I'm trying to understand why Bitcoin NFTs aren't ready.

Ordinals, a new Bitcoin protocol, has been controversial. NFTs can be added to Bitcoin transactions using the protocol. They are not tokens or fungible. Bitcoin NFTs are transaction metadata. Yes. They're not owned.

In January, the Ordinals protocol allowed data like photos to be directly encoded onto sats, the smallest units of Bitcoin worth 0.00000001 BTC, on the Bitcoin blockchain. Ordinals does not need a sidechain or token like other techniques. The Ordinals protocol has encoded JPEG photos, digital art, new profile picture (PFP) projects, and even 1993 DOOM onto the Bitcoin network.

Ordinals inscriptions are permanent digital artifacts preserved on the Bitcoin blockchain. It differs from Ethereum, Solana, and Stacks NFT technologies that allow smart contract creators to change information. Ordinals store the whole image or content on the blockchain, not just a link to an external server, unlike centralized databases, which can change the linked image, description, category, or contract identifier.

So far, more than 50,000 ordinals have been produced on the Bitcoin blockchain, and some of them have already been sold for astronomical amounts. The Ethereum-based CryptoPunks NFT collection spawned Ordinal Punk. Inscription 620 sold for 9.5 BTC, or $218,000, the most.

Segwit and Taproot, two important Bitcoin blockchain updates, enabled this. These protocols store transaction metadata, unlike Ethereum, where the NFT is the token. Bitcoin's NFT is a sat's transaction details.

What effects do ordinary values and NFTs have on the Bitcoin blockchain?

Ordinals will likely have long-term effects on the Bitcoin Ecosystem since they store, transact, and compute more data.

Charges Ordinals introduce scalability challenges. The Bitcoin network has limited transaction throughput and increased fees during peak demand. NFTs could make network transactions harder and more expensive. Ordinals currently occupy over 50% of block space, according to Glassnode.

One of the protocols that supported Ordinals Taproot has also seen a huge uptick:

Taproot use increases block size and transaction costs.

This could cause network congestion but also support more L2s with Ordinals-specific use cases. Dune info here.

Storage Needs The Bitcoin blockchain would need to store more data to store NFT data directly. Since ordinals were introduced, blocksize has tripled from 0.7mb to over 2.2mb, which could increase storage costs and make it harder for nodes to join the network.

Use Case Diversity On the other hand, NFTs on the Bitcoin blockchain could broaden Bitcoin's use cases beyond storage and payment. This could expand Bitcoin's user base. This is two-sided. Bitcoin was designed to be trustless, decentralized, peer-to-peer money.

Chain to permanently store NFTs as ordinals will change everything.

Popularity rise This new use case will boost Bitcoin appeal, according to some. This argument fails since Bitcoin is the most popular cryptocurrency. Popularity doesn't require a new use case. Cryptocurrency adoption boosts Bitcoin. It need not compete with Ethereum or provide extra benefits to crypto investors. If there was a need for another chain that supports NFTs (there isn't), why would anyone choose the slowest and most expensive network? It appears contradictory and unproductive.

Nonetheless, holding an NFT on the Bitcoin blockchain is more secure than any other blockchain, but this has little utility.

Bitcoin NFTs are undoubtedly controversial. NFTs are strange and perhaps harmful to Bitcoin's mission. If Bitcoin NFTs are here to stay, I hope a sidechain or rollup solution will take over and leave the base chain alone.

Most crypto is probably too.

The goals of Web 3 and the metaverse are admirable and attractive. Who doesn't want an internet owned by users? Who wouldn't want a digital realm where anything is possible? A better way to collaborate and visit pals.

