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
Jeff John Roberts
3 years ago
Jack Dorsey and Jay-Z Launch 'Bitcoin Academy' in Brooklyn rapper's home
The new Bitcoin Academy will teach Jay-Marcy Z's Houses neighbors "What is Cryptocurrency."
Jay-Z grew up in Brooklyn's Marcy Houses. The rapper and Block CEO Jack Dorsey are giving back to his hometown by creating the Bitcoin Academy.
The Bitcoin Academy will offer online and in-person classes, including "What is Money?" and "What is Blockchain?"
The program will provide participants with a mobile hotspot and a small amount of Bitcoin for hands-on learning.
Students will receive dinner and two evenings of instruction until early September. The Shawn Carter Foundation will help with on-the-ground instruction.
Jay-Z and Dorsey announced the program Thursday morning. It will begin at Marcy Houses but may be expanded.
Crypto Blockchain Plug and Black Bitcoin Billionaire, which has received a grant from Block, will teach the classes.
Jay-Z, Dorsey reunite
Jay-Z and Dorsey have previously worked together to promote a Bitcoin and crypto-based future.
In 2021, Dorsey's Block (then Square) acquired the rapper's streaming music service Tidal, which they propose using for NFT distribution.
Dorsey and Jay-Z launched an endowment in 2021 to fund Bitcoin development in Africa and India.
Dorsey is funding the new Bitcoin Academy out of his own pocket (as is Jay-Z), but he's also pushed crypto-related charitable endeavors at Block, including a $5 million fund backed by corporate Bitcoin interest.
This post is a summary. Read full article here
Modern Eremite
3 years ago
The complete, easy-to-understand guide to bitcoin
Introduction
Markets rely on knowledge.
The internet provided practically endless knowledge and wisdom. Humanity has never seen such leverage. Technology's progress drives us to adapt to a changing world, changing our routines and behaviors.
In a digital age, people may struggle to live in the analogue world of their upbringing. Can those who can't adapt change their lives? I won't answer. We should teach those who are willing to learn, nevertheless. Unravel the modern world's riddles and give them wisdom.
Adapt or die . Accept the future or remain behind.
This essay will help you comprehend Bitcoin better than most market participants and the general public. Let's dig into Bitcoin.
Join me.
Ascension
Bitcoin.org was registered in August 2008. Bitcoin whitepaper was published on 31 October 2008. The document intrigued and motivated people around the world, including technical engineers and sovereignty seekers. Since then, Bitcoin's whitepaper has been read and researched to comprehend its essential concept.
I recommend reading the whitepaper yourself. You'll be able to say you read the Bitcoin whitepaper instead of simply Googling "what is Bitcoin" and reading the fundamental definition without knowing the revolution's scope. The article links to Bitcoin's whitepaper. To avoid being overwhelmed by the whitepaper, read the following article first.
Bitcoin isn't the first peer-to-peer digital currency. Hashcash or Bit Gold were once popular cryptocurrencies. These two Bitcoin precursors failed to gain traction and produce the network effect needed for general adoption. After many struggles, Bitcoin emerged as the most successful cryptocurrency, leading the way for others.
Satoshi Nakamoto, an active bitcointalk.org user, created Bitcoin. Satoshi's identity remains unknown. Satoshi's last bitcointalk.org login was 12 December 2010. Since then, he's officially disappeared. Thus, conspiracies and riddles surround Bitcoin's creators. I've heard many various theories, some insane and others well-thought-out.
It's not about who created it; it's about knowing its potential. Since its start, Satoshi's legacy has changed the world and will continue to.
Block-by-block blockchain
Bitcoin is a distributed ledger. What's the meaning?
Everyone can view all blockchain transactions, but no one can undo or delete them.
Imagine you and your friends routinely eat out, but only one pays. You're careful with money and what others owe you. How can everyone access the info without it being changed?
You'll keep a notebook of your evening's transactions. Everyone will take a page home. If one of you changed the page's data, the group would notice and reject it. The majority will establish consensus and offer official facts.
