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
3 years ago
👏 Awesome post! When is part 3 coming?
Trent Lapinski
3 years ago
Very complex topic, great explanation
More on Web3 & Crypto
Sam Hickmann
2 years ago
Nomad.xyz got exploited for $190M
Key Takeaways:
Another hack. This time was different. This is a doozy.
Why? Nomad got exploited for $190m. It was crypto's 5th-biggest hack. Ouch.
It wasn't hackers, but random folks. What happened:
A Nomad smart contract flaw was discovered. They couldn't drain the funds at once, so they tried numerous transactions. Rookie!
People noticed and copied the attack.
They just needed to discover a working transaction, substitute the other person's address with theirs, and run it.
In a two-and-a-half-hour attack, $190M was siphoned from Nomad Bridge.
Nomad is a novel approach to blockchain interoperability that leverages an optimistic mechanism to increase the security of cross-chain communication. — nomad.xyz
This hack was permissionless, therefore anyone could participate.
After the fatal blow, people fought over the scraps.
Cross-chain bridges remain a DeFi weakness and exploit target. When they collapse, it's typically total.
$190M...gobbled.
Unbacked assets are hurting Nomad-dependent chains. Moonbeam, EVMOS, and Milkomeda's TVLs dropped.
This incident is every-man-for-himself, although numerous whitehats exploited the issue...
But what triggered the feeding frenzy?
How did so many pick the bones?
After a normal upgrade in June, the bridge's Replica contract was initialized with a severe security issue. The 0x00 address was a trusted root, therefore all messages were valid by default.
After a botched first attempt (costing $350k in gas), the original attacker's exploit tx called process() without first 'proving' its validity.
The process() function executes all cross-chain messages and checks the merkle root of all messages (line 185).
The upgrade caused transactions with a'messages' value of 0 (invalid, according to old logic) to be read by default as 0x00, a trusted root, passing validation as 'proven'
Any process() calls were valid. In reality, a more sophisticated exploiter may have designed a contract to drain the whole bridge.
Copycat attackers simply copied/pasted the same process() function call using Etherscan, substituting their address.
The incident was a wild combination of crowdhacking, whitehat activities, and MEV-bot (Maximal Extractable Value) mayhem.
For example, 🍉🍉🍉. eth stole $4M from the bridge, but claims to be whitehat.
Others stood out for the wrong reasons. Repeat criminal Rari Capital (Artibrum) exploited over $3M in stablecoins, which moved to Tornado Cash.
The top three exploiters (with 95M between them) are:
$47M: 0x56D8B635A7C88Fd1104D23d632AF40c1C3Aac4e3
$40M: 0xBF293D5138a2a1BA407B43672643434C43827179
$8M: 0xB5C55f76f90Cc528B2609109Ca14d8d84593590E
Here's a list of all the exploiters:
The project conducted a Quantstamp audit in June; QSP-19 foreshadowed a similar problem.
The auditor's comments that "We feel the Nomad team misinterpreted the issue" speak to a troubling attitude towards security that the project's "Long-Term Security" plan appears to confirm:
Concerns were raised about the team's response time to a live, public exploit; the team's official acknowledgement came three hours later.
"Removing the Replica contract as owner" stopped the exploit, but it was too late to preserve the cash.
Closed blockchain systems are only as strong as their weakest link.
The Harmony network is in turmoil after its bridge was attacked and lost $100M in late June.
What's next for Nomad's ecosystems?
Moonbeam's TVL is now $135M, EVMOS's is $3M, and Milkomeda's is $20M.
Loss of confidence may do more damage than $190M.
Cross-chain infrastructure is difficult to secure in a new, experimental sector. Bridge attacks can pollute an entire ecosystem or more.
Nomadic liquidity has no permanent home, so consumers will always migrate in pursuit of the "next big thing" and get stung when attentiveness wanes.
DeFi still has easy prey...
Sources: rekt.news & The Milk Road.
Matt Ward
2 years ago
Is Web3 nonsense?
Crypto and blockchain have rebranded as web3. They probably thought it sounded better and didn't want the baggage of scam ICOs, STOs, and skirted securities laws.
It was like Facebook becoming Meta. Crypto's biggest players wanted to change public (and regulator) perception away from pump-and-dump schemes.
After the 2018 ICO gold rush, it's understandable. Every project that raised millions (or billions) never shipped a meaningful product.
Like many crazes, charlatans took the money and ran.
Despite its grifter past, web3 is THE hot topic today as more founders, venture firms, and larger institutions look to build the future decentralized internet.
Supposedly.
How often have you heard: This will change the world, fix the internet, and give people power?
