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Alison Randel

Alison Randel

3 years ago

Raising the Bar on Your 1:1s

More on Leadership

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.

Hunter Walk

Hunter Walk

2 years ago

Is it bad of me to want our portfolio companies to generate greater returns for outside investors than they did for us as venture capitalists?

Wishing for Lasting Companies, Not Penny Stocks or Goodwill Write-Downs

Get me a NASCAR-style company-logoed cremation urn (notice to the executor of my will, theres gonna be a lot of weird requests). I believe in working on projects that would be on your tombstone. As the Homebrew logo is tattooed on my shoulder, expanding the portfolio to my posthumous commemoration is easy. But this isn't an IRR victory lap; it's a hope that the firms we worked for would last beyond my lifetime.

a little boy planting a dollar bill in the ground and pouring a watering can out on it, digital art [DALL-E]

Venture investors too often take credit or distance themselves from startups based on circumstances. Successful companies tell stories of crucial introductions, strategy conversations, and other value. Defeats Even whether our term involves Board service or systematic ethical violations, I'm just a little investment, so there's not much I can do. Since I'm guilty, I'm tossing stones from within the glass home (although we try to own our decisions through the lifecycle).

Post-exit company trajectories are usually unconfounded. Off the cap table, no longer a shareholder (or a diminishing one as you sell off/distribute), eventually leaving the Board. You can cheer for the squad or forget about it, but you've freed the corporation and it's back to portfolio work.

As I look at the downward track of most SPACs and other tarnished IPOs from the last few years, I wonder how I would feel if those were my legacy. Is my job done? Yes. When investing in a business, the odds are against it surviving, let alone thriving and being able to find sunlight. SPAC sponsors, institutional buyers, retail investments. Free trade in an open market is their right. Risking and losing capital is the system working! But

We were lead or co-lead investors in our first three funds, but as additional VCs joined the company, we were pushed down the cap table. Voting your shares rarely matters; supporting the firm when they need it does. Being valuable, consistent, and helping the company improve builds trust with the founders.

I hope every startup we sponsor becomes a successful public company before, during, and after we benefit. My perspective of American capitalism. Well, a stock ticker has a lot of garbage, and I support all types of regulation simplification (in addition to being a person investor in the Long-Term Stock Exchange). Yet being owned by a large group of investors and making actual gains for them is great. Likewise does seeing someone you met when they were just starting out become a public company CEO without losing their voice, leadership, or beliefs.

I'm just thinking about what we can do from the start to realize value from our investments and build companies with bright futures. Maybe seed venture financing shouldn't impact those outcomes, but I'm not comfortable giving up that obligation.

Christian Soschner

Christian Soschner

3 years ago

Steve Jobs' Secrets Revealed

From 1984 until 2011, he ran Apple using the same template.

What is a founder CEO's most crucial skill?

Presentation, communication, and sales

As a Business Angel Investor, I saw many pitch presentations and met with investors one-on-one to promote my companies.

There is always the conception of “Investors have to invest,” so there is no need to care about the presentation.

It's false. Nobody must invest. Many investors believe that entrepreneurs must convince them to invest in their business.

Sometimes — like in 2018–2022 — too much money enters the market, and everyone makes good money.

Do you recall the Buy Now, Pay Later Movement? This amazing narrative had no return potential. Only buyers who couldn't acquire financing elsewhere shopped at these companies.

Klarna's failing business concept led to high valuations.

Investors become more cautious when the economy falters. 2022 sees rising inflation, interest rates, wars, and civil instability. It's like the apocalypse's four horsemen have arrived.


Storytelling is important in rough economies.

When investors draw back, how can entrepreneurs stand out?

In Q2/2022, every study I've read said:

Investors cease investing

Deals are down in almost all IT industries from previous quarters.

What do founders need to do?

Differentiate yourself.

Storytelling talents help.


The Steve Jobs Way

Every time I watch a Steve Jobs presentation, I'm enthralled.

I'm a techie. Everything technical interests me. But, I skim most presentations.

What's Steve Jobs's secret?

Steve Jobs created Apple in 1976 and made it a profitable software and hardware firm in the 1980s. Macintosh goods couldn't beat IBM's. This mistake sacked him in 1985.

Before rejoining Apple in 1997, Steve Jobs founded Next Inc. and Pixar.

