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
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
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.
Vitalik
3 years ago
Fairness alternatives to selling below market clearing prices (or community sentiment, or fun)
When a seller has a limited supply of an item in high (or uncertain and possibly high) demand, they frequently set a price far below what "the market will bear." As a result, the item sells out quickly, with lucky buyers being those who tried to buy first. This has happened in the Ethereum ecosystem, particularly with NFT sales and token sales/ICOs. But this phenomenon is much older; concerts and restaurants frequently make similar choices, resulting in fast sell-outs or long lines.
Why do sellers do this? Economists have long wondered. A seller should sell at the market-clearing price if the amount buyers are willing to buy exactly equals the amount the seller has to sell. If the seller is unsure of the market-clearing price, they should sell at auction and let the market decide. So, if you want to sell something below market value, don't do it. It will hurt your sales and it will hurt your customers. The competitions created by non-price-based allocation mechanisms can sometimes have negative externalities that harm third parties, as we will see.
However, the prevalence of below-market-clearing pricing suggests that sellers do it for good reason. And indeed, as decades of research into this topic has shown, there often are. So, is it possible to achieve the same goals with less unfairness, inefficiency, and harm?
Selling at below market-clearing prices has large inefficiencies and negative externalities
An item that is sold at market value or at an auction allows someone who really wants it to pay the high price or bid high in the auction. So, if a seller sells an item below market value, some people will get it and others won't. But the mechanism deciding who gets the item isn't random, and it's not always well correlated with participant desire. It's not always about being the fastest at clicking buttons. Sometimes it means waking up at 2 a.m. (but 11 p.m. or even 2 p.m. elsewhere). Sometimes it's just a "auction by other means" that's more chaotic, less efficient, and has far more negative externalities.
There are many examples of this in the Ethereum ecosystem. Let's start with the 2017 ICO craze. For example, an ICO project would set the price of the token and a hard maximum for how many tokens they are willing to sell, and the sale would start automatically at some point in time. The sale ends when the cap is reached.
So what? In practice, these sales often ended in 30 seconds or less. Everyone would start sending transactions in as soon as (or just before) the sale started, offering higher and higher fees to encourage miners to include their transaction first. Instead of the token seller receiving revenue, miners receive it, and the sale prices out all other applications on-chain.
The most expensive transaction in the BAT sale set a fee of 580,000 gwei, paying a fee of $6,600 to get included in the sale.
Many ICOs after that tried various strategies to avoid these gas price auctions; one ICO notably had a smart contract that checked the transaction's gasprice and rejected it if it exceeded 50 gwei. But that didn't solve the issue. Buyers hoping to game the system sent many transactions hoping one would get through. An auction by another name, clogging the chain even more.
ICOs have recently lost popularity, but NFTs and NFT sales have risen in popularity. But the NFT space didn't learn from 2017; they do fixed-quantity sales just like ICOs (eg. see the mint function on lines 97-108 of this contract here). So what?
That's not the worst; some NFT sales have caused gas price spikes of up to 2000 gwei.
High gas prices from users fighting to get in first by sending higher and higher transaction fees. An auction renamed, pricing out all other applications on-chain for 15 minutes.
So why do sellers sometimes sell below market price?
Selling below market value is nothing new, and many articles, papers, and podcasts have written (and sometimes bitterly complained) about the unwillingness to use auctions or set prices to market-clearing levels.
Many of the arguments are the same for both blockchain (NFTs and ICOs) and non-blockchain examples (popular restaurants and concerts). Fairness and the desire not to exclude the poor, lose fans or create tension by being perceived as greedy are major concerns. The 1986 paper by Kahneman, Knetsch, and Thaler explains how fairness and greed can influence these decisions. I recall that the desire to avoid perceptions of greed was also a major factor in discouraging the use of auction-like mechanisms in 2017.
Aside from fairness concerns, there is the argument that selling out and long lines create a sense of popularity and prestige, making the product more appealing to others. Long lines should have the same effect as high prices in a rational actor model, but this is not the case in reality. This applies to ICOs and NFTs as well as restaurants. Aside from increasing marketing value, some people find the game of grabbing a limited set of opportunities first before everyone else is quite entertaining.
But there are some blockchain-specific factors. One argument for selling ICO tokens below market value (and one that persuaded the OmiseGo team to adopt their capped sale strategy) is community dynamics. The first rule of community sentiment management is to encourage price increases. People are happy if they are "in the green." If the price drops below what the community members paid, they are unhappy and start calling you a scammer, possibly causing a social media cascade where everyone calls you a scammer.
