More on Entrepreneurship/Creators

Sanjay Priyadarshi
2 years ago
Using Ruby code, a programmer created a $48,000,000,000 product that Elon Musk admired.
Unexpected Success
Shopify CEO and co-founder Tobias Lutke. Shopify is worth $48 billion.
World-renowned entrepreneur Tobi
Tobi never expected his first online snowboard business to become a multimillion-dollar software corporation.
Tobi founded Shopify to establish a 20-person company.
The publicly traded corporation employs over 10,000 people.
Here's Tobi Lutke's incredible story.
Elon Musk tweeted his admiration for the Shopify creator.
30-October-2019.
Musk praised Shopify founder Tobi Lutke on Twitter.
Happened:
Explore this programmer's journey.
What difficulties did Tobi experience as a young child?
Germany raised Tobi.
Tobi's parents realized he was smart but had trouble learning as a toddler.
Tobi was learning disabled.
Tobi struggled with school tests.
Tobi's learning impairments were undiagnosed.
Tobi struggled to read as a dyslexic.
Tobi also found school boring.
Germany's curriculum didn't inspire Tobi's curiosity.
“The curriculum in Germany was taught like here are all the solutions you might find useful later in life, spending very little time talking about the problem…If I don’t understand the problem I’m trying to solve, it’s very hard for me to learn about a solution to a problem.”
Studying computer programming
After tenth grade, Tobi decided school wasn't for him and joined a German apprenticeship program.
This curriculum taught Tobi software engineering.
He was an apprentice in a small Siemens subsidiary team.
Tobi worked with rebellious Siemens employees.
Team members impressed Tobi.
Tobi joined the team for this reason.
Tobi was pleased to get paid to write programming all day.
His life could not have been better.
Devoted to snowboarding
Tobi loved snowboarding.
He drove 5 hours to ski at his folks' house.
His friends traveled to the US to snowboard when he was older.
However, the cheap dollar conversion rate led them to Canada.
2000.
Tobi originally decided to snowboard instead than ski.
Snowboarding captivated him in Canada.
On the trip to Canada, Tobi encounters his wife.
Tobi meets his wife Fiona McKean on his first Canadian ski trip.
They maintained in touch after the trip.
Fiona moved to Germany after graduating.
Tobi was a startup coder.
Fiona found work in Germany.
Her work included editing, writing, and academics.
“We lived together for 10 months and then she told me that she need to go back for the master's program.”
With Fiona, Tobi immigrated to Canada.
Fiona invites Tobi.
Tobi agreed to move to Canada.
Programming helped Tobi move in with his girlfriend.
Tobi was an excellent programmer, therefore what he did in Germany could be done anywhere.
He worked remotely for his German employer in Canada.
Tobi struggled with remote work.
Due to poor communication.
No slack, so he used email.
Programmers had trouble emailing.
Tobi's startup was developing a browser.
After the dot-com crash, individuals left that startup.
It ended.
Tobi didn't intend to work for any major corporations.
Tobi left his startup.
He believed he had important skills for any huge corporation.
He refused to join a huge corporation.
Because of Siemens.
Tobi learned to write professional code and about himself while working at Siemens in Germany.
Siemens culture was odd.
Employees were distrustful.
Siemens' rigorous dress code implies that the corporation doesn't trust employees' attire.
It wasn't Tobi's place.
“There was so much bad with it that it just felt wrong…20-year-old Tobi would not have a career there.”
Focused only on snowboarding
Tobi lived in Ottawa with his girlfriend.
Canada is frigid in winter.
Ottawa's winters last.
Almost half a year.
Tobi wanted to do something worthwhile now.
So he snowboarded.
Tobi began snowboarding seriously.
He sought every snowboarding knowledge.
He researched the greatest snowboarding gear first.
He created big spreadsheets for snowboard-making technologies.
Tobi grew interested in selling snowboards while researching.
He intended to sell snowboards online.
He had no choice but to start his own company.
A small local company offered Tobi a job.
Interested.
He must sign papers to join the local company.
He needed a work permit when he signed the documents.
Tobi had no work permit.
He was allowed to stay in Canada while applying for permanent residency.
“I wasn’t illegal in the country, but my state didn’t give me a work permit. I talked to a lawyer and he told me it’s going to take a while until I get a permanent residency.”
Tobi's lawyer told him he cannot get a work visa without permanent residence.
