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
Vivek Singh
3 years ago
A Warm Welcome to Web3 and the Future of the Internet
Let's take a look back at the internet's history and see where we're going — and why.
Tim Berners Lee had a problem. He was at CERN, the world's largest particle physics factory, at the time. The institute's stated goal was to study the simplest particles with the most sophisticated scientific instruments. The institute completed the LEP Tunnel in 1988, a 27 kilometer ring. This was Europe's largest civil engineering project (to study smaller particles — electrons).
The problem Tim Berners Lee found was information loss, not particle physics. CERN employed a thousand people in 1989. Due to team size and complexity, people often struggled to recall past project information. While these obstacles could be overcome, high turnover was nearly impossible. Berners Lee addressed the issue in a proposal titled ‘Information Management'.
When a typical stay is two years, data is constantly lost. The introduction of new people takes a lot of time from them and others before they understand what is going on. An emergency situation may require a detective investigation to recover technical details of past projects. Often, the data is recorded but cannot be found. — Information Management: A Proposal
He had an idea. Create an information management system that allowed users to access data in a decentralized manner using a new technology called ‘hypertext'.
To quote Berners Lee, his proposal was “vague but exciting...”. The paper eventually evolved into the internet we know today. Here are three popular W3C standards used by billions of people today:
(credit: CERN)
HTML (Hypertext Markup)
A web formatting language.
URI (Unique Resource Identifier)
Each web resource has its own “address”. Known as ‘a URL'.
HTTP (Hypertext Transfer Protocol)
Retrieves linked resources from across the web.
These technologies underpin all computer work. They were the seeds of our quest to reorganize information, a task as fruitful as particle physics.
Tim Berners-Lee would probably think the three decades from 1989 to 2018 were eventful. He'd be amazed by the billions, the inspiring, the novel. Unlocking innovation at CERN through ‘Information Management'.
The fictional character would probably need a drink, walk, and a few deep breaths to fully grasp the internet's impact. He'd be surprised to see a few big names in the mix.
Then he'd say, "Something's wrong here."
We should review the web's history before going there. Was it a success after Berners Lee made it public? Web1 and Web2: What is it about what we are doing now that so many believe we need a new one, web3?
Per Outlier Ventures' Jamie Burke:
Web 1.0 was read-only.
Web 2.0 was the writable
Web 3.0 is a direct-write web.
Let's explore.
Web1: The Read-Only Web
Web1 was the digital age. We put our books, research, and lives ‘online'. The web made information retrieval easier than any filing cabinet ever. Massive amounts of data were stored online. Encyclopedias, medical records, and entire libraries were put away into floppy disks and hard drives.
In 2015, the web had around 305,500,000,000 pages of content (280 million copies of Atlas Shrugged).
Initially, one didn't expect to contribute much to this database. Web1 was an online version of the real world, but not yet a new way of using the invention.
One gets the impression that the web has been underutilized by historians if all we can say about it is that it has become a giant global fax machine. — Daniel Cohen, The Web's Second Decade (2004)
That doesn't mean developers weren't building. The web was being advanced by great minds. Web2 was born as technology advanced.
Web2: Read-Write Web
Remember when you clicked something on a website and the whole page refreshed? Is it too early to call the mid-2000s ‘the good old days'?
Browsers improved gradually, then suddenly. AJAX calls augmented CGI scripts, and applications began sending data back and forth without disrupting the entire web page. One button to ‘digg' a post (see below). Web experiences blossomed.
In 2006, Digg was the most active ‘Web 2.0' site. (Photo: Ethereum Foundation Taylor Gerring)
Interaction was the focus of new applications. Posting, upvoting, hearting, pinning, tweeting, liking, commenting, and clapping became a lexicon of their own. It exploded in 2004. Easy ways to ‘write' on the internet grew, and continue to grow.
Facebook became a Web2 icon, where users created trillions of rows of data. Google and Amazon moved from Web1 to Web2 by better understanding users and building products and services that met their needs.
Business models based on Software-as-a-Service and then managing consumer data within them for a fee have exploded.
Web2 Emerging Issues
Unbelievably, an intriguing dilemma arose. When creating this read-write web, a non-trivial question skirted underneath the covers. Who owns it all?
