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.

They depend heavily on open source..

Discord users send billions of messages daily. Users wish to search these messages. How do we index these to search by message keywords?

Let’s find out.

1. Discord utilizes Elasticsearch. Elasticsearch is a free, open search engine for textual, numerical, geographical, structured, and unstructured data. Apache Lucene powers Elasticsearch.
   

2. How does elastic search store data? It stores it as numerous key-value pairs in JSON documents.
   

3. How does elastic search index? Elastic search's index is inverted. An inverted index lists every unique word in every page and where it appears.

4. Elasticsearch indexes documents and generates an inverted index to make data searchable in near real-time. The index API adds or updates JSON documents in a given index.

1. Let's examine how discord uses Elastic Search. Elasticsearch prefers bulk indexing. Discord couldn't index real-time messages. You can't search posted messages. You want outdated messages.

6. Let's check what bulk indexing requires.
1. A temporary queue for incoming communications.
2. Indexer workers that index messages into elastic search.

1. Discord's queue is Celery. The queue is open-source. Elastic search won't run on a single server. It's clustered. Where should a message go? Where?

8. A shard allocator decides where to put the message. Nevertheless. Shattered? A shard combines elastic search and index on. So, these two form a shard which is used as a unit by discord. The elastic search itself has some shards. But this is different, so don’t get confused.

1. Now, the final part is service discovery — to discover the elastic search clusters and the hosts within that cluster. This, they do with the help of etcd another open source tool.
   

A great thing to notice here is that discord relies heavily on open source systems and their base implementations which is very different from a lot of other products.

A few days ago, I was discussing dall-e with two art and tech pals. One artist acquaintance said she knew a frightened illustrator. Would the ability to create anything with a click derail her career? The artist feared this. My curator friend smiled and said this has always been a dread among artists. When the camera was invented, didn't painters say this? Even in the Instagram era, painting exists.

When art and technology collide, there's room for innovation, experimentation, and fear — especially if the technology replicates or replaces art making. What is art's future with dall-e? How does technology affect music, beyond visual art? Recently, I saw "ABBA Voyage," a holographic ABBA concert in London.

"Abba voyage?" my phone asked in early March. A Gen X friend I met through a fashion blogging ring texted me.

"What's abba Voyage?" I asked while opening my front door with keys and coffee.

We're going! Marti, visiting London, took me to a show.

"Absolutely no ABBA songs here." I responded.

My parents didn't play ABBA much, so I don't know much about them. Dad liked Jimi Hendrix, Cream, Deep Purple, and New Orleans jazz. Marti told me ABBA Voyage was a holographic ABBA show with a live band.

The show was fun, extraordinary fun. Nearly everyone on the dance floor wore wigs, ankle-breaking platforms, sequins, and bellbottoms. I saw some millennials and Zoomers among the boomers.

I was intoxicated by the experience.

Automatons date back to the 18th-century mechanical turk. The mechanical turk was a chess automaton operated by a person. The mechanical turk seemed to perform like a human without human intervention, but it required a human in the loop to work properly.

Humans have used non-humans in entertainment for centuries, such as puppets, shadow play, and smoke and mirrors. A show can have animatronic, technological, and non-technological elements, and a live show can blur real and illusion. From medieval puppet shows to mechanical turks to AI filters, bots, and holograms, entertainment has evolved over time.

I'm not a hologram skeptic, but I'm skeptical of technology, especially since I work with it. I love live performances, I love hearing singers breathe, forget lines, and make jokes. Live shows are my favorite because I love watching performers make mistakes or interact with the audience. ABBA Voyage was different.

Marti and I traveled to Manchester after ABBA Voyage to see Liam Gallagher. Similar but different vibe. Similar in that thousands dressed up for the show. ABBA's energy was dizzying. 90s chic replaced sequins in the crowd. Doc Martens, nylon jackets, bucket hats, shaggy hair. The Charlatans and Liam Gallagher opened and closed, respectively. Fireworks. Incredible. People went crazy. Yelling exhausted my voice.

This week in music featured AI-enabled holograms and a decades-old rocker. Both are warm and gooey in our memories.

After seeing both, I'm wondering if we need AI hologram shows. Why? Is it good?

