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

Matt Ward
3 years ago
Is Web3 nonsense?
Crypto and blockchain have rebranded as web3. They probably thought it sounded better and didn't want the baggage of scam ICOs, STOs, and skirted securities laws.
It was like Facebook becoming Meta. Crypto's biggest players wanted to change public (and regulator) perception away from pump-and-dump schemes.
After the 2018 ICO gold rush, it's understandable. Every project that raised millions (or billions) never shipped a meaningful product.
Like many crazes, charlatans took the money and ran.
Despite its grifter past, web3 is THE hot topic today as more founders, venture firms, and larger institutions look to build the future decentralized internet.
Supposedly.
How often have you heard: This will change the world, fix the internet, and give people power?
Why are most of web3's biggest proponents (and beneficiaries) the same rich, powerful players who built and invested in the modern internet? It's like they want to remake and own the internet.
Something seems off about that.
Why are insiders getting preferential presale terms before the public, allowing early investors and proponents to flip dirt cheap tokens and advisors shares almost immediately after the public sale?
It's a good gig with guaranteed markups, no risk or progress.
If it sounds like insider trading, it is, at least practically. This is clear when people talk about blockchain/web3 launches and tokens.
Fast money, quick flips, and guaranteed markups/returns are common.
Incentives-wise, it's hard to blame them. Who can blame someone for following the rules to win? Is it their fault or regulators' for not leveling the playing field?
It's similar to oil companies polluting for profit, Instagram depressing you into buying a new dress, or pharma pushing an unnecessary pill.
All of that is fair game, at least until we change the playbook, because people (and corporations) change for pain or love. Who doesn't love money?
belief based on money gain
Sinclair:
“It is difficult to get a man to understand something when his salary depends upon his not understanding it.”
Bitcoin, blockchain, and web3 analogies?
Most blockchain and web3 proponents are true believers, not cynical capitalists. They believe blockchain's inherent transparency and permissionless trust allow humanity to evolve beyond our reptilian ways and build a better decentralized and democratic world.
They highlight issues with the modern internet and monopoly players like Google, Facebook, and Apple. Decentralization fixes everything
If we could give power back to the people and get governments/corporations/individuals out of the way, we'd fix everything.
Blockchain solves supply chain and child labor issues in China.
To meet Paris climate goals, reduce emissions. Create a carbon token.
Fixing online hatred and polarization Web3 Twitter and Facebook replacement.
Web3 must just be the answer for everything… your “perfect” silver bullet.
Nothing fits everyone. Blockchain has pros and cons like everything else.
Blockchain's viral, ponzi-like nature has an MLM (mid level marketing) feel. If you bought Taylor Swift's NFT, your investment is tied to her popularity.
Probably makes you promote Swift more. Play music loudly.
Here's another example:
Imagine if Jehovah’s Witnesses (or evangelical preachers…) got paid for every single person they converted to their cause.
It becomes a self-fulfilling prophecy as their faith and wealth grow.
Which breeds extremism? Ultra-Orthodox Jews are an example. maximalists
Bitcoin and blockchain are causes, religions. It's a money-making movement and ideal.
We're good at convincing ourselves of things we want to believe, hence filter bubbles.
I ignore anything that doesn't fit my worldview and seek out like-minded people, which algorithms amplify.
Then what?
Is web3 merely a new scam?
No, never!
Blockchain has many crucial uses.
Sending money home/abroad without bank fees;
Like fleeing a war-torn country and converting savings to Bitcoin;
Like preventing Twitter from silencing dissidents.
Permissionless, trustless databases could benefit society and humanity. There are, however, many limitations.
Lost password?
What if you're cheated?
What if Trump/Putin/your favorite dictator incites a coup d'état?
What-ifs abound. Decentralization's openness brings good and bad.
No gatekeepers or firefighters to rescue you.
ISIS's fundraising is also frictionless.
Community-owned apps with bad interfaces and service.
Trade-offs rule.
So what compromises does web3 make?
What are your trade-offs? Decentralization has many strengths and flaws. Like Bitcoin's wasteful proof-of-work or Ethereum's political/wealth-based proof-of-stake.
To ensure the survival and veracity of the network/blockchain and to safeguard its nodes, extreme measures have been designed/put in place to prevent hostile takeovers aimed at altering the blockchain, i.e., adding money to your own wallet (account), etc.
