More on Technology

Ossiana Tepfenhart
3 years ago
Has anyone noticed what an absolute shitshow LinkedIn is?
After viewing its insanity, I had to leave this platform.
I joined LinkedIn recently. That's how I aim to increase my readership and gain recognition. LinkedIn's premise appealed to me: a Facebook-like platform for professional networking.
I don't use Facebook since it's full of propaganda. It seems like a professional, apolitical space, right?
I expected people to:
be more formal and respectful than on Facebook.
Talk about the inclusiveness of the workplace. Studies consistently demonstrate that inclusive, progressive workplaces outperform those that adhere to established practices.
Talk about business in their industry. Yep. I wanted to read articles with advice on how to write better and reach a wider audience.
Oh, sh*t. I hadn't anticipated that.
After posting and reading about inclusivity and pro-choice, I was startled by how many professionals acted unprofessionally. I've seen:
Men have approached me in the DMs in a really aggressive manner. Yikes. huge yikes Not at all professional.
I've heard pro-choice women referred to as infant killers by many people. If I were the CEO of a company and I witnessed one of my employees acting that poorly, I would immediately fire them.
Many posts are anti-LGBTQIA+, as I've noticed. a lot, like, a lot. Some are subtly stating that the world doesn't need to know, while others are openly making fun of transgender persons like myself.
Several medical professionals were posting explicitly racist comments. Even if you are as white as a sheet like me, you should be alarmed by this. Who's to guarantee a patient who is black won't unintentionally die?
I won't even get into how many men in STEM I observed pushing for the exclusion of women from their fields. I shouldn't be surprised considering the majority of those men I've encountered have a passionate dislike for women, but goddamn, dude.
Many people appear entirely too at ease displaying their bigotry on their professional profiles.
As a white female, I'm always shocked by people's open hostility. Professional environments are very important.
I don't know if this is still true (people seem too politicized to care), but if I heard many of these statements in person, I'd suppose they feel ashamed. Really.
Are you not ashamed of being so mean? Are you so weak that competing with others terrifies you? Isn't this embarrassing?
LinkedIn isn't great at censoring offensive comments. These people aren't getting warnings. So they were safe while others were unsafe.
The CEO in me would want to know if I had placed a bigot on my staff.
I always wondered if people's employers knew about their online behavior. If they know how horrible they appear, they don't care.
As a manager, I was picky about hiring. Obviously. In most industries, it costs $1,000 or more to hire a full-time employee, so be sure it pays off.
Companies that embrace diversity and tolerance (and are intolerant of intolerance) are more profitable, likely to recruit top personnel, and successful.
People avoid businesses that alienate them. That's why I don't eat at Chic-Fil-A and why folks avoid MyPillow. Being inclusive is good business.
CEOs are harmed by online bigots. Image is an issue. If you're a business owner, you can fire staff who don't help you.
On the one hand, I'm delighted it makes it simpler to identify those with whom not to do business.
Don’t get me wrong. I'm glad I know who to avoid when hiring, getting references, or searching for a job. When people are bad, it saves me time.
What's up with professionalism?
Really. I need to know. I've crossed the boundary between acceptable and unacceptable behavior, but never on a professional platform. I got in trouble for not wearing bras even though it's not part of my gender expression.
If I behaved like that at my last two office jobs, my supervisors would have fired me immediately. Some of the behavior I've seen is so outrageous, I can't believe these people have employment. Some are even leaders.
Like…how? Is hatred now normalized?
Please pay attention whether you're seeking for a job or even simply a side gig.
Do not add to the tragedy that LinkedIn comments can be, or at least don't make uninformed comments. Even if you weren't banned, the site may still bite you.
Recruiters can and do look at your activity. Your writing goes on your résumé. The wrong comment might lose you a job.
Recruiters and CEOs might reject candidates whose principles contradict with their corporate culture. Bigotry will get you banned from many companies, especially if others report you.
If you want a high-paying job, avoid being a LinkedIn asshole. People care even if you think no one does. Before speaking, ponder. Is this how you want to be perceived?
Better advice:
If your politics might turn off an employer, stop posting about them online and ask yourself why you hold such objectionable ideas.

Asha Barbaschow
3 years ago
Apple WWDC 2022 Announcements
WWDC 2022 began early Tuesday morning. WWDC brought a ton of new features (which went for just shy of two hours).
