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
4 years ago
👏 Awesome post! When is part 3 coming?
Trent Lapinski
4 years ago
Very complex topic, great explanation
More on Web3 & Crypto
Jonathan Vanian
4 years ago
What is Terra? Your guide to the hot cryptocurrency
With cryptocurrencies like Bitcoin, Ether, and Dogecoin gyrating in value over the past few months, many people are looking at so-called stablecoins like Terra to invest in because of their more predictable prices.
Terraform Labs, which oversees the Terra cryptocurrency project, has benefited from its rising popularity. The company said recently that investors like Arrington Capital, Lightspeed Venture Partners, and Pantera Capital have pledged $150 million to help it incubate various crypto projects that are connected to Terra.
Terraform Labs and its partners have built apps that operate on the company’s blockchain technology that helps keep a permanent and shared record of the firm’s crypto-related financial transactions.
Here’s what you need to know about Terra and the company behind it.
What is Terra?
Terra is a blockchain project developed by Terraform Labs that powers the startup’s cryptocurrencies and financial apps. These cryptocurrencies include the Terra U.S. Dollar, or UST, that is pegged to the U.S. dollar through an algorithm.
Terra is a stablecoin that is intended to reduce the volatility endemic to cryptocurrencies like Bitcoin. Some stablecoins, like Tether, are pegged to more conventional currencies, like the U.S. dollar, through cash and cash equivalents as opposed to an algorithm and associated reserve token.
To mint new UST tokens, a percentage of another digital token and reserve asset, Luna, is “burned.” If the demand for UST rises with more people using the currency, more Luna will be automatically burned and diverted to a community pool. That balancing act is supposed to help stabilize the price, to a degree.
“Luna directly benefits from the economic growth of the Terra economy, and it suffers from contractions of the Terra coin,” Terraform Labs CEO Do Kwon said.
Each time someone buys something—like an ice cream—using UST, that transaction generates a fee, similar to a credit card transaction. That fee is then distributed to people who own Luna tokens, similar to a stock dividend.
Who leads Terra?
The South Korean firm Terraform Labs was founded in 2018 by Daniel Shin and Kwon, who is now the company’s CEO. Kwon is a 29-year-old former Microsoft employee; Shin now heads the Chai online payment service, a Terra partner. Kwon said many Koreans have used the Chai service to buy goods like movie tickets using Terra cryptocurrency.
Terraform Labs does not make money from transactions using its crypto and instead relies on outside funding to operate, Kwon said. It has raised $57 million in funding from investors like HashKey Digital Asset Group, Divergence Digital Currency Fund, and Huobi Capital, according to deal-tracking service PitchBook. The amount raised is in addition to the latest $150 million funding commitment announced on July 16.
What are Terra’s plans?
Terraform Labs plans to use Terra’s blockchain and its associated cryptocurrencies—including one pegged to the Korean won—to create a digital financial system independent of major banks and fintech-app makers. So far, its main source of growth has been in Korea, where people have bought goods at stores, like coffee, using the Chai payment app that’s built on Terra’s blockchain. Kwon said the company’s associated Mirror trading app is experiencing growth in China and Thailand.
Meanwhile, Kwon said Terraform Labs would use its latest $150 million in funding to invest in groups that build financial apps on Terra’s blockchain. He likened the scouting and investing in other groups as akin to a “Y Combinator demo day type of situation,” a reference to the popular startup pitch event organized by early-stage investor Y Combinator.
The combination of all these Terra-specific financial apps shows that Terraform Labs is “almost creating a kind of bank,” said Ryan Watkins, a senior research analyst at cryptocurrency consultancy Messari.
In addition to cryptocurrencies, Terraform Labs has a number of other projects including the Anchor app, a high-yield savings account for holders of the group’s digital coins. Meanwhile, people can use the firm’s associated Mirror app to create synthetic financial assets that mimic more conventional ones, like “tokenized” representations of corporate stocks. These synthetic assets are supposed to be helpful to people like “a small retail trader in Thailand” who can more easily buy shares and “get some exposure to the upside” of stocks that they otherwise wouldn’t have been able to obtain, Kwon said. But some critics have said the U.S. Securities and Exchange Commission may eventually crack down on synthetic stocks, which are currently unregulated.
What do critics say?
Terra still has a long way to go to catch up to bigger cryptocurrency projects like Ethereum.
Most financial transactions involving Terra-related cryptocurrencies have originated in Korea, where its founders are based. Although Terra is becoming more popular in Korea thanks to rising interest in its partner Chai, it’s too early to say whether Terra-related currencies will gain traction in other countries.
Terra’s blockchain runs on a “limited number of nodes,” said Messari’s Watkins, referring to the computers that help keep the system running. That helps reduce latency that may otherwise slow processing of financial transactions, he said.
But the tradeoff is that Terra is less “decentralized” than other blockchain platforms like Ethereum, which is powered by thousands of interconnected computing nodes worldwide. That could make Terra less appealing to some blockchain purists.
Caleb Naysmith
3 years ago Draft
A Myth: Decentralization
It’s simply not conceivable, or at least not credible.
One of the most touted selling points of Crypto has always been this grandiose idea of decentralization. Bitcoin first arose in 2009 after the housing crisis and subsequent crash that came with it. It aimed to solve this supposed issue of centralization. Nobody “owns” Bitcoin in theory, so the idea then goes that it won’t be subject to the same downfalls that led to the 2008 crash or similarly speculative events that led to the 2008 disaster. The issue is the banks, not the human nature associated with the greedy individuals running them.