Miners add a new Bitcoin block to the main blockchain every 10 minutes. The appended block contains miner-verified transactions. Now that the next block has been added, the network will receive the next set of user transactions.
Bitcoin Proof of Work—prove you earned it
Any firm needs hardworking personnel to expand and serve clients. Bitcoin isn't that different.
Bitcoin's Proof of Work consensus system needs individuals to validate and create new blocks and check for malicious actors. I'll discuss Bitcoin's blockchain consensus method.
Proof of Work helps Bitcoin reach network consensus. The network is checked and safeguarded by CPU, GPU, or ASIC Bitcoin-mining machines (Application-Specific Integrated Circuit).
Every 10 minutes, miners are rewarded in Bitcoin for securing and verifying the network. It's unlikely you'll finish the block. Miners build pools to increase their chances of winning by combining their processing power.
In the early days of Bitcoin, individual mining systems were more popular due to high maintenance costs and larger earnings prospects. Over time, people created larger and larger Bitcoin mining facilities that required a lot of space and sophisticated cooling systems to keep machines from overheating.
Proof of Work is a vital part of the Bitcoin network, as network security requires the processing power of devices purchased with fiat currency. Miners must invest in mining facilities, which creates a new business branch, mining facilities ownership. Bitcoin mining is a topic for a future article.
More mining, less reward
Bitcoin is usually scarce.
Why is it rare? It all comes down to 21,000,000 Bitcoins.
Were all Bitcoins mined? Nope. Bitcoin's supply grows until it hits 21 million coins. Initially, 50BTC each block was mined, and each block took 10 minutes. Around 2140, the last Bitcoin will be mined.
But 50BTC every 10 minutes does not give me the year 2140. Indeed careful reader. So important is Bitcoin's halving process.
What is halving?
The block reward is halved every 210,000 blocks, which takes around 4 years. The initial payout was 50BTC per block and has been decreased to 25BTC after 210,000 blocks. First halving occurred on November 28, 2012, when 10,500,000 BTC (50%) had been mined. As of April 2022, the block reward is 6.25BTC and will be lowered to 3.125BTC by 19 March 2024.
The halving method is tied to Bitcoin's hashrate. Here's what "hashrate" means.
What if we increased the number of miners and hashrate they provide to produce a block every 10 minutes? Wouldn't we manufacture blocks faster?
Every 10 minutes, blocks are generated with little asymmetry. Due to the built-in adaptive difficulty algorithm, the overall hashrate does not affect block production time. With increased hashrate, it's harder to construct a block. We can estimate when the next halving will occur because 10 minutes per block is fixed.
Building with nodes and blocks
For someone new to crypto, the unusual terms and words may be overwhelming. You'll also find everyday words that are easy to guess or have a vague idea of what they mean, how they work, and what they do. Consider blockchain technology.
Nodes and blocks: Think about that for a moment. What is your first idea?
The blockchain is a chain of validated blocks added to the main chain. What's a "block"? What's inside?
The block is another page in the blockchain book that has been filled with transaction information and accepted by the majority.
We won't go into detail about what each block includes and how it's built, as long as you understand its purpose.
What about nodes?
Nodes, along with miners, verify the blockchain's state independently. But why?
To create a full blockchain node, you must download the whole Bitcoin blockchain and check every transaction against Bitcoin's consensus criteria.
What's Bitcoin's size?
In April 2022, the Bitcoin blockchain was 389.72GB.
Bitcoin's blockchain has miners and node runners.
Let's revisit the US gold rush. Miners mine gold with their own power (physical and monetary resources) and are rewarded with gold (Bitcoin). All become richer with more gold, and so does the country.
Nodes are like sheriffs, ensuring everything is done according to consensus rules and that there are no rogue miners or network users.
Lost and held bitcoin
Does the Bitcoin exchange price match each coin's price? How many coins remain after 21,000,000? 21 million or less?
