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
Tim Denning
3 years ago
The Dogecoin millionaire mysteriously disappeared.
The American who bought a meme cryptocurrency.
Cryptocurrency is the financial underground.
I love it. But there’s one thing I hate: scams. Over the last few years the Dogecoin cryptocurrency saw massive gains.
Glauber Contessoto overreacted. He shared his rags-to-riches cryptocurrency with the media.
He's only wealthy on paper. No longer Dogecoin millionaire.
Here's what he's doing now. It'll make you rethink cryptocurrency investing.
Strange beginnings
Glauber once had a $36,000-a-year job.
He grew up poor and wanted to make his mother proud. Tesla was his first investment. He bought GameStop stock after Reddit boosted it.
He bought whatever was hot.
He was a young investor. Memes, not research, influenced his decisions.
Elon Musk (aka Papa Elon) began tweeting about Dogecoin.
Doge is a 2013 cryptocurrency. One founder is Australian. He insists it's funny.
He was shocked anyone bought it LOL.
Doge is a Shiba Inu-themed meme. Now whenever I see a Shiba Inu, I think of Doge.
Elon helped drive up the price of Doge by talking about it in 2020 and 2021 (don't take investment advice from Elon; he's joking and gaslighting you).
Glauber caved. He invested everything in Doge. He borrowed from family and friends. He maxed out his credit card to buy more Doge. Yuck.
Internet dubbed him a genius. Slumdog millionaire and The Dogefather were nicknames. Elon pumped Doge on social media.
Good times.
From $180,000 to $1,000,000+
TikTok skyrocketed Doge's price.
Reddit fueled up. Influencers recommended buying Doge because of its popularity. Glauber's motto:
Scared money doesn't earn.
Glauber was no broke ass anymore.
His $180,000 Dogecoin investment became $1M. He championed investing. He quit his dumb job like a rebellious millennial.
A puppy dog meme captivated the internet.
Rise and fall
Whenever I invest in anything I ask myself “what utility does this have?”
Dogecoin is useless.
You buy it for the cute puppy face and hope others will too, driving up the price. All cryptocurrencies fell in 2021's second half.
Central banks raised interest rates, and inflation became a pain.
Dogecoin fell more than others. 90% decline.
Glauber’s Dogecoin is now worth $323K. Still no sales. His dog god is unshakeable. Confidence rocks. Dogecoin millionaire recently said...
“I should have sold some.”
Yes, sir.
He now avoids speculative cryptocurrencies like Dogecoin and focuses on Bitcoin and Ethereum.
I've long said this. Starbucks is building on Ethereum.
It's useful. Useful. Developers use Ethereum daily. Investing makes you wiser over time, like the Dogecoin millionaire.
When risk b*tch slaps you, humility follows, as it did for me when I lost money.
You have to lose money to make money. Few understand.
Dogecoin's omissions
You might be thinking Dogecoin is crap.
I'll take a contrarian stance. Dogecoin does nothing, but it has a strong community. Dogecoin dominates internet memes.
It's silly.
Not quite. The message of crypto that many people forget is that it’s a change in business model.
Businesses create products and services, then advertise to find customers. Crypto Web3 works backwards. A company builds a fanbase but sells them nothing.
Once the community reaches MVC (minimum viable community), a business can be formed.
Community members are relational versus transactional. They're invested in a cause and care about it (typically ownership in the business via crypto).
In this new world, Dogecoin has the most important feature.
Summary
While Dogecoin does have a community I still dislike it.
It's all shady. Anything Elon Musk recommends is a bad investment (except SpaceX & Tesla are great companies).
Dogecoin Millionaire has wised up and isn't YOLOing into more dog memes.
Don't follow the crowd or the hype. Investing is a long-term sport based on fundamentals and research.
Since Ethereum's inception, I've spent 10,000 hours researching.
Dogecoin will be the foundation of something new, like Pets.com at the start of the dot-com revolution. But I doubt Doge will boom.
Be safe!
Langston Thomas
3 years ago
A Simple Guide to NFT Blockchains
Ethereum's blockchain rules NFTs. Many consider it the one-stop shop for NFTs, and it's become the most talked-about and trafficked blockchain in existence.
