More on Entrepreneurship/Creators

Tim Denning
3 years ago
Bills are paid by your 9 to 5. 6 through 12 help you build money.
40 years pass. After 14 years of retirement, you die. Am I the only one who sees the problem?
I’m the Jedi master of escaping the rat race.
Not to impress. I know this works since I've tried it. Quitting a job to make money online is worse than Kim Kardashian's internet-burning advice.
Let me help you rethink the move from a career to online income to f*ck you money.
To understand why a job is a joke, do some life math.
Without a solid why, nothing makes sense.
The retirement age is 65. Our processed food consumption could shorten our 79-year average lifespan.
You spend 40 years working.
After 14 years of retirement, you die.
Am I alone in seeing the problem?
Life is too short to work a job forever, especially since most people hate theirs. After-hours skills are vital.
Money equals unrestricted power, f*ck you.
F*ck you money is the answer.
Jack Raines said it first. He says we can do anything with the money. Jack, a young rebel straight out of college, can travel and try new foods.
F*ck you money signifies not checking your bank account before buying.
F*ck you” money is pure, unadulterated freedom with no strings attached.
Jack claims you're rich when you rarely think about money.
Avoid confusion.
This doesn't imply you can buy a Lamborghini. It indicates your costs, income, lifestyle, and bank account are balanced.
Jack established an online portfolio while working for UPS in Atlanta, Georgia. So he gained boundless power.
The portion that many erroneously believe
Yes, you need internet abilities to make money, but they're not different from 9-5 talents.
Sahil Lavingia, Gumroad's creator, explains.
A job is a way to get paid to learn.
Mistreat your boss 9-5. Drain his skills. Defuse him. Love and leave him (eventually).
Find another employment if yours is hazardous. Pick an easy job. Make sure nothing sneaks into your 6-12 time slot.
The dumb game that makes you a sheep
A 9-5 job requires many job interviews throughout life.
You email your résumé to employers and apply for jobs through advertisements. This game makes you a sheep.
You're competing globally. Work-from-home makes the competition tougher. If you're not the cheapest, employers won't hire you.
After-hours online talents (say, 6 pm-12 pm) change the game. This graphic explains it better:
Online talents boost after-hours opportunities.
You go from wanting to be picked to picking yourself. More chances equal more money. Your f*ck you fund gets the extra cash.
A novel method of learning is essential.
College costs six figures and takes a lifetime to repay.
Informal learning is distinct. 6-12pm:
Observe the carefully controlled Twitter newsfeed.
Make use of Teachable and Gumroad's online courses.
Watch instructional YouTube videos
Look through the top Substack newsletters.
Informal learning is more effective because it's not obvious. It's fun to follow your curiosity and hobbies.
The majority of people lack one attitude. It's simple to learn.
One big impediment stands in the way of f*ck you money and time independence. So often.
Too many people plan after 6-12 hours. Dreaming. Big-thinkers. Strategically. They fill their calendar with meetings.
This is after-hours masturb*tion.
Sahil Bloom reminded me that a bias towards action will determine if this approach works for you.
The key isn't knowing what to do from 6-12 a.m. Trust yourself and develop abilities as you go. It's for building the parachute after you jump.
Sounds risky. We've eliminated the risk by finishing this process after hours while you work 9-5.
With no risk, you can have an I-don't-care attitude and still be successful.
When you choose to move forward, this occurs.
Once you try 9-5/6-12, you'll tell someone.
It's bad.
Few of us hang out with problem-solvers.
It's how much of society operates. So they make reasons so they can feel better about not giving you money.
Matthew Kobach told me chasing f*ck you money is easier with like-minded folks.
Without f*ck you money friends, loneliness will take over and you'll think you've messed up when you just need to keep going.
Steal this easy guideline
Let's act. No more fluffing and caressing.
1. Learn
If you detest your 9-5 talents or don't think they'll work online, get new ones. If you're skilled enough, continue.
Easlo recommends these skills:
Designer for Figma
Designer Canva
bubble creators
editor in Photoshop
Automation consultant for Zapier
Designer of Webflow
video editor Adobe
Ghostwriter for Twitter
Idea consultant
Artist in Blender Studio
2. Develop the ability
Every night from 6-12, apply the skill.
Practicing ghostwriting? Write someone's tweets for free. Do someone's website copy to learn copywriting. Get a website to the top of Google for a keyword to understand SEO.
Free practice is crucial. Your 9-5 pays the money, so work for free.
3. Take off stealthily like a badass
Another mistake. Sell to few. Don't be the best. Don't claim expertise.
Sell your new expertise to others behind you.
Two ways:
Using a digital good
By providing a service,
Point 1 also includes digital service examples. Digital products include eBooks, communities, courses, ad-supported podcasts, and templates. It's easy. Your 9-5 job involves one of these.
Take ideas from work.
Why? They'll steal your time for profit.
4. Iterate while feeling awful
First-time launches always fail. You'll feel terrible. Okay. Remember your 9-5?
Find improvements. Ask free and paying consumers what worked.
Multiple relaunches, each 1% better.
5. Discover more
Never stop learning. Improve your skill. Add a relevant skill. Learn copywriting if you write online.
After-hours students earn the most.
6. Continue
Repetition is key.
7. Make this one small change.
Consistently. The 6-12 momentum won't make you rich in 30 days; that's success p*rn.
Consistency helps wage slaves become f*ck you money. Most people can't switch between the two.
Putting everything together
It's easy. You're probably already doing some.
This formula explains why, how, and what to do. It's a 5th-grade-friendly blueprint. Good.
Reduce financial risk with your 9-to-5. Replace Netflix with 6-12 money-making talents.
Life is short; do whatever you want. Today.

