More on Web3 & Crypto
Vitalik
3 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
Nitin Sharma
2 years ago
Web3 Terminology You Should Know
The easiest online explanation.
Web3 is growing. Crypto companies are growing.
Instagram, Adidas, and Stripe adopted cryptocurrency.
Bitcoin and other cryptocurrencies made web3 famous.
Most don't know where to start. Cryptocurrency, DeFi, etc. are investments.
Since we don't understand web3, I'll help you today.
Let’s go.
1. Web3
It is the third generation of the web, and it is built on the decentralization idea which means no one can control it.
There are static webpages that we can only read on the first generation of the web (i.e. Web 1.0).
Web 2.0 websites are interactive. Twitter, Medium, and YouTube.
Each generation controlled the website owner. Simply put, the owner can block us. However, data breaches and selling user data to other companies are issues.
They can influence the audience's mind since they have control.
Assume Twitter's CEO endorses Donald Trump. Result? Twitter would have promoted Donald Trump with tweets and graphics, enhancing his chances of winning.
We need a decentralized, uncontrollable system.
And then there’s Web3.0 to consider. As Bitcoin and Ethereum values climb, so has its popularity. Web3.0 is uncontrolled web evolution. It's good and bad.
Dapps, DeFi, and DAOs are here. It'll all be explained afterwards.
2. Cryptocurrencies:
No need to elaborate.
Bitcoin, Ethereum, Cardano, and Dogecoin are cryptocurrencies. It's digital money used for payments and other uses.
Programs must interact with cryptocurrencies.
3. Blockchain:
Blockchain facilitates bitcoin transactions, investments, and earnings.
This technology governs Web3. It underpins the web3 environment.
Let us delve much deeper.
Blockchain is simple. However, the name expresses the meaning.
Blockchain is a chain of blocks.
Let's use an image if you don't understand.
The graphic above explains blockchain. Think Blockchain. The block stores related data.
Here's more.
4. Smart contracts
Programmers and developers must write programs. Smart contracts are these blockchain apps.
That’s reasonable.
Decentralized web3.0 requires immutable smart contracts or programs.
5. NFTs
Blockchain art is NFT. Non-Fungible Tokens.
Explaining Non-Fungible Token may help.
Two sorts of tokens:
These tokens are fungible, meaning they can be changed. Think of Bitcoin or cash. The token won't change if you sell one Bitcoin and acquire another.
Non-Fungible Token: Since these tokens cannot be exchanged, they are exclusive. For instance, music, painting, and so forth.
Right now, Companies and even individuals are currently developing worthless NFTs.
The concept of NFTs is much improved when properly handled.
6. Dapp
Decentralized apps are Dapps. Instagram, Twitter, and Medium apps in the same way that there is a lot of decentralized blockchain app.
Curve, Yearn Finance, OpenSea, Axie Infinity, etc. are dapps.
7. DAOs
DAOs are member-owned and governed.
Consider it a company with a core group of contributors.
8. DeFi
We all utilize centrally regulated financial services. We fund these banks.
If you have $10,000 in your bank account, the bank can invest it and retain the majority of the profits.
We only get a penny back. Some banks offer poor returns. To secure a loan, we must trust the bank, divulge our information, and fill out lots of paperwork.
DeFi was built for such issues.
Decentralized banks are uncontrolled. Staking, liquidity, yield farming, and more can earn you money.
Web3 beginners should start with these resources.
Sam Hickmann
3 years ago
A quick guide to formatting your text on INTΞGRITY
[06/20/2022 update] We have now implemented a powerful text editor, but you can still use markdown.
Markdown:
Headers
SYNTAX:
# This is a heading 1
## This is a heading 2
### This is a heading 3
#### This is a heading 4
RESULT:
This is a heading 1
This is a heading 2
This is a heading 3
This is a heading 4
Emphasis
SYNTAX:
**This text will be bold**
~~Strikethrough~~
*You **can** combine them*
RESULT:
This text will be italic
This text will be bold
You can combine them
Images
SYNTAX:
RESULT:
Videos
SYNTAX:
https://www.youtube.com/watch?v=7KXGZAEWzn0
RESULT:
Links
SYNTAX:
[Int3grity website](https://www.int3grity.com)
RESULT:
Tweets
SYNTAX:
https://twitter.com/samhickmann/status/1503800505864130561
RESULT:
Blockquotes
SYNTAX:
> Human beings face ever more complex and urgent problems, and their effectiveness in dealing with these problems is a matter that is critical to the stability and continued progress of society. \- Doug Engelbart, 1961
RESULT:
Human beings face ever more complex and urgent problems, and their effectiveness in dealing with these problems is a matter that is critical to the stability and continued progress of society. - Doug Engelbart, 1961
Inline code
SYNTAX:
Text inside `backticks` on a line will be formatted like code.
