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
Elnaz Sarraf
3 years ago
Why Bitcoin's Crash Could Be Good for Investors
The crypto market crashed in June 2022. Bitcoin and other cryptocurrencies hit their lowest prices in over a year, causing market panic. Some believe this crash will benefit future investors.
Before I discuss how this crash might help investors, let's examine why it happened. Inflation in the U.S. reached a 30-year high in 2022 after Russia invaded Ukraine. In response, the U.S. Federal Reserve raised interest rates by 0.5%, the most in almost 20 years. This hurts cryptocurrencies like Bitcoin. Higher interest rates make people less likely to invest in volatile assets like crypto, so many investors sold quickly.
The crypto market collapsed. Bitcoin, Ethereum, and Binance dropped 40%. Other cryptos crashed so hard they were delisted from almost every exchange. Bitcoin peaked in April 2022 at $41,000, but after the May interest rate hike, it crashed to $28,000. Bitcoin investors were worried. Even in bad times, this crash is unprecedented.
Bitcoin wasn't "doomed." Before the crash, LUNA was one of the top 5 cryptos by market cap. LUNA was trading around $80 at the start of May 2022, but after the rate hike?
Less than 1 cent. LUNA lost 99.99% of its value in days and was removed from every crypto exchange. Bitcoin's "crash" isn't as devastating when compared to LUNA.
Many people said Bitcoin is "due" for a LUNA-like crash and that the only reason it hasn't crashed is because it's bigger. Still false. If so, Bitcoin should be worth zero by now. We didn't. Instead, Bitcoin reached 28,000, then 29k, 30k, and 31k before falling to 18k. That's not the world's greatest recovery, but it shows Bitcoin's safety.
Bitcoin isn't falling constantly. It fell because of the initial shock of interest rates, but not further. Now, Bitcoin's value is more likely to rise than fall. Bitcoin's low price also attracts investors. They know what prices Bitcoin can reach with enough hype, and they want to capitalize on low prices before it's too late.
Bitcoin's crash was bad, but in a way it wasn't. To understand, consider 2021. In March 2021, Bitcoin surpassed $60k for the first time. Elon Musk's announcement in May that he would no longer support Bitcoin caused a massive crash in the crypto market. In May 2017, Bitcoin's price hit $29,000. Elon Musk's statement isn't worth more than the Fed raising rates. Many expected this big announcement to kill Bitcoin.
Not so. Bitcoin crashed from $58k to $31k in 2021. Bitcoin fell from $41k to $28k in 2022. This crash is smaller. Bitcoin's price held up despite tensions and stress, proving investors still believe in it. What happened after the initial crash in the past?
Bitcoin fell until mid-July. This is also something we’re not seeing today. After a week, Bitcoin began to improve daily. Bitcoin's price rose after mid-July. Bitcoin's price fluctuated throughout the rest of 2021, but it topped $67k in November. Despite no major changes, the peak occurred after the crash. Elon Musk seemed uninterested in crypto and wasn't likely to change his mind soon. What triggered this peak? Nothing, really. What really happened is that people got over the initial statement. They forgot.
Internet users have goldfish-like attention spans. People quickly forgot the crash's cause and were back investing in crypto months later. Despite the market's setbacks, more crypto investors emerged by the end of 2017. Who gained from these peaks? Bitcoin investors who bought low. Bitcoin not only recovered but also doubled its ROI. It was like a movie, and it shows us what to expect from Bitcoin in the coming months.
The current Bitcoin crash isn't as bad as the last one. LUNA is causing market panic. LUNA and Bitcoin are different cryptocurrencies. LUNA crashed because Terra wasn’t able to keep its peg with the USD. Bitcoin is unanchored. It's one of the most decentralized investments available. LUNA's distrust affected crypto prices, including Bitcoin, but it won't last forever.
This is why Bitcoin will likely rebound in the coming months. In 2022, people will get over the rise in interest rates and the crash of LUNA, just as they did with Elon Musk's crypto stance in 2021. When the world moves on to the next big controversy, Bitcoin's price will soar.