From then on, Apple became America's most valuable firm.

Steve Jobs understood people's needs. He said:

“People don’t know what they want until you show it to them. That’s why I never rely on market research. Our task is to read things that are not yet on the page.”

In his opinion, people talk about problems. A lot. Entrepreneurs must learn what the population's pressing problems are and create a solution.

Steve Jobs showed people what they needed before they realized it.

I'll explain:


Present a Big Vision

Steve Jobs starts every presentation by describing his long-term goals for Apple.

1984's Macintosh presentation set up David vs. Goliath. In a George Orwell-style dystopia, IBM computers were bad. It was 1984.

Apple will save the world, like Jedis.

Why do customers and investors like Big Vision?

People want a wider perspective, I think. Humans love improving the planet.

Apple users often cite emotional reasons for buying the brand.

Revolutionizing several industries with breakthrough inventions


Establish Authority

Everyone knows Apple in 2022. It's hard to find folks who confuse Apple with an apple around the world.

Apple wasn't as famous as it is today until Steve Jobs left in 2011.

Most entrepreneurs lack experience. They may market their company or items to folks who haven't heard of it.

Steve Jobs presented the company's historical accomplishments to overcome opposition.

In his presentation of the first iPhone, he talked about the Apple Macintosh, which altered the computing sector, and the iPod, which changed the music industry.

People who have never heard of Apple feel like they're seeing a winner. It raises expectations that the new product will be game-changing and must-have.


The Big Reveal

A pitch or product presentation always has something new.

Steve Jobs doesn't only demonstrate the product. I don't think he'd skip the major point of a company presentation.

He consistently discusses present market solutions, their faults, and a better consumer solution.

No solution exists yet.

It's a multi-faceted play:

  • It's comparing the new product to something familiar. This makes novelty and the product more relatable.

  • Describe a desirable solution.

  • He's funny. He demonstrated an iPod with an 80s phone dial in his iPhone presentation.

Then he reveals the new product. Macintosh presented itself.


Show the benefits

He outlines what Apple is doing differently after demonstrating the product.

How do you distinguish from others? The Big Breakthrough Presentation.

A few hundred slides might list all benefits.

Everyone would fall asleep. Have you ever had similar presentations?

When the brain is overloaded with knowledge, the limbic system changes to other duties, like lunch planning.

What should a speaker do? There's a classic proverb:

Tell me and I forget, teach me and I may remember, involve me and I learn” (— Not Benjamin Franklin).

Steve Jobs showcased the product live.

Again, using ordinary scenarios to highlight the product's benefits makes it relatable.

The 2010 iPad Presentation uses this technique.


Invite the Team and Let Them Run the Presentation

CEOs spend most time outside the organization. Many companies elect to have only one presenter.

It sends the incorrect message to investors. Product presentations should always include the whole team.

Let me explain why.

Companies needing investment money frequently have shaky business strategies or no product-market fit or robust corporate structure.

Investors solely bet on a team's ability to implement ideas and make a profit.

Early team involvement helps investors understand the company's drivers. Travel costs are worthwhile.

But why for product presentations?

Presenters of varied ages, genders, social backgrounds, and skillsets are relatable. CEOs want relatable products.

Some customers may not believe a white man's message. A black woman's message may be more accepted.

Make the story relatable when you have the best product that solves people's concerns.


Best example: 1984 Macintosh presentation with development team panel.

What is the largest error people make when companies fail?

Saving money on the corporate and product presentation.

Invite your team to five partner meetings when five investors are shortlisted.

Rehearse the presentation till it's natural. Let the team speak.

Successful presentations require structure, rehearsal, and a team. Steve Jobs nailed it.

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Khyati Jain

Khyati Jain

3 years ago

By Engaging in these 5 Duplicitous Daily Activities, You Rapidly Kill Your Brain Cells

No, it’s not smartphones, overeating, or sugar.

Freepik

Everyday practices affect brain health. Good brain practices increase memory and cognition.

Bad behaviors increase stress, which destroys brain cells.

Bad behaviors can reverse evolution and diminish the brain. So, avoid these practices for brain health.

1. The silent assassin

Introverts appreciated quarantine.

Before the pandemic, they needed excuses to remain home; thereafter, they had enough.