Companies pursue profits endlessly. Infinite growth and revenue are expected, and if a corporation needs to sacrifice profits to safeguard users, the CEO, board of directors, and any executives will lose to the system of incentives that (1) retains workers with shares and (2) makes a company answerable to all of its shareholders. Only the government can guarantee user protections, but we know how successful that is. This is nothing new, just a problem with modern capitalism and tech platforms that a user-owned internet might remedy. Moxie, the founder of Signal, has a good articulation of some of these current Web 2 tech platform problems (but I forget the timestamp); thoughts on JRE aside, this episode is worth listening to (it’s about a bunch of other stuff too).

Moxie Marlinspike, founder of Signal, on the Joe Rogan Experience podcast.

Source: https://open.spotify.com/episode/2uVHiMqqJxy8iR2YB63aeP?si=4962b5ecb1854288

Web 3 champions are premature. There was so much spectacular growth during Web 2 that the next wave of founders want to make an even bigger impact, while investors old and new want a chance to get a piece of the moonshot action. Worse, crypto enthusiasts believe — and financially need — the fact of its success to be true, whether or not it is.

I’m doubtful that it will play out like current proponents say. Crypto has been the white-hot focus of SV’s best and brightest for a long time yet still struggles to come up any mainstream use case other than ‘buy, HODL, and believe’: a store of value for your financial goals and wishes. Some kind of the metaverse is likely, but will it be decentralized, mostly in VR, or will Meta (previously FB) play a big role? Unlikely.

METAVERSE

The metaverse exists already. Our digital lives span apps, platforms, and games. I can design a 3D house, invite people, use Discord, and hang around in an artificial environment. Millions of gamers do this in Rust, Minecraft, Valheim, and Animal Crossing, among other games. Discord's voice chat and Slack-like servers/channels are the present social anchor, but the interface, integrations, and data portability will improve. Soon you can stream YouTube videos on digital house walls. You can doodle, create art, play Jackbox, and walk through a door to play Apex Legends, Fortnite, etc. Not just gaming. Digital whiteboards and screen sharing enable real-time collaboration. They’ll review code and operate enterprises. Music is played and made. In digital living rooms, they'll watch movies, sports, comedy, and Twitch. They'll tweet, laugh, learn, and shittalk.

The metaverse is the evolution of our digital life at home, the third place. The closest analog would be Discord and the integration of Facebook, Slack, YouTube, etc. into a single, 3D, customizable hangout space.

I'm not certain this experience can be hugely decentralized and smoothly choreographed, managed, and run, or that VR — a luxury, cumbersome, and questionably relevant technology — must be part of it. Eventually, VR will be pragmatic, achievable, and superior to real life in many ways. A total sensory experience like the Matrix or Sword Art Online, where we're physically hooked into the Internet yet in our imaginations we're jumping, flying, and achieving athletic feats we never could in reality; exploring realms far grander than our own (as grand as it is). That VR is different from today's.

https://podcasts.google.com/feed/aHR0cHM6Ly9leHBvbmVudC5mbS9mZWVkLw/episode/aHR0cHM6Ly9leHBvbmVudC5mbS8_cD00MzM?hl=en&ved=2ahUKEwjH5u6r4rv2AhUjc98KHeybAP8QjrkEegQIChAF&ep=6

Ben Thompson released an episode of Exponent after Facebook changed its name to Meta. Ben was suspicious about many metaverse champion claims, but he made a good analogy between Oculus and the PC. The PC was initially far too pricey for the ordinary family to afford. It began as a business tool. It got so powerful and pervasive that it affected our personal life. Price continues to plummet and so much consumer software was produced that it's impossible to envision life without a home computer (or in our pockets). If Facebook shows product market fit with VR in business, through use cases like remote work and collaboration, maybe VR will become practical in our personal lives at home.

Before PCs, we relied on Blockbuster, the Yellow Pages, cabs to get to the airport, handwritten taxes, landline phones to schedule social events, and other archaic methods. It is impossible for me to conceive what VR, in the form of headsets and hand controllers, stands to give both professional and especially personal digital experiences that is an order of magnitude better than what we have today. Is looking around better than using a mouse to examine a 3D landscape? Do the hand controls make x10 or x100 work or gaming more fun or efficient? Will VR replace scalable Web 2 methods and applications like Web 1 and Web 2 did for analog? I don't know.

