Integrity
Write
Loading...
rekt

rekt

3 years ago

LCX is the latest CEX to have suffered a private key exploit.

The attack began around 10:30 PM +UTC on January 8th.

Peckshield spotted it first, then an official announcement came shortly after.

We’ve said it before; if established companies holding millions of dollars of users’ funds can’t manage their own hot wallet security, what purpose do they serve?

The Unique Selling Proposition (USP) of centralised finance grows smaller by the day.

The official incident report states that 7.94M USD were stolen in total, and that deposits and withdrawals to the platform have been paused.

LCX hot wallet: 0x4631018f63d5e31680fb53c11c9e1b11f1503e6f

Hacker’s wallet: 0x165402279f2c081c54b00f0e08812f3fd4560a05

Stolen funds:

  • 162.68 ETH (502,671 USD)
  • 3,437,783.23 USDC (3,437,783 USD)
  • 761,236.94 EURe (864,840 USD)
  • 101,249.71 SAND Token (485,995 USD)
  • 1,847.65 LINK (48,557 USD)
  • 17,251,192.30 LCX Token (2,466,558 USD)
  • 669.00 QNT (115,609 USD)
  • 4,819.74 ENJ (10,890 USD)
  • 4.76 MKR (9,885 USD)

**~$1M worth of $LCX remains in the address, along with 611k EURe which has been frozen by Monerium.

The rest, a total of 1891 ETH (~$6M) was sent to Tornado Cash.**

Why can’t they keep private keys private?

Is it really that difficult for a traditional corporate structure to maintain good practice?

CeFi hacks leave us with little to say - we can only go on what the team chooses to tell us.

Next time, they can write this article themselves.

See below for a template.

More on Web3 & Crypto

Max Parasol

Max Parasol

3 years ago

Are DAOs the future or just a passing fad?

How do you DAO? Can DAOs scale?

DAO: Decentralized Autonomous. Organization.

“The whole phrase is a misnomer. They're not decentralized, autonomous, or organizations,” says Monsterplay blockchain consultant David Freuden.

As part of the DAO initiative, Freuden coauthored a 51-page report in May 2020. “We need DAOs,” he says. “‘Shareholder first' is a 1980s/90s concept. Profits became the focus, not products.”

His predictions for DAOs have come true nearly two years later. DAOs had over 1.6 million participants by the end of 2021, up from 13,000 at the start of the year. Wyoming, in the US, will recognize DAOs and the Marshall Islands in 2021. Australia may follow that example in 2022.

But what is a DAO?

Members buy (or are rewarded with) governance tokens to vote on how the DAO operates and spends its money. “DeFi spawned DAOs as an investment vehicle. So a DAO is tokenomics,” says Freuden.

DAOs are usually built around a promise or a social cause, but they still want to make money. “If you can't explain why, the DAO will fail,” he says. “A co-op without tokenomics is not a DAO.”

Operating system DAOs, protocol DAOs, investment DAOs, grant DAOs, service DAOs, social DAOs, collector DAOs, and media DAOs are now available.

Freuden liked the idea of people rallying around a good cause. Speculators and builders make up the crypto world, so it needs a DAO for them.

,Speculators and builders, or both, have mismatched expectations, causing endless, but sometimes creative friction.

Organisms that boost output

Launching a DAO with an original product such as a cryptocurrency, an IT protocol or a VC-like investment fund like FlamingoDAO is common. DAOs enable distributed open-source contributions without borders. The goal is vital. Sometimes, after a product is launched, DAOs emerge, leaving the company to eventually transition to a DAO, as Uniswap did.

Doing things together is a DAO. So it's a way to reward a distributed workforce. DAOs are essentially productivity coordination organisms.

“Those who work for the DAO make permissionless contributions and benefit from fragmented employment,” argues Freuden. DAOs are, first and foremost, a new form of cooperation.

DAO? Distributed not decentralized

In decentralized autonomous organizations, words have multiple meanings. DAOs can emphasize one aspect over another. Autonomy is a trade-off for decentralization.

DAOstack CEO Matan Field says a DAO is a distributed governance system. Power is shared. However, there are two ways to understand a DAO's decentralized nature. This clarifies the various DAO definitions.

A decentralized infrastructure allows a DAO to be decentralized. It could be created on a public permissionless blockchain to prevent a takeover.

As opposed to a company run by executives or shareholders, a DAO is distributed. Its leadership does not wield power

Option two is clearly distributed.

