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
Alex Bentley
3 years ago
Why Bill Gates thinks Bitcoin, crypto, and NFTs are foolish
Microsoft co-founder Bill Gates assesses digital assets while the bull is caged.
Bill Gates is well-respected.
Reasonably. He co-founded and led Microsoft during its 1980s and 1990s revolution.
After leaving Microsoft, Bill Gates pursued other interests. He and his wife founded one of the world's largest philanthropic organizations, Bill & Melinda Gates Foundation. He also supports immunizations, population control, and other global health programs.
When Gates criticized Bitcoin, cryptocurrencies, and NFTs, it made news.
Bill Gates said at the 58th Munich Security Conference...
“You have an asset class that’s 100% based on some sort of greater fool theory that somebody’s going to pay more for it than I do.”
Gates means digital assets. Like many bitcoin critics, he says digital coins and tokens are speculative.
And he's not alone. Financial experts have dubbed Bitcoin and other digital assets a "bubble" for a decade.
Gates also made fun of Bored Ape Yacht Club and NFTs, saying, "Obviously pricey digital photographs of monkeys will help the world."
Why does Bill Gates dislike digital assets?
According to Gates' latest comments, Bitcoin, cryptos, and NFTs aren't good ways to hold value.
Bill Gates is a better investor than Elon Musk.
“I’m used to asset classes, like a farm where they have output, or like a company where they make products,” Gates said.
The Guardian claimed in April 2021 that Bill and Melinda Gates owned the most U.S. farms. Over 242,000 acres of farmland.
The Gates couple has enough farmland to cover Hong Kong.
Bill Gates is a classic investor. He wants companies with an excellent track record, strong fundamentals, and good management. Or tangible assets like land and property.
Gates prefers the "old economy" over the "new economy"
Gates' criticism of Bitcoin and cryptocurrency ventures isn't surprising. These digital assets lack all of Gates's investing criteria.
Volatile digital assets include Bitcoin. Their costs might change dramatically in a day. Volatility scares risk-averse investors like Gates.
Gates has a stake in the old financial system. As Microsoft's co-founder, Gates helped develop a dominant tech company.
Because of his business, he's one of the world's richest men.
Bill Gates is invested in protecting the current paradigm.
He won't invest in anything that could destroy the global economy.
When Gates criticizes Bitcoin, cryptocurrencies, and NFTs, he's suggesting they're a hoax. These soapbox speeches are one way he protects his interests.
Digital assets aren't a bad investment, though. Many think they're the future.
Changpeng Zhao and Brian Armstrong are two digital asset billionaires. Two crypto exchange CEOs. Binance/Coinbase.
Digital asset revolution won't end soon.
If you disagree with Bill Gates and plan to invest in Bitcoin, cryptocurrencies, or NFTs, do your own research and understand the risks.
But don’t take Bill Gates’ word for it.
He’s just an old rich guy with a lot of farmland.
He has a lot to lose if Bitcoin and other digital assets gain global popularity.
This post is a summary. Read the full article here.
Ren & Heinrich
2 years ago
200 DeFi Projects were examined. Here is what I learned.
I analyze the top 200 DeFi crypto projects in this article.
This isn't a study. The findings benefit crypto investors.
Let’s go!
A set of data
I analyzed data from defillama.com. In my analysis, I used the top 200 DeFis by TVL in October 2022.
Total Locked Value
The chart below shows platform-specific locked value.
14 platforms had $1B+ TVL. 65 platforms have $100M-$1B TVL. The remaining 121 platforms had TVLs below $100 million, with the lowest being $23 million.
TVLs are distributed Pareto. Top 40% of DeFis account for 80% of TVLs.
Compliant Blockchains
Ethereum's blockchain leads DeFi. 96 of the examined projects offer services on Ethereum. Behind BSC, Polygon, and Avalanche.
Five platforms used 10+ blockchains. 36 between 2-10 159 used 1 blockchain.
Use Cases for DeFi
The chart below shows platform use cases. Each platform has decentralized exchanges, liquid staking, yield farming, and lending.
These use cases are DefiLlama's main platform features.
Which use case costs the most? Chart explains. Collateralized debt, liquid staking, dexes, and lending have high TVLs.
The DeFi Industry
I compared three high-TVL platforms (Maker DAO, Balancer, AAVE). The columns show monthly TVL and token price changes. The graph shows monthly Bitcoin price changes.
Each platform's market moves similarly.
Probably because most DeFi deposits are cryptocurrencies. Since individual currencies are highly correlated with Bitcoin, it's not surprising that they move in unison.
Takeaways
This analysis shows that the most common DeFi services (decentralized exchanges, liquid staking, yield farming, and lending) also have the highest average locked value.
Some projects run on one or two blockchains, while others use 15 or 20. Our analysis shows that a project's blockchain count has no correlation with its success.
It's hard to tell if certain use cases are rising. Bitcoin's price heavily affects the entire DeFi market.
TVL seems to be a good indicator of a DeFi platform's success and quality. Higher TVL platforms are cheaper. They're a better long-term investment because they gain or lose less value than DeFis with lower TVLs.
