More on Web3 & Crypto

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

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.

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
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Sara_Mednick
3 years ago
Since I'm a scientist, I oppose biohacking
Understanding your own energy depletion and restoration is how to truly optimize
Hack has meant many bad things for centuries. In the 1800s, a hack was a meager horse used to transport goods.
Modern usage describes a butcher or ax murderer's cleaver chop. The 1980s programming boom distinguished elegant code from "hacks". Both got you to your goal, but the latter made any programmer cringe and mutter about changing the code. From this emerged the hacker trope, the friendless anti-villain living in a murky hovel lit by the computer monitor, eating junk food and breaking into databases to highlight security system failures or steal hotdog money.
Now, start-a-billion-dollar-business-from-your-garage types have shifted their sights from app development to DIY biology, coining the term "bio-hack". This is a required keyword and meta tag for every fitness-related podcast, book, conference, app, or device.
Bio-hacking involves bypassing your body and mind's security systems to achieve a goal. Many biohackers' initial goals were reasonable, like lowering blood pressure and weight. Encouraged by their own progress, self-determination, and seemingly exquisite control of their biology, they aimed to outsmart aging and death to live 180 to 1000 years (summarized well in this vox.com article).
With this grandiose north star, the hunt for novel supplements and genetic engineering began.
Companies selling do-it-yourself biological manipulations cite lab studies in mice as proof of their safety and success in reversing age-related diseases or promoting longevity in humans (the goal changes depending on whether a company is talking to the federal government or private donors).
The FDA is slower than science, they say. Why not alter your biochemistry by buying pills online, editing your DNA with a CRISPR kit, or using a sauna delivered to your home? How about a microchip or electrical stimulator?
What could go wrong?
I'm not the neo-police, making citizen's arrests every time someone introduces a new plumbing gadget or extrapolates from animal research on resveratrol or catechins that we should drink more red wine or eat more chocolate. As a scientist who's spent her career asking, "Can we get better?" I've come to view bio-hacking as misguided, profit-driven, and counterproductive to its followers' goals.
We're creatures of nature. Despite all the new gadgets and bio-hacks, we still use Roman plumbing technology, and the best way to stay fit, sharp, and happy is to follow a recipe passed down since the beginning of time. Bacteria, plants, and all natural beings are rhythmic, with alternating periods of high activity and dormancy, whether measured in seconds, hours, days, or seasons. Nature repeats successful patterns.
During the Upstate, every cell in your body is naturally primed and pumped full of glycogen and ATP (your cells' energy currencies), as well as cortisol, which supports your muscles, heart, metabolism, cognitive prowess, emotional regulation, and general "get 'er done" attitude. This big energy release depletes your batteries and requires the Downstate, when your subsystems recharge at the cellular level.
Downstates are when you give your heart a break from pumping nutrient-rich blood through your body; when you give your metabolism a break from inflammation, oxidative stress, and sympathetic arousal caused by eating fast food — or just eating too fast; or when you give your mind a chance to wander, think bigger thoughts, and come up with new creative solutions. When you're responding to notifications, emails, and fires, you can't relax.
Downstates aren't just for consistently recharging your battery. By spending time in the Downstate, your body and brain get extra energy and nutrients, allowing you to grow smarter, faster, stronger, and more self-regulated. This state supports half-marathon training, exam prep, and mediation. As we age, spending more time in the Downstate is key to mental and physical health, well-being, and longevity.
When you prioritize energy-demanding activities during Upstate periods and energy-replenishing activities during Downstate periods, all your subsystems, including cardiovascular, metabolic, muscular, cognitive, and emotional, hum along at their optimal settings. When you synchronize the Upstates and Downstates of these individual rhythms, their functioning improves. A hard workout causes autonomic stress, which triggers Downstate recovery.
By choosing the right timing and type of exercise during the day, you can ensure a deeper recovery and greater readiness for the next workout by working with your natural rhythms and strengthening your autonomic and sleep Downstates.
Morning cardio workouts increase deep sleep compared to afternoon workouts. Timing and type of meals determine when your sleep hormone melatonin is released, ushering in sleep.
Rhythm isn't a hack. It's not a way to cheat the system or the boss. Nature has honed its optimization wisdom over trillions of days and nights. Stop looking for quick fixes. You're a whole system made of smaller subsystems that must work together to function well. No one pill or subsystem will make it all work. Understanding and coordinating your rhythms is free, easy, and only benefits you.
Dr. Sara C. Mednick is a cognitive neuroscientist at UC Irvine and author of The Power of the Downstate (HachetteGO)

