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
(Edited)
Hackernoon
4 years ago
👏 Awesome post! When is part 3 coming?
Trent Lapinski
4 years ago
Very complex topic, great explanation
More on Web3 & Crypto
Vitalik
3 years ago
Fairness alternatives to selling below market clearing prices (or community sentiment, or fun)
When a seller has a limited supply of an item in high (or uncertain and possibly high) demand, they frequently set a price far below what "the market will bear." As a result, the item sells out quickly, with lucky buyers being those who tried to buy first. This has happened in the Ethereum ecosystem, particularly with NFT sales and token sales/ICOs. But this phenomenon is much older; concerts and restaurants frequently make similar choices, resulting in fast sell-outs or long lines.
Why do sellers do this? Economists have long wondered. A seller should sell at the market-clearing price if the amount buyers are willing to buy exactly equals the amount the seller has to sell. If the seller is unsure of the market-clearing price, they should sell at auction and let the market decide. So, if you want to sell something below market value, don't do it. It will hurt your sales and it will hurt your customers. The competitions created by non-price-based allocation mechanisms can sometimes have negative externalities that harm third parties, as we will see.
However, the prevalence of below-market-clearing pricing suggests that sellers do it for good reason. And indeed, as decades of research into this topic has shown, there often are. So, is it possible to achieve the same goals with less unfairness, inefficiency, and harm?
Selling at below market-clearing prices has large inefficiencies and negative externalities
An item that is sold at market value or at an auction allows someone who really wants it to pay the high price or bid high in the auction. So, if a seller sells an item below market value, some people will get it and others won't. But the mechanism deciding who gets the item isn't random, and it's not always well correlated with participant desire. It's not always about being the fastest at clicking buttons. Sometimes it means waking up at 2 a.m. (but 11 p.m. or even 2 p.m. elsewhere). Sometimes it's just a "auction by other means" that's more chaotic, less efficient, and has far more negative externalities.
There are many examples of this in the Ethereum ecosystem. Let's start with the 2017 ICO craze. For example, an ICO project would set the price of the token and a hard maximum for how many tokens they are willing to sell, and the sale would start automatically at some point in time. The sale ends when the cap is reached.
So what? In practice, these sales often ended in 30 seconds or less. Everyone would start sending transactions in as soon as (or just before) the sale started, offering higher and higher fees to encourage miners to include their transaction first. Instead of the token seller receiving revenue, miners receive it, and the sale prices out all other applications on-chain.
The most expensive transaction in the BAT sale set a fee of 580,000 gwei, paying a fee of $6,600 to get included in the sale.
Many ICOs after that tried various strategies to avoid these gas price auctions; one ICO notably had a smart contract that checked the transaction's gasprice and rejected it if it exceeded 50 gwei. But that didn't solve the issue. Buyers hoping to game the system sent many transactions hoping one would get through. An auction by another name, clogging the chain even more.
ICOs have recently lost popularity, but NFTs and NFT sales have risen in popularity. But the NFT space didn't learn from 2017; they do fixed-quantity sales just like ICOs (eg. see the mint function on lines 97-108 of this contract here). So what?
That's not the worst; some NFT sales have caused gas price spikes of up to 2000 gwei.
High gas prices from users fighting to get in first by sending higher and higher transaction fees. An auction renamed, pricing out all other applications on-chain for 15 minutes.
So why do sellers sometimes sell below market price?
Selling below market value is nothing new, and many articles, papers, and podcasts have written (and sometimes bitterly complained) about the unwillingness to use auctions or set prices to market-clearing levels.
Many of the arguments are the same for both blockchain (NFTs and ICOs) and non-blockchain examples (popular restaurants and concerts). Fairness and the desire not to exclude the poor, lose fans or create tension by being perceived as greedy are major concerns. The 1986 paper by Kahneman, Knetsch, and Thaler explains how fairness and greed can influence these decisions. I recall that the desire to avoid perceptions of greed was also a major factor in discouraging the use of auction-like mechanisms in 2017.