Why are most of web3's biggest proponents (and beneficiaries) the same rich, powerful players who built and invested in the modern internet? It's like they want to remake and own the internet.
Something seems off about that.
Why are insiders getting preferential presale terms before the public, allowing early investors and proponents to flip dirt cheap tokens and advisors shares almost immediately after the public sale?
It's a good gig with guaranteed markups, no risk or progress.
If it sounds like insider trading, it is, at least practically. This is clear when people talk about blockchain/web3 launches and tokens.
Fast money, quick flips, and guaranteed markups/returns are common.
Incentives-wise, it's hard to blame them. Who can blame someone for following the rules to win? Is it their fault or regulators' for not leveling the playing field?
It's similar to oil companies polluting for profit, Instagram depressing you into buying a new dress, or pharma pushing an unnecessary pill.
All of that is fair game, at least until we change the playbook, because people (and corporations) change for pain or love. Who doesn't love money?
belief based on money gain
Sinclair:
“It is difficult to get a man to understand something when his salary depends upon his not understanding it.”
Bitcoin, blockchain, and web3 analogies?
Most blockchain and web3 proponents are true believers, not cynical capitalists. They believe blockchain's inherent transparency and permissionless trust allow humanity to evolve beyond our reptilian ways and build a better decentralized and democratic world.
They highlight issues with the modern internet and monopoly players like Google, Facebook, and Apple. Decentralization fixes everything
If we could give power back to the people and get governments/corporations/individuals out of the way, we'd fix everything.
Blockchain solves supply chain and child labor issues in China.
To meet Paris climate goals, reduce emissions. Create a carbon token.
Fixing online hatred and polarization Web3 Twitter and Facebook replacement.
Web3 must just be the answer for everything… your “perfect” silver bullet.
Nothing fits everyone. Blockchain has pros and cons like everything else.
Blockchain's viral, ponzi-like nature has an MLM (mid level marketing) feel. If you bought Taylor Swift's NFT, your investment is tied to her popularity.
Probably makes you promote Swift more. Play music loudly.
Here's another example:
Imagine if Jehovah’s Witnesses (or evangelical preachers…) got paid for every single person they converted to their cause.
It becomes a self-fulfilling prophecy as their faith and wealth grow.
Which breeds extremism? Ultra-Orthodox Jews are an example. maximalists
Bitcoin and blockchain are causes, religions. It's a money-making movement and ideal.
We're good at convincing ourselves of things we want to believe, hence filter bubbles.
I ignore anything that doesn't fit my worldview and seek out like-minded people, which algorithms amplify.
Then what?
Is web3 merely a new scam?
No, never!
Blockchain has many crucial uses.
Sending money home/abroad without bank fees;
Like fleeing a war-torn country and converting savings to Bitcoin;
Like preventing Twitter from silencing dissidents.
Permissionless, trustless databases could benefit society and humanity. There are, however, many limitations.
Lost password?
What if you're cheated?
What if Trump/Putin/your favorite dictator incites a coup d'état?
What-ifs abound. Decentralization's openness brings good and bad.
No gatekeepers or firefighters to rescue you.
ISIS's fundraising is also frictionless.
Community-owned apps with bad interfaces and service.
Trade-offs rule.
So what compromises does web3 make?
What are your trade-offs? Decentralization has many strengths and flaws. Like Bitcoin's wasteful proof-of-work or Ethereum's political/wealth-based proof-of-stake.
To ensure the survival and veracity of the network/blockchain and to safeguard its nodes, extreme measures have been designed/put in place to prevent hostile takeovers aimed at altering the blockchain, i.e., adding money to your own wallet (account), etc.
These protective measures require significant resources and pose challenges. Reduced speed and throughput, high gas fees (cost to submit/write a transaction to the blockchain), and delayed development times, not to mention forked blockchain chains oops, web3 projects.
Protecting dissidents or rogue regimes makes sense. You need safety, privacy, and calm.
First-world life?
What if you assumed EVERYONE you saw was out to rob/attack you? You'd never travel, trust anyone, accomplish much, or live fully. The economy would collapse.
It's like an ant colony where half the ants do nothing but wait to be attacked.
Waste of time and money.
11% of the US budget goes to the military. Imagine what we could do with the $766B+ we spend on what-ifs annually.
Is so much hypothetical security needed?
Blockchain and web3 are similar.
Does your app need permissionless decentralization? Does your scooter-sharing company really need a proof-of-stake system and 1000s of nodes to avoid Russian hackers? Why?