Subsequent blockchains have attempted to fix many of the issues of Bitcoin by increasing capacity, decreasing the costs and processing times associated with Bitcoin, and expanding what can be done with their blockchains. Since nobody owns Bitcoin, it hasn’t really been able to be expanded on. You have people like Vitalk Buterin, however, that actively work on Ethereum though.
The leap from Bitcoin to Ethereum was a massive leap toward centralization, and the trend has only gotten worse. In fact, crypto has since become almost exclusively centralized in recent years.
Decentralization is only good in theory
It’s a good idea. In fact, it’s a wonderful idea. However, like other utopian societies, individuals misjudge human nature and greed. In a perfect world, decentralization would certainly be a wonderful idea because sure, people may function as their own banks, move payments immediately, remain anonymous, and so on. However, underneath this are a couple issues:
You can already send money instantaneously today.
They are not decentralized.
Decentralization is a bad idea.
Being your own bank is a stupid move.
Let’s break these down. Some are quite simple, but lets have a look.
Sending money right away
One thing with crypto is the idea that you can send payments instantly. This has pretty much been entirely solved in current times. You can transmit significant sums of money instantly for a nominal cost and it’s instantaneously cleared. Venmo was launched in 2009 and has since increased to prominence, and currently is on most people's phones. I can directly send ANY amount of money quickly from my bank to another person's Venmo account.
Comparing that with ETH and Bitcoin, Venmo wins all around. I can send money to someone for free instantly in dollars and the only fee paid is optional depending on when you want it.
Both Bitcoin and Ethereum are subject to demand. If the blockchains have a lot of people trying to process transactions fee’s go up, and the time that it takes to receive your crypto takes longer. When Ethereum gets bad, people have reported spending several thousand of dollars on just 1 transaction.
These transactions take place via “miners” bundling and confirming transactions, then recording them on the blockchain to confirm that the transaction did indeed happen. They charge fees to do this and are also paid in Bitcoin/ETH. When a transaction is confirmed, it's then sent to the other users wallet. This within itself is subject to lots of controversy because each transaction needs to be confirmed 6 times, this takes massive amounts of power, and most of the power is wasted because this is an adversarial system in which the person that mines the transaction gets paid, and everyone else is out of luck. Also, these could theoretically be subject to a “51% attack” in which anyone with over 51% of the mining hash rate could effectively control all of the transactions, and reverse transactions while keeping the BTC resulting in “double spending”.
There are tons of other issues with this, but essentially it means: They rely on these third parties to confirm the transactions. Without people confirming these transactions, Bitcoin stalls completely, and if anyone becomes too dominant they can effectively control bitcoin.
Not to mention, these transactions are in Bitcoin and ETH, not dollars. So, you need to convert them to dollars still, and that's several more transactions, and likely to take several days anyway as the centralized exchange needs to send you the money by traditional methods.
They are not distributed
That takes me to the following point. This isn’t decentralized, at all. Bitcoin is the closest it gets because Satoshi basically closed it to new upgrades, although its still subject to:
Whales
Miners
It’s vital to realize that these are often the same folks. While whales aren’t centralized entities typically, they can considerably effect the price and outcome of Bitcoin. If the largest wallets holding as much as 1 million BTC were to sell, it’d effectively collapse the price perhaps beyond repair. However, Bitcoin can and is pretty much controlled by the miners. Further, Bitcoin is more like an oligarchy than decentralized. It’s been effectively used to make the rich richer, and both the mining and price is impacted by the rich. The overwhelming minority of those actually using it are retail investors. The retail investors are basically never the ones generating money from it either.
As far as ETH and other cryptos go, there is realistically 0 case for them being decentralized. Vitalik could not only kill it but even walking away from it would likely lead to a significant decline. It has tons of issues right now that Vitalik has promised to fix with the eventual Ethereum 2.0., and stepping away from it wouldn’t help.
Most tokens as well are generally tied to some promise of future developments and creators. The same is true for most NFT projects. The reason 99% of crypto and NFT projects fail is because they failed to deliver on various promises or bad dev teams, or poor innovation, or the founders just straight up stole from everyone. I could go more in-depth than this but go find any project and if there is a dev team, company, or person tied to it then it's likely, not decentralized. The success of that project is directly tied to the dev team, and if they wanted to, most hold large wallets and could sell it all off effectively killing the project. Not to mention, any crypto project that doesn’t have a locked contract can 100% be completely rugged and they can run off with all of the money.
Decentralization is undesirable
Even if they were decentralized then it would not be a good thing. The graphic above indicates this is effectively a rich person’s unregulated playground… so it’s exactly like… the very issue it tried to solve?
Not to mention, it’s supposedly meant to prevent things like 2008, but is regularly subjected to 50–90% drawdowns in value? Back when Bitcoin was only known in niche parts of the dark web and illegal markets, it would regularly drop as much as 90% and has a long history of massive drawdowns.
The majority of crypto is blatant scams, and ALL of crypto is a “zero” or “negative” sum game in that it relies on the next person buying for people to make money. This is not a good thing. This has yet to solve any issues around what caused the 2008 crisis. Rather, it seemingly amplified all of the bad parts of it actually. Crypto is the ultimate speculative asset and realistically has no valuation metric. People invest in Apple because it has revenue and cash on hand. People invest in crypto purely for speculation. The lack of regulation or accountability means this is amplified to the most extreme degree where anything goes: Fraud, deception, pump and dumps, scams, etc. This results in a pure speculative madhouse where, unsurprisingly, only the rich win. Not only that but the deck is massively stacked in against the everyday investor because you can’t do a pump and dump without money.