Other blockchains are becoming popular in NFTs. Crypto-artists and NFT enthusiasts have sought new places to mint and trade NFTs due to Ethereum's high transaction costs and environmental impact.
When choosing a blockchain to mint on, there are several factors to consider. Size, creator costs, consumer spending habits, security, and community input are important. We've created a high-level summary of blockchains for NFTs to help clarify the fast-paced world of web3 tech.
Ethereum
Ethereum currently has the most NFTs. It's decentralized and provides financial and legal services without intermediaries. It houses popular NFT marketplaces (OpenSea), projects (CryptoPunks and the Bored Ape Yacht Club), and artists (Pak and Beeple).
It's also expensive and energy-intensive. This is because Ethereum works using a Proof-of-Work (PoW) mechanism. PoW requires computers to solve puzzles to add blocks and transactions to the blockchain. Solving these puzzles requires a lot of computer power, resulting in astronomical energy loss.
You should consider this blockchain first due to its popularity, security, decentralization, and ease of use.
Solana
Solana is a fast programmable blockchain. Its proof-of-history and proof-of-stake (PoS) consensus mechanisms eliminate complex puzzles. Reduced validation times and fees result.
PoS users stake their cryptocurrency to become a block validator. Validators get SOL. This encourages and rewards users to become stakers. PoH works with PoS to cryptographically verify time between events. Solana blockchain ensures transactions are in order and found by the correct leader (validator).
Solana's PoS and PoH mechanisms keep transaction fees and times low. Solana isn't as popular as Ethereum, so there are fewer NFT marketplaces and blockchain traders.
Tezos
Tezos is a greener blockchain. Tezos rose in 2021. Hic et Nunc was hailed as an economic alternative to Ethereum-centric marketplaces until Nov. 14, 2021.
Similar to Solana, Tezos uses a PoS consensus mechanism and only a PoS mechanism to reduce computational work. This blockchain uses two million times less energy than Ethereum. It's cheaper than Ethereum (but does cost more than Solana).
Tezos is a good place to start minting NFTs in bulk. Objkt is the largest Tezos marketplace.
Flow
Flow is a high-performance blockchain for NFTs, games, and decentralized apps (dApps). Flow is built with scalability in mind, so billions of people could interact with NFTs on the blockchain.
Flow became the NBA's blockchain partner in 2019. Flow, a product of Dapper labs (the team behind CryptoKitties), launched and hosts NBA Top Shot, making the blockchain integral to the popularity of non-fungible tokens.
Flow uses PoS to verify transactions, like Tezos. Developers are working on a model to handle 10,000 transactions per second on the blockchain. Low transaction fees.
Flow NFTs are tradeable on Blocktobay, OpenSea, Rarible, Foundation, and other platforms. NBA, NFL, UFC, and others have launched NFT marketplaces on Flow. Flow isn't as popular as Ethereum, resulting in fewer NFT marketplaces and blockchain traders.
Asset Exchange (WAX)
WAX is king of virtual collectibles. WAX is popular for digitalized versions of legacy collectibles like trading cards, figurines, memorabilia, etc.
Wax uses a PoS mechanism, but also creates carbon offset NFTs and partners with Climate Care. Like Flow, WAX transaction fees are low, and network fees are redistributed to the WAX community as an incentive to collectors.
WAX marketplaces host Topps, NASCAR, Hot Wheels, and cult classic film franchises like Godzilla, The Princess Bride, and Spiderman.
Binance Smart Chain
BSC is another good option for balancing fees and performance. High-speed transactions and low fees hurt decentralization. BSC is most centralized.
Binance Smart Chain uses Proof of Staked Authority (PoSA) to support a short block time and low fees. The 21 validators needed to run the exchange switch every 24 hours. 11 of the 21 validators are directly connected to the Binance Crypto Exchange, according to reports.
While many in the crypto and NFT ecosystems dislike centralization, the BSC NFT market picked up speed in 2021. OpenBiSea, AirNFTs, JuggerWorld, and others are gaining popularity despite not having as robust an ecosystem as Ethereum.
