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.

This could cost you.

Content creators may have heard about Google's "Helpful content upgrade."

This change is another Google effort to remove low-quality, repetitive, and AI-generated content.

Why should content creators care?

Because too much content manipulates search results.

My experience includes the following.

Website admins seek high-quality guest posts from me. They send me AI-generated text after I say "yes." My readers are irrelevant. Backlinks are needed.

Companies copy high-ranking content to boost their Google rankings. Unfortunately, it's common.

What does this content offer?

Nothing.

Despite Google's updates and efforts to clean search results, webmasters create manipulative content.

As a marketer, I knew about AI-powered content generation tools. However, I've never tried them.

I use old-fashioned content creation methods to grow my website from 0 to 3,000 monthly views in one year.

Last year, I launched a niche website.

I do keyword research, analyze search intent and competitors' content, write an article, proofread it, and then optimize it.

This strategy is time-consuming.

But it yields results!

Here's proof from Google Analytics:

Proven strategies yield promising results.

To validate my assumptions and find new strategies, I run many experiments.

I tested an AI-powered content generator.

I used a tool to write this Google-optimized article about SEO for startups.

I wanted to analyze AI-generated content's Google performance.

Here are the outcomes of my test.

First, quality.

I dislike "meh" content. I expect articles to answer my questions. If not, I've wasted my time.

My essays usually include research, personal anecdotes, and what I accomplished and achieved.

AI-generated articles aren't as good because they lack individuality.

Read my AI-generated article about startup SEO to see what I mean.

It's dry and shallow, IMO.

It seems robotic.

I'd use quotes and personal experience to show how SEO for startups is different.

My article paraphrases top-ranked articles on a certain topic.

It's readable but useless. Similar articles abound online. Why read it?

AI-generated content is low-quality.

Let me show you how this content ranks on Google.

The Google Search Console report shows impressions, clicks, and average position.

Low numbers.

No one opens the 5th Google search result page to read the article. Too far!

You may say the new article will improve.

Marketing-wise, I doubt it.

This article is shorter and less comprehensive than top-ranking pages. It's unlikely to win because of this.

AI-generated content's terrible reality.

I'll compare how this content I wrote for readers and SEO performs.

Both the AI and my article are fresh, but trends are emerging.

My article's CTR and average position are higher.

I spent a week researching and producing that piece, unlike AI-generated content. My expert perspective and unique consequences make it interesting to read.

Human-made.

In summary

No content generator can duplicate a human's tone, writing style, or creativity. Artificial content is always inferior.

Not "bad," but inferior.

Demand for content production tools will rise despite Google's efforts to eradicate thin content.

Most won't spend hours producing link-building articles. Costly.

As guest and sponsored posts, artificial content will thrive.

Before accepting a new arrangement, content creators and website owners should consider this.

Traditional sales organizations used the concept of a sales “funnel” to describe the process through which potential customers move, ending up with sales at the end. Winners today have abandoned that way of thinking in favor of building flywheels — business models in which every element reinforces every other.

Ah, the marketing funnel…

Prospective clients go through a predictable set of experiences, students learn in business school marketing classes. It looks like this:

Understanding the funnel helps evaluate sales success indicators. Gail Goodwin, former CEO of small business direct mail provider Constant Contact, said managing the pipeline was key to escaping the sluggish SaaS ramp of death.

Like the funnel concept. To predict how well your business will do, measure how many potential clients are aware of it (awareness) and how many take the next step. If 1,000 people heard about your offering and 10% showed interest, you'd have 100 at that point. If 50% of these people made buyer-like noises, you'd know how many were, etc. It helped model buying trends.

TV, magazine, and radio advertising are pricey for B2C enterprises. Traditional B2B marketing involved armies of sales reps, which was expensive and a barrier to entry.

Cracks in the funnel model

Digital has exposed the funnel's limitations. Hubspot was born at a time when buyers and sellers had huge knowledge asymmetries, according to co-founder Brian Halligan. Those selling a product could use the buyer's lack of information to become a trusted partner.

As the world went digital, getting information and comparing offerings became faster, easier, and cheaper. Buyers didn't need a seller to move through a funnel. Interactions replaced transactions, and the relationship didn't end with a sale.

Instead, buyers and sellers interacted in a constant flow. In many modern models, the sale is midway through the process (particularly true with subscription and software-as-a-service models). Example:

You're creating a winding journey with many touch points, not a funnel (and lots of opportunities for customers to get lost).

From winding journey to flywheel

Beyond this revised view of an interactive customer journey, a company can create what Jim Collins famously called a flywheel. Imagine rolling a heavy disc on its axis. The first few times you roll it, you put in a lot of effort for a small response. The same effort yields faster turns as it gains speed. Over time, the flywheel gains momentum and turns without your help.

Modern digital organizations have created flywheel business models, in which any additional force multiplies throughout the business. The flywheel becomes a force multiplier, according to Collins.

Amazon is a famous flywheel example. Collins explained the concept to Amazon CEO Jeff Bezos at a corporate retreat in 2001. In The Everything Store, Brad Stone describes in his book The Everything Store how he immediately understood Amazon's levers.

The result (drawn on a napkin):

Low prices and a large selection of products attracted customers, while a focus on customer service kept them coming back, increasing traffic. Third-party sellers then increased selection. Low-cost structure supports low-price commitment. It's brilliant! Every wheel turn creates acceleration.

Where from here?