At the heart of all of this is still the same issues: greed and human nature. However, in setting out to solve the issues that allowed 2008 to happen, they made something that literally took all of the bad parts of 2008 and then amplified it. 2008, similarly, was due to greed and human nature but was allowed to happen due to lack of oversite, rich people's excessive leverage over the poor, and excessive speculation. Crypto trades SOLELY on human emotion, has 0 oversite, is pure speculation, and the power dynamic is just as bad or worse.
Why should each individual be their own bank?
This is the last one, and it's short and basic. Why do we want people functioning as their own bank? Everything we do relies on another person. Without the internet, and internet providers there is no crypto. We don’t have people functioning as their own home and car manufacturers or internet service providers. Sure, you might specialize in some of these things, but masquerading as your own bank is a horrible idea.
I am not in the banking industry so I don’t know all the issues with banking. Most people aren’t in banking or crypto, so they don’t know the ENDLESS scams associated with it, and they are bound to lose their money eventually.
If you appreciate this article and want to read more from me and authors like me, without any limits, consider buying me a coffee: buymeacoffee.com/calebnaysmith
joyce shen
4 years ago
Framework to Evaluate Metaverse and Web3
Everywhere we turn, there's a new metaverse or Web3 debut. Microsoft recently announced a $68.7 BILLION cash purchase of Activision.
Like AI in 2013 and blockchain in 2014, NFT growth in 2021 feels like this year's metaverse and Web3 growth. We are all bombarded with information, conflicting signals, and a sensation of FOMO.
How can we evaluate the metaverse and Web3 in a noisy, new world? My framework for evaluating upcoming technologies and themes is shown below. I hope you will also find them helpful.
Understand the “pipes” in a new space.
Whatever people say, Metaverse and Web3 will have to coexist with the current Internet. Companies who host, move, and store data over the Internet have a lot of intriguing use cases in Metaverse and Web3, whether in infrastructure, data analytics, or compliance. Hence the following point.
## Understand the apps layer and their infrastructure.
Gaming, crypto exchanges, and NFT marketplaces would not exist today if not for technology that enables rapid app creation. Yes, according to Chainalysis and other research, 30–40% of Ethereum is self-hosted, with the rest hosted by large cloud providers. For Microsoft to acquire Activision makes strategic sense. It's not only about the games, but also the infrastructure that supports them.
Follow the money
Understanding how money and wealth flow in a complex and dynamic environment helps build clarity. Unless you are exceedingly wealthy, you have limited ability to significantly engage in the Web3 economy today. Few can just buy 10 ETH and spend it in one day. You must comprehend who benefits from the process, and how that 10 ETH circulates now and possibly tomorrow. Major holders and players control supply and liquidity in any market. Today, most Web3 apps are designed to increase capital inflow so existing significant holders can utilize it to create a nascent Web3 economy. When you see a new Metaverse or Web3 application, remember how money flows.
What is the use case?
What does the app do? If there is no clear use case with clear makers and consumers solving a real problem, then the euphoria soon fades, and the only stakeholders who remain enthused are those who have too much to lose.
Time is a major competition that is often overlooked.
We're only busier, but each day is still 24 hours. Using new apps may mean that time is lost doing other things. The user must be eager to learn. Metaverse and Web3 vs. our time? I don't think we know the answer yet (at least for working adults whose cost of time is higher).
I don't think we know the answer yet (at least for working adults whose cost of time is higher).
People and organizations need security and transparency.
For new technologies or apps to be widely used, they must be safe, transparent, and trustworthy. What does secure Metaverse and Web3 mean? This is an intriguing subject for both the business and public sectors. Cloud adoption grew in part due to improved security and data protection regulations.
The following frameworks can help analyze and understand new technologies and emerging technological topics, unless you are a significant investment fund with the financial ability to gamble on numerous initiatives and essentially form your own “index fund”.
I write on VC, startups, and leadership.
More on https://www.linkedin.com/in/joycejshen/ and https://joyceshen.substack.com/
This writing is my own opinion and does not represent investment advice.
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Hudson Rennie
3 years ago
Meet the $5 million monthly controversy-selling King of Toxic Masculinity.
Trigger warning — Andrew Tate is running a genius marketing campaign
Andrew Tate is a 2022 internet celebrity.
Kickboxing world champion became rich playboy with controversial views on gender roles.
Andrew's get-rich-quick scheme isn't new. His social media popularity is impressive.
He’s currently running one of the most genius marketing campaigns in history.
He pulls society's pendulum away from diversity and inclusion and toward diversion and exclusion. He's unstoppable.
Here’s everything you need to know about Andrew Tate. And how he’s playing chess while the world plays checkers.
Cobra Tate is the name he goes by.
American-born, English-raised entrepreneur Andrew Tate lives in Romania.
Romania? Says Andrew,
“I prefer a country in which corruption is available to everyone.”
Andrew was a professional kickboxer with the ring moniker Cobra before starting Hustlers University.
Before that, he liked chess and worshipped his father.
Emory Andrew Tate III is named after his grandmaster chess player father.
Emory was the first black-American chess champion. He was military, martial arts-trained, and multilingual. A superhuman.
He lived in his car to make ends meet.
Andrew and Tristan relocated to England with their mother when their parents split.
