More on Web3 & Crypto
Vitalik
4 years ago
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
Alex Bentley
3 years ago
Why Bill Gates thinks Bitcoin, crypto, and NFTs are foolish
Microsoft co-founder Bill Gates assesses digital assets while the bull is caged.
Bill Gates is well-respected.
Reasonably. He co-founded and led Microsoft during its 1980s and 1990s revolution.
After leaving Microsoft, Bill Gates pursued other interests. He and his wife founded one of the world's largest philanthropic organizations, Bill & Melinda Gates Foundation. He also supports immunizations, population control, and other global health programs.
When Gates criticized Bitcoin, cryptocurrencies, and NFTs, it made news.
Bill Gates said at the 58th Munich Security Conference...
“You have an asset class that’s 100% based on some sort of greater fool theory that somebody’s going to pay more for it than I do.”
Gates means digital assets. Like many bitcoin critics, he says digital coins and tokens are speculative.
And he's not alone. Financial experts have dubbed Bitcoin and other digital assets a "bubble" for a decade.
Gates also made fun of Bored Ape Yacht Club and NFTs, saying, "Obviously pricey digital photographs of monkeys will help the world."
Why does Bill Gates dislike digital assets?
According to Gates' latest comments, Bitcoin, cryptos, and NFTs aren't good ways to hold value.
Bill Gates is a better investor than Elon Musk.
“I’m used to asset classes, like a farm where they have output, or like a company where they make products,” Gates said.
The Guardian claimed in April 2021 that Bill and Melinda Gates owned the most U.S. farms. Over 242,000 acres of farmland.
The Gates couple has enough farmland to cover Hong Kong.
Bill Gates is a classic investor. He wants companies with an excellent track record, strong fundamentals, and good management. Or tangible assets like land and property.
Gates prefers the "old economy" over the "new economy"
Gates' criticism of Bitcoin and cryptocurrency ventures isn't surprising. These digital assets lack all of Gates's investing criteria.
Volatile digital assets include Bitcoin. Their costs might change dramatically in a day. Volatility scares risk-averse investors like Gates.
Gates has a stake in the old financial system. As Microsoft's co-founder, Gates helped develop a dominant tech company.
Because of his business, he's one of the world's richest men.
Bill Gates is invested in protecting the current paradigm.
He won't invest in anything that could destroy the global economy.
When Gates criticizes Bitcoin, cryptocurrencies, and NFTs, he's suggesting they're a hoax. These soapbox speeches are one way he protects his interests.
Digital assets aren't a bad investment, though. Many think they're the future.
Changpeng Zhao and Brian Armstrong are two digital asset billionaires. Two crypto exchange CEOs. Binance/Coinbase.
Digital asset revolution won't end soon.
If you disagree with Bill Gates and plan to invest in Bitcoin, cryptocurrencies, or NFTs, do your own research and understand the risks.
But don’t take Bill Gates’ word for it.
He’s just an old rich guy with a lot of farmland.
He has a lot to lose if Bitcoin and other digital assets gain global popularity.
This post is a summary. Read the full article here.
Stephen Moore
3 years ago
Web 2 + Web 3 = Web 5.
Monkey jpegs and shitcoins have tarnished Web3's reputation. Let’s move on.
Web3 was called "the internet's future."
Well, 'crypto bros' shouted about it loudly.
As quickly as it arrived to be the next internet, it appears to be dead. It's had scandals, turbulence, and crashes galore:
Web 3.0's cryptocurrencies have crashed. Bitcoin's all-time high was $66,935. This month, Ethereum fell from $2130 to $1117. Six months ago, the cryptocurrency market peaked at $3 trillion. Worst is likely ahead.
Gas fees make even the simplest Web3 blockchain transactions unsustainable.
Terra, Luna, and other dollar pegs collapsed, hurting crypto markets. Celsius, a crypto lender backed by VCs and Canada's second-largest pension fund, and Binance, a crypto marketplace, have withheld money and coins. They're near collapse.
NFT sales are falling rapidly and losing public interest.
Web3 has few real-world uses, like most crypto/blockchain technologies. Web3's image has been tarnished by monkey profile pictures and shitcoins while failing to become decentralized (the whole concept is controlled by VCs).
The damage seems irreparable, leaving Web3 in the gutter.
Step forward our new saviour — Web5
Fear not though, as hero awaits to drag us out of the Web3 hellscape. Jack Dorsey revealed his plan to save the internet quickly.
Dorsey has long criticized Web3, believing that VC capital and silicon valley insiders have created a centralized platform. In a tweet that upset believers and VCs (he was promptly blocked by Marc Andreessen), Dorsey argued, "You don't own "Web3." VCs and LPs do. Their incentives prevent it. It's a centralized organization with a new name.
Dorsey announced Web5 on June 10 in a very Elon-like manner. Block's TBD unit will work on the project (formerly Square).
Web5's pitch is that users will control their own data and identity. Bitcoin-based. Sound familiar? The presentation pack's official definition emphasizes decentralization. Web5 is a decentralized web platform that enables developers to write decentralized web apps using decentralized identifiers, verifiable credentials, and decentralized web nodes, returning ownership and control over identity and data to individuals.
