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Jason Kottke

3 years ago

Lessons on Leadership from the Dancing Guy

More on Leadership

Mike Tarullo

Mike Tarullo

3 years ago

Even In a Crazy Market, Hire the Best People: The "First Ten" Rules

The Pareto Principle is a way of life for First Ten people.

Hiring is difficult, but you shouldn't compromise on team members. Or it may suggest you need to look beyond years in a similar role/function.

Every hire should be someone we'd want as one of our first ten employees.

If you hire such people, your team will adapt, initiate, and problem-solve, and your company will grow. You'll stay nimble even as you scale, and you'll learn from your colleagues.

If you only hire for a specific role or someone who can execute the job, you'll become a cluster of optimizers, and talent will depart for a more fascinating company. A startup is continually changing, therefore you want individuals that embrace it.

As a leader, establishing ideal conditions for talent and having a real ideology should be high on your agenda. You can't eliminate attrition, nor would you want to, but you can hire people who will become your company's leaders.

In my last four jobs I was employee 2, 5, 3, and 5. So while this is all a bit self serving, you’re the one reading my writing — and I have some experience with who works out in the first ten!

First, we'll examine what they do well (and why they're beneficial for startups), then what they don't, and how to hire them.

First 10 are:

  • Business partners: Because it's their company, they take care of whatever has to be done and have ideas about how to do it. You can rely on them to always put the success of the firm first because it is their top priority (company success is strongly connected with success for early workers). This approach will eventually take someone to leadership positions.

  • High Speed Learners: They process knowledge quickly and can reach 80%+ competency in a new subject matter rather quickly. A growing business that is successful tries new things frequently. We have all lost a lot of money and time on employees who follow the wrong playbook or who wait for someone else within the company to take care of them.

  • Autodidacts learn by trial and error, osmosis, networking with others, applying first principles, and reading voraciously (articles, newsletters, books, and even social media). Although teaching is wonderful, you won't have time.

  • Self-scaling: They figure out a means to deal with issues and avoid doing the grunt labor over the long haul, increasing their leverage. Great people don't keep doing the same thing forever; as they expand, they use automation and delegation to fill in their lower branches. This is a crucial one; even though you'll still adore them, you'll have to manage their scope or help them learn how to scale on their own.

  • Free Range: You can direct them toward objectives rather than specific chores. Check-ins can be used to keep them generally on course without stifling invention instead of giving them precise instructions because doing so will obscure their light.

  • When people are inspired, they bring their own ideas about what a firm can be and become animated during discussions about how to get there.

  • Novelty Seeking: They look for business and personal growth chances. Give them fresh assignments and new directions to follow around once every three months.


Here’s what the First Ten types may not be:

  • Domain specialists. When you look at their resumes, you'll almost certainly think they're unqualified. Fortunately, a few strategically positioned experts may empower a number of First Ten types by serving on a leadership team or in advising capacities.

  • Balanced. These people become very invested, and they may be vulnerable to many types of stress. You may need to assist them in managing their own stress and coaching them through obstacles. If you are reading this and work at Banza, I apologize for not doing a better job of supporting this. I need to be better at it.

  • Able to handle micromanagement with ease. People who like to be in charge will suppress these people. Good decision-making should be delegated to competent individuals. Generally speaking, if you wish to scale.

Great startup team members have versatility, learning, innovation, and energy. When we hire for the function, not the person, we become dull and staid. Could this person go to another department if needed? Could they expand two levels in a few years?

First Ten qualities and experience level may have a weak inverse association. People with 20+ years of experience who had worked at larger organizations wanted to try something new and had a growth mentality. College graduates may want to be told what to do and how to accomplish it so they can stay in their lane and do what their management asks.

Does the First Ten archetype sound right for your org? Cool, let’s go hiring. How will you know when you’ve found one?

  • They exhibit adaptive excellence, excelling at a variety of unrelated tasks. It could be hobbies or professional talents. This suggests that they will succeed in the next several endeavors they pursue.

