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.

As a tech-savvy person (and software engineer) or just a casual technology user, I'm sure you've had this same question countless times: How do I make money online? and how do I make money with my PC/Mac?
You're in luck! Today, I will list the top 5 easiest ways to make money online. Maybe a top ten in the future? Top 5 tips for 2022.

1. Using the gig economy

There are many websites on the internet that allow you to earn extra money using skills and equipment that you already own.
I'm referring to the gig economy. It's a great way to earn a steady passive income from the comfort of your own home. For some sites, premium subscriptions are available to increase sales and access features like bidding on more proposals.
Some of these are:

• Freelancer
• Upwork
• Fiverr (⭐ my personal favorite)
• TaskRabbit

2. Mineprize

MINEPRIZE is a great way to make money online. What's more, You need not do anything! You earn money by lending your idle CPU power to MINEPRIZE.
To register with MINEPRIZE, all you need is an email address and a password. Let MINEPRIZE use your resources, and watch the money roll in! You can earn up to $100 per month by letting your computer calculate. That's insane.

3. Writing

“O Romeo, Romeo, why art thou Romeo?” Okay, I admit that not all writing is Shakespearean. To be a copywriter, you'll need to be fluent in English. Thankfully, we don't have to use typewriters anymore.

Writing is a skill that can earn you a lot of money (claps for the rhyme).
Here are a few ways you can make money typing on your fancy keyboard:
Self-publish a book
Write scripts for video creators
Write for social media
Book-checking
Content marketing help
What a list within a list!

4. Coding

Yes, kids. You've probably coded before if you understand 
You've probably coded before if you understand 

Computational thinking (or coding) is one of the most lucrative ways to earn extra money, or even as a main source of income.
Of course, there are hardcode coders (like me) who write everything line by line, binary di — okay, that last part is a bit exaggerated.
But you can also make money by writing websites or apps or creating low code or no code platforms.
But you can also make money by writing websites or apps or creating low code or no code platforms.
Some low-code platforms
Sheet : spreadsheets to apps :
Loading... We'll install your new app... No-Code Your team can create apps and automate tasks. Agile…
www.appsheet.com

Low-code platform | Business app creator - Zoho Creator
Work is going digital, and businesses of all sizes must adapt quickly. Zoho Creator is a...
www.zoho.com

Sell your data with TrueSource. NO CODE NEEDED
Upload data, configure your product, and earn in minutes.
www.truesource.io

Cool, huh?

5. Created Content

If we use the internet correctly, we can gain unfathomable wealth and extra money. But this one is a bit more difficult. Unlike some of the other items on this list, it takes a lot of time up front.
I'm referring to sites like YouTube and Medium. It's a great way to earn money both passively and actively. With the likes of Jake- and Logan Paul, PewDiePie (a.k.a. Felix Kjellberg) and others, it's never too late to become a millionaire on YouTube. YouTubers are always rising to the top with great content.

6. NFTs and Cryptocurrency

It is now possible to amass large sums of money by buying and selling digital assets on NFTs and cryptocurrency exchanges. Binance's Initial Game Offer rewards early investors who produce the best results.
One awesome game sold a piece of its plot for US$7.2 million! It's Axie Infinity. It's free and available on Google Play and Apple Store.

7. Affiliate Marketing

Affiliate marketing is a form of advertising where businesses pay others (like bloggers) to promote their goods and services. Here's an example. I write a blog (like this one) and post an affiliate link to an item I recommend buying — say, a camera — and if you buy the camera, I get a commission!
These programs pay well:

• Elementor
• AWeber
• Sendinblue
• ConvertKit\sLeadpages
• GetResponse
• SEMRush\sFiverr
• Pabbly

8. Start a blog

Now, if you're a writer or just really passionate about something or a niche, blogging could potentially monetize that passion!
Create a blog about anything you can think of. It's okay to start right here on Medium, as I did.

9. Dropshipping

And I mean that in the best possible way — drop shopping is ridiculously easy to set up, but difficult to maintain for some.
Luckily, Shopify has made setting up an online store a breeze. Drop-shipping from Alibaba and DHGate is quite common. You've got a winner if you can find a local distributor willing to let you drop ship their product!

10. Set up an Online Course

If you have a skill and can articulate it, online education is for you.
Skillshare, Pluralsight, and Coursera have all made inroads in recent years, upskilling people with courses that YOU can create and earn from.

That's it for today! Please share if you liked this post. If not, well —

The metaverse is the most commonly used term in current technology discussions. While the entire tech ecosystem awaits the metaverse's full arrival, defining it is difficult. Imagine the internet in the '80s! The metaverse is a three-dimensional virtual world where users can interact with digital solutions and each other as digital avatars.
The metaverse is a three-dimensional virtual world where users can interact with digital solutions and each other as digital avatars.

Among the metaverse hype, the Decentraland vs Sandbox debate has gained traction. Both are decentralized metaverse platforms with no central authority. So, what's the difference and which is better? Let us examine the distinctions between Decentraland and Sandbox.

2 Popular Metaverse Platforms Explained

The first step in comparing sandbox and Decentraland is to outline the definitions. Anyone keeping up with the metaverse news has heard of the two current leaders. Both have many similarities, but also many differences. Let us start with defining both platforms to see if there is a winner.

Decentraland

Decentraland, a fully immersive and engaging 3D metaverse, launched in 2017. It allows players to buy land while exploring the vast virtual universe. Decentraland offers a wide range of activities for its visitors, including games, casinos, galleries, and concerts. It is currently the longest-running metaverse project.

