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
Sam Hickmann
4 years ago
A quick guide to formatting your text on INTΞGRITY
[06/20/2022 update] We have now implemented a powerful text editor, but you can still use markdown.
Markdown:
Headers
SYNTAX:
# This is a heading 1
## This is a heading 2
### This is a heading 3
#### This is a heading 4
RESULT:
This is a heading 1
This is a heading 2
This is a heading 3
This is a heading 4
Emphasis
SYNTAX:
**This text will be bold**
~~Strikethrough~~
*You **can** combine them*
RESULT:
This text will be italic
This text will be bold
You can combine them
Images
SYNTAX:
RESULT:
Videos
SYNTAX:
https://www.youtube.com/watch?v=7KXGZAEWzn0
RESULT:
Links
SYNTAX:
[Int3grity website](https://www.int3grity.com)
RESULT:
Tweets
SYNTAX:
https://twitter.com/samhickmann/status/1503800505864130561
RESULT:
Blockquotes
SYNTAX:
> Human beings face ever more complex and urgent problems, and their effectiveness in dealing with these problems is a matter that is critical to the stability and continued progress of society. \- Doug Engelbart, 1961
RESULT:
Human beings face ever more complex and urgent problems, and their effectiveness in dealing with these problems is a matter that is critical to the stability and continued progress of society. - Doug Engelbart, 1961
Inline code
SYNTAX:
Text inside `backticks` on a line will be formatted like code.
RESULT:
Text inside backticks on a line will be formatted like code.
Code blocks
SYNTAX:
'''js
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
'''
RESULT:
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
Maths
We support LaTex to typeset math. We recommend reading the full documentation on the official website
SYNTAX:
$$[x^n+y^n=z^n]$$
RESULT:
[x^n+y^n=z^n]
Tables
SYNTAX:
| header a | header b |
| ---- | ---- |
| row 1 col 1 | row 1 col 2 |
RESULT:
| header a | header b | header c |
|---|---|---|
| row 1 col 1 | row 1 col 2 | row 1 col 3 |
Caleb Naysmith
3 years ago Draft
A Myth: Decentralization
It’s simply not conceivable, or at least not credible.
One of the most touted selling points of Crypto has always been this grandiose idea of decentralization. Bitcoin first arose in 2009 after the housing crisis and subsequent crash that came with it. It aimed to solve this supposed issue of centralization. Nobody “owns” Bitcoin in theory, so the idea then goes that it won’t be subject to the same downfalls that led to the 2008 crash or similarly speculative events that led to the 2008 disaster. The issue is the banks, not the human nature associated with the greedy individuals running them.
Subsequent blockchains have attempted to fix many of the issues of Bitcoin by increasing capacity, decreasing the costs and processing times associated with Bitcoin, and expanding what can be done with their blockchains. Since nobody owns Bitcoin, it hasn’t really been able to be expanded on. You have people like Vitalk Buterin, however, that actively work on Ethereum though.
The leap from Bitcoin to Ethereum was a massive leap toward centralization, and the trend has only gotten worse. In fact, crypto has since become almost exclusively centralized in recent years.
Decentralization is only good in theory
It’s a good idea. In fact, it’s a wonderful idea. However, like other utopian societies, individuals misjudge human nature and greed. In a perfect world, decentralization would certainly be a wonderful idea because sure, people may function as their own banks, move payments immediately, remain anonymous, and so on. However, underneath this are a couple issues:
You can already send money instantaneously today.
They are not decentralized.
Decentralization is a bad idea.
Being your own bank is a stupid move.
Let’s break these down. Some are quite simple, but lets have a look.
Sending money right away
One thing with crypto is the idea that you can send payments instantly. This has pretty much been entirely solved in current times. You can transmit significant sums of money instantly for a nominal cost and it’s instantaneously cleared. Venmo was launched in 2009 and has since increased to prominence, and currently is on most people's phones. I can directly send ANY amount of money quickly from my bank to another person's Venmo account.
Comparing that with ETH and Bitcoin, Venmo wins all around. I can send money to someone for free instantly in dollars and the only fee paid is optional depending on when you want it.
Both Bitcoin and Ethereum are subject to demand. If the blockchains have a lot of people trying to process transactions fee’s go up, and the time that it takes to receive your crypto takes longer. When Ethereum gets bad, people have reported spending several thousand of dollars on just 1 transaction.
