More on Science
Jack Burns
3 years ago
Here's what to expect from NASA Artemis 1 and why it's significant.
NASA's Artemis 1 mission will help return people to the Moon after a half-century break. The mission is a shakedown cruise for NASA's Space Launch System and Orion Crew Capsule.
The spaceship will visit the Moon, deploy satellites, and enter orbit. NASA wants to practice operating the spacecraft, test the conditions people will face on the Moon, and ensure a safe return to Earth.
We asked Jack Burns, a space scientist at the University of Colorado Boulder and former member of NASA's Presidential Transition Team, to describe the mission, explain what the Artemis program promises for space exploration, and reflect on how the space program has changed in the half-century since humans last set foot on the moon.
What distinguishes Artemis 1 from other rockets?
Artemis 1 is the Space Launch System's first launch. NASA calls this a "heavy-lift" vehicle. It will be more powerful than Apollo's Saturn V, which transported people to the Moon in the 1960s and 1970s.
It's a new sort of rocket system with two strap-on solid rocket boosters from the space shuttle. It's a mix of the shuttle and Saturn V.
The Orion Crew Capsule will be tested extensively. It'll spend a month in the high-radiation Moon environment. It will also test the heat shield, which protects the capsule and its occupants at 25,000 mph. The heat shield must work well because this is the fastest capsule descent since Apollo.
This mission will also carry miniature Moon-orbiting satellites. These will undertake vital precursor science, including as examining further into permanently shadowed craters where scientists suspect there is water and measuring the radiation environment to see long-term human consequences.
Artemis 1 will launch, fly to the Moon, place satellites, orbit it, return to Earth, and splash down in the ocean. NASA.
What's Artemis's goal? What launches are next?
The mission is a first step toward Artemis 3, which will lead to the first human Moon missions since 1972. Artemis 1 is unmanned.
Artemis 2 will have astronauts a few years later. Like Apollo 8, it will be an orbital mission that circles the Moon and returns. The astronauts will orbit the Moon longer and test everything with a crew.
Eventually, Artemis 3 will meet with the SpaceX Starship on the Moon's surface and transfer people. Orion will stay in orbit while the lunar Starship lands astronauts. They'll go to the Moon's south pole to investigate the water ice there.
Artemis is reminiscent of Apollo. What's changed in 50 years?
Kennedy wanted to beat the Soviets to the Moon with Apollo. The administration didn't care much about space flight or the Moon, but the goal would place America first in space and technology.
You live and die by the sword if you do that. When the U.S. reached the Moon, it was over. Russia lost. We planted flags and did science experiments. Richard Nixon canceled the program after Apollo 11 because the political goals were attained.
Large rocket with two boosters between two gates
NASA's new Space Launch System is brought to a launchpad. NASA
50 years later... It's quite different. We're not trying to beat the Russians, Chinese, or anyone else, but to begin sustainable space exploration.
Artemis has many goals. It includes harnessing in-situ resources like water ice and lunar soil to make food, fuel, and building materials.
SpaceX is part of this first journey to the Moon's surface, therefore the initiative is also helping to develop a lunar and space economy. NASA doesn't own the Starship but is buying seats for astronauts. SpaceX will employ Starship to transport cargo, private astronauts, and foreign astronauts.
Fifty years of technology advancement has made getting to the Moon cheaper and more practical, and computer technology allows for more advanced tests. 50 years of technological progress have changed everything. Anyone with enough money can send a spacecraft to the Moon, but not humans.
Commercial Lunar Payload Services engages commercial companies to develop uncrewed Moon landers. We're sending a radio telescope to the Moon in January. Even 10 years ago, that was impossible.
Since humans last visited the Moon 50 years ago, technology has improved greatly.
What other changes does Artemis have in store?
The government says Artemis 3 will have at least one woman and likely a person of color.
I'm looking forward to seeing more diversity so young kids can say, "Hey, there's an astronaut that looks like me. I can do this. I can be part of the space program.”
Adam Frank
3 years ago
Humanity is not even a Type 1 civilization. What might a Type 3 be capable of?
The Kardashev scale grades civilizations from Type 1 to Type 3 based on energy harvesting.
