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
Percy Bolmér
3 years ago
Ethereum No Longer Consumes A Medium-Sized Country's Electricity To Run
The Merge cut Ethereum's energy use by 99.5%.
The Crypto community celebrated on September 15, 2022. This day, Ethereum Merged. The entire blockchain successfully merged with the Beacon chain, and it was so smooth you barely noticed.
Many have waited, dreaded, and longed for this day.
Some investors feared the network would break down, while others envisioned a seamless merging.
Speculators predict a successful Merge will lead investors to Ethereum. This could boost Ethereum's popularity.
What Has Changed Since The Merge
The merging transitions Ethereum mainnet from PoW to PoS.
PoW sends a mathematical riddle to computers worldwide (miners). First miner to solve puzzle updates blockchain and is rewarded.
The puzzles sent are power-intensive to solve, so mining requires a lot of electricity. It's sent to every miner competing to solve it, requiring duplicate computation.
PoS allows investors to stake their coins to validate a new transaction. Instead of validating a whole block, you validate a transaction and get the fees.
You can validate instead of mine. A validator stakes 32 Ethereum. After staking, the validator can validate future blocks.
Once a validator validates a block, it's sent to a randomly selected group of other validators. This group verifies that a validator is not malicious and doesn't validate fake blocks.
This way, only one computer needs to solve or validate the transaction, instead of all miners. The validated block must be approved by a small group of validators, causing duplicate computation.
PoS is more secure because validating fake blocks results in slashing. You lose your bet tokens. If a validator signs a bad block or double-signs conflicting blocks, their ETH is burned.
Theoretically, Ethereum has one block every 12 seconds, so a validator forging a block risks burning 1 Ethereum for 12 seconds of transactions. This makes mistakes expensive and risky.
What Impact Does This Have On Energy Use?
Cryptocurrency is a natural calamity, sucking electricity and eating away at the earth one transaction at a time.
Many don't know the environmental impact of cryptocurrencies, yet it's tremendous.
A single Ethereum transaction used to use 200 kWh and leave a large carbon imprint. This update reduces global energy use by 0.2%.
Ethereum will submit a challenge to one validator, and that validator will forward it to randomly selected other validators who accept it.
This reduces the needed computing power.
They expect a 99.5% reduction, therefore a single transaction should cost 1 kWh.
Carbon footprint is 0.58 kgCO2, or 1,235 VISA transactions.
This is a big Ethereum blockchain update.
I love cryptocurrency and Mother Earth.
Jeff John Roberts
3 years ago
Jack Dorsey and Jay-Z Launch 'Bitcoin Academy' in Brooklyn rapper's home
The new Bitcoin Academy will teach Jay-Marcy Z's Houses neighbors "What is Cryptocurrency."
Jay-Z grew up in Brooklyn's Marcy Houses. The rapper and Block CEO Jack Dorsey are giving back to his hometown by creating the Bitcoin Academy.
The Bitcoin Academy will offer online and in-person classes, including "What is Money?" and "What is Blockchain?"
The program will provide participants with a mobile hotspot and a small amount of Bitcoin for hands-on learning.
Students will receive dinner and two evenings of instruction until early September. The Shawn Carter Foundation will help with on-the-ground instruction.
Jay-Z and Dorsey announced the program Thursday morning. It will begin at Marcy Houses but may be expanded.
Crypto Blockchain Plug and Black Bitcoin Billionaire, which has received a grant from Block, will teach the classes.
Jay-Z, Dorsey reunite
Jay-Z and Dorsey have previously worked together to promote a Bitcoin and crypto-based future.
In 2021, Dorsey's Block (then Square) acquired the rapper's streaming music service Tidal, which they propose using for NFT distribution.
Dorsey and Jay-Z launched an endowment in 2021 to fund Bitcoin development in Africa and India.
Dorsey is funding the new Bitcoin Academy out of his own pocket (as is Jay-Z), but he's also pushed crypto-related charitable endeavors at Block, including a $5 million fund backed by corporate Bitcoin interest.
This post is a summary. Read full article here
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Alex Mathers
3 years ago
12 habits of the zenith individuals I know
Calmness is a vital life skill.
