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.

I was entering tens of millions of records per hour when I first published Slonik PostgreSQL client for Node.js. The data being entered was usually flat, making it straightforward to use INSERT INTO ... SELECT * FROM unnset() pattern. I advocated the unnest approach for inserting rows in groups (that was part I).

However, today I’ve found a better way: jsonb_to_recordset.

jsonb_to_recordset expands the top-level JSON array of objects to a set of rows having the composite type defined by an AS clause.

jsonb_to_recordset allows us to query and insert records from arbitrary JSON, like unnest. Since we're giving JSON to PostgreSQL instead of unnest, the final format is more expressive and powerful.

SELECT *
FROM json_to_recordset('[{"name":"John","tags":["foo","bar"]},{"name":"Jane","tags":["baz"]}]')
AS t1(name text, tags text[]);
 name |   tags
------+-----------
 John | {foo,bar}
 Jane | {baz}
(2 rows)

Let’s demonstrate how you would use it to insert data.

Inserting data using json_to_recordset

Say you need to insert a list of people with attributes into the database.

const persons = [
  {
    name: 'John',
    tags: ['foo', 'bar']
  },
  {
    name: 'Jane',
    tags: ['baz']
  }
];

You may be tempted to traverse through the array and insert each record separately, e.g.

for (const person of persons) {
  await pool.query(sql`
    INSERT INTO person (name, tags)
    VALUES (
      ${person.name},
      ${sql.array(person.tags, 'text[]')}
    )
  `);
}

It's easier to read and grasp when working with a few records. If you're like me and troubleshoot a 2M+ insert query per day, batching inserts may be beneficial.

What prompted the search for better alternatives.

Inserting using unnest pattern might look like this:

await pool.query(sql`
  INSERT INTO public.person (name, tags)
  SELECT t1.name, t1.tags::text[]
  FROM unnest(
    ${sql.array(['John', 'Jane'], 'text')},
    ${sql.array(['{foo,bar}', '{baz}'], 'text')}
  ) AS t1.(name, tags);
`);

You must convert arrays into PostgreSQL array strings and provide them as text arguments, which is unsightly. Iterating the array to create slices for each column is likewise unattractive.

However, with jsonb_to_recordset, we can:

await pool.query(sql`
  INSERT INTO person (name, tags)
  SELECT *
  FROM jsonb_to_recordset(${sql.jsonb(persons)}) AS t(name text, tags text[])
`);

In contrast to the unnest approach, using jsonb_to_recordset we can easily insert complex nested data structures, and we can pass the original JSON document to the query without needing to manipulate it.

In terms of performance they are also exactly the same. As such, my current recommendation is to prefer jsonb_to_recordset whenever inserting lots of rows or nested data structures.

And why we must keep arming Ukraine

Russian expatriates write about horrific news from home.

Read this from Nadin Brzezinski. She's not a native English speaker, so there are grammar errors, but her tale smells true.

Terrible truth.

There's much more that reveals Russia's grim reality.

Non-leadership. Millions of missing supplies are presumably sold for profit, leaving untrained troops without food or gear. Missile attacks pause because they run out. Fake schemes to hold talks as a way of stalling while they scramble for solutions.

Street men were mobilized. Millions will be ground up to please a crazed despot. Fear, wrath, and hunger pull apart civilization.

It's the most dystopian story, but Ukraine is worse. Destruction of a society, country, and civilization. Only the invaders' corruption and incompetence save the Ukrainians.

Rochester, NY. My suburb had many Soviet-era Ukrainian refugees. Their kids were my classmates. Fifty years later, many are still my friends. I loved their food and culture. My town has 20,000 Ukrainians.

Grieving but determined. They don't quit. They won't quit. Russians are eternal enemies.

It's the Russian people's willingness to tolerate corruption, abuse, and stupidity by their leaders. They are paying. 65000 dead. Ruined economy. No freedom to speak. Americans do not appreciate that freedom as we should.

It lets me write/publish.

Russian friends are shocked. Many are here because their parents escaped Russian anti-semitism and authoritarian oppression. A Russian cultural legacy says a strongman's methods are admirable.

A legacy of a slavery history disguised as serfdom. Peasants and Princes.

Read Tolstoy. Then Anna Karenina. The main characters are princes and counts, whose leaders are incompetent idiots with wealth and power.

Peasants who die in their wars due to incompetence are nameless ciphers.

Sound familiar?

From oil to attention.

Oil has been the most important commodity for a century. It's sparked wars. Pearl Harbor was a preemptive strike to guarantee Japanese access to Indonesian oil, and it made desert tribes rich. Oil's heyday is over. From oil to attention.

We talked about an information economy. In an age of abundant information, what's scarce? Attention. Scale of the world's largest enterprises, wealth of its richest people, and power of governments all stem from attention extraction, monetization, and custody.

Attention-grabbing isn't new. Humans have competed for attention and turned content into wealth since Aeschylus' Oresteia. The internal combustion engine, industrial revolutions in mechanization and plastics, and the emergence of a mobile Western lifestyle boosted oil. Digitization has put wells in pockets, on automobile dashboards, and on kitchen counters, drilling for attention.

The most valuable firms are attention-seeking enterprises, not oil companies. Big Tech dominates the top 4. Tech and media firms are the sheikhs and wildcatters who capture our attention. Blood will flow as the oil economy rises.

Attention to Detail

More than IT and media companies compete for attention. Podcasting is a high-growth, low-barrier-to-entry chance for newbies to gain attention and (for around 1%) make money. Conferences are good for capturing in-person attention. Salesforce paid $30 billion for Slack's dominance of workplace attention, while Spotify is transforming music listening attention into a media platform.

Conferences, newsletters, and even music streaming are artisan projects. Even 130,000-person Comic Con barely registers on the attention economy's Richter scale. Big players have hundreds of millions of monthly users.

Supermajors

Even titans can be disrupted in the attention economy. TikTok is fracking king Chesapeake Energy, a rule-breaking insurgent with revolutionary extraction technologies. Attention must be extracted, processed, and monetized. Innovators disrupt the attention economy value chain.

Attention pre-digital Entrepreneurs commercialized intriguing or amusing stuff like a newspaper or TV show through subscriptions and ads. Digital storage and distribution's limitless capacity drove the initial wave of innovation. Netflix became dominant by releasing old sitcoms and movies. More ad-free content gained attention. By 2016, Netflix was greater than cable TV. Linear scale, few network effects.

Social media introduced two breakthroughs. First, users produced and paid for content. Netflix's economics are dwarfed by TikTok and YouTube, where customers create the content drill rigs that the platforms monetize.

Next, social media businesses expanded content possibilities. Twitter, Facebook, and Reddit offer traditional content, but they transform user comments into more valuable (addictive) emotional content. By emotional resonance, I mean they satisfy a craving for acceptance or anger us. Attention and emotion are mined from comments/replies, piss-fights, and fast-brigaded craziness. Exxon has turned exhaust into heroin. Should we be so linked without a commensurate presence? You wouldn't say this in person. Anonymity allows fraudulent accounts and undesirable actors, which platforms accept to profit from more pollution.

FrackTok

A new entrepreneur emerged as ad-driven social media anger contaminated the water table. TikTok is remaking the attention economy. Short-form video platform relies on user-generated content, although delivery is narrower and less social.

Netflix grew on endless options. Choice requires cognitive effort. TikTok is the least demanding platform since TV. App video plays when opened. Every video can be skipped with a swipe. An algorithm watches how long you watch, what you finish, and whether you like or follow to create a unique streaming network. You can follow creators and respond, but the app is passive. TikTok's attention economy recombination makes it apex predator. The app has more users than Facebook and Instagram combined. Among teens, it's overtaking the passive king, TV.

Externalities

Now we understand fossil fuel externalities. A carbon-based economy has harmed the world. Fracking brought large riches and rebalanced the oil economy, but at a cost: flammable water, earthquakes, and chemical leaks.

TikTok has various concerns associated with algorithmically generated content and platforms. A Wall Street Journal analysis discovered new accounts listed as belonging to 13- to 15-year-olds would swerve into rabbitholes of sex- and drug-related films in mere days. TikTok has a unique externality: Chinese Communist Party ties. Our last two presidents realized the relationship's perils. Concerned about platform's propaganda potential.

No evidence suggests the CCP manipulated information to harm American interests. A headjack implanted on America's youth, who spend more time on TikTok than any other network, connects them to a neural network that may be modified by the CCP. If the product and ownership can't be separated, the app should be banned. Putting restrictions near media increases problems. We should have a reciprocal approach with China regarding media firms. Ban TikTok

It was a conference theme. I anticipated Axel Springer CEO Mathias Döpfner to say, "We're watching them." (That's CEO protocol.) TikTok should be outlawed in every democracy as an espionage tool. Rumored regulations could lead to a ban, and FCC Commissioner Brendan Carr pushes for app store prohibitions. Why not restrict Chinese propaganda? Some disagree: Several renowned tech writers argued my TikTok diatribe last week distracted us from privacy and data reform. The situation isn't zero-sum. I've warned about Facebook and other tech platforms for years. Chewing gum while walking is possible.