With so many announcements, we thought we'd compile them. And now...
WWDC?
WWDC is Apple's developer conference. This includes iOS, macOS, watchOS, and iPadOS (all of its iPads). It's where Apple announces new features for developers to use. It's also where Apple previews new software.
Virtual WWDC runs June 6-10. You can rewatch the stream on Apple's website.
WWDC 2022 news:
Completely everything. Really. iOS 16 first.
iOS 16.
iOS 16 is a major iPhone update. iOS 16 adds the ability to customize the Lock Screen's color/theme. And widgets. It also organizes notifications and pairs Lock Screen with Focus themes. Edit or recall recently sent messages, recover recently deleted messages, and mark conversations as unread. Apple gives us yet another reason to stay in its walled garden with iMessage.
New iOS includes family sharing. Parents can set up a child's account with parental controls to restrict apps, movies, books, and music. iOS 16 lets large families and friend pods share iCloud photos. Up to six people can contribute photos to a separate iCloud library.
Live Text is getting creepier. Users can interact with text in any video frame. Touch and hold an image's subject to remove it from its background and place it in apps like messages. Dictation offers a new on-device voice-and-touch experience. Siri can run app shortcuts without setup in iOS 16. Apple also unveiled a new iOS 16 feature to help people break up with abusive partners who track their locations or read their messages. Safety Check.
Apple Pay Later allows iPhone users to buy products and pay for them later. iOS 16 pushes Mail. Users can schedule emails and cancel delivery before it reaches a recipient's inbox (be quick!). Mail now detects if you forgot an attachment, as Gmail has for years. iOS 16's Maps app gets "Multi-Stop Routing," .
Apple News also gets an iOS 16 update. Apple News adds My Sports. With iOS 16, the Apple Watch's Fitness app is also coming to iOS and the iPhone, using motion-sensing tech to track metrics and performance (as long as an athlete is wearing or carrying the device on their person).
iOS 16 includes accessibility updates like Door Detection.
watchOS9
Many of Apple's software updates are designed to take advantage of the larger screens in recent models, but they also improve health and fitness tracking.
The most obvious reason to upgrade watchOS every year is to get new watch faces from Apple. WatchOS 9 will add four new faces.
Runners' workout metrics improve.
Apple quickly realized that fitness tracking would be the Apple Watch's main feature, even though it's been the killer app for wearables since their debut. For watchOS 9, the Apple Watch will use its accelerometer and gyroscope to track a runner's form, stride length, and ground contact time. It also introduces the ability to specify heart rate zones, distance, and time intervals, with vibrating haptic feedback and voice alerts.
The Apple Watch's Fitness app is coming to iOS and the iPhone, using the smartphone's motion-sensing tech to track metrics and performance (as long as an athlete is wearing or carrying the device on their person).
We'll get sleep tracking, medication reminders, and drug interaction alerts. Your watch can create calendar events. A new Week view shows what meetings or responsibilities stand between you and the weekend.
iPadOS16
WWDC 2022 introduced iPad updates. iPadOS 16 is similar to iOS for the iPhone, but has features for larger screens and tablet accessories. The software update gives it many iPhone-like features.
iPadOS 16's Home app, like iOS 16, will have a new design language. iPad users who want to blame it on the rain finally have a Weather app. iPadOS 16 will have iCloud's Shared Photo Library, Live Text and Visual Look Up upgrades, and FaceTime Handoff, so you can switch between devices during a call.
Apple highlighted iPadOS 16's multitasking at WWDC 2022. iPad's Stage Manager sounds like a community theater app. It's a powerful multitasking tool for tablets and brings them closer to emulating laptops. Apple's iPadOS 16 supports multi-user collaboration. You can share content from Files, Keynote, Numbers, Pages, Notes, Reminders, Safari, and other third-party apps in Apple Messages.
M2-chip
WWDC 2022 revealed Apple's M2 chip. Apple has started the next generation of Apple Silicon for the Mac with M2. Apple says this device improves M1's performance.
M2's second-generation 5nm chip has 25% more transistors than M1's. 100GB/s memory bandwidth (50 per cent more than M1). M2 has 24GB of unified memory, up from 16GB but less than some ultraportable PCs' 32GB. The M2 chip has 10% better multi-core CPU performance than the M2, and it's nearly twice as fast as the latest 10-core PC laptop chip at the same power level (CPU performance is 18 per cent greater than M1).