It was there that Andrew began his climb toward becoming one of the internet’s greatest villains.
Andrew fell in love with kickboxing.
Andrew spent his 20s as a professional kickboxer and reality TV star, featuring on Big Brother UK and The Ultimate Traveller.
These 3 incidents, along with a chip on his shoulder, foreshadowed Andrews' social media breakthrough.
Chess
Combat sports
Reality television
A dangerous trio.
Andrew started making money online after quitting kickboxing in 2017 due to an eye issue.
Andrew didn't suddenly become popular.
Andrew's web work started going viral in 2022.
Due to his contentious views on patriarchy and gender norms, he's labeled the King of Toxic Masculinity. His most contentious views (trigger warning):
“Women are intrinsically lazy.”
“Female promiscuity is disgusting.”
“Women shouldn’t drive cars or fly planes.”
“A lot of the world’s problems would be solved if women had their body count tattooed on their foreheads.”
Andrew's two main beliefs are:
“These are my personal opinions based on my experiences.”
2. “I believe men are better at some things and women are better at some things. We are not equal.”
Andrew intentionally offends.
Andrew's thoughts began circulating online in 2022.
In July 2022, he was one of the most Googled humans, surpassing:
Joe Biden
Donald Trump
Kim Kardashian
Andrews' rise is a mystery since no one can censure or suppress him. This is largely because Andrew nor his team post his clips.
But more on that later.
Andrew's path to wealth.
Andrew Tate is a self-made millionaire. His morality is uncertain.
Andrew and Tristan needed money soon after retiring from kickboxing.
“I owed some money to some dangerous people. I had $70K and needed $100K to stay alive.”
Andrews lost $20K on roulette at a local casino.
Andrew had one week to make $50,000, so he started planning. Andrew locked himself in a chamber like Thomas Edison to solve an energy dilemma.
He listed his assets.
Physical strength (but couldn’t fight)
a BMW (worth around $20K)
Intelligence (but no outlet)
A lightbulb.
He had an epiphany after viewing a webcam ad. He sought aid from women, ironically. His 5 international girlfriends are assets.
Then, a lightbulb.
Andrew and Tristan messaged and flew 7 women to a posh restaurant. Selling desperation masked as opportunity, Andrew pitched his master plan:
A webcam business — with a 50/50 revenue split.
5 women left.
2 stayed.
Andrew Tate, a broke kickboxer, became Top G, Cobra Tate.
The business model was simple — yet sad.
Andrew's girlfriends moved in with him and spoke online for 15+ hours a day. Andrew handled ads and equipment as the women posed.
Andrew eventually took over their keyboards, believing he knew what men wanted more than women.
Andrew detailed on the Full Send Podcast how he emotionally manipulated men for millions. They sold houses, automobiles, and life savings to fuel their companionship addiction.
When asked if he felt bad, Andrew said,
“F*ck no.“
Andrew and Tristan wiped off debts, hired workers, and diversified.
Tristan supervised OnlyFans models.
Andrew bought Romanian casinos and MMA league RXF (Real Xtreme Fighting).
Pandemic struck suddenly.
Andrew couldn't run his 2 businesses without a plan. Another easy moneymaker.
He banked on Hustlers University.
The actual cause of Andrew's ubiquity.
On a Your Mom’s House episode Andrew's 4 main revenue sources:
Hustler’s University
2. Owning casinos in Romania
3. Owning 10% of the Romanian MMA league “RXF”
4. “The War Room” — a society of rich and powerful men
When the pandemic hit, 3/4 became inoperable.
So he expanded Hustlers University.
But what is Hustler’s University?
Andrew says Hustlers University teaches 18 wealth-building tactics online. Examples:
Real estate
Copywriting
Amazon FBA
Dropshipping
Flipping Cryptos
How to swiftly become wealthy.
Lessons are imprecise, rudimentary, and macro-focused, say reviews. Invest wisely, etc. Everything is free online.
You pay for community. One unique income stream.
The only money-making mechanism that keeps the course from being a scam.
The truth is, many of Andrew’s students are actually making money. Maybe not from the free YouTube knowledge Andrew and his professors teach in the course, but through Hustler’s University’s affiliate program.
Affiliates earn 10% commission for each new student = $5.
Students can earn $10 for each new referral in the first two months.
Andrew earns $50 per membership per month.
This affiliate program isn’t anything special — in fact, it’s on the lower end of affiliate payouts. Normally, it wouldn’t be very lucrative.
But it has one secret weapon— Andrew and his viral opinions.
Andrew is viral. Andrew went on a media tour in January 2022 after appearing on Your Mom's House.
And many, many more…
He chatted with Twitch streamers. Hustlers University wanted more controversy (and clips).
Here’s the strategy behind Hustler’s University that has (allegedly) earned students upwards of $10K per month:
Make a social media profile with Andrew Tates' name and photo.
Post any of the online videos of Andrews that have gone viral.
Include a referral link in your bio.
Effectively simple.
Andrew's controversy attracts additional students. More student clips circulate as more join. Andrew's students earn more and promote the product as he goes viral.
A brilliant plan that's functioning.
At the beginning of his media tour, Hustler’s University had 5,000 students. 6 months in, and he now has over 100,000.
One income stream generates $5 million every month.
Andrew's approach is not new.
But it is different.
In the early 2010s, Tai Lopez dominated the internet.
His viral video showed his house.
“Here in my garage. Just bought this new Lamborghini.”
Tais' marketing focused on intellect, not strength, power, and wealth to attract women.