These transactions take place via “miners” bundling and confirming transactions, then recording them on the blockchain to confirm that the transaction did indeed happen. They charge fees to do this and are also paid in Bitcoin/ETH. When a transaction is confirmed, it's then sent to the other users wallet. This within itself is subject to lots of controversy because each transaction needs to be confirmed 6 times, this takes massive amounts of power, and most of the power is wasted because this is an adversarial system in which the person that mines the transaction gets paid, and everyone else is out of luck. Also, these could theoretically be subject to a “51% attack” in which anyone with over 51% of the mining hash rate could effectively control all of the transactions, and reverse transactions while keeping the BTC resulting in “double spending”.
There are tons of other issues with this, but essentially it means: They rely on these third parties to confirm the transactions. Without people confirming these transactions, Bitcoin stalls completely, and if anyone becomes too dominant they can effectively control bitcoin.
Not to mention, these transactions are in Bitcoin and ETH, not dollars. So, you need to convert them to dollars still, and that's several more transactions, and likely to take several days anyway as the centralized exchange needs to send you the money by traditional methods.
They are not distributed
That takes me to the following point. This isn’t decentralized, at all. Bitcoin is the closest it gets because Satoshi basically closed it to new upgrades, although its still subject to:
Whales
Miners
It’s vital to realize that these are often the same folks. While whales aren’t centralized entities typically, they can considerably effect the price and outcome of Bitcoin. If the largest wallets holding as much as 1 million BTC were to sell, it’d effectively collapse the price perhaps beyond repair. However, Bitcoin can and is pretty much controlled by the miners. Further, Bitcoin is more like an oligarchy than decentralized. It’s been effectively used to make the rich richer, and both the mining and price is impacted by the rich. The overwhelming minority of those actually using it are retail investors. The retail investors are basically never the ones generating money from it either.
As far as ETH and other cryptos go, there is realistically 0 case for them being decentralized. Vitalik could not only kill it but even walking away from it would likely lead to a significant decline. It has tons of issues right now that Vitalik has promised to fix with the eventual Ethereum 2.0., and stepping away from it wouldn’t help.
Most tokens as well are generally tied to some promise of future developments and creators. The same is true for most NFT projects. The reason 99% of crypto and NFT projects fail is because they failed to deliver on various promises or bad dev teams, or poor innovation, or the founders just straight up stole from everyone. I could go more in-depth than this but go find any project and if there is a dev team, company, or person tied to it then it's likely, not decentralized. The success of that project is directly tied to the dev team, and if they wanted to, most hold large wallets and could sell it all off effectively killing the project. Not to mention, any crypto project that doesn’t have a locked contract can 100% be completely rugged and they can run off with all of the money.
Decentralization is undesirable
Even if they were decentralized then it would not be a good thing. The graphic above indicates this is effectively a rich person’s unregulated playground… so it’s exactly like… the very issue it tried to solve?
Not to mention, it’s supposedly meant to prevent things like 2008, but is regularly subjected to 50–90% drawdowns in value? Back when Bitcoin was only known in niche parts of the dark web and illegal markets, it would regularly drop as much as 90% and has a long history of massive drawdowns.
The majority of crypto is blatant scams, and ALL of crypto is a “zero” or “negative” sum game in that it relies on the next person buying for people to make money. This is not a good thing. This has yet to solve any issues around what caused the 2008 crisis. Rather, it seemingly amplified all of the bad parts of it actually. Crypto is the ultimate speculative asset and realistically has no valuation metric. People invest in Apple because it has revenue and cash on hand. People invest in crypto purely for speculation. The lack of regulation or accountability means this is amplified to the most extreme degree where anything goes: Fraud, deception, pump and dumps, scams, etc. This results in a pure speculative madhouse where, unsurprisingly, only the rich win. Not only that but the deck is massively stacked in against the everyday investor because you can’t do a pump and dump without money.
At the heart of all of this is still the same issues: greed and human nature. However, in setting out to solve the issues that allowed 2008 to happen, they made something that literally took all of the bad parts of 2008 and then amplified it. 2008, similarly, was due to greed and human nature but was allowed to happen due to lack of oversite, rich people's excessive leverage over the poor, and excessive speculation. Crypto trades SOLELY on human emotion, has 0 oversite, is pure speculation, and the power dynamic is just as bad or worse.