But not all of this is “automated.”

Think quorum, not robot.

DAOs can be autonomous in the sense that smart contracts are self-enforcing and self-executing. So every blockchain transaction is a simplified smart contract.


Dao landscape

The DAO landscape is evolving.

Consider how Ethereum's smart contracts work. They are more like self-executing computer code, which Vitalik Buterin calls “persistent scripts”.

However, a DAO is self-enforcing once its members agree on its rules. As such, a DAO is “automated upon approval by the governance committee.” This distinguishes them from traditional organizations whose rules must be interpreted and applied.

Why a DAO? They move fast

A DAO can quickly adapt to local conditions as a governance mechanism. It's a collaborative decision-making tool.

Like UkraineDAO, created in response to Putin's invasion of Ukraine by Ukrainian expat Alona Shevchenko, Nadya Tolokonnikova, Trippy Labs, and PleasrDAO. The DAO sought to support Ukrainian charities by selling Ukrainian flag NFTs. With a single mission, a DAO can quickly raise funds for a country accepting crypto where banks are distrusted.

This could be a watershed moment for DAOs.

ConstitutionDAO was another clever use case for DAOs for Freuden. In a failed but “beautiful experiment in a single-purpose DAO,” ConstitutionDAO tried to buy a copy of the US Constitution from a Sotheby's auction. In November 2021, ConstitutionDAO raised $47 million from 19,000 people, but a hedge fund manager outbid them.

Contributions were returned or lost if transactional gas fees were too high. The ConstitutionDAO, as a “beautiful experiment,” proved exceptionally fast at organizing and crowdsourcing funds for a specific purpose.

We may soon be applauding UkraineDAO's geopolitical success in support of the DAO concept.

Some of the best use cases for DAOs today, according to Adam Miller, founder of DAOplatform.io and MIDAO Directory Services, involve DAO structures.

That is, a “flat community is vital.” Prototyping by the crowd is a good example.  To succeed,  members must be enthusiastic about DAOs as an alternative to starting a company. Because DAOs require some hierarchy, he agrees that "distributed is a better acronym."

Miller sees DAOs as a “new way of organizing people and resources.” He started DAOplatform.io, a DAO tooling advisery that is currently transitioning to a DAO due to the “woeful tech options for running a DAO,” which he says mainly comprises of just “multisig admin keys and a voting system.” So today he's advising on DAO tech stacks.

Miller identifies three key elements.

Tokenization is a common method and tool. Second, governance mechanisms connected to the DAO's treasury. Lastly, community.”

How a DAO works...

They can be more than glorified Discord groups if they have a clear mission. This mission is a mix of financial speculation and utopianism. The spectrum is vast.

The founder of Dash left the cryptocurrency project in 2017. It's the story of a prophet without an heir. So creating a global tokenized evangelical missionary community via a DAO made sense.

Evan Duffield, a “libertarian/anarchist” visionary, forked Bitcoin in January 2014 to make it instant and essentially free. He went away for a while, and DASH became a DAO.

200,000 US retailers, including Walmart and Barnes & Noble, now accept Dash as payment. This payment system works like a gift card.

Arden Goldstein, Dash's head of crypto, DAO, and blockchain marketing, claims Dash is the “first successful DAO.” It was founded in 2016 and disbanded after a hack, an Ethereum hard fork and much controversy. But what are the success metrics?

Crypto success is measured differently, says Goldstein. To achieve common goals, people must participate or be motivated in a healthy DAO. People are motivated to complete tasks in a successful DAO. And, crucially, when tasks get completed.

“Yes or no, 1 or 0, voting is not a new idea. The challenge is getting people to continue to participate and keep building a community.” A DAO motivates volunteers: Nothing keeps people from building. The DAO “philosophy is old news. You need skin in the game to play.”

MasterNodes must stake 1000 Dash. Those members are rewarded with DASH for marketing (and other tasks). It uses an outsourced team to onboard new users globally.

Joining a DAO is part of the fun of meeting crazy or “very active” people on Discord. No one gets fired (usually). If your work is noticed, you may be offered a full-time job.

DAO community members worldwide are rewarded for brand building. Dash is also a great product for developing countries with high inflation and undemocratic governments. The countries with the most Dash DAO members are Russia, Brazil, Venezuela, India, China, France, Italy, and the Philippines.