This effect can only be avoided by pricing low enough that post-launch market prices will almost certainly be higher. But how do you do this without creating a rush for the gates that leads to an auction?
Interesting solutions
It's 2021. We have a blockchain. The blockchain is home to a powerful decentralized finance ecosystem, as well as a rapidly expanding set of non-financial tools. The blockchain also allows us to reset social norms. Where decades of economists yelling about "efficiency" failed, blockchains may be able to legitimize new uses of mechanism design. If we could use our more advanced tools to create an approach that more directly solves the problems, with fewer side effects, wouldn't that be better than fiddling with a coarse-grained one-dimensional strategy space of selling at market price versus below market price?
Begin with the goals. We'll try to cover ICOs, NFTs, and conference tickets (really a type of NFT) all at the same time.
1. Fairness: don't completely exclude low-income people from participation; give them a chance. The goal of token sales is to avoid high initial wealth concentration and have a larger and more diverse initial token holder community.
2. Don’t create races: Avoid situations where many people rush to do the same thing and only a few get in (this is the type of situation that leads to the horrible auctions-by-another-name that we saw above).
3. Don't require precise market knowledge: the mechanism should work even if the seller has no idea how much demand exists.
4. Fun: The process of participating in the sale should be fun and game-like, but not frustrating.
5. Give buyers positive expected returns: in the case of a token (or an NFT), buyers should expect price increases rather than decreases. This requires selling below market value.
Let's start with (1). From Ethereum's perspective, there is a simple solution. Use a tool designed for the job: proof of personhood protocols! Here's one quick idea:
Mechanism 1 Each participant (verified by ID) can buy up to ‘’X’’ tokens at price P, with the option to buy more at an auction.
With the per-person mechanism, buyers can get positive expected returns for the portion sold through the per-person mechanism, and the auction part does not require sellers to understand demand levels. Is it race-free? The number of participants buying through the per-person pool appears to be high. But what if the per-person pool isn't big enough to accommodate everyone?
Make the per-person allocation amount dynamic.
Mechanism 2 Each participant can deposit up to X tokens into a smart contract to declare interest. Last but not least, each buyer receives min(X, N / buyers) tokens, where N is the total sold through the per-person pool (some other amount can also be sold by auction). The buyer gets their deposit back if it exceeds the amount needed to buy their allocation.
No longer is there a race condition based on the number of buyers per person. No matter how high the demand, it's always better to join sooner rather than later.
Here's another idea if you like clever game mechanics with fancy quadratic formulas.
Mechanism 3 Each participant can buy X units at a price P X 2 up to a maximum of C tokens per buyer. C starts low and gradually increases until enough units are sold.
The quantity allocated to each buyer is theoretically optimal, though post-sale transfers will degrade this optimality over time. Mechanisms 2 and 3 appear to meet all of the above objectives. They're not perfect, but they're good starting points.
One more issue. For fixed and limited supply NFTs, the equilibrium purchased quantity per participant may be fractional (in mechanism 2, number of buyers > N, and in mechanism 3, setting C = 1 may already lead to over-subscription). With fractional sales, you can offer lottery tickets: if there are N items available, you have a chance of N/number of buyers of getting the item, otherwise you get a refund. For a conference, groups could bundle their lottery tickets to guarantee a win or a loss. The certainty of getting the item can be auctioned.
The bottom tier of "sponsorships" can be used to sell conference tickets at market rate. You may end up with a sponsor board full of people's faces, but is that okay? After all, John Lilic was on EthCC's sponsor board!
Simply put, if you want to be reliably fair to people, you need an input that explicitly measures people. Authentication protocols do this (and if desired can be combined with zero knowledge proofs to ensure privacy). So we should combine the efficiency of market and auction-based pricing with the equality of proof of personhood mechanics.
Answers to possible questions
Q: Won't people who don't care about your project buy the item and immediately resell it?
A: Not at first. Meta-games take time to appear in practice. If they do, making them untradeable for a while may help mitigate the damage. Using your face to claim that your previous account was hacked and that your identity, including everything in it, should be moved to another account works because proof-of-personhood identities are untradeable.
Q: What if I want to make my item available to a specific community?
A: Instead of ID, use proof of participation tokens linked to community events. Another option, also serving egalitarian and gamification purposes, is to encrypt items within publicly available puzzle solutions.
Q: How do we know they'll accept? Strange new mechanisms have previously been resisted.
A: Having economists write screeds about how they "should" accept a new mechanism that they find strange is difficult (or even "equity"). However, abrupt changes in context effectively reset people's expectations. So the blockchain space is the best place to try this. You could wait for the "metaverse", but it's possible that the best version will run on Ethereum anyway, so start now.