Web5 would be permission-less, open, and token-less. What that means for Earth is anyone's guess. Identity. Ownership. Blockchains. Bitcoin. Different.
Web4 appears to have been skipped, forever destined to wish it could have shown the world what it could have been. (It was probably crap.) As this iteration combines Web2 and Web3, simple math and common sense add up to 5. Or something.
Dorsey and his team have had this idea simmering for a while. Daniel Buchner, a member of Block's Decentralized Identity team, said, "We're finishing up Web5's technical components."
Web5 could be the project that decentralizes the internet. It must be useful to users and convince everyone to drop the countless Web3 projects, products, services, coins, blockchains, and websites being developed as I write this.
Web5 may be too late for Dorsey and the incoming flood of creators.
Web6 is planned!
The next months and years will be hectic and less stable than the transition from Web 1.0 to Web 2.0.
Web1 was around 1991-2004.
Web2 ran from 2004 to 2021. (though the Web3 term was first used in 2014, it only really gained traction years later.)
Web3 lasted a year.
Web4 is dead.
Silicon Valley billionaires are turning it into a startup-style race, each disrupting the next iteration until they crack it. Or destroy it completely.
Web5 won't last either.
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Scott Stockdale
3 years ago
A Day in the Life of Lex Fridman Can Help You Hit 6-Month Goals
The Lex Fridman podcast host has interviewed Elon Musk.
Lex is a minimalist YouTuber. His videos are sloppy. Suits are his trademark.
In a video, he shares a typical day. I've smashed my 6-month goals using its ideas.
Here's his schedule.
Morning Mantra
Not woo-woo. Lex's mantra reflects his practicality.
Four parts.
Rulebook
"I remember the game's rules," he says.
Among them:
Sleeping 6–8 hours nightly
1–3 times a day, he checks social media.
Every day, despite pain, he exercises. "I exercise uninjured body parts."
Visualize
He imagines his day. "Like Sims..."
He says three things he's grateful for and contemplates death.
"Today may be my last"
Objectives
Then he visualizes his goals. He starts big. Five-year goals.
Short-term goals follow. Lex says they're year-end goals.
Near but out of reach.
Principles
He lists his principles. Assertions. His goals.
He acknowledges his cliche beliefs. Compassion, empathy, and strength are key.
Here's my mantra routine:
Four-Hour Deep Work
Lex begins a four-hour deep work session after his mantra routine. Today's toughest.
AI is Lex's specialty. His video doesn't explain what he does.
Clearly, he works hard.
Before starting, he has water, coffee, and a bathroom break.
"During deep work sessions, I minimize breaks."
He's distraction-free. Phoneless. Silence. Nothing. Any loose ideas are typed into a Google doc for later. He wants to work.
"Just get the job done. Don’t think about it too much and feel good once it’s complete." — Lex Fridman
30-Minute Social Media & Music
After his first deep work session, Lex rewards himself.
10 minutes on social media, 20 on music. Upload content and respond to comments in 10 minutes. 20 minutes for guitar or piano.
"In the real world, I’m currently single, but in the music world, I’m in an open relationship with this beautiful guitar. Open relationship because sometimes I cheat on her with the acoustic." — Lex Fridman
Two-hour exercise
Then exercise for two hours.
Daily runs six miles. Then he chooses how far to go. Run time is an hour.
He does bodyweight exercises. Every minute for 15 minutes, do five pull-ups and ten push-ups. It's David Goggins-inspired. He aims for an hour a day.
He's hungry. Before running, he takes a salt pill for electrolytes.
He'll then take a one-minute cold shower while listening to cheesy songs. Afterward, he might eat.
Four-Hour Deep Work
Lex's second work session.
He works 8 hours a day.
Again, zero distractions.
Eating
The video's meal doesn't look appetizing, but it's healthy.
It's ground beef with vegetables. Cauliflower is his "ground-floor" veggie. "Carrots are my go-to party food."
Lex's keto diet includes 1800–2000 calories.
He drinks a "nutrient-packed" Atheltic Greens shake and takes tablets. It's:
One daily tablet of sodium.
Magnesium glycinate tablets stopped his keto headaches.
Potassium — "For electrolytes"
Fish oil: healthy joints
“So much of nutrition science is barely a science… I like to listen to my own body and do a one-person, one-subject scientific experiment to feel good.” — Lex Fridman
Four-hour shallow session
This work isn't as mentally taxing.
Lex planned to:
Finish last session's deep work (about an hour)
Adobe Premiere podcasting (about two hours).
Email-check (about an hour). Three times a day max. First, check for emergencies.
If he's sick, he may watch Netflix or YouTube documentaries or visit friends.
“The possibilities of chaos are wide open, so I can do whatever the hell I want.” — Lex Fridman
Two-hour evening reading
Nonstop work.
Lex ends the day reading academic papers for an hour. "Today I'm skimming two machine learning and neuroscience papers"
This helps him "think beyond the paper."
He reads for an hour.
“When I have a lot of energy, I just chill on the bed and read… When I’m feeling tired, I jump to the desk…” — Lex Fridman
Takeaways
Lex's day-in-the-life video is inspiring.
