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Vitalik

Vitalik

4 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

(Edited)

Hackernoon

Hackernoon

4 years ago


👏 Awesome post! When is part 3 coming?

Trent Lapinski

Trent Lapinski

4 years ago

Very complex topic, great explanation

More on Web3 & Crypto

TheRedKnight

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.

Onchain Wizard

Onchain Wizard

3 years ago

Three Arrows Capital  & Celsius Updates

I read 1k+ page 3AC liquidation documentation so you don't have to. Also sharing revised Celsius recovery plans.

3AC's liquidation documents:

Someone disclosed 3AC liquidation records in the BVI courts recently. I'll discuss the leak's timeline and other highlights.

Three Arrows Capital began trading traditional currencies in emerging markets in 2012. They switched to equities and crypto, then purely crypto in 2018.

By 2020, the firm had $703mm in net assets and $1.8bn in loans (these guys really like debt).

Three Arrows Capital statement of Assets and Liabilities

The firm's net assets under control reached $3bn in April 2022, according to the filings. 3AC had $600mm of LUNA/UST exposure before May 9th 2022, which put them over.

LUNA and UST go to zero quickly (I wrote about the mechanics of the blowup here). Kyle Davies, 3AC co-founder, told Blockchain.com on May 13 that they have $2.4bn in assets and $2.3bn NAV vs. $2bn in borrowings. As BTC and ETH plunged 33% and 50%, the company became insolvent by mid-2022.

Three Arrows Capital Assets Under Management letter, Net Assets Value

3AC sent $32mm to Tai Ping Shen, a Cayman Islands business owned by Su Zhu and Davies' partner, Kelly Kaili Chen (who knows what is going on here).

3AC had borrowed over $3.5bn in notional principle, with Genesis ($2.4bn) and Voyager ($650mm) having the most exposure.

Genesis demanded $355mm in further collateral in June.

Genesis Capital Margin Call to Three Arrows Capital

Deribit (another 3AC investment) called for $80 million in mid-June.

Three Arrows Capital main account overview

Even in mid-June, the corporation was trying to borrow more money to stay afloat. They approached Genesis for another $125mm loan (to pay another lender) and HODLnauts for BTC & ETH loans.

Pretty crazy. 3AC founders used borrowed money to buy a $50 million boat, according to the leak.

Su requesting for $5m + Chen Kaili Kelly asserting they loaned $65m unsecured to 3AC are identified as creditors.

Mr Zhu

Ms Chen Kaili Kelly

Celsius:

This bankruptcy presentation shows the Celsius breakdown from March to July 14, 2022. From $22bn to $4bn, crypto assets plummeted from $14.6bn to $1.8bn (ouch). $16.5bn in user liabilities dropped to $4.72bn.

Celcius Asset Snapshot

In my recent post, I examined if "forced selling" is over, with Celsius' crypto assets being a major overhang. In this presentation, it looks that Chapter 11 will provide clients the opportunity to accept cash at a discount or remain long crypto. Provided that a fresh source of money is unlikely to enter the Celsius situation, cash at a discount or crypto given to customers will likely remain a near-term market risk - cash at a discount will likely come from selling crypto assets, while customers who receive crypto could sell at any time. I'll share any Celsius updates I find.

Conclusion

Only Celsius and the Mt Gox BTC unlock remain as forced selling catalysts. While everything went through a "relief" pump, with ETH up 75% from the bottom and numerous alts multiples higher, there are still macro dangers to equities + risk assets. There's a lot of wealth waiting to be deployed in crypto ($153bn in stables), but fund managers are risk apprehensive (lower than 2008 levels).

Taking higher than normal risk levels

We're hopefully over crypto's "bottom," with peak anxiety and forced selling behind us, but we may chop around.


To see the full article, click here.

Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 1)

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.

You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.

In the context of blockchains, this has two very powerful applications:

  1. Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
  2. Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.

But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.

Why ZK-SNARKs "should" be hard

Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.

A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.

One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?

Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.

But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.


It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.

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? There is a clever solution.

see part 2

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DC Palter

DC Palter

3 years ago

How Will You Generate $100 Million in Revenue? The Startup Business Plan

A top-down company plan facilitates decision-making and impresses investors.

Photo by Andy Hermawan on Unsplash

A startup business plan starts with the product, the target customers, how to reach them, and how to grow the business.

Bottom-up is terrific unless venture investors fund it.

If it can prove how it can exceed $100M in sales, investors will invest. If not, the business may be wonderful, but it's not venture capital-investable.

As a rule, venture investors only fund firms that expect to reach $100M within 5 years.

Investors get nothing until an acquisition or IPO. To make up for 90% of failed investments and still generate 20% annual returns, portfolio successes must exit with a 25x return. A $20M-valued company must be acquired for $500M or more.

This requires $100M in sales (or being on a nearly vertical trajectory to get there). The company has 5 years to attain that milestone and create the requisite ROI.

This motivates venture investors (venture funds and angel investors) to hunt for $100M firms within 5 years. When you pitch investors, you outline how you'll achieve that aim.

I'm wary of pitches after seeing a million hockey sticks predicting $5M to $100M in year 5 that never materialized. Doubtful.

Startups fail because they don't have enough clients, not because they don't produce a great product. That jump from $5M to $100M never happens. The company reaches $5M or $10M, growing at 10% or 20% per year.  That's great, but not enough for a $500 million deal.

Once it becomes clear the company won’t reach orbit, investors write it off as a loss. When a corporation runs out of money, it's shut down or sold in a fire sale. The company can survive if expenses are trimmed to match revenues, but investors lose everything.