My guess is that the metaverse will arrive slowly, initially on displays we presently use, with more app interoperability. I doubt that it will be controlled by the people or by Facebook, a corporation that struggles to properly innovate internally, as practically every large digital company does. Large tech organizations are lousy at hiring product-savvy employees, and if they do, they rarely let them explore new things.

These companies act like business schools when they seek founders' results, with bureaucracy and dependency. Which company launched the last popular consumer software product that wasn't a clone or acquisition? Recent examples are scarce.

Web 3

Investors and entrepreneurs of Web 3 firms are declaring victory: 'Web 3 is here!' Web 3 is the future! Many profitable Web 2 enterprises existed when Web 2 was defined. The word was created to explain user behavior shifts, not a personal pipe dream.

Origins of Web 2: http://www.oreilly.com/pub/a/web2/archive/what-is-web-20.html

One of these Web 3 startups may provide the connecting tissue to link all these experiences or become one of the major new digital locations. Even so, successful players will likely use centralized power arrangements, as Web 2 businesses do now. Some Web 2 startups integrated our digital lives. Rockmelt (2010–2013) was a customizable browser with bespoke connectors to every program a user wanted; imagine seeing Facebook, Twitter, Discord, Netflix, YouTube, etc. all in one location. Failure. Who knows what Opera's doing?

Silicon Valley and tech Twitter in general have a history of jumping on dumb bandwagons that go nowhere. Dot-com crash in 2000? The huge deployment of capital into bad ideas and businesses is well-documented. And live video. It was the future until it became a niche sector for gamers. Live audio will play out a similar reality as CEOs with little comprehension of audio and no awareness of lasting new user behavior deceive each other into making more and bigger investments on fool's gold. Twitter trying to buy Clubhouse for $4B, Spotify buying Greenroom, Facebook exploring live audio and 'Tiktok for audio,' and now Amazon developing a live audio platform. This live audio frenzy won't be worth their time or energy. Blind guides blind. Instead of learning from prior failures like Twitter buying Periscope for $100M pre-launch and pre-product market fit, they're betting on unproven and uncompelling experiences.

NFTs

NFTs are also nonsense. Take Loot, a time-limited bag drop of "things" (text on the blockchain) for a game that didn't exist, bought by rich techies too busy to play video games and foolish enough to think they're getting in early on something with a big reward. What gaming studio is incentivized to use these items? Who's encouraged to join? No one cares besides Loot owners who don't have NFTs. Skill, merit, and effort should be rewarded with rare things for gamers. Even if a small minority of gamers can make a living playing, the average game's major appeal has never been to make actual money - that's a profession.

No game stays popular forever, so how is this objective sustainable? Once popularity and usage drop, exclusive crypto or NFTs will fall. And if NFTs are designed to have cross-game appeal, incentives apart, 30 years from now any new game will need millions of pre-existing objects to build around before they start. It doesn’t work.

Many games already feature item economies based on real in-game scarcity, generally for cosmetic things to avoid pay-to-win, which undermines scaled gaming incentives for huge player bases. Counter-Strike, Rust, etc. may be bought and sold on Steam with real money. Since the 1990s, unofficial cross-game marketplaces have sold in-game objects and currencies. NFTs aren't needed. Making a popular, enjoyable, durable game is already difficult.

With NFTs, certain JPEGs on the internet went from useless to selling for $69 million. Why? Crypto, Web 3, early Internet collectibles. NFTs are digital Beanie Babies (unlike NFTs, Beanie Babies were a popular children's toy; their destinies are the same). NFTs are worthless and scarce. They appeal to crypto enthusiasts seeking for a practical use case to support their theory and boost their own fortune. They also attract to SV insiders desperate not to miss the next big thing, not knowing what it will be. NFTs aren't about paying artists and creators who don't get credit for their work.

