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
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Nathan Reiff
3 years ago
Howey Test and Cryptocurrencies: 'Every ICO Is a Security'
What Is the Howey Test?
To determine whether a transaction qualifies as a "investment contract" and thus qualifies as a security, the Howey Test refers to the U.S. Supreme Court cass: the Securities Act of 1933 and the Securities Exchange Act of 1934. According to the Howey Test, an investment contract exists when "money is invested in a common enterprise with a reasonable expectation of profits from others' efforts."
The test applies to any contract, scheme, or transaction. The Howey Test helps investors and project backers understand blockchain and digital currency projects. ICOs and certain cryptocurrencies may be found to be "investment contracts" under the test.
Understanding the Howey Test
The Howey Test comes from the 1946 Supreme Court case SEC v. W.J. Howey Co. The Howey Company sold citrus groves to Florida buyers who leased them back to Howey. The company would maintain the groves and sell the fruit for the owners. Both parties benefited. Most buyers had no farming experience and were not required to farm the land.
The SEC intervened because Howey failed to register the transactions. The court ruled that the leaseback agreements were investment contracts.
This established four criteria for determining an investment contract. Investing contract:
- An investment of money
- n a common enterprise
- With the expectation of profit
- To be derived from the efforts of others
In the case of Howey, the buyers saw the transactions as valuable because others provided the labor and expertise. An income stream was obtained by only investing capital. As a result of the Howey Test, the transaction had to be registered with the SEC.
Howey Test and Cryptocurrencies
Bitcoin is notoriously difficult to categorize. Decentralized, they evade regulation in many ways. Regardless, the SEC is looking into digital assets and determining when their sale qualifies as an investment contract.
The SEC claims that selling digital assets meets the "investment of money" test because fiat money or other digital assets are being exchanged. Like the "common enterprise" test.
Whether a digital asset qualifies as an investment contract depends on whether there is a "expectation of profit from others' efforts."
For example, buyers of digital assets may be relying on others' efforts if they expect the project's backers to build and maintain the digital network, rather than a dispersed community of unaffiliated users. Also, if the project's backers create scarcity by burning tokens, the test is met. Another way the "efforts of others" test is met is if the project's backers continue to act in a managerial role.
These are just a few examples given by the SEC. If a project's success is dependent on ongoing support from backers, the buyer of the digital asset is likely relying on "others' efforts."
Special Considerations
If the SEC determines a cryptocurrency token is a security, many issues arise. It means the SEC can decide whether a token can be sold to US investors and forces the project to register.
In 2017, the SEC ruled that selling DAO tokens for Ether violated federal securities laws. Instead of enforcing securities laws, the SEC issued a warning to the cryptocurrency industry.
Due to the Howey Test, most ICOs today are likely inaccessible to US investors. After a year of ICOs, then-SEC Chair Jay Clayton declared them all securities.
SEC Chairman Gensler Agrees With Predecessor: 'Every ICO Is a Security'
Howey Test FAQs
How Do You Determine If Something Is a Security?
The Howey Test determines whether certain transactions are "investment contracts." Securities are transactions that qualify as "investment contracts" under the Securities Act of 1933 and the Securities Exchange Act of 1934.
The Howey Test looks for a "investment of money in a common enterprise with a reasonable expectation of profits from others' efforts." If so, the Securities Act of 1933 and the Securities Exchange Act of 1934 require disclosure and registration.
Why Is Bitcoin Not a Security?
Former SEC Chair Jay Clayton clarified in June 2018 that bitcoin is not a security: "Cryptocurrencies: Replace the dollar, euro, and yen with bitcoin. That type of currency is not a security," said Clayton.
Bitcoin, which has never sought public funding to develop its technology, fails the SEC's Howey Test. However, according to Clayton, ICO tokens are securities.
A Security Defined by the SEC
In the public and private markets, securities are fungible and tradeable financial instruments. The SEC regulates public securities sales.
The Supreme Court defined a security offering in SEC v. W.J. Howey Co. In its judgment, the court defines a security using four criteria:
- An investment contract's existence
- The formation of a common enterprise
- The issuer's profit promise
- Third-party promotion of the offering
Read original post.
Rishi Dean
3 years ago
Coinbase's web3 app
Use popular Ethereum dapps with Coinbase’s new dapp wallet and browser
Tl;dr: This post highlights the ability to access web3 directly from your Coinbase app using our new dapp wallet and browser.
