who has expressed her own concerns about the need for legislation.
Legislation on Digital Assets in 2021
While regulators and members of Congress talked about the need for legislation, and the debate over cryptocurrency tax reporting in the 2021 infrastructure bill generated headlines, House and Senate bills proposing specific solutions to various issues quietly started to emerge.
Digital Token Sales
Several House bills attempt to address securities law barriers to digital token sales—some of them by building on ideas proposed by regulators in past years.
Exclusion from the definition of a security. Congressional Blockchain Caucus members have been introducing bills to exclude digital tokens from the definition of a security since 2018, and they have revived those bills in 2021. They include the Token Taxonomy Act of 2021 (H.R. 1628), successor to identically named bills in 2018 and 2019, and the Securities Clarity Act (H.R. 4451), successor to a 2020 namesake.
Safe harbor. SEC Commissioner Hester Peirce proposed a regulatory safe harbor for token sales in 2020, and two 2021 bills have proposed statutory safe harbors. Rep. Patrick McHenry (R-N.C.), Republican leader of the House Financial Services Committee, introduced a Clarity for Digital Tokens Act of 2021 (H.R. 5496) that would amend the Securities Act to create a safe harbor providing a grace period of exemption from Securities Act registration requirements. The Digital Asset Market Structure and Investor Protection Act (H.R. 4741) from Rep. Don Beyer (D-Va.) would amend the Securities Exchange Act to define a new type of security—a “digital asset security”—and add issuers of digital asset securities to an existing provision for delayed registration of securities.
Stablecoins
Stablecoins—digital currencies linked to the value of the U.S. dollar or other fiat currencies—have not yet been the subject of regulatory action, although Treasury Secretary Janet Yellen and Federal Reserve Chair Jerome Powell have each underscored the need to create a regulatory framework for them. The Beyer bill proposes to create a regulatory regime for stablecoins by amending Title 31 of the U.S. Code. Treasury Department approval would be required for any “digital asset fiat-based stablecoin” to be issued or used, under an application process to be established by Treasury in consultation with the Federal Reserve, the SEC, and the CFTC.
Serious consideration for any of these proposals in the current session of Congress may be unlikely. A spate of autumn bills on crypto ransom payments (S. 2666, S. 2923, S. 2926, H.R. 5501) shows that Congress is more inclined to pay attention first to issues that are more spectacular and less arcane. Moreover, the arcaneness of digital asset regulatory issues is likely only to increase further, now that major industry players such as Coinbase and Andreessen Horowitz are starting to roll out their own regulatory proposals.
Digital Dollar vs. Digital Yuan
Impetus to pass legislation on another type of digital asset, a central bank digital currency (CBDC), may come from a different source: rivalry with China.
China established itself as a world leader in developing a CBDC with a pilot project launched in 2020, and in 2021, the People’s Bank of China announced that its CBDC will be used at the Beijing Winter Olympics in February 2022. Republican Senators responded by calling for the U.S. Olympic Committee to forbid use of China’s CBDC by U.S. athletes in Beijing and introducing a bill (S. 2543) to require a study of its national security implications.
The Beijing Olympics could motivate a legislative mandate to accelerate implementation of a U.S. digital dollar, which the Federal Reserve has been in the process of considering in 2021. Antecedents to such legislation already exist. A House bill sponsored by 46 Republicans (H.R. 4792) has a provision that would require the Treasury Department to assess China’s CBDC project and report on the status of Federal Reserve work on a CBDC, and the Beyer bill includes a provision amending the Federal Reserve Act to authorize issuing a digital dollar.
Both parties are likely to support creating a digital dollar. The Covid-19 pandemic made a digital dollar for delivery of relief payments a popular idea in 2020, and House Democrats introduced bills with provisions for creating one in 2020 and 2021. Bipartisan support for a bill on a digital dollar, based on concerns both foreign and domestic in nature, could result.
International rivalry and bipartisan support may make the digital dollar a gateway issue for digital asset legislation in 2022. Legislative work on a digital dollar may open the door for considering further digital asset issues—including the regulatory issues that have been emerging for years—in 2022 and beyond.
Isaac Benson
3 years ago
What's the difference between Proof-of-Time and Proof-of-History?