Common reason suggests a 21 million-coin supply.
What if I lost 1BTC from a cold wallet?
What if I saved 1000BTC on paper in 2010 and it was damaged?
What if I mined Bitcoin in 2010 and lost the keys?
Satoshi Nakamoto's coins? Since then, those coins haven't moved.
How many BTC are truly in circulation?
Many people are trying to answer this question, and you may discover a variety of studies and individual research on the topic. Be cautious of the findings because they can't be evaluated and the statistics are hazy guesses.
On the other hand, we have long-term investors who won't sell their Bitcoin or will sell little amounts to cover mining or living needs.
The price of Bitcoin is determined by supply and demand on exchanges using liquid BTC. How many BTC are left after subtracting lost and non-custodial BTC?
We have significantly less Bitcoin in circulation than you think, thus the price may not reflect demand if we knew the exact quantity of coins available.
True HODLers and diamond-hand investors won't sell you their coins, no matter the market.
What's UTXO?
Unspent (U) Transaction (TX) Output (O)
Imagine taking a $100 bill to a store. After choosing a drink and munchies, you walk to the checkout to pay. The cashier takes your $100 bill and gives you $25.50 in change. It's in your wallet.
Is it simply 100$? No way.
The $25.50 in your wallet is unrelated to the $100 bill you used. Your wallet's $25.50 is just bills and coins. Your wallet may contain these coins and bills:
2x 10$ 1x 10$
1x 5$ or 3x 5$
1x 0.50$ 2x 0.25$
Any combination of coins and bills can equal $25.50. You don't care, and I'd wager you've never ever considered it.
That is UTXO. Now, I'll detail the Bitcoin blockchain and how UTXO works, as it's crucial to know what coins you have in your (hopefully) cold wallet.
You purchased 1BTC. Is it all? No. UTXOs equal 1BTC. Then send BTC to a cold wallet. Say you pay 0.001BTC and send 0.999BTC to your cold wallet. Is it the 1BTC you got before? Well, yes and no. The UTXOs are the same or comparable as before, but the blockchain address has changed. It's like if you handed someone a wallet, they removed the coins needed for a network charge, then returned the rest of the coins and notes.
UTXO is a simple concept, but it's crucial to grasp how it works to comprehend dangers like dust attacks and how coins may be tracked.
Lightning Network: fast cash
You've probably heard of "Layer 2 blockchain" projects.
What does it mean?
Layer 2 on a blockchain is an additional layer that increases the speed and quantity of transactions per minute and reduces transaction fees.
Imagine going to an obsolete bank to transfer money to another account and having to pay a charge and wait. You can transfer funds via your bank account or a mobile app without paying a fee, or the fee is low, and the cash appear nearly quickly. Layer 1 and 2 payment systems are different.
Layer 1 is not obsolete; it merely has more essential things to focus on, including providing the blockchain with new, validated blocks, whereas Layer 2 solutions strive to offer Layer 1 with previously processed and verified transactions. The primary blockchain, Bitcoin, will only receive the wallets' final state. All channel transactions until shutting and balancing are irrelevant to the main chain.
Layer 2 and the Lightning Network's goal are now clear. Most Layer 2 solutions on multiple blockchains are created as blockchains, however Lightning Network is not. Remember the following remark, as it best describes Lightning.
Lightning Network connects public and private Bitcoin wallets.
Opening a private channel with another wallet notifies just two parties. The creation and opening of a public channel tells the network that anyone can use it.
Why create a public Lightning Network channel?
Every transaction through your channel generates fees.
Money, if you don't know.
See who benefits when in doubt.
Anonymity, huh?
Bitcoin anonymity? Bitcoin's anonymity was utilized to launder money.
Well… You've heard similar stories. When you ask why or how it permits people to remain anonymous, the conversation ends as if it were just a story someone heard.
Bitcoin isn't private. Pseudonymous.