Worst-case scenario? It's not life or death, unless you overstate the what-ifs. Web3 proponents find improbable scenarios to justify decentralization and tokenization.
Do I need a token to prove ownership of my painting? Unless I'm a master thief, I probably bought it.
despite losing the receipt.
I do, however, love Web 3.
Enough Web3 bashing for now. Understand? Decentralization isn't perfect, but it has huge potential when applied to the right problems.
I see many of the right problems as disrupting big tech's ruthless monopolies. I wrote several years ago about how tokenized blockchains could be used to break big tech's stranglehold on platforms, marketplaces, and social media.
Tokenomics schemes can be used for good and are powerful. Here’s how.
Before the ICO boom, I made a series of predictions about blockchain/crypto's future. It's still true.
Here's where I was then and where I see web3 going:
My 11 Big & Bold Predictions for Blockchain
In the near future, people may wear crypto cash rings or bracelets.
While some governments repress cryptocurrency, others will start to embrace it.
Blockchain will fundamentally alter voting and governance, resulting in a more open election process.
Money freedom will lead to a more geographically open world where people will be more able to leave when there is unrest.
Blockchain will make record keeping significantly easier, eliminating the need for a significant portion of government workers whose sole responsibility is paperwork.
Overrated are smart contracts.
6. Tokens will replace company stocks.
7. Blockchain increases real estate's liquidity, value, and volatility.
8. Healthcare may be most affected.
9. Crypto could end privacy and lead to Minority Report.
10. New companies with network effects will displace incumbents.
11. Soon, people will wear rings or bracelets with crypto cash.
Some have already happened, while others are still possible.
Time will tell if they happen.
And finally:
What will web3 be?
Who will be in charge?
Closing remarks
Hope you enjoyed this web3 dive. There's much more to say, but that's for another day.
We're writing history as we go.
Tech regulation, mergers, Bitcoin surge How will history remember us?
What about web3 and blockchain?
Is this a revolution or a tulip craze?
Remember, actions speak louder than words (share them in the comments).
Your turn.
Dylan Smyth
3 years ago
10 Ways to Make Money Online in 2022
As a tech-savvy person (and software engineer) or just a casual technology user, I'm sure you've had this same question countless times: How do I make money online? and how do I make money with my PC/Mac?
You're in luck! Today, I will list the top 5 easiest ways to make money online. Maybe a top ten in the future? Top 5 tips for 2022.
1. Using the gig economy
There are many websites on the internet that allow you to earn extra money using skills and equipment that you already own.
I'm referring to the gig economy. It's a great way to earn a steady passive income from the comfort of your own home. For some sites, premium subscriptions are available to increase sales and access features like bidding on more proposals.
Some of these are:
- Freelancer
- Upwork
- Fiverr (⭐ my personal favorite)
- TaskRabbit
2. Mineprize
MINEPRIZE is a great way to make money online. What's more, You need not do anything! You earn money by lending your idle CPU power to MINEPRIZE.
To register with MINEPRIZE, all you need is an email address and a password. Let MINEPRIZE use your resources, and watch the money roll in! You can earn up to $100 per month by letting your computer calculate. That's insane.
3. Writing
“O Romeo, Romeo, why art thou Romeo?” Okay, I admit that not all writing is Shakespearean. To be a copywriter, you'll need to be fluent in English. Thankfully, we don't have to use typewriters anymore.
Writing is a skill that can earn you a lot of money (claps for the rhyme).
Here are a few ways you can make money typing on your fancy keyboard:
Self-publish a book
Write scripts for video creators
Write for social media
Book-checking
Content marketing help
What a list within a list!
4. Coding
Yes, kids. You've probably coded before if you understand
You've probably coded before if you understand
print("hello world");
Computational thinking (or coding) is one of the most lucrative ways to earn extra money, or even as a main source of income.
Of course, there are hardcode coders (like me) who write everything line by line, binary di — okay, that last part is a bit exaggerated.
But you can also make money by writing websites or apps or creating low code or no code platforms.
But you can also make money by writing websites or apps or creating low code or no code platforms.
Some low-code platforms
Sheet : spreadsheets to apps :
Loading... We'll install your new app... No-Code Your team can create apps and automate tasks. Agile…
www.appsheet.com
Low-code platform | Business app creator - Zoho Creator
Work is going digital, and businesses of all sizes must adapt quickly. Zoho Creator is a...
www.zoho.com
Sell your data with TrueSource. NO CODE NEEDED
Upload data, configure your product, and earn in minutes.
www.truesource.io
Cool, huh?
5. Created Content
If we use the internet correctly, we can gain unfathomable wealth and extra money. But this one is a bit more difficult. Unlike some of the other items on this list, it takes a lot of time up front.