Bitcoin may recover for another reason. Like controversy, interest rates fluctuate. The Russian invasion caused this inflation. World markets will stabilize, prices will fall, and interest rates will drop.
Next, lower interest rates could boost Bitcoin's price. Eventually, it will happen. The U.S. economy can't sustain such high interest rates. Investors will put every last dollar into Bitcoin if interest rates fall again.
Bitcoin has proven to be a stable investment. This boosts its investment reputation. Even if Ethereum dethrones Bitcoin as crypto king one day (or any other crypto, for that matter). Bitcoin may stay on top of the crypto ladder for a while. We'll have to wait a few months to see if any of this is true.
This post is a summary. Read the full article here.
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.
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Alex Mathers
3 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.
Michael Salim
3 years ago
300 Signups, 1 Landing Page, 0 Products
I placed a link on HackerNews and got 300 signups in a week. This post explains what happened.
Product Concept
The product is DbSchemaLibrary. A library of Database Schema.
I'm not sure where this idea originated from. Very fast. Build fast, fail fast, test many ideas, and one will be a hit. I tried it. Let's try it anyway, even though it'll probably fail. I finished The Lean Startup book and wanted to use it.
Database job bores me. Important! I get drowsy working on it. Someone must do it. I remember this happening once. I needed examples at the time. Something similar to Recall (my other project) that I can copy — or at least use as a reference.
Frequently googled. Many tabs open. The results were useless. I raised my hand and agreed to construct the database myself.
It resurfaced. I decided to do something.
Due Diligence
Lean Startup emphasizes validated learning. Everything the startup does should result in learning. I may build something nobody wants otherwise. That's what happened to Recall.
So, I wrote a business plan document. This happens before I code. What am I solving? What is my proposed solution? What is the leap of faith between the problem and solution? Who would be my target audience?
My note:
In my previous project, I did the opposite!
I wrote my expectations after reading the book's advice.
“Failure is a prerequisite to learning. The problem with the notion of shipping a product and then seeing what happens is that you are guaranteed to succeed — at seeing what happens.” — The Lean Startup book
These are successful metrics. If I don't reach them, I'll drop the idea and try another. I didn't understand numbers then. Below are guesses. But it’s a start!
I then wrote the project's What and Why. I'll use this everywhere. Before, I wrote a different pitch each time. I thought certain words would be better. I felt the audience might want something unusual.
Occasionally, this works. I'm unsure if it's a good idea. No stats, just my writing-time opinion. Writing every time is time-consuming and sometimes hazardous. Having a copy saved me duplication.
I can measure and learn from performance.
Last, I identified communities that might demand the product. This became an exercise in creativity.
The MVP
So now it’s time to build.
A MVP can test my assumptions. Business may learn from it. Not low-quality. We should learn from the tiniest thing.
I like the example of how Dropbox did theirs. They assumed that if the product works, people will utilize it. How can this be tested without a quality product? They made a movie demonstrating the software's functionality. Who knows how much functionality existed?
So I tested my biggest assumption. Users want schema references. How can I test if users want to reference another schema? I'd love this. Recall taught me that wanting something doesn't mean others do.
I made an email-collection landing page. Describe it briefly. Reference library. Each email sender wants a reference. They're interested in the product. Few other reasons exist.
Header and footer were skipped. No name or logo. DbSchemaLibrary is a name I thought of after the fact. 5-minute logo. I expected a flop. Recall has no users after months of labor. What could happen to a 2-day project?
I didn't compromise learning validation. How many visitors sign up? To draw a conclusion, I must track these results.
Posting Time
Now that the job is done, gauge interest. The next morning, I posted on all my channels. I didn't want to be spammy, therefore it required more time.
I made sure each channel had at least one fan of this product. I also answer people's inquiries in the channel.
My list stinks. Several channels wouldn't work. The product's target market isn't there. Posting there would waste our time. This taught me to create marketing channels depending on my persona.