Flywheel over sales funnel! Consider these business terms.

Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

Using math to write efficient code in any language

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

Inbuilt max and min functions can minimize verbose if statements.

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.

New ventures are exciting. It's fun to imagine yourself rich, successful, and famous (if that's your thing). How you'll help others and make your family proud. This excitement can pull you forward for years, even when you intuitively realize that the path you're on may not lead to your desired success.

Know when to change course. Switching course can mean pivoting or changing direction.

In this not-so-short blog, I'll describe the journey of building your dream. And how the journey might look when you think you're building your dream, but fall short of that vision. Both can feel similar in the beginning, but there are subtle differences.

Let’s dive in.

How an exciting journey to a dead end looks and feels.

You want to help many people. You're business-minded, creative, and ambitious. You jump into entrepreneurship. You're excited, free, and in control.

I'll use tech as an example because that's what I know best, but this applies to any entrepreneurial endeavor.

So you start learning the basics of your field, say coding/software development. You read books, take courses, and may even join a bootcamp. You start practicing, and the journey begins. Once you reach a certain level of skill (which can take months, usually 12-24), you gain the confidence to speak with others in the field and find common ground. You might attract a co-founder this way with time. You and this person embark on a journey (Tip: the idea you start with is rarely the idea you end with).

Amateur mistake #1: You spend months building a product before speaking to customers.

Building something pulls you forward blindly. You make mistakes, avoid customers, and build with your co-founder or small team in the dark for months, usually 6-12 months.

You're excited when the product launches. We'll be billionaires! The market won't believe it. This excites you and the team. Launch.

….

Nothing happens.

Some people may sign up out of pity, only to never use the product or service again.

You and the team are confused, discouraged and in denial. They don't get what we've built yet. We need to market it better, we need to talk to more investors, someone will understand our vision.

This is a hopeless path, and your denial could last another 6 months. If you're lucky, while talking to consumers and investors (which you should have done from the start), someone who has been there before would pity you and give you an idea to pivot into that can create income.

Suppose you get this idea and pivot your business. Again, you've just pivoted into something limited by what you've already built. It may be a revenue-generating idea, but it's rarely new. Now you're playing catch-up, doing something others are doing but you can do better. (Tip #2: Don't be late.) Your chances of winning are slim, and you'll likely never catch up.

You're finally seeing revenue and feel successful. You can compete, but if you're not a first mover, you won't earn enough over time. You'll get by or work harder than ever to earn what a skilled trade could provide. You didn't go into business to stress out and make $100,000 or $200,000 a year. When you can make the same amount by becoming a great software developer, electrician, etc.

You become stuck. Either your firm continues this way for years until you realize there isn't enough growth to recruit a strong team and remove yourself from day-to-day operations due to competition. Or a catastrophic economic event forces you to admit that what you were building wasn't new and unique and wouldn't get you where you wanted to be.

This realization could take 6-10 years. No kidding.

The good news is, you’ve learned a lot along the way and this information can be used towards your next venture (if you have the energy).

Key Lesson: Don’t build something if you aren’t one of the first in the space building it just for the sake of building something.

-

Let's discuss what it's like to build something that can make your dream come true.

Case 2: Building something the market loves is difficult but rewarding.

It starts with a problem that hasn't been adequately solved for a long time but is now solvable due to technology. Or a new problem due to a change in how things are done.

Let's examine each example.

Example #1: Mass communication. The problem is now solvable due to some technological breakthrough.

Twitter — One of the first web 2 companies that became successful with the rise of smart mobile computing.

People can share their real-time activities via mobile device with friends, family, and strangers. Web 2 and smartphones made it easy and fun.

Example #2: A new problem has emerged due to some change in the way things are conducted.

Zoom- A web-conferencing company that reached massive success due to the movement towards “work from home”, remote/hybrid work forces.

Online web conferencing allows for face-to-face communication.

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These two examples show how to build a unicorn-type company. It's a mix of solving the right problem at the right time, either through a technological breakthrough that opens up new opportunities or by fundamentally changing how people do things.

Let's find these opportunities.

Start by examining problems, such as how the world has changed and how we can help it adapt. It can also be both. Start team brainstorming. Research technologies, current world-trends, use common sense, and make a list. Then, choose the top 3 that you're most excited about and seem most workable based on your skillsets, values, and passion.

Once you have this list, create the simplest MVP you can and test it with customers. The prototype can be as simple as a picture or diagram of user flow and end-user value. No coding required. Market-test. Twitter's version 1 was simple. It was a web form that asked, "What are you doing?" Then publish it from your phone. A global status update, wherever you are. Currently, this company has a $50 billion market cap.

Here's their MVP screenshot.

Small things grow. Tiny. Simplify.

Remember Frequency and Value when brainstorming. Your product is high frequency (Twitter, Instagram, Snapchat, TikTok) or high value (Airbnb for renting travel accommodations), or both (Gmail).

Once you've identified product ideas that meet the above criteria, they're simple, have a high frequency of use, or provide deep value. You then bring it to market in the simplest, most cost-effective way. You can sell a half-working prototype with imagination and sales skills. You need just enough of a prototype to convey your vision to a user or customer.

With this, you can approach real people. This will do one of three things: give you a green light to continue on your vision as is, show you that there is no opportunity and people won't use it, or point you in a direction that is a blend of what you've come up with and what the customer / user really wants, and you update the prototype and go back to the maze. Repeat until you have enough yeses and conviction to build an MVP.