More on Entrepreneurship/Creators

Dani Herrera
3 years ago
What prevents companies from disclosing salary information?
Yes, salary details ought to be mentioned in job postings. Recruiters and candidates both agree, so why doesn't it happen?
The short answer is “Unfortunately, it’s not the Recruiter’s decision”. The longer answer is well… A LOT.
Starting in November 2022, NYC employers must include salary ranges in job postings. It should have started in May, but companies balked.
I'm thrilled about salary transparency. This decision will promote fair, inclusive, and equitable hiring practices, and I'm sure other states will follow suit. Good news!
Candidates, recruiters, and ED&I practitioners have advocated for pay transparency for years. Why the opposition?
Let's quickly review why companies have trouble sharing salary bands.
💰 Pay Parity
Many companies and leaders still oppose pay parity. Yes, even in 2022.
💰 Pay Equity
Many companies believe in pay parity and have reviewed their internal processes and systems to ensure equality.
However, Pay Equity affects who gets roles/promotions/salary raises/bonuses and when. Enter the pay gap!
💰Pay Transparency and its impact on Talent Retention
Sharing salary bands with external candidates (and the world) means current employees will have access to that information, which is one of the main reasons companies don't share salary data.
If a company has Pay Parity and Pay Equity issues, they probably have a Pay Transparency policy as well.
Sharing salary information with external candidates without ensuring current employees understand their own salary bands and how promotions/raises are decided could impact talent retention strategies.
This information should help clarify recent conversations.
Atown Research
2 years ago
Meet the One-Person Businesses Earning Millions in Sales from Solo Founders
I've spent over 50 hours researching one-person firms, which interest me. I've found countless one-person enterprises that made millions on the founder's determination and perseverance.
Throughout my investigation, I found three of the most outstanding one-person enterprises. These enterprises show that people who work hard and dedicate themselves to their ideas may succeed.
Eric Barone (@ConcernedApe) created Stardew Valley in 2011 to better his job prospects. Eric loved making the game, in which players inherit a farm, grow crops, raise livestock, make friends with the villagers, and form a family.
Eric handled complete game production, including 3D graphics, animations, and music, to maintain creative control. He stopped job hunting and worked 8-15 hours a day on the game.
Eric developed a Stardew Valley website and subreddit to engage with gamers and get feedback. Eric's devoted community helped him meet Steam's minimum vote requirement for single creators.
Stardew Valley sold 1 million copies in two months after Eric launched it for $15 in 2016. The game has sold 20 million copies and made $300 million.
The game's inexpensive price, outsourcing of PR, marketing, and publication, and loyal player base helped it succeed. Eric has turned down million-dollar proposals from Sony and Nintendo to sell the game and instead updates and improves it. Haunted Chocolatier is Eric's new game.
Is farming not profitable? Ask Stardew Valley creator Eric Barone.
Gary Brewer established BuiltWith to assist users find website technologies and services. BuiltWith boasts 3000 paying customers and $14 million in yearly revenue, making it a significant resource for businesses wishing to generate leads, do customer analytics, obtain business insight, compare websites, or search websites by keyword.
BuiltWith has one full-time employee, Gary, and one or two part-time contractors that help with the blog. Gary handles sales, customer service, and other company functions alone.
BuiltWith acquired popularity through blog promotions and a top Digg ranking. About Us, a domain directory, connected to BuiltWith on every domain page, boosting it. Gary introduced $295–$995 monthly subscriptions to search technology, keywords, and potential consumers in response to customer demand.
Gary uses numerous methods to manage a firm without staff. He spends one to two hours every day answering user queries, most of which are handled quickly by linking to BuiltWiths knowledge store. Gary creates step-by-step essays or videos for complex problems. Gary can focus on providing new features based on customer comments and requests since he makes it easy to unsubscribe.
BuiltWith is entirely automated and successful due to its unique approach and useful offerings. It works for Google, Meta, Amazon, and Twitter.
Digital Inspiration develops Google Documents, Sheets, and Slides plugins. Digital Inspiration, founded by Amit Agarwal, receives 5 million monthly visits and earns $10 million. 40 million individuals have downloaded Digital Inspirations plugins.