New MacBooks
Apple introduced the M2-powered MacBook Air. Apple's entry-level laptop has a larger display, a new processor, new colors, and a notch.
M2 also powers the 13-inch MacBook Pro. The 13-inch MacBook Pro has 24GB of unified memory and 50% more memory bandwidth. New MacBook Pro batteries last 20 hours. As I type on the 2021 MacBook Pro, I can only imagine how much power the M2 will add.
macOS 13.0 (or, macOS Ventura)
macOS Ventura will take full advantage of M2 with new features like Stage Manager and Continuity Camera and Handoff for FaceTime. Safari, Mail, Messages, Spotlight, and more get updates in macOS Ventura.
Apple hasn't run out of California landmarks to name its OS after yet. macOS 13 will be called Ventura when it's released in a few months, but it's more than a name change and new wallpapers.
Stage Manager organizes windows
Stage Manager is a new macOS tool that organizes open windows and applications so they're still visible while focusing on a specific task. The main app sits in the middle of the desktop, while other apps and documents are organized and piled up to the side.
Improved Searching
Spotlight is one of macOS's least appreciated features, but with Ventura, it's becoming even more useful. Live Text lets you extract text from Spotlight results without leaving the window, including images from the photo library and the web.
Mail lets you schedule or unsend emails.
We've all sent an email we regret, whether it contained regrettable words or was sent at the wrong time. In macOS Ventura, Mail users can cancel or reschedule a message after sending it. Mail will now intelligently determine if a person was forgotten from a CC list or if a promised attachment wasn't included. Procrastinators can set a reminder to read a message later.
Safari adds tab sharing and password passkeys
Apple is updating Safari to make it more user-friendly... mostly. Users can share a group of tabs with friends or family, a useful feature when researching a topic with too many tabs. Passkeys will replace passwords in Safari's next version. Instead of entering random gibberish when creating a new account, macOS users can use TouchID to create an on-device passkey. Using an iPhone's camera and a QR system, Passkey syncs and works across all Apple devices and Windows computers.
Continuity adds Facetime device switching and iPhone webcam.
With macOS Ventura, iPhone users can transfer a FaceTime call from their phone to their desktop or laptop using Handoff, or vice versa if they started a call at their desk and need to continue it elsewhere. Apple finally admits its laptop and monitor webcams aren't the best. Continuity makes the iPhone a webcam. Apple demonstrated a feature where the wide-angle lens could provide a live stream of the desk below, while the standard zoom lens could focus on the speaker's face. New iPhone laptop mounts are coming.
System Preferences
System Preferences is Now System Settings and Looks Like iOS
Ventura's System Preferences has been renamed System Settings and is much more similar in appearance to iOS and iPadOS. As the iPhone and iPad are gateway devices into Apple's hardware ecosystem, new Mac users should find it easier to adjust.
This post is a summary. Read full article here

Stephen Moore
3 years ago
A Meta-Reversal: Zuckerberg's $71 Billion Loss
The company's epidemic gains are gone.
Mark Zuckerberg was in line behind Jeff Bezos and Bill Gates less than two years ago. His wealth soared to $142 billion. Facebook's shares reached $382 in September 2021.
What comes next is either the start of something truly innovative or the beginning of an epic rise and fall story.
In order to start over (and avoid Facebook's PR issues), he renamed the firm Meta. Along with the new logo, he announced a turn into unexplored territory, the Metaverse, as the next chapter for the internet after mobile. Or, Zuckerberg believed Facebook's death was near, so he decided to build a bigger, better, cooler ship. Then we saw his vision (read: dystopian nightmare) in a polished demo that showed Zuckerberg in a luxury home and on a spaceship with aliens. Initially, it looked entertaining. A problem was obvious, though. He might claim this was the future and show us using the Metaverse for business, play, and more, but when I took off my headset, I'd realize none of it was genuine.
The stock price is almost as low as January 2019, when Facebook was dealing with the aftermath of the Cambridge Analytica crisis.
Irony surrounded the technology's aim. Zuckerberg says the Metaverse connects people. Despite some potential uses, this is another step away from physical touch with people. Metaverse worlds can cause melancholy, addiction, and mental illness. But forget all the cool stuff you can't afford. (It may be too expensive online, too.)