When I hear a pitch, I'm not looking for bright income projections but a viable plan to achieve them. Answer these questions in your pitch.

  • Is the market size sufficient to generate $100 million in revenue?

  • Will the initial beachhead market serve as a springboard to the larger market or as quicksand that hinders progress?

  • What marketing plan will bring in $100 million in revenue? Is the market diffuse and will cost millions of dollars in advertising, or is it one, focused market that can be tackled with a team of salespeople?

  • Will the business be able to bridge the gap from a small but fervent set of early adopters to a larger user base and avoid lock-in with their current solution?

  • Will the team be able to manage a $100 million company with hundreds of people, or will hypergrowth force the organization to collapse into chaos?

  • Once the company starts stealing market share from the industry giants, how will it deter copycats?

The requirement to reach $100M may be onerous, but it provides a context for difficult decisions: What should the product be? Where should we concentrate? who should we hire? Every strategic choice must consider how to reach $100M in 5 years.

Focusing on $100M streamlines investor pitches. Instead of explaining everything, focus on how you'll attain $100M.

As an investor, I know I'll lose my money if the startup doesn't reach this milestone, so the revenue prediction is the first thing I look at in a pitch deck.

Reaching the $100M goal needs to be the first thing the entrepreneur thinks about when putting together the business plan, the central story of the pitch, and the criteria for every important decision the company makes.

xuanling11

xuanling11

3 years ago

Reddit NFT Achievement

https://reddit.zendesk.com/hc/article_attachments/7582537085332/1._What_are_Collectible_Avatars_.png

Reddit's NFT market is alive and well.

NFT owners outnumber OpenSea on Reddit.

Reddit NFTs flip in OpenSea in days:

Fast-selling.

NFT sales will make Reddit's current communities more engaged.

I don't think NFTs will affect existing groups, but they will build hype for people to acquire them.

The first season of Collectibles is unique, but many missed the first season.

Second-season NFTs are less likely to be sold for a higher price than first-season ones.

If you use Reddit, it's fun to own NFTs.

Hector de Isidro

Hector de Isidro

3 years ago

Why can't you speak English fluently even though you understand it?

Many of us have struggled for years to master a second language (in my case, English). Because (at least in my situation) we've always used an input-based system or method.

I'll explain in detail, but briefly: We can understand some conversations or sentences (since we've trained), but we can't give sophisticated answers or speak fluently (because we have NOT trained at all).

What exactly is input-based learning?

Reading, listening, writing, and speaking are key language abilities (if you look closely at that list, it seems that people tend to order them in this way: inadvertently giving more priority to the first ones than to the last ones).

These talents fall under two learning styles:

  • Reading and listening are input-based activities (sometimes referred to as receptive skills or passive learning).

  • Writing and speaking are output-based tasks (also known as the productive skills and/or active learning).

by Anson Wong

What's the best learning style? To learn a language, we must master four interconnected skills. The difficulty is how much time and effort we give each.

According to Shion Kabasawa's books The Power of Input: How to Maximize Learning and The Power of Output: How to Change Learning to Outcome (available only in Japanese), we spend 7:3 more time on Input Based skills than Output Based skills when we should be doing the opposite, leaning more towards Output (Input: Output->3:7).

I can't tell you how he got those numbers, but I think he's not far off because, for example, think of how many people say they're learning a second language and are satisfied bragging about it by only watching TV, series, or movies in VO (and/or reading a book or whatever) their Input is: 7:0 output!

You can't be good at a sport by watching TikTok videos about it; you must play.

“being pushed to produce language puts learners in a better position to notice the ‘gaps’ in their language knowledge”, encouraging them to ‘upgrade’ their existing interlanguage system. And, as they are pushed to produce language in real time and thereby forced to automate low-level operations by incorporating them into higher-level routines, it may also contribute to the development of fluency. — Scott Thornbury (P is for Push)

How may I practice output-based learning more?

I know that listening or reading is easy and convenient because we can do it on our own in a wide range of situations, even during another activity (although, as you know, it's not ideal), writing can be tedious/boring (it's funny that we almost always excuse ourselves in the lack of ideas), and speaking requires an interlocutor. But we must leave our comfort zone and modify our thinking to go from 3:7 to 7:3. (or at least balance it better to something closer). Gradually.

“You don’t have to do a lot every day, but you have to do something. Something. Every day.” — Callie Oettinger (Do this every day)

We can practice speaking like boxers shadow box.

Speaking out loud strengthens the mind-mouth link (otherwise, you will still speak fluently in your mind but you will choke when speaking out loud). This doesn't mean we should talk to ourselves on the way to work, while strolling, or on public transportation. We should try to do it without disturbing others, such as explaining what we've heard, read, or seen (the list is endless: you can TALK about what happened yesterday, your bedtime book, stories you heard at the office, that new kitten video you saw on Instagram, an experience you had, some new fact, that new boring episode you watched on Netflix, what you ate, what you're going to do next, your upcoming vacation, what’s trending, the news of the day)

Who will correct my grammar, vocabulary, or pronunciation with an imagined friend? We can't have everything, but tools and services can help [1].

Lack of bravery

Fear of speaking a language different than one's mother tongue in front of native speakers is global. It's easier said than done, because strangers, not your friends, will always make fun of your accent or faults. Accept it and try again. Karma will prevail.

Perfectionism is a trap. Stop self-sabotaging. Communication is key (and for that you have to practice the Output too ).

“Don’t forget to have fun and enjoy the process.” — Ruri Ohama

[1] Grammarly, Deepl, Google Translate, etc.