Aside from fairness concerns, there is the argument that selling out and long lines create a sense of popularity and prestige, making the product more appealing to others. Long lines should have the same effect as high prices in a rational actor model, but this is not the case in reality. This applies to ICOs and NFTs as well as restaurants. Aside from increasing marketing value, some people find the game of grabbing a limited set of opportunities first before everyone else is quite entertaining.
But there are some blockchain-specific factors. One argument for selling ICO tokens below market value (and one that persuaded the OmiseGo team to adopt their capped sale strategy) is community dynamics. The first rule of community sentiment management is to encourage price increases. People are happy if they are "in the green." If the price drops below what the community members paid, they are unhappy and start calling you a scammer, possibly causing a social media cascade where everyone calls you a scammer.
This effect can only be avoided by pricing low enough that post-launch market prices will almost certainly be higher. But how do you do this without creating a rush for the gates that leads to an auction?
Interesting solutions
It's 2021. We have a blockchain. The blockchain is home to a powerful decentralized finance ecosystem, as well as a rapidly expanding set of non-financial tools. The blockchain also allows us to reset social norms. Where decades of economists yelling about "efficiency" failed, blockchains may be able to legitimize new uses of mechanism design. If we could use our more advanced tools to create an approach that more directly solves the problems, with fewer side effects, wouldn't that be better than fiddling with a coarse-grained one-dimensional strategy space of selling at market price versus below market price?
Begin with the goals. We'll try to cover ICOs, NFTs, and conference tickets (really a type of NFT) all at the same time.
1. Fairness: don't completely exclude low-income people from participation; give them a chance. The goal of token sales is to avoid high initial wealth concentration and have a larger and more diverse initial token holder community.
2. Don’t create races: Avoid situations where many people rush to do the same thing and only a few get in (this is the type of situation that leads to the horrible auctions-by-another-name that we saw above).
3. Don't require precise market knowledge: the mechanism should work even if the seller has no idea how much demand exists.
4. Fun: The process of participating in the sale should be fun and game-like, but not frustrating.
5. Give buyers positive expected returns: in the case of a token (or an NFT), buyers should expect price increases rather than decreases. This requires selling below market value.
Let's start with (1). From Ethereum's perspective, there is a simple solution. Use a tool designed for the job: proof of personhood protocols! Here's one quick idea:
Mechanism 1 Each participant (verified by ID) can buy up to ‘’X’’ tokens at price P, with the option to buy more at an auction.
With the per-person mechanism, buyers can get positive expected returns for the portion sold through the per-person mechanism, and the auction part does not require sellers to understand demand levels. Is it race-free? The number of participants buying through the per-person pool appears to be high. But what if the per-person pool isn't big enough to accommodate everyone?
Make the per-person allocation amount dynamic.
Mechanism 2 Each participant can deposit up to X tokens into a smart contract to declare interest. Last but not least, each buyer receives min(X, N / buyers) tokens, where N is the total sold through the per-person pool (some other amount can also be sold by auction). The buyer gets their deposit back if it exceeds the amount needed to buy their allocation.
No longer is there a race condition based on the number of buyers per person. No matter how high the demand, it's always better to join sooner rather than later.
Here's another idea if you like clever game mechanics with fancy quadratic formulas.
Mechanism 3 Each participant can buy X units at a price P X 2 up to a maximum of C tokens per buyer. C starts low and gradually increases until enough units are sold.
The quantity allocated to each buyer is theoretically optimal, though post-sale transfers will degrade this optimality over time. Mechanisms 2 and 3 appear to meet all of the above objectives. They're not perfect, but they're good starting points.
One more issue. For fixed and limited supply NFTs, the equilibrium purchased quantity per participant may be fractional (in mechanism 2, number of buyers > N, and in mechanism 3, setting C = 1 may already lead to over-subscription). With fractional sales, you can offer lottery tickets: if there are N items available, you have a chance of N/number of buyers of getting the item, otherwise you get a refund. For a conference, groups could bundle their lottery tickets to guarantee a win or a loss. The certainty of getting the item can be auctioned.
