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.

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. 

VeeFriends is one of the most popular and unique NFT collections. VeeFriends launched around the same time as other PFP NFTs like Bored Ape Yacht Club.

Vaynerchuk (GaryVee) took a unique approach to his large-scale project, which has influenced the NFT ecosystem. GaryVee's VeeFriends is one of the most successful NFT membership use-cases, allowing him to build a community around his creative and business passions.

What is VeeFriends?

GaryVee's NFT collection, VeeFriends, was released on May 11, 2021. VeeFriends [Mini Drops], Book Games, and a forthcoming large-scale "Series 2" collection all stem from the initial drop of 10,255 tokens.

In "Series 1," there are G.O.O. tokens (Gary Originally Owned). GaryVee reserved 1,242 NFTs (over 12% of the supply) for his own collection, so only 9,013 were available at the Series 1 launch.

Each Series 1 token represents one of 268 human traits hand-drawn by Vaynerchuk. Gary Vee's NFTs offer owners incentives.

Who made VeeFriends?

Gary Vaynerchuk, AKA GaryVee, is influential in NFT. Vaynerchuk is the chairman of New York-based communications company VaynerX. Gary Vee, CEO of VaynerMedia, VaynerSports, and bestselling author, is worth $200 million.

GaryVee went from NFT collector to creator, launching VaynerNFT to help celebrities and brands.

Vaynerchuk's influence spans the NFT ecosystem as one of its most prolific voices. He's one of the most influential NFT figures, and his VeeFriends ecosystem keeps growing.

Vaynerchuk, a trend expert, thinks NFTs will be around for the rest of his life and VeeFriends will be a landmark project.

Why use VeeFriends NFTs?

The first VeeFriends collection has sold nearly $160 million via OpenSea. GaryVee insisted that the first 10,255 VeeFriends were just the beginning.

Book Games were announced to the VeeFriends community in August 2021. Mini Drops joined VeeFriends two months later.

Book Games

GaryVee's book "Twelve and a Half: Leveraging the Emotional Ingredients for Business Success" inspired Book Games. Even prior to the announcement Vaynerchuk had mapped out the utility of the book on an NFT scale. Book Games tied his book to the VeeFriends ecosystem and solidified its place in the collection.

GaryVee says Book Games is a layer 2 NFT project with 125,000 burnable tokens. Vaynerchuk's NFT fans were incentivized to buy as many copies of his new book as possible to receive NFT rewards later.

First, a bit about “layer 2.”

Layer 2 blockchain solutions help scale applications by routing transactions away from Ethereum Mainnet (layer 1). These solutions benefit from Mainnet's decentralized security model but increase transaction speed and reduce gas fees.

Polygon (integrated into OpenSea) and Immutable X are popular Ethereum layer 2 solutions. GaryVee chose Immutable X to reduce gas costs (transaction fees). Given the large supply of Book Games tokens, this decision will likely benefit the VeeFriends community, especially if the games run forever.

What's the strategy?

The VeeFriends patriarch announced on Aug. 27, 2021, that for every 12 books ordered during the Book Games promotion, customers would receive one NFT via airdrop. After nearly 100 days, GV sold over a million copies and announced that Book Games would go gamified on Jan. 10, 2022.

Immutable X's trading options make Book Games a "game." Book Games players can trade NFTs for other NFTs, sports cards, VeeCon tickets, and other prizes. Book Games can also whitelist other VeeFirends projects, which we'll cover in Series 2.

VeeFriends Mini Drops

GaryVee launched VeeFriends Mini Drops two months after Book Games, focusing on collaboration, scarcity, and the characters' "cultural longevity."

Spooky Vees, a collection of 31 1/1 Halloween-themed VeeFriends, was released on Halloween. First-come, first-served VeeFriend owners could claim these NFTs.

Mini Drops includes Gift Goat NFTs. By holding the Gift Goat VeeFriends character, collectors will receive 18 exclusive gifts curated by GaryVee and the team. Each gifting experience includes one physical gift and one NFT out of 555, to match the 555 Gift Goat tokens.

Gift Goat holders have gotten NFTs from Danny Cole (Creature World), Isaac "Drift" Wright (Where My Vans Go), Pop Wonder, and more.

GaryVee is poised to release the largest expansion of the VeeFriends and VaynerNFT ecosystem to date with VeeFriends Series 2.

VeeCon 101

By owning VeeFriends NFTs, collectors can join the VeeFriends community and attend VeeCon in 2022. The conference is only open to VeeCon NFT ticket holders (VeeFreinds + possibly more TBA) and will feature Beeple, Steve Aoki, and even Snoop Dogg.

The VeeFreinds floor in 2022 Q1 has remained at 16 ETH ($52,000), making VeeCon unattainable for most NFT enthusiasts. Why would someone spend that much crypto on a Minneapolis "superconference" ticket? Because of Gary Vaynerchuk.

Everything to know about VeeFriends Series 2

Vaynerchuk revealed in April 2022 that the VeeFriends ecosystem will grow by 55,555 NFTs after months of teasing.

With VeeFriends Series 2, each token will cost $995 USD in ETH, allowing NFT enthusiasts to join at a lower cost. The new series will be released on multiple dates in April.

Book Games NFT holders on the Friends List (whitelist) can mint Series 2 NFTs on April 12. Book Games holders have 32,000 NFTs.

VeeFriends Series 1 NFT holders can claim Series 2 NFTs on April 12. This allotment's supply is 10,255, like Series 1's.

On April 25, the public can buy 10,000 Series 2 NFTs. Unminted Friends List NFTs will be sold on this date, so this number may change.

The VeeFriends ecosystem will add 15 new characters (220 tokens each) on April 27. One character will be released per day for 15 days, and the only way to get one is to enter a daily raffle with Book Games tokens.

Series 2 NFTs won't give owners VeeCon access, but they will offer other benefits within the VaynerNFT ecosystem. Book Games and Series 2 will get new token burn mechanics in the upcoming drop.

Visit the VeeFriends blog for the latest collection info.

Where can you buy Gary Vee’s NFTs?

Need a VeeFriend NFT? Gary Vee recommends doing "50 hours of homework" before buying. OpenSea sells VeeFriends NFTs.