More on Society & Culture

Sam Warain
2 years ago
The Brilliant Idea Behind Kim Kardashian's New Private Equity Fund
Kim Kardashian created Skky Partners. Consumer products, internet & e-commerce, consumer media, hospitality, and luxury are company targets.
Some call this another Kardashian publicity gimmick.
This maneuver is brilliance upon closer inspection. Why?
1) Kim has amassed a sizable social media fan base:
Over 320 million Instagram and 70 million Twitter users follow Kim Kardashian.
Kim Kardashian's Instagram account ranks 8th. Three Kardashians in top 10 is ridiculous.
This gives her access to consumer data. She knows what people are discussing. Investment firms need this data.
Quality, not quantity, of her followers matters. Studies suggest that her following are more engaged than Selena Gomez and Beyonce's.
Kim's followers are worth roughly $500 million to her brand, according to a research. They trust her and buy what she recommends.
2) She has a special aptitude for identifying trends.
Kim Kardashian can sense trends.
She's always ahead of fashion and beauty trends. She's always trying new things, too. She doesn't mind making mistakes when trying anything new. Her desire to experiment makes her a good business prospector.
Kim has also created a lifestyle brand that followers love. Kim is an entrepreneur, mom, and role model, not just a reality TV star or model. She's established a brand around her appearance, so people want to buy her things.
Her fragrance collection has sold over $100 million since its 2009 introduction, and her Sears apparel line did over $200 million in its first year.
SKIMS is her latest $3.2bn brand. She can establish multibillion-dollar firms with her enormous distribution platform.
Early founders would kill for Kim Kardashian's network.
Making great products is hard, but distribution is more difficult. — David Sacks, All-in-Podcast
3) She can delegate the financial choices to Jay Sammons, one of the greatest in the industry.
Jay Sammons is well-suited to develop Kim Kardashian's new private equity fund.
Sammons has 16 years of consumer investing experience at Carlyle. This will help Kardashian invest in consumer-facing enterprises.
Sammons has invested in Supreme and Beats Electronics, both of which have grown significantly. Sammons' track record and competence make him the obvious choice.
Kim Kardashian and Jay Sammons have joined forces to create a new business endeavor. The agreement will increase Kardashian's commercial empire. Sammons can leverage one of the world's most famous celebrities.
“Together we hope to leverage our complementary expertise to build the next generation consumer and media private equity firm” — Kim Kardashian
Kim Kardashian is a successful businesswoman. She developed an empire by leveraging social media to connect with fans. By developing a global lifestyle brand, she has sold things and experiences that have made her one of the world's richest celebrities.
She's a shrewd entrepreneur who knows how to maximize on herself and her image.
Imagine how much interest Kim K will bring to private equity and venture capital.
I'm curious about the company's growth.