Like everything tech-related, my answer is "maybe." Because context and performance matter. Liam Gallagher and ABBA both had great, different shows.

For a hologram to work, it must be impossible and big. It must be big, showy, and improbable to justify a hologram. It must feel...expensive, like a stadium pop show. According to a quick search, ABBA broke up on bad terms. Reuniting is unlikely. This is also why Prince or Tupac hologram shows work. We can only engage with their legacy through covers or...holograms.

I drove around listening to the radio a few weeks ago. "Dreaming of You" by Selena played. Selena's music defined my childhood. I sang along and turned up the volume (or as loud as my husband would allow me while driving on the highway).

I discovered Selena's music six months after her death, so I never saw her perform live. My babysitter Melissa played me her album after I moved to Houston. Melissa took me to see the Selena movie five times when it came out. I quickly wore out my VHS copy. I constantly sang "Bibi Bibi Bom Bom" and "Como la Flor." I love Selena. A Selena hologram? Yes, probably.

Instagram advertised a cellist's Arthur Russell tribute show. Russell is another deceased artist I love. I almost walked down the aisle to "This is How We Walk on the Moon," but our cellist couldn't find it. Instead, I walked to Magnetic Fields' "The Book of Love." I "discovered" Russell after a friend introduced me to his music a few years ago.

I use these as analogies for the Liam Gallagher and ABBA concerts.

You have no idea how much I'd pay to see a hologram of Selena's 1995 Houston Livestock Show and Rodeo concert. Arthur Russell's hologram is unnecessary. Russell's work was intimate and performance-based. We can't separate his life from his legacy; popular audiences overlooked his genius. He died of AIDS broke. Like Selena, he died prematurely. Given his music and history, another performer would be a better choice than a hologram. He's no Selena. Selena could have rivaled Beyonce.

Pop shows' size works for holograms. Along with ABBA holograms, there was an anime movie and a light show that would put Tron to shame. ABBA created a tourable stadium show. The event was lavish, expensive, and well-planned. Pop, unlike rock, isn't gritty. Liam Gallagher hologram? No longer impossible, it wouldn't work. He's touring. I'm not sure if a rockstar alone should be rendered as a hologram; it was the show that made ABBA a hologram.

Holograms, like AI, are part of the future of entertainment, but not all of it. Because only modern interpretations of Arthur Russell's work reveal his legacy. That's his legacy.

Large-scale arena performers may use holograms in the future, but the experience must be impossible. A teacher once said that the only way to convey emotion in opera is through song, and I feel the same way about holograms, AR, VR, and mixed reality. A story's impossibility must make sense, like in opera. Impossibility and bombastic performance must be present for an immersive element to "work." ABBA was an impossible and improbable experience, which made it magical. It helped the holographic show work.

Marti told me about ABBA Voyage. She said it was a great concert. Marti has worked in music since the 1990s. She's a music expert; she's seen many shows.

Ai isn't a god or sentient, and the ABBA holograms aren't real. The renderings were glassy-eyed, flat, and robotic, like the Polar Express or the Jaws shark. Even today, the uncanny valley is insurmountable. We know it's not real because it's not about reality. It was about a suspended moment and performance feelings.

I knew this was impossible, an 'unreal' experience, but the emotions I felt were real, like watching a movie or tv show. Perhaps this is one of the better uses of AI, like CGI and special effects, like the beauty of entertainment- we were enraptured and entertained for hours. I've been playing ABBA since then.

German stellarator revamped to run longer, hotter, compete with tokamaks

Tokamaks have dominated the search for fusion energy for decades. Just as ITER, the world's largest and most expensive tokamak, nears completion in southern France, a smaller, twistier testbed will start up in Germany.

If the 16-meter-wide stellarator can match or outperform similar-size tokamaks, fusion experts may rethink their future. Stellarators can keep their superhot gases stable enough to fuse nuclei and produce energy. They can theoretically run forever, but tokamaks must pause to reset their magnet coils.

The €1 billion German machine, Wendelstein 7-X (W7-X), is already getting "tokamak-like performance" in short runs, claims plasma physicist David Gates, preventing particles and heat from escaping the superhot gas. If W7-X can go long, "it will be ahead," he says. "Stellarators excel" Eindhoven University of Technology theorist Josefine Proll says, "Stellarators are back in the game." A few of startup companies, including one that Gates is leaving Princeton Plasma Physics Laboratory, are developing their own stellarators.