Blockchain validates transactions with consensus algorithms. Bitcoin and Ethereum use Proof-of-Work, while Polkadot and Cardano use Proof-of-Stake.
Other consensus protocols are used to verify transactions besides these two. This post focuses on Proof-of-Time (PoT), used by Analog, and Proof-of-History (PoH), used by Solana as a hybrid consensus protocol.
PoT and PoH may seem similar to users, but they are actually very different protocols.
Proof-of-Time (PoT)
Analog developed Proof-of-Time (PoT) based on Delegated Proof-of-Stake (DPoS). Users select "delegates" to validate the next block in DPoS. PoT uses a ranking system, and validators stake an equal amount of tokens. Validators also "self-select" themselves via a verifiable random function."
The ranking system gives network validators a performance score, with trustworthy validators with a long history getting higher scores. System also considers validator's fixed stake. PoT's ledger is called "Timechain."
Voting on delegates borrows from DPoS, but there are changes. PoT's first voting stage has validators (or "time electors" putting forward a block to be included in the ledger).
Validators are chosen randomly based on their ranking score and fixed stake. One validator is chosen at a time using a Verifiable Delay Function (VDF).
Validators use a verifiable delay function to determine if they'll propose a Timechain block. If chosen, they validate the transaction and generate a VDF proof before submitting both to other Timechain nodes.
This leads to the second process, where the transaction is passed through 1,000 validators selected using the same method. Each validator checks the transaction to ensure it's valid.
If the transaction passes, validators accept the block, and if over 2/3 accept it, it's added to the Timechain.
Proof-of-History (PoH)
Proof-of-History is a consensus algorithm that proves when a transaction occurred. PoH uses a VDF to verify transactions, like Proof-of-Time. Similar to Proof-of-Work, VDFs use a lot of computing power to calculate but little to verify transactions, similar to (PoW).
This shows users and validators how long a transaction took to verify.
PoH uses VDFs to verify event intervals. This process uses cryptography to prevent determining output from input.
The outputs of one transaction are used as inputs for the next. Timestamps record the inputs' order. This checks if data was created before an event.
PoT vs. PoH
PoT and PoH differ in that:
PoT uses VDFs to select validators (or time electors), while PoH measures time between events.
PoH uses a VDF to validate transactions, while PoT uses a ranking system.
PoT's VDF-elected validators verify transactions proposed by a previous validator. PoH uses a VDF to validate transactions and data.
Conclusion
Both Proof-of-Time (PoT) and Proof-of-History (PoH) validate blockchain transactions differently. PoT uses a ranking system to randomly select validators to verify transactions.
PoH uses a Verifiable Delay Function to validate transactions, verify how much time has passed between two events, and allow validators to quickly verify a transaction without malicious actors knowing the input.
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obimy.app
3 years ago
How TikTok helped us grow to 6 million users
This resulted to obimy's new audience.
Hi! obimy's official account. Here, we'll teach app developers and marketers. In 2022, our downloads increased dramatically, so we'll share what we learned.
obimy is what we call a ‘senseger’. It's a new method to communicate digitally. Instead of text, obimy users connect through senses and moods. Feeling playful? Flirt with your partner, pat a pal, or dump water on a classmate. Each feeling is an interactive animation with vibration. It's a wordless app. App Store and Google Play have obimy.
We had 20,000 users in 2022. Two to five thousand of them opened the app monthly. Our DAU metric was 500.
We have 6 million users after 6 months. 500,000 individuals use obimy daily. obimy was the top lifestyle app this week in the U.S.
And TikTok helped.
TikTok fuels obimys' growth. It's why our app exploded. How and what did we learn? Our Head of Marketing, Anastasia Avramenko, knows.
our actions prior to TikTok
We wanted to achieve product-market fit through organic expansion. Quora, Reddit, Facebook Groups, Facebook Ads, Google Ads, Apple Search Ads, and social media activity were tested. Nothing worked. Our CPI was sometimes $4, so unit economics didn't work.
We studied our markets and made audience hypotheses. We promoted our goods and studied our audience through social media quizzes. Our target demographic was Americans in long-distance relationships. I designed quizzes like Test the Strength of Your Relationship to better understand the user base. After each quiz, we encouraged users to download the app to enhance their connection and bridge the distance.