How reading quicker leads to financial freedom in 67 steps.
Years later, it was revealed that Tai Lopez rented the mansion and Lamborghini as a marketing ploy to build social proof. Meanwhile, he was living in his friend’s trailer.
Faked success is an old tactic.
Andrew is doing something similar. But with one major distinction.
Andrew outsources his virality — making him nearly impossible to cancel.
In 2022, authorities searched Andrews' estate over human trafficking suspicions. Investigation continues despite withdrawn charges.
Andrew's divisive nature would normally get him fired. Andrew's enterprises and celebrity don't rely on social media.
He doesn't promote or pay for ads. Instead, he encourages his students and anyone wishing to get rich quick to advertise his work.
Because everything goes through his affiliate program. Old saying:
“All publicity is good publicity.”
Final thoughts: it’s ok to feel triggered.
Tate is divisive.
His emotionally charged words are human nature. Andrews created the controversy.
It's non-personal.
His opinions are those of one person. Not world nor generational opinion.
Briefly:
It's easy to understand why Andrews' face is ubiquitous. Money.
The world wide web is a chessboard. Misdirection is part of it.
It’s not personal, it’s business.
Controversy sells
Sometimes understanding the ‘why’, can help you deal with the ‘what.’
Peter Steven Ho
3 years ago
Thank You for 21 Fantastic Years, iPod
Apple's latest revelation may shock iPod fans and former owners.
Apple discontinued the iPod touch on May 11, 2022. After 21 years, Apple killed the last surviving iPod, a device Steve Jobs believed would revolutionize the music industry.
Jobs was used to making bold predictions, but few expected Apple's digital music player to change the music industry. It did.
This chaos created new business opportunities. Spotify, YouTube, and Amazon are products of that chaotic era.
As the digital landscape changes, so do consumers, and the iPod has lost favor. I'm sure Apple realizes the importance of removing an icon. The iPod was Apple like the Mac and iPhone. I think it's bold to retire such a key Apple cornerstone. What would Jobs do?
iPod evolution across the ages
Here's an iPod family tree for all you enthusiasts.
iPod vintage (Oct 2001 to Sep 2014, 6 generations)
The original iPod had six significant upgrades since 2001. Apple announced an 80 GB ($249) and 160 GB ($349) iPod classic in 2007.
Apple updated the 80 GB model with a 120 GB device in September 2008. Apple upgraded the 120 GB model with a 160 GB variant a year later (2009). This was the last iteration, and Apple discontinued the classic in September 2014.
iPod nano (Jan 2004 to Sep 2005, 2 generations)
Apple debuted a smaller, brightly-colored iPod in 2004. The first model featured 4 GB, enough for 1,000 songs.
Apple produced a new 4 GB or 6 GB iPod mini in February 2005 and discontinued it in September when they released a better-looking iPod nano.
iTouch nano (Sep 2005 to July 2017, 7 generations)
I loved the iPod nano. It was tiny and elegant with enough tech to please most music aficionados, unless you carry around your complete music collection.
Apple owed much of the iPod nano's small form and success to solid-state flash memory. Flash memory doesn't need power because it has no moving parts. This makes the iPod nano more durable than the iPod classic and mini, which employ hard drives.
Apple manufactured seven generations of the iPod nano, improving its design, display screen, memory, battery, and software, but abandoned it in July 2017 due to dwindling demand.
Shuffle iPod (Jan 2005 to Jul 2017, 4 generations)
The iPod shuffle was entry-level. It was a simple, lightweight, tiny music player. The iPod shuffle was perfect for lengthy bike trips, runs, and hikes.
Apple sold 10 million iPod shuffles in the first year and kept making them for 12 years, through four significant modifications.
iOS device (Sep 2007 to May 2022, 7 generations)
The iPod touch's bigger touchscreen interface made it a curious addition to the iPod family. The iPod touch resembled an iPhone more than the other iPods, making them hard to tell apart.
Many were dissatisfied that Apple removed functionality from the iPod touch to avoid making it too similar to the iPhone. Seven design improvements over 15 years brought the iPod touch closer to the iPhone, but not completely.
The iPod touch uses the same iOS operating system as the iPhone, giving it access to many apps, including handheld games.
The iPod touch's long production run is due to the next generation of music-loving gamers.
What made the iPod cool
iPod revolutionized music listening. It was the first device to store and play MP3 music, allowing you to carry over 1,000 songs anywhere.
The iPod changed consumer electronics with its scroll wheel and touchscreen. Jobs valued form and function equally. He showed people that a product must look good to inspire an emotional response and ignite passion.
The elegant, tiny iPod was a tremendous sensation when it arrived for $399 in October 2001. Even at this price, it became a must-have for teens to CEOs.
It's hard to identify any technology that changed how music was downloaded and played like the iPod. Apple iPod and iTunes had 63% of the paid music download market in the fourth quarter of 2012.
The demise of the iPod was inevitable
Apple discontinuing the iPod touch after 21 years is sad. This ends a 00s music icon.
Jobs was a genius at anticipating market needs and opportunities, and Apple launched the iPod at the correct time.
Few consumer electronics items have had such a lasting impact on music lovers and the music industry as the iPod.
Smartphones and social media have contributed to the iPod's decline. Instead of moving to the music, the new generation of consumers is focused on social media. They're no longer passive content consumers; they're active content creators seeking likes and followers. Here, the smartphone has replaced the iPod.