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Desiree Peralta
2 years ago
How to Use the 2023 Recession to Grow Your Wealth Exponentially
This season's three best money moves.
“Millionaires are made in recessions.” — Time Capital
We're in a serious downturn, whether or not we're in a recession.
97% of business owners are decreasing costs by more than 10%, and all markets are down 30%.
If you know what you're doing and analyze the markets correctly, this is your chance to become a millionaire.
In any recession, there are always excellent possibilities to seize. Real estate, crypto, stocks, enterprises, etc.
What you do with your money could influence your future riches.
This article analyzes the three key markets, their circumstances for 2023, and how to profit from them.
Ways to make money on the stock market.
If you're conservative like me, you should invest in an index fund. Most of these funds are down 10-30% of ATH:
In earlier recessions, most money index funds lost 20%. After this downturn, they grew and passed the ATH in subsequent months.
Now is the greatest moment to invest in index funds to grow your money in a low-risk approach and make 20%.
If you want to be risky but wise, pick companies that will get better next year but are struggling now.
Even while we can't be 100% confident of a company's future performance, we know some are strong and will have a fantastic year.
Microsoft (down 22%), JPMorgan Chase (15.6%), Amazon (45%), and Disney (33.8%).
These firms give dividends, so you can earn passively while you wait.
So I consider that a good strategy to make wealth in the current stock market is to create two portfolios: one based on index funds to earn 10% to 20% profit when the corrections end, and the other based on individual stocks of popular and strong companies to earn 20%-30% return and dividends while you wait.
How to profit from the downturn in the real estate industry.
With rising mortgage rates, it's the worst moment to buy a home if you don't want to be eaten by banks. In the U.S., interest rates are double what they were three years ago, so buying now looks foolish.
Due to these rates, property prices are falling, but that won't last long since individuals will take advantage.
According to historical data, now is the ideal moment to buy a house for the next five years and perhaps forever.
If you can buy a house, do it. You can refinance the interest at a lower rate with acceptable credit, but not the house price.
Take advantage of the housing market prices now because you won't find a decent deal when rates normalize.
How to profit from the cryptocurrency market.
This is the riskiest market to tackle right now, but it could offer the most opportunities if done appropriately.
The most powerful cryptocurrencies are down more than 60% from last year: $68,990 for BTC and $4,865 for ETH.
If you focus on those two coins, you can make 30%-60% without waiting for them to return to their ATH, and they're low enough to be a solid investment.
I don't encourage trying other altcoins because the crypto market is in crisis and you can lose everything if you're greedy.
Still, the main Cryptos are a good investment provided you store them in an external wallet and follow financial gurus' security advice.
Last thoughts
We can't anticipate a recession until it ends. We can't forecast a market or asset's lowest point, therefore waiting makes little sense.
If you want to develop your wealth, assess the money prospects on all the marketplaces and initiate long-term trades.
Many millionaires are made during recessions because they don't fear negative figures and use them to scale their money.
Erik Engheim
3 years ago
You Misunderstand the Russian Nuclear Threat
Many believe Putin is simply sabre rattling and intimidating us. They see no threat of nuclear war. We can send NATO troops into Ukraine without risking a nuclear war.
I keep reading that Putin is just using nuclear blackmail and that a strong leader will call the bluff. That, in my opinion, misunderstands the danger of sending NATO into Ukraine.
It assumes that once NATO moves in, Putin can either push the red nuclear button or not.
Sure, Putin won't go nuclear if NATO invades Ukraine. So we're safe? Can't we just move NATO?
No, because history has taught us that wars often escalate far beyond our initial expectations. One domino falls, knocking down another. That's why having clear boundaries is vital. Crossing a seemingly harmless line can set off a chain of events that are unstoppable once started.
One example is WWI. The assassin of Archduke Franz Ferdinand could not have known that his actions would kill millions. They couldn't have known that invading Serbia to punish them for not handing over the accomplices would start a world war. Every action triggered a counter-action, plunging Europe into a brutal and bloody war. Each leader saw their actions as limited, not realizing how they kept the dominos falling.
Nobody can predict the future, but it's easy to imagine how NATO intervention could trigger a chain of events leading to a total war. Let me suggest some outcomes.
NATO creates a no-fly-zone. In retaliation, Russia bombs NATO airfields. Russia may see this as a limited counter-move that shouldn't cause further NATO escalation. They think it's a reasonable response to force NATO out of Ukraine. Nobody has yet thought to use the nuke.
Will NATO act? Polish airfields bombed, will they be stuck? Is this an article 5 event? If so, what should be done?
It could happen. Maybe NATO sends troops into Ukraine to punish Russia. Maybe NATO will bomb Russian airfields.
Putin's response Is bombing Russian airfields an invasion or an attack? Remember that Russia has always used nuclear weapons for defense, not offense. But let's not panic, let's assume Russia doesn't go nuclear.
Maybe Russia retaliates by attacking NATO military bases with planes. Maybe they use ships to attack military targets. How does NATO respond? Will they fight Russia in Ukraine or escalate? Will they invade Russia or attack more military installations there?
Seen the pattern? As each nation responds, smaller limited military operations can grow in scope.