Decentralized autonomous organizations (DAOs) and decentralized finance (DeFi) have gained popularity in the last year (DAOs). The total value locked (TVL) of DeFi investments on the Ethereum blockchain has grown to over $110B USD, while NFTs sales have grown to over $30B USD in the last 12 months (LTM). New innovative real-world applications are emerging every day.
Today, a small group of Coinbase app users can access Ethereum-based dapps. Buying NFTs on Coinbase NFT and OpenSea, trading on Uniswap and Sushiswap, and borrowing and lending on Curve and Compound are examples.
Our new dapp wallet and dapp browser enable you to access and explore web3 directly from your Coinbase app.
Web3 in the Coinbase app
Users can now access dapps without a recovery phrase. This innovative dapp wallet experience uses Multi-Party Computation (MPC) technology to secure your on-chain wallet. This wallet's design allows you and Coinbase to share the 'key.' If you lose access to your device, the key to your dapp wallet is still safe and Coinbase can help recover it.
Set up your new dapp wallet by clicking the "Browser" tab in the Android app's navigation bar. Once set up, the Coinbase app's new dapp browser lets you search, discover, and use Ethereum-based dapps.
Looking forward
We want to enable everyone to seamlessly and safely participate in web3, and today’s launch is another step on that journey. We're rolling out the new dapp wallet and browser in the US on Android first to a small subset of users and plan to expand soon. Stay tuned!
William Brucee
3 years ago
This person is probably Satoshi Nakamoto.
Who founded bitcoin is the biggest mystery in technology today, not how it works.
On October 31, 2008, Satoshi Nakamoto posted a whitepaper to a cryptography email list. Still confused by the mastermind who changed monetary history.
Journalists and bloggers have tried in vain to uncover bitcoin's creator. Some candidates self-nominated. We're still looking for the mystery's perpetrator because none of them have provided proof.
One person. I'm confident he invented bitcoin. Let's assess Satoshi Nakamoto before I reveal my pick. Or what he wants us to know.
Satoshi's P2P Foundation biography says he was born in 1975. He doesn't sound or look Japanese. First, he wrote the whitepaper and subsequent articles in flawless English. His sleeping habits are unusual for a Japanese person.
Stefan Thomas, a Bitcoin Forum member, displayed Satoshi's posting timestamps. Satoshi Nakamoto didn't publish between 2 and 8 p.m., Japanese time. Satoshi's identity may not be real.
Why would he disguise himself?
There is a legitimate explanation for this
Phil Zimmermann created PGP to give dissidents an open channel of communication, like Pretty Good Privacy. US government seized this technology after realizing its potential. Police investigate PGP and Zimmermann.
This technology let only two people speak privately. Bitcoin technology makes it possible to send money for free without a bank or other intermediary, removing it from government control.
How much do we know about the person who invented bitcoin?
Here's what we know about Satoshi Nakamoto now that I've covered my doubts about his personality.
Satoshi Nakamoto first appeared with a whitepaper on metzdowd.com. On Halloween 2008, he presented a nine-page paper on a new peer-to-peer electronic monetary system.
Using the nickname satoshi, he created the bitcointalk forum. He kept developing bitcoin and created bitcoin.org. Satoshi mined the genesis block on January 3, 2009.
Satoshi Nakamoto worked with programmers in 2010 to change bitcoin's protocol. He engaged with the bitcoin community. Then he gave Gavin Andresen the keys and codes and transferred community domains. By 2010, he'd abandoned the project.
The bitcoin creator posted his goodbye on April 23, 2011. Mike Hearn asked Satoshi if he planned to rejoin the group.
“I’ve moved on to other things. It’s in good hands with Gavin and everyone.”
Nakamoto Satoshi
The man who broke the banking system vanished. Why?
Satoshi's wallets held 1,000,000 BTC. In December 2017, when the price peaked, he had over US$19 billion. Nakamoto had the 44th-highest net worth then. He's never cashed a bitcoin.
This data suggests something happened to bitcoin's creator. I think Hal Finney is Satoshi Nakamoto .
Hal Finney had ALS and died in 2014. I suppose he created the future of money, then he died, leaving us with only rumors about his identity.
Hal Finney, who was he?