umair haque
2 years ago
The reasons why our civilization is deteriorating
The Industrial Revolution's Curse: Why One Age's Power Prevents the Next Ones
A surprising fact. Recently, Big Oil's 1970s climate change projections were disturbingly accurate. Of course, we now know that it worked tirelessly to deny climate change, polluting our societies to this day. That's a small example of the Industrial Revolution's curse.
Let me rephrase this nuanced and possibly weird thought. The chart above? Disruptive science is declining. The kind that produces major discoveries, new paradigms, and shattering prejudices.
Not alone. Our civilisation reached a turning point suddenly. Progress stopped and reversed for the first time in centuries.
The Industrial Revolution's Big Bang started it all. At least some humans had riches for the first time, if not all, and with that wealth came many things. Longer, healthier lives since now health may be publicly and privately invested in. For the first time in history, wealthy civilizations could invest their gains in pure research, a good that would have sounded frivolous to cultures struggling to squeeze out the next crop, which required every shoulder to the till.
So. Don't confuse me with the Industrial Revolution's curse. Industry progressed. Contrary. I'm claiming that the Big Bang of Progress is slowing, plateauing, and ultimately reversing. All social indicators show that. From progress itself to disruptive, breakthrough research, everything is slowing down.
It's troubling. Because progress slows and plateaus, pre-modern social problems like fascism, extremism, and fundamentalism return. People crave nostalgic utopias when they lose faith in modernity. That strongman may shield me from this hazardous life. If I accept my place in a blood-and-soil hierarchy, I have a stable, secure position and someone to punch and detest. It's no coincidence that as our civilization hits a plateau of progress, there is a tsunami pulling the world backwards, with people viscerally, openly longing for everything from theocracy to fascism to fundamentalism, an authoritarian strongman to soothe their fears and tell them what to do, whether in Britain, heartland America, India, China, and beyond.
However, one aspect remains unknown. Technology. Let me clarify.
How do most people picture tech? Say that without thinking. Most people think of social media or AI. Well, small correlation engines called artificial neurons are a far cry from biological intelligence, which functions in far more obscure and intricate ways, down to the subatomic level. But let's try it.
Today, tech means AI. But. Do you foresee it?
Consider why civilisation is plateauing and regressing. Because we can no longer provide the most basic necessities at the same rate. On our track, clean air, water, food, energy, medicine, and healthcare will become inaccessible to huge numbers within a decade or three. Not enough. There isn't, therefore prices for food, medicine, and energy keep rising, with occasional relief.
Why our civilizations are encountering what economists like me term a budget constraint—a hard wall of what we can supply—should be evident. Global warming and extinction. Megafires, megadroughts, megafloods, and failed crops. On a civilizational scale, good luck supplying the fundamentals that way. Industrial food production cannot feed a planet warming past two degrees. Crop failures, droughts, floods. Another example: glaciers melt, rivers dry up, and the planet's fresh water supply contracts like a heart attack.
Now. Let's talk tech again. Mostly AI, maybe phone apps. The unsettling reality is that current technology cannot save humanity. Not much.
AI can do things that have become cliches to titillate the masses. It may talk to you and act like a person. It can generate art, which means reproduce it, but nonetheless, AI art! Despite doubts, it promises to self-drive cars. Unimportant.
We need different technology now. AI won't grow crops in ash-covered fields, cleanse water, halt glaciers from melting, or stop the clear-cutting of the planet's few remaining forests. It's not useless, but on a civilizational scale, it's much less beneficial than its proponents claim. By the time it matures, AI can help deliver therapy, keep old people company, and even drive cars more efficiently. None of it can save our culture.
Expand that scenario. AI's most likely use? Replacing call-center workers. Support. It may help doctors diagnose, surgeons orient, or engineers create more fuel-efficient motors. This is civilizationally marginal.
Non-disruptive. Do you see the connection with the paper that indicated disruptive science is declining? AI exemplifies that. It's called disruptive, yet it's a textbook incremental technology. Oh, cool, I can communicate with a bot instead of a poor human in an underdeveloped country and have the same or more trouble being understood. This bot is making more people unemployed. I can now view a million AI artworks.
AI illustrates our civilization's trap. Its innovative technologies will change our lives. But as you can see, its incremental, delivering small benefits at most, and certainly not enough to balance, let alone solve, the broader problem of steadily dropping living standards as our society meets a wall of being able to feed itself with fundamentals.
Contrast AI with disruptive innovations we need. What do we need to avoid a post-Roman Dark Age and preserve our civilization in the coming decades? We must be able to post-industrially produce all our basic needs. We need post-industrial solutions for clean water, electricity, cement, glass, steel, manufacture for garments and shoes, starting with the fossil fuel-intensive plastic, cotton, and nylon they're made of, and even food.