  • Successful risk-taking is doing something that wasn't certain to succeed, sometimes more than once, and making it do so. It's an attitude.

  • Rapid Rise: They regularly change roles and get promoted. However, they don't leave companies when the going gets tough. Look for promotions at every stop and at least one position with three or more years of experience.

You can ask them:

  • Tell me about a time when you started from scratch or achieved success. What occurred en route? You might request a variety of tales from various occupations or even aspects of life. They ought to be energized by this.

  • What new skills have you just acquired? It is not required to be work-related. They must be able to describe it and unintentionally become enthusiastic about it.

  • Tell me about a moment when you encountered a challenge and had to alter your strategy. The core of a startup is reinventing itself when faced with obstacles.

  • Tell me about a moment when you eliminated yourself from a position at work. They've demonstrated they can permanently solve one issue and develop into a new one, as stated above.

  • Why do you want to leave X position or Y duty? These people ought to be moving forward, not backward, all the time. Instead, they will discuss what they are looking forward to visiting your location.

  • Any questions? Due to their inherent curiosity and desire to learn new things, they should practically never run out of questions. You can really tell if they are sufficiently curious at this point.

People who see their success as being the same as the success of the organization are the best-case team members, in any market. They’ll grow and change with the company, and always try to prioritize what matters. You’ll find yourself more energized by your work because you’re surrounded by others who are as well. Happy teambuilding!

Greg Satell

Greg Satell

2 years ago

Focus: The Deadly Strategic Idea You've Never Heard Of (But Definitely Need To Know!

Photo by Shane on Unsplash

Steve Jobs' initial mission at Apple in 1997 was to destroy. He killed the Newton PDA and Macintosh clones. Apple stopped trying to please everyone under Jobs.

Afterward, there were few highly targeted moves. First, the pink iMac. Modest success. The iPod, iPhone, and iPad made Apple the world's most valuable firm. Each maneuver changed the company's center of gravity and won.

That's the idea behind Schwerpunkt, a German military term meaning "focus." Jobs didn't need to win everywhere, just where it mattered, so he focused Apple's resources on a few key goods. Finding your Schwerpunkt is more important than charts and analysis for excellent strategy.

Comparison of Relative Strength and Relative Weakness

The iPod, Apple's first major hit after Jobs' return, didn't damage Microsoft and the PC, but instead focused Apple's emphasis on a fledgling, fragmented market that generated "sucky" products. Apple couldn't have taken on the computer titans at this stage, yet it beat them.

The move into music players used Apple's particular capabilities, especially its ability to build simple, easy-to-use interfaces. Jobs' charisma and stature, along his understanding of intellectual property rights from Pixar, helped him build up iTunes store, which was a quagmire at the time.

In Good Strategy | Bad Strategy, management researcher Richard Rumelt argues that good strategy uses relative strength to counter relative weakness. To discover your main point, determine your abilities and where to effectively use them.

Steve Jobs did that at Apple. Microsoft and Dell, who controlled the computer sector at the time, couldn't enter the music player business. Both sought to produce iPod competitors but failed. Apple's iPod was nobody else's focus.

Finding The Center of Attention

In a military engagement, leaders decide where to focus their efforts by assessing commanders intent, the situation on the ground, the topography, and the enemy's posture on that terrain. Officers spend their careers learning about schwerpunkt.

Business executives must assess internal strengths including personnel, technology, and information, market context, competitive environment, and external partner ecosystems. Steve Jobs was a master at analyzing forces when he returned to Apple.

He believed Apple could integrate technology and design for the iPod and that the digital music player industry sucked. By analyzing competitors' products, he was convinced he could produce a smash by putting 1000 tunes in my pocket.

The only difficulty was there wasn't the necessary technology. External ecosystems were needed. On a trip to Japan to meet with suppliers, a Toshiba engineer claimed the company had produced a tiny memory drive approximately the size of a silver dollar.