Amit started Digital Inspiration by advertising his blog at tech events and getting Indian filter blogs and other newspapers to promote his articles. Amit built plugins and promoted them on the blog once the blog acquired popularity, using ideas from comments, friends, and Reddit. Digital Inspiration has over 20 free and premium plugins.
Mail Merge, Notifications for Google Forms, YouTube Uploader, and Document Studio are some of Digital Inspiration's most popular plugins. Mail Merge allows users to send personalized emails in bulk and track email opens and clicks.
Since Amits manages Digital Inspiration alone, his success is astounding. Amit developed a successful company via hard work and creativity, despite platform dependence. His tale inspires entrepreneurs.

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:
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.
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.
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.
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.
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Sofien Kaabar, CFA
2 years ago
Innovative Trading Methods: The Catapult Indicator
Python Volatility-Based Catapult Indicator
As a catapult, this technical indicator uses three systems: Volatility (the fulcrum), Momentum (the propeller), and a Directional Filter (Acting as the support). The goal is to get a signal that predicts volatility acceleration and direction based on historical patterns. We want to know when the market will move. and where. This indicator outperforms standard indicators.
Knowledge must be accessible to everyone. This is why my new publications Contrarian Trading Strategies in Python and Trend Following Strategies in Python now include free PDF copies of my first three books (Therefore, purchasing one of the new books gets you 4 books in total). GitHub-hosted advanced indications and techniques are in the two new books above.
The Foundation: Volatility
The Catapult predicts significant changes with the 21-period Relative Volatility Index.
The Average True Range, Mean Absolute Deviation, and Standard Deviation all assess volatility. Standard Deviation will construct the Relative Volatility Index.
Standard Deviation is the most basic volatility. It underpins descriptive statistics and technical indicators like Bollinger Bands. Before calculating Standard Deviation, let's define Variance.
Variance is the squared deviations from the mean (a dispersion measure). We take the square deviations to compel the distance from the mean to be non-negative, then we take the square root to make the measure have the same units as the mean, comparing apples to apples (mean to standard deviation standard deviation). Variance formula:
As stated, standard deviation is:
# The function to add a number of columns inside an array
def adder(Data, times):
for i in range(1, times + 1):
new_col = np.zeros((len(Data), 1), dtype = float)
Data = np.append(Data, new_col, axis = 1)
return Data
# The function to delete a number of columns starting from an index
def deleter(Data, index, times):
for i in range(1, times + 1):
Data = np.delete(Data, index, axis = 1)
return Data
# The function to delete a number of rows from the beginning
def jump(Data, jump):
Data = Data[jump:, ]
return Data
# Example of adding 3 empty columns to an array
my_ohlc_array = adder(my_ohlc_array, 3)
# Example of deleting the 2 columns after the column indexed at 3
my_ohlc_array = deleter(my_ohlc_array, 3, 2)
# Example of deleting the first 20 rows
my_ohlc_array = jump(my_ohlc_array, 20)
# Remember, OHLC is an abbreviation of Open, High, Low, and Close and it refers to the standard historical data file
def volatility(Data, lookback, what, where):
for i in range(len(Data)):
try:
Data[i, where] = (Data[i - lookback + 1:i + 1, what].std())
except IndexError:
pass
return Data
The RSI is the most popular momentum indicator, and for good reason—it excels in range markets. Its 0–100 range simplifies interpretation. Fame boosts its potential.
The more traders and portfolio managers look at the RSI, the more people will react to its signals, pushing market prices. Technical Analysis is self-fulfilling, therefore this theory is obvious yet unproven.