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Teronie Donalson
3 years ago
The best financial advice I've ever received and how you can use it.
Taking great financial advice is key to financial success.
A wealthy man told me to INVEST MY MONEY when I was young.
As I entered Starbucks, an older man was leaving. I noticed his watch and expensive-looking shirt, not like the guy in the photo, but one made of fine fabric like vicuna wool, which can only be shorn every two to three years. His Bentley confirmed my suspicions about his wealth.
This guy looked like James Bond, so I asked him how to get rich like him.
"Drug dealer?" he laughed.
Whether he was telling the truth, I'll never know, and I didn't want to be an accessory, but he quickly added, "Kid, invest your money; it will do wonders." He left.
When he told me to invest, he didn't say what. Later, I realized the investment game has so many levels that even if he drew me a blueprint, I wouldn't understand it.
The best advice I received was to invest my earnings. I must decide where to invest.
I'll preface by saying I'm not a financial advisor or Your financial advisor, but I'll share what I've learned from books, links, and sources. The rest is up to you.
Basically:
Invest your Money
Money is money, whether you call it cake, dough, moolah, benjamins, paper, bread, etc.
If you're lucky, you can buy one of the gold shirts in the photo.
Investing your money today means putting it towards anything that could be profitable.
According to the website Investopedia:
“Investing is allocating money to generate income or profit.”
You can invest in a business, real estate, or a skill that will pay off later.
Everyone has different goals and wants at different stages of life, so investing varies.
He was probably a sugar daddy with his Bentley, nice shirt, and Rolex.
In my twenties, I started making "good" money; now, in my forties, with a family and three kids, I'm building a legacy for my grandkids.
“It’s not how much money you make, but how much money you keep, how hard it works for you, and how many generations you keep it for.” — Robert Kiyosaki.
Money isn't evil, but lack of it is.
Financial stress is a major source of problems, according to studies.
Being broke hurts, especially if you want to provide for your family or do things.
“An investment in knowledge pays the best interest.” — Benjamin Franklin.
Investing in knowledge is invaluable. Before investing, do your homework.
You probably didn't learn about investing when you were young, like I didn't. My parents were in survival mode, making investing difficult.
In my 20s, I worked in banking to better understand money.
So, why invest?
Growth requires investment.
Investing puts money to work and can build wealth. Your money may outpace inflation with smart investing. Compounding and the risk-return tradeoff boost investment growth.
Investing your money means you won't have to work forever — unless you want to.
Two common ways to make money are;
-working hard,
and
-interest or capital gains from investments.
Capital gains can help you invest.
“How many millionaires do you know who have become wealthy by investing in savings accounts? I rest my case.” — Robert G. Allen
If you keep your money in a savings account, you'll earn less than 2% interest at best; the bank makes money by loaning it out.
Savings accounts are a safe bet, but the low-interest rates limit your gains.
Don't skip it. An emergency fund should be in a savings account, not the market.
Other reasons to invest:
Investing can generate regular income.
If you own rental properties, the tenant's rent will add to your cash flow.
Daily, weekly, or monthly rentals (think Airbnb) generate higher returns year-round.
Capital gains are taxed less than earned income if you own dividend-paying or appreciating stock.
Time is on your side
“Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t — pays it.” — Albert Einstein
Historical data shows that young investors outperform older investors. So you can use compound interest over decades instead of investing at 45 and having less time to earn.
If I had taken that man's advice and invested in my twenties, I would have made a decent return by my thirties. (Depending on my investments)
So for those who live a YOLO (you only live once) life, investing can't hurt.
Investing increases your knowledge.
Lessons are clearer when you're invested. Each win boosts confidence and draws attention to losses. Losing money prompts you to investigate.
Before investing, I read many financial books, but I didn't understand them until I invested.
Now what?
What do you invest in? Equities, mutual funds, ETFs, retirement accounts, savings, business, real estate, cryptocurrencies, marijuana, insurance, etc.
The key is to start somewhere. Know you don't know everything. You must care.
“A journey of a thousand miles must begin with a single step.” — Lao Tzu.
Start simple because there's so much information. My first investment book was:
Robert Kiyosaki's "Rich Dad, Poor Dad"
This easy-to-read book made me hungry for more. This book is about the money lessons rich parents teach their children, which poor and middle-class parents neglect. The poor and middle-class work for money, while the rich let their assets work for them, says Kiyosaki.
There is so much to learn, but you gotta start somewhere.
More books:
***Wisdom
I hope I'm not suggesting that investing makes everything rosy. Remember three rules:
1. Losing money is possible.
2. Losing money is possible.
3. Losing money is possible.
You can lose money, so be careful.