Why should each individual be their own bank?
This is the last one, and it's short and basic. Why do we want people functioning as their own bank? Everything we do relies on another person. Without the internet, and internet providers there is no crypto. We don’t have people functioning as their own home and car manufacturers or internet service providers. Sure, you might specialize in some of these things, but masquerading as your own bank is a horrible idea.
I am not in the banking industry so I don’t know all the issues with banking. Most people aren’t in banking or crypto, so they don’t know the ENDLESS scams associated with it, and they are bound to lose their money eventually.
If you appreciate this article and want to read more from me and authors like me, without any limits, consider buying me a coffee: buymeacoffee.com/calebnaysmith
Marco Manoppo
3 years ago
Failures of DCG and Genesis
Don't sleep with your own sister.
70% of lottery winners go broke within five years. You've heard the last one. People who got rich quickly without setbacks and hard work often lose it all. My father said, "Easy money is easily lost," and a wealthy friend who owns a family office said, "The first generation makes it, the second generation spends it, and the third generation blows it."
This is evident. Corrupt politicians in developing countries live lavishly, buying their third wives' fifth Hermès bag and celebrating New Year's at The Brando Resort. A successful businessperson from humble beginnings is more conservative with money. More so if they're atom-based, not bit-based. They value money.
Crypto can "feel" easy. I have nothing against capital market investing. The global financial system is shady, but that's another topic. The problem started when those who took advantage of easy money started affecting other businesses. VCs did minimal due diligence on FTX because they needed deal flow and returns for their LPs. Lenders did minimum diligence and underwrote ludicrous loans to 3AC because they needed revenue.
Alameda (hence FTX) and 3AC made "easy money" Genesis and DCG aren't. Their businesses are more conventional, but they underestimated how "easy money" can hurt them.
Genesis has been the victim of easy money hubris and insolvency, losing $1 billion+ to 3AC and $200M to FTX. We discuss the implications for the broader crypto market.
Here are the quick takeaways:
Genesis is one of the largest and most notable crypto lenders and prime brokerage firms.
DCG and Genesis have done related party transactions, which can be done right but is a bad practice.
Genesis owes DCG $1.5 billion+.
If DCG unwinds Grayscale's GBTC, $9-10 billion in BTC will hit the market.
DCG will survive Genesis.
What happened?
Let's recap the FTX shenanigan from two weeks ago. Shenanigans! Delphi's tweet sums up the craziness. Genesis has $175M in FTX.
Cred's timeline: I hate bad crisis management. Yes, admitting their balance sheet hole right away might've sparked more panic, and there's no easy way to convey your trouble, but no one ever learns.
By November 23, rumors circulated online that the problem could affect Genesis' parent company, DCG. To address this, Barry Silbert, Founder, and CEO of DCG released a statement to shareholders.
A few things are confirmed thanks to this statement.
DCG owes $1.5 billion+ to Genesis.
$500M is due in 6 months, and the rest is due in 2032 (yes, that’s not a typo).
Unless Barry raises new cash, his last-ditch efforts to repay the money will likely push the crypto market lower.
Half a year of GBTC fees is approximately $100M.
They can pay $500M with GBTC.
With profits, sell another port.
Genesis has hired a restructuring adviser, indicating it is in trouble.
Rehypothecation
Every crypto problem in the past year seems to be rehypothecation between related parties, excessive leverage, hubris, and the removal of the money printer. The Bankless guys provided a chart showing 2021 crypto yield.
In June 2022, @DataFinnovation published a great investigation about 3AC and DCG. Here's a summary.
3AC borrowed BTC from Genesis and pledged it to create Grayscale's GBTC shares.
3AC uses GBTC to borrow more money from Genesis.
This lets 3AC leverage their capital.
3AC's strategy made sense because GBTC had a premium, creating "free money."
GBTC's discount and LUNA's implosion caused problems.
3AC lost its loan money in LUNA.
Margin called on 3ACs' GBTC collateral.
DCG bought GBTC to avoid a systemic collapse and a larger discount.
Genesis lost too much money because 3AC can't pay back its loan. DCG "saved" Genesis, but the FTX collapse hurt Genesis further, forcing DCG and Genesis to seek external funding.
bruh…
Learning Experience
Co-borrowing. Unnecessary rehypothecation. Extra space. Governance disaster. Greed, hubris. Crypto has repeatedly shown it can recreate traditional financial system disasters quickly. Working in crypto is one of the best ways to learn crazy financial tricks people will do for a quick buck much faster than if you dabble in traditional finance.