His lawyer said something else intriguing.
Tobis lawyer advised him to start a business.
Tobi declined this local company's job offer because of this.
Tobi considered opening an internet store with his technical skills.
He sold snowboards online.
“I was thinking of setting up an online store software because I figured that would exist and use it as a way to sell snowboards…make money while snowboarding and hopefully have a good life.”
What brought Tobi and his co-founder together, and how did he support Tobi?
Tobi lived with his girlfriend's parents.
In Ottawa, Tobi encounters Scott Lake.
Scott was Tobis girlfriend's family friend and worked for Tobi's future employer.
Scott and Tobi snowboarded.
Tobi pitched Scott his snowboard sales software idea.
Scott liked the idea.
They planned a business together.
“I was looking after the technology and Scott was dealing with the business side…It was Scott who ended up developing relationships with vendors and doing all the business set-up.”
Issues they ran into when attempting to launch their business online
Neither could afford a long-term lease.
That prompted their online business idea.
They would open a store.
Tobi anticipated opening an internet store in a week.
Tobi seeks open-source software.
Most existing software was pricey.
Tobi and Scott couldn't afford pricey software.
“In 2004, I was sitting in front of my computer absolutely stunned realising that we hadn’t figured out how to create software for online stores.”
They required software to:
to upload snowboard images to the website.
people to look up the types of snowboards that were offered on the website. There must be a search feature in the software.
Online users transmit payments, and the merchant must receive them.
notifying vendors of the recently received order.
No online selling software existed at the time.
Online credit card payments were difficult.
How did they advance the software while keeping expenses down?
Tobi and Scott needed money to start selling snowboards.
Tobi and Scott funded their firm with savings.
“We both put money into the company…I think the capital we had was around CAD 20,000(Canadian Dollars).”
Despite investing their savings.
They minimized costs.
They tried to conserve.
No office rental.
They worked in several coffee shops.
Tobi lived rent-free at his girlfriend's parents.
He installed software in coffee cafes.
How were the software issues handled?
Tobi found no online snowboard sales software.
Two choices remained:
Change your mind and try something else.
Use his programming expertise to produce something that will aid in the expansion of this company.
Tobi knew he was the sole programmer working on such a project from the start.
“I had this realisation that I’m going to be the only programmer who has ever worked on this, so I don’t have to choose something that lots of people know. I can choose just the best tool for the job…There is been this programming language called Ruby which I just absolutely loved ”
Ruby was open-source and only had Japanese documentation.
Latin is the source code.
Tobi used Ruby twice.
He assumed he could pick the tool this time.
Why not build with Ruby?
How did they find their first time operating a business?
Tobi writes applications in Ruby.
He wrote the initial software version in 2.5 months.
Tobi and Scott founded Snowdevil to sell snowboards.
Tobi coded for 16 hours a day.
His lifestyle was unhealthy.
He enjoyed pizza and coke.
“I would never recommend this to anyone, but at the time there was nothing more interesting to me in the world.”
Their initial purchase and encounter with it
Tobi worked in cafes then.
“I was working in a coffee shop at this time and I remember everything about that day…At some time, while I was writing the software, I had to type the email that the software would send to tell me about the order.”
Tobi recalls everything.
He checked the order on his laptop at the coffee shop.
Pennsylvanian ordered snowboard.
Tobi walked home and called Scott. Tobi told Scott their first order.
They loved the order.
How were people made aware about Snowdevil?
2004 was very different.
Tobi and Scott attempted simple website advertising.
Google AdWords was new.
Ad clicks cost 20 cents.
Online snowboard stores were scarce at the time.
Google ads propelled the snowdevil brand.
Snowdevil prospered.
They swiftly recouped their original investment in the snowboard business because to its high profit margin.
Tobi and Scott struggled with inventories.
“Snowboards had really good profit margins…Our biggest problem was keeping inventory and getting it back…We were out of stock all the time.”
Selling snowboards returned their investment and saved them money.
They did not appoint a business manager.
They accomplished everything alone.
Sales dipped in the spring, but something magical happened.
Spring sales plummeted.
They considered stocking different boards.
They naturally wanted to add boards and grow the business.
However, magic occurred.
Tobi coded and improved software while running Snowdevil.
He modified software constantly. He wanted speedier software.
He experimented to make the software more resilient.