What if someone tracks your transactions and discovers your wallet address? Where is your anonymity then?
Bitcoin is like bulletproof glass storage; you can't take or change the money. If you dig and analyze the data, you can see what's inside.
Every online action leaves a trace, and traces may be tracked. People often forget this guideline.
A tool like that can help you observe what the major players, or whales, are doing with their coins when the market is uncertain. Many people spend time analyzing on-chain data. Worth it?
Ask yourself a question. What are the big players' options? Do you think they're letting you see their wallets for a small on-chain data fee?
Instead of short-term behaviors, focus on long-term trends.
More wallet transactions leave traces. Having nothing to conceal isn't a defect. Can it lead to regulating Bitcoin so every transaction is tracked like in banks today?
But wait. How can criminals pay out Bitcoin? They're doing it, aren't they?
Mixers can anonymize your coins, letting you to utilize them freely. This is not a guide on how to make your coins anonymous; it could do more harm than good if you don't know what you're doing.
Remember, being anonymous attracts greater attention.
Bitcoin isn't the only cryptocurrency we can use to buy things. Using cryptocurrency appropriately can provide usability and anonymity. Monero (XMR), Zcash (ZEC), and Litecoin (LTC) following the Mimblewimble upgrade are examples.
Summary
Congratulations! You've reached the conclusion of the article and learned about Bitcoin and cryptocurrency. You've entered the future.
You know what Bitcoin is, how its blockchain works, and why it's not anonymous. I bet you can explain Lightning Network and UTXO to your buddies.
Markets rely on knowledge. Prepare yourself for success before taking the first step. Let your expertise be your edge.
This article is a summary of this one.
Ajay Shrestha
2 years ago
Bitcoin's technical innovation: addressing the issue of the Byzantine generals
The 2008 Bitcoin white paper solves the classic computer science consensus problem.
Issue Statement
The Byzantine Generals Problem (BGP) is called after an allegory in which several generals must collaborate and attack a city at the same time to win (figure 1-left). Any general who retreats at the last minute loses the fight (figure 1-right). Thus, precise messengers and no rogue generals are essential. This is difficult without a trusted central authority.
In their 1982 publication, Leslie Lamport, Robert Shostak, and Marshall Please termed this topic the Byzantine Generals Problem to simplify distributed computer systems.
Consensus in a distributed computer network is the issue. Reaching a consensus on which systems work (and stay in the network) and which don't makes maintaining a network tough (i.e., needs to be removed from network). Challenges include unreliable communication routes between systems and mis-reporting systems.
Solving BGP can let us construct machine learning solutions without single points of failure or trusted central entities. One server hosts model parameters while numerous workers train the model. This study describes fault-tolerant Distributed Byzantine Machine Learning.
Bitcoin invented a mechanism for a distributed network of nodes to agree on which transactions should go into the distributed ledger (blockchain) without a trusted central body. It solved BGP implementation. Satoshi Nakamoto, the pseudonymous bitcoin creator, solved the challenge by cleverly combining cryptography and consensus mechanisms.
Disclaimer
This is not financial advice. It discusses a unique computer science solution.
Bitcoin
Bitcoin's white paper begins:
“A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.” Source: https://www.ussc.gov/sites/default/files/pdf/training/annual-national-training-seminar/2018/Emerging_Tech_Bitcoin_Crypto.pdf
Bitcoin's main parts:
The open-source and versioned bitcoin software that governs how nodes, miners, and the bitcoin token operate.
The native kind of token, known as a bitcoin token, may be created by mining (up to 21 million can be created), and it can be transferred between wallet addresses in the bitcoin network.
Distributed Ledger, which contains exact copies of the database (or "blockchain") containing each transaction since the first one in January 2009.
distributed network of nodes (computers) running the distributed ledger replica together with the bitcoin software. They broadcast the transactions to other peer nodes after validating and accepting them.