Metaverse activity slowed for a while. In early February 2022, we got an earnings call update. Not good. Reality Labs lost $10 billion on Oculus and Zuckerberg's Metaverse. Zuckerberg expects losses to rise. Meta's value dropped 20% in 11 minutes after markets closed.
It was a sign of things to come.
The corporation has failed to create interest in Metaverse, and there is evidence the public has lost interest. Meta still relies on Facebook's ad revenue machine, which is also struggling. In July, the company announced a decrease in revenue and missed practically all its forecasts, ending a decade of exceptional growth and relentless revenue. They blamed a dismal advertising demand climate, and Apple's monitoring changes smashed Meta's ad model. Throw in whistleblowers, leaked data revealing the firm knows Instagram negatively affects teens' mental health, the current Capital Hill probe, and the fact TikTok is eating its breakfast, lunch, and dinner, and 2022 might be the corporation's worst year ever.
After a rocky start, tech saw unprecedented growth during the pandemic. It was a tech bubble and then some.
The gains reversed after the dust settled and stock markets adjusted. Meta's year-to-date decline is 60%. Apple Inc is down 14%, Amazon is down 26%, and Alphabet Inc is down 29%. At the time of writing, Facebook's stock price is almost as low as January 2019, when the Cambridge Analytica scandal broke. Zuckerberg owns 350 million Meta shares. This drop costs him $71 billion.
The company's problems are growing, and solutions won't be easy.
Facebook's period of unabated expansion and exorbitant ad revenue is ended, and the company's impact is dwindling as it continues to be the program that only your parents use. Because of the decreased ad spending and stagnant user growth, Zuckerberg will have less time to create his vision for the Metaverse because of the declining stock value and decreasing ad spending.
Instagram is progressively dying in its attempt to resemble TikTok, alienating its user base and further driving users away from Meta-products.
And now that the corporation has shifted its focus to the Metaverse, it is clear that, in its eagerness to improve its image, it fired the launch gun too early. You're fighting a lost battle when you announce an idea and then claim it won't happen for 10-15 years. When the idea is still years away from becoming a reality, the public is already starting to lose interest.
So, as I questioned earlier, is it the beginning of a technological revolution that will take this firm to stratospheric growth and success, or are we witnessing the end of Meta and Zuckerberg himself?
You might also like

Pat Vieljeux
3 years ago
The three-year business plan is obsolete for startups.
If asked, run.
An entrepreneur asked me about her pitch deck. A Platform as a Service (PaaS).
She told me she hadn't done her 5-year forecasts but would soon.
I said, Don't bother. I added "time-wasting."
“I've been asked”, she said.
“Who asked?”
“a VC”
“5-year forecast?”
“Yes”
“Get another VC. If he asks, it's because he doesn't understand your solution or to waste your time.”
Some VCs are lagging. They're still using steam engines.
10-years ago, 5-year forecasts were requested.
Since then, we've adopted a 3-year plan.
But It's outdated.
Max one year.
What has happened?
Revolutionary technology. NO-CODE.
Revolution's consequences?
Product viability tests are shorter. Hugely. SaaS and PaaS.
Let me explain:
Building a minimum viable product (MVP) that works only takes a few months.
1 to 2 months for practical testing.
Your company plan can be validated or rejected in 4 months as a consequence.
After validation, you can ask for VC money. Even while a prototype can generate revenue, you may not require any.
Good VCs won't ask for a 3-year business plan in that instance.
One-year, though.
If you want, establish a three-year plan, but realize that the second year will be different.
You may have changed your business model by then.
A VC isn't interested in a three-year business plan because your solution may change.
Your ability to create revenue will be key.
But also, to pivot.
They will be interested in your value proposition.
They will want to know what differentiates you from other competitors and why people will buy your product over another.
What will interest them is your resilience, your ability to bounce back.
Not to mention your mindset. The fact that you won’t get discouraged at the slightest setback.
The grit you have when facing adversity, as challenges will surely mark your journey.
The authenticity of your approach. They’ll want to know that you’re not just in it for the money, let alone to show off.
The fact that you put your guts into it and that you are passionate about it. Because entrepreneurship is a leap of faith, a leap into the void.