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Nikhil Vemu
2 years ago
7 Mac Apps That Are Exorbitantly Priced But Totally Worth It
Wish you more bang for your buck
By ‘Cost a Bomb’ I didn’t mean to exaggerate. It’s an idiom that means ‘To be very expensive’. In fact, no app on the planet costs a bomb lol.
So, to the point.
Chronicle
(Freemium. For Pro, $24.99 | Available on Setapp)
You probably have trouble keeping track of dozens of bills and subscriptions each month.
Try Chronicle.
Easy-to-use app
Add payment due dates and receive reminders,
Save payment documentation,
Analyze your spending by season, year, and month.
Observe expenditure trends and create new budgets.
Best of all, Chronicle features an integrated browser for fast payment and logging.
iOS and macOS sync.
SoundSource
($39 for lifetime)
Background Music, a free macOS program, was featured in #6 of this post last month.
It controls per-app volume, stereo balance, and audio over its max level.
Background Music is fully supported. Additionally,
Connect various speakers to various apps (Wow! ),
change the audio sample rate for each app,
To facilitate access, add a floating SoundSource window.
Use its blocks in Shortcuts app,
On the menu bar, include meters for output/input devices and running programs.
PixelSnap
($39 for lifetime | Available on Setapp)
This software is heaven for UI designers.
It aids you.
quickly calculate screen distances (in pixels) ,
Drag an area around an object to determine its borders,
Measure the distances between the additional guides,
screenshots should be pixel-perfect.
What’s more.
You can
Adapt your tolerance for items with poor contrast and shadows.
Use your Touch Bar to perform important tasks, if you have one.
Mate Translation
($3.99 a month / $29.99 a year | Available on Setapp)
Mate Translate resembles a roided-up version of BarTranslate, which I wrote about in #1 of this piece last month.
If you translate often, utilize Mate Translate on macOS and Safari.
I'm really vocal about it.
It stays on the menu bar, and is accessible with a click or ⌥+shift+T hotkey.
It lets you
Translate in 103 different languages,
To translate text, double-click or right-click on it.
Totally translate websites. Additionally, Netflix subtitles,
Listen to their pronunciation to see how close it is to human.
iPhone and Mac sync Mate-ing history.
Swish
($16 for lifetime | Available on Setapp)
Swish is awesome!
Swipe, squeeze, tap, and hold movements organize chaotic desktop windows. Swish operates with mouse and trackpad.
Some gestures:
• Pinch Once: Close an app
• Pinch Twice: Quit an app
• Swipe down once: Minimise an app
• Pinch Out: Enter fullscreen mode
• Tap, Hold, & Swipe: Arrange apps in grids
and many more...
After getting acquainted to the movements, your multitasking will improve.
Unite
($24.99 for lifetime | Available on Setapp)
It turns webapps into macOS apps. The end.
Unite's functionality is a million times better.
Provide extensive customization (incl. its icon, light and dark modes)
make menu bar applications,
Get badges for web notifications and automatically refresh websites,
Replace any dock icon in the window with it (Wow!) by selecting that portion of the window.
Use PiP (Picture-in-Picture) on video sites that support it.
Delete advertising,
Throughout macOS, use floating windows
and many more…
I feel $24.99 one-off for this tool is a great deal, considering all these features. What do you think?
CleanShot X
(Basic: $29 one-off. Pro: $8/month | Available on Setapp)
CleanShot X can achieve things the macOS screenshot tool cannot. Complete screenshot toolkit.
CleanShot X, like Pixel Snap 2 (#3), is fantastic.
Allows
Scroll to capture a long page,
screen recording,
With webcam on,
• With mic and system audio,
• Highlighting mouse clicks and hotkeys.
Maintain floating screenshots for reference
While capturing, conceal desktop icons and notifications.
Recognize text in screenshots (OCR),
You may upload and share screenshots using the built-in cloud.
These are just 6 in 50+ features, and you’re already saying Wow!
Alex Mathers
2 years ago
How to Produce Enough for People to Not Neglect You
Internet's fantastic, right?
We've never had a better way to share our creativity.
I can now draw on my iPad and tweet or Instagram it to thousands. I may get some likes.