RSI is determined simply. Start with one-period pricing discrepancies. We must remove each closing price from the previous one. We then divide the smoothed average of positive differences by the smoothed average of negative differences. The RSI algorithm converts the Relative Strength from the last calculation into a value between 0 and 100.
def ma(Data, lookback, close, where):
Data = adder(Data, 1)
for i in range(len(Data)):
try:
Data[i, where] = (Data[i - lookback + 1:i + 1, close].mean())
except IndexError:
pass
# Cleaning
Data = jump(Data, lookback)
return Data
def ema(Data, alpha, lookback, what, where):
alpha = alpha / (lookback + 1.0)
beta = 1 - alpha
# First value is a simple SMA
Data = ma(Data, lookback, what, where)
# Calculating first EMA
Data[lookback + 1, where] = (Data[lookback + 1, what] * alpha) + (Data[lookback, where] * beta)
# Calculating the rest of EMA
for i in range(lookback + 2, len(Data)):
try:
Data[i, where] = (Data[i, what] * alpha) + (Data[i - 1, where] * beta)
except IndexError:
pass
return Datadef rsi(Data, lookback, close, where, width = 1, genre = 'Smoothed'):
# Adding a few columns
Data = adder(Data, 7)
# Calculating Differences
for i in range(len(Data)):
Data[i, where] = Data[i, close] - Data[i - width, close]
# Calculating the Up and Down absolute values
for i in range(len(Data)):
if Data[i, where] > 0:
Data[i, where + 1] = Data[i, where]
elif Data[i, where] < 0:
Data[i, where + 2] = abs(Data[i, where])
# Calculating the Smoothed Moving Average on Up and Down
absolute values
lookback = (lookback * 2) - 1 # From exponential to smoothed
Data = ema(Data, 2, lookback, where + 1, where + 3)
Data = ema(Data, 2, lookback, where + 2, where + 4)
# Calculating the Relative Strength
Data[:, where + 5] = Data[:, where + 3] / Data[:, where + 4]
# Calculate the Relative Strength Index
Data[:, where + 6] = (100 - (100 / (1 + Data[:, where + 5])))
# Cleaning
Data = deleter(Data, where, 6)
Data = jump(Data, lookback)
return Datadef relative_volatility_index(Data, lookback, close, where):
# Calculating Volatility
Data = volatility(Data, lookback, close, where)
# Calculating the RSI on Volatility
Data = rsi(Data, lookback, where, where + 1)
# Cleaning
Data = deleter(Data, where, 1)
return DataThe Arm Section: Speed
The Catapult predicts momentum direction using the 14-period Relative Strength Index.
As a reminder, the RSI ranges from 0 to 100. Two levels give contrarian signals:
A positive response is anticipated when the market is deemed to have gone too far down at the oversold level 30, which is 30.
When the market is deemed to have gone up too much, at overbought level 70, a bearish reaction is to be expected.
Comparing the RSI to 50 is another intriguing use. RSI above 50 indicates bullish momentum, while below 50 indicates negative momentum.
The direction-finding filter in the frame
The Catapult's directional filter uses the 200-period simple moving average to keep us trending. This keeps us sane and increases our odds.
Moving averages confirm and ride trends. Its simplicity and track record of delivering value to analysis make them the most popular technical indicator. They help us locate support and resistance, stops and targets, and the trend. Its versatility makes them essential trading tools.
This is the plain mean, employed in statistics and everywhere else in life. Simply divide the number of observations by their total values. Mathematically, it's:
We defined the moving average function above. Create the Catapult indication now.
Indicator of the Catapult
The indicator is a healthy mix of the three indicators:
The first trigger will be provided by the 21-period Relative Volatility Index, which indicates that there will now be above average volatility and, as a result, it is possible for a directional shift.
If the reading is above 50, the move is likely bullish, and if it is below 50, the move is likely bearish, according to the 14-period Relative Strength Index, which indicates the likelihood of the direction of the move.
The likelihood of the move's direction will be strengthened by the 200-period simple moving average. When the market is above the 200-period moving average, we can infer that bullish pressure is there and that the upward trend will likely continue. Similar to this, if the market falls below the 200-period moving average, we recognize that there is negative pressure and that the downside is quite likely to continue.
lookback_rvi = 21
lookback_rsi = 14
lookback_ma = 200
my_data = ma(my_data, lookback_ma, 3, 4)
my_data = rsi(my_data, lookback_rsi, 3, 5)
my_data = relative_volatility_index(my_data, lookback_rvi, 3, 6)Two-handled overlay indicator Catapult. The first exhibits blue and green arrows for a buy signal, and the second shows blue and red for a sell signal.