Tobi received emails requesting the Snowdevil license.
They intended to create something similar.
“I didn’t stop programming, I was just like Ok now let me try things, let me make it faster and try different approaches…Increasingly I got people sending me emails and asking me If I would like to licence snowdevil to them. People wanted to start something similar.”
Software or skateboards, your choice
Scott and Tobi had to choose a hobby in 2005.
They might sell alternative boards or use software.
The software was a no-brainer from demand.
Daniel Weinand is invited to join Tobi's business.
Tobis German best friend is Daniel.
Tobi and Scott chose to use the software.
Tobi and Scott kept the software service.
Tobi called Daniel to invite him to Canada to collaborate.
Scott and Tobi had quit snowboarding until then.
How was Shopify launched, and whence did the name come from?
The three chose Shopify.
Named from two words.
First:
Shop
Final part:
Simplify
Shopify
Shopify's crew has always had one goal:
creating software that would make it simple and easy for people to launch online storefronts.
Launched Shopify after raising money for the first time.
Shopify began fundraising in 2005.
First, they borrowed from family and friends.
They needed roughly $200k to run the company efficiently.
$200k was a lot then.
When questioned why they require so much money. Tobi told them to trust him with their goals. The team raised seed money from family and friends.
Shopify.com has a landing page. A demo of their goal was on the landing page.
In 2006, Shopify had about 4,000 emails.
Shopify rented an Ottawa office.
“We sent a blast of emails…Some people signed up just to try it out, which was exciting.”
How things developed after Scott left the company
Shopify co-founder Scott Lake left in 2008.
Scott was CEO.
“He(Scott) realized at some point that where the software industry was going, most of the people who were the CEOs were actually the highly technical person on the founding team.”
Scott leaving the company worried Tobi.
Tobis worried about finding a new CEO.
To Tobi:
A great VC will have the network to identify the perfect CEO for your firm.
Tobi started visiting Silicon Valley to meet with venture capitalists to recruit a CEO.
Initially visiting Silicon Valley
Tobi came to Silicon Valley to start a 20-person company.
This company creates eCommerce store software.
Tobi never wanted a big corporation. He desired a fulfilling existence.
“I stayed in a hostel in the Bay Area. I had one roommate who was also a computer programmer. I bought a bicycle on Craiglist. I was there for a week, but ended up staying two and a half weeks.”
Tobi arrived unprepared.
When venture capitalists asked him business questions.
He answered few queries.
Tobi didn't comprehend VC meetings' terminology.
He wrote the terms down and looked them up.
Some were fascinated after he couldn't answer all these queries.
“I ended up getting the kind of term sheets people dream about…All the offers were conditional on moving our company to Silicon Valley.”
Canada received Tobi.
He wanted to consult his team before deciding. Shopify had five employees at the time.
2008.
A global recession greeted Tobi in Canada. The recession hurt the market.
His term sheets were useless.
The economic downturn in the world provided Shopify with a fantastic opportunity.
The global recession caused significant job losses.
Fired employees had several ideas.
They wanted online stores.
Entrepreneurship was desired. They wanted to quit work.
People took risks and tried new things during the global slump.
Shopify subscribers skyrocketed during the recession.
“In 2009, the company reached neutral cash flow for the first time…We were in a position to think about long-term investments, such as infrastructure projects.”
Then, Tobi Lutke became CEO.
How did Tobi perform as the company's CEO?
“I wasn’t good. My team was very patient with me, but I had a lot to learn…It’s a very subtle job.”
2009–2010.
Tobi limited the company's potential.
He deliberately restrained company growth.
Tobi had one costly problem:
Whether Shopify is a venture or a lifestyle business.
The company's annual revenue approached $1 million.
Tobi battled with the firm and himself despite good revenue.
His wife was supportive, but the responsibility was crushing him.
“It’s a crushing responsibility…People had families and kids…I just couldn’t believe what was going on…My father-in-law gave me money to cover the payroll and it was his life-saving.”
Throughout this trip, everyone supported Tobi.
They believed it.
$7 million in donations received
Tobi couldn't decide if this was a lifestyle or a business.
Shopify struggled with marketing then.
Later, Tobi tried 5 marketing methods.
He told himself that if any marketing method greatly increased their growth, he would call it a venture, otherwise a lifestyle.
The Shopify crew brainstormed and voted on marketing concepts.