I'm referring to sites like YouTube and Medium. It's a great way to earn money both passively and actively. With the likes of Jake- and Logan Paul, PewDiePie (a.k.a. Felix Kjellberg) and others, it's never too late to become a millionaire on YouTube. YouTubers are always rising to the top with great content.
6. NFTs and Cryptocurrency
It is now possible to amass large sums of money by buying and selling digital assets on NFTs and cryptocurrency exchanges. Binance's Initial Game Offer rewards early investors who produce the best results.
One awesome game sold a piece of its plot for US$7.2 million! It's Axie Infinity. It's free and available on Google Play and Apple Store.
7. Affiliate Marketing
Affiliate marketing is a form of advertising where businesses pay others (like bloggers) to promote their goods and services. Here's an example. I write a blog (like this one) and post an affiliate link to an item I recommend buying — say, a camera — and if you buy the camera, I get a commission!
These programs pay well:
- Elementor
- AWeber
- Sendinblue
- ConvertKit\sLeadpages
- GetResponse
- SEMRush\sFiverr
- Pabbly
8. Start a blog
Now, if you're a writer or just really passionate about something or a niche, blogging could potentially monetize that passion!
Create a blog about anything you can think of. It's okay to start right here on Medium, as I did.
9. Dropshipping
And I mean that in the best possible way — drop shopping is ridiculously easy to set up, but difficult to maintain for some.
Luckily, Shopify has made setting up an online store a breeze. Drop-shipping from Alibaba and DHGate is quite common. You've got a winner if you can find a local distributor willing to let you drop ship their product!
10. Set up an Online Course
If you have a skill and can articulate it, online education is for you.
Skillshare, Pluralsight, and Coursera have all made inroads in recent years, upskilling people with courses that YOU can create and earn from.
That's it for today! Please share if you liked this post. If not, well —
You might also like
Katharine Valentino
2 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.
Christianlauer
2 years ago
Looker Studio Pro is now generally available, according to Google.
Great News about the new Google Business Intelligence Solution
Google has renamed Data Studio to Looker Studio and Looker Studio Pro.
Now, Google releases Looker Studio Pro. Similar to the move from Data Studio to Looker Studio, Looker Studio Pro is basically what Looker was previously, but both solutions will merge. Google says the Pro edition will acquire new enterprise management features, team collaboration capabilities, and SLAs.
![Dashboard Example in Looker Studio Pro — Image Source: Google[2]](https://storage.googleapis.com/int3grity/posts/m9yb4IqJCm7D/images/ZuJudlWT6GUeTKKNVduA5)
In addition to Google's announcements and sales methods, additional features include:
Looker Studio assets can now have organizational ownership. Customers can link Looker Studio to a Google Cloud project and migrate existing assets once. This provides:
Your users' created Looker Studio assets are all kept in a Google Cloud project.
When the users who own assets leave your organization, the assets won't be removed.
Using IAM, you may provide each Looker Studio asset in your company project-level permissions.
Other Cloud services can access Looker Studio assets that are owned by a Google Cloud project.
Looker Studio Pro clients may now manage report and data source access at scale using team workspaces.
Google announcing these features for the pro version is fascinating. Both products will likely converge, but Google may only release many features in the premium version in the future. Microsoft with Power BI and its free and premium variants already achieves this.
Sources and Further Readings
Google, Release Notes (2022)
Google, Looker (2022)
Ari Joury, PhD
2 years ago
7 ways to turn into a major problem-solver
For some people, the glass is half empty. For others, it’s half full. And for some, the question is, How do I get this glass totally full again?
Problem-solvers are the last group. They're neutral. Pragmatists.
Problems surround them. They fix things instead of judging them. Problem-solvers improve the world wherever they go.
Some fail. Sometimes their good intentions have terrible results. Like when they try to help a grandma cross the road because she can't do it alone but discover she never wanted to.
Most programmers, software engineers, and data scientists solve problems. They use computer code to fix problems they see.
Coding is best done by understanding and solving the problem.
Despite your best intentions, building the wrong solution may have negative consequences. Helping an unwilling grandma cross the road.
How can you improve problem-solving?
1. Examine your presumptions.
Don’t think There’s a grandma, and she’s unable to cross the road. Therefore I must help her over the road. Instead think This grandma looks unable to cross the road. Let’s ask her whether she needs my help to cross it.
Maybe the grandma can’t cross the road alone, but maybe she can. You can’t tell for sure just by looking at her. It’s better to ask.