You have no control over [Web 2] online SaaS. People didn't realize this because SaaS was so new. People have realized this is the real issue in recent years.
Even if these organizations have good intentions, their incentive is not on the users' side.
“You are not their customer, therefore you are their product,” they say. With Laura Shin, Vitalik Buterin, Unchained
A good plot line emerges. Many amazing, world-changing software products quietly lost users' data control.
For example: Facebook owns much of your social graph data. Even if you hate Facebook, you can't leave without giving up that data. There is no ‘export' or ‘exit'. The platform owns ownership.
While many companies can pull data on you, you cannot do so.
On the surface, this isn't an issue. These companies use my data better than I do! A complex group of stakeholders, each with their own goals. One is maximizing shareholder value for public companies. Tim Berners-Lee (and others) dislike the incentives created.
“Show me the incentive and I will show you the outcome.” — Berkshire Hathaway's CEO
It's easy to see what the read-write web has allowed in retrospect. We've been given the keys to create content instead of just consume it. On Facebook and Twitter, anyone with a laptop and internet can participate. But the engagement isn't ours. Platforms own themselves.
Web3: The ‘Unmediated’ Read-Write Web
Tim Berners Lee proposed a decade ago that ‘linked data' could solve the internet's data problem.
However, until recently, the same principles that allowed the Web of documents to thrive were not applied to data...
The Web of Data also allows for new domain-specific applications. Unlike Web 2.0 mashups, Linked Data applications work with an unbound global data space. As new data sources appear on the Web, they can provide more complete answers.
At around the same time as linked data research began, Satoshi Nakamoto created Bitcoin. After ten years, it appears that Berners Lee's ideas ‘link' spiritually with cryptocurrencies.
What should Web 3 do?
Here are some quick predictions for the web's future.
Users' data:
Users own information and provide it to corporations, businesses, or services that will benefit them.
Defying censorship:
No government, company, or institution should control your access to information (1, 2, 3)
Connect users and platforms:
Create symbiotic rather than competitive relationships between users and platform creators.
Open networks:
“First, the cryptonetwork-participant contract is enforced in open source code. Their voices and exits are used to keep them in check.” Dixon, Chris (4)
Global interactivity:
Transacting value, information, or assets with anyone with internet access, anywhere, at low cost
Self-determination:
Giving you the ability to own, see, and understand your entire digital identity.
Not pull, push:
‘Push' your data to trusted sources instead of ‘pulling' it from others.
Where Does This Leave Us?
Change incentives, change the world. Nick Babalola
People believe web3 can help build a better, fairer system. This is not the same as equal pay or outcomes, but more equal opportunity.
It should be noted that some of these advantages have been discussed previously. Will the changes work? Will they make a difference? These unanswered questions are technical, economic, political, and philosophical. Unintended consequences are likely.
We hope Web3 is a more democratic web. And we think incentives help the user. If there’s one thing that’s on our side, it’s that open has always beaten closed, given a long enough timescale.
We are at the start.
Olga Kharif
3 years ago
A month after freezing customer withdrawals, Celsius files for bankruptcy.
Alex Mashinsky, CEO of Celsius, speaks at Web Summit 2021 in Lisbon.
Celsius Network filed for Chapter 11 bankruptcy a month after freezing customer withdrawals, joining other crypto casualties.
Celsius took the step to stabilize its business and restructure for all stakeholders. The filing was done in the Southern District of New York.
The company, which amassed more than $20 billion by offering 18% interest on cryptocurrency deposits, paused withdrawals and other functions in mid-June, citing "extreme market conditions."
As the Fed raises interest rates aggressively, it hurts risk sentiment and squeezes funding costs. Voyager Digital Ltd. filed for Chapter 11 bankruptcy this month, and Three Arrows Capital has called in liquidators.
Celsius called the pause "difficult but necessary." Without the halt, "the acceleration of withdrawals would have allowed certain customers to be paid in full while leaving others to wait for Celsius to harvest value from illiquid or longer-term asset deployment activities," it said.
Celsius declined to comment. CEO Alex Mashinsky said the move will strengthen the company's future.
