More on Marketing

Jon Brosio
3 years ago
This Landing Page is a (Legal) Money-Printing Machine
and it’s easy to build.
A landing page with good copy is a money-maker.
Let's be honest, page-builder templates are garbage.
They can help you create a nice-looking landing page, but not persuasive writing.
Over the previous 90 days, I've examined 200+ landing pages.
What's crazy?
Top digital entrepreneurs use a 7-part strategy to bring in email subscribers, generate prospects, and (passively) sell their digital courses.
Steal this 7-part landing page architecture to maximize digital product sales.
The offer
Landing pages require offers.
Newsletter, cohort, or course offer.
Your reader should see this offer first. Includind:
Headline
Imagery
Call-to-action
Clear, persuasive, and simplicity are key. Example: the Linkedin OS course home page of digital entrepreneur Justin Welsh offers:
A distinctly defined problem
Everyone needs an enemy.
You need an opponent on your landing page. Problematic.
Next, employ psychology to create a struggle in your visitor's thoughts.
Don't be clever here; label your customer's problem. The more particular you are, the bigger the situation will seem.
When you build a clear monster, you invite defeat. I appreciate Theo Ohene's Growth Roadmaps landing page.
Exacerbation of the effects
Problem identification doesn't motivate action.
What would an unresolved problem mean?
This is landing page copy. When you describe the unsolved problem's repercussions, you accomplish several things:
You write a narrative (and stories are remembered better than stats)
You cause the reader to feel something.
You help the reader relate to the issue
Important!
My favorite script is:
"Sure, you can let [problem] go untreated. But what will happen if you do? Soon, you'll begin to notice [new problem 1] will start to arise. That might bring up [problem 2], etc."
Take the copywriting course, digital writer and entrepreneur Dickie Bush illustrates below when he labels the problem (see: "poor habit") and then illustrates the repercussions.
The tale of transformation
Every landing page needs that "ah-ha!" moment.
Transformation stories do this.
Did you find a solution? Someone else made the discovery? Have you tested your theory?
Next, describe your (or your subject's) metamorphosis.
Kieran Drew nails his narrative (and revelation) here. Right before the disclosure, he introduces his "ah-ha!" moment:
Testimonials
Social proof completes any landing page.
Social proof tells the reader, "If others do it, it must be worthwhile."
This is your argument.
Positive social proof helps (obviously).
Offer "free" training in exchange for a testimonial if you need social evidence. This builds social proof.
Most social proof is testimonies (recommended). Kurtis Hanni's creative take on social proof (using a screenshot of his colleague) is entertaining.
Bravo.
Reveal your offer
Now's the moment to act.
Describe the "bundle" that provides the transformation.
Here's:
Course
Cohort
Ebook
Whatever you're selling.
Include a product or service image, what the consumer is getting ("how it works"), the price, any "free" bonuses (preferred), and a CTA ("buy now").
Clarity is key. Don't make a cunning offer. Make sure your presentation emphasizes customer change (benefits). Dan Koe's Modern Mastery landing page makes an offer. Consider:
An ultimatum
Offering isn't enough.
You must give your prospect an ultimatum.
They can buy your merchandise from you.
They may exit the webpage.
That’s it.
It's crucial to show what happens if the reader does either. Stress the consequences of not buying (again, a little consequence amplification). Remind them of the benefits of buying.
I appreciate Charles Miller's product offer ending:
The top online creators use a 7-part landing page structure:
Offer the service
Describe the problem
Amplify the consequences
Tell the transformational story
Include testimonials and social proof.
Reveal the offer (with any bonuses if applicable)
Finally, give the reader a deadline to encourage them to take action.
Sequence these sections to develop a landing page that (essentially) prints money.