He has positive energy and works hard every day.
Schedule:
Mantra Routine includes rules, visualizing, goals, and principles.
Deep Work Session #1: Four hours of focus.
10 minutes social media, 20 minutes guitar or piano. "Music brings me joy"
Six-mile run, then bodyweight workout. Two hours total.
Deep Work #2: Four hours with no distractions. Google Docs stores random thoughts.
Lex supplements his keto diet.
This four-hour session is "open to chaos."
Evening reading: academic papers followed by fiction.
"I value some things in life. Work is one. The other is loving others. With those two things, life is great." — Lex Fridman
Emils Uztics
3 years ago
This billionaire created a side business that brings around $90,000 per month.
Dharmesh Shah co-founded HubSpot. WordPlay reached $90,000 per month in revenue without utilizing any of his wealth.
His method:
Take Advantage Of An Established Trend
Remember Wordle? Dharmesh was instantly hooked. As was the tech world.
HubSpot's co-founder noted inefficiencies in a recent My First Million episode. He wanted to play daily. Dharmesh, a tinkerer and software engineer, decided to design a word game.
He's a billionaire. How could he?
Wordle had limitations in his opinion;
Dharmesh is fundamentally a developer. He desired to start something new and increase his programming knowledge;
This project may serve as an excellent illustration for his son, who had begun learning about software development.
Better It Up
Building a new Wordle wasn't successful.
WordPlay lets you play with friends and family. You could challenge them and compare the results. It is a built-in growth tool.
WordPlay features:
the capacity to follow sophisticated statistics after creating an account;
continuous feedback on your performance;
Outstanding domain name (wordplay.com).
Project Development
WordPlay has 9.5 million visitors and 45 million games played since February.
HubSpot co-founder credits tremendous growth to flywheel marketing, pushing the game through his own following.
Choosing an exploding specialty and making sharing easy also helped.
Shah enabled Google Ads on the website to test earning potential. Monthly revenue was $90,000.
That's just Google Ads. If monetization was the goal, a specialized ad network like Ezoic could double or triple the amount.
Wordle was a great buy for The New York Times at $1 million.
The woman
3 years ago
The best lesson from Sundar Pichai is that success and stress don't mix.
His regular regimen teaches stress management.
In 1995, an Indian graduate visited the US. He obtained a scholarship to Stanford after graduating from IIT with a silver medal. First flight. His ticket cost a year's income. His head was full.
Pichai Sundararajan is his full name. He became Google's CEO and a world leader. Mr. Pichai transformed technology and inspired millions to dream big.
This article reveals his daily schedule.
Mornings
While many of us dread Mondays, Mr. Pichai uses the day to contemplate.
A typical Indian morning. He awakens between 6:30 and 7 a.m. He avoids working out in the mornings.
Mr. Pichai oversees the internet, but he reads a real newspaper every morning.
Pichai mentioned that he usually enjoys a quiet breakfast during which he reads the news to get a good sense of what’s happening in the world. Pichai often has an omelet for breakfast and reads while doing so. The native of Chennai, India, continues to enjoy his daily cup of tea, which he describes as being “very English.”
Pichai starts his day. BuzzFeed's Mat Honan called the CEO Banana Republic dad.
Overthinking in the morning is a bad idea. It's crucial to clear our brains and give ourselves time in the morning before we hit traffic.
Mr. Pichai's morning ritual shows how to stay calm. Wharton Business School found that those who start the day calmly tend to stay that way. It's worth doing regularly.
And he didn't forget his roots.
Afternoons
He has a busy work schedule, as you can imagine. Running one of the world's largest firm takes time, energy, and effort. He prioritizes his work. Monitoring corporate performance and guaranteeing worker efficiency.
Sundar Pichai spends 7-8 hours a day to improve Google. He's noted for changing the company's culture. He wants to boost employee job satisfaction and performance.
His work won him recognition within the company.
Pichai received a 96% approval rating from Glassdoor users in 2017.
Mr. Pichai stresses work satisfaction. Each day is a new canvas for him to find ways to enrich people's job and personal lives.
His work offers countless lessons. According to several profiles and press sources, the Google CEO is a savvy negotiator. Mr. Pichai's success came from his strong personality, work ethic, discipline, simplicity, and hard labor.
Evenings
His evenings are spent with family after a busy day. Sundar Pichai's professional and personal lives are balanced. Sundar Pichai is a night owl who re-energizes about 9 p.m.
However, he claims to be most productive after 10 p.m., and he thinks doing a lot of work at that time is really useful. But he ensures he sleeps for around 7–8 hours every day. He enjoys long walks with his dog and enjoys watching NSDR on YouTube. It helps him in relaxing and sleep better.
His regular routine teaches us what? Work wisely, not hard, discipline, vision, etc. His stress management is key. Leading one of the world's largest firm with 85,000 employees is scary.
The pressure to achieve may ruin a day. Overworked employees are more likely to make mistakes or be angry with coworkers, according to the Family Work Institute. They can't handle daily problems, making the house more stressful than the office.
Walking your dog, having fun with friends, and having hobbies are as vital as your office.