The company wants to keep operating. It's not requesting permission to allow customer withdrawals right now; Chapter 11 will handle customer claims. The filing estimates assets and liabilities between $1 billion and $10 billion.
Celsius is advised by Kirkland & Ellis, Centerview Partners, and Alvarez & Marsal.
Yield-promises
Celsius promised 18% returns on crypto loans. It lent those coins to institutional investors and participated in decentralized-finance apps.
When TerraUSD (UST) and Luna collapsed in May, Celsius pulled its funds from Terra's Anchor Protocol, which offered 20% returns on UST deposits. Recently, another large holding, staked ETH, or stETH, which is tied to Ether, became illiquid and discounted to Ether.
The lender is one of many crypto companies hurt by risky bets in the bear market. Also, Babel halted withdrawals. Voyager Digital filed for bankruptcy, and crypto hedge fund Three Arrows Capital filed for Chapter 15 bankruptcy.
According to blockchain data and tracker Zapper, Celsius repaid all of its debt in Aave, Compound, and MakerDAO last month.
Celsius charged Symbolic Capital Partners Ltd. 2,000 Ether as collateral for a cash loan on June 13. According to company filings, Symbolic was charged 2,545.25 Ether on June 11.
In July 6 filings, it said it reshuffled its board, appointing two new members and firing others.
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Tech With Dom
2 years ago
6 Awesome Desk Accessories You Must Have!
I'm gadget-obsessed. So I shared my top 6 desk gadgets.
These gadgets improve my workflow and are handy for working from home.
Without further ado...
Computer light bar Xiaomi Mi
I've previously recommended the Xiaomi Mi Light Bar, and I still do. It's stylish and convenient.
The Mi bar is a monitor-mounted desk lamp. The lamp's hue and brightness can be changed with a stylish wireless remote.
Changeable hue and brightness make it ideal for late-night work.
Desk Mat 2.
I wasn't planning to include a desk surface in this article, but I find it improves computer use.
The mouse feels smoother and is a better palm rest than wood or glass.
I'm currently using the overkill Razer Goliathus Extended Chroma RGB Gaming Surface, but I like RGB.
Using a desk surface or mat makes computer use more comfortable, and it's not expensive.
Third, the Logitech MX Master 3 Mouse
The Logitech MX Master 3 or any from the MX Master series is my favorite mouse.
The side scroll wheel on these mice is a feature I've never seen on another mouse.
Side scroll wheels are great for spreadsheets and video editing. It would be hard for me to switch from my Logitech MX Master 3 to another mouse. Only gaming is off-limits.
Google Nest 4.
Without a smart assistant, my desk is useless. I'm currently using the second-generation Google Nest Hub, but I've also used the Amazon Echo Dot, Echo Spot, and Apple HomePod Mini.
As a Pixel 6 Pro user, the Nest Hub works best with my phone.
My Nest Hub plays news, music, and calendar events. It also lets me control lights and switches with my smartphone. It plays YouTube videos.
Google Pixel Stand, No. 5
A wireless charger on my desk is convenient for charging my phone and other devices while I work. My desk has two wireless chargers. I have a Satechi aluminum fast charger and a second-generation Google Pixel Stand.
If I need to charge my phone and earbuds simultaneously, I use two wireless chargers. Satechi chargers are well-made and fast. Micro-USB is my only complaint.
The Pixel Stand converts compatible devices into a smart display for adjusting charging speeds and controlling other smart devices. My Pixel 6 Pro charges quickly. Here's my video review.
6. Anker Power Bank
Anker's 65W charger is my final recommendation. This online find was a must-have. This can charge my laptop and several non-wireless devices, perfect for any techie!
The charger has two USB-A ports and two USB-C ports, one with 45W and the other with 20W, so it can charge my iPad Pro and Pixel 6 Pro simultaneously.
Summary
These are some of my favorite office gadgets. My kit page has an updated list.
Links to the products mentioned in this article are in the appropriate sections. These are affiliate links.
You're up! Share the one desk gadget you can't live without and why.
Karthik Rajan
3 years ago
11 Cooking Hacks I Wish I Knew Earlier
Quick, easy and tasty (and dollops of parenting around food).
My wife and mom are both great mothers. They're super-efficient planners. They soak and ferment food. My 104-year-old grandfather loved fermented foods.