Emma Jade
3 years ago
6 hacks to create content faster
Content gurus' top time-saving hacks.
I'm a content strategist, writer, and graphic designer. Time is more valuable than money.
Money is always available. Even if you're poor. Ways exist.
Time is passing, and one day we'll run out.
Sorry to be morbid.
In today's digital age, you need to optimize how you create content for your organization. Here are six content creation hacks.
1. Use templates
Use templates to streamline your work whether generating video, images, or documents.
Setup can take hours. Using a free resource like Canva, you can create templates for any type of material.
This will save you hours each month.
2. Make a content calendar
You post without a plan? A content calendar solves 50% of these problems.
You can prepare, organize, and plan your material ahead of time so you're not scrambling when you remember, "Shit, it's Mother's Day!"
3. Content Batching
Batching content means creating a lot in one session. This is helpful for video content that requires a lot of setup time.
Batching monthly content saves hours. Time is a valuable resource.
When working on one type of task, it's easy to get into a flow state. This saves time.
4. Write Caption
On social media, we generally choose the image first and then the caption. Writing captions first sometimes work better, though.
Writing the captions first can allow you more creative flexibility and be easier if you're not excellent with language.
Say you want to tell your followers something interesting.
Writing a caption first is easier than choosing an image and then writing a caption to match.
Not everything works. You may have already-created content that needs captioning. When you don't know what to share, think of a concept, write the description, and then produce a video or graphic.
Cats can be skinned in several ways..
5. Repurpose
Reuse content when possible. You don't always require new stuff. In fact, you’re pretty stupid if you do #SorryNotSorry.
Repurpose old content. All those blog entries, videos, and unfinished content on your desk or hard drive.
This blog post can be turned into a social media infographic. Canva's motion graphic function can animate it. I can record a YouTube video regarding this issue for a podcast. I can make a post on each point in this blog post and turn it into an eBook or paid course.
And it doesn’t stop there.
My point is, to think outside the box and really dig deep into ways you can leverage the content you’ve already created.
6. Schedule Them
If you're still manually posting content, get help. When you batch your content, schedule it ahead of time.
Some scheduling apps are free or cheap. No excuses.
Don't publish and ghost.
Scheduling saves time by preventing you from doing it manually. But if you never engage with your audience, the algorithm won't reward your material.
Be online and engage your audience.
Content Machine
Use these six content creation hacks. They help you succeed and save time.

Jano le Roux
3 years ago
Here's What I Learned After 30 Days Analyzing Apple's Microcopy
Move people with tiny words.

Apple fanboy here.
Macs are awesome.
Their iPhones rock.
$19 cloths are great.
$999 stands are amazing.
I love Apple's microcopy even more.
It's like the marketing goddess bit into the Apple logo and blessed the world with microcopy.
I took on a 30-day micro-stalking mission.
Every time I caught myself wasting time on YouTube, I had to visit Apple’s website to learn the secrets of the marketing goddess herself.
We've learned. Golden apples are calling.
Cut the friction
Benefit-first, not commitment-first.
Brands lose customers through friction.
Most brands don't think like customers.
Brands want sales.
Brands want newsletter signups.
Here's their microcopy:
“Buy it now.”
“Sign up for our newsletter.”
Both are difficult. They ask for big commitments.
People are simple creatures. Want pleasure without commitment.
Apple nails this.
So, instead of highlighting the commitment, they highlight the benefit of the commitment.

Saving on the latest iPhone sounds easier than buying it. Everyone saves, but not everyone buys.
A subtle change in framing reduces friction.
Apple eliminates customer objections to reduce friction.

Less customer friction means simpler processes.
Apple's copy expertly reassures customers about shipping fees and not being home. Apple assures customers that returning faulty products is easy.
Apple knows that talking to a real person is the best way to reduce friction and improve their copy.
Always rhyme
Learn about fine rhyme.
Poets make things beautiful with rhyme.
Copywriters use rhyme to stand out.
Apple’s copywriters have mastered the art of corporate rhyme.
Two techniques are used.
1. Perfect rhyme
Here, rhymes are identical.

2. Imperfect rhyme
Here, rhyming sounds vary.

Apple prioritizes meaning over rhyme.
Apple never forces rhymes that don't fit.
It fits so well that the copy seems accidental.
Add alliteration
Alliteration always entertains.
Alliteration repeats initial sounds in nearby words.
Apple's copy uses alliteration like no other brand I've seen to create a rhyming effect or make the text more fun to read.
For example, in the sentence "Sam saw seven swans swimming," the initial "s" sound is repeated five times. This creates a pleasing rhythm.
Microcopy overuse is like pouring ketchup on a Michelin-star meal.
Alliteration creates a memorable phrase in copywriting. It's subtler than rhyme, and most people wouldn't notice; it simply resonates.