Tested.
“Every single idea worked…We did Adwords, published a book on the concept, sponsored a podcast and all the ones we tracked worked.”
To Silicon Valley once more
Shopify marketing concepts worked once.
Tobi returned to Silicon Valley to pitch investors.
He raised $7 million, valuing Shopify at $25 million.
All investors had board seats.
“I find it very helpful…I always had a fantastic relationship with everyone who’s invested in my company…I told them straight that I am not going to pretend I know things, I want you to help me.”
Tobi developed skills via running Shopify.
Shopify had 20 employees.
Leaving his wife's parents' home
Tobi left his wife's parents in 2014.
Tobi had a child.
Shopify has 80,000 customers and 300 staff in 2013.
Public offering in 2015
Shopify investors went public in 2015.
Shopify powers 4.1 million e-Commerce sites.
Shopify stores are 65% US-based.
It is currently valued at $48 billion.

Victoria Kurichenko
3 years ago
Updates From Google For Content Producers What You Should Know Is This
People-first update.
Every Google upgrade causes website owners to panic.
Some have just recovered from previous algorithm tweaks and resumed content development.
If you follow Google's Webmaster rules, you shouldn't fear its adjustments.
Everyone has a view of them. Miscommunication and confusion result.
Now, for some (hopefully) exciting news.
Google tweeted on August 18, 2022 about a fresh content update.
This change is another Google effort to remove low-quality, repetitive, and AI-generated content.
The algorithm generates and analyzes search results, not humans.
Google spends a lot to teach its algorithm what searchers want. Intent isn't always clear.
Google's content update aims to:
“… ensure people see more original, helpful content written by people, for people, in search results.”
Isn't it a noble goal?
However, what does it mean for content creators and website owners?
How can you ensure you’re creating content that will be successful after the updates roll out?
Let's first define people-first content.
What does "people-first-content" mean?
If asked, I'd say information written to answer queries and solve problems.
Like others, I read it from the term.
Content creators and marketers disagree. They need more information to follow recommendations.
Google gives explicit instructions for creating people-first content.
According to Google, if you answer yes to the following questions, you have a people-first attitude.
Do you have customers who might find your content useful if they contacted you directly?
Does your content show the breadth of your knowledge?
Do you have a niche or a focus for your website?
After reading your content, will readers learn something new to aid them in achieving their goals?
Are readers happy after reading your content?
Have you been adhering to Google's fundamental updates and product reviews?
As an SEO writer, I'm not scared.
I’ve been following these rules consciously while creating content for my website. That’s why it’s been steadily growing despite me publishing just one or two stories a month.
If you avoid AI-generated text and redundant, shallow material, your website won't suffer.
If you use unscrupulous methods to boost your website's traffic, including link buying or keyword stuffing, stop. Google is getting smarter and will find and punish your site eventually.
For those who say, “SEO is no longer working,” I dedicated the whole paragraph below.
This does not imply that SEO is obsolete.
Google:
“People-first content creators focus on creating satisfying content, while also utilizing SEO best practices to bring searchers additional value.”
The official helpful content update page lists two people-first content components:
meeting user needs
best practices for SEO
Always read official guidelines, not unsolicited suggestions.
SEO will work till search engines die.
How to use the update
Google said the changes will arrive in August 2022.
They pledged to post updates on Google's search ranking updates page.
Google also tweets this info. If you haven't followed it already, I recommend it.
Ranking adjustments could take two weeks and will affect English searches internationally initially.
Google affirmed plans to extend to other languages.
If you own a website, monitor your rankings and traffic to see if it's affected.

cdixon
3 years ago
2000s Toys, Secrets, and Cycles
During the dot-com bust, I started my internet career. People used the internet intermittently to check email, plan travel, and do research. The average internet user spent 30 minutes online a day, compared to 7 today. To use the internet, you had to "log on" (most people still used dial-up), unlike today's always-on, high-speed mobile internet. In 2001, Amazon's market cap was $2.2B, 1/500th of what it is today. A study asked Americans if they'd adopt broadband, and most said no. They didn't see a need to speed up email, the most popular internet use. The National Academy of Sciences ranked the internet 13th among the 100 greatest inventions, below radio and phones. The internet was a cool invention, but it had limited uses and wasn't a good place to build a business.