Sammy Abdullah
3 years ago
SaaS payback period data
It's ok and even desired to be unprofitable if you're gaining revenue at a reasonable cost and have 100%+ net dollar retention, meaning you never lose customers and expand them. To estimate the acceptable cost of new SaaS revenue, we compare new revenue to operating loss and payback period. If you pay back the customer acquisition cost in 1.5 years and never lose them (100%+ NDR), you're doing well.
To evaluate payback period, we compared new revenue to net operating loss for the last 73 SaaS companies to IPO since October 2017. (55 out of 73). Here's the data. 1/(new revenue/operating loss) equals payback period. New revenue/operating loss equals cost of new revenue.
Payback averages a year. 55 SaaS companies that weren't profitable at IPO got a 1-year payback. Outstanding. If you pay for a customer in a year and never lose them (100%+ NDR), you're establishing a valuable business. The average was 1.3 years, which is within the 1.5-year range.
New revenue costs $0.96 on average. These SaaS companies lost $0.96 every $1 of new revenue last year. Again, impressive. Average new revenue per operating loss was $1.59.
Loss-in-operations definition. Operating loss revenue COGS S&M R&D G&A (technical point: be sure to use the absolute value of operating loss). It's wrong to only consider S&M costs and ignore other business costs. Operating loss and new revenue are measured over one year to eliminate seasonality.
Operating losses are desirable if you never lose a customer and have a quick payback period, especially when SaaS enterprises are valued on ARR. The payback period should be under 1.5 years, the cost of new income < $1, and net dollar retention 100%.

NonConformist
2 years ago
Before 6 AM, read these 6 quotations.
These quotes will change your perspective.
I try to reflect on these quotes daily. Reading it in the morning can affect your day, decisions, and priorities. Let's start.
1. Friedrich Nietzsche once said, "He who has a why to live for can bear almost any how."
What's your life goal?
80% of people don't know why they live or what they want to accomplish in life if you ask them randomly.
Even those with answers may not pursue their why. Without a purpose, life can be dull.
Your why can guide you through difficult times.
Create a life goal. Growing may change your goal. Having a purpose in life prevents feeling lost.
2. Seneca said, "He who fears death will never do anything fit for a man in life."
FAILURE STINKS Yes.
This quote is great if you're afraid to try because of failure. What if I'm not made for it? What will they think if I fail?
This wastes most of our lives. Many people prefer not failing over trying something with a better chance of success, according to studies.
Failure stinks in the short term, but it can transform our lives over time.
3. Two men peered through the bars of their cell windows; one saw mud, the other saw stars. — Dale Carnegie
It’s not what you look at that matters; it’s what you see.
The glass-full-or-empty meme is everywhere. It's hard to be positive when facing adversity.
This is a skill. Positive thinking can change our future.
We should stop complaining about our life and how easy success is for others.
Seductive pessimism. Realize this and start from first principles.
4. “Smart people learn from everything and everyone, average people from their experiences, and stupid people already have all the answers.” — Socrates.
Knowing we're ignorant can be helpful.
Every person and situation teaches you something. You can learn from others' experiences so you don't have to. Analyzing your and others' actions and applying what you learn can be beneficial.
Reading (especially non-fiction or biographies) is a good use of time. Walter Issacson wrote Benjamin Franklin's biography. Ben Franklin's early mistakes and successes helped me in some ways.
Knowing everything leads to disaster. Every incident offers lessons.
5. “We must all suffer one of two things: the pain of discipline or the pain of regret or disappointment.“ — James Rohn
My favorite Jim Rohn quote.
Exercise hurts. Healthy eating can be painful. But they're needed to get in shape. Avoiding pain can ruin our lives.
Always choose progress over hopelessness. Myth: overnight success Everyone who has mastered a craft knows that mastery comes from overcoming laziness.
Turn off your inner critic and start working. Try Can't Hurt Me by David Goggins.
6. “A champion is defined not by their wins, but by how they can recover when they fail.“ — Serena Williams
Have you heard of Traf-o-Data?
Gates and Allen founded Traf-O-Data. After some success, it failed. Traf-o-Data's failure led to Microsoft.
Allen said Traf-O-Data's setback was important for Microsoft's first product a few years later. Traf-O-Data was a business failure, but it helped them understand microprocessors, he wrote in 2017.
“The obstacle in the path becomes the path. Never forget, within every obstacle is an opportunity to improve our condition.” — Ryan Holiday.
Bonus Quotes
More helpful quotes:
“Those who cannot change their minds cannot change anything.” — George Bernard Shaw.
“Do something every day that you don’t want to do; this is the golden rule for acquiring the habit of doing your duty without pain.” — Mark Twain.
“Never give up on a dream just because of the time it will take to accomplish it. The time will pass anyway.” — Earl Nightingale.
“A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.” — George Bernard Shaw.
“We don’t stop playing because we grow old; we grow old because we stop playing.” — George Bernard Shaw.
Conclusion
Words are powerful. Utilize it. Reading these inspirational quotes will help you.