Moving Forward
I think the crypto industry needs to consider its future. This is especially true for professionals. I'm not trying to scare you. In 2018 and 2020, I had doubts. No doubts now. Detailing the crypto industry's potential outcomes helped me gain certainty and confidence in its future. This includes VCs' benefits and talking points during the bull market, as well as what would happen if government regulations became hostile, etc. Even if that happens, I'm certain. This is permanent. I may write a post about that soon.
Sincerely,
M.
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Katharine Valentino
3 years ago
A Gun-toting Teacher Is Like a Cook With Rat Poison
Pink or blue AR-15s?
A teacher teaches; a gun kills. Killing isn't teaching. Killing is opposite of teaching.
Without 27 school shootings this year, we wouldn't be talking about arming teachers. Gun makers, distributors, and the NRA cause most school shootings. Gun makers, distributors, and the NRA wouldn't be huge business if weapons weren't profitable.
Guns, ammo, body armor, holsters, concealed carriers, bore sights, cleaner kits, spare magazines and speed loaders, gun safes, and ear protection are sold. And more guns.
And lots more profit.
Guns aren't bread. You eat a loaf of bread in a week or so and then must buy more. Bread makers will make money. Winchester 94.30–30 1899 Lever Action Rifle from 1894 still kills. (For safety, I won't link to the ad.) Gun makers don't object if you collect antique weapons, but they need you to buy the latest, in-style killing machine. The youngster who killed 19 students and 2 teachers at Robb Elementary School in Uvalde, Texas, used an AR-15. Better yet, two.
Salvador Ramos, the Robb Elementary shooter, is a "killing influencer" He pushes consumers to buy items, which benefits manufacturers and distributors. Like every previous AR-15 influencer, he profits Colt, the rifle's manufacturer, and 52,779 gun dealers in the U.S. Ramos and other AR-15 influences make us fear for our safety and our children's. Fearing for our safety, we acquire 20 million firearms a year and live in a gun culture.
So now at school, we want to arm teachers.
Consider. Which of your teachers would you have preferred in body armor with a gun drawn?
Miss Summers? Remember her bringing daisies from her yard to second grade? She handed each student a beautiful flower. Miss Summers loved everyone, even those with AR-15s. She can't shoot.
Frasier? Mr. Frasier turned a youngster over down to explain "invert." Mr. Frasier's hands shook when he wasn't flipping fifth-graders and fractions. He may have shot wrong.
Mrs. Barkley barked in high school English class when anyone started an essay with "But." Mrs. Barkley dubbed Abie a "Jewboy" and gave him terrible grades. Arming Miss Barkley is like poisoning the chef.
Think back. Do you remember a teacher with a gun? No. Arming teachers so the gun industry can make more money is the craziest idea ever.
Or maybe you agree with Ted Cruz, the gun lobby-bought senator, that more guns reduce gun violence. After the next school shooting, you'll undoubtedly talk about arming teachers and pupils. Colt will likely develop a backpack-sized, lighter version of its popular killing machine in pink and blue for kids and boys. The MAR-15? (M for mini).
This post is a summary. Read the full one here.
Florian Wahl
3 years ago
An Approach to Product Strategy
I've been pondering product strategy and how to articulate it. Frameworks helped guide our thinking.
If your teams aren't working together or there's no clear path to victory, your product strategy may not be well-articulated or communicated (if you have one).
Before diving into a product strategy's details, it's important to understand its role in the bigger picture — the pieces that move your organization forward.
the overall picture
A product strategy is crucial, in my opinion. It's part of a successful product or business. It's the showpiece.
To simplify, we'll discuss four main components:
Vision
Product Management
Goals
Roadmap
Vision
Your company's mission? Your company/product in 35 years? Which headlines?
The vision defines everything your organization will do in the long term. It shows how your company impacted the world. It's your organization's rallying cry.
An ambitious but realistic vision is needed.
Without a clear vision, your product strategy may be inconsistent.
Product Management
Our main subject. Product strategy connects everything. It fulfills the vision.
In Part 2, we'll discuss product strategy.
Goals
This component can be goals, objectives, key results, targets, milestones, or whatever goal-tracking framework works best for your organization.