Hal Finney graduated from Caltech in 1979. Student peers voted him the smartest. He took a doctoral-level gravitational field theory course as a freshman. Finney's intelligence meets the first requirement for becoming Satoshi Nakamoto.
Students remember Finney holding an Ayn Rand book. If he'd read this, he may have developed libertarian views.
His beliefs led him to a small group of freethinking programmers. In the 1990s, he joined Cypherpunks. This action promoted the use of strong cryptography and privacy-enhancing technologies for social and political change. Finney helped them achieve a crypto-anarchist perspective as self-proclaimed privacy defenders.
Zimmermann knew Finney well.
Hal replied to a Cypherpunk message about Phil Zimmermann and PGP. He contacted Phil and became PGP Corporation's first member, retiring in 2011. Satoshi Nakamoto quit bitcoin in 2011.
Finney improved the new PGP protocol, but he had to do so secretly. He knew about Phil's PGP issues. I understand why he wanted to hide his identity while creating bitcoin.
Why did he pretend to be from Japan?
His envisioned persona was spot-on. He resided near scientist Dorian Prentice Satoshi Nakamoto. Finney could've assumed Nakamoto's identity to hide his. Temple City has 36,000 people, so what are the chances they both lived there? A cryptographic genius with the same name as Bitcoin's creator: coincidence?
Things went differently, I think.
I think Hal Finney sent himself Satoshis messages. I know it's odd. If you want to conceal your involvement, do as follows. He faked messages and transferred the first bitcoins to himself to test the transaction mechanism, so he never returned their money.
Hal Finney created the first reusable proof-of-work system. The bitcoin protocol. In the 1990s, Finney was intrigued by digital money. He invented CRypto cASH in 1993.
Legacy
Hal Finney's contributions should not be forgotten. Even if I'm wrong and he's not Satoshi Nakamoto, we shouldn't forget his bitcoin contribution. He helped us achieve a better future.
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Evgenii Nelepko
3 years ago
My 3 biggest errors as a co-founder and CEO
Reflections on the closed company Hola! Dating app
I'll discuss my fuckups as an entrepreneur and CEO. All of them refer to the dating app Hola!, which I co-founded and starred in.
Spring 2021 was when we started. Two techies and two non-techies created a dating app. Pokemon Go and Tinder were combined.
Online dating is a business, and it takes two weeks from a like to a date. We questioned online dating app users if they met anyone offline last year.
75% replied yes, 50% sometimes, 25% usually.
Offline dating is popular, yet people have concerns.
Men are reluctant to make mistakes in front of others.
Women are curious about the background of everyone who approaches them.
We designed unique mechanics that let people date after a match. No endless chitchat. Women would be safe while men felt like cowboys.
I wish to emphasize three faults that lead to founders' estrangement.
This detachment ultimately led to us shutting down the company.
The wrong technology stack
Situation
Instead of generating a faster MVP and designing an app in a universal stack for iOS and Android, I argued we should pilot the app separately for iOS and Android. Technical founders' expertise made this possible.
Self-reflection
Mistaken strategy. We lost time and resources developing two apps at once. We chose iOS since it's more profitable. Apple took us out after the release, citing Guideline 4.3 Spam. After 4 months, we had nothing. We had a long way to go to get the app on Android and the Store.
I suggested creating a uniform platform for the company's growth. This makes parallel product development easier. The strategist's lack of experience and knowledge made it a piece of crap.
What would I have changed if I could?
We should have designed an Android universal stack. I expected Apple to have issues with a dating app.
Our approach should have been to launch something and subsequently improve it, but prejudice won.
The lesson
Discuss the IT stack with your CTO. It saves time and money. Choose the easiest MVP method.
2. A tardy search for investments
Situation
Though the universe and other founders encouraged me to locate investors first, I started pitching when we almost had an app.
When angels arrived, it was time to close. The app was banned, war broke out, I left the country, and the other co-founders stayed. We had no savings.
Self-reflection
I loved interviewing users. I'm proud of having done 1,000 interviews. I wanted to understand people's pain points and improve the product.
Interview results no longer affected the product. I was terrified to start pitching. I filled out accelerator applications and redid my presentation. You must go through that so you won't be terrified later.
What would I have changed if I could?
Get an external or internal mentor to help me with my first pitch as soon as possible. I'd be supported if criticized. He'd cheer with me if there was enthusiasm.