Consider. We have no post-industrial food system. What happens when crop failures—already dangerously accelerating—reach a critical point? Our civilization is vulnerable. Think of ancient civilizations that couldn't survive the drying up of their water sources, the failure of their primary fields, which they assumed the gods would preserve forever, or an earthquake or sickness that killed most of their animals. Bang. Lost. They failed. They splintered, fragmented, and abandoned vast capitols and cities, and suddenly, in history's sight, poof, they were gone.
We're getting close. Decline equals civilizational peril.
We believe dumb notions about AI becoming disruptive when it's incremental. Most of us don't realize our civilization's risk because we believe these falsehoods. Everyone should know that we cannot create any thing at civilizational scale without fossil fuels. Most of us don't know it, thus we don't realize that the breakthrough technologies and systems we need don't manipulate information anymore. Instead, biotechnologies, largely but not genes, generate food without fossil fuels.
We need another Industrial Revolution. AI, apps, bots, and whatnot won't matter unless you think you can eat and drink them while the world dies and fascists, lunatics, and zealots take democracy's strongholds. That's dramatic, but only because it's already happening. Maybe AI can entertain you in that bunker while society collapses with smart jokes or a million Mondrian-like artworks. If civilization is to survive, it cannot create the new Industrial Revolution.
The revolution has begun, but only in small ways. Post-industrial fundamental systems leaders are developing worldwide. The Netherlands is leading post-industrial agriculture. That's amazing because it's a tiny country performing well. Correct? Discover how large-scale agriculture can function, not just you and me, aged hippies, cultivating lettuce in our backyards.
Iceland is leading bioplastics, which, if done well, will be a major advance. Of sure, microplastics are drowning the oceans. What should we do since we can't live without it? We need algae-based bioplastics for green plastic.
That's still young. Any of the above may not function on a civilizational scale. Bioplastics use algae, which can cause problems if overused. None of the aforementioned indicate the next Industrial Revolution is here. Contrary. Slowly.
We have three decades until everything fails. Before life ends. Curtain down. No more fields, rivers, or weather. Freshwater and life stocks have plummeted. Again, we've peaked and declined in our ability to live at today's relatively rich standards. Game over—no more. On a dying planet, producing the fundamentals for a civilisation that left it too late to construct post-industrial systems becomes next to impossible, with output dropping faster and quicker each year, quarter, and day.
Too slow. That's because it's not really happening. Most people think AI when I say tech. I get a politicized response if I say Green New Deal or Clean Industrial Revolution. Half the individuals I talk to have been politicized into believing that climate change isn't real and that any breakthrough technical progress isn't required, desirable, possible, or genuine. They'll suffer.
The Industrial Revolution curse. Every revolution creates new authorities, which ossify and refuse to relinquish their privileges. For fifty years, Big Oil has denied climate change, even though their scientists predicted it. We also have a software industry and its venture capital power centers that are happy for the average person to think tech means chatbots, not being able to produce basics for a civilization without destroying the planet, and billionaires who buy comms platforms for the same eye-watering amount of money it would take to save life on Earth.
The entire world's vested interests are against the next industrial revolution, which is understandable since they were established from fossil money. From finance to energy to corporate profits to entertainment, power in our world is the result of the last industrial revolution, which means it has no motivation or purpose to give up fossil money, as we are witnessing more brutally out in the open.
Thus, the Industrial Revolution's curse—fossil power—rules our globe. Big Agriculture, Big Pharma, Wall St., Silicon Valley, and many others—including politics, which they buy and sell—are basically fossil power, and they have no interest in generating or letting the next industrial revolution happen. That's why tiny enterprises like those creating bioplastics in Iceland or nations savvy enough to shun fossil power, like the Netherlands, which has a precarious relationship with nature, do it. However, fossil power dominates politics, economics, food, clothes, energy, and medicine, and it has no motivation to change.
Allow disruptive innovations again. As they occur, its position becomes increasingly vulnerable. If you were fossil power, would you allow another industrial revolution to destroy its privilege and wealth?
You might, since power and money haven't corrupted you. However, fossil power prevents us from building, creating, and growing what we need to survive as a society. I mean the entire economic, financial, and political power structure from the last industrial revolution, not simply Big Oil. My friends, fossil power's chokehold over our society is likely to continue suffocating the advances that could have spared our civilization from a decline that's now here and spiraling closer to oblivion.