Read, research, invest.
Golden rules for Investing your money
Never invest money you can't lose.
Financial freedom is possible regardless of income.
"Courage taught me that any sound investment will pay off, no matter how bad a crisis gets." Helu Carlos
"I'll tell you Wall Street's secret to wealth. When others are afraid, you're greedy. You're afraid when others are greedy. Buffett
Buy low, sell high, and have an exit strategy.
Ask experts or wealthy people for advice.
"With a good understanding of history, we can have a clear vision of the future." Helu Carlos
"It's not whether you're right or wrong, but how much money you make when you're right." Soros
"The individual investor should act as an investor, not a speculator." Graham
"It's different this time" is the most dangerous investment phrase. Templeton
Lastly,
Avoid quick-money schemes. Building wealth takes years, not months.
Start small and work your way up.
Thanks for reading!
This post is a summary. Read the full article here
Mark Shpuntov
3 years ago
How to Produce a Month's Worth of Content for Social Media in a Day
New social media producers' biggest error
The Treadmill of Social Media Content
New creators focus on the wrong platforms.
They post to Instagram, Twitter, TikTok, etc.
They create daily material, but it's never enough for social media algorithms.
Creators recognize they're on a content creation treadmill.
They have to keep publishing content daily just to stay on the algorithm’s good side and avoid losing the audience they’ve built on the platform.
This is exhausting and unsustainable, causing creator burnout.
They focus on short-lived platforms, which is an issue.
Comparing low- and high-return social media platforms
Social media networks are great for reaching new audiences.
Their algorithm is meant to viralize material.
Social media can use you for their aims if you're not careful.
To master social media, focus on the right platforms.
To do this, we must differentiate low-ROI and high-ROI platforms:
Low ROI platforms are ones where content has a short lifespan. High ROI platforms are ones where content has a longer lifespan.
A tweet may be shown for 12 days. If you write an article or blog post, it could get visitors for 23 years.
ROI is drastically different.
New creators have limited time and high learning curves.
Nothing is possible.
First create content for high-return platforms.
ROI for social media platforms
Here are high-return platforms:
Your Blog - A single blog article can rank and attract a ton of targeted traffic for a very long time thanks to the power of SEO.
YouTube - YouTube has a reputation for showing search results or sidebar recommendations for videos uploaded 23 years ago. A superb video you make may receive views for a number of years.
Medium - A platform dedicated to excellent writing is called Medium. When you write an article about a subject that never goes out of style, you're building a digital asset that can drive visitors indefinitely.
These high ROI platforms let you generate content once and get visitors for years.
This contrasts with low ROI platforms:
Twitter
Instagram
TikTok
LinkedIn
Facebook
The posts you publish on these networks have a 23-day lifetime. Instagram Reels and TikToks are exceptions since viral content can last months.
If you want to make content creation sustainable and enjoyable, you must focus the majority of your efforts on creating high ROI content first. You can then use the magic of repurposing content to publish content to the lower ROI platforms to increase your reach and exposure.
How To Use Your Content Again
So, you’ve decided to focus on the high ROI platforms.
Great!
You've published an article or a YouTube video.
You worked hard on it.
Now you have fresh stuff.
What now?
If you are not repurposing each piece of content for multiple platforms, you are throwing away your time and efforts.
You've created fantastic material, so why not distribute it across platforms?
Repurposing Content Step-by-Step
For me, it's writing a blog article, but you might start with a video or podcast.
The premise is the same regardless of the medium.
Start by creating content for a high ROI platform (YouTube, Blog Post, Medium). Then, repurpose, edit, and repost it to the lower ROI platforms.
Here's how to repurpose pillar material for other platforms:
Post the article on your blog.
Put your piece on Medium (use the canonical link to point to your blog as the source for SEO)
Create a video and upload it to YouTube using the talking points from the article.
Rewrite the piece a little, then post it to LinkedIn.
Change the article's format to a Thread and share it on Twitter.
Find a few quick quotes throughout the article, then use them in tweets or Instagram quote posts.
Create a carousel for Instagram and LinkedIn using screenshots from the Twitter Thread.
Go through your film and select a few valuable 30-second segments. Share them on LinkedIn, Facebook, Twitter, TikTok, YouTube Shorts, and Instagram Reels.
Your video's audio can be taken out and uploaded as a podcast episode.
If you (or your team) achieve all this, you'll have 20-30 pieces of social media content.
If you're just starting, I wouldn't advocate doing all of this at once.
Instead, focus on a few platforms with this method.