These protective measures require significant resources and pose challenges. Reduced speed and throughput, high gas fees (cost to submit/write a transaction to the blockchain), and delayed development times, not to mention forked blockchain chains oops, web3 projects.
Protecting dissidents or rogue regimes makes sense. You need safety, privacy, and calm.
First-world life?
What if you assumed EVERYONE you saw was out to rob/attack you? You'd never travel, trust anyone, accomplish much, or live fully. The economy would collapse.
It's like an ant colony where half the ants do nothing but wait to be attacked.
Waste of time and money.
11% of the US budget goes to the military. Imagine what we could do with the $766B+ we spend on what-ifs annually.
Is so much hypothetical security needed?
Blockchain and web3 are similar.
Does your app need permissionless decentralization? Does your scooter-sharing company really need a proof-of-stake system and 1000s of nodes to avoid Russian hackers? Why?
Worst-case scenario? It's not life or death, unless you overstate the what-ifs. Web3 proponents find improbable scenarios to justify decentralization and tokenization.
Do I need a token to prove ownership of my painting? Unless I'm a master thief, I probably bought it.
despite losing the receipt.
I do, however, love Web 3.
Enough Web3 bashing for now. Understand? Decentralization isn't perfect, but it has huge potential when applied to the right problems.
I see many of the right problems as disrupting big tech's ruthless monopolies. I wrote several years ago about how tokenized blockchains could be used to break big tech's stranglehold on platforms, marketplaces, and social media.
Tokenomics schemes can be used for good and are powerful. Here’s how.
Before the ICO boom, I made a series of predictions about blockchain/crypto's future. It's still true.
Here's where I was then and where I see web3 going:
My 11 Big & Bold Predictions for Blockchain
In the near future, people may wear crypto cash rings or bracelets.
While some governments repress cryptocurrency, others will start to embrace it.
Blockchain will fundamentally alter voting and governance, resulting in a more open election process.
Money freedom will lead to a more geographically open world where people will be more able to leave when there is unrest.
Blockchain will make record keeping significantly easier, eliminating the need for a significant portion of government workers whose sole responsibility is paperwork.
Overrated are smart contracts.
6. Tokens will replace company stocks.
7. Blockchain increases real estate's liquidity, value, and volatility.
8. Healthcare may be most affected.
9. Crypto could end privacy and lead to Minority Report.
10. New companies with network effects will displace incumbents.
11. Soon, people will wear rings or bracelets with crypto cash.
Some have already happened, while others are still possible.
Time will tell if they happen.
And finally:
What will web3 be?
Who will be in charge?
Closing remarks
Hope you enjoyed this web3 dive. There's much more to say, but that's for another day.
We're writing history as we go.
Tech regulation, mergers, Bitcoin surge How will history remember us?
What about web3 and blockchain?
Is this a revolution or a tulip craze?
Remember, actions speak louder than words (share them in the comments).
Your turn.

Jayden Levitt
3 years ago
The country of El Salvador's Bitcoin-obsessed president lost $61.6 million.
It’s only a loss if you sell, right?
Nayib Bukele proclaimed himself “the world’s coolest dictator”.
His jokes aren't clear.
El Salvador's 43rd president self-proclaimed “CEO of El Salvador” couldn't be less presidential.
His thin jeans, aviator sunglasses, and baseball caps like a cartel lord.
He's popular, though.
Bukele won 53% of the vote by fighting violent crime and opposition party corruption.
El Salvador's 6.4 million inhabitants are riding the cryptocurrency volatility wave.
They were powerless.
Their autocratic leader, a former Yamaha Motors salesperson and Bitcoin believer, wants to help 70% unbanked locals.
He intended to give the citizens a way to save money and cut the country's $200 million remittance cost.
Transfer and deposit costs.
This makes logical sense when the president’s theatrics don’t blind you.
El Salvador's Bukele revealed plans to make bitcoin legal tender.
Remittances total $5.9 billion (23%) of the country's expenses.
Anything that reduces costs could boost the economy.
The country’s unbanked population is staggering. Here’s the data by % of people who either have a bank account (Blue) or a mobile money account (Black).