So far, the Russian military has shown that they begin with less brutal methods. As losses and failures increase, brutal means are used. Syria had the same. Assad used chemical weapons and attacked hospitals, schools, residential areas, etc.
A NATO invasion of Ukraine would cost Russia dearly. “Oh, this isn't looking so good, better pull out and finish this war,” do you think? No way. Desperate, they will resort to more brutal tactics. If desperate, Russia has a huge arsenal of ugly weapons. They have nerve agents, chemical weapons, and other nasty stuff.
What happens if Russia uses chemical weapons? What if Russian nerve agents kill NATO soldiers horribly? West calls for retaliation will grow. Will we invade Russia? Will we bomb them?
We are angry and determined to punish war criminal Putin, so NATO tanks may be heading to Moscow. We want vengeance for his chemical attacks and bombing of our cities.
Do you think the distance between that red nuclear button and Putin's finger will be that far once NATO tanks are on their way to Moscow?
We might avoid a nuclear apocalypse. A NATO invasion force or even Western cities may be used by Putin. Not as destructive as ICBMs. Putin may think we won't respond to tactical nukes with a full nuclear counterattack. Why would we risk a nuclear Holocaust by launching ICBMs on Russia?
Maybe. My point is that at every stage of the escalation, one party may underestimate the other's response. This war is spiraling out of control and the chances of a nuclear exchange are increasing. Nobody really wants it.
Fear, anger, and resentment cause it. If Putin and his inner circle decide their time is up, they may no longer care about the rest of the world. We saw it with Hitler. Hitler, seeing the end of his empire, ordered the destruction of Germany. Nobody should win if he couldn't. He wanted to destroy everything, including Paris.
In other words, the danger isn't what happens after NATO intervenes The danger is the potential chain reaction. Gambling has a psychological equivalent. It's best to exit when you've lost less. We humans are willing to take small risks for big rewards. To avoid losses, we are willing to take high risks. Daniel Kahneman describes this behavior in his book Thinking, Fast and Slow.
And so bettors who have lost a lot begin taking bigger risks to make up for it. We get a snowball effect. NATO involvement in the Ukraine conflict is akin to entering a casino and placing a bet. We'll start taking bigger risks as we start losing to Russian retaliation. That's the game's psychology.
It's impossible to stop. So will politicians and citizens from both Russia and the West, until we risk the end of human civilization.
You can avoid spiraling into ever larger bets in the Casino by drawing a hard line and declaring “I will not enter that Casino.” We're doing it now. We supply Ukraine. We send money and intelligence but don't cross that crucial line.
It's difficult to watch what happened in Bucha without demanding NATO involvement. What should we do? Of course, I'm not in charge. I'm a writer. My hope is that people will think about the consequences of the actions we demand. My hope is that you think ahead not just one step but multiple dominos.
More and more, we are driven by our emotions. We cannot act solely on emotion in matters of life and death. If we make the wrong choice, more people will die.
Read the original post here.
Merve Yılmaz
3 years ago
Dopamine detox
This post is for you if you can't read or study for 5 minutes.
If you clicked this post, you may be experiencing problems focusing on tasks. A few minutes of reading may tire you. Easily distracted? Using social media and video games for hours without being sidetracked may impair your dopamine system.
When we achieve a goal, the brain secretes dopamine. It might be as simple as drinking water or as crucial as college admission. Situations vary. Various events require different amounts.
Dopamine is released when we start learning but declines over time. Social media algorithms provide new material continually, making us happy. Social media use slows down the system. We can't continue without an award. We return to social media and dopamine rewards.
Mice were given a button that released dopamine into their brains to study the hormone. The mice lost their hunger, thirst, and libido and kept pressing the button. Think this is like someone who spends all day gaming or on Instagram?
When we cause our brain to release so much dopamine, the brain tries to balance it in 2 ways:
1- Decreases dopamine production
2- Dopamine cannot reach its target.
Too many quick joys aren't enough. We'll want more joys. Drugs and alcohol are similar. Initially, a beer will get you drunk. After a while, 3-4 beers will get you drunk.
Social media is continually changing. Updates to these platforms keep us interested. When social media conditions us, we can't read a book.
Same here. I used to complete a book in a day and work longer without distraction. Now I'm addicted to Instagram. Daily, I spend 2 hours on social media. This must change. My life needs improvement. So I started the 50-day challenge.
I've compiled three dopamine-related methods.
Recommendations:
Day-long dopamine detox
First, take a day off from all your favorite things. Social media, gaming, music, junk food, fast food, smoking, alcohol, friends. Take a break.
Hanging out with friends or listening to music may seem pointless. Our minds are polluted. One day away from our pleasures can refresh us.
2. One-week dopamine detox by selecting
Choose one or more things to avoid. Social media, gaming, music, junk food, fast food, smoking, alcohol, friends. Try a week without Instagram or Twitter. I use this occasionally.
One week all together
One solid detox week. It's the hardest program. First or second options are best for dopamine detox. Time will help you.
You can walk, read, or pray during a dopamine detox. Many options exist. If you want to succeed, you must avoid instant gratification. Success after hard work is priceless.