Isaiah McCall
3 years ago
Is TikTok slowly destroying a new generation?
It's kids' digital crack

TikTok is a destructive social media platform.
The interface shortens attention spans and dopamine receptors.
TikTok shares more data than other apps.
Seeing an endless stream of dancing teens on my glowing box makes me feel like a Blade Runner extra.
TikTok did in one year what MTV, Hollywood, and Warner Music tried to do in 20 years. TikTok has psychotized the two-thirds of society Aldous Huxley said were hypnotizable.
Millions of people, mostly kids, are addicted to learning a new dance, lip-sync, or prank, and those who best dramatize this collective improvisation get likes, comments, and shares.
TikTok is a great app. So what?
The Commercial Magnifying Glass TikTok made me realize my generation's time was up and the teenage Zoomers were the target.
I told my 14-year-old sister, "Enjoy your time under the commercial magnifying glass."
TikTok sells your every move, gesture, and thought. Data is the new oil. If you tell someone, they'll say, "Yeah, they collect data, but who cares? I have nothing to hide."
It's a George Orwell novel's beginning. Look up Big Brother Award winners to see if TikTok won.

TikTok shares your data more than any other social media app, and where it goes is unclear. TikTok uses third-party trackers to monitor your activity after you leave the app.
Consumers can't see what data is shared or how it will be used. — Genius URL
32.5 percent of Tiktok's users are 10 to 19 and 29.5% are 20 to 29.
TikTok is the greatest digital marketing opportunity in history, and they'll use it to sell you things, track you, and control your thoughts. Any of its users will tell you, "I don't care, I just want to be famous."
TikTok manufactures mental illness
TikTok's effect on dopamine and the brain is absurd. Dopamine controls the brain's pleasure and reward centers. It's like a switch that tells your brain "this feels good, repeat."
Dr. Julie Albright, a digital culture and communication sociologist, said TikTok users are "carried away by dopamine." It's hypnotic, you'll keep watching."
TikTok constantly releases dopamine. A guy on TikTok recently said he didn't like books because they were slow and boring.
The US didn't ban Tiktok.
Biden and Trump agree on bad things. Both agree that TikTok threatens national security and children's mental health.
The Chinese Communist Party owns and operates TikTok, but that's not its only problem.
There’s borderline child porn on TikTok
It's unsafe for children and violated COPPA.
It's also Chinese spyware. I'm not a Trump supporter, but I was glad he wanted TikTok regulated and disappointed when he failed.
Full-on internet censorship is rare outside of China, so banning it may be excessive. US should regulate TikTok more.
We must reject a low-quality present for a high-quality future.
TikTok vs YouTube
People got mad when I wrote about YouTube's death.
They didn't like when I said TikTok was YouTube's first real challenger.
Indeed. TikTok is the fastest-growing social network. In three years, the Chinese social media app TikTok has gained over 1 billion active users. In the first quarter of 2020, it had the most downloads of any app in a single quarter.
TikTok is the perfect social media app in many ways. It's brief and direct.

Can you believe they had a YouTube vs TikTok boxing match? We are doomed as a species.
YouTube hosts my favorite videos. That’s why I use it. That’s why you use it. New users expect more. They want something quicker, more addictive.
TikTok's impact on other social media platforms frustrates me. YouTube copied TikTok to compete.
It's all about short, addictive content.
I'll admit I'm probably wrong about TikTok. My friend says his feed is full of videos about food, cute animals, book recommendations, and hot lesbians.
Whatever.
TikTok makes us bad
TikTok is the opposite of what the Ancient Greeks believed about wisdom.
It encourages people to be fake. It's like a never-ending costume party where everyone competes.
It does not mean that Gen Z is doomed.
They could be the saviors of the world for all I know.
TikTok feels like a step towards Mike Judge's "Idiocracy," where the average person is a pleasure-seeking moron.
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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

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

James White
3 years ago
Three Books That Can Change Your Life in a Day
I've summarized each.
Anne Lamott said books are important. Books help us understand ourselves and our behavior. They teach us about community, friendship, and death.
I read. One of my few life-changing habits. 100+ books a year improve my life. I'll list life-changing books you can read in a day. I hope you like them too.
Let's get started!
1) Seneca's Letters from a Stoic
One of my favorite philosophy books. Ryan Holiday, Naval Ravikant, and other prolific readers recommend it.
Seneca wrote 124 letters at the end of his life after working for Nero. Death, friendship, and virtue are discussed.
It's worth rereading. When I'm in trouble, I consult Seneca.
It's brief. The book could be read in one day. However, use it for guidance during difficult times.
My favorite book quotes:
Many men find that becoming wealthy only alters their problems rather than solving them.
You will never be poor if you live in harmony with nature; you will never be wealthy if you live according to what other people think.
We suffer more frequently in our imagination than in reality; there are more things that are likely to frighten us than to crush us.
2) Steven Pressfield's book The War of Art
I’ve read this book twice. I'll likely reread it before 2022 is over.
The War Of Art is the best productivity book. Steven offers procrastination-fighting tips.
Writers, musicians, and creative types will love The War of Art. Workplace procrastinators should also read this book.
My favorite book quotes:
The act of creation is what matters most in art. Other than sitting down and making an effort every day, nothing else matters.
Working creatively is not a selfish endeavor or an attempt by the actor to gain attention. It serves as a gift for all living things in the world. Don't steal your contribution from us. Give us everything you have.
Fear is healthy. Fear is a signal, just like self-doubt. Fear instructs us on what to do. The more terrified we are of a task or calling, the more certain we can be that we must complete it.
3) Darren Hardy's The Compound Effect
The Compound Effect offers practical tips to boost productivity by 10x.
The author believes each choice shapes your future. Pizza may seem harmless. However, daily use increases heart disease risk.
Positive outcomes too. Daily gym visits improve fitness. Reading an hour each night can help you learn. Writing 1,000 words per day would allow you to write a novel in under a year.
Your daily choices affect compound interest and your future. Thus, better habits can improve your life.
My favorite book quotes:
Until you alter a daily habit, you cannot change your life. The key to your success can be found in the actions you take each day.
The hundreds, thousands, or millions of little things are what distinguish the ordinary from the extraordinary; it is not the big things that add up in the end.
Don't worry about willpower. Time to use why-power. Only when you relate your decisions to your aspirations and dreams will they have any real meaning. The decisions that are in line with what you define as your purpose, your core self, and your highest values are the wisest and most inspiring ones. To avoid giving up too easily, you must want something and understand why you want it.