The Future

Is TikTok the attention-economy titans' final evolution? The attention economy acts like it. No original content. CNN+ was unplugged, Netflix is losing members and has lost 70% of its market cap, and households are canceling cable and streaming subscriptions in historic numbers. Snap Originals closed in August after YouTube Originals in January.

Everyone is outTik-ing the Tok. Netflix debuted Fast Laughs, Instagram Reels, YouTube Shorts, Snap Spotlight, Roku The Buzz, Pinterest Watch, and Twitter is developing a TikTok-like product. I think they should call it Vine. Just a thought.

Meta's internal documents show that users spend less time on Instagram Reels than TikTok. Reels engagement is dropping, possibly because a third of the videos were generated elsewhere (usually TikTok, complete with watermark). Meta has tried to downrank these videos, but they persist. Users reject product modifications. Kim Kardashian and Kylie Jenner posted a meme urging Meta to Make Instagram Instagram Again, resulting in 312,000 signatures. Mark won't hear the petition. Meta is the fastest follower in social (see Oculus and legless hellscape fever nightmares). Meta's stock is at a five-year low, giving those who opposed my demands to break it up a compelling argument.

Blue Pill

TikTok's short-term dominance in attention extraction won't be stopped by anyone who doesn't hear Hail to the Chief every time they come in. Will TikTok still be a supermajor in five years? If not, YouTube will likely rule and protect Kings Landing.

56% of Americans regularly watch YouTube. Compared to Facebook and TikTok, 95% of teens use Instagram. YouTube users upload more than 500 hours of video per minute, a number that's likely higher today. Last year, the platform garnered $29 billion in advertising income, equivalent to Netflix's total.

Business and biology both value diversity. Oil can be found in the desert, under the sea, or in the Arctic. Each area requires a specific ability. Refiners turn crude into gas, lubricants, and aspirin. YouTube's variety is unmatched. One-second videos to 12-hour movies. Others are studio-produced. (My Bill Maher appearance was edited for YouTube.)

You can dispute in the comment section or just stream videos. YouTube is used for home improvement, makeup advice, music videos, product reviews, etc. You can load endless videos on a topic or creator, subscribe to your favorites, or let the suggestion algo take over. YouTube relies on user content, but it doesn't wait passively. Strategic partners advise 12,000 creators. According to a senior director, if a YouTube star doesn’t post once week, their manager is “likely to know why.”

YouTube's kevlar is its middle, especially for creators. Like TikTok, users can start with low-production vlogs and selfie videos. As your following expands, so does the scope of your production, bringing longer videos, broadcast-quality camera teams and performers, and increasing prices. MrBeast, a YouTuber, is an example. MrBeast made gaming videos and YouTube drama comments.

Donaldson's YouTube subscriber base rose. MrBeast invests earnings to develop impressive productions. His most popular video was a $3.5 million Squid Game reenactment (the cost of an episode of Mad Men). 300 million people watched. TikTok's attention-grabbing tech is too limiting for this type of material. Now, Donaldson is focusing on offline energy with a burger restaurant and cloud kitchen enterprise.

Steps to Take

Rapid wealth growth has externalities. There is no free lunch. OK, maybe caffeine. The externalities are opaque, and the parties best suited to handle them early are incentivized to construct weapons of mass distraction to postpone and obfuscate while achieving economic security for themselves and their families. The longer an externality runs unchecked, the more damage it causes and the more it costs to fix. Vanessa Pappas, TikTok's COO, didn't shine before congressional hearings. Her comms team over-consulted her and said ByteDance had no headquarters because it's scattered. Being full of garbage simply promotes further anger against the company and the awkward bond it's built between the CCP and a rising generation of American citizens.

This shouldn't distract us from the (still existent) harm American platforms pose to our privacy, teenagers' mental health, and civic dialogue. Leaders of American media outlets don't suffer from immorality but amorality, indifference, and dissonance. Money rain blurs eyesight.

Autocratic governments that undermine America's standing and way of life are immoral. The CCP has and will continue to use all its assets to harm U.S. interests domestically and abroad. TikTok should be spun to Western investors or treated the way China treats American platforms: kicked out.

So rich,