South Park's Underpants Gnomes

NFTs are a benign, foolish plan to earn money on par with South Park's underpants gnomes. At worst, they're the world of hucksterism and poor performers. Or those with money and enormous followings who, like everyone, don't completely grasp cryptocurrencies but are motivated by greed and status and believe Gary Vee's claim that CryptoPunks are the next Facebook. Gary's watertight logic: if NFT prices dip, they're on the same path as the most successful corporation in human history; buy the dip! NFTs aren't businesses or museum-worthy art. They're bs.

Gary Vee compares NFTs to Amazon.com. vm.tiktok.com/TTPdA9TyH2

We grew up collecting: Magic: The Gathering (MTG) cards printed in the 90s are now worth over $30,000. Imagine buying a digital Magic card with no underlying foundation. No one plays the game because it doesn't exist. An NFT is a contextless image someone conned you into buying a certificate for, but anyone may copy, paste, and use. Replace MTG with Pokemon for younger readers.

When Gary Vee strongarms 30 tech billionaires and YouTube influencers into buying CryptoPunks, they'll talk about it on Twitch, YouTube, podcasts, Twitter, etc. That will convince average folks that the product has value. These guys are smart and/or rich, so I'll get in early like them. Cryptography is similar. No solid, scaled, mainstream use case exists, and no one knows where it's headed, but since the global crypto financial bubble hasn't burst and many people have made insane fortunes, regular people are putting real money into something that is highly speculative and could be nothing because they want a piece of the action. Who doesn’t want free money? Rich techies and influencers won't be affected; normal folks will.

Imagine removing every $1 invested in Bitcoin instantly. What would happen? How far would Bitcoin fall? Over 90%, maybe even 95%, and Bitcoin would be dead. Bitcoin as an investment is the only scalable widespread use case: it's confidence that a better use case will arise and that being early pays handsomely. It's like pouring a trillion dollars into a company with no business strategy or users and a CEO who makes vague future references.

New tech and efforts may provoke a 'get off my lawn' mentality as you approach 40, but I've always prided myself on having a decent bullshit detector, and it's flying off the handle at this foolishness. If we can accomplish a functional, responsible, equitable, and ethical user-owned internet, I'm for it.

Postscript:

I wanted to summarize my opinions because I've been angry about this for a while but just sporadically tweeted about it. A friend handed me a Dan Olson YouTube video just before publication. He's more knowledgeable, articulate, and convincing about crypto. It's worth seeing:

This post is a summary. See the original one here.

The human brain is amazing. As more scientists examine the brain, we learn how much it can store.

The human brain has 1 billion neurons, according to Scientific American. Each neuron creates 1,000 connections, totaling over a trillion. If each neuron could store one memory, we'd run out of room. [1]

What if you could store and access more info, freeing up brain space for problem-solving and creativity?

Build a second brain to keep up with rising knowledge (what I refer to as a Digital Brain). Effectively managing information entails realizing you can't recall everything.

Every action requires information. You need the correct information to learn a new skill, complete a project at work, or establish a business. You must manage information properly to advance your profession and improve your life.

How to construct a second brain to organize information and achieve goals.

What Is a Second Brain?

How often do you forget an article or book's key point? Have you ever wasted hours looking for a saved file?

If so, you're not alone. Information overload affects millions of individuals worldwide. Information overload drains mental resources and causes anxiety.

This is when the second brain comes in.

Building a second brain doesn't involve duplicating the human brain. Building a system that captures, organizes, retrieves, and archives ideas and thoughts. The second brain improves memory, organization, and recall.

Digital tools are preferable to analog for building a second brain.

Digital tools are portable and accessible. Due to these benefits, we'll focus on digital second-brain building.

Brainware

Digital Brains are external hard drives. It stores, organizes, and retrieves. This means improving your memory won't be difficult. 