Statistics! What actually happened
My favorite part! 23 channels received the link.
I stopped posting to Discord despite its high conversion rate. I eliminated some channels because they didn't fit. According to the numbers, some users like it. Most users think it's spam.
I was skeptical. And 12 people viewed it.
I didn't expect much attention on a startup subreddit. I'll likely examine Reddit further in the future. As I have enough info, I didn't post much. Time for the next validated learning
No comment. The post had few views, therefore the numbers are low.
The targeted people come next.
I'm a Toptal freelancer. There's a member-only Slack channel. Most people can't use this marketing channel, but you should! It's not as spectacular as discord's 27% conversion rate. But I think the users here are better.
I don’t really have a following anywhere so this isn’t something I can leverage.
The best yet. 10% is converted. With more data, I expect to attain a 10% conversion rate from other channels. Stable number.
This number required some work. Did you know that people use many different clients to read HN?
Unknowns
Untrackable views and signups abound. 1136 views and 135 signups are untraceable. It's 11%. I bet much of that came from Hackernews.
Overall Statistics
The 7-day signup-to-visit ratio was 17%. (Hourly data points)
First-day percentages were lower, which is noteworthy. Initially, it was little above 10%. The HN post started getting views then.
When traffic drops, the number reaches just around 20%. More individuals are interested in the connection. hn.algolia.com sent 2 visitors. This means people are searching and finding my post.
Interesting discoveries
1. HN post struggled till the US woke up.
11am UTC. After an hour, it lost popularity. It seemed over. 7 signups converted 13%. Not amazing, but I would've thought ahead.
After 4pm UTC, traffic grew again. 4pm UTC is 9am PDT. US awakened. 10am PDT saw 512 views.
2. The product was highlighted in a newsletter.
I found Revue references when gathering data. Newsletter platform. Someone posted the newsletter link. 37 views and 3 registrations.
3. HN numbers are extremely reliable
I don't have a time-lapse graph (yet). The statistics were constant all day.
2717 views later 272 new users, or 10.1%
With 293 signups at 2856 views, 10.25%
At 306 signups at 2965 views, 10.32%
Learnings
1. My initial estimations were wildly inaccurate
I wrote 30% conversion. Reading some articles, looks like 10% is a good number to aim for.
2. Paying attention to what matters rather than vain metrics
The Lean Startup discourages vanity metrics. Feel-good metrics that don't measure growth or traction. Considering the proportion instead of the total visitors made me realize there was something here.
What’s next?
There are lots of work to do. Data aggregation, display, website development, marketing, legal issues. Fun! It's satisfying to solve an issue rather than investigate its cause.
In the meantime, I’ve already written the first project update in another post. Continue reading it if you’d like to know more about the project itself! Shifting from Quantity to Quality — DbSchemaLibrary
David G Chen
3 years ago
If you want to earn money, stop writing for entertainment.
When you stop blogging for a few weeks, your views and profits plummet.
Because you're writing fascinating posts for others. Everyone's done ithat…
If I keep writing, the graph should maintain velocity, you could say. If I wrote more, it could rise.
However, entertaining pieces still tend to roller coaster and jump.
this type of writing is like a candle. They burn out and must be replaced. You must continuously light new ones to maintain the illumination.
When you quit writing, your income stops.
A substitute
Instead of producing amusing articles, try solving people's issues. You should answer their search questions.
Here's what happens when you answer their searches.
My website's Google analytics. As a dentist, I answer oral health questions.
This chart vs. Medium is pretty glaring, right?
As of yesterday, it was averaging 15k page views each day.
How much would you make on Medium with 15k daily views?
Evergreen materials
In SEO, this is called evergreen content.
Your content is like a lush, evergreen forest, and by green I mean Benjamins.
Do you have knowledge that you can leverage? Why not help your neighbors and the world?
Answer search inquiries and help others. You'll be well rewarded.
This is better than crafting candle-like content that fizzles out quickly.
Is beauty really ephemeral like how flowers bloom? Nah, I prefer watching forests grow instead (: