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.

Believe what you see, what people say

It’s sad that we never get trained to leave assumptions behind. - Sebastian Thrun

Many problems in software development are not because of code but because developers create the wrong software. This isn't rare because software is emergent and most individuals only realize what they want after it's built.

Inquisitive developers who pass the yellow cat test can improve the process.

Carpenters measure twice and cut the wood once. Developers are rarely so careful.

The Yellow Cat Test

Game of Thrones made dragons cool again, so I am reading The Game of Thrones book.

The yellow cat exam is from Syrio Forel, Arya Stark's fencing instructor.

Syrio tells Arya he'll strike left when fencing. He hits her after she dodges left. Arya says “you lied”. Syrio says his words lied, but his eyes and arm told the truth.

Arya learns how Syrio became Bravos' first sword.

“On the day I am speaking of, the first sword was newly dead, and the Sealord sent for me. Many bravos had come to him, and as many had been sent away, none could say why. When I came into his presence, he was seated, and in his lap was a fat yellow cat. He told me that one of his captains had brought the beast to him, from an island beyond the sunrise. ‘Have you ever seen her like?’ he asked of me.

“And to him I said, ‘Each night in the alleys of Braavos I see a thousand like him,’ and the Sealord laughed, and that day I was named the first sword.”

Arya screwed up her face. “I don’t understand.”

Syrio clicked his teeth together. “The cat was an ordinary cat, no more. The others expected a fabulous beast, so that is what they saw. How large it was, they said. It was no larger than any other cat, only fat from indolence, for the Sealord fed it from his own table. What curious small ears, they said. Its ears had been chewed away in kitten fights. And it was plainly a tomcat, yet the Sealord said ‘her,’ and that is what the others saw. Are you hearing?” Reddit discussion.

Development teams should not believe what they are told.

We created an appointment booking system. We thought it was an appointment-booking system. Later, we realized the software's purpose was to book the right people for appointments and discourage the unneeded ones.

The first 3 months of the project had half-correct requirements and software understanding.

Open your eyes

“Open your eyes is all that is needed. The heart lies and the head plays tricks with us, but the eyes see true. Look with your eyes, hear with your ears. Taste with your mouth. Smell with your nose. Feel with your skin. Then comes the thinking afterwards, and in that way, knowing the truth” Syrio Ferel

We must see what exists, not what individuals tell the development team or how developers think the software should work. Initial criteria cover 50/70% and change.

Developers build assumptions problems by assuming how software should work. Developers must quickly explain assumptions.

When a development team's assumptions are inaccurate, they must alter the code, DevOps, documentation, and tests.

It’s always faster and easier to fix requirements before code is written.

First-draft requirements can be based on old software. Development teams must grasp corporate goals and consider needs from many angles.

Testers help rethink requirements. They look at how software requirements shouldn't operate.

Technical features and benefits might misdirect software projects.

The initiatives that focused on technological possibilities developed hard-to-use software that needed extensive rewriting following user testing.

Software development

High-level criteria are different from detailed ones.

• The interpretation of words determines their meaning.

• Presentations are lofty, upbeat, and prejudiced.

• People's perceptions may be unclear, incorrect, or just based on one perspective (half the story)

• Developers can be misled by requirements, circumstances, people, plans, diagrams, designs, documentation, and many other things.

Developers receive misinformation, misunderstandings, and wrong assumptions. The development team must avoid building software with erroneous specifications.

Once code and software are written, the development team changes and fixes them.

Developers create software with incomplete information, they need to fill in the blanks to create the complete picture.

Conclusion

Yellow cats are often inaccurate when communicating requirements.

Before writing code, clarify requirements, assumptions, etc.

Everyone will pressure the development team to generate code rapidly, but this will slow down development.

Code changes are harder than requirements.

A TECHNICAL THOUGHT

The IT giant is seeding the digital Great Renaissance.

Recently, technology has been dull.

We're still fascinated by processing speeds. Wearables are no longer an engineer's dream.

Apple has been quiet and avoided huge announcements. Slowness speaks something. Everything in the spaceship HQ seems to be turning slowly, unlike competitors around buzzwords.

Is this a sign of the impending storm?

Metas stock has fallen while Google milks dumb people. Microsoft steals money from corporations and annexes platforms like Linkedin.

Just surface bubbles?

Is Apple, one of the technology continents, pushing against all others to create a paradigm shift?

The fundamental human right to privacy

Apple's unusual remarks emphasize privacy. They incorporate it into their business models and judgments.

Apple believes privacy is a human right. There are no compromises.

This makes it hard for other participants to gain Apple's ecosystem's efficiencies.

Other players without hardware platforms lose.

Apple delivers new kidneys without rejection, unlike other software vendors. Nothing compromises your privacy.

Corporate citizenship will become more popular.

Apples have full coffers. They've started using that flow to better communities, which is great.

Apple's $2.5B home investment is one example. Google and Facebook are building or proposing to build workforce housing.

Apple's funding helps marginalized populations in more than 25 California counties, not just Apple employees.

Is this a trend, and does Apple keep giving back? Hope so.

I'm not cynical enough to suspect these investments have malicious motives.

The last frontier is the environment.

Climate change is a battle-to-win.

Long-term winners will be companies that protect the environment, turning climate change dystopia into sustainable growth.

Apple has been quietly changing its supply chain to be carbon-neutral by 2030.

“Apple is dedicated to protecting the planet we all share with solutions that are supporting the communities where we work.” Lisa Jackson, Apple’s vice president of environment.

Apple's $4.7 billion Green Bond investment will produce 1.2 gigawatts of green energy for the corporation and US communities. Apple invests $2.2 billion in Europe's green energy. In the Philippines, Thailand, Nigeria, Vietnam, Colombia, Israel, and South Africa, solar installations are helping communities obtain sustainable energy.

Apple is already carbon neutral today for its global corporate operations, and this new commitment means that by 2030, every Apple device sold will have net zero climate impact. -Apple.

Apple invests in green energy and forests to reduce its paper footprint in China and the US. Apple and the Conservation Fund are safeguarding 36,000 acres of US working forest, according to GreenBiz.

Apple's packaging paper is recycled or from sustainably managed forests.

What matters is the scale.

$1 billion is a rounding error for Apple.

These small investments originate from a tree with deep, spreading roots.

Apple's genes are anchored in building the finest products possible to improve consumers' lives.

I felt it when I switched to my iPhone while waiting for a train and had to pack my Macbook. iOS 16 dictation makes writing more enjoyable. Small change boosts productivity. Smooth transition from laptop to small screen and dictation.

Apples' tiny, well-planned steps have great growth potential for all consumers in everything they do.

There is clearly disruption, but it doesn't have to be violent

Digital channels, methods, and technologies have globalized human consciousness. One person's responsibility affects many.

Apple gives us tools to be privately connected. These technologies foster creativity, innovation, fulfillment, and safety.

Apple has invented a mountain of technologies, services, and channels to assist us adapt to the good future or combat evil forces who cynically aim to control us and ruin the environment and communities. Apple has quietly disrupted sectors for decades.

Google, Microsoft, and Meta, among others, should ride this wave. It's a tsunami, but it doesn't have to be devastating if we care, share, and cooperate with political decision-makers and community leaders worldwide.

A fresh Renaissance

Renaissance geniuses Michelangelo and Da Vinci. Different but seeing something no one else could yet see. Both were talented in many areas and could discover art in science and science in art.

These geniuses exemplified a period that changed humanity for the better. They created, used, and applied new, valuable things. It lives on.

Apple is a digital genius orchard. Wozniak and Jobs offered us fertile ground for the digital renaissance. We'll build on their legacy.

We may put our seeds there and see them bloom despite corporate greed and political ignorance.

I think the coming tsunami will illuminate our planet like the Renaissance.

While we played checkers, we thought billionaires played 3D chess. They're playing the same game on a fancier board.

Every medium has nuances and norms. Texting is authentic and casual. A smaller circle has access, creating intimacy and immediacy. Most people read all their texts, but not all their email and mail. Many of us no longer listen to our voicemails, and calling your kids ages you.

Live interviews and testimony under oath inspire real moments, rare in a world where communications departments sanitize everything powerful people say. When (some of) Elon's text messages became public in Twitter v. Musk, we got a glimpse into tech power. It's bowels.

These texts illuminate the tech community's upper caste.

Checkers, Not Chess

Elon texts with Larry Ellison, Joe Rogan, Sam Bankman-Fried, Satya Nadella, and Jack Dorsey. They reveal astounding logic, prose, and discourse. The world's richest man and his followers are unsophisticated, obtuse, and petty. Possibly. While we played checkers, we thought billionaires played 3D chess. They're playing the same game on a fancier board.

They fumble with their computers.

They lean on others to get jobs for their kids (no surprise).

No matter how rich, they always could use more (money).

Differences A social hierarchy exists. Among this circle, the currency of deference is... currency. Money increases sycophantry. Oculus and Elon's "friends'" texts induce nausea.

Autocorrect frustrates everyone.

Elon doesn't stand out to me in these texts; he comes off mostly OK in my view. It’s the people around him. It seems our idolatry of innovators has infected the uber-wealthy, giving them an uncontrollable urge to kill the cool kid for a seat at his cafeteria table. "I'd grenade for you." If someone says this and they're not fighting you, they're a fan, not a friend.

Many powerful people are undone by their fake friends. Facilitators, not well-wishers. When Elon-Twitter started, I wrote about power. Unchecked power is intoxicating. This is a scientific fact, not a thesis. Power causes us to downplay risk, magnify rewards, and act on instincts more quickly. You lose self-control and must rely on others.

You'd hope the world's richest person has advisers who push back when necessary (i.e., not yes men). Elon's reckless, childish behavior and these texts show there is no truth-teller. I found just one pushback in the 151-page document. It came from Twitter CEO Parag Agrawal, who, in response to Elon’s unhelpful “Is Twitter dying?” tweet, let Elon know what he thought: It was unhelpful. Elon’s response? A childish, terse insult.

Scale

The texts are mostly unremarkable. There are some, however, that do remind us the (super-)rich are different. Specifically, the discussions of possible equity investments from crypto-billionaire Sam Bankman-Fried (“Does he have huge amounts of money?”) and this exchange with Larry Ellison:

Ellison, who co-founded $175 billion Oracle, is wealthy. Less clear is whether he can text a billion dollars. Who hasn't been texted $1 billion? Ellison offered 8,000 times the median American's net worth, enough to buy 3,000 Ferraris or the Chicago Blackhawks. It's a bedrock principle of capitalism to have incredibly successful people who are exponentially wealthier than the rest of us. It creates an incentive structure that inspires productivity and prosperity. When people offer billions over text to help a billionaire's vanity project in a country where 1 in 5 children are food insecure, isn't America messed up?

Elon's Morgan Stanley banker, Michael Grimes, tells him that Web3 ventures investor Bankman-Fried can invest $5 billion in the deal: “could do $5bn if everything vision lock... Believes in your mission." The message bothers Elon. In Elon's world, $5 billion doesn't warrant a worded response. $5 billion is more than many small nations' GDP, twice the SEC budget, and five times the NRC budget.

If income inequality worries you after reading this, trust your gut.

Billionaires aren't like the rich.

As an entrepreneur, academic, and investor, I've met modest-income people, rich people, and billionaires. Rich people seem different to me. They're smarter and harder working than most Americans. Monty Burns from The Simpsons is a cartoon about rich people. Rich people have character and know how to make friends. Success requires supporters.

I've never noticed a talent or intelligence gap between wealthy and ultra-wealthy people. Conflating talent and luck infects the tech elite. Timing is more important than incremental intelligence when going from millions to hundreds of millions or billions. Proof? Elon's texting. Any man who electrifies the auto industry and lands two rockets on barges is a genius. His mega-billions come from a well-regulated capital market, enforceable contracts, thousands of workers, and billions of dollars in government subsidies, including a $465 million DOE loan that allowed Tesla to produce the Model S. So, is Mr. Musk a genius or an impressive man in a unique time and place?

The Point

Elon's texts taught us more? He can't "fix" Twitter. For two weeks in April, he was all in on blockchain Twitter, brainstorming Dogecoin payments for tweets with his brother — i.e., paid speech — while telling Twitter's board he was going to make a hostile tender offer. Kimbal approved. By May, he was over crypto and "laborious blockchain debates." (Mood.)

Elon asked the Twitter CEO for "an update from the Twitter engineering team" No record shows if he got the meeting. It doesn't "fix" Twitter either. And this is Elon's problem. He's a grown-up child with all the toys and no boundaries. His yes-men encourage his most facile thoughts, and shitposts and errant behavior diminish his genius and ours.

Post-Apocalyptic

The universe's titans have a sense of humor.

Every day, we must ask: Who keeps me real? Who will disagree with me? Who will save me from my psychosis, which has brought down so many successful people? Elon Musk doesn't need anyone to jump on a grenade for him; he needs to stop throwing them because one will explode in his hand.

Massive Layoffs, record low VC investment, debate over crash... why is it happening and what’s the endgame?

This article generalizes a diverse industry. For objectivity, specific tech company challenges like growing competition within named segments won't be considered. Please comment on the posts.

According to Layoffs.fyi, nearly 120.000 people have been fired from startups since March 2020. More than 700 startups have fired 1% to 100% of their workforce. "The tech market is crashing"

Venture capital investment dropped 19% QoQ in the first four months of 2022, a 2018 low. Since January 2022, Nasdaq has dropped 27%. Some believe the tech market is collapsing.

It's bad, but nothing has crashed yet. We're about to get super technical, so buckle up!

I've written a follow-up article about what's next. For a more optimistic view of the crisis' aftermath, see: Tech Diaspora and Silicon Valley crisis

What happened?

Insanity reigned. Last decade, everyone became a unicorn. Seed investments can be made without a product or team. While the "real world" economy suffered from the pandemic for three years, tech companies enjoyed the "new normal."

COVID sped up technology adoption on several fronts, but this "new normal" wasn't so new after many restrictions were lifted. Worse, it lived with disrupted logistics chains, high oil prices, and WW3. The consumer market has felt the industry's boom for almost 3 years. Inflation, unemployment, mental distress...what looked like a fast economic recovery now looks like unfulfilled promises.

People rethink everything they eat. Paying a Netflix subscription instead of buying beef is moronic if you can watch it for free on your cousin’s account. No matter how great your real estate app's UI is, buying a house can wait until mortgage rates drop. PLGProduct Led Growth (PLG) isn't the go-to strategy when consumers have more basic expense priorities.

Exponential growth and investment

Until recently, tech companies believed that non-exponential revenue growth was fatal. Exponential growth entails doing more with less. From Salim Ismail words:

An Exponential Organization (ExO) has 10x the impact of its peers.

Many tech companies' theories are far from reality.

Investors have funded (sometimes non-exponential) growth. Scale-driven companies throw people at problems until they're solved. Need an entire closing team because you’ve just bought a TV prime time add? Sure. Want gold-weight engineers to colorize buttons? Why not?

Tech companies don't need cash flow to do it; they can just show revenue growth and get funding. Even though it's hard to get funding, this was the market's momentum until recently.

The graph at the beginning of this section shows how industry heavyweights burned money until 2020, despite being far from their market-share seed stage. Being big and being sturdy are different things, and a lot of the tech startups out there are paper tigers. Without investor money, they have no foundation.

A little bit about interest rates

Inflation-driven high interest rates are said to be causing tough times. Investors would rather leave money in the bank than spend it (I myself said it some days ago). It’s not wrong, but it’s also not that simple.

The USA central bank (FED) is a good proxy of global economics. Dollar treasury bonds are the safest investment in the world. Buying U.S. debt, the only country that can print dollars, guarantees payment.

The graph above shows that FED interest rates are low and 10+ year bond yields are near 2018 levels. Nobody was firing at 2018. What’s with that then?

Full explanation is too technical for this article, so I'll just summarize: Bond yields rise due to lack of demand or market expectations of longer-lasting inflation. Safe assets aren't a "easy money" tactic for investors. If that were true, we'd have seen the current scenario before.

Long-term investors are protecting their capital from inflation.

Not a crash, a landing

I bombarded you with info... Let's review:

• Consumption is down, hurting revenue.

• Tech companies of all ages have been hiring to grow revenue at the expense of profit.

• Investors expect inflation to last longer, reducing future investment gains.

Inflation puts pressure on a wheel that was rolling full speed not long ago. Investment spurs hiring, growth, and more investment. Worried investors and consumers reduce the cycle, and hiring follows.

Long-term investors back startups. When the invested company goes public or is sold, it's ok to burn money. What happens when the payoff gets further away? What if all that money sinks? Investors want immediate returns.

Why isn't the market crashing? Technology is not losing capital. It’s expecting change. The market realizes it threw moderation out the window and is reversing course. Profitability is back on the menu.

People solve problems and make money, but they also cost money. Huge cost for the tech industry. Engineers, Product Managers, and Designers earn up to 100% more than similar roles. Businesses must be careful about who they keep and in what positions to avoid wasting money.

What the future holds

From here on, it's all speculation. I found many great articles while researching this piece. Some are cited, others aren't (like this and this). We're in an adjustment period that may or may not last long.

Big companies aren't laying off many workers. Netflix firing 100 people makes headlines, but it's only 1% of their workforce. The biggest seem to prefer not hiring over firing.

Smaller startups beyond the seeding stage may be hardest hit. Without structure or product maturity, many will die.

I expect layoffs to continue for some time, even at Meta or Amazon. I don't see any industry names falling like they did during the .com crisis, but the market will shrink.

If you are currently employed, think twice before moving out and where to.
If you've been fired, hurry, there are still many opportunities.
If you're considering a tech career, wait.
If you're starting a business, I respect you. Good luck.