I love how Apple uses alliteration and contrast between "wonders" and "ease".
Assonance, or repeating vowels, isn't Apple's thing.
You ≠ Hero, Customer = Hero
Your brand shouldn't be the hero.
Because they'll be using your product or service, your customer should be the hero of your copywriting. With your help, they should feel like they can achieve their goals.
I love how Apple emphasizes what you can do with the machine in this microcopy.

It's divine how they position their tools as sidekicks to help below.

This one takes the cake:

Dialogue-style writing
Conversational copy engages.
Excellent copy Like sharing gum with a friend.
This helps build audience trust.

Apple does this by using natural connecting words like "so" and phrases like "But that's not all."
Snowclone-proof
The mother of all microcopy techniques.
A snowclone uses an existing phrase or sentence to create a new one. The new phrase or sentence uses the same structure but different words.
It’s usually a well know saying like:
To be or not to be.
This becomes a formula:
To _ or not to _.
Copywriters fill in the blanks with cause-related words. Example:
To click or not to click.

Apple turns "survival of the fittest" into "arrival of the fittest."
It's unexpected and surprises the reader.
So this was fun.
But my fun has just begun.
Microcopy is 21st-century poetry.
I came as an Apple fanboy.
I leave as an Apple fanatic.
Now I’m off to find an apple tree.
Cause you know how it goes.
(Apples, trees, etc.)
This post is a summary. Original post available here.
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Leon Ho
3 years ago
Digital Brainbuilding (Your Second Brain)
The human brain is amazing. As more scientists examine the brain, we learn how much it can store.
The human brain has 1 billion neurons, according to Scientific American. Each neuron creates 1,000 connections, totaling over a trillion. If each neuron could store one memory, we'd run out of room. [1]
What if you could store and access more info, freeing up brain space for problem-solving and creativity?
Build a second brain to keep up with rising knowledge (what I refer to as a Digital Brain). Effectively managing information entails realizing you can't recall everything.
Every action requires information. You need the correct information to learn a new skill, complete a project at work, or establish a business. You must manage information properly to advance your profession and improve your life.
How to construct a second brain to organize information and achieve goals.
What Is a Second Brain?
How often do you forget an article or book's key point? Have you ever wasted hours looking for a saved file?
If so, you're not alone. Information overload affects millions of individuals worldwide. Information overload drains mental resources and causes anxiety.
This is when the second brain comes in.
Building a second brain doesn't involve duplicating the human brain. Building a system that captures, organizes, retrieves, and archives ideas and thoughts. The second brain improves memory, organization, and recall.
Digital tools are preferable to analog for building a second brain.
Digital tools are portable and accessible. Due to these benefits, we'll focus on digital second-brain building.
Brainware
Digital Brains are external hard drives. It stores, organizes, and retrieves. This means improving your memory won't be difficult.
Memory has three components in computing:
Recording — storing the information
Organization — archiving it in a logical manner
Recall — retrieving it again when you need it
For example:
Due to rigorous security settings, many websites need you to create complicated passwords with special characters.
You must now memorize (Record), organize (Organize), and input this new password the next time you check in (Recall).
Even in this simple example, there are many pieces to remember. We can't recognize this new password with our usual patterns. If we don't use the password every day, we'll forget it. You'll type the wrong password when you try to remember it.
It's common. Is it because the information is complicated? Nope. Passwords are basically letters, numbers, and symbols.
It happens because our brains aren't meant to memorize these. Digital Brains can do heavy lifting.
Why You Need a Digital Brain
Dual minds are best. Birth brain is limited.
The cerebral cortex has 125 trillion synapses, according to a Stanford Study. The human brain can hold 2.5 million terabytes of digital data. [2]
Building a second brain improves learning and memory.
Learn and store information effectively
Faster information recall
Organize information to see connections and patterns
Build a Digital Brain to learn more and reach your goals faster. Building a second brain requires time and work, but you'll have more time for vital undertakings.
Why you need a Digital Brain:
1. Use Brainpower Effectively
Your brain has boundaries, like any organ. This is true while solving a complex question or activity. If you can't focus on a work project, you won't finish it on time.
Second brain reduces distractions. A robust structure helps you handle complicated challenges quickly and stay on track. Without distractions, it's easy to focus on vital activities.
2. Staying Organized
Professional and personal duties must be balanced. With so much to do, it's easy to neglect crucial duties. This is especially true for skill-building. Digital Brain will keep you organized and stress-free.
Life success requires action. Organized people get things done. Organizing your information will give you time for crucial tasks.