I am an introvert, and I didn’t hate quarantine. There are billions of people like me who avoid people.

Social relationships are important for brain health. Social anxiety harms your brain.

Antisocial behavior changes brains. It lowers IQ and increases drug abuse risk.

What you can do is as follows:

  • Make a daily commitment to engage in conversation with a stranger. Who knows, you might turn out to be your lone mate.

  • Get outside for at least 30 minutes each day.

  • Shop for food locally rather than online.

  • Make a call to a friend you haven't spoken to in a while.

2. Try not to rush things.

People love hustle culture. This economy requires a side gig to save money.

Long hours reduce brain health. A side gig is great until you burn out.

Work ages your wallet and intellect. Overworked brains age faster and lose cognitive function.

Working longer hours can help you make extra money, but it can harm your brain.

Side hustle but don't overwork.

What you can do is as follows:

  • Decide what hour you are not permitted to work after.

  • Three hours prior to night, turn off your laptop.

  • Put down your phone and work.

  • Assign due dates to each task.

3. Location is everything!

The environment may cause brain fog. High pollution can cause brain damage.

Air pollution raises Alzheimer's risk. Air pollution causes cognitive and behavioral abnormalities.

Polluted air can trigger early development of incurable brain illnesses, not simply lung harm.

Your city's air quality is uncontrollable. You may take steps to improve air quality.

In Delhi, schools and colleges are closed to protect pupils from polluted air. So I've adapted.

What you can do is as follows:

  • To keep your mind healthy and young, make an investment in a high-quality air purifier.

  • Enclose your windows during the day.

  • Use a N95 mask every day.

4. Don't skip this meal.

Fasting intermittently is trendy. Delaying breakfast to finish fasting is frequent.

Some skip breakfast and have a hefty lunch instead.

Skipping breakfast might affect memory and focus. Skipping breakfast causes low cognition, delayed responsiveness, and irritation.

Breakfast affects mood and productivity.

Intermittent fasting doesn't prevent healthy breakfasts.

What you can do is as follows:

  • Try to fast for 14 hours, then break it with a nutritious breakfast.

  • So that you can have breakfast in the morning, eat dinner early.

  • Make sure your breakfast is heavy in fiber and protein.

5. The quickest way to damage the health of your brain

Brain health requires water. 1% dehydration can reduce cognitive ability by 5%.

Cerebral fog and mental clarity might result from 2% brain dehydration. Dehydration shrinks brain cells.

Dehydration causes midday slumps and unproductivity. Water improves work performance.

Dehydration can harm your brain, so drink water throughout the day.

What you can do is as follows:

  • Always keep a water bottle at your desk.

  • Enjoy some tasty herbal teas.

  • With a big glass of water, begin your day.

  • Bring your own water bottle when you travel.

Conclusion

Bad habits can harm brain health. Low cognition reduces focus and productivity.

Unproductive work leads to procrastination, failure, and low self-esteem.

Avoid these harmful habits to optimize brain health and function.

Thomas Huault

Thomas Huault

3 years ago

A Mean Reversion Trading Indicator Inspired by Classical Mechanics Is The Kinetic Detrender

DATA MINING WITH SUPERALGORES

Old pots produce the best soup.

Photo by engin akyurt on Unsplash

Science has always inspired indicator design. From physics to signal processing, many indicators use concepts from mechanical engineering, electronics, and probability. In Superalgos' Data Mining section, we've explored using thermodynamics and information theory to construct indicators and using statistical and probabilistic techniques like reduced normal law to take advantage of low probability events.

An asset's price is like a mechanical object revolving around its moving average. Using this approach, we could design an indicator using the oscillator's Total Energy. An oscillator's energy is finite and constant. Since we don't expect the price to follow the harmonic oscillator, this energy should deviate from the perfect situation, and the maximum of divergence may provide us valuable information on the price's moving average.

Definition of the Harmonic Oscillator in Few Words

Sinusoidal function describes a harmonic oscillator. The time-constant energy equation for a harmonic oscillator is:

With

Time saves energy.

In a mechanical harmonic oscillator, total energy equals kinetic energy plus potential energy. The formula for energy is the same for every kind of harmonic oscillator; only the terms of total energy must be adapted to fit the relevant units. Each oscillator has a velocity component (kinetic energy) and a position to equilibrium component (potential energy).