They’ll want to make sure you are prepared for it because it’s not going to be a walk in the park.
They’ll want to know your background and why you got into it.
They’ll also want to know your family history.
And what you’re like in real life.
So a 5-year plan…. You can bet they won’t give a damn. Like their first pair of shoes.

Alexander Nguyen
3 years ago
A Comparison of Amazon, Microsoft, and Google's Compensation
Learn or earn
In 2020, I started software engineering. My base wage has progressed as follows:
Amazon (2020): $112,000
Microsoft (2021): $123,000
Google (2022): $169,000
I didn't major in math, but those jumps appear more than a 7% wage increase. Here's a deeper look at the three.
The Three Categories of Compensation
Most software engineering compensation packages at IT organizations follow this format.
Minimum Salary
Base salary is pre-tax income. Most organizations give a base pay. This is paid biweekly, twice monthly, or monthly.
Recruiting Bonus
Sign-On incentives are one-time rewards to new hires. Companies need an incentive to switch. If you leave early, you must pay back the whole cost or a pro-rated amount.
Equity
Equity is complex and requires its own post. A company will promise to give you a certain amount of company stock but when you get it depends on your offer. 25% per year for 4 years, then it's gone.
If a company gives you $100,000 and distributes 25% every year for 4 years, expect $25,000 worth of company stock in your stock brokerage on your 1 year work anniversary.
Performance Bonus
Tech offers may include yearly performance bonuses. Depends on performance and funding. I've only seen 0-20%.
Engineers' overall compensation usually includes:
Base Salary + Sign-On + (Total Equity)/4 + Average Performance Bonus
Amazon: (TC: 150k)
Base Pay System
Amazon pays Seattle employees monthly on the first work day. I'd rather have my money sooner than later, even if it saves processing and pay statements.
The company upped its base pay cap from $160,000 to $350,000 to compete with other tech companies.
Performance Bonus
Amazon has no performance bonus, so you can work as little or as much as you like and get paid the same. Amazon is savvy to avoid promising benefits it can't deliver.
Sign-On Bonus
Amazon gives two two-year sign-up bonuses. First-year workers could receive $20,000 and second-year workers $15,000. It's probably to make up for the company's strange equity structure.
If you leave during the first year, you'll owe the entire money and a prorated amount for the second year bonus.
Equity
Most organizations prefer a 25%, 25%, 25%, 25% equity structure. Amazon takes a different approach with end-heavy equity:
the first year, 5%
15% after one year.
20% then every six months
We thought it was constructed this way to keep staff longer.
Microsoft (TC: 185k)
Base Pay System
Microsoft paid biweekly.
Gainful Performance
My offer letter suggested a 0%-20% performance bonus. Everyone will be satisfied with a 10% raise at year's end.
But misleading press where the budget for the bonus is doubled can upset some employees because they won't earn double their expected bonus. Still barely 10% for 2022 average.
Sign-On Bonus
Microsoft's sign-on bonus is a one-time payout. The contract can require 2-year employment. You must negotiate 1 year. It's pro-rated, so that's fair.
Equity
Microsoft is one of those companies that has standard 25% equity structure. Except if you’re a new graduate.
In that case it’ll be
25% six months later
25% each year following that
New grads will acquire equity in 3.5 years, not 4. I'm guessing it's to keep new grads around longer.
Google (TC: 300k)
Base Pay Structure
Google pays biweekly.
Performance Bonus
Google's offer letter specifies a 15% bonus. It's wonderful there's no cap, but I might still get 0%. A little more than Microsoft’s 10% and a lot more than Amazon’s 0%.
Sign-On Bonus
Google gave a 1-year sign-up incentive. If the contract is only 1 year, I can move without any extra obligations.
Not as fantastic as Amazon's sign-up bonuses, but the remainder of the package might compensate.
Equity
We covered Amazon's tail-heavy compensation structure, so Google's front-heavy equity structure may surprise you.
Annual structure breakdown
33% Year 1
33% Year 2
22% Year 3
12% Year 4
The goal is to get them to Google and keep them there.
Final Thoughts
This post hopefully helped you understand the 3 firms' compensation arrangements.
There's always more to discuss, such as refreshers, 401k benefits, and business discounts, but I hope this shows a distinction between these 3 firms.

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