Grassroots activism makes this DAO work. A DAO is local. Venezuelans can't access Dash.org, so DAO members help them use a VPN. DAO members are investors, fervent evangelicals, and local product experts.

Every month, proposals and grant applications are voted on via the Dash platform. However, the DAO may decide not to fund you. For example, the DAO once hired a PR firm, but the community complained about the lack of press coverage. This raises a great question: How are real-world contractual obligations met by a DAO?

Does the DASH DAO work?

“I see the DAO defund projects I thought were valuable,” Goldstein says. Despite working full-time, I must submit a funding proposal. “Much faster than other companies I've worked on,” he says.

Dash DAO is a headless beast. Ryan Taylor is the CEO of the company overseeing the DASH Core Group project. 

The issue is that “we don't know who has the most tokens [...] because we don't know who our customers are.” As a result, “the loudest voices usually don't have the most MasterNodes and aren't the most invested.”

Goldstein, the only female in the DAO, says she worked hard. “I was proud of the DAO when I made the logo pink for a day and got great support from the men.” This has yet to entice a major influx of female DAO members.

Many obstacles stand in the way of utopian dreams.

Governance problems remain

And what about major token holders behaving badly?

In early February, a heated crypto Twitter debate raged on about inclusion, diversity, and cancel culture in relation to decentralized projects. In this case, the question was how a DAO addresses alleged inappropriate behavior.

In a corporation, misconduct can result in termination. In a DAO, founders usually hold a large number of tokens and the keys to the blockchain (multisignature) or otherwise.

Brantly Millegan, the director of operations of Ethereum Name Service (ENS), made disparaging remarks about the LGBTQ community and other controversial topics. The screenshotted comments were made in 2016 and brought to the ENS board's attention in early 2022.

His contract with ENS has expired. But what of his large DAO governance token holdings?

Members of the DAO proposed a motion to remove Millegan from the DAO. His “delegated” votes net 370,000. He was and is the DAO's largest delegate.

What if he had refused to accept the DAO's decision?

Freuden says the answer is not so simple.

“Can a DAO kick someone out who built the project?”

The original mission “should be dissolved” if it no longer exists. “Does a DAO fail and return the money? They must r eturn the money with interest if the marriage fails.”

Before an IPO, VCs might try to remove a problematic CEO.

While DAOs use treasury as a governance mechanism, it is usually controlled (at least initially) by the original project creators. Or, in the case of Uniswap, the venture capital firm a16z has so much voting power that it has delegated it to student-run blockchain organizations.

So, can DAOs really work at scale? How to evolve voting paradigms beyond token holdings?

The whale token holder issue has some solutions. Multiple tokens, such as a utility token on top of a governance token, and quadratic voting for whales, are now common. Other safeguards include multisignature blockchain keys and decision time locks that allow for any automated decision to be made. The structure of each DAO will depend on the assets at stake.

In reality, voter turnout is often a bigger issue.

Is DAO governance scalable?

Many DAOs have low participation. Due to a lack of understanding of technology, apathy, or busy lives. “The bigger the DAO, the fewer voters who vote,” says Freuden.

Freuden's report cites British anthropologist Dunbar's Law, who argued that people can only maintain about 150 relationships.

"As the DAO grows in size, the individual loses influence because they perceive their voting power as being diminished or insignificant. The Ringelmann Effect and Dunbar's Rule show that as a group grows in size, members become lazier, disenfranchised, and detached.

Freuden says a DAO requires “understanding human relationships.” He believes DAOs work best as investment funds rooted in Cryptoland and small in scale. In just three weeks, SyndicateDAO enabled the creation of 450 new investment group DAOs.

Due to SEC regulations, FlamingoDAO, a famous NFT curation investment DAO, could only have 100 investors. The “LAO” is a member-directed venture capital fund and a US LLC. To comply with US securities law, they only allow 100 members with a 120ETH minimum staking contribution.

But how did FlamingoDAO make investment decisions? How often did all 70 members vote? Art and NFTs are highly speculative.

So, investment DAOs are thought to work well in a small petri dish environment. This is due to a crypto-native club's pooled capital (maximum 7% per member) and crowdsourced knowledge.

While scalability is a concern, each DAO will operate differently depending on the goal, technology stage, and personalities. Meetups and hackathons are common ways for techies to collaborate on a cause or test an idea. But somebody still organizes the hack.

Holographic consensus voting

But clever people are working on creative solutions to every problem.