The Price Oscillator and the Energy Formula

Considering the harmonic oscillator definition, we must specify kinetic and potential components for our price oscillator. We define oscillator velocity as the rate of change and equilibrium position as the price's distance from its moving average.

Price kinetic energy:

It's like:

With

and

L is the number of periods for the rate of change calculation and P for the close price EMA calculation.

Total price oscillator energy =

Given that an asset's price can theoretically vary at a limitless speed and be endlessly far from its moving average, we don't expect this formula's outcome to be constrained. We'll normalize it using Z-Score for convenience of usage and readability, which also allows probabilistic interpretation.

Over 20 periods, we'll calculate E's moving average and standard deviation.

We calculated Z on BTC/USDT with L = 10 and P = 21 using Knime Analytics.

The graph is detrended. We added two horizontal lines at +/- 1.6 to construct a 94.5% probability zone based on reduced normal law tables. Price cycles to its moving average oscillate clearly. Red and green arrows illustrate where the oscillator crosses the top and lower limits, corresponding to the maximum/minimum price oscillation. Since the results seem noisy, we may apply a non-lagging low-pass or multipole filter like Butterworth or Laguerre filters and employ dynamic bands at a multiple of Z's standard deviation instead of fixed levels.

Kinetic Detrender Implementation in Superalgos

The Superalgos Kinetic detrender features fixed upper and lower levels and dynamic volatility bands.

The code is pretty basic and does not require a huge amount of code lines.

It starts with the standard definitions of the candle pointer and the constant declaration :

let candle = record.current
let len = 10
let P = 21
let T = 20
let up = 1.6
let low = 1.6

Upper and lower dynamic volatility band constants are up and low.

We proceed to the initialization of the previous value for EMA :

if (variable.prevEMA === undefined) {
    variable.prevEMA = candle.close
}

And the calculation of EMA with a function (it is worth noticing the function is declared at the end of the code snippet in Superalgos) :

variable.ema = calculateEMA(P, candle.close, variable.prevEMA)
//EMA calculation
function calculateEMA(periods, price, previousEMA) {
    let k = 2 / (periods + 1)
    return price * k + previousEMA * (1 - k)
}

The rate of change is calculated by first storing the right amount of close price values and proceeding to the calculation by dividing the current close price by the first member of the close price array:

variable.allClose.push(candle.close)
if (variable.allClose.length > len) {
    variable.allClose.splice(0, 1)
}
if (variable.allClose.length === len) {
    variable.roc = candle.close / variable.allClose[0]
} else {
    variable.roc = 1
}

Finally, we get energy with a single line:

variable.E = 1 / 2 * len * variable.roc + 1 / 2 * P * candle.close / variable.ema

The Z calculation reuses code from Z-Normalization-based indicators:

variable.allE.push(variable.E)
if (variable.allE.length > T) {
    variable.allE.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allE.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allE[i]
    }
    variable.MA = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allE[i] - variable.MA, 2)
    }
    variable.sigma = Math.sqrt(variable.SQ / T)
variable.Z = (variable.E - variable.MA) / variable.sigma
} else {
    variable.Z = 0
}
variable.allZ.push(variable.Z)
if (variable.allZ.length > T) {
    variable.allZ.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allZ.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allZ[i]
    }
    variable.MAZ = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allZ[i] - variable.MAZ, 2)
    }
    variable.sigZ = Math.sqrt(variable.SQ / T)
} else {
    variable.MAZ = variable.Z
    variable.sigZ = variable.MAZ * 0.02
}
variable.upper = variable.MAZ + up * variable.sigZ
variable.lower = variable.MAZ - low * variable.sigZ

We also update the EMA value.

variable.prevEMA = variable.EMA
BTD/USDT candle chart at 01-hs timeframe with the Kinetic detrender and its 2 red fixed level and black dynamic levels

Conclusion

We showed how to build a detrended oscillator using simple harmonic oscillator theory. Kinetic detrender's main line oscillates between 2 fixed levels framing 95% of the values and 2 dynamic levels, leading to auto-adaptive mean reversion zones.

Superalgos' Normalized Momentum data mine has the Kinetic detrender indication.

All the material here can be reused and integrated freely by linking to this article and Superalgos.

This post is informative and not financial advice. Seek expert counsel before trading. Risk using this material.

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