Jobs knew the memory drive was his focus. He wrote a $10 million cheque and acquired exclusive technical rights. For a time, none of his competitors would be able to recreate his iPod with the 1000 songs in my pocket.

How to Enter the OODA Loop

John Boyd invented the OODA loop as a pilot to better his own decision-making. First OBSERVE your surroundings, then ORIENT that information using previous knowledge and experiences. Then you DECIDE and ACT, which changes the circumstance you must observe, orient, decide, and act on.

Steve Jobs used the OODA loop to decide to give Toshiba $10 million for a technology it had no use for. He compared the new information with earlier observations about the digital music market.

Then something much more interesting happened. The iPod was an instant hit, changing competition. Other computer businesses that competed in laptops, desktops, and servers created digital music players. Microsoft's Zune came out in 2006, Dell's Digital Jukebox in 2004. Both flopped.

By then, Apple was poised to unveil the iPhone, which would cause its competitors to Observe, Orient, Decide, and Act. Boyd named this OODA Loop infiltration. They couldn't gain the initiative by constantly reacting to Apple.

Microsoft and Dell were titans back then, but it's hard to recall. Apple went from near bankruptcy to crushing its competition via Schwerpunkt.

Rather than a destination, it is a journey

Trying to win everywhere is a strategic blunder. Win significant fights, not trivial skirmishes. Identifying a focal point to direct resources and efforts is the essence of Schwerpunkt.

When Steve Jobs returned to Apple, PC firms were competing, but he focused on digital music players, and the iPod made Apple a player. He launched the iPhone when his competitors were still reacting. When Steve Jobs said, "One more thing," at the end of a product presentation, he had a new focus.

Schwerpunkt isn't static; it's dynamic. Jobs' ability to observe, refocus, and modify the competitive backdrop allowed Apple to innovate consistently. His strategy was tailored to Apple's capabilities, customers, and ecosystem. Microsoft or Dell, better suited for the enterprise sector, couldn't succeed with a comparable approach.

There is no optimal strategy, only ones suited to a given environment, when relative strength might be used against relative weakness. Discovering the center of gravity where you can break through is more of a journey than a destination; it will become evident after you reach.

Nir Zicherman

Nir Zicherman

3 years ago

The Great Organizational Conundrum

Only two of the following three options can be achieved: consistency, availability, and partition tolerance

A DALL-E 2 generated “photograph of a teddy bear who is frustrated because it can’t finish a jigsaw puzzle”

Someone told me that growing from 30 to 60 is the biggest adjustment for a team or business.

I remember thinking, That's random. Each company is unique. I've seen teams of all types confront the same issues during development periods. With new enterprises starting every year, we should be better at navigating growing difficulties.

As a team grows, its processes and systems break down, requiring reorganization or declining results. Why always? Why isn't there a perfect scaling model? Why hasn't that been found?

The Three Things Productive Organizations Must Have

Any company should be efficient and productive. Three items are needed:

First, it must verify that no two team members have conflicting information about the roadmap, strategy, or any input that could affect execution. Teamwork is required.

Second, it must ensure that everyone can receive the information they need from everyone else quickly, especially as teams become more specialized (an inevitability in a developing organization). It requires everyone's accessibility.

Third, it must ensure that the organization can operate efficiently even if a piece is unavailable. It's partition-tolerant.

From my experience with the many teams I've been on, invested in, or advised, achieving all three is nearly impossible. Why a perfect organization model cannot exist is clear after analysis.

The CAP Theorem: What is it?

Eric Brewer of Berkeley discovered the CAP Theorem, which argues that a distributed data storage should have three benefits. One can only have two at once.

The three benefits are consistency, availability, and partition tolerance, which implies that even if part of the system is offline, the remainder continues to work.