Miller of DAOplatform.io cites DXdao as a successful DAO. Decentralized product and service creator DXdao runs the DAO entirely on-chain. “You earn voting rights by contributing to the community.”

DXdao, a DAOstack fork, uses holographic consensus, a voting algorithm invented by DAOstack founder Matan Field. The system lets a random or semi-random subset make group-wide decisions.

By acting as a gatekeeper for voters, DXdao's Luke Keenan explains that “a small predictions market economy emerges around the likely outcome of a proposal as tokens are staked on it.” Also, proposals that have been financially boosted have fewer requirements to be successful, increasing system efficiency.” DXdao “makes decisions by removing voting power as an economic incentive.”

Field explains that holographic consensus “does not require a quorum to render a vote valid.”

“Rather, it provides a parallel process. It is a game played (for profit) by ‘predictors' who make predictions about whether or not a vote will be approved by the voters. The voting process is valid even when the voting quorum is low if enough stake is placed on the outcome of the vote.

“In other words, a quorum is not a scalable DAO governance strategy,” Field says.

You don't need big votes on everything. If only 5% vote, fine. To move significant value or make significant changes, you need a longer voting period (say 30 days) and a higher quorum,” says Miller.

Clearly, DAOs are maturing. The emphasis is on tools like Orca and processes that delegate power to smaller sub-DAOs, committees, and working groups.

Miller also claims that “studies in psychology show that rewarding people too much for volunteering disincentivizes them.” So, rather than giving out tokens for every activity, you may want to offer symbolic rewards like POAPs or contributor levels.

“Free lunches are less rewarding. Random rewards can boost motivation.”

Culture and motivation

DAOs (and Web3 in general) can give early adopters a sense of ownership. In theory, they encourage early participation and bootstrapping before network effects.

"A double-edged sword," says Goldstein. In the developing world, they may not be fully scalable.

“There must always be a leader,” she says. “People won't volunteer if they don't want to.”

DAO members sometimes feel entitled. “They are not the boss, but they think they should be able to see my calendar or get a daily report,” Goldstein gripes. Say, “I own three MasterNodes and need to know X, Y, and Z.”

In most decentralized projects, strong community leaders are crucial to influencing culture.

Freuden says “the DAO's community builder is the cryptoland influencer.” They must “disseminate the DAO's culture, cause, and rally the troops” in English, not tech.

They must keep members happy.

So the community builder is vital. Building a community around a coin that promises riches is simple, but keeping DAO members motivated is difficult.

It's a human job. But tools like SourceCred or coordinate that measure contributions and allocate tokens are heavily marketed. Large growth funds/community funds/grant programs are common among DAOs.

The Future?

Onboarding, committed volunteers, and an iconic community builder may be all DAOs need.

It takes a DAO just one day to bring together a passionate (and sometimes obsessive) community. For organizations with a common goal, managing stakeholder expectations is critical.

A DAO's core values are community and cause, not scalable governance. “DAOs will work at scale like gaming communities, but we will have sub-DAOs everywhere like committees,” says Freuden.

So-called holographic consensuses “can handle, in principle, increasing rates of proposals by turning this tension between scale and resilience into an economical cost,” Field writes. Scalability is not guaranteed.

The DAO's key innovation is the fragmented workplace. “Voting is a subset of engagement,” says Freuden. DAO should allow for permissionless participation and engagement. DAOs allow for remote work.”

In 20 years, DAOs may be the AI-powered self-organizing concept. That seems far away now. But a new breed of productivity coordination organisms is maturing.

Vivek Singh

Vivek Singh

3 years ago

A Warm Welcome to Web3 and the Future of the Internet

Let's take a look back at the internet's history and see where we're going — and why.

Tim Berners Lee had a problem. He was at CERN, the world's largest particle physics factory, at the time. The institute's stated goal was to study the simplest particles with the most sophisticated scientific instruments. The institute completed the LEP Tunnel in 1988, a 27 kilometer ring. This was Europe's largest civil engineering project (to study smaller particles — electrons).

The problem Tim Berners Lee found was information loss, not particle physics. CERN employed a thousand people in 1989. Due to team size and complexity, people often struggled to recall past project information. While these obstacles could be overcome, high turnover was nearly impossible. Berners Lee addressed the issue in a proposal titled ‘Information Management'.