W7-X has been running at the Max Planck Institute for Plasma Physics (IPP) in Greifswald, Germany, since 2015, albeit only at low power and for brief runs. W7-X's developers took it down and replaced all inner walls and fittings with water-cooled equivalents, allowing for longer, hotter runs. The team reported at a W7-X board meeting last week that the revised plasma vessel has no leaks. It's expected to restart later this month to show if it can get plasma to fusion-igniting conditions.

Wendelstein 7-X's water-cooled inner surface allows for longer runs.

HOSAN/IPP

Both stellarators and tokamaks create magnetic gas cages hot enough to melt metal. Microwaves or particle beams heat. Extreme temperatures create a plasma, a seething mix of separated nuclei and electrons, and cause the nuclei to fuse, releasing energy. A fusion power plant would use deuterium and tritium, which react quickly. Non-energy-generating research machines like W7-X avoid tritium and use hydrogen or deuterium instead.

Tokamaks and stellarators use electromagnetic coils to create plasma-confining magnetic fields. A greater field near the hole causes plasma to drift to the reactor's wall.

Tokamaks control drift by circulating plasma around a ring. Streaming creates a magnetic field that twists and stabilizes ionized plasma. Stellarators employ magnetic coils to twist, not plasma. Once plasma physicists got powerful enough supercomputers, they could optimize stellarator magnets to improve plasma confinement.

W7-X is the first large, optimized stellarator with 50 6- ton superconducting coils. Its construction began in the mid-1990s and cost roughly twice the €550 million originally budgeted.

The wait hasn't disappointed researchers. W7-X director Thomas Klinger: "The machine operated immediately." "It's a friendly machine." It did everything we asked." Tokamaks are prone to "instabilities" (plasma bulging or wobbling) or strong "disruptions," sometimes associated to halted plasma flow. IPP theorist Sophia Henneberg believes stellarators don't employ plasma current, which "removes an entire branch" of instabilities.

In early stellarators, the magnetic field geometry drove slower particles to follow banana-shaped orbits until they collided with other particles and leaked energy. Gates believes W7-X's ability to suppress this effect implies its optimization works.

W7-X loses heat through different forms of turbulence, which push particles toward the wall. Theorists have only lately mastered simulating turbulence. W7-X's forthcoming campaign will test simulations and turbulence-fighting techniques.

A stellarator can run constantly, unlike a tokamak, which pulses. W7-X has run 100 seconds—long by tokamak standards—at low power. The device's uncooled microwave and particle heating systems only produced 11.5 megawatts. The update doubles heating power. High temperature, high plasma density, and extensive runs will test stellarators' fusion power potential. Klinger wants to heat ions to 50 million degrees Celsius for 100 seconds. That would make W7-X "a world-class machine," he argues. The team will push for 30 minutes. "We'll move step-by-step," he says.

W7-X's success has inspired VCs to finance entrepreneurs creating commercial stellarators. Startups must simplify magnet production.

Princeton Stellarators, created by Gates and colleagues this year, has $3 million to build a prototype reactor without W7-X's twisted magnet coils. Instead, it will use a mosaic of 1000 HTS square coils on the plasma vessel's outside. By adjusting each coil's magnetic field, operators can change the applied field's form. Gates: "It moves coil complexity to the control system." The company intends to construct a reactor that can fuse cheap, abundant deuterium to produce neutrons for radioisotopes. If successful, the company will build a reactor.

Renaissance Fusion, situated in Grenoble, France, raised €16 million and wants to coat plasma vessel segments in HTS. Using a laser, engineers will burn off superconductor tracks to carve magnet coils. They want to build a meter-long test segment in 2 years and a full prototype by 2027.

Type One Energy in Madison, Wisconsin, won DOE money to bend HTS cables for stellarator magnets. The business carved twisting grooves in metal with computer-controlled etching equipment to coil cables. David Anderson of the University of Wisconsin, Madison, claims advanced manufacturing technology enables the stellarator.

Anderson said W7-X's next phase will boost stellarator work. “Half-hour discharges are steady-state,” he says. “This is a big deal.”