You can outsource this as your company expands. (If you'd want to learn more about content repurposing, contact me.)
You may focus on relevant work while someone else grows your social media on autopilot.
You develop high-ROI pillar content, and it's automatically chopped up and posted on social media.
This lets you use social media algorithms without getting sucked in.
Thanks for reading!
Simon Ash
2 years ago
The Three Most Effective Questions for Ongoing Development
The Traffic Light Approach to Reviewing Personal, Team and Project Development
What needs improvement? If you want to improve, you need to practice your sport, musical instrument, habit, or work project. You need to assess your progress.
Continuous improvement is the foundation of focused practice and a growth mentality. Not just individually. High-performing teams pursue improvement. Right? Why is it hard?
As a leadership coach, senior manager, and high-level athlete, I've found three key questions that may unlock high performance in individuals and teams.
Problems with Reviews
Reviewing and improving performance is crucial, however I hate seeing review sessions in my diary. I rarely respond to questionnaire pop-ups or emails. Why?
Time constrains. Requests to fill out questionnaires often state they will take 10–15 minutes, but I can think of a million other things to do with that time. Next, review overload. Businesses can easily request comments online. No matter what you buy, someone will ask for your opinion. This bombardment might make feedback seem bad, which is bad.
The problem is that we might feel that way about important things like personal growth and work performance. Managers and team leaders face a greater challenge.
When to Conduct a Review
We must be wise about reviewing things that matter to us. Timing and duration matter. Reviewing the experience as quickly as possible preserves information and sentiments. Time must be brief. The review's importance and size will determine its length. We might only take a few seconds to review our morning coffee, but we might require more time for that six-month work project.
These post-event reviews should be supplemented by periodic reflection. Journaling can help with daily reflections, but I also like to undertake personal reviews every six months on vacation or at a retreat.
As an employee or line manager, you don't want to wait a year for a performance assessment. Little and frequently is best, with a more formal and in-depth assessment (typically with a written report) in 6 and 12 months.
The Easiest Method to Conduct a Review Session
I follow Einstein's review process:
“Make things as simple as possible but no simpler.”
Thus, it should be brief but deliver the necessary feedback. Quality critique is hard to receive if the process is overly complicated or long.
I have led or participated in many review processes, from strategic overhauls of big organizations to personal goal coaching. Three key questions guide the process at either end:
What ought to stop being done?
What should we do going forward?
What should we do first?
Following the Rule of 3, I compare it to traffic lights. Red, amber, and green lights:
Red What ought should we stop?
Amber What ought to we keep up?
Green Where should we begin?
This approach is easy to understand and self-explanatory, however below are some examples under each area.
Red What ought should we stop?
As a team or individually, we must stop doing things to improve.
Sometimes they're bad. If we want to lose weight, we should avoid sweets. If a team culture is bad, we may need to stop unpleasant behavior like gossiping instead of having difficult conversations.
Not all things we should stop are wrong. Time matters. Since it is finite, we sometimes have to stop nice things to focus on the most important. Good to Great author Jim Collins famously said:
“Don’t let the good be the enemy of the great.”
Prioritizing requires this idea. Thus, decide what to stop to prioritize.
Amber What ought to we keep up?
Should we continue with the amber light? It helps us decide what to keep doing during review. Many items fall into this category, so focus on those that make the most progress.
Which activities have the most impact? Which behaviors create the best culture? Success-building habits?
Use these questions to find positive momentum. These are the fly-wheel motions, according to Jim Collins. The Compound Effect author Darren Hardy says:
“Consistency is the key to achieving and maintaining momentum.”
What can you do consistently to reach your goal?
Green Where should we begin?
Finally, green lights indicate new beginnings. Red/amber difficulties may be involved. Stopping a red issue may give you more time to do something helpful (in the amber).
This green space inspires creativity. Kolbs learning cycle requires active exploration to progress. Thus, it's crucial to think of new approaches, try them out, and fail if required.
This notion underpins lean start-build, up's measure, learn approach and agile's trying, testing, and reviewing. Try new things until you find what works. Thomas Edison, the lighting legend, exclaimed:
“There is a way to do it better — find it!”
Failure is acceptable, but if you want to fail forward, look back on what you've done.
John Maxwell concurred with Edison:
“Fail early, fail often, but always fail forward”
A good review procedure lets us accomplish that. To avoid failure, we must act, experiment, and reflect.
Use the traffic light system to prioritize queries. Ask:
Red What needs to stop?
Amber What should continue to occur?
Green What might be initiated?
Take a moment to reflect on your day. Check your priorities with these three questions. Even if merely to confirm your direction, it's a terrific exercise!