Aaron Dinin, PhD
2 years ago
Are You Unintentionally Creating the Second Difficult Startup Type?
Most don't understand the issue until it's too late.
My first startup was what entrepreneurs call the hardest. A two-sided marketplace.
Two-sided marketplaces are the hardest startups because founders must solve the chicken or the egg conundrum.
A two-sided marketplace needs suppliers and buyers. Without suppliers, buyers won't come. Without buyers, suppliers won't come. An empty marketplace and a founder striving to gain momentum result.
My first venture made me a struggling founder seeking to achieve traction for a two-sided marketplace. The company failed, and I vowed never to start another like it.
I didn’t. Unfortunately, my second venture was almost as hard. It failed like the second-hardest startup.
What kind of startup is the second-hardest?
The second-hardest startup, which is almost as hard to develop, is rarely discussed in the startup community. Because of this, I predict more founders fail each year trying to develop the second-toughest startup than the hardest.
Fairly, I have no proof. I see many startups, so I have enough of firsthand experience. From what I've seen, for every entrepreneur developing a two-sided marketplace, I'll meet at least 10 building this other challenging startup.
I'll describe a startup I just met with its two co-founders to explain the second hardest sort of startup and why it's so hard. They created a financial literacy software for parents of high schoolers.
The issue appears plausible. Children struggle with money. Parents must teach financial responsibility. Problems?
It's possible.
Buyers and users are different.
Buyer-user mismatch.
The financial literacy app I described above targets parents. The parent doesn't utilize the app. Child is end-user. That may not seem like much, but it makes customer and user acquisition and onboarding difficult for founders.
The difficulty of a buyer-user imbalance
The company developing a product faces a substantial operational burden when the buyer and end customer are different. Consider classic firms where the buyer is the end user to appreciate that responsibility.
Entrepreneurs selling directly to end users must educate them about the product's benefits and use. Each demands a lot of time, effort, and resources.
Imagine selling a financial literacy app where the buyer and user are different. To make the first sale, the entrepreneur must establish all the items I mentioned above. After selling, the entrepreneur must supply a fresh set of resources to teach, educate, or train end-users.
Thus, a startup with a buyer-user mismatch must market, sell, and train two organizations at once, requiring twice the work with the same resources.
The second hardest startup is hard for reasons other than the chicken-or-the-egg conundrum. It takes a lot of creativity and luck to solve the chicken-or-egg conundrum.
The buyer-user mismatch problem cannot be overcome by innovation or luck. Buyer-user mismatches must be solved by force. Simply said, when a product buyer is different from an end-user, founders have a lot more work. If they can't work extra, their companies fail.

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.
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Jano le Roux
3 years ago
Here's What I Learned After 30 Days Analyzing Apple's Microcopy
Move people with tiny words.

Apple fanboy here.
Macs are awesome.
Their iPhones rock.
$19 cloths are great.
$999 stands are amazing.
I love Apple's microcopy even more.
It's like the marketing goddess bit into the Apple logo and blessed the world with microcopy.
I took on a 30-day micro-stalking mission.
Every time I caught myself wasting time on YouTube, I had to visit Apple’s website to learn the secrets of the marketing goddess herself.
We've learned. Golden apples are calling.
Cut the friction
Benefit-first, not commitment-first.
Brands lose customers through friction.
Most brands don't think like customers.
Brands want sales.
Brands want newsletter signups.
Here's their microcopy:
“Buy it now.”
“Sign up for our newsletter.”
Both are difficult. They ask for big commitments.
People are simple creatures. Want pleasure without commitment.
Apple nails this.
So, instead of highlighting the commitment, they highlight the benefit of the commitment.

Saving on the latest iPhone sounds easier than buying it. Everyone saves, but not everyone buys.
A subtle change in framing reduces friction.
Apple eliminates customer objections to reduce friction.