When a typical stay is two years, data is constantly lost. The introduction of new people takes a lot of time from them and others before they understand what is going on. An emergency situation may require a detective investigation to recover technical details of past projects. Often, the data is recorded but cannot be found. — Information Management: A Proposal

He had an idea. Create an information management system that allowed users to access data in a decentralized manner using a new technology called ‘hypertext'.
To quote Berners Lee, his proposal was “vague but exciting...”. The paper eventually evolved into the internet we know today. Here are three popular W3C standards used by billions of people today:


(credit: CERN)

HTML (Hypertext Markup)

A web formatting language.

URI (Unique Resource Identifier)

Each web resource has its own “address”. Known as ‘a URL'.

HTTP (Hypertext Transfer Protocol)

Retrieves linked resources from across the web.

These technologies underpin all computer work. They were the seeds of our quest to reorganize information, a task as fruitful as particle physics.

Tim Berners-Lee would probably think the three decades from 1989 to 2018 were eventful. He'd be amazed by the billions, the inspiring, the novel. Unlocking innovation at CERN through ‘Information Management'.
The fictional character would probably need a drink, walk, and a few deep breaths to fully grasp the internet's impact. He'd be surprised to see a few big names in the mix.

Then he'd say, "Something's wrong here."

We should review the web's history before going there. Was it a success after Berners Lee made it public? Web1 and Web2: What is it about what we are doing now that so many believe we need a new one, web3?

Per Outlier Ventures' Jamie Burke:

Web 1.0 was read-only.
Web 2.0 was the writable
Web 3.0 is a direct-write web.

Let's explore.

Web1: The Read-Only Web

Web1 was the digital age. We put our books, research, and lives ‘online'. The web made information retrieval easier than any filing cabinet ever. Massive amounts of data were stored online. Encyclopedias, medical records, and entire libraries were put away into floppy disks and hard drives.

In 2015, the web had around 305,500,000,000 pages of content (280 million copies of Atlas Shrugged).

Initially, one didn't expect to contribute much to this database. Web1 was an online version of the real world, but not yet a new way of using the invention.

One gets the impression that the web has been underutilized by historians if all we can say about it is that it has become a giant global fax machine. — Daniel Cohen, The Web's Second Decade (2004)

That doesn't mean developers weren't building. The web was being advanced by great minds. Web2 was born as technology advanced.

Web2: Read-Write Web

Remember when you clicked something on a website and the whole page refreshed? Is it too early to call the mid-2000s ‘the good old days'?
Browsers improved gradually, then suddenly. AJAX calls augmented CGI scripts, and applications began sending data back and forth without disrupting the entire web page. One button to ‘digg' a post (see below). Web experiences blossomed.

In 2006, Digg was the most active ‘Web 2.0' site. (Photo: Ethereum Foundation Taylor Gerring)

Interaction was the focus of new applications. Posting, upvoting, hearting, pinning, tweeting, liking, commenting, and clapping became a lexicon of their own. It exploded in 2004. Easy ways to ‘write' on the internet grew, and continue to grow.

Facebook became a Web2 icon, where users created trillions of rows of data. Google and Amazon moved from Web1 to Web2 by better understanding users and building products and services that met their needs.

Business models based on Software-as-a-Service and then managing consumer data within them for a fee have exploded.

Web2 Emerging Issues

Unbelievably, an intriguing dilemma arose. When creating this read-write web, a non-trivial question skirted underneath the covers. Who owns it all?

You have no control over [Web 2] online SaaS. People didn't realize this because SaaS was so new. People have realized this is the real issue in recent years.

Even if these organizations have good intentions, their incentive is not on the users' side.
“You are not their customer, therefore you are their product,” they say. With Laura Shin, Vitalik Buterin, Unchained

A good plot line emerges. Many amazing, world-changing software products quietly lost users' data control.
For example: Facebook owns much of your social graph data. Even if you hate Facebook, you can't leave without giving up that data. There is no ‘export' or ‘exit'. The platform owns ownership.

While many companies can pull data on you, you cannot do so.

On the surface, this isn't an issue. These companies use my data better than I do! A complex group of stakeholders, each with their own goals. One is maximizing shareholder value for public companies. Tim Berners-Lee (and others) dislike the incentives created.

“Show me the incentive and I will show you the outcome.” — Berkshire Hathaway's CEO

It's easy to see what the read-write web has allowed in retrospect. We've been given the keys to create content instead of just consume it. On Facebook and Twitter, anyone with a laptop and internet can participate. But the engagement isn't ours. Platforms own themselves.