We got 1,000 responses for $50. This helped us comprehend the audience's grief and coping strategies (aka our rivals). I based action items on answers given. If you can't embrace a loved one, use obimy.
We also tried Facebook and Google ads. From the start, we knew it wouldn't work.
We were desperate to discover a free way to get more users.
Our journey to TikTok
TikTok is a great venue for emerging creators. It also helped reach people. Before obimy, my TikTok videos garnered 12 million views without sponsored promotion.
We had to act. TikTok was required.
I wasn't a TikTok user before obimy. Initially, I uploaded promotional content. Call-to-actions appear strange next to dancing challenges and my money don't jiggle jiggle. I learned TikTok. Watch TikTok for an hour was on my to-do list. What a dream job!
Our most popular movies presented the app alongside text outlining what it does. We started promoting them in Europe and the U.S. and got a 16% CTR and $1 CPI, an improvement over our previous efforts.
Somehow, we were expanding. So we came up with new hypotheses, calls to action, and content.
Four months passed, yet we saw no organic growth.
Russia attacked Ukraine.
Our app aimed to be helpful. For now, we're focusing on our Ukrainian audience. I posted sloppy TikToks illustrating how obimy can help during shelling or air raids.
In two hours, Kostia sent me our visitor count. Our servers crashed.
Initially, we had several thousand daily users. Over 200,000 users joined obimy in a week. They posted obimy videos on TikTok, drawing additional users. We've also resumed U.S. video promotion.
We gained 2,000,000 new members with less than $100 in ads, primarily in the U.S. and U.K.
TikTok helped.
The figures
We were confident we'd chosen the ideal tool for organic growth.
Over 45 million people have viewed our own videos plus a ton of user-generated content with the hashtag #obimy.
About 375 thousand people have liked all of our individual videos.
The number of downloads and the virality of videos are directly correlated.
Where are we now?
TikTok fuels our organic growth. We post 56 videos every week and pay to promote viral content.
We use UGC and influencers. We worked with Universal Music Italy on Eurovision. They offered to promote us through their million-follower TikTok influencers. We thought their followers would improve our audience, but it didn't matter. Integration didn't help us. Users that share obimy videos with their followers can reach several million views, which affects our download rate.
After the dust settled, we determined our key audience was 13-18-year-olds. They want to express themselves, but it's sometimes difficult. We're searching for methods to better engage with our users. We opened a Discord server to discuss anime and video games and gather app and content feedback.
TikTok helps us test product updates and hypotheses. Example: I once thought we might raise MAU by prompting users to add strangers as friends. Instead of asking our team to construct it, I made a TikTok urging users to share invite URLs. Users share links under every video we upload, embracing people worldwide.
Key lessons
Don't direct-sell. TikTok isn't for Instagram, Facebook, or YouTube promo videos. Conventional advertisements don't fit. Most users will swipe up and watch humorous doggos.
More product videos are better. Finally. So what?
Encourage interaction. Tagging friends in comments or making videos with the app promotes it more than any marketing spend.
Be odd and risqué. A user mistakenly sent a French kiss to their mom in one of our most popular videos.
TikTok helps test hypotheses and build your user base. It also helps develop apps. In our upcoming blog, we'll guide you through obimy's design revisions based on TikTok. Follow us on Twitter, Instagram, and TikTok.
Esteban
3 years ago
The Berkus Startup Valuation Method: What Is It?
What Is That?
Berkus is a pre-revenue valuation method based exclusively on qualitative criteria, like Scorecard.
Few firms match their financial estimates, especially in the early stages, so valuation methodologies like the Berkus method are a good way to establish a valuation when the economic measures are not reliable.
How does it work?
This technique evaluates five key success factors.
Fundamental principle
Technology
Execution
Strategic alliances in its primary market
Production, followed by sales
The Berkus technique values the business idea and four success factors. As seen in the matrix below, each of these dimensions poses a danger to the startup's success.
It assigns $0-$500,000 to each of these beginning regions. This approach enables a maximum $2.5M pre-money valuation.
This approach relies significantly on geography and uses the US as a baseline, as it differs in every country in Europe.