According to Bukele, 46% of the population has downloaded the Chivo Bitcoin Wallet.
In 2021, 36% of El Salvadorans had bank accounts.
Large rural countries like Kenya seem to have resolved their unbanked dilemma.
An economy surfaced where village locals would sell, trade and store network minutes and data as a store of value.
Kenyan phone networks realized unbanked people needed a safe way to accumulate wealth and have an emergency fund.
96% of Kenyans utilize M-PESA, which doesn't require a bank account.
The software involves human agents who hang out with cash and a phone.
These people are like ATMs.
You offer them cash to deposit money in your mobile money account or withdraw cash.
In a country with a faulty banking system, cash availability and a safe place to deposit it are important.
William Jack and Tavneet Suri found that M-PESA brought 194,000 Kenyan households out of poverty by making transactions cheaper and creating a safe store of value.
Mobile money, a service that allows monetary value to be stored on a mobile phone and sent to other users via text messages, has been adopted by most Kenyan households. We estimate that access to the Kenyan mobile money system M-PESA increased per capita consumption levels and lifted 194,000 households, or 2% of Kenyan households, out of poverty.
The impacts, which are more pronounced for female-headed households, appear to be driven by changes in financial behaviour — in particular, increased financial resilience and saving. Mobile money has therefore increased the efficiency of the allocation of consumption over time while allowing a more efficient allocation of labour, resulting in a meaningful reduction of poverty in Kenya.
Currently, El Salvador has 2,301 Bitcoin.
At publication, it's worth $44 million. That remains 41% of Bukele's original $105.6 million.
Unknown if the country has sold Bitcoin, but Bukeles keeps purchasing the dip.
It's still falling.
This might be a fantastic move for the impoverished country over the next five years, if they can live economically till Bitcoin's price recovers.
The evidence demonstrates that a store of value pulls individuals out of poverty, but others say Bitcoin is premature.
You may regard it as an aggressive endeavor to front run the next wave of adoption, offering El Salvador a financial upside.

CyberPunkMetalHead
3 years ago
195 countries want Terra Luna founder Do Kwon
Interpol has issued a red alert on Terraform Labs' CEO, South Korean prosecutors said.
After the May crash of Terra Luna revealed tax evasion issues, South Korean officials filed an arrest warrant for Do Kwon, but he is missing.
Do Kwon is now a fugitive in 195 countries after Seoul prosecutors placed him to Interpol's red list. Do Kwon hasn't commented since then. The red list allows any country's local authorities to apprehend Do Kwon.
Do Dwon and Terraform Labs were believed to have moved to Singapore days before the $40 billion wipeout, but Singapore authorities said he fled the country on September 17. Do Kwon tweeted that he wasn't on the run and cited privacy concerns.
Do Kwon was not on the red list at the time and said he wasn't "running," only to reply to his own tweet saying he hasn't jogged in a while and needed to trim calories.
Whether or not it makes sense to read too much into this, the reality is that Do Kwon is now on Interpol red list, despite the firmly asserts on twitter that he does absolutely nothing to hide.
UPDATE:
South Korean authorities are investigating alleged withdrawals of over $60 million U.S. and seeking to freeze these assets. Korean authorities believe a new wallet exchanged over 3000 BTC through OKX and Kucoin.
Do Kwon and the Luna Foundation Guard (of whom Do Kwon is a key member of) have declined all charges and dubbed this disinformation.
Singapore's Luna Foundation Guard (LFG) manages the Terra Ecosystem.
The Legal Situation
Multiple governments are searching for Do Kwon and five other Terraform Labs employees for financial markets legislation crimes.
South Korean authorities arrested a man suspected of tax fraud and Ponzi scheme.
The U.S. SEC is also examining Terraform Labs on how UST was advertised as a stablecoin. No legal precedent exists, so it's unclear what's illegal.
The future of Terraform Labs, Terra, and Terra 2 is unknown, and despite what Twitter shills say about LUNC, the company remains in limbo awaiting a decision that will determine its fate. This project isn't a wise investment.
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Glorin Santhosh
3 years ago
In his final days, Steve Jobs sent an email to himself. What It Said Was This
An email capturing Steve Jobs's philosophy.
Steve Jobs may have been the most inspired and driven entrepreneur.