Web3: The ‘Unmediated’ Read-Write Web

Tim Berners Lee proposed a decade ago that ‘linked data' could solve the internet's data problem.

However, until recently, the same principles that allowed the Web of documents to thrive were not applied to data...

The Web of Data also allows for new domain-specific applications. Unlike Web 2.0 mashups, Linked Data applications work with an unbound global data space. As new data sources appear on the Web, they can provide more complete answers.

At around the same time as linked data research began, Satoshi Nakamoto created Bitcoin. After ten years, it appears that Berners Lee's ideas ‘link' spiritually with cryptocurrencies.

What should Web 3 do?

Here are some quick predictions for the web's future.

Users' data:
Users own information and provide it to corporations, businesses, or services that will benefit them.

Defying censorship:

No government, company, or institution should control your access to information (1, 2, 3)

Connect users and platforms:

Create symbiotic rather than competitive relationships between users and platform creators.

Open networks:

“First, the cryptonetwork-participant contract is enforced in open source code. Their voices and exits are used to keep them in check.” Dixon, Chris (4)

Global interactivity:

Transacting value, information, or assets with anyone with internet access, anywhere, at low cost

Self-determination:

Giving you the ability to own, see, and understand your entire digital identity.

Not pull, push:

‘Push' your data to trusted sources instead of ‘pulling' it from others.

Where Does This Leave Us?

Change incentives, change the world. Nick Babalola

People believe web3 can help build a better, fairer system. This is not the same as equal pay or outcomes, but more equal opportunity.

It should be noted that some of these advantages have been discussed previously. Will the changes work? Will they make a difference? These unanswered questions are technical, economic, political, and philosophical. Unintended consequences are likely.

We hope Web3 is a more democratic web. And we think incentives help the user. If there’s one thing that’s on our side, it’s that open has always beaten closed, given a long enough timescale.

We are at the start. 

Vitalik

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

You might also like

Matthew Royse

Matthew Royse

3 years ago

7 ways to improve public speaking

How to overcome public speaking fear and give a killer presentation

Photo by Kenny Eliason on Unsplash

"Public speaking is people's biggest fear, according to studies. Death's second. The average person is better off in the casket than delivering the eulogy."  — American comedian, actor, writer, and producer Jerry Seinfeld

People fear public speaking, according to research. Public speaking can be intimidating.

Most professions require public speaking, whether to 5, 50, 500, or 5,000 people. Your career will require many presentations. In a small meeting, company update, or industry conference.

You can improve your public speaking skills. You can reduce your anxiety, improve your performance, and feel more comfortable speaking in public.

If I returned to college, I'd focus on writing and public speaking. Effective communication is everything.” — 38th president Gerald R. Ford

You can deliver a great presentation despite your fear of public speaking. There are ways to stay calm while speaking and become a more effective public speaker.

Seven tips to improve your public speaking today. Let's help you overcome your fear (no pun intended).

Know your audience.

"You're not being judged; the audience is." — Entrepreneur, author, and speaker Seth Godin

Understand your audience before speaking publicly. Before preparing a presentation, know your audience. Learn what they care about and find useful.

Your presentation may depend on where you're speaking. A classroom is different from a company meeting.

Determine your audience before developing your main messages. Learn everything about them. Knowing your audience helps you choose the right words, information (thought leadership vs. technical), and motivational message.

2. Be Observant

Observe others' speeches to improve your own. Watching free TED Talks on education, business, science, technology, and creativity can teach you a lot about public speaking.

What worked and what didn't?

  • What would you change?

  • Their strengths

  • How interesting or dull was the topic?

Note their techniques to learn more. Studying the best public speakers will amaze you.

Learn how their stage presence helped them communicate and captivated their audience. Please note their pauses, humor, and pacing.

3. Practice

"A speaker should prepare based on what he wants to learn, not say." — Author, speaker, and pastor Tod Stocker

Practice makes perfect when it comes to public speaking. By repeating your presentation, you can find your comfort zone.

When you've practiced your presentation many times, you'll feel natural and confident giving it. Preparation helps overcome fear and anxiety. Review notes and important messages.

When you know the material well, you can explain it better. Your presentation preparation starts before you go on stage.

Keep a notebook or journal of ideas, quotes, and examples. More content means better audience-targeting.

4. Self-record

Videotape your speeches. Check yourself. Body language, hands, pacing, and vocabulary should be reviewed.

Best public speakers evaluate their performance to improve.