It aids communication. It boosts creativity and performance.
I've studied calm people's habits for years. Commonalities:
Have mastered the art of self-humor.
Protectors take their job seriously, draining the room's energy.
They are fixated on positive pursuits like making cool things, building a strong physique, and having fun with others rather than on depressing influences like the news and gossip.
Every day, spend at least 20 minutes moving, whether it's walking, yoga, or lifting weights.
Discover ways to take pleasure in life's challenges.
Since perspective is malleable, they change their view.
Set your own needs first.
Stressed people neglect themselves and wonder why they struggle.
Prioritize self-care.
Don't ruin your life to please others.
Make something.
Calm people create more than react.
They love creating beautiful things—paintings, children, relationships, and projects.
Don’t hold their breath.
If you're stressed or angry, you may be surprised how much time you spend holding your breath and tightening your belly.
Release, breathe, and relax to find calm.
Stopped rushing.
Rushing is disadvantageous.
Calm people handle life better.
Are aware of their own dietary requirements.
They avoid junk food and eat foods that keep them healthy, happy, and calm.
Don’t take anything personally.
Stressed people control everything.
Self-conscious.
Calm people put others and their work first.
Keep their surroundings neat.
Maintaining an uplifting and clutter-free environment daily calms the mind.
Minimise negative people.
Calm people are ruthless with their boundaries and avoid negative and drama-prone people.
Yucel F. Sahan
3 years ago
How I Created the Day's Top Product on Product Hunt
In this article, I'll describe a weekend project I started to make something. It was Product Hunt's #1 of the Day, #2 Weekly, and #4 Monthly product.
How did I make Landing Page Checklist so simple? Building and launching took 3 weeks. I worked 3 hours a day max. Weekends were busy.
It's sort of a long story, so scroll to the bottom of the page to see what tools I utilized to create Landing Page Checklist :x
As a matter of fact, it all started with the startups-investments blog; Startup Bulletin, that I started writing in 2018. No, don’t worry, I won’t be going that far behind. The twitter account where I shared the blog posts of this newsletter was inactive for a looong time. I was holding this Twitter account since 2009, I couldn’t bear to destroy it. At the same time, I was thinking how to evaluate this account.
So I looked for a weekend assignment.
Weekend undertaking: Generate business names
Barash and I established a weekend effort to stay current. Building things helped us learn faster.
Simple. Startup Name Generator The utility generated random startup names. After market research for SEO purposes, we dubbed it Business Name Generator.
Backend developer Barash dislikes frontend work. He told me to write frontend code. Chakra UI and Tailwind CSS were recommended.
It was the first time I have heard about Tailwind CSS.
Before this project, I made mobile-web app designs in Sketch and shared them via Zeplin. I can read HTML-CSS or React code, but not write it. I didn't believe myself but followed Barash's advice.
My home page wasn't responsive when I started. Here it was:)
And then... Product Hunt had something I needed. Me-only! A website builder that gives you clean Tailwind CSS code and pre-made web components (like Elementor). Incredible.
I bought it right away because it was so easy to use. Best part: It's not just index.html. It includes all needed files. Like
postcss.config.js
README.md
package.json
among other things, tailwind.config.js
This is for non-techies.
Tailwind.build; which is Shuffle now, allows you to create and export projects for free (with limited features). You can try it by visiting their website.
After downloading the project, you can edit the text and graphics in Visual Studio (or another text editor). This HTML file can be hosted whenever.
Github is an easy way to host a landing page.
your project via Shuffle for export
your website's content, edit
Create a Gitlab, Github, or Bitbucket account.
to Github, upload your project folder.
Integrate Vercel with your Github account (or another platform below)
Allow them to guide you in steps.
Finally. If you push your code to Github using Github Desktop, you'll do it quickly and easily.
Speaking of; here are some hosting and serverless backend services for web applications and static websites for you host your landing pages for FREE!
I host landingpage.fyi on Vercel but all is fine. You can choose any platform below with peace in mind.
Vercel
Render
Netlify
After connecting your project/repo to Vercel, you don’t have to do anything on Vercel. Vercel updates your live website when you update Github Desktop. Wow!