With such a great, free tool, you're not alone.
Millions more bright-eyed artists are sharing their work online.
The issue is getting innovative work noticed, not sharing it.
In a world where creators want attention, attention is valuable.
We build for attention.
Attention helps us establish a following, make money, get notoriety, and make a difference.
Most of us require attention to stay sane while creating wonderful things.
I know how hard it is to work hard and receive little views.
How do we receive more attention, more often, in a sea of talent?
Advertising and celebrity endorsements are options. These may work temporarily.
To attract true, organic, and long-term attention, you must create in high quality, high volume, and consistency.
Adapting Steve Martin's Be so amazing, they can't ignore you (with a mention to Dan Norris in his great book Create or Hate for the reminder)
Create a lot.
Eventually, your effort will gain traction.
Traction shows your work's influence.
Traction is when your product sells more. Traction is exponential user growth. Your work is shared more.
No matter how good your work is, it will always have minimal impact on the world.
Your work can eventually dent or puncture. Daily, people work to dent.
To achieve this tipping point, you must consistently produce exceptional work.
Expect traction after hundreds of outputs.
Dilbert creator Scott Adams says repetition persuades. If you don't stop, you can persuade practically anyone with anything.
Volume lends believability. So make more.
I worked as an illustrator for at least a year and a half without any recognition. After 150 illustrations on iStockphoto, my work started selling.
With 350 illustrations on iStock, I started getting decent client commissions.
Producing often will improve your craft and draw attention.
It's the only way to succeed. More creation means better results and greater attention.
Austin Kleon says you can improve your skill in relative anonymity before you become famous. Before obtaining traction, generate a lot and become excellent.
Most artists, even excellent ones, don't create consistently enough to get traction.
It may hurt. For makers who don't love and flow with their work, it's extremely difficult.
Your work must bring you to life.
To generate so much that others can't ignore you, decide what you'll accomplish every day (or most days).
Commit and be patient.
Prepare for zero-traction.
Anticipating this will help you persevere and create.
My online guru Grant Cardone says: Anything worth doing is worth doing every day.
Do.
Matthew O'Riordan
3 years ago
Trends in SaaS Funding from 2016 to 2022
Christopher Janz of Point Nine Capital created the SaaS napkin in 2016. This post shows how founders have raised cash in the last 6 years. View raw data.
Round size
Unsurprisingly, round sizes have expanded and will taper down in 2022. In 2016, pre-seed rounds were $200k to $500k; currently, they're $1-$2m. Despite the macroeconomic scenario, Series A have expanded from $3m to $12m in 2016 to $6m and $18m in 2022.
Valuation
There are hints that valuations are rebounding this year. Pre-seed valuations in 2022 are $12m from $3m in 2016, and Series B prices are $270m from $100m in 2016.
Compared to public SaaS multiples, Series B valuations more closely reflect the market, but Seed and Series A prices seem to be inflated regardless of the market.
I'd like to know how each annual cohort performed for investors, based on the year they invested and the valuations. I can't access this information.
ARR
Seed firms' ARR forecasts have risen from $0 to $0.6m to $0 to $1m. 2016 expected $1.2m to $3m, 2021 $0.5m to $4m, and this year $0.5m to $2.5m, suggesting that Series A firms may raise with less ARR today. Series B minutes fell from $4.2m to $3m.
Capitalization Rate
2022 is the year that VCs start discussing capital efficiency in portfolio meetings. Given the economic shift in the markets and the stealthy VC meltdown, it's not surprising. Christopher Janz added capital efficiency to the SaaS Napkin as a new statistic for Series A (3.5x) and Series B. (2.5x). Your investors must live under a rock if they haven't asked about capital efficiency. If you're unsure:
The Capital Efficiency Ratio is the ratio of how much a company has spent growing revenue and how much they’re receiving in return. It is the broadest measure of company effectiveness in generating ARR
What next?
No one knows what's next, including me. All startup and growing enterprises around me are tightening their belts and extending their runways in anticipation of a difficult fundraising ride. If you're wanting to raise money but can wait, wait till the market is more stable and access to money is easier.