Less customer friction means simpler processes.
Apple's copy expertly reassures customers about shipping fees and not being home. Apple assures customers that returning faulty products is easy.
Apple knows that talking to a real person is the best way to reduce friction and improve their copy.
Always rhyme
Learn about fine rhyme.
Poets make things beautiful with rhyme.
Copywriters use rhyme to stand out.
Apple’s copywriters have mastered the art of corporate rhyme.
Two techniques are used.
1. Perfect rhyme
Here, rhymes are identical.

2. Imperfect rhyme
Here, rhyming sounds vary.

Apple prioritizes meaning over rhyme.
Apple never forces rhymes that don't fit.
It fits so well that the copy seems accidental.
Add alliteration
Alliteration always entertains.
Alliteration repeats initial sounds in nearby words.
Apple's copy uses alliteration like no other brand I've seen to create a rhyming effect or make the text more fun to read.
For example, in the sentence "Sam saw seven swans swimming," the initial "s" sound is repeated five times. This creates a pleasing rhythm.
Microcopy overuse is like pouring ketchup on a Michelin-star meal.
Alliteration creates a memorable phrase in copywriting. It's subtler than rhyme, and most people wouldn't notice; it simply resonates.

I love how Apple uses alliteration and contrast between "wonders" and "ease".
Assonance, or repeating vowels, isn't Apple's thing.
You ≠ Hero, Customer = Hero
Your brand shouldn't be the hero.
Because they'll be using your product or service, your customer should be the hero of your copywriting. With your help, they should feel like they can achieve their goals.
I love how Apple emphasizes what you can do with the machine in this microcopy.

It's divine how they position their tools as sidekicks to help below.

This one takes the cake:

Dialogue-style writing
Conversational copy engages.
Excellent copy Like sharing gum with a friend.
This helps build audience trust.

Apple does this by using natural connecting words like "so" and phrases like "But that's not all."
Snowclone-proof
The mother of all microcopy techniques.
A snowclone uses an existing phrase or sentence to create a new one. The new phrase or sentence uses the same structure but different words.
It’s usually a well know saying like:
To be or not to be.
This becomes a formula:
To _ or not to _.
Copywriters fill in the blanks with cause-related words. Example:
To click or not to click.

Apple turns "survival of the fittest" into "arrival of the fittest."
It's unexpected and surprises the reader.
So this was fun.
But my fun has just begun.
Microcopy is 21st-century poetry.
I came as an Apple fanboy.
I leave as an Apple fanatic.
Now I’m off to find an apple tree.
Cause you know how it goes.
(Apples, trees, etc.)
This post is a summary. Original post available here.

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

Tora Northman
3 years ago
Pixelmon NFTs are so bad, they are almost good!
Bored Apes prices continue to rise, HAPEBEAST launches, Invisible Friends hype continues to grow. Sadly, not all projects are as successful.
Of course, there are many factors to consider when buying an NFT. Is the project a scam? Will the reveal derail the project? Possibly, but when Pixelmon first teased its launch, it generated a lot of buzz.
With a primary sale mint price of 3 ETH ($8,100 USD), it started as an expensive project, with plenty of fans willing to invest in what was sold as a game. After it was revealed, it fell rapidly.
Why? It was overpromised and under delivered.
According to the project's creator[^1], the funds generated will be used to develop the artwork. "The Pixelmon reveal was wrong. This is what our Pixelmon look like in-game. "Despite the fud, I will not go anywhere," he wrote on Twitter. The goal remains. The funds will still be used to build our game. I will finish this project."
The project raised $70 million USD, but the NFTs buyers received were not the project's original teasers. Some call it "the worst NFT project ever," while others call it a complete scam.
But there's hope for some buyers. Kevin emerged from the ashes as the project was roasted over the fire.
A Minecraft character meets Salad Fingers - that's Kevin. He's a frog-like creature whose reveal was such a terrible NFT that it became part of history – and a meme.
If you're laughing at people paying $8K for a silly pixelated image, you might need to take it back. Precisely because of this, lucky holders who minted Kevin have been able to sell the now-memed NFT for over 8 ETH (around $24,000 USD), with some currently listed for 100 ETH.
Of course, Twitter has been awash in memes mocking those who invested in the project, because what else can you do when so many people lose money?
It's still unclear if the NFT project is a scam, but the team behind it was hired on Upwork. There's still hope for redemption, but Kevin's rise to fame appears to be the only positive outcome so far.
[^1] This is not the first time the creator (A 20-yo New Zealanders) has sought money via an online platform and had people claiming he under-delivered. He raised $74,000 on Kickstarter for a card game called Psycho Chicken. There are hundreds of comments on the Kickstarter project saying they haven't received the product and pleading for a refund or an update.