The bottom tier of "sponsorships" can be used to sell conference tickets at market rate. You may end up with a sponsor board full of people's faces, but is that okay? After all, John Lilic was on EthCC's sponsor board!
Simply put, if you want to be reliably fair to people, you need an input that explicitly measures people. Authentication protocols do this (and if desired can be combined with zero knowledge proofs to ensure privacy). So we should combine the efficiency of market and auction-based pricing with the equality of proof of personhood mechanics.
Answers to possible questions
Q: Won't people who don't care about your project buy the item and immediately resell it?
A: Not at first. Meta-games take time to appear in practice. If they do, making them untradeable for a while may help mitigate the damage. Using your face to claim that your previous account was hacked and that your identity, including everything in it, should be moved to another account works because proof-of-personhood identities are untradeable.
Q: What if I want to make my item available to a specific community?
A: Instead of ID, use proof of participation tokens linked to community events. Another option, also serving egalitarian and gamification purposes, is to encrypt items within publicly available puzzle solutions.
Q: How do we know they'll accept? Strange new mechanisms have previously been resisted.
A: Having economists write screeds about how they "should" accept a new mechanism that they find strange is difficult (or even "equity"). However, abrupt changes in context effectively reset people's expectations. So the blockchain space is the best place to try this. You could wait for the "metaverse", but it's possible that the best version will run on Ethereum anyway, so start now.
Langston Thomas
3 years ago
A Simple Guide to NFT Blockchains
Ethereum's blockchain rules NFTs. Many consider it the one-stop shop for NFTs, and it's become the most talked-about and trafficked blockchain in existence.
Other blockchains are becoming popular in NFTs. Crypto-artists and NFT enthusiasts have sought new places to mint and trade NFTs due to Ethereum's high transaction costs and environmental impact.
When choosing a blockchain to mint on, there are several factors to consider. Size, creator costs, consumer spending habits, security, and community input are important. We've created a high-level summary of blockchains for NFTs to help clarify the fast-paced world of web3 tech.
Ethereum
Ethereum currently has the most NFTs. It's decentralized and provides financial and legal services without intermediaries. It houses popular NFT marketplaces (OpenSea), projects (CryptoPunks and the Bored Ape Yacht Club), and artists (Pak and Beeple).
It's also expensive and energy-intensive. This is because Ethereum works using a Proof-of-Work (PoW) mechanism. PoW requires computers to solve puzzles to add blocks and transactions to the blockchain. Solving these puzzles requires a lot of computer power, resulting in astronomical energy loss.
You should consider this blockchain first due to its popularity, security, decentralization, and ease of use.
Solana
Solana is a fast programmable blockchain. Its proof-of-history and proof-of-stake (PoS) consensus mechanisms eliminate complex puzzles. Reduced validation times and fees result.
PoS users stake their cryptocurrency to become a block validator. Validators get SOL. This encourages and rewards users to become stakers. PoH works with PoS to cryptographically verify time between events. Solana blockchain ensures transactions are in order and found by the correct leader (validator).
Solana's PoS and PoH mechanisms keep transaction fees and times low. Solana isn't as popular as Ethereum, so there are fewer NFT marketplaces and blockchain traders.
Tezos
Tezos is a greener blockchain. Tezos rose in 2021. Hic et Nunc was hailed as an economic alternative to Ethereum-centric marketplaces until Nov. 14, 2021.
Similar to Solana, Tezos uses a PoS consensus mechanism and only a PoS mechanism to reduce computational work. This blockchain uses two million times less energy than Ethereum. It's cheaper than Ethereum (but does cost more than Solana).
Tezos is a good place to start minting NFTs in bulk. Objkt is the largest Tezos marketplace.
Flow
Flow is a high-performance blockchain for NFTs, games, and decentralized apps (dApps). Flow is built with scalability in mind, so billions of people could interact with NFTs on the blockchain.