You'll finish projects faster with good materials and methods. As you succeed, you'll gain creative confidence. You can then tackle greater jobs.
3. Creativity Process
Creativity drives today's world. Creativity is mysterious and surprising for millions worldwide. Immersing yourself in others' associations, triggers, thoughts, and ideas can generate inspiration and creativity.
Building a second brain is crucial to establishing your creative process and building habits that will help you reach your goals. Creativity doesn't require perfection or overthinking.
4. Transforming Your Knowledge Into Opportunities
This is the age of entrepreneurship. Today, you can publish online, build an audience, and make money.
Whether it's a business or hobby, you'll have several job alternatives. Knowledge can boost your economy with ideas and insights.
5. Improving Thinking and Uncovering Connections
Modern career success depends on how you think. Instead of overthinking or perfecting, collect the best images, stories, metaphors, anecdotes, and observations.
This will increase your creativity and reveal connections. Increasing your imagination can help you achieve your goals, according to research. [3]
Your ability to recognize trends will help you stay ahead of the pack.
6. Credibility for a New Job or Business
Your main asset is experience-based expertise. Others won't be able to learn without your help. Technology makes knowledge tangible.
This lets you use your time as you choose while helping others. Changing professions or establishing a new business become learning opportunities when you have a Digital Brain.
7. Using Learning Resources
Millions of people use internet learning materials to improve their lives. Online resources abound. These include books, forums, podcasts, articles, and webinars.
These resources are mostly free or inexpensive. Organizing your knowledge can save you time and money. Building a Digital Brain helps you learn faster. You'll make rapid progress by enjoying learning.
How does a second brain feel?
Digital Brain has helped me arrange my job and family life for years.
No need to remember 1001 passwords. I never forget anything on my wife's grocery lists. Never miss a meeting. I can access essential information and papers anytime, anywhere.
Delegating memory to a second brain reduces tension and anxiety because you'll know what to do with every piece of information.
No information will be forgotten, boosting your confidence. Better manage your fears and concerns by writing them down and establishing a strategy. You'll understand the plethora of daily information and have a clear head.
How to Develop Your Digital Brain (Your Second Brain)
It's cheap but requires work.
Digital Brain development requires:
Recording — storing the information
Organization — archiving it in a logical manner
Recall — retrieving it again when you need it
1. Decide what information matters before recording.
To succeed in today's environment, you must manage massive amounts of data. Articles, books, webinars, podcasts, emails, and texts provide value. Remembering everything is impossible and overwhelming.
What information do you need to achieve your goals?
You must consolidate ideas and create a strategy to reach your aims. Your biological brain can imagine and create with a Digital Brain.
2. Use the Right Tool
We usually record information without any preparation - we brainstorm in a word processor, email ourselves a message, or take notes while reading.
This information isn't used. You must store information in a central location.
Different information needs different instruments.
Evernote is a top note-taking program. Audio clips, Slack chats, PDFs, text notes, photos, scanned handwritten pages, emails, and webpages can be added.
Pocket is a great software for saving and organizing content. Images, videos, and text can be sorted. Web-optimized design
Calendar apps help you manage your time and enhance your productivity by reminding you of your most important tasks. Calendar apps flourish. The best calendar apps are easy to use, have many features, and work across devices. These calendars include Google, Apple, and Outlook.
To-do list/checklist apps are useful for managing tasks. Easy-to-use, versatility, budget, and cross-platform compatibility are important when picking to-do list apps. Google Keep, Google Tasks, and Apple Notes are good to-do apps.
3. Organize data for easy retrieval
How should you organize collected data?
When you collect and organize data, you'll see connections. An article about networking can assist you comprehend web marketing. Saved business cards can help you find new clients.
Choosing the correct tools helps organize data. Here are some tools selection criteria:
Can the tool sync across devices?
Personal or team?
Has a search function for easy information retrieval?
Does it provide easy data categorization?
Can users create lists or collections?
Does it offer easy idea-information connections?
Does it mind map and visually organize thoughts?
Conclusion
Building a Digital Brain (second brain) helps us save information, think creatively, and implement ideas. Your second brain is a biological extension. It prevents amnesia, allowing you to tackle bigger creative difficulties.
People who love learning often consume information without using it. Every day, they postpone life-improving experiences until they're forgotten. Useful information becomes strength.
Reference
[1] ^ Scientific American: What Is the Memory Capacity of the Human Brain?
[2] ^ Clinical Neurology Specialists: What is the Memory Capacity of a Human Brain?
[3] ^ National Library of Medicine: Imagining Success: Multiple Achievement Goals and the Effectiveness of Imagery