A small but growing movement of developers and founders believed the internet could be more than a read-only medium, allowing anyone to create and publish. This is web 2. The runner up name was read-write web. (These terms were used in prominent publications and conferences.)
Web 2 concepts included letting users publish whatever they want ("user generated content" was a buzzword), social graphs, APIs and mashups (what we call composability today), and tagging over hierarchical navigation. Technical innovations occurred. A seemingly simple but important one was dynamically updating web pages without reloading. This is now how people expect web apps to work. Mobile devices that could access the web were niche (I was an avid Sidekick user).
The contrast between what smart founders and engineers discussed over dinner and on weekends and what the mainstream tech world took seriously during the week was striking. Enterprise security appliances, essentially preloaded servers with security software, were a popular trend. Many of the same people would talk about "serious" products at work, then talk about consumer internet products and web 2. It was tech's biggest news. Web 2 products were seen as toys, not real businesses. They were hobbies, not work-related.
There's a strong correlation between rich product design spaces and what smart people find interesting, which took me some time to learn and led to blog posts like "The next big thing will start out looking like a toy" Web 2's novel product design possibilities sparked dinner and weekend conversations. Imagine combining these features. What if you used this pattern elsewhere? What new product ideas are next? This excited people. "Serious stuff" like security appliances seemed more limited.
The small and passionate web 2 community also stood out. I attended the first New York Tech meetup in 2004. Everyone fit in Meetup's small conference room. Late at night, people demoed their software and chatted. I have old friends. Sometimes I get asked how I first met old friends like Fred Wilson and Alexis Ohanian. These topics didn't interest many people, especially on the east coast. We were friends. Real community. Alex Rampell, who now works with me at a16z, is someone I met in 2003 when a friend said, "Hey, I met someone else interested in consumer internet." Rare. People were focused and enthusiastic. Revolution seemed imminent. We knew a secret nobody else did.
My web 2 startup was called SiteAdvisor. When my co-founders and I started developing the idea in 2003, web security was out of control. Phishing and spyware were common on Internet Explorer PCs. SiteAdvisor was designed to warn users about security threats like phishing and spyware, and then, using web 2 concepts like user-generated reviews, add more subjective judgments (similar to what TrustPilot seems to do today). This staged approach was common at the time; I called it "Come for the tool, stay for the network." We built APIs, encouraged mashups, and did SEO marketing.
Yahoo's 2005 acquisitions of Flickr and Delicious boosted web 2 in 2005. By today's standards, the amounts were small, around $30M each, but it was a signal. Web 2 was assumed to be a fun hobby, a way to build cool stuff, but not a business. Yahoo was a savvy company that said it would make web 2 a priority.
As I recall, that's when web 2 started becoming mainstream tech. Early web 2 founders transitioned successfully. Other entrepreneurs built on the early enthusiasts' work. Competition shifted from ideation to execution. You had to decide if you wanted to be an idealistic indie bar band or a pragmatic stadium band.
Web 2 was booming in 2007 Facebook passed 10M users, Twitter grew and got VC funding, and Google bought YouTube. The 2008 financial crisis tested entrepreneurs' resolve. Smart people predicted another great depression as tech funding dried up.
Many people struggled during the recession. 2008-2011 was a golden age for startups. By 2009, talented founders were flooding Apple's iPhone app store. Mobile apps were booming. Uber, Venmo, Snap, and Instagram were all founded between 2009 and 2011. Social media (which had replaced web 2), cloud computing (which enabled apps to scale server side), and smartphones converged. Even if social, cloud, and mobile improve linearly, the combination could improve exponentially.
This chart shows how I view product and financial cycles. Product and financial cycles evolve separately. The Nasdaq index is a proxy for the financial sentiment. Financial sentiment wildly fluctuates.
Next row shows iconic startup or product years. Bottom-row product cycles dictate timing. Product cycles are more predictable than financial cycles because they follow internal logic. In the incubation phase, enthusiasts build products for other enthusiasts on nights and weekends. When the right mix of technology, talent, and community knowledge arrives, products go mainstream. (I show the biggest tech cycles in the chart, but smaller ones happen, like web 2 in the 2000s and fintech and SaaS in the 2010s.)

Tech has changed since the 2000s. Few tech giants dominate the internet, exerting economic and cultural influence. In the 2000s, web 2 was ignored or dismissed as trivial. Entrenched interests respond aggressively to new movements that could threaten them. Creative patterns from the 2000s continue today, driven by enthusiasts who see possibilities where others don't. Know where to look. Crypto and web 3 are where I'd start.