Memory has three components in computing:

Recording — storing the information

Organization — archiving it in a logical manner

Recall — retrieving it again when you need it

For example:

Due to rigorous security settings, many websites need you to create complicated passwords with special characters.

You must now memorize (Record), organize (Organize), and input this new password the next time you check in (Recall).

Even in this simple example, there are many pieces to remember. We can't recognize this new password with our usual patterns. If we don't use the password every day, we'll forget it. You'll type the wrong password when you try to remember it.

It's common. Is it because the information is complicated? Nope. Passwords are basically letters, numbers, and symbols.

It happens because our brains aren't meant to memorize these. Digital Brains can do heavy lifting.

Why You Need a Digital Brain

Dual minds are best. Birth brain is limited.

The cerebral cortex has 125 trillion synapses, according to a Stanford Study. The human brain can hold 2.5 million terabytes of digital data. [2]

Building a second brain improves learning and memory.

Learn and store information effectively

Faster information recall

Organize information to see connections and patterns

Build a Digital Brain to learn more and reach your goals faster. Building a second brain requires time and work, but you'll have more time for vital undertakings. 

Why you need a Digital Brain:

1. Use Brainpower Effectively

Your brain has boundaries, like any organ. This is true while solving a complex question or activity. If you can't focus on a work project, you won't finish it on time.

Second brain reduces distractions. A robust structure helps you handle complicated challenges quickly and stay on track. Without distractions, it's easy to focus on vital activities.

2. Staying Organized

Professional and personal duties must be balanced. With so much to do, it's easy to neglect crucial duties. This is especially true for skill-building. Digital Brain will keep you organized and stress-free.

Life success requires action. Organized people get things done. Organizing your information will give you time for crucial tasks.

You'll finish projects faster with good materials and methods. As you succeed, you'll gain creative confidence. You can then tackle greater jobs.

3. Creativity Process

Creativity drives today's world. Creativity is mysterious and surprising for millions worldwide. Immersing yourself in others' associations, triggers, thoughts, and ideas can generate inspiration and creativity.

Building a second brain is crucial to establishing your creative process and building habits that will help you reach your goals. Creativity doesn't require perfection or overthinking.

4. Transforming Your Knowledge Into Opportunities

This is the age of entrepreneurship. Today, you can publish online, build an audience, and make money.

Whether it's a business or hobby, you'll have several job alternatives. Knowledge can boost your economy with ideas and insights.

5. Improving Thinking and Uncovering Connections

Modern career success depends on how you think. Instead of overthinking or perfecting, collect the best images, stories, metaphors, anecdotes, and observations.

This will increase your creativity and reveal connections. Increasing your imagination can help you achieve your goals, according to research. [3]

Your ability to recognize trends will help you stay ahead of the pack.

6. Credibility for a New Job or Business

Your main asset is experience-based expertise. Others won't be able to learn without your help. Technology makes knowledge tangible.

This lets you use your time as you choose while helping others. Changing professions or establishing a new business become learning opportunities when you have a Digital Brain.

7. Using Learning Resources

Millions of people use internet learning materials to improve their lives. Online resources abound. These include books, forums, podcasts, articles, and webinars.

These resources are mostly free or inexpensive. Organizing your knowledge can save you time and money. Building a Digital Brain helps you learn faster. You'll make rapid progress by enjoying learning.

How does a second brain feel?

Digital Brain has helped me arrange my job and family life for years.

No need to remember 1001 passwords. I never forget anything on my wife's grocery lists. Never miss a meeting. I can access essential information and papers anytime, anywhere.

Delegating memory to a second brain reduces tension and anxiety because you'll know what to do with every piece of information.

No information will be forgotten, boosting your confidence. Better manage your fears and concerns by writing them down and establishing a strategy. You'll understand the plethora of daily information and have a clear head.

How to Develop Your Digital Brain (Your Second Brain)

It's cheap but requires work.