RESULT:
Text inside backticks on a line will be formatted like code.
Code blocks
SYNTAX:
'''js
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
'''
RESULT:
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
Maths
We support LaTex to typeset math. We recommend reading the full documentation on the official website
SYNTAX:
$$[x^n+y^n=z^n]$$
RESULT:
[x^n+y^n=z^n]
Tables
SYNTAX:
| header a | header b |
| ---- | ---- |
| row 1 col 1 | row 1 col 2 |
RESULT:
| header a | header b | header c |
|---|---|---|
| row 1 col 1 | row 1 col 2 | row 1 col 3 |
You might also like
Chris Moyse
3 years ago
Sony and LEGO raise $2 billion for Epic Games' metaverse
‘Kid-friendly’ project holds $32 billion valuation
Epic Games announced today that it has raised $2 billion USD from Sony Group Corporation and KIRKBI (holding company of The LEGO Group). Both companies contributed $1 billion to Epic Games' upcoming ‘metaverse' project.
“We need partners who share our vision as we reimagine entertainment and play. Our partnership with Sony and KIRKBI has found this,” said Epic Games CEO Tim Sweeney. A new metaverse will be built where players can have fun with friends and brands create creative and immersive experiences, as well as creators thrive.
Last week, LEGO and Epic Games announced their plans to create a family-friendly metaverse where kids can play, interact, and create in digital environments. The service's users' safety and security will be prioritized.
With this new round of funding, Epic Games' project is now valued at $32 billion.
“Epic Games is known for empowering creators large and small,” said KIRKBI CEO Sren Thorup Srensen. “We invest in trends that we believe will impact the world we and our children will live in. We are pleased to invest in Epic Games to support their continued growth journey, with a long-term focus on the future metaverse.”
Epic Games is expected to unveil its metaverse plans later this year, including its name, details, services, and release date.
Jack Burns
3 years ago
Here's what to expect from NASA Artemis 1 and why it's significant.
NASA's Artemis 1 mission will help return people to the Moon after a half-century break. The mission is a shakedown cruise for NASA's Space Launch System and Orion Crew Capsule.
The spaceship will visit the Moon, deploy satellites, and enter orbit. NASA wants to practice operating the spacecraft, test the conditions people will face on the Moon, and ensure a safe return to Earth.
We asked Jack Burns, a space scientist at the University of Colorado Boulder and former member of NASA's Presidential Transition Team, to describe the mission, explain what the Artemis program promises for space exploration, and reflect on how the space program has changed in the half-century since humans last set foot on the moon.
What distinguishes Artemis 1 from other rockets?
Artemis 1 is the Space Launch System's first launch. NASA calls this a "heavy-lift" vehicle. It will be more powerful than Apollo's Saturn V, which transported people to the Moon in the 1960s and 1970s.
It's a new sort of rocket system with two strap-on solid rocket boosters from the space shuttle. It's a mix of the shuttle and Saturn V.
The Orion Crew Capsule will be tested extensively. It'll spend a month in the high-radiation Moon environment. It will also test the heat shield, which protects the capsule and its occupants at 25,000 mph. The heat shield must work well because this is the fastest capsule descent since Apollo.
This mission will also carry miniature Moon-orbiting satellites. These will undertake vital precursor science, including as examining further into permanently shadowed craters where scientists suspect there is water and measuring the radiation environment to see long-term human consequences.
Artemis 1 will launch, fly to the Moon, place satellites, orbit it, return to Earth, and splash down in the ocean. NASA.
What's Artemis's goal? What launches are next?
The mission is a first step toward Artemis 3, which will lead to the first human Moon missions since 1972. Artemis 1 is unmanned.
Artemis 2 will have astronauts a few years later. Like Apollo 8, it will be an orbital mission that circles the Moon and returns. The astronauts will orbit the Moon longer and test everything with a crew.
Eventually, Artemis 3 will meet with the SpaceX Starship on the Moon's surface and transfer people. Orion will stay in orbit while the lunar Starship lands astronauts. They'll go to the Moon's south pole to investigate the water ice there.
Artemis is reminiscent of Apollo. What's changed in 50 years?
Kennedy wanted to beat the Soviets to the Moon with Apollo. The administration didn't care much about space flight or the Moon, but the goal would place America first in space and technology.
You live and die by the sword if you do that. When the U.S. reached the Moon, it was over. Russia lost. We planted flags and did science experiments. Richard Nixon canceled the program after Apollo 11 because the political goals were attained.