When I'm hungry and need something fast, I waffle to the pantry. Like most people, I like to improvise. I wish I knew these 11 hacks sooner.
1. The world's best pasta sauce only has 3 ingredients.
You watch recipe videos with prepped ingredients. In reality, prepping and washing take time. The food's taste isn't guaranteed. The raw truth at a sublime level is not talked about often.
Sometimes a radical recipe comes along that's so easy and tasty, you're dumbfounded. The Classic Italian Cook Book has a pasta recipe.
One 28-ounce can of whole, peeled tomatoes, one medium peeled onion, and 5 tablespoons of butter. And salt to taste.
Combine everything in a single pot and simmer for 45 minutes, uncovered. Stir occasionally. Toss the onion halves after 45 minutes and pour the sauce over pasta. Finish!
This simple recipe fights our deepest fears.
Salt to taste! Customized to perfection, no frills.
2. Reheating rice with ice. Magical.
Most of the world eats rice. I was raised in south India. My grandfather farmed rice in the Cauvery river delta.
The problem with rice With growing kids, you can't cook just enough. Leftovers are a norm. Microwaves help most people. Ice cubes are the frosting.
Before reheating rice in the microwave, add an ice cube. The ice will steam the rice, making it fluffy and delicious again.
3. Pineapple leaf
if it comes off easy, it is ripe enough to cut. No rethinking.
My daughter loves pineapples like her dad. One daddy task is cutting them. Sharing immediate results is therapeutic.
Timing the cut has been the most annoying part over the years. The pineapple leaf tip reveals the fruitiness inside. Always loved it.
4. Magic knife words (rolling and curling)
Cutting hand: Roll the blade's back, not its tip, to cut.
Other hand: If you can’t see your finger tips, you can’t cut them. So curl your fingers.
I dislike that schools don't teach financial literacy or cutting skills.
My wife and I used scissors differently for 25 years. We both used the thumb. My index finger, her middle. We googled the difference when I noticed it and laughed. She's right.
This video teaches knifing skills:
5. Best advice about heat
If it's done in the pan, it's overdone on the plate.
This simple advice stands out when we worry about ingredients and proportions.
6. The truth about pasta water
Pasta water should be sea-salty.
Properly seasoning food separates good from great. Salt depends is a good line.
Want delicious pasta? Well, then kind of a lot, to be perfectly honest.
7. Clean as you go
Clean blender as you go by blending water and dish soap.
I find clean as you go easier than clean afterwords. This easy tip is gold.
8. Clean as you go (bis)
Microwave a bowl of water, vinegar, and a toothpick for 5 minutes.
2 cups water, 2 tablespoons vinegar, and a toothpick to prevent overflow.
5-minute microwave. Let the steam work for another 2 minutes. Sponge-off dirt and food. Simple.
9 and 10. Tools,tools, tools
Immersion blender and pressure cooker save time and money.
Narrative: I experienced fatherly pride. My middle-schooler loves science. We discussed boiling. I spoke. Water doesn't need 100°C to boil. She looked confused. 100 degrees assume something. The world around the water is a normal room. Changing water pressure affects its boiling point. This saves energy. Pressure cooker magic.
I captivated her. She's into science and sustainable living.
Whistling is a subliminal form of self-expression when done right. Pressure cookers remind me of simple pleasures.
Your handiness depends on your home tools. Immersion blenders are great for pre- and post-cooking. It eliminates chopping and washing. Second to the dishwasher, in my opinion.
11. One pepper is plenty
A story I share with my daughters.
Once, everyone thought about spice (not spicy). More valuable than silk. One of the three mighty oceans was named after a source country. Columbus sailed the wrong way and found America. The explorer called the natives after reaching his spice destination.
It was pre-internet days. His Google wasn't working.
My younger daughter listens in awe. Strong roots. Image cast. She can contextualize one of the ocean names.
I struggle with spices in daily life. Combinations are mind-boggling. I have more spices than Columbus. Flavor explosion has repercussions. You must closely follow the recipe without guarantees. Best aha. Double down on one spice and move on. If you like it, it's great.
I naturally gravitate towards cumin soups, fennel dishes, mint rice, oregano pasta, basil thai curry and cardamom pudding.