A set of standards for analyzing each dimension individually
Fundamental principle (or strength of the idea)
Ideas are worthless; execution matters. Most of us can relate to seeing a new business open in our area or a startup get funded and thinking, "I had this concept years ago!" Someone did it.
The concept remains. To assess the idea's viability, we must consider several criteria.
The concept's exclusivity It is necessary to protect a product or service's concept using patents and copyrights. Additionally, it must be capable of generating large profits.
Planned growth and growth that goes in a specific direction have a lot of potential, therefore incorporating them into a business is really advantageous.
The ability of a concept to grow A venture's ability to generate scalable revenue is a key factor in its emergence and continuation. A startup needs a scalable idea in order to compete successfully in the market.
The attraction of a business idea to a broad spectrum of people is significantly influenced by the current socio-political climate. Thus, the requirement for the assumption of conformity.
Concept Validation Ideas must go through rigorous testing with a variety of audiences in order to lower risk during the implementation phase.
Technology (Prototype)
This aspect reduces startup's technological risk. How good is the startup prototype when facing cyber threats, GDPR compliance (in Europe), tech stack replication difficulty, etc.?
Execution
Check the management team's efficacy. A potential angel investor must verify the founders' experience and track record with previous ventures. Good leadership is needed to chart a ship's course.
Strategic alliances in its primary market
Existing and new relationships will play a vital role in the development of both B2B and B2C startups. What are the startup's synergies? potential ones?
Production, followed by sales (product rollout)
Startup success depends on its manufacturing and product rollout. It depends on the overall addressable market, the startup's ability to market and sell their product, and their capacity to provide consistent, high-quality support.
Example
We're now founders of EyeCaramba, a machine vision-assisted streaming platform. My imagination always goes to poor puns when naming a startup.
Since we're first-time founders and the Berkus technique depends exclusively on qualitative methods and the evaluator's skill, we ask our angel-investor acquaintance for a pre-money appraisal of EyeCaramba.
Our friend offers us the following table:
Because we're first-time founders, our pal lowered our Execution score. He knows the idea's value and that the gaming industry is red-hot, with worse startup ideas getting funded, therefore he gave the Basic value the highest value (idea).
EyeCaramba's pre-money valuation is $400,000 + $250,000 + $75,000 + $275,000 + $164,000 (1.16M). Good.
References
https://medium.com/humble-ventures/how-angel-investors-value-pre-revenue-startups-part-iii-8271405f0774#:~:text=pre%2Drevenue%20startups.-,Berkus%20Method,potential%20of%20the%20idea%20itself.%E2%80%9D
https://eqvista.com/berkus-valuation-method-for-startups/
https://www.venionaire.com/early-stage-startup-valuation-part-2-the-berkus-method/
Alex Mathers
2 years ago
400 articles later, nobody bothered to read them.
Writing for readers:
14 years of daily writing.
I post practically everything on social media. I authored hundreds of articles, thousands of tweets, and numerous volumes to almost no one.
Tens of thousands of readers regularly praise me.
I despised writing. I'm stuck now.
I've learned what readers like and what doesn't.
Here are some essential guidelines for writing with impact:
Readers won't understand your work if you can't.
Though obvious, this slipped me up. Share your truths.
Stories engage human brains.
Showing the journey of a person from worm to butterfly inspires the human spirit.
Overthinking hinders powerful writing.
The best ideas come from inner understanding in between thoughts.
Avoid writing to find it. Write.
Writing a masterpiece isn't motivating.
Write for five minutes to simplify. Step-by-step, entertaining, easy steps.
Good writing requires a willingness to make mistakes.
So write loads of garbage that you can edit into a good piece.
Courageous writing.
A courageous story will move readers. Personal experience is best.
Go where few dare.
Templates, outlines, and boundaries help.
Limitations enhance writing.
Excellent writing is straightforward and readable, removing all the unnecessary fat.
Use five words instead of nine.
Use ordinary words instead of uncommon ones.
Readers desire relatability.
Too much perfection will turn it off.
Write to solve an issue if you can't think of anything to write.
Instead, read to inspire. Best authors read.
Every tweet, thread, and novel must have a central idea.
What's its point?
This can make writing confusing.
️ Don't direct your reader.
Readers quit reading. Demonstrate, describe, and relate.
Even if no one responds, have fun. If you hate writing it, the reader will too.