He worked on projects because he wanted to leave a legacy.
Steve Jobs' final email to himself encapsulated his philosophy.
After his death from pancreatic cancer in October 2011, Laurene Powell Jobs released the email. He was 56.
Read: Steve Jobs by Walter Isaacson (#BestSeller)
The Email:
September 2010 Steve Jobs email:
“I grow little of the food I eat, and of the little I do grow, I do not breed or perfect the seeds.” “I do not make my own clothing. I speak a language I did not invent or refine,” he continued. “I did not discover the mathematics I use… I am moved by music I did not create myself.”
Jobs ended his email by reflecting on how others created everything he uses.
He wrote:
“When I needed medical attention, I was helpless to help myself survive.”
The Apple co-founder concluded by praising humanity.
“I did not invent the transistor, the microprocessor, object-oriented programming, or most of the technology I work with. I love and admire my species, living and dead, and am totally dependent on them for my life and well-being,” he concluded.
The email was made public as a part of the Steve Jobs Archive, a website that was launched in tribute to his legacy.
Steve Jobs' widow founded the internet archive. Apple CEO Tim Cook and former design leader Jony Ive were prominent guests.
Steve Jobs has always inspired because he shows how even the best can be improved.
High expectations were always there, and they were consistently met.
We miss him because he was one of the few with lifelong enthusiasm and persona.

Nick Nolan
3 years ago
How to Make $1,037,100 in 4 Months with This Weird Website
One great idea might make you rich.
Imagine having a million-dollar concept in college that made a million.
2005 precisely.
Alex Tew, 21, from Wiltshire, England, created The Million Dollar Homepage in August 2005. The idea is basic but beyond the ordinary, which is why it worked.
Alex built a 1,000,000-pixel webpage.
Each website pixel would cost $1. Since pixels are hard to discern, he sold 10x10 squares for $100.
He'd make a million if all the spots sold.
He may have thought about NFTs and the Metaverse decades ago.
MillionDollarHomepage.com launched in 2005.
Businesses and individuals could buy a website spot and add their logo, website link, and tagline. You bought an ad, but nobody visited the website.
If a few thousand people visited the website, it could drive traffic to your business's site.
Alex promised buyers the website would be up for 5 years, so it was a safe bet.
Alex's friend with a music website was the first to buy real estate on the site. Within two weeks, 4,700 pixels sold, and a tracker showed how many were sold and available.
Word-of-mouth marketing got the press's attention quickly. Everyone loves reading about new ways to make money, so it was a good news story.
By September, over 250,000 pixels had been sold, according to a BBC press release.
Alex and the website gained more media and public attention, so traffic skyrocketed. Two months after the site launched, 1,400 customers bought more than 500,000 pixels.
Businesses bought online real estate. They heard thousands visited the site, so they could get attention cheaply.
Unless you bought a few squares, I'm not sure how many people would notice your ad or click your link.
A sponge website owner emailed Alex:
“We tried Million Dollar Homepage because we were impressed at the level of ingenuity and the sheer simplicity of it. If we’re honest, we didn’t expect too much from it. Now, as a direct result, we are pitching for £18,000 GBP worth of new clients and have seen our site traffic increase over a hundred-fold. We’re even going to have to upgrade our hosting facility! It’s been exceptional.”
Web.archive.org screenshots show how the website changed.
“The idea is to create something of an internet time capsule: a homepage that is unique and permanent. Everything on the internet keeps changing so fast, it will be nice to have something that stays solid and permanent for many years. You can be a part of that!” Alex Tew, 2005
The last 1,000 pixels were sold on January 1, 2006.
By then, the homepage had hundreds of thousands of monthly visitors. Alex put the last space on eBay due to high demand.
MillionDollarWeightLoss.com won the last pixels for $38,100, bringing revenue to $1,037,100 in 4 months.
Many have tried to replicate this website's success. They've all failed.
This idea only worked because no one had seen this website before.
This winner won't be repeated, but it should inspire you to try something new and creative.
Still popular, you could buy one of the linked domains. You can't buy pixels, but you can buy an expired domain.
One link I clicked costs $59,888.
You'd own a piece of internet history if you spent that much on a domain.
Someone bought stablesgallery.co.uk after the domain expired and restored it.