Digital Brain development requires:

Recording — storing the information

Organization — archiving it in a logical manner

Recall — retrieving it again when you need it

1. Decide what information matters before recording.

To succeed in today's environment, you must manage massive amounts of data. Articles, books, webinars, podcasts, emails, and texts provide value. Remembering everything is impossible and overwhelming.

What information do you need to achieve your goals?

You must consolidate ideas and create a strategy to reach your aims. Your biological brain can imagine and create with a Digital Brain.

2. Use the Right Tool

We usually record information without any preparation - we brainstorm in a word processor, email ourselves a message, or take notes while reading.

This information isn't used. You must store information in a central location.

Different information needs different instruments.

Evernote is a top note-taking program. Audio clips, Slack chats, PDFs, text notes, photos, scanned handwritten pages, emails, and webpages can be added.

Pocket is a great software for saving and organizing content. Images, videos, and text can be sorted. Web-optimized design

Calendar apps help you manage your time and enhance your productivity by reminding you of your most important tasks. Calendar apps flourish. The best calendar apps are easy to use, have many features, and work across devices. These calendars include Google, Apple, and Outlook.

To-do list/checklist apps are useful for managing tasks. Easy-to-use, versatility, budget, and cross-platform compatibility are important when picking to-do list apps. Google Keep, Google Tasks, and Apple Notes are good to-do apps.

3. Organize data for easy retrieval

How should you organize collected data?

When you collect and organize data, you'll see connections. An article about networking can assist you comprehend web marketing. Saved business cards can help you find new clients.

Choosing the correct tools helps organize data. Here are some tools selection criteria:

• Can the tool sync across devices?

• Personal or team?

• Has a search function for easy information retrieval?

• Does it provide easy data categorization?

• Can users create lists or collections?

• Does it offer easy idea-information connections?

• Does it mind map and visually organize thoughts?

Conclusion

Building a Digital Brain (second brain) helps us save information, think creatively, and implement ideas. Your second brain is a biological extension. It prevents amnesia, allowing you to tackle bigger creative difficulties.

People who love learning often consume information without using it. Every day, they postpone life-improving experiences until they're forgotten. Useful information becomes strength. 

Reference

[1] ^ Scientific American: What Is the Memory Capacity of the Human Brain?

[2] ^ Clinical Neurology Specialists: What is the Memory Capacity of a Human Brain?

[3] ^ National Library of Medicine: Imagining Success: Multiple Achievement Goals and the Effectiveness of Imagery

After 10 years of working in scale-ups, I've embraced a few concepts for scaling Tech and Product teams.

First, cross-functionalize teams. Product Managers represent the business, Product Designers the consumer, and Engineers build.

I organize teams of 5-10 individuals, following AWS's two pizza teams guidelines, with a Product Trio guiding each.

If more individuals are needed to reach a goal, I group teams under a Product Trio.

With Engineering being the biggest group, Staff/Principal Engineers often support the Trio on cross-team technical decisions.

Product Managers, Engineering Managers, or Engineers in the team may manage projects (depending on the project or aim), but the trio is collectively responsible for the team's output and outcome.

Once the Product Trio model is created, roles, duties, team ceremonies, and cooperation models must be clarified.

Keep reporting lines by discipline. Line managers are accountable for each individual's advancement, thus it's crucial that they know the work in detail.

Cross-team collaboration becomes more important after 3 teams (15-30 people). Teams can easily diverge in how they write code, run ceremonies, and build products.

Establishing groups of people that are cross-team, but grouped by discipline and skills, sharing and agreeing on working practices becomes critical.

The “Spotify Guild” model has been where I’ve taken a lot of my inspiration from.

Last, establish a taxonomy for communication channels.

In Slack, I create one channel per team and one per guild (and one for me to have discussions with the team leads).

These are just some of the basic principles I follow to organize teams.

A book I particularly like about team types and how they interact with each other is https://teamtopologies.com/.

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.