Flow became the NBA's blockchain partner in 2019. Flow, a product of Dapper labs (the team behind CryptoKitties), launched and hosts NBA Top Shot, making the blockchain integral to the popularity of non-fungible tokens.
Flow uses PoS to verify transactions, like Tezos. Developers are working on a model to handle 10,000 transactions per second on the blockchain. Low transaction fees.
Flow NFTs are tradeable on Blocktobay, OpenSea, Rarible, Foundation, and other platforms. NBA, NFL, UFC, and others have launched NFT marketplaces on Flow. Flow isn't as popular as Ethereum, resulting in fewer NFT marketplaces and blockchain traders.
Asset Exchange (WAX)
WAX is king of virtual collectibles. WAX is popular for digitalized versions of legacy collectibles like trading cards, figurines, memorabilia, etc.
Wax uses a PoS mechanism, but also creates carbon offset NFTs and partners with Climate Care. Like Flow, WAX transaction fees are low, and network fees are redistributed to the WAX community as an incentive to collectors.
WAX marketplaces host Topps, NASCAR, Hot Wheels, and cult classic film franchises like Godzilla, The Princess Bride, and Spiderman.
Binance Smart Chain
BSC is another good option for balancing fees and performance. High-speed transactions and low fees hurt decentralization. BSC is most centralized.
Binance Smart Chain uses Proof of Staked Authority (PoSA) to support a short block time and low fees. The 21 validators needed to run the exchange switch every 24 hours. 11 of the 21 validators are directly connected to the Binance Crypto Exchange, according to reports.
While many in the crypto and NFT ecosystems dislike centralization, the BSC NFT market picked up speed in 2021. OpenBiSea, AirNFTs, JuggerWorld, and others are gaining popularity despite not having as robust an ecosystem as Ethereum.
Scott Hickmann
4 years ago
YouTube
This is a YouTube video:
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Pat Vieljeux
3 years ago
In 5 minutes, you can tell if a startup will succeed.
Or the “lie to me” method.
I can predict a startup's success in minutes.
Just interview its founder.
Ask "why?"
I question "why" till I sense him.
I need to feel the person I have in front of me. I need to know if he or she can deliver. Startups aren't easy. Without abilities, a brilliant idea will fail.
Good entrepreneurs have these qualities: He's a leader, determined, and resilient.
For me, they can be split in two categories.
The first entrepreneur aspires to live meaningfully. The second wants to get rich. The second is communicative. He wants to wow the crowd. He's motivated by the thought of one day sailing a boat past palm trees and sunny beaches.
What drives the first entrepreneur is evident in his speech, face, and voice. He will not speak about his product. He's (nearly) uninterested. He's not selling anything. He's not a salesman. He wants to succeed. The product is his fuel.
He'll explain his decision. He'll share his motivations. His desire. And he'll use meaningful words.
Paul Ekman has shown that face expressions aren't cultural. His study influenced the American TV series "lie to me" about body language and speech.
Passionate entrepreneurs are obvious. It's palpable. Faking passion is tough. Someone who wants your favor and money will expose his actual motives through his expressions and language.
The good liar will be able to fool you for a while, but not for long if you pay attention to his body language and how he expresses himself.
And also, if you look at his business plan.
His business plan reveals his goals. Read between the lines.
Entrepreneur 1 will focus on his "why", whereas Entrepreneur 2 will focus on the "how".
Entrepreneur 1 will develop a vision-driven culture.
The second, on the other hand, will focus on his EBITDA.
Why is the culture so critical? Because it will allow entrepreneur 1 to develop a solid team that can tackle his problems and trials. His team's "why" will keep them together in tough times.
"Give me a terrific start-up team with a mediocre idea over a weak one any day." Because a great team knows when to pivot and trusts each other. Weak teams fail.” — Bernhard Schroeder
Closings thoughts
Every VC must ask Why. Entrepreneur's motivations. This "why" will create the team's culture. This culture will help the team adjust to any setback.
Dr. Linda Dahl
3 years ago
We eat corn in almost everything. Is It Important?