It's hard not to feel a feeling of loss, another part of my adolescence now forgotten by the following generation.
So, if you’re lucky enough to have a working iPod, hang on to that relic and enjoy the music and the nostalgia.
John Rampton
3 years ago
Ideas for Samples of Retirement Letters
Ready to quit full-time? No worries.
Baby Boomer retirement has accelerated since COVID-19 began. In 2020, 29 million boomers retire. Over 3 million more than in 2019. 75 million Baby Boomers will retire by 2030.
First, quit your work to enjoy retirement. Leave a professional legacy. Your retirement will start well. It all starts with a retirement letter.
Retirement Letter
Retirement letters are formal resignation letters. Different from other resignation letters, these don't tell your employer you're leaving. Instead, you're quitting.
Since you're not departing over grievances or for a better position or higher income, you may usually terminate the relationship amicably. Consulting opportunities are possible.
Thank your employer for their support and give them transition information.
Resignation letters aren't merely a formality. This method handles wages, insurance, and retirement benefits.
Retirement letters often accompany verbal notices to managers. Schedule a meeting before submitting your retirement letter to discuss your plans. The letter will be stored alongside your start date, salary, and benefits in your employee file.
Retirement is typically well-planned. Employers want 6-12 months' notice.
Summary
Guidelines for Giving Retirement Notice
Components of a Successful Retirement Letter
Template for Retirement Letter
Ideas for Samples of Retirement Letters
First Example of Retirement Letter
Second Example of Retirement Letter
Third Example of Retirement Letter
Fourth Example of Retirement Letter
Fifth Example of Retirement Letter
Sixth Example of Retirement Letter
Seventh Example of Retirement Letter
Eighth Example of Retirement Letter
Ninth Example of Retirement Letter
Tenth Example of Retirement Letter
Frequently Asked Questions
1. What is a letter of retirement?
2. Why should you include a letter of retirement?
3. What information ought to be in your retirement letter?
4. Must I provide notice?
5. What is the ideal retirement age?
Guidelines for Giving Retirement Notice
While starting a new phase, you're also leaving a job you were qualified for. You have years of experience. So, it may not be easy to fill a retirement-related vacancy.
Talk to your boss in person before sending a letter. Notice is always appreciated. Properly announcing your retirement helps you and your organization transition.
How to announce retirement:
Learn about the retirement perks and policies offered by the company. The first step in figuring out whether you're eligible for retirement benefits is to research your company's retirement policy.
Don't depart without providing adequate notice. You should give the business plenty of time to replace you if you want to retire in a few months.
Help the transition by offering aid. You could be a useful resource if your replacement needs training.
Contact the appropriate parties. The original copy should go to your boss. Give a copy to HR because they will manage your 401(k), pension, and health insurance.
Investigate the option of working as a consultant or part-time. If you desire, you can continue doing some limited work for the business.
Be nice to others. Describe your achievements and appreciation. Additionally, express your gratitude for giving you the chance to work with such excellent coworkers.
Make a plan for your future move. Simply updating your employer on your goals will help you maintain a good working relationship.
Use a formal letter or email to formalize your plans. The initial step is to speak with your supervisor and HR in person, but you must also give written notice.
Components of a Successful Retirement Letter
To write a good retirement letter, keep in mind the following:
A formal salutation. Here, the voice should be deliberate, succinct, and authoritative.
Be specific about your intentions. The key idea of your retirement letter is resignation. Your decision to depart at this time should be reflected in your letter. Remember that your intention must be clear-cut.
Your deadline. This information must be in resignation letters. Laws and corporate policies may both stipulate a minimum amount of notice.
A kind voice. Your retirement letter shouldn't contain any resentments, insults, or other unpleasantness. Your letter should be a model of professionalism and grace. A straightforward thank you is a terrific approach to accomplish that.
Your ultimate goal. Chaos may start to happen as soon as you turn in your resignation letter. Your position will need to be filled. Additionally, you will have to perform your obligations up until a successor is found. Your availability during the interim period should be stated in your resignation letter.
Give us a way to reach you. Even if you aren't consulting, your company will probably get in touch with you at some point. They might send you tax documents and details on perks. By giving your contact information, you can make this process easier.
Template for Retirement Letter
Identify
Title you held
Address
Supervisor's name
Supervisor’s position
Company name
HQ address
Date
[SUPERVISOR],
1.
Inform that you're retiring. Include your last day worked.
2.
Employer thanks. Mention what you're thankful for. Describe your accomplishments and successes.
3.
Helping moves things ahead. Plan your retirement. Mention your consultancy interest.
Sincerely,
[Signature]
First and last name
Phone number
Personal Email
Ideas for Samples of Retirement Letters
First Example of Retirement Letter
Martin D. Carey
123 Fleming St
Bloomfield, New Jersey 07003
(555) 555-1234
June 6th, 2022
Willie E. Coyote
President
Acme Co
321 Anvil Ave
Fairfield, New Jersey 07004
Dear Mr. Coyote,
This letter notifies Acme Co. of my retirement on August 31, 2022.
There has been no other organization that has given me that sense of belonging and purpose.
My fifteen years at the helm of the Structural Design Division have given me a strong sense of purpose. I’ve been fortunate to have your support, and I’ll be always grateful for the opportunity you offered me.
I had a difficult time making this decision. As a result of finding a small property in Arizona where we will be able to spend our remaining days together, my wife and I have decided to officially retire.
In spite of my regret at being unable to contribute to the firm we’ve built, I believe it is wise to move on.