Large rocket with two boosters between two gates
NASA's new Space Launch System is brought to a launchpad. NASA
50 years later... It's quite different. We're not trying to beat the Russians, Chinese, or anyone else, but to begin sustainable space exploration.
Artemis has many goals. It includes harnessing in-situ resources like water ice and lunar soil to make food, fuel, and building materials.
SpaceX is part of this first journey to the Moon's surface, therefore the initiative is also helping to develop a lunar and space economy. NASA doesn't own the Starship but is buying seats for astronauts. SpaceX will employ Starship to transport cargo, private astronauts, and foreign astronauts.
Fifty years of technology advancement has made getting to the Moon cheaper and more practical, and computer technology allows for more advanced tests. 50 years of technological progress have changed everything. Anyone with enough money can send a spacecraft to the Moon, but not humans.
Commercial Lunar Payload Services engages commercial companies to develop uncrewed Moon landers. We're sending a radio telescope to the Moon in January. Even 10 years ago, that was impossible.
Since humans last visited the Moon 50 years ago, technology has improved greatly.
What other changes does Artemis have in store?
The government says Artemis 3 will have at least one woman and likely a person of color.
I'm looking forward to seeing more diversity so young kids can say, "Hey, there's an astronaut that looks like me. I can do this. I can be part of the space program.”
NonConformist
3 years ago
Before 6 AM, read these 6 quotations.
These quotes will change your perspective.
I try to reflect on these quotes daily. Reading it in the morning can affect your day, decisions, and priorities. Let's start.
1. Friedrich Nietzsche once said, "He who has a why to live for can bear almost any how."
What's your life goal?
80% of people don't know why they live or what they want to accomplish in life if you ask them randomly.
Even those with answers may not pursue their why. Without a purpose, life can be dull.
Your why can guide you through difficult times.
Create a life goal. Growing may change your goal. Having a purpose in life prevents feeling lost.
2. Seneca said, "He who fears death will never do anything fit for a man in life."
FAILURE STINKS Yes.
This quote is great if you're afraid to try because of failure. What if I'm not made for it? What will they think if I fail?
This wastes most of our lives. Many people prefer not failing over trying something with a better chance of success, according to studies.
Failure stinks in the short term, but it can transform our lives over time.
3. Two men peered through the bars of their cell windows; one saw mud, the other saw stars. — Dale Carnegie
It’s not what you look at that matters; it’s what you see.
The glass-full-or-empty meme is everywhere. It's hard to be positive when facing adversity.
This is a skill. Positive thinking can change our future.
We should stop complaining about our life and how easy success is for others.
Seductive pessimism. Realize this and start from first principles.
4. “Smart people learn from everything and everyone, average people from their experiences, and stupid people already have all the answers.” — Socrates.
Knowing we're ignorant can be helpful.
Every person and situation teaches you something. You can learn from others' experiences so you don't have to. Analyzing your and others' actions and applying what you learn can be beneficial.
Reading (especially non-fiction or biographies) is a good use of time. Walter Issacson wrote Benjamin Franklin's biography. Ben Franklin's early mistakes and successes helped me in some ways.
Knowing everything leads to disaster. Every incident offers lessons.
5. “We must all suffer one of two things: the pain of discipline or the pain of regret or disappointment.“ — James Rohn
My favorite Jim Rohn quote.
Exercise hurts. Healthy eating can be painful. But they're needed to get in shape. Avoiding pain can ruin our lives.
Always choose progress over hopelessness. Myth: overnight success Everyone who has mastered a craft knows that mastery comes from overcoming laziness.
Turn off your inner critic and start working. Try Can't Hurt Me by David Goggins.
6. “A champion is defined not by their wins, but by how they can recover when they fail.“ — Serena Williams
Have you heard of Traf-o-Data?
Gates and Allen founded Traf-O-Data. After some success, it failed. Traf-o-Data's failure led to Microsoft.
Allen said Traf-O-Data's setback was important for Microsoft's first product a few years later. Traf-O-Data was a business failure, but it helped them understand microprocessors, he wrote in 2017.
“The obstacle in the path becomes the path. Never forget, within every obstacle is an opportunity to improve our condition.” — Ryan Holiday.
Bonus Quotes
More helpful quotes:
“Those who cannot change their minds cannot change anything.” — George Bernard Shaw.
“Do something every day that you don’t want to do; this is the golden rule for acquiring the habit of doing your duty without pain.” — Mark Twain.
“Never give up on a dream just because of the time it will take to accomplish it. The time will pass anyway.” — Earl Nightingale.
“A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.” — George Bernard Shaw.
“We don’t stop playing because we grow old; we grow old because we stop playing.” — George Bernard Shaw.
Conclusion
Words are powerful. Utilize it. Reading these inspirational quotes will help you.