This notion is usually applied to computer science, but I've realized it's also true for human organizations. In a post-COVID world, many organizations are hiring non-co-located staff as they grow. CAP Theorem is more important than ever. Growing teams sometimes think they can develop ways to bypass this law, dooming themselves to a less-than-optimal team dynamic. They should adopt CAP to maximize productivity.

Path 1: Consistency and availability equal no tolerance for partitions

Let's imagine you want your team to always be in sync (i.e., for someone to be the source of truth for the latest information) and to be able to share information with each other. Only division into domains will do.

Numerous developing organizations do this, especially after the early stage (say, 30 people) when everyone may wear many hats and be aware of all the moving elements. After a certain point, it's tougher to keep generalists aligned than to divide them into specialized tasks.

In a specialized, segmented team, leaders optimize consistency and availability (i.e. every function is up-to-speed on the latest strategy, no one is out of sync, and everyone is able to unblock and inform everyone else).

Partition tolerance suffers. If any component of the organization breaks down (someone goes on vacation, quits, underperforms, or Gmail or Slack goes down), productivity stops. There's no way to give the team stability, availability, and smooth operation during a hiccup.

Path 2: Partition Tolerance and Availability = No Consistency

Some businesses avoid relying too heavily on any one person or sub-team by maximizing availability and partition tolerance (the organization continues to function as a whole even if particular components fail). Only redundancy can do that. Instead of specializing each member, the team spreads expertise so people can work in parallel. I switched from Path 1 to Path 2 because I realized too much reliance on one person is risky.

What happens after redundancy? Unreliable. The more people may run independently and in parallel, the less anyone can be the truth. Lack of alignment or updated information can lead to people executing slightly different strategies. So, resources are squandered on the wrong work.

Path 3: Partition and Consistency "Tolerance" equates to "absence"

The third, least-used path stresses partition tolerance and consistency (meaning answers are always correct and up-to-date). In this organizational style, it's most critical to maintain the system operating and keep everyone aligned. No one is allowed to read anything without an assurance that it's up-to-date (i.e. there’s no availability).

Always short-lived. In my experience, a business that prioritizes quality and scalability over speedy information transmission can get bogged down in heavy processes that hinder production. Large-scale, this is unsustainable.

Accepting CAP

When two puzzle pieces fit, the third won't. I've watched developing teams try to tackle these difficulties, only to find, as their ancestors did, that they can never be entirely solved. Idealized solutions fail in reality, causing lost effort, confusion, and lower production.

As teams develop and change, they should embrace CAP, acknowledge there is a limit to productivity in a scaling business, and choose the best two-out-of-three path.

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umair haque

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

Image Credit: Nature

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.

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

Bastian Hasslinger

Bastian Hasslinger

3 years ago

Before 2021, most startups had excessive valuations. It is currently causing issues.

Higher startup valuations are often favorable for all parties. High valuations show a business's potential. New customers and talent are attracted. They earn respect.

Everyone benefits if a company's valuation rises.

Founders and investors have always been incentivized to overestimate a company's value.

Post-money valuations were inflated by 2021 market expectations and the valuation model's mechanisms.

Founders must understand both levers to handle a normalizing market.

2021, the year of miracles

2021 must've seemed miraculous to entrepreneurs, employees, and VCs. Valuations rose, and funding resumed after the first Covid-19 epidemic caution.

In 2021, VC investments increased from $335B to $643B. 518 new worldwide unicorns vs. 134 in 2020; 951 US IPOs vs. 431.

Things can change quickly, as 2020-21 showed.

Rising interest rates, geopolitical developments, and normalizing technology conditions drive down share prices and tech company market caps in 2022. Zoom, the poster-child of early lockdown success, is down 37% since 1st Jan.

Once-inflated valuations can become a problem in a normalizing market, especially for founders, employees, and early investors.

the reason why startups are always overvalued

To see why inflated valuations are a problem, consider one of its causes.

Private company values only fluctuate following a new investment round, unlike publicly-traded corporations. The startup's new value is calculated simply:

(Latest round share price) x (total number of company shares)

This is the industry standard Post-Money Valuation model.