Maybe the grandma wants to cross the road. But maybe she doesn’t. It’s better to ask!
Building software is similar. Do only I find this website ugly? Who can I consult?
We all have biases, mental shortcuts, and worldviews. They simplify life.
Problem-solving requires questioning all assumptions. They might be wrong!
Think less. Ask more.
Secondly, fully comprehend the issue.
Grandma wants to cross the road? Does she want flowers from the shop across the street?
Understanding the problem advances us two steps. Instead of just watching people and their challenges, try to read their intentions.
Don't ask, How can I help grandma cross the road? Why would this grandma cross the road? What's her goal?
Understand what people want before proposing solutions.
3. Request more information. This is not a scam!
People think great problem solvers solve problems immediately. False!
Problem-solvers study problems. Understanding the problem makes solving it easy.
When you see a grandma struggling to cross the road, you want to grab her elbow and pull her over. However, a good problem solver would ask grandma what she wants. So:
Problem solver: Excuse me, ma’am? Do you wish to get over the road? Grandma: Yes indeed, young man! Thanks for asking. Problem solver: What do you want to do on the other side? Grandma: I want to buy a bouquet of flowers for my dear husband. He loves flowers! I wish the shop wasn’t across this busy road… Problem solver: Which flowers does your husband like best? Grandma: He loves red dahlia. I usually buy about 20 of them. They look so pretty in his vase at the window! Problem solver: I can get those dahlia for you quickly. Go sit on the bench over here while you’re waiting; I’ll be back in five minutes. Grandma: You would do that for me? What a generous young man you are!
A mediocre problem solver would have helped the grandma cross the road, but he might have forgotten that she needs to cross again. She must watch out for cars and protect her flowers on the way back.
A good problem solver realizes that grandma's husband wants 20 red dahlias and completes the task.
4- Rapid and intense brainstorming
Understanding a problem makes solutions easy. However, you may not have all the information needed to solve the problem.
Additionally, retrieving crucial information can be difficult.
You could start a blog. You don't know your readers' interests. You can't ask readers because you don't know who they are.
Brainstorming works here. Set a stopwatch (most smartphones have one) to ring after five minutes. In the remaining time, write down as many topics as possible.
No answer is wrong. Note everything.
Sort these topics later. Programming or data science? What might readers scroll past—are these your socks this morning?
Rank your ideas intuitively and logically. Write Medium stories using the top 35 ideas.
5 - Google it.
Doctor Google may answer this seemingly insignificant question. If you understand your problem, try googling or binging.
Someone has probably had your problem before. The problem-solver may have posted their solution online.
Use others' experiences. If you're social, ask a friend or coworker for help.
6 - Consider it later
Rest your brain.
Reread. Your brain needs rest to function.
Hustle culture encourages working 24/7. It doesn't take a neuroscientist to see that this is mental torture.
Leave an unsolvable problem. Visit friends, take a hot shower, or do whatever you enjoy outside of problem-solving.
Nap.
I get my best ideas in the morning after working on a problem. I couldn't have had these ideas last night.
Sleeping subconsciously. Leave it alone and you may be surprised by the genius it produces.
7 - Learn to live with frustration
There are problems that you’ll never solve.
Mathematicians are world-class problem-solvers. The brightest minds in history have failed to solve many mathematical problems.
A Gordian knot problem can frustrate you. You're smart!
Frustration-haters don't solve problems well. They choose simple problems to avoid frustration.
No. Great problem solvers want to solve a problem but know when to give up.
Frustration initially hurts. You adapt.
Famous last words
If you read this article, you probably solve problems. We've covered many ways to improve, so here's a summary:
Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?
Recognize the issue completely. On the surface, a problem may seem straightforward, but what's really going on? Try to see what the current situation might be building up to by thinking two steps ahead of the current situation.
Request more information. You are no longer a high school student. A two-sentence problem statement is not sufficient to provide a solution. Ask away if you need more details!
Think quickly and thoroughly. In a constrained amount of time, try to write down all your thoughts. All concepts are worthwhile! Later, you can order them.
Google it. There is a purpose for the internet. Use it.
Consider it later at night. A rested mind is more creative. It might seem counterintuitive to leave a problem unresolved. But while you're sleeping, your subconscious will handle the laborious tasks.
Accept annoyance as a normal part of life. Don't give up if you're feeling frustrated. It's a step in the procedure. It's also perfectly acceptable to give up on a problem because there are other, more pressing issues that need to be addressed.
You might feel stupid sometimes, but that just shows that you’re human. You care about the world and you want to make it better.
At the end of the day, that’s all there is to problem solving — making the world a little bit better.