Many of the linked websites have expired or been redirected, but some still link to the original. I couldn't find sponge's website. Can you?
This is a great example of how a simple creative idea can go viral.
Comment on this amazing success story.

Ian Writes
3 years ago
Rich Dad, Poor Dad is a Giant Steaming Pile of Sh*t by Robert Kiyosaki.
Don't promote it.
I rarely read a post on how Rich Dad, Poor Dad motivated someone to grow rich or change their investing/finance attitude. Rich Dad, Poor Dad is a sham, though. This book isn't worth anyone's attention.
Robert Kiyosaki, the author of this garbage, doesn't deserve recognition or attention. This first finance guru wanted to build his own wealth at your expense. These charlatans only care about themselves.
The reason why Rich Dad, Poor Dad is a huge steaming piece of trash
The book's ideas are superficial, apparent, and unsurprising to entrepreneurs and investors. The book's themes may seem profound to first-time readers.
Apparently, starting a business will make you rich.
The book supports founding or buying a business, making it self-sufficient, and being rich through it. Starting a business is time-consuming, tough, and expensive. Entrepreneurship isn't for everyone. Rarely do enterprises succeed.
Robert says we should think like his mentor, a rich parent. Robert never said who or if this guy existed. He was apparently his own father. Robert proposes investing someone else's money in several enterprises and properties. The book proposes investing in:
“have returns of 100 percent to infinity. Investments that for $5,000 are soon turned into $1 million or more.”
In rare cases, a business may provide 200x returns, but 65% of US businesses fail within 10 years. Australia's first-year business failure rate is 60%. A business that lasts 10 years doesn't mean its owner is rich. These statistics only include businesses that survive and pay their owners.
Employees are depressed and broke.
The novel portrays employees as broke and sad. The author degrades workers.
I've owned and worked for a business. I was broke and miserable as a business owner, working 80 hours a week for absolutely little salary. I work 50 hours a week and make over $200,000 a year. My work is hard, intriguing, and I'm surrounded by educated individuals. Self-employed or employee?
Don't listen to a charlatan's tax advice.
From a bad advise perspective, Robert's tax methods were funny. Robert suggests forming a corporation to write off holidays as board meetings or health club costs as business expenses. These actions can land you in serious tax trouble.
Robert dismisses college and traditional schooling. Rich individuals learn by doing or living, while educated people are agitated and destitute, says Robert.
Rich dad says:
“All too often business schools train employees to become sophisticated bean-counters. Heaven forbid a bean counter takes over a business. All they do is look at the numbers, fire people, and kill the business.”
And then says:
“Accounting is possibly the most confusing, boring subject in the world, but if you want to be rich long-term, it could be the most important subject.”
Get rich by avoiding paying your debts to others.
While this book has plenty of bad advice, I'll end with this: Robert advocates paying yourself first. This man's work with Trump isn't surprising.
Rich Dad's book says:
“So you see, after paying myself, the pressure to pay my taxes and the other creditors is so great that it forces me to seek other forms of income. The pressure to pay becomes my motivation. I’ve worked extra jobs, started other companies, traded in the stock market, anything just to make sure those guys don’t start yelling at me […] If I had paid myself last, I would have felt no pressure, but I’d be broke.“
Paying yourself first shouldn't mean ignoring debt, damaging your credit score and reputation, or paying unneeded fees and interest. Good business owners pay employees, creditors, and other costs first. You can pay yourself after everyone else.
If you follow Robert Kiyosaki's financial and business advice, you might as well follow Donald Trump's, the most notoriously ineffective businessman and swindle artist.
This book's popularity is unfortunate. Robert utilized the book's fame to promote paid seminars. At these seminars, he sold more expensive seminars to the gullible. This strategy was utilized by several conmen and Trump University.
It's reasonable that many believed him. It sounded appealing because he was pushing to get rich by thinking like a rich person. Anyway. At a time when most persons addressing wealth development advised early sacrifices (such as eschewing luxury or buying expensive properties), Robert told people to act affluent now and utilize other people's money to construct their fantasy lifestyle. It's exciting and fast.
I often voice my skepticism and scorn for internet gurus now that social media and platforms like Medium make it easier to promote them. Robert Kiyosaki was a guru. Many people still preach his stuff because he was so good at pushing it.