In 99% of cases, I'm comfortable jumping into the unknown, but there are exceptions. The mentor's encouragement would have prompted me to act sooner.
The lesson
Begin fundraising immediately. Months may pass. Show investors your pre-MVP project. Draw inferences from feedback.
3. Role ambiguity
Situation
My technical co-founders were also part-time lead developers, which produced communication issues. As co-founders, we communicated well and recognized the problems. Stakes, vesting, target markets, and approach were agreed upon.
We were behind schedule. Technical debt and strategic gap grew.
Bi-daily and weekly reviews didn't help. Each time, there were explanations. Inside, I was freaking out.
Self-reflection
I am a fairly easy person to talk to. I always try to stick to agreements; otherwise, my head gets stuffed with unnecessary information, interpretations, and emotions.
Sit down -> talk -> decide -> do -> evaluate the results. Repeat it.
If I don't get detailed comments, I start ruining everyone's mood. If there's a systematic violation of agreements without a good justification, I won't join the project or I'll end the collaboration.
What would I have done otherwise?
This is where it’s scariest to draw conclusions. Probably the most logical thing would have been not to start the project as we started it. But that was already a completely different project. So I would not have done anything differently and would have failed again.
But I drew conclusions for the future.
The lesson
First-time founders should find an adviser or team coach for a strategic session. It helps split the roles and responsibilities.
Thomas Smith
3 years ago
ChatGPT Is Experiencing a Lightbulb Moment
Why breakthrough technologies must be accessible
ChatGPT has exploded. Over 1 million people have used the app, and coding sites like Stack Overflow have banned its answers. It's huge.
I wouldn't have called that as an AI researcher. ChatGPT uses the same GPT-3 technology that's been around for over two years.
More than impressive technology, ChatGPT 3 shows how access makes breakthroughs usable. OpenAI has finally made people realize the power of AI by packaging GPT-3 for normal users.
We think of Thomas Edison as the inventor of the lightbulb, not because he invented it, but because he popularized it.
Going forward, AI companies that make using AI easy will thrive.
Use-case importance
Most modern AI systems use massive language models. These language models are trained on 6,000+ years of human text.
GPT-3 ate 8 billion pages, almost every book, and Wikipedia. It created an AI that can write sea shanties and solve coding problems.
Nothing new. I began beta testing GPT-3 in 2020, but the system's basics date back further.
Tools like GPT-3 are hidden in many apps. Many of the AI writing assistants on this platform are just wrappers around GPT-3.
Lots of online utilitarian text, like restaurant menu summaries or city guides, is written by AI systems like GPT-3. You've probably read GPT-3 without knowing it.
Accessibility
Why is ChatGPT so popular if the technology is old?
ChatGPT makes the technology accessible. Free to use, people can sign up and text with the chatbot daily. ChatGPT isn't revolutionary. It does it in a way normal people can access and be amazed by.
Accessibility isn't easy. OpenAI's Sam Altman tweeted that opening ChatGPT to the public increased computing costs.
Each chat costs "low-digit cents" to process. OpenAI probably spends several hundred thousand dollars a day to keep ChatGPT running, with no immediate business case.
Academic researchers and others who developed GPT-3 couldn't afford it. Without resources to make technology accessible, it can't be used.
Retrospective
This dynamic is old. In the history of science, a researcher with a breakthrough idea was often overshadowed by an entrepreneur or visionary who made it accessible to the public.
We think of Thomas Edison as the inventor of the lightbulb. But really, Vasilij Petrov, Thomas Wright, and Joseph Swan invented the lightbulb. Edison made technology visible and accessible by electrifying public buildings, building power plants, and wiring.
Edison probably lost a ton of money on stunts like building a power plant to light JP Morgan's home, the NYSE, and several newspaper headquarters.
People wanted electric lights once they saw their benefits. By making the technology accessible and visible, Edison unlocked a hugely profitable market.
Similar things are happening in AI. ChatGPT shows that developing breakthrough technology in the lab or on B2B servers won't change the culture.
AI must engage people's imaginations to become mainstream. Before the tech impacts the world, people must play with it and see its revolutionary power.
As the field evolves, companies that make the technology widely available, even at great cost, will succeed.
OpenAI's compute fees are eye-watering. Revolutions are costly.
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.