Write down what you did best, what you could improve and what you should stop doing after watching a recording of yourself. Seeing yourself can be unsettling. This is how you improve.

5. Remove text from slides

"Humans can't read and comprehend screen text while listening to a speaker. Therefore, lots of text and long, complete sentences are bad, bad, bad.” —Communications expert Garr Reynolds

Presentation slides shouldn't have too much text. 100-slide presentations bore the audience. Your slides should preview what you'll say to the audience.

Use slides to emphasize your main point visually.

If you add text, use at least 40-point font. Your slides shouldn't require squinting to read. You want people to watch you, not your slides.

6. Body language

"Body language is powerful." We had body language before speech, and 80% of a conversation is read through the body, not the words." — Dancer, writer, and broadcaster Deborah Bull

Nonverbal communication dominates. Our bodies speak louder than words. Don't fidget, rock, lean, or pace.

Relax your body to communicate clearly and without distraction through nonverbal cues. Public speaking anxiety can cause tense body language.

Maintain posture and eye contact. Don’t put your hand in your pockets, cross your arms, or stare at your notes. Make purposeful hand gestures that match what you're saying.

7. Beginning/ending Strong

Beginning and end are memorable. Your presentation must start strong and end strongly. To engage your audience, don't sound robotic.

Begin with a story, stat, or quote. Conclude with a summary of key points. Focus on how you will start and end your speech.

You should memorize your presentation's opening and closing. Memorize something naturally. Excellent presentations start and end strong because people won't remember the middle.


Bringing It All Together

Seven simple yet powerful ways to improve public speaking. Know your audience, study others, prepare and rehearse, record yourself, remove as much text as possible from slides, and start and end strong.

Follow these tips to improve your speaking and audience communication. Prepare, practice, and learn from great speakers to reduce your fear of public speaking.

"Speaking to one person or a thousand is public speaking." — Vocal coach Roger Love

Muhammad Rahmatullah

Muhammad Rahmatullah

3 years ago

The Pyramid of Coding Principles

A completely operating application requires many processes and technical challenges. Implementing coding standards can make apps right, work, and faster.

My reverse pyramid of coding basics

With years of experience working in software houses. Many client apps are scarcely maintained.

Why are these programs "barely maintainable"? If we're used to coding concepts, we can probably tell if an app is awful or good from its codebase.

This is how I coded much of my app.

Make It Work

Before adopting any concept, make sure the apps are completely functional. Why have a fully maintained codebase if the app can't be used?

The user doesn't care if the app is created on a super server or uses the greatest coding practices. The user just cares if the program helps them.

After the application is working, we may implement coding principles.

You Aren’t Gonna Need It

As a junior software engineer, I kept unneeded code, components, comments, etc., thinking I'd need them later.

In reality, I never use that code for weeks or months.

First, we must remove useless code from our primary codebase. If you insist on keeping it because "you'll need it later," employ version control.

If we remove code from our codebase, we can quickly roll back or copy-paste the previous code without preserving it permanently.

The larger the codebase, the more maintenance required.

Keep It Simple Stupid

example code smells/critics using rubocop

Indeed. Keep things simple.

Why complicate something if we can make it simpler?

Our code improvements should lessen the server load and be manageable by others.

If our code didn't pass those benchmarks, it's too convoluted and needs restructuring. Using an open-source code critic or code smell library, we can quickly rewrite the code.

Simpler codebases and processes utilize fewer server resources.

Don't Repeat Yourself

Have you ever needed an action or process before every action, such as ensuring the user is logged in before accessing user pages?

As you can see from the above code, I try to call is user login? in every controller action, and it should be optimized, because if we need to rename the method or change the logic, etc. We can improve this method's efficiency.

We can write a constructor/middleware/before action that calls is_user_login?

The code is more maintainable and readable after refactoring.

Each programming language or framework handles this issue differently, so be adaptable.

Clean Code

Clean code is a broad notion that you've probably heard of before.

When creating a function, method, module, or variable name, the first rule of clean code is to be precise and simple.

The name should express its value or logic as a whole, and follow code rules because every programming language is distinct.

If you want to learn more about this topic, I recommend reading https://www.amazon.com/Clean-Code-Handbook-Software-Craftsmanship/dp/0132350882.

Standing On The Shoulder of Giants

Use industry standards and mature technologies, not your own(s).

There are several resources that explain how to build boilerplate code with tools, how to code with best practices, etc.