The chart below shows recent EURUSD hourly values.
def signal(Data, rvi_col, signal):
Data = adder(Data, 10)
for i in range(len(Data)):
if Data[i, rvi_col] < 30 and \
Data[i - 1, rvi_col] > 30 and \
Data[i - 2, rvi_col] > 30 and \
Data[i - 3, rvi_col] > 30 and \
Data[i - 4, rvi_col] > 30 and \
Data[i - 5, rvi_col] > 30:
Data[i, signal] = 1
return DataSignals are straightforward. The indicator can be utilized with other methods.
my_data = signal(my_data, 6, 7)Lumiwealth shows how to develop all kinds of algorithms. I recommend their hands-on courses in algorithmic trading, blockchain, and machine learning.
Summary
To conclude, my goal is to contribute to objective technical analysis, which promotes more transparent methods and strategies that must be back-tested before implementation. Technical analysis will lose its reputation as subjective and unscientific.
After you find a trading method or approach, follow these steps:
Put emotions aside and adopt an analytical perspective.
Test it in the past in conditions and simulations taken from real life.
Try improving it and performing a forward test if you notice any possibility.
Transaction charges and any slippage simulation should always be included in your tests.
Risk management and position sizing should always be included in your tests.
After checking the aforementioned, monitor the plan because market dynamics may change and render it unprofitable.

Katharine Valentino
3 years ago
A Gun-toting Teacher Is Like a Cook With Rat Poison
Pink or blue AR-15s?
A teacher teaches; a gun kills. Killing isn't teaching. Killing is opposite of teaching.
Without 27 school shootings this year, we wouldn't be talking about arming teachers. Gun makers, distributors, and the NRA cause most school shootings. Gun makers, distributors, and the NRA wouldn't be huge business if weapons weren't profitable.
Guns, ammo, body armor, holsters, concealed carriers, bore sights, cleaner kits, spare magazines and speed loaders, gun safes, and ear protection are sold. And more guns.
And lots more profit.
Guns aren't bread. You eat a loaf of bread in a week or so and then must buy more. Bread makers will make money. Winchester 94.30–30 1899 Lever Action Rifle from 1894 still kills. (For safety, I won't link to the ad.) Gun makers don't object if you collect antique weapons, but they need you to buy the latest, in-style killing machine. The youngster who killed 19 students and 2 teachers at Robb Elementary School in Uvalde, Texas, used an AR-15. Better yet, two.
Salvador Ramos, the Robb Elementary shooter, is a "killing influencer" He pushes consumers to buy items, which benefits manufacturers and distributors. Like every previous AR-15 influencer, he profits Colt, the rifle's manufacturer, and 52,779 gun dealers in the U.S. Ramos and other AR-15 influences make us fear for our safety and our children's. Fearing for our safety, we acquire 20 million firearms a year and live in a gun culture.
So now at school, we want to arm teachers.
Consider. Which of your teachers would you have preferred in body armor with a gun drawn?
Miss Summers? Remember her bringing daisies from her yard to second grade? She handed each student a beautiful flower. Miss Summers loved everyone, even those with AR-15s. She can't shoot.
Frasier? Mr. Frasier turned a youngster over down to explain "invert." Mr. Frasier's hands shook when he wasn't flipping fifth-graders and fractions. He may have shot wrong.
Mrs. Barkley barked in high school English class when anyone started an essay with "But." Mrs. Barkley dubbed Abie a "Jewboy" and gave him terrible grades. Arming Miss Barkley is like poisoning the chef.
Think back. Do you remember a teacher with a gun? No. Arming teachers so the gun industry can make more money is the craziest idea ever.
Or maybe you agree with Ted Cruz, the gun lobby-bought senator, that more guns reduce gun violence. After the next school shooting, you'll undoubtedly talk about arming teachers and pupils. Colt will likely develop a backpack-sized, lighter version of its popular killing machine in pink and blue for kids and boys. The MAR-15? (M for mini).
This post is a summary. Read the full one here.

Vitalik
4 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