Variety enhances life. Each of my dishes is unique.
To each their own comfort food and nostalgic memories.
Happy living!
Nir Zicherman
3 years ago
The Great Organizational Conundrum
Only two of the following three options can be achieved: consistency, availability, and partition tolerance
Someone told me that growing from 30 to 60 is the biggest adjustment for a team or business.
I remember thinking, That's random. Each company is unique. I've seen teams of all types confront the same issues during development periods. With new enterprises starting every year, we should be better at navigating growing difficulties.
As a team grows, its processes and systems break down, requiring reorganization or declining results. Why always? Why isn't there a perfect scaling model? Why hasn't that been found?
The Three Things Productive Organizations Must Have
Any company should be efficient and productive. Three items are needed:
First, it must verify that no two team members have conflicting information about the roadmap, strategy, or any input that could affect execution. Teamwork is required.
Second, it must ensure that everyone can receive the information they need from everyone else quickly, especially as teams become more specialized (an inevitability in a developing organization). It requires everyone's accessibility.
Third, it must ensure that the organization can operate efficiently even if a piece is unavailable. It's partition-tolerant.
From my experience with the many teams I've been on, invested in, or advised, achieving all three is nearly impossible. Why a perfect organization model cannot exist is clear after analysis.
The CAP Theorem: What is it?
Eric Brewer of Berkeley discovered the CAP Theorem, which argues that a distributed data storage should have three benefits. One can only have two at once.
The three benefits are consistency, availability, and partition tolerance, which implies that even if part of the system is offline, the remainder continues to work.
This notion is usually applied to computer science, but I've realized it's also true for human organizations. In a post-COVID world, many organizations are hiring non-co-located staff as they grow. CAP Theorem is more important than ever. Growing teams sometimes think they can develop ways to bypass this law, dooming themselves to a less-than-optimal team dynamic. They should adopt CAP to maximize productivity.
Path 1: Consistency and availability equal no tolerance for partitions
Let's imagine you want your team to always be in sync (i.e., for someone to be the source of truth for the latest information) and to be able to share information with each other. Only division into domains will do.
Numerous developing organizations do this, especially after the early stage (say, 30 people) when everyone may wear many hats and be aware of all the moving elements. After a certain point, it's tougher to keep generalists aligned than to divide them into specialized tasks.
In a specialized, segmented team, leaders optimize consistency and availability (i.e. every function is up-to-speed on the latest strategy, no one is out of sync, and everyone is able to unblock and inform everyone else).
Partition tolerance suffers. If any component of the organization breaks down (someone goes on vacation, quits, underperforms, or Gmail or Slack goes down), productivity stops. There's no way to give the team stability, availability, and smooth operation during a hiccup.
Path 2: Partition Tolerance and Availability = No Consistency
Some businesses avoid relying too heavily on any one person or sub-team by maximizing availability and partition tolerance (the organization continues to function as a whole even if particular components fail). Only redundancy can do that. Instead of specializing each member, the team spreads expertise so people can work in parallel. I switched from Path 1 to Path 2 because I realized too much reliance on one person is risky.
What happens after redundancy? Unreliable. The more people may run independently and in parallel, the less anyone can be the truth. Lack of alignment or updated information can lead to people executing slightly different strategies. So, resources are squandered on the wrong work.
Path 3: Partition and Consistency "Tolerance" equates to "absence"
The third, least-used path stresses partition tolerance and consistency (meaning answers are always correct and up-to-date). In this organizational style, it's most critical to maintain the system operating and keep everyone aligned. No one is allowed to read anything without an assurance that it's up-to-date (i.e. there’s no availability).
Always short-lived. In my experience, a business that prioritizes quality and scalability over speedy information transmission can get bogged down in heavy processes that hinder production. Large-scale, this is unsustainable.
Accepting CAP
When two puzzle pieces fit, the third won't. I've watched developing teams try to tackle these difficulties, only to find, as their ancestors did, that they can never be entirely solved. Idealized solutions fail in reality, causing lost effort, confusion, and lower production.
As teams develop and change, they should embrace CAP, acknowledge there is a limit to productivity in a scaling business, and choose the best two-out-of-three path.