How do technologically proficient civilizations emerge across timescales measuring in the tens of thousands or even millions of years? This is a question that worries me as a researcher in the search for “technosignatures” from other civilizations on other worlds. Since it is already established that longer-lived civilizations are the ones we are most likely to detect, knowing something about their prospective evolutionary trajectories could be translated into improved search tactics. But even more than knowing what to seek for, what I really want to know is what happens to a society after so long time. What are they capable of? What do they become?
This was the question Russian SETI pioneer Nikolai Kardashev asked himself back in 1964. His answer was the now-famous “Kardashev Scale.” Kardashev was the first, although not the last, scientist to try and define the processes (or stages) of the evolution of civilizations. Today, I want to launch a series on this question. It is crucial to technosignature studies (of which our NASA team is hard at work), and it is also important for comprehending what might lay ahead for mankind if we manage to get through the bottlenecks we have now.
The Kardashev scale
Kardashev’s question can be expressed another way. What milestones in a civilization’s advancement up the ladder of technical complexity will be universal? The main notion here is that all (or at least most) civilizations will pass through some kind of definable stages as they progress, and some of these steps might be mirrored in how we could identify them. But, while Kardashev’s major focus was identifying signals from exo-civilizations, his scale gave us a clear way to think about their evolution.
The classification scheme Kardashev employed was not based on social systems of ethics because they are something that we can probably never predict about alien cultures. Instead, it was built on energy, which is something near and dear to the heart of everybody trained in physics. Energy use might offer the basis for universal stages of civilisation progression because you cannot do the work of establishing a civilization without consuming energy. So, Kardashev looked at what energy sources were accessible to civilizations as they evolved technologically and used those to build his scale.
From Kardashev’s perspective, there are three primary levels or “types” of advancement in terms of harvesting energy through which a civilization should progress.
Type 1: Civilizations that can capture all the energy resources of their native planet constitute the first stage. This would imply capturing all the light energy that falls on a world from its host star. This makes it reasonable, given solar energy will be the largest source available on most planets where life could form. For example, Earth absorbs hundreds of atomic bombs’ worth of energy from the Sun every second. That is a rather formidable energy source, and a Type 1 race would have all this power at their disposal for civilization construction.
Type 2: These civilizations can extract the whole energy resources of their home star. Nobel Prize-winning scientist Freeman Dyson famously anticipated Kardashev’s thinking on this when he imagined an advanced civilization erecting a large sphere around its star. This “Dyson Sphere” would be a machine the size of the complete solar system for gathering stellar photons and their energy.
Type 3: These super-civilizations could use all the energy produced by all the stars in their home galaxy. A normal galaxy has a few hundred billion stars, so that is a whole lot of energy. One way this may be done is if the civilization covered every star in their galaxy with Dyson spheres, but there could also be more inventive approaches.
Implications of the Kardashev scale
Climbing from Type 1 upward, we travel from the imaginable to the god-like. For example, it is not hard to envisage utilizing lots of big satellites in space to gather solar energy and then beaming that energy down to Earth via microwaves. That would get us to a Type 1 civilization. But creating a Dyson sphere would require chewing up whole planets. How long until we obtain that level of power? How would we have to change to get there? And once we get to Type 3 civilizations, we are virtually thinking about gods with the potential to engineer the entire cosmos.
For me, this is part of the point of the Kardashev scale. Its application for thinking about identifying technosignatures is crucial, but even more strong is its capacity to help us shape our imaginations. The mind might become blank staring across hundreds or thousands of millennia, and so we need tools and guides to focus our attention. That may be the only way to see what life might become — what we might become — once it arises to start out beyond the boundaries of space and time and potential.
This is a summary. Read the full article here.
Laura Sanders
3 years ago
Xenobots, tiny living machines, can duplicate themselves.
Strange and complex behavior of frog cell blobs
A xenobot “parent,” shaped like a hungry Pac-Man (shown in red false color), created an “offspring” xenobot (green sphere) by gathering loose frog cells in its opening.
Tiny “living machines” made of frog cells can make copies of themselves. This newly discovered renewal mechanism may help create self-renewing biological machines.
According to Kirstin Petersen, an electrical and computer engineer at Cornell University who studies groups of robots, “this is an extremely exciting breakthrough.” She says self-replicating robots are a big step toward human-free systems.
Researchers described the behavior of xenobots earlier this year (SN: 3/31/21). Small clumps of skin stem cells from frog embryos knitted themselves into small spheres and started moving. Cilia, or cellular extensions, powered the xenobots around their lab dishes.
The findings are published in the Proceedings of the National Academy of Sciences on Dec. 7. The xenobots can gather loose frog cells into spheres, which then form xenobots.
The researchers call this type of movement-induced reproduction kinematic self-replication. The study's coauthor, Douglas Blackiston of Tufts University in Medford, Massachusetts, and Harvard University, says this is typical. For example, sexual reproduction requires parental sperm and egg cells. Sometimes cells split or budded off from a parent.
“This is unique,” Blackiston says. These xenobots “find loose parts in the environment and cobble them together.” This second generation of xenobots can move like their parents, Blackiston says.
The researchers discovered that spheroid xenobots could only produce one more generation before dying out. The original xenobots' shape was predicted by an artificial intelligence program, allowing for four generations of replication.
A C shape, like an openmouthed Pac-Man, was predicted to be a more efficient progenitor. When improved xenobots were let loose in a dish, they began scooping up loose cells into their gaping “mouths,” forming more sphere-shaped bots (see image below). As many as 50 cells clumped together in the opening of a parent to form a mobile offspring. A xenobot is made up of 4,000–6,000 frog cells.
Petersen likes the Xenobots' small size. “The fact that they were able to do this at such a small scale just makes it even better,” she says. Miniature xenobots could sculpt tissues for implantation or deliver therapeutics inside the body.
Beyond the xenobots' potential jobs, the research advances an important science, says study coauthor and Tufts developmental biologist Michael Levin. The science of anticipating and controlling the outcomes of complex systems, he says.
“No one could have predicted this,” Levin says. “They regularly surprise us.” Researchers can use xenobots to test the unexpected. “This is about advancing the science of being less surprised,” Levin says.
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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.
Navdeep Yadav
3 years ago
31 startup company models (with examples)
Many people find the internet's various business models bewildering.
This article summarizes 31 startup e-books.
1. Using the freemium business model (free plus premium),
The freemium business model offers basic software, games, or services for free and charges for enhancements.
Examples include Slack, iCloud, and Google Drive
Provide a rudimentary, free version of your product or service to users.
Google Drive and Dropbox offer 15GB and 2GB of free space but charge for more.
Freemium business model details (Click here)
2. The Business Model of Subscription
Subscription business models sell a product or service for recurring monthly or yearly revenue.
Examples: Tinder, Netflix, Shopify, etc
It's the next step to Freemium if a customer wants to pay monthly for premium features.
Subscription Business Model (Click here)
3. A market-based business strategy
It's an e-commerce site or app where third-party sellers sell products or services.
Examples are Amazon and Fiverr.
On Amazon's marketplace, a third-party vendor sells a product.
Freelancers on Fiverr offer specialized skills like graphic design.
Marketplace's business concept is explained.
4. Business plans using aggregates
In the aggregator business model, the service is branded.
Uber, Airbnb, and other examples
Marketplace and Aggregator business models differ.
Amazon and Fiverr link merchants and customers and take a 10-20% revenue split.
Uber and Airbnb-style aggregator Join these businesses and provide their products.
5. The pay-as-you-go concept of business
This is a consumption-based pricing system. Cloud companies use it.
Example: Amazon Web Service and Google Cloud Platform (GCP) (AWS)
AWS, an Amazon subsidiary, offers over 200 pay-as-you-go cloud services.
“In short, the more you use the more you pay”
When it's difficult to divide clients into pricing levels, pay-as-you is employed.
6. The business model known as fee-for-service (FFS)
FFS charges fixed and variable fees for each successful payment.
For instance, PayU, Paypal, and Stripe
Stripe charges 2.9% + 30 per payment.
These firms offer a payment gateway to take consumer payments and deposit them to a business account.
Fintech business model
7. EdTech business strategy
In edtech, you generate money by selling material or teaching as a service.
edtech business models
Freemium When course content is free but certification isn't, e.g. Coursera
FREE TRIAL SkillShare offers free trials followed by monthly or annual subscriptions.
Self-serving marketplace approach where you pick what to learn.
Ad-revenue model The company makes money by showing adverts to its huge user base.
Lock-in business strategy
Lock in prevents customers from switching to a competitor's brand or offering.
It uses switching costs or effort to transmit (soft lock-in), improved brand experience, or incentives.
Apple, SAP, and other examples
Apple offers an iPhone and then locks you in with extra hardware (Watch, Airpod) and platform services (Apple Store, Apple Music, cloud, etc.).
9. Business Model for API Licensing
APIs let third-party apps communicate with your service.
Uber and Airbnb use Google Maps APIs for app navigation.
Examples are Google Map APIs (Map), Sendgrid (Email), and Twilio (SMS).
Business models for APIs
Free: The simplest API-driven business model that enables unrestricted API access for app developers. Google Translate and Facebook are two examples.
Developer Pays: Under this arrangement, service providers such as AWS, Twilio, Github, Stripe, and others must be paid by application developers.
The developer receives payment: These are the compensated content producers or developers who distribute the APIs utilizing their work. For example, Amazon affiliate programs
10. Open-source enterprise
Open-source software can be inspected, modified, and improved by anybody.
For instance, use Firefox, Java, or Android.
Google paid Mozilla $435,702 million to be their primary search engine in 2018.
Open-source software profits in six ways.
Paid assistance The Project Manager can charge for customization because he is quite knowledgeable about the codebase.
A full database solution is available as a Software as a Service (MongoDB Atlas), but there is a fee for the monitoring tool.
Open-core design R studio is a better GUI substitute for open-source applications.
sponsors of GitHub Sponsorships benefit the developers in full.
demands for paid features Earn Money By Developing Open Source Add-Ons for Current Products
Open-source business model
11. The business model for data
If the software or algorithm collects client data to improve or monetize the system.
Open AI GPT3 gets smarter with use.
Foursquare allows users to exchange check-in locations.
Later, they compiled large datasets to enable retailers like Starbucks launch new outlets.
12. Business Model Using Blockchain
Blockchain is a distributed ledger technology that allows firms to deploy smart contracts without a central authority.
Examples include Alchemy, Solana, and Ethereum.
Business models using blockchain
Economy of tokens or utility When a business uses a token business model, it issues some kind of token as one of the ways to compensate token holders or miners. For instance, Solana and Ethereum
Bitcoin Cash P2P Business Model Peer-to-peer (P2P) blockchain technology permits direct communication between end users. as in IPFS
Enterprise Blockchain as a Service (Baas) BaaS focuses on offering ecosystem services similar to those offered by Amazon (AWS) and Microsoft (Azure) in the web 3 sector. Example: Ethereum Blockchain as a Service with Bitcoin (EBaaS).
Blockchain-Based Aggregators With AWS for blockchain, you can use that service by making an API call to your preferred blockchain. As an illustration, Alchemy offers nodes for many blockchains.
13. The free-enterprise model
In the freeterprise business model, free professional accounts are led into the funnel by the free product and later become B2B/enterprise accounts.
For instance, Slack and Zoom
Freeterprise companies flourish through collaboration.
Start with a free professional account to build an enterprise.
14. Business plan for razor blades
It's employed in hardware where one piece is sold at a loss and profits are made through refills or add-ons.
Gillet razor & blades, coffee machine & beans, HP printer & cartridge, etc.
Sony sells the Playstation console at a loss but makes up for it by selling games and charging for online services.
Advantages of the Razor-Razorblade Method
lowers the risk a customer will try a product. enables buyers to test the goods and services without having to pay a high initial investment.
The product's ongoing revenue stream has the potential to generate sales that much outweigh the original investments.
Razor blade business model
15. The business model of direct-to-consumer (D2C)
In D2C, the company sells directly to the end consumer through its website using a third-party logistic partner.
Examples include GymShark and Kylie Cosmetics.
D2C brands can only expand via websites, marketplaces (Amazon, eBay), etc.
D2C benefits
Lower reliance on middlemen = greater profitability
You now have access to more precise demographic and geographic customer data.
Additional space for product testing
Increased customisation throughout your entire product line-Inventory Less
16. Business model: White Label vs. Private Label
Private label/White label products are made by a contract or third-party manufacturer.
Most amazon electronics are made in china and white-labeled.
Amazon supplements and electronics.
Contract manufacturers handle everything after brands select product quantities on design labels.
17. The franchise model
The franchisee uses the franchisor's trademark, branding, and business strategy (company).