Decentraland began with a $24 million ICO and went public in 2020. The platform's virtual real estate parcels allow users to create a variety of experiences. MANA and LAND are two distinct tokens associated with Decentraland. MANA is the platform's native ERC-20 token, and users can burn MANA to get LAND, which is ERC-721 compliant. The MANA coin can be used to buy avatars, wearables, products, and names on Decentraland.

Sandbox

Sandbox, the next major player, began as a blockchain-based virtual world in 2011 and migrated to a 3D gaming platform in 2017. The virtual world allows users to create, play, own, and monetize their virtual experiences. Sandbox aims to empower artists, creators, and players in the blockchain community to customize the platform. Sandbox gives the ideal means for unleashing creativity in the development of the modern gaming ecosystem.

The project combines NFTs and DAOs to empower a growing community of gamers. A new play-to-earn model helps users grow as gamers and creators. The platform offers a utility token, SAND, which is required for all transactions.

What are the key points from both metaverse definitions to compare Decentraland vs sandbox?

It is ideal for individuals, businesses, and creators seeking new artistic, entertainment, and business opportunities. It is one of the rapidly growing Decentralized Autonomous Organization projects. Holders of MANA tokens also control the Decentraland domain.

Sandbox, on the other hand, is a blockchain-based virtual world that runs on the native token SAND. On the platform, users can create, sell, and buy digital assets and experiences, enabling blockchain-based gaming. Sandbox focuses on user-generated content and building an ecosystem of developers.

Sandbox vs. Decentraland

If you try to find what is better Sandbox or Decentraland, then you might struggle with only the basic definitions. Both are metaverse platforms offering immersive 3D experiences. Users can freely create, buy, sell, and trade digital assets. However, both have significant differences, especially in MANA vs SAND.

For starters, MANA has a market cap of $5,736,097,349 versus $4,528,715,461, giving Decentraland an advantage.
The MANA vs SAND pricing comparison is also noteworthy. A SAND is currently worth $3664, while a MANA is worth $2452.

The value of the native tokens and the market capitalization of the two metaverse platforms are not enough to make a choice. Let us compare Sandbox vs Decentraland based on the following factors.

Workstyle

The way Decentraland and Sandbox work is one of the main comparisons. From a distance, they both appear to work the same way. But there's a lot more to learn about both platforms' workings. Decentraland has 90,601 digital parcels of land.

Individual parcels of virtual real estate or estates with multiple parcels of land are assembled. It also has districts with similar themes and plazas, which are non-tradeable parcels owned by the community. It has three token types: MANA, LAND, and WEAR.

Sandbox has 166,464 plots of virtual land that can be grouped into estates. Estates are owned by one person, while districts are owned by two or more people. The Sandbox metaverse has four token types: SAND, GAMES, LAND, and ASSETS.

Age

The maturity of metaverse projects is also a factor in the debate. Decentraland is clearly the winner in terms of maturity. It was the first solution to create a 3D blockchain metaverse. Decentraland made the first working proof of concept public. However, Sandbox has only made an Alpha version available to the public.

Backing

The MANA vs SAND comparison would also include support for both platforms. Digital Currency Group, FBG Capital, and CoinFund are all supporters of Decentraland. It has also partnered with Polygon, the South Korean government, Cyberpunk, and Samsung.

SoftBank, a Japanese multinational conglomerate focused on investment management, is another major backer. Sandbox has the backing of one of the world's largest investment firms, as well as Slack and Uber.

Compatibility

Wallet compatibility is an important factor in comparing the two metaverse platforms. Decentraland currently has a competitive advantage. How? Both projects' marketplaces accept ERC-20 wallets. However, Decentraland has recently improved by bridging with Walletconnect. So it can let Polygon users join Decentraland.

Scalability

Because Sandbox and Decentraland use the Ethereum blockchain, scalability is an issue. Both platforms' scalability is constrained by volatile tokens and high gas fees. So, scalability issues can hinder large-scale adoption of both metaverse platforms.

Buying Land

Decentraland vs Sandbox comparisons often include virtual real estate. However, the ability to buy virtual land on both platforms defines the user experience and differentiates them. In this case, Sandbox offers better options for users to buy virtual land by combining OpenSea and Sandbox. In fact, Decentraland users can only buy from the MANA marketplace.

Innovation

The rate of development distinguishes Sandbox and Decentraland. Both platforms have been developing rapidly new features. However, Sandbox wins by adopting Polygon NFT layer 2 solutions, which consume almost 100 times less energy than Ethereum.

Collaborations

The platforms' collaborations are the key to determining "which is better Sandbox or Decentraland." Adoption of metaverse platforms like the two in question can be boosted by association with reputable brands. Among the partners are Atari, Cyberpunk, and Polygon. Rather, Sandbox has partnered with well-known brands like OpenSea, CryptoKitties, The Walking Dead, Snoop Dogg, and others.

Platform Adaptivity

Another key feature that distinguishes Sandbox and Decentraland is the ease of use. Sandbox clearly wins in terms of platform access. It allows easy access via social media, email, or a Metamask wallet. However, Decentraland requires a wallet connection.

Prospects

The future development plans also play a big role in defining Sandbox vs Decentraland. Sandbox's future development plans include bringing the platform to mobile devices. This includes consoles like PlayStation and Xbox. By the end of 2023, the platform expects to have around 5000 games.

Decentraland, on the other hand, has no set plan. In fact, the team defines the decisions that appear to have value. They plan to add celebrities, creators, and brands soon, along with NFT ads and drops.

Final Words

The comparison of Decentraland vs Sandbox provides a balanced view of both platforms. You can see how difficult it is to determine which decentralized metaverse is better now. Sandbox is still in Alpha, whereas Decentraland has a working proof of concept.

Sandbox, on the other hand, has better graphics and is backed by some big names. But both have a long way to go in the larger decentralized metaverse.