Proof of work (PoW) is a cryptographic requirement that must be met in order for a miner to be granted permission to add a new block of transactions to the blockchain of the cryptocurrency bitcoin. It takes the form of a valid hash digest. In order to produce new blocks on average every 10 minutes, Bitcoin features a built-in difficulty adjustment function that modifies the valid hash requirement (length of nonce). PoW requires a lot of energy since it must continually generate new hashes at random until it satisfies the criteria.
The competing parties known as miners carry out continuous computing processing to address recurrent cryptography issues. Transaction fees and some freshly minted (mined) bitcoin are the rewards they receive. The amount of hashes produced each second—or hash rate—is a measure of mining capacity.
Cryptography, decentralization, and the proof-of-work consensus method are Bitcoin's most unique features.
Bitcoin uses encryption
Bitcoin employs this established cryptography.
Hashing
digital signatures based on asymmetric encryption
Hashing (SHA-256) (SHA-256)
Hashing converts unique plaintext data into a digest. Creating the plaintext from the digest is impossible. Bitcoin miners generate new hashes using SHA-256 to win block rewards.
A new hash is created from the current block header and a variable value called nonce. To achieve the required hash, mining involves altering the nonce and re-hashing.
The block header contains the previous block hash and a Merkle root, which contains hashes of all transactions in the block. Thus, a chain of blocks with increasing hashes links back to the first block. Hashing protects new transactions and makes the bitcoin blockchain immutable. After a transaction block is mined, it becomes hard to fabricate even a little entry.
Asymmetric Cryptography Digital Signatures
Asymmetric cryptography (public-key encryption) requires each side to have a secret and public key. Public keys (wallet addresses) can be shared with the transaction party, but private keys should not. A message (e.g., bitcoin payment record) can only be signed by the owner (sender) with the private key, but any node or anybody with access to the public key (visible in the blockchain) can verify it. Alex will submit a digitally signed transaction with a desired amount of bitcoin addressed to Bob's wallet to a node to send bitcoin to Bob. Alex alone has the secret keys to authorize that amount. Alex's blockchain public key allows anyone to verify the transaction.
Solution
Now, apply bitcoin to BGP. BGP generals resemble bitcoin nodes. The generals' consensus is like bitcoin nodes' blockchain block selection. Bitcoin software on all nodes can:
Check transactions (i.e., validate digital signatures)
2. Accept and propagate just the first miner to receive the valid hash and verify it accomplished the task. The only way to guess the proper hash is to brute force it by repeatedly producing one with the fixed/current block header and a fresh nonce value.
Thus, PoW and a dispersed network of nodes that accept blocks from miners that solve the unfalsifiable cryptographic challenge solve consensus.
Suppose:
Unreliable nodes
Unreliable miners
Bitcoin accepts the longest chain if rogue nodes cause divergence in accepted blocks. Thus, rogue nodes must outnumber honest nodes in accepting/forming the longer chain for invalid transactions to reach the blockchain. As of November 2022, 7000 coordinated rogue nodes are needed to takeover the bitcoin network.
Dishonest miners could also try to insert blocks with falsified transactions (double spend, reverse, censor, etc.) into the chain. This requires over 50% (51% attack) of miners (total computational power) to outguess the hash and attack the network. Mining hash rate exceeds 200 million (source). Rewards and transaction fees encourage miners to cooperate rather than attack. Quantum computers may become a threat.
Visit my Quantum Computing post.
Quantum computers—what are they? Quantum computers will have a big influence. towardsdatascience.com
Nodes have more power than miners since they can validate transactions and reject fake blocks. Thus, the network is secure if honest nodes are the majority.
Summary
Table 1 compares three Byzantine Generals Problem implementations.
Bitcoin white paper and implementation solved the consensus challenge of distributed systems without central governance. It solved the illusive Byzantine Generals Problem.