Today's negative financial sentiment reminds me of 2008. If we face a prolonged downturn, we can learn from 2008 by preserving capital and focusing on the long term. Keep an eye on the product cycle. Smart people are interested in things with product potential. This becomes true. Toys become necessities. Hobbies become mainstream. Optimists build the future, not cynics.
Full article is available here
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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
JEFF JOHN ROBERTS
2 years ago
What just happened in cryptocurrency? A plain-English Q&A about Binance's FTX takedown.
Crypto people have witnessed things. They've seen big hacks, mind-boggling swindles, and amazing successes. They've never seen a day like Tuesday, when the world's largest crypto exchange murdered its closest competition.
Here's a primer on Binance and FTX's lunacy and why it matters if you're new to crypto.
What happened?
CZ, a shrewd Chinese-Canadian billionaire, runs Binance. FTX, a newcomer, has challenged Binance in recent years. SBF (Sam Bankman-Fried)—a young American with wild hair—founded FTX (initials are a thing in crypto).
Last weekend, CZ complained about SBF's lobbying and then exploited Binance's market power to attack his competition.
How did CZ do that?
CZ invested in SBF's new cryptocurrency exchange when they were friends. CZ sold his investment in FTX for FTT when he no longer wanted it. FTX clients utilize those tokens to get trade discounts, although they are less liquid than Bitcoin.
SBF made a mistake by providing CZ just too many FTT tokens, giving him control over FTX. It's like Pepsi handing Coca-Cola a lot of stock it could sell at any time. CZ got upset with SBF and flooded the market with FTT tokens.
SBF owns a trading fund with many FTT tokens, therefore this was catastrophic. SBF sought to defend FTT's worth by selling other assets to buy up the FTT tokens flooding the market, but it didn't succeed, and as FTT's value plummeted, his liabilities exceeded his assets. By Tuesday, his companies were insolvent, so he sold them to his competition.
Crazy. How could CZ do that?
CZ likely did this to crush a rising competition. It was also personal. In recent months, regulators have been tough toward the crypto business, and Binance and FTX have been trying to stay on their good side. CZ believed SBF was poisoning U.S. authorities by saying CZ was linked to China, so CZ took retribution.
“We supported previously, but we won't pretend to make love after divorce. We're neutral. But we won't assist people that push against other industry players behind their backs," CZ stated in a tragic tweet on Sunday. He crushed his rival's company two days later.
So does Binance now own FTX?
No. Not yet. CZ has only stated that Binance signed a "letter of intent" to acquire FTX. CZ and SBF say Binance will protect FTX consumers' funds.
Who’s to blame?
You could blame CZ for using his control over FTX to destroy it. SBF is also being criticized for not disclosing the full overlap between FTX and his trading company, which controlled plenty of FTT. If he had been upfront, someone might have warned FTX about this vulnerability earlier, preventing this mess.
Others have alleged that SBF utilized customer monies to patch flaws in his enterprises' balance accounts. That happened to multiple crypto startups that collapsed this spring, which is unfortunate. These are allegations, not proof.
Why does this matter? Isn't this common in crypto?
Crypto is notorious for shady executives and pranks. FTX is the second-largest crypto business, and SBF was largely considered as the industry's golden boy who would help it get on authorities' good side. Thus far.
Does this affect cryptocurrency prices?
Short-term, it's bad. Prices fell on suspicions that FTX was in peril, then rallied when Binance rescued it, only to fall again later on Tuesday.
These occurrences have hurt FTT and SBF's Solana token. It appears like a huge token selloff is affecting the rest of the market. Bitcoin fell 10% and Ethereum 15%, which is bad but not catastrophic for the two largest coins by market cap.

Isaiah McCall
2 years ago
There is a new global currency emerging, but it is not bitcoin.
America should avoid BRICS
Vladimir Putin has watched videos of Muammar Gaddafi's CIA-backed demise.
Gaddafi...
Thief.
Did you know Gaddafi wanted a gold-backed dinar for Africa? Because he considered our global financial system was a Ponzi scheme, he wanted to discontinue trading oil in US dollars.