These product strategy metrics will help your team prioritize strategies and roadmaps.
Your company's goals should be unified. This fuels success.
Roadmap
The roadmap is your product strategy's timeline. It provides a prioritized view of your team's upcoming deliverables.
A roadmap is time-bound and includes measurable goals for your company. Your team's steps and capabilities for executing product strategy.
If your team has trouble prioritizing or defining a roadmap, your product strategy or vision is likely unclear.
Formulation of a Product Strategy
Now that we've discussed where your product strategy fits in the big picture, let's look at a framework.
A product strategy should include challenges, an approach, and actions.
Challenges
First, analyze the problems/situations you're solving. It can be customer- or company-focused.
The analysis should explain the problems and why they're important. Try to simplify the situation and identify critical aspects.
Some questions:
What issues are we attempting to resolve?
What obstacles—internal or otherwise—are we attempting to overcome?
What is the opportunity, and why should we pursue it, in your opinion?
Decided Method
Second, describe your approach. This can be a set of company policies for handling the challenge. It's the overall approach to the first part's analysis.
The approach can be your company's bets, the solutions you've found, or how you'll solve the problems you've identified.
Again, these questions can help:
What is the value that we hope to offer to our clients?
Which market are we focusing on first?
What makes us stand out? Our benefit over rivals?
Actions
Third, identify actions that result from your approach. Second-part actions should be these.
Coordinate these actions. You may need to add products or features to your roadmap, acquire new capabilities through partnerships, or launch new marketing campaigns. Whatever fits your challenges and strategy.
Final questions:
What skills do we need to develop or obtain?
What is the chosen remedy? What are the main outputs?
What else ought to be added to our road map?
Put everything together
… and iterate!
Strategy isn't one-and-done. Changes occur. Economies change. Competitors emerge. Customer expectations change.
One unexpected event can make strategies obsolete quickly. Muscle it. Review, evaluate, and course-correct your strategies with your teams. Quarterly works. In a new or unstable industry, more often.
Alex Mathers
2 years ago
How to Produce Enough for People to Not Neglect You
Internet's fantastic, right?
We've never had a better way to share our creativity.
I can now draw on my iPad and tweet or Instagram it to thousands. I may get some likes.
With such a great, free tool, you're not alone.
Millions more bright-eyed artists are sharing their work online.
The issue is getting innovative work noticed, not sharing it.
In a world where creators want attention, attention is valuable.
We build for attention.
Attention helps us establish a following, make money, get notoriety, and make a difference.
Most of us require attention to stay sane while creating wonderful things.
I know how hard it is to work hard and receive little views.
How do we receive more attention, more often, in a sea of talent?
Advertising and celebrity endorsements are options. These may work temporarily.
To attract true, organic, and long-term attention, you must create in high quality, high volume, and consistency.
Adapting Steve Martin's Be so amazing, they can't ignore you (with a mention to Dan Norris in his great book Create or Hate for the reminder)
Create a lot.
Eventually, your effort will gain traction.
Traction shows your work's influence.
Traction is when your product sells more. Traction is exponential user growth. Your work is shared more.
No matter how good your work is, it will always have minimal impact on the world.
Your work can eventually dent or puncture. Daily, people work to dent.
To achieve this tipping point, you must consistently produce exceptional work.
Expect traction after hundreds of outputs.
Dilbert creator Scott Adams says repetition persuades. If you don't stop, you can persuade practically anyone with anything.
Volume lends believability. So make more.
I worked as an illustrator for at least a year and a half without any recognition. After 150 illustrations on iStockphoto, my work started selling.
With 350 illustrations on iStock, I started getting decent client commissions.
Producing often will improve your craft and draw attention.
It's the only way to succeed. More creation means better results and greater attention.
Austin Kleon says you can improve your skill in relative anonymity before you become famous. Before obtaining traction, generate a lot and become excellent.
Most artists, even excellent ones, don't create consistently enough to get traction.
It may hurt. For makers who don't love and flow with their work, it's extremely difficult.
Your work must bring you to life.
To generate so much that others can't ignore you, decide what you'll accomplish every day (or most days).
Commit and be patient.
Prepare for zero-traction.
Anticipating this will help you persevere and create.
My online guru Grant Cardone says: Anything worth doing is worth doing every day.
Do.