Resources
Resources
Source-code for Bitcoin Core Software — https://github.com/bitcoin/bitcoin
Bitcoin white paper — https://bitcoin.org/bitcoin.pdf
https://www.microsoft.com/en-us/research/publication/byzantine-generals-problem/
https://www.microsoft.com/en-us/research/uploads/prod/2016/12/The-Byzantine-Generals-Problem.pdf
Genuinely Distributed Byzantine Machine Learning, El-Mahdi El-Mhamdi et al., 2020. ACM, New York, NY, https://doi.org/10.1145/3382734.3405695
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Alex Mathers
3 years ago Draft
12 practices of the zenith individuals I know
Calmness is a vital life skill.
It aids communication. It boosts creativity and performance.
I've studied calm people's habits for years. Commonalities:
Have learned to laugh at themselves.
Those who have something to protect can’t help but make it a very serious business, which drains the energy out of the room.
They are fixated on positive pursuits like making cool things, building a strong physique, and having fun with others rather than on depressing influences like the news and gossip.
Every day, spend at least 20 minutes moving, whether it's walking, yoga, or lifting weights.
Discover ways to take pleasure in life's challenges.
Since perspective is malleable, they change their view.
Set your own needs first.
Stressed people neglect themselves and wonder why they struggle.
Prioritize self-care.
Don't ruin your life to please others.
Make something.
Calm people create more than react.
They love creating beautiful things—paintings, children, relationships, and projects.
Hold your breath, please.
If you're stressed or angry, you may be surprised how much time you spend holding your breath and tightening your belly.
Release, breathe, and relax to find calm.
Stopped rushing.
Rushing is disadvantageous.
Calm people handle life better.
Are attuned to their personal dietary needs.
They avoid junk food and eat foods that keep them healthy, happy, and calm.
Don’t take anything personally.
Stressed people control everything.
Self-conscious.
Calm people put others and their work first.
Keep their surroundings neat.
Maintaining an uplifting and clutter-free environment daily calms the mind.
Minimise negative people.
Calm people are ruthless with their boundaries and avoid negative and drama-prone people.
Alex Mathers
24 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.
Matthew O'Riordan
3 years ago
Trends in SaaS Funding from 2016 to 2022
Christopher Janz of Point Nine Capital created the SaaS napkin in 2016. This post shows how founders have raised cash in the last 6 years. View raw data.
Round size
Unsurprisingly, round sizes have expanded and will taper down in 2022. In 2016, pre-seed rounds were $200k to $500k; currently, they're $1-$2m. Despite the macroeconomic scenario, Series A have expanded from $3m to $12m in 2016 to $6m and $18m in 2022.
Valuation
There are hints that valuations are rebounding this year. Pre-seed valuations in 2022 are $12m from $3m in 2016, and Series B prices are $270m from $100m in 2016.
Compared to public SaaS multiples, Series B valuations more closely reflect the market, but Seed and Series A prices seem to be inflated regardless of the market.
I'd like to know how each annual cohort performed for investors, based on the year they invested and the valuations. I can't access this information.
ARR
Seed firms' ARR forecasts have risen from $0 to $0.6m to $0 to $1m. 2016 expected $1.2m to $3m, 2021 $0.5m to $4m, and this year $0.5m to $2.5m, suggesting that Series A firms may raise with less ARR today. Series B minutes fell from $4.2m to $3m.
Capitalization Rate
2022 is the year that VCs start discussing capital efficiency in portfolio meetings. Given the economic shift in the markets and the stealthy VC meltdown, it's not surprising. Christopher Janz added capital efficiency to the SaaS Napkin as a new statistic for Series A (3.5x) and Series B. (2.5x). Your investors must live under a rock if they haven't asked about capital efficiency. If you're unsure:
The Capital Efficiency Ratio is the ratio of how much a company has spent growing revenue and how much they’re receiving in return. It is the broadest measure of company effectiveness in generating ARR
What next?
No one knows what's next, including me. All startup and growing enterprises around me are tightening their belts and extending their runways in anticipation of a difficult fundraising ride. If you're wanting to raise money but can wait, wait till the market is more stable and access to money is easier.