Nikhil Vemu
2 years ago
7 Mac Apps That Are Exorbitantly Priced But Totally Worth It
Wish you more bang for your buck
By ‘Cost a Bomb’ I didn’t mean to exaggerate. It’s an idiom that means ‘To be very expensive’. In fact, no app on the planet costs a bomb lol.
So, to the point.
Chronicle
(Freemium. For Pro, $24.99 | Available on Setapp)
You probably have trouble keeping track of dozens of bills and subscriptions each month.
Try Chronicle.
Easy-to-use app
Add payment due dates and receive reminders,
Save payment documentation,
Analyze your spending by season, year, and month.
Observe expenditure trends and create new budgets.
Best of all, Chronicle features an integrated browser for fast payment and logging.
iOS and macOS sync.
SoundSource
($39 for lifetime)
Background Music, a free macOS program, was featured in #6 of this post last month.
It controls per-app volume, stereo balance, and audio over its max level.
Background Music is fully supported. Additionally,
Connect various speakers to various apps (Wow! ),
change the audio sample rate for each app,
To facilitate access, add a floating SoundSource window.
Use its blocks in Shortcuts app,
On the menu bar, include meters for output/input devices and running programs.
PixelSnap
($39 for lifetime | Available on Setapp)
This software is heaven for UI designers.
It aids you.
quickly calculate screen distances (in pixels) ,
Drag an area around an object to determine its borders,
Measure the distances between the additional guides,
screenshots should be pixel-perfect.
What’s more.
You can
Adapt your tolerance for items with poor contrast and shadows.
Use your Touch Bar to perform important tasks, if you have one.
Mate Translation
($3.99 a month / $29.99 a year | Available on Setapp)
Mate Translate resembles a roided-up version of BarTranslate, which I wrote about in #1 of this piece last month.
If you translate often, utilize Mate Translate on macOS and Safari.
I'm really vocal about it.
It stays on the menu bar, and is accessible with a click or ⌥+shift+T hotkey.
It lets you
Translate in 103 different languages,
To translate text, double-click or right-click on it.
Totally translate websites. Additionally, Netflix subtitles,
Listen to their pronunciation to see how close it is to human.
iPhone and Mac sync Mate-ing history.
Swish
($16 for lifetime | Available on Setapp)
Swish is awesome!
Swipe, squeeze, tap, and hold movements organize chaotic desktop windows. Swish operates with mouse and trackpad.
Some gestures:
• Pinch Once: Close an app
• Pinch Twice: Quit an app
• Swipe down once: Minimise an app
• Pinch Out: Enter fullscreen mode
• Tap, Hold, & Swipe: Arrange apps in grids
and many more...
After getting acquainted to the movements, your multitasking will improve.
Unite
($24.99 for lifetime | Available on Setapp)
It turns webapps into macOS apps. The end.
Unite's functionality is a million times better.
Provide extensive customization (incl. its icon, light and dark modes)
make menu bar applications,
Get badges for web notifications and automatically refresh websites,
Replace any dock icon in the window with it (Wow!) by selecting that portion of the window.
Use PiP (Picture-in-Picture) on video sites that support it.
Delete advertising,
Throughout macOS, use floating windows
and many more…
I feel $24.99 one-off for this tool is a great deal, considering all these features. What do you think?
CleanShot X
(Basic: $29 one-off. Pro: $8/month | Available on Setapp)
CleanShot X can achieve things the macOS screenshot tool cannot. Complete screenshot toolkit.
CleanShot X, like Pixel Snap 2 (#3), is fantastic.
Allows
Scroll to capture a long page,
screen recording,
With webcam on,
• With mic and system audio,
• Highlighting mouse clicks and hotkeys.
Maintain floating screenshots for reference
While capturing, conceal desktop icons and notifications.
Recognize text in screenshots (OCR),
You may upload and share screenshots using the built-in cloud.
These are just 6 in 50+ features, and you’re already saying Wow!

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