Corn Kid got viral on TikTok after being interviewed by Recess Therapy. Tariq, called the Corn Kid, ate a buttery ear of corn in the video. He's corn crazy. He thinks everyone just has to try it. It turns out, whether we know it or not, we already have.
Corn is a fruit, veggie, and grain. It's the second-most-grown crop. Corn makes up 36% of U.S. exports. In the U.S., it's easy to grow and provides high yields, as proven by the vast corn belt spanning the Midwest, Great Plains, and Texas panhandle. Since 1950, the corn crop has doubled to 10 billion bushels.
You say, "Fine." We shouldn't just grow because we can. Why so much corn? What's this corn for?
Why is practical and political. Michael Pollan's The Omnivore's Dilemma has the full narrative. Early 1970s food costs increased. Nixon subsidized maize to feed the public. Monsanto genetically engineered corn seeds to make them hardier, and soon there was plenty of corn. Everyone ate. Woot! Too much corn followed. The powers-that-be had to decide what to do with leftover corn-on-the-cob.
They are fortunate that corn has a wide range of uses.
First, the edible variants. I divide corn into obvious and stealth.
Obvious corn includes popcorn, canned corn, and corn on the cob. This form isn't always digested and often comes out as entire, polka-dotting poop. Cornmeal can be ground to make cornbread, polenta, and corn tortillas. Corn provides antioxidants, minerals, and vitamins in moderation. Most synthetic Vitamin C comes from GMO maize.
Corn oil, corn starch, dextrose (a sugar), and high-fructose corn syrup are often overlooked. They're stealth corn because they sneak into practically everything. Corn oil is used for frying, baking, and in potato chips, mayonnaise, margarine, and salad dressing. Baby food, bread, cakes, antibiotics, canned vegetables, beverages, and even dairy and animal products include corn starch. Dextrose appears in almost all prepared foods, excluding those with high-fructose corn syrup. HFCS isn't as easily digested as sucrose (from cane sugar). It can also cause other ailments, which we'll discuss later.
Most foods contain corn. It's fed to almost all food animals. 96% of U.S. animal feed is corn. 39% of U.S. corn is fed to livestock. But animals prefer other foods. Omnivore chickens prefer insects, worms, grains, and grasses. Captive cows are fed a total mixed ration, which contains corn. These animals' products, like eggs and milk, are also corn-fed.
There are numerous non-edible by-products of corn that are employed in the production of items like:
fuel-grade ethanol
plastics
batteries
cosmetics
meds/vitamins binder
carpets, fabrics
glutathione
crayons
Paint/glue
How does corn influence you? Consider quick food for dinner. You order a cheeseburger, fries, and big Coke at the counter (or drive-through in the suburbs). You tell yourself, "No corn." All that contains corn. Deconstruct:
Cows fed corn produce meat and cheese. Meat and cheese were bonded with corn syrup and starch (same). The bun (corn flour and dextrose) and fries were fried in maize oil. High fructose corn syrup sweetens the drink and helps make the cup and straw.
Just about everything contains corn. Then what? A cornspiracy, perhaps? Is eating too much maize an issue, or should we strive to stay away from it whenever possible?
As I've said, eating some maize can be healthy. 92% of U.S. corn is genetically modified, according to the Center for Food Safety. The adjustments are expected to boost corn yields. Some sweet corn is genetically modified to produce its own insecticide, a protein deadly to insects made by Bacillus thuringiensis. It's safe to eat in sweet corn. Concerns exist about feeding agricultural animals so much maize, modified or not.
High fructose corn syrup should be consumed in moderation. Fructose, a sugar, isn't easily metabolized. Fructose causes diabetes, fatty liver, obesity, and heart disease. It causes inflammation, which might aggravate gout. Candy, packaged sweets, soda, fast food, juice drinks, ice cream, ice cream topping syrups, sauces & condiments, jams, bread, crackers, and pancake syrup contain the most high fructose corn syrup. Everyday foods with little nutrients. Check labels and choose cane sugar or sucrose-sweetened goods. Or, eat corn like the Corn Kid.
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.