Or, Gaddafi's Libya enjoyed Africa's highest quality of living before becoming freed. Pictured:
Vladimir Putin is a nasty guy, but he had his reasons for not mentioning NATO assisting Ukraine in resisting US imperialism. Nobody tells you. Sure.
The US dollar's corruption post-2008, debasement by quantitative easing, and lack of value are key factors. BRICS will replace the dollar.
BRICS aren't bricks.
Economy-related.
Brazil, Russia, India, China, and South Africa have cooperated for 14 years to fight U.S. hegemony with a new international currency: BRICS.
BRICS is mostly comical. Now. Saudi Arabia, the second-largest oil hegemon, wants to join.
So what?
The New World Currency is BRICS
Russia was kicked out of G8 for its aggressiveness in Crimea in 2014.
It's now G7.
No biggie, said Putin, he said, and I quote, “Bon appetite.”
He was prepared. China, India, and Brazil lead the New World Order.
Together, they constitute 40% of the world's population and, according to the IMF, 50% of the world's GDP by 2030.
Here’s what the BRICS president Marcos Prado Troyjo had to say earlier this year about no longer needing the US dollar: “We have implemented the mechanism of mutual settlements in rubles and rupees, and there is no need for our countries to use the dollar in mutual settlements. And today a similar mechanism of mutual settlements in rubles and yuan is being developed by China.”
Ick. That's D.C. and NYC warmongers licking their chops for WW3 nasty.
Here's a lovely picture of BRICS to relax you:
If Saudi Arabia joins BRICS, as President Mohammed Bin Salman has expressed interest, a majority of the Middle East will have joined forces to construct a new world order not based on the US currency.
I'm not sure of the new acronym.
SBRICSS? CIRBSS? CRIBSS?
The Reason America Is Harvesting What It Sowed
BRICS began 14 years ago.
14 years ago, what occurred? Concentrate. It involved CDOs, bad subprime mortgages, and Wall Street quants crunching numbers.
2008 recession
When two nations trade, they do so in US dollars, not Euros or gold.
What happened when 2008, an avoidable crisis caused by US banks' cupidity and ignorance, what happened?
Everyone WORLDWIDE felt the pain.
Mostly due to corporate America's avarice.
This should have been a warning that China and Russia had enough of our bs. Like when France sent a battleship to America after Nixon scrapped the gold standard. The US was warned to shape up or be dethroned (or at least try).
Nixon improved in 1971. Kinda. Invented PetroDollar.
Another BS system that unfairly favors America and possibly pushed Russia, China, and Saudi Arabia into BRICS.
The PetroDollar forces oil-exporting nations to trade in US dollars and invest in US Treasury bonds. Brilliant. Genius evil.
Our misdeeds are:
In conflicts that are not its concern, the USA uses the global reserve currency as a weapon.
Targeted nations abandon the dollar, and rightfully so, as do nations that depend on them for trade in vital resources.
The dollar's position as the world's reserve currency is in jeopardy, which could have disastrous economic effects.
Although we have actually sown our own doom, we appear astonished. According to the Bible, whomever sows to appease his sinful nature will reap destruction from that nature whereas whoever sows to appease the Spirit will reap eternal life from the Spirit.
Americans, even our leaders, lack caution and delayed pleasure. When our unsustainable systems fail, we double down. Bailouts of the banks in 2008 were myopic, puerile, and another nail in America's hegemony.
America has screwed everyone.
We're unpopular.
The BRICS's future
It's happened before.
Saddam Hussein sold oil in Euros in 2000, and the US invaded Iraq a month later. The media has devalued the word conspiracy. The Iraq conspiracy.
There were no WMDs, but NYT journalists like Judy Miller drove Americans into a warmongering frenzy because Saddam would ruin the PetroDollar. Does anyone recall that this war spawned ISIS?
I think America has done good for the world. You can make a convincing case that we're many people's villain.
Learn more in Confessions of an Economic Hitman, The Devil's Chessboard, or Tyranny of the Federal Reserve. Or ignore it. That's easier.
We, America, should extend an olive branch, ask for forgiveness, and learn from our faults, as the Tao Te Ching advises. Unlikely. Our population is apathetic and stupid, and our government is corrupt.
Argentina, Iran, Egypt, and Turkey have also indicated interest in joining BRICS. They're also considering making it gold-backed, making it a new world reserve currency.
You should pay attention.
Thanks for reading!