I propose following current conventions, best practices, and standardization since we shouldn't innovate on top of them until it gives us a competitive edge.

Boy Scout Rule

What reduces programmers' productivity?

When we have to maintain or build a project with messy code, our productivity decreases.

Having to cope with sloppy code will slow us down (shame of us).

How to cope? Uncle Bob's book says, "Always leave the campground cleaner than you found it."

When developing new features or maintaining current ones, we must improve our codebase. We can fix minor issues too. Renaming variables, deleting whitespace, standardizing indentation, etc.

Make It Fast

After making our code more maintainable, efficient, and understandable, we can speed up our app.

Whether it's database indexing, architecture, caching, etc.

A smart craftsman understands that refactoring takes time and it's preferable to balance all the principles simultaneously. Don't YAGNI phase 1.

Using these ideas in each iteration/milestone, while giving the bottom items less time/care.

You can check one of my articles for further information. https://medium.com/life-at-mekari/why-does-my-website-run-very-slowly-and-how-do-i-optimize-it-for-free-b21f8a2f0162

https://medium.com/life-at-mekari/what-you-need-to-make-your-app-a-high-availability-system-tackling-the-technical-challenges-8896abec363f

Nicolas Tresegnie

Nicolas Tresegnie

3 years ago

Launching 10 SaaS applications in 100 days

Photo by Mauro Sbicego / Unsplash

Apocodes helps entrepreneurs create SaaS products without writing code. This post introduces micro-SaaS and outlines its basic strategy.

Strategy

Vision and strategy differ when starting a startup.

  • The company's long-term future state is outlined in the vision. It establishes the overarching objectives the organization aims to achieve while also justifying its existence. The company's future is outlined in the vision.

  • The strategy consists of a collection of short- to mid-term objectives, the accomplishment of which will move the business closer to its vision. The company gets there through its strategy.

The vision should be stable, but the strategy must be adjusted based on customer input, market conditions, or previous experiments.

Begin modestly and aim high.

Be truthful. It's impossible to automate SaaS product creation from scratch. It's like climbing Everest without running a 5K. Physical rules don't prohibit it, but it would be suicide.

Apocodes 5K equivalent? Two options:

  • (A) Create a feature that includes every setting option conceivable. then query potential clients “Would you choose us to build your SaaS solution if we offered 99 additional features of the same caliber?” After that, decide which major feature to implement next.

  • (B) Build a few straightforward features with just one or two configuration options. Then query potential clients “Will this suffice to make your product?” What's missing if not? Finally, tweak the final result a bit before starting over.

(A) is an all-or-nothing approach. It's like training your left arm to climb Mount Everest. My right foot is next.

(B) is a better method because it's iterative and provides value to customers throughout.

Focus on a small market sector, meet its needs, and expand gradually. Micro-SaaS is Apocode's first market.

What is micro-SaaS.

Micro-SaaS enterprises have these characteristics:

  • A limited range: They address a specific problem with a small number of features.

  • A small group of one to five individuals.

  • Low external funding: The majority of micro-SaaS companies have Total Addressable Markets (TAM) under $100 million. Investors find them unattractive as a result. As a result, the majority of micro-SaaS companies are self-funded or bootstrapped.

  • Low competition: Because they solve problems that larger firms would rather not spend time on, micro-SaaS enterprises have little rivalry.

  • Low upkeep: Because of their simplicity, they require little care.

  • Huge profitability: Because providing more clients incurs such a small incremental cost, high profit margins are possible.

Micro-SaaS enterprises created with no-code are Apocode's ideal first market niche.

We'll create our own micro-SaaS solutions to better understand their needs. Although not required, we believe this will improve community discussions.

The challenge

In 100 days (September 12–December 20, 2022), we plan to build 10 micro-SaaS enterprises using Apocode.

They will be:

  • Self-serve: Customers will be able to use the entire product experience without our manual assistance.

  • Real: They'll deal with actual issues. They won't be isolated proofs of concept because we'll keep up with them after the challenge.

  • Both free and paid options: including a free plan and a free trial period. Although financial success would be a good result, the challenge's stated objective is not financial success.

This will let us design Apocodes features, showcase them, and talk to customers.

(Edit: The first micro-SaaS was launched!)

Follow along

If you want to follow the story of Apocode or our progress in this challenge, you can subscribe here.

If you are interested in using Apocode, sign up here.

If you want to provide feedback, discuss the idea further or get involved, email me at nicolas.tresegnie@gmail.com