My heart will always belong to Acme Co. Thank you for the opportunity and best of luck in the years to come.
Sincerely,
Martin D. Carey
Second Example of Retirement Letter
Gustavo Fring
Los Pollas Hermanos
12000–12100 Coors Rd SW,
Albuquerque, New Mexico 87045
Dear Mr. Fring,
I write this letter to announce my formal retirement from Los Pollas Hermanos as manager, effective October 15.
As an employee at Los Pollas Hermanos, I appreciate all the great opportunities you have given me. It has been a pleasure to work with and learn from my colleagues for the past 10 years, and I am looking forward to my next challenge.
If there is anything I can do to assist during this time, please let me know.
Sincerely,
Linda T. Crespo
Third Example of Retirement Letter
William M. Arviso
4387 Parkview Drive
Tustin, CA 92680
May 2, 2023
Tony Stark
Owner
Stark Industries
200 Industrial Avenue
Long Beach, CA 90803
Dear Tony:
I’m writing to inform you that my final day of work at Stark Industries will be May14, 2023. When that time comes, I intend to retire.
As I embark on this new chapter in my life, I would like to thank you and the entire Stark Industries team for providing me with so many opportunities. You have all been a pleasure to work with and I will miss you all when I retire.
I am glad to assist you with the transition in any way I can to ensure your new hire has a seamless experience. All ongoing projects will be completed until my retirement date, and all key information will be handed over to the team.
Once again, thank you for the opportunity to be part of the Stark Industries team. All the best to you and the team in the days to come.
Please do not hesitate to contact me if you require any additional information. In order to finalize my retirement plans, I’ll meet with HR and can provide any details that may be necessary.
Sincerely,
(Signature)
William M. Arviso
Fourth Example of Retirement Letter
Garcia, Barbara
First Street, 5432
New York City, NY 10001
(1234) (555) 123–1234
1 October 2022
Gunther
Owner
Central Perk
199 Lafayette St.
New York City, NY 10001
Mr. Gunther,
The day has finally arrived. As I never imagined, I will be formally retiring from Central Perk on November 1st, 2022.
Considering how satisfied I am with my current position, this may surprise you. It would be best if I retired now since my health has deteriorated, so I think this is a good time to do so.
There is no doubt that the past two decades have been wonderful. Over the years, I have seen a small coffee shop grow into one of the city’s top destinations.
It will be hard for me to leave this firm without wondering what more success we could have achieved. But I’m confident that you and the rest of the Central Perk team will achieve great things.
My family and I will never forget what you’ve done for us, and I am grateful for the chance you’ve given me. My house is always open to you.
Sincerely Yours
Garcia, Barbara
Fifth Example of Retirement Letter
Pat Williams
618 Spooky Place
Monstropolis, 23221
123–555–0031
pwilliams@email.com
Feb. 16, 2022
Mike Wazowski
Co-CEO
Monters, Inc.
324 Scare Road
Monstropolis
Dear Mr. Wazowski,
As a formal notice of my upcoming retirement, I am submitting this letter. I will be leaving Monters, Inc. on April 13.
These past 10 years as a marketing associate have provided me with many opportunities. Since we started our company a decade ago, we have seen the face of harnessing screams change dramatically into harnessing laughter. During my time working with this dynamic marketing team, I learned a lot about customer behavior and marketing strategies. Working closely with some of our long-standing clients, such as Boo, was a particular pleasure.
I would be happy to assist with the transition following my retirement. It would be my pleasure to assist in the hiring or training of my replacement. In order to spend more time with my family, I will also be able to offer part-time consulting services.
After I retire, I plan to cash out the eight unused vacation days I’ve accumulated and take my pension as a lump sum.
Thank you for the opportunity to work with Monters, Inc. In the years to come, I wish you all the best!
Sincerely,
Paul Williams
Sixth Example of Retirement Letter
Dear Micheal,
As In my tenure at Dunder Mifflin Paper Company, I have given everything I had. It has been an honor to work here. But I have decided to move on to new challenges and retire from my position — mainly bears, beets, and Battlestar Galactia.
I appreciate the opportunity to work here and learn so much. During my time at this company, I will always remember the good times and memories we shared. Wishing you all the best in the future.
Sincerely,
Dwight K. Shrute
Your signature
May 16
Seventh Example of Retirement Letter
Greetings, Bill
I am announcing my retirement from Initech, effective March 15, 2023.
Over the course of my career here, I’ve had the privilege of working with so many talented and inspiring people.
In 1999, when I began working as a customer service representative, we were a small organization located in a remote office park.
The fact that we now occupy a floor of the Main Street office building with over 150 employees continues to amaze me.
I am looking forward to spending more time with family and traveling the country in our RV. Although I will be sad to leave.
Please let me know if there are any extra steps I can take to facilitate this transfer.
Sincerely,
Frankin, RenitaEighth Example of Retirement Letter
Height Example of Retirement Letter
Bruce,
Please accept my resignation from Wayne Enterprises as Marketing Communications Director. My last day will be August 1, 2022.
The decision to retire has been made after much deliberation. Now that I have worked in the field for forty years, I believe it is a good time to begin completing my bucket list.
It was not easy for me to decide to leave the company. Having worked at Wayne Enterprises has been rewarding both professionally and personally. There are still a lot of memories associated with my first day as a college intern.
My intention was not to remain with such an innovative company, as you know. I was able to see the big picture with your help, however. Today, we are a force that is recognized both nationally and internationally.