Let’s illustrate how it works with an example. If a VC invests $10M for 1M shares (at $10/share), and the company has 10M shares after the round, its Post-Money Valuation is $100M (10/share x 10M shares).

This approach might seem like the most natural way to assess a business, but the model often unintentionally overstates the underlying value of the company even if the share price paid by the investor is fair. All shares aren't equal.

New investors in a corporation will always try to minimize their downside risk, or the amount they lose if things go wrong. New investors will try to negotiate better terms and pay a premium.

How the value of a struggling SpaceX increased

SpaceX's 2008 Series D is an example. Despite the financial crisis and unsuccessful rocket launches, the company's Post-Money Valuation was 36% higher after the investment round. Why?

Series D SpaceX shares were protected. In case of liquidation, Series D investors were guaranteed a 2x return before other shareholders.

Due to downside protection, investors were willing to pay a higher price for this new share class.

The Post-Money Valuation model overpriced SpaceX because it viewed all the shares as equal (they weren't).

Why entrepreneurs, workers, and early investors stand to lose the most

Post-Money Valuation is an effective and sufficient method for assessing a startup's valuation, despite not taking share class disparities into consideration.

In a robust market, where the firm valuation will certainly expand with the next fundraising round or exit, the inflated value is of little significance.

Fairness endures. If a corporation leaves at a greater valuation, each stakeholder will receive a proportional distribution. (i.e., 5% of a $100M corporation yields $5M).

SpaceX's inherent overvaluation was never a problem. Had it been sold for less than its Post-Money Valuation, some shareholders, including founders, staff, and early investors, would have seen their ownership drop.

The unforgiving world of 2022

In 2022, founders, employees, and investors who benefited from inflated values will face below-valuation exits and down-rounds.

For them, 2021 will be a curse, not a blessing.

Some tech giants are worried. Klarna's valuation fell from $45B (Oct 21) to $30B (Jun 22), Canvas from $40B to $27B, and GoPuffs from $17B to $8.3B.

Shazam and Blue Apron have to exit or IPO at a cheaper price. Premium share classes are protected, while others receive less. The same goes for bankrupts.

Those who continue at lower valuations will lose reputation and talent. When their value declines by half, generous employee stock options become less enticing, and their ability to return anything is questioned.

What can we infer about the present situation?

Such techniques to enhance your company's value or stop a normalizing market are fiction.

The current situation is a painful reminder for entrepreneurs and a crucial lesson for future firms.

The devastating market fall of the previous six months has taught us one thing:

  1. Keep in mind that any valuation is speculative. Money Post A startup's valuation is a highly simplified approximation of its true value, particularly in the early phases when it lacks significant income or a cutting-edge product. It is merely a projection of the future and a hypothetical meter. Until it is achieved by an exit, a valuation is nothing more than a number on paper.

  2. Assume the value of your company is lower than it was in the past. Your previous valuation might not be accurate now due to substantial changes in the startup financing markets. There is little reason to think that your company's value will remain the same given the 50%+ decline in many newly listed IT companies. Recognize how the market situation is changing and use caution.

  3. Recognize the importance of the stake you hold. Each share class has a unique value that varies. Know the sort of share class you own and how additional contractual provisions affect the market value of your security. Frameworks have been provided by Metrick and Yasuda (Yale & UC) and Gornall and Strebulaev (Stanford) for comprehending the terms that affect investors' cash-flow rights upon withdrawal. As a result, you will be able to more accurately evaluate your firm and determine the worth of each share class.

  4. Be wary of approving excessively protective share terms.
    The trade-offs should be considered while negotiating subsequent rounds. Accepting punitive contractual terms could first seem like a smart option in order to uphold your inflated worth, but you should proceed with caution. Such provisions ALWAYS result in misaligned shareholders, with common shareholders (such as you and your staff) at the bottom of the list.