The Habit of Learning implies constantly learning something new. One daily habit will make you successful. Learning will help you succeed.

Most successful people continually learn. Success requires this behavior. Daily learning.

Success loves books. Books offer expert advice. Everything is online today. Most books are online, so you can skip the library. You must download it and study for 15-30 minutes daily. This habit changes your thinking.

Typical Successful People

• Warren Buffett reads 500 pages of corporate reports and five newspapers for five to six hours each day.

• Each year, Bill Gates reads 50 books.

• Every two weeks, Mark Zuckerberg reads at least one book.

• According to his brother, Elon Musk studied two books a day as a child and taught himself engineering and rocket design.

Learning & Making Money Online

No worries if you can't afford books. Everything is online. YouTube, free online courses, etc.

How can you create this behavior in yourself?

1) Consider what you want to know

Before learning, know what's most important. So, move together.

Set a goal and schedule learning.

After deciding what you want to study, create a goal and plan learning time.

3) GATHER RESOURCES

Get the most out of your learning resources. Online or offline.

“Perfectionism is the enemy of the idea muscle. " — James Altucher

Writer's block is a typical explanation for low output. Success requires productivity.

In four years of writing, I've never had writer's block. And you shouldn't care.

You'll never run out of content ideas if you follow a few tactics. No, I'm not overpromising.

Take Note of Ideas

Brains are strange machines. Blank when it's time to write. Idiot. Nothing. We get the best article ideas when we're away from our workstation.

• In the shower

• Driving

• In our dreams

• Walking

• During dull chats

• Meditating

• In the gym

No accident. The best ideas come in the shower, in nature, or while exercising.

(Your workstation is the worst place for creativity.)

The brain has time and space to link 'dots' of information during rest. It's eureka! New idea.

If you're serious about writing, capture thoughts as they come.

Immediately write down a new thought. Capture it. Don't miss it. Your future self will thank you.

As a writer, entrepreneur, or creative, letting ideas slide is bad.

I recommend using Evernote, Notion, or your device's basic note-taking tool to capture article ideas.

It doesn't matter whatever app you use as long as you collect article ideas.

When you practice 'idea-capturing' enough, you'll have an unending list of article ideas when writer's block hits.

High-Quality Content

More books, films, Medium pieces, and Youtube videos I consume, the more I'm inspired to write.

What you eat shapes who you are.

Celebrity gossip and fear-mongering news won't help your writing. It won't help you write regularly.

Instead, read expert-written books. Watch documentaries to improve your worldview. Follow amazing people online.

Develop your 'idea muscle' Daily creativity takes practice. The more you exercise your 'idea muscles,' the easier it is to generate article ideas.

I've trained my 'concept muscle' using James Altucher's exercise.

Write 10 ideas daily.

Write ten book ideas every day if you're an author. Write down 10 business ideas per day if you're an entrepreneur. Write down 10 investing ideas per day.

Write 10 article ideas per day. You become a content machine.

It doesn't state you need ten amazing ideas. You don't need 10 ideas. Ten ideas, regardless of quality.

Like at the gym, reps are what matter. With each article idea, you gain creativity. Writer's block is no match for this workout.

Quit Perfectionism

Perfectionism is bad for writers. You'll have bad articles. You'll have bad ideas. OK. It's creative.

Writing success requires prolificacy. You can't have 'perfect' articles.

“Perfectionism is the enemy of the idea muscle. Perfectionism is your brain trying to protect you from harm.” — James Altucher

Vincent van Gogh painted 900 pieces. The Starry Night is the most famous.

Thomas Edison invented 1093 things, but not all were as important as the lightbulb or the first movie camera.

Mozart composed nearly 600 compositions, but only Serenade No13 became popular.

Always do your best. Perfectionism shouldn't stop you from working. Write! Publicize. Make. Even if imperfect.

Write Your Story

Living an interesting life gives you plenty to write about. If you travel a lot, share your stories or lessons learned.

Describe your business's successes and shortcomings.

Share your experiences with difficulties or addictions.

More experiences equal more writing material.

If you stay indoors, perusing social media, you won't be inspired to write.

Have fun. Travel. Strive. Build a business. Be bold. Live a life worth writing about, and you won't run out of material.