In addition to your guidance, the bold, visionary leadership of our company contributed to the growth of our company.
My departure from the company coincides with a particularly hectic time. Despite my best efforts, I am unable to postpone my exit.
My position would be well served by an internal solution. I have a more than qualified marketing manager in Caroline Crown. It would be a pleasure to speak with you about this.
In case I can be of assistance during the switchover, please let me know. Contact us at (555)555–5555. As part of my responsibilities, I am responsible for making sure all work is completed to Wayne Enterprise’s stringent requirements. Having the opportunity to work with you has been a pleasure. I wish you continued success with your thriving business.
Sincerely,
Cash, Cole
Marketing/Communications
Ninth Example of Retirement Letter
Norman, Jamie
2366 Hanover Street
Whitestone, NY 11357
555–555–5555
15 October 2022
Mr. Lippman
Head of Pendant Publishing
600 Madison Ave.
New York, New York
Respected Mr. Lippman,
Please accept my resignation effective November 1, 2022.
Over the course of my ten years at Pendant Publishing, I’ve had a great deal of fun and I’m quite grateful for all the assistance I’ve received.
It was a pleasure to wake up and go to work every day because of our outstanding corporate culture and the opportunities for promotion and professional advancement available to me.
While I am excited about retiring, I am going to miss being part of our team. It’s my hope that I’ll be able to maintain the friendships I’ve formed here for a long time to come.
In case I can be of assistance prior to or following my departure, please let me know. If I can assist in any way to ensure a smooth transfer to my successor, I would be delighted to do so.
Sincerely,
Signed (hard copy letter)
Norman, Jamie
Tenth Example of Retirement Letter
17 January 2023
Greg S. Jackson
Cyberdyne Systems
18144 El Camino Real,
Sunnyvale, CA
Respected Mrs. Duncan,
I am writing to inform you that I will be resigning from Cyberdyne Systems as of March 1, 2023. I’m grateful to have had this opportunity, and it was a difficult decision to make.
My development as a programmer and as a more seasoned member of the organization has been greatly assisted by your coaching.
I have been proud of Cyberdyne Systems’ ethics and success throughout my 25 years at the company. Starting as a mailroom clerk and currently serving as head programmer.
The portfolios of our clients have always been handled with the greatest care by my colleagues. It is our employees and services that have made Cyberdyne Systems the success it is today.
During my tenure as head of my division, I’ve increased our overall productivity by 800 percent, and I expect that trend to continue after I retire.
In light of the fact that the process of replacing me may take some time, I would like to offer my assistance in any way I can.
The greatest contender for this job is Troy Ledford, my current assistant.
Also, before I leave, I would be willing to teach any partners how to use the programmer I developed to track and manage the development of Skynet.
Over the next few months, I’ll be enjoying vacations with my wife as well as my granddaughter moving to college.
If Cyberdyne Systems has any openings for consultants, please let me know. It has been a pleasure working with you over the last 25 years. I appreciate your concern and care.
Sincerely,
Greg S, Jackson
Questions and Answers
1. What is a letter of retirement?
Retirement letters tell your supervisor you're retiring. This informs your employer that you're departing, like a letter. A resignation letter also requests retirement benefits.
Supervisors frequently receive retirement letters and verbal resignations. Before submitting your retirement letter, meet to discuss your plans. This letter will be filed with your start date, salary, and benefits.
2. Why should you include a letter of retirement?
Your retirement letter should explain why you're leaving. When you quit, your manager and HR department usually know. Regardless, a retirement letter might help you leave on a positive tone. It ensures they have the necessary papers.
In your retirement letter, you tell the firm your plans so they can find your replacement. You may need to stay in touch with your company after sending your retirement letter until a successor is identified.
3. What information ought to be in your retirement letter?
Format it like an official letter. Include your retirement plans and retirement-specific statistics. Date may be most essential.
In some circumstances, benefits depend on when you resign and retire. A date on the letter helps HR or senior management verify when you gave notice and how long.
In addition to your usual salutation, address your letter to your manager or supervisor.
The letter's body should include your retirement date and transition arrangements. Tell them whether you plan to help with the transition or train a new employee. You may have a three-month time limit.
Tell your employer your job title, how long you've worked there, and your biggest successes. Personalize your letter by expressing gratitude for your career and outlining your retirement intentions. Finally, include your contact info.
4. Must I provide notice?
Two-week notice isn't required. Your company may require it. Some state laws contain exceptions.
Check your contract, company handbook, or HR to determine your retirement notice. Resigning may change the policy.
Regardless of your company's policy, notification is standard. Entry-level or junior jobs can be let go so the corporation can replace them.
Middle managers, high-level personnel, and specialists may take months to replace. Two weeks' notice is a courtesy. Start planning months ahead.
You can finish all jobs at that period. Prepare transition documents for coworkers and your replacement.
5. What is the ideal retirement age?
Depends on finances, state, and retirement plan. The average American retires at 62. The average retirement age is 66, according to Gallup's 2021 Economy and Personal Finance Survey.
Remember:
Before the age of 59 1/2, withdrawals from pre-tax retirement accounts, such as 401(k)s and IRAs, are subject to a penalty.
Benefits from Social Security can be accessed as early as age 62.
Medicare isn't available to you till you're 65,
Depending on the year of your birth, your Full Retirement Age (FRA) will be between 66 and 67 years old.
If you haven't taken them already, your Social Security benefits increase by 8% annually between ages 6 and 77.