Tails came out while I was using tailwind.build. Although it's prettier, tailwind.build is more mobile-friendly. I couldn't resist their lovely parts. Tails :)
Tails have several well-designed parts. Some components looked awful on mobile, but this bug helped me understand Tailwind CSS.
Unlike Shuffle, Tails does not include files when you export such as config.js, main.js, README.md. It just gives you the HTML code. Suffle.dev is a bit ahead in this regard and with mobile-friendly blocks if you ask me. Of course, I took advantage of both.
creativebusinessnames.co is inactive, but I'll leave a deployment link :)
Adam Wathan's YouTube videos and Tailwind's official literature helped me, but I couldn't have done it without Tails and Shuffle. These tools helped me make landing pages. I shouldn't have started over.
So began my Tailwind CSS adventure. I didn't build landingpage. I didn't plan it to be this long; sorry.
I learnt a lot while I was playing around with Shuffle and Tails Builders.
Long story short I built landingpage.fyi with the help of these tools;
Learning, building, and distribution
Shuffle (Started with a Shuffle Template)
Tails (Used components from here)
Sketch (to handle icons, logos, and .svg’s)
metatags.io (Auto Generator Meta Tags)
Vercel (Hosting)
Github Desktop (Pushing code to Github -super easy-)
Visual Studio Code (Edit my code)
Mailerlite (Capture Emails)
Jarvis / Conversion.ai (%90 of the text on website written by AI 😇 )
CookieHub (Consent Management)
That's all. A few things:
The Outcome
.fyi Domain: Why?
I'm often asked this.
I don't know, but I wanted to include the landing page term. Popular TLDs are gone. I saw my alternatives. brief and catchy.
CSS Tailwind Resources
I'll share project resources like Tails and Shuffle.
Beginner Tailwind (I lately enrolled in this course but haven’t completed it yet.)
Thanks for reading my blog's first post. Please share if you like it.
Sneaker News
3 years ago
This Month Will See The Release Of Travis Scott x Nike Footwear
Following the catastrophes at Astroworld, Travis Scott was swiftly vilified by both media outlets and fans alike, and the names who had previously supported him were quickly abandoned. Nike, on the other hand, remained silent, only delaying the release of La Flame's planned collaborations, such as the Air Max 1 and Air Trainer 1, indefinitely. While some may believe it is too soon for the artist to return to the spotlight, the Swoosh has other ideas, as Nice Kicks reveals that these exact sneakers will be released in May.
Both the Travis Scott x Nike Air Max 1 and the Travis Scott x Nike Air Trainer 1 are set to come in two colorways this month. Tinker Hatfield's renowned runner will meet La Flame's "Baroque Brown" and "Saturn Gold" make-ups, which have been altered with backwards Swooshes and outdoors-themed webbing. The high-top trainer is being customized with Hatfield's "Wheat" and "Grey Haze" palettes, both of which include zippers across the heel, co-branded patches, and other details.
See below for a closer look at the four footwear. TravisScott.com is expected to release the shoes on May 20th, according to Nice Kicks. Following that, on May 27th, Nike SNKRS will release the shoe.
Travis Scott x Nike Air Max 1 "Baroque Brown"
Release Date: 2022
Color: Baroque Brown/Lemon Drop/Wheat/Chile Red
Mens: $160
Style Code: DO9392-200
Pre-School: $85
Style Code: DN4169-200
Infant & Toddler: $70
Style Code: DN4170-200
Travis Scott x Nike Air Max 1 "Saturn Gold"
Release Date: 2022
Color: N/A
Mens: $160
Style Code: DO9392-700
Travis Scott x Nike Air Trainer 1 "Wheat"
Restock Date: May 27th, 2022 (Friday)
Original Release Date: May 20th, 2022 (Friday)
Color: N/A
Mens: $140
Style Code: DR7515-200
Travis Scott x Nike Air Trainer 1 "Grey Haze"
Restock Date: May 27th, 2022 (Friday)
Original Release Date: May 20th, 2022 (Friday)
Color: N/A
Mens: $140
Style Code: DR7515-001