For instance, KFC, Domino's, etc.
Subway, Domino, Burger King, etc. use this business strategy.
Many people pick a franchise because opening a restaurant is risky.
18. Ad-based business model
Social media and search engine giants exploit search and interest data to deliver adverts.
Google, Meta, TikTok, and Snapchat are some examples.
Users don't pay for the service or product given, e.g. Google users don't pay for searches.
In exchange, they collected data and hyper-personalized adverts to maximize revenue.
19. Business plan for octopuses
Each business unit functions separately but is connected to the main body.
Instance: Oyo
OYO is Asia's Airbnb, operating hotels, co-working, co-living, and vacation houses.
20, Transactional business model, number
Sales to customers produce revenue.
E-commerce sites and online purchases employ SSL.
Goli is an ex-GymShark.
21. The peer-to-peer (P2P) business model
In P2P, two people buy and sell goods and services without a third party or platform.
Consider OLX.
22. P2P lending as a manner of operation
In P2P lending, one private individual (P2P Lender) lends/invests or borrows money from another (P2P Borrower).
Instance: Kabbage
Social lending lets people lend and borrow money directly from each other without an intermediary financial institution.
23. A business model for brokers
Brokerages charge a commission or fee for their services.
Examples include eBay, Coinbase, and Robinhood.
Brokerage businesses are common in Real estate, finance, and online and operate on this model.
Buy/sell similar models Examples include financial brokers, insurance brokers, and others who match purchase and sell transactions and charge a commission.
These brokers charge an advertiser a fee based on the date, place, size, or type of an advertisement. This is known as the classified-advertiser model. For instance, Craiglist
24. Drop shipping as an industry
Dropshipping allows stores to sell things without holding physical inventories.
When a customer orders, use a third-party supplier and logistic partners.
Retailer product portfolio and customer experience Fulfiller The consumer places the order.
Dropshipping advantages
Less money is needed (Low overhead-No Inventory or warehousing)
Simple to start (costs under $100)
flexible work environment
New product testing is simpler
25. Business Model for Space as a Service
It's centered on a shared economy that lets millennials live or work in communal areas without ownership or lease.
Consider WeWork and Airbnb.
WeWork helps businesses with real estate, legal compliance, maintenance, and repair.
26. The business model for third-party logistics (3PL)
In 3PL, a business outsources product delivery, warehousing, and fulfillment to an external logistics company.
Examples include Ship Bob, Amazon Fulfillment, and more.
3PL partners warehouse, fulfill, and return inbound and outbound items for a charge.
Inbound logistics involves bringing products from suppliers to your warehouse.
Outbound logistics refers to a company's production line, warehouse, and customer.
27. The last-mile delivery paradigm as a commercial strategy
Last-mile delivery is the collection of supply chain actions that reach the end client.
Examples include Rappi, Gojek, and Postmates.
Last-mile is tied to on-demand and has a nighttime peak.
28. The use of affiliate marketing
Affiliate marketing involves promoting other companies' products and charging commissions.
Examples include Hubspot, Amazon, and Skillshare.
Your favorite youtube channel probably uses these short amazon links to get 5% of sales.
Affiliate marketing's benefits
In exchange for a success fee or commission, it enables numerous independent marketers to promote on its behalf.
Ensure system transparency by giving the influencers a specific tracking link and an online dashboard to view their profits.
Learn about the newest bargains and have access to promotional materials.
29. The business model for virtual goods
This is an in-app purchase for an intangible product.
Examples include PubG, Roblox, Candy Crush, etc.
Consumables are like gaming cash that runs out. Non-consumable products provide a permanent advantage without repeated purchases.
30. Business Models for Cloud Kitchens
Ghost, Dark, Black Box, etc.
Delivery-only restaurant.
These restaurants don't provide dine-in, only delivery.
For instance, NextBite and Faasos
31. Crowdsourcing as a Business Model
Crowdsourcing = Using the crowd as a platform's source.
In crowdsourcing, you get support from people around the world without hiring them.
Crowdsourcing sites
Open-Source Software gives access to the software's source code so that developers can edit or enhance it. Examples include Firefox browsers and Linux operating systems.
Crowdfunding The oculus headgear would be an example of crowdfunding in essence, with no expectations.
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