The 2008 Bitcoin white paper solves the classic computer science consensus problem.

Issue Statement

The Byzantine Generals Problem (BGP) is called after an allegory in which several generals must collaborate and attack a city at the same time to win (figure 1-left). Any general who retreats at the last minute loses the fight (figure 1-right). Thus, precise messengers and no rogue generals are essential. This is difficult without a trusted central authority.

In their 1982 publication, Leslie Lamport, Robert Shostak, and Marshall Please termed this topic the Byzantine Generals Problem to simplify distributed computer systems.

Consensus in a distributed computer network is the issue. Reaching a consensus on which systems work (and stay in the network) and which don't makes maintaining a network tough (i.e., needs to be removed from network). Challenges include unreliable communication routes between systems and mis-reporting systems.

Solving BGP can let us construct machine learning solutions without single points of failure or trusted central entities. One server hosts model parameters while numerous workers train the model. This study describes fault-tolerant Distributed Byzantine Machine Learning.

Bitcoin invented a mechanism for a distributed network of nodes to agree on which transactions should go into the distributed ledger (blockchain) without a trusted central body. It solved BGP implementation. Satoshi Nakamoto, the pseudonymous bitcoin creator, solved the challenge by cleverly combining cryptography and consensus mechanisms.

Disclaimer

This is not financial advice. It discusses a unique computer science solution.

Bitcoin

Bitcoin's white paper begins:

“A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.” Source: https://www.ussc.gov/sites/default/files/pdf/training/annual-national-training-seminar/2018/Emerging_Tech_Bitcoin_Crypto.pdf

Bitcoin's main parts:

1. The open-source and versioned bitcoin software that governs how nodes, miners, and the bitcoin token operate.

2. The native kind of token, known as a bitcoin token, may be created by mining (up to 21 million can be created), and it can be transferred between wallet addresses in the bitcoin network.

3. Distributed Ledger, which contains exact copies of the database (or "blockchain") containing each transaction since the first one in January 2009.

4. distributed network of nodes (computers) running the distributed ledger replica together with the bitcoin software. They broadcast the transactions to other peer nodes after validating and accepting them.

5. Proof of work (PoW) is a cryptographic requirement that must be met in order for a miner to be granted permission to add a new block of transactions to the blockchain of the cryptocurrency bitcoin. It takes the form of a valid hash digest. In order to produce new blocks on average every 10 minutes, Bitcoin features a built-in difficulty adjustment function that modifies the valid hash requirement (length of nonce). PoW requires a lot of energy since it must continually generate new hashes at random until it satisfies the criteria.

6. The competing parties known as miners carry out continuous computing processing to address recurrent cryptography issues. Transaction fees and some freshly minted (mined) bitcoin are the rewards they receive. The amount of hashes produced each second—or hash rate—is a measure of mining capacity.

Cryptography, decentralization, and the proof-of-work consensus method are Bitcoin's most unique features.

Bitcoin uses encryption

Bitcoin employs this established cryptography.

1. Hashing

2. digital signatures based on asymmetric encryption

Hashing (SHA-256) (SHA-256)

Hashing converts unique plaintext data into a digest. Creating the plaintext from the digest is impossible. Bitcoin miners generate new hashes using SHA-256 to win block rewards.

A new hash is created from the current block header and a variable value called nonce. To achieve the required hash, mining involves altering the nonce and re-hashing.

The block header contains the previous block hash and a Merkle root, which contains hashes of all transactions in the block. Thus, a chain of blocks with increasing hashes links back to the first block. Hashing protects new transactions and makes the bitcoin blockchain immutable. After a transaction block is mined, it becomes hard to fabricate even a little entry.

Asymmetric Cryptography Digital Signatures

Asymmetric cryptography (public-key encryption) requires each side to have a secret and public key. Public keys (wallet addresses) can be shared with the transaction party, but private keys should not. A message (e.g., bitcoin payment record) can only be signed by the owner (sender) with the private key, but any node or anybody with access to the public key (visible in the blockchain) can verify it. Alex will submit a digitally signed transaction with a desired amount of bitcoin addressed to Bob's wallet to a node to send bitcoin to Bob. Alex alone has the secret keys to authorize that amount. Alex's blockchain public key allows anyone to verify the transaction.

Solution

Now, apply bitcoin to BGP. BGP generals resemble bitcoin nodes. The generals' consensus is like bitcoin nodes' blockchain block selection. Bitcoin software on all nodes can:

Check transactions (i.e., validate digital signatures)

2. Accept and propagate just the first miner to receive the valid hash and verify it accomplished the task. The only way to guess the proper hash is to brute force it by repeatedly producing one with the fixed/current block header and a fresh nonce value.

Thus, PoW and a dispersed network of nodes that accept blocks from miners that solve the unfalsifiable cryptographic challenge solve consensus.

Suppose:

1. Unreliable nodes

2. Unreliable miners

Bitcoin accepts the longest chain if rogue nodes cause divergence in accepted blocks. Thus, rogue nodes must outnumber honest nodes in accepting/forming the longer chain for invalid transactions to reach the blockchain. As of November 2022, 7000 coordinated rogue nodes are needed to takeover the bitcoin network.

Dishonest miners could also try to insert blocks with falsified transactions (double spend, reverse, censor, etc.) into the chain. This requires over 50% (51% attack) of miners (total computational power) to outguess the hash and attack the network. Mining hash rate exceeds 200 million (source). Rewards and transaction fees encourage miners to cooperate rather than attack. Quantum computers may become a threat.

Visit my Quantum Computing post.

Quantum computers—what are they? Quantum computers will have a big influence. towardsdatascience.com

Nodes have more power than miners since they can validate transactions and reject fake blocks. Thus, the network is secure if honest nodes are the majority.

Summary

Table 1 compares three Byzantine Generals Problem implementations.

Bitcoin white paper and implementation solved the consensus challenge of distributed systems without central governance. It solved the illusive Byzantine Generals Problem.

Resources

Resources

1. https://en.wikipedia.org/wiki/Byzantine_fault

2. Source-code for Bitcoin Core Software — https://github.com/bitcoin/bitcoin

3. Bitcoin white paper — https://bitcoin.org/bitcoin.pdf

4. https://en.wikipedia.org/wiki/Bitcoin

5. https://www.microsoft.com/en-us/research/publication/byzantine-generals-problem/

6. https://www.microsoft.com/en-us/research/uploads/prod/2016/12/The-Byzantine-Generals-Problem.pdf

7. https://en.wikipedia.org/wiki/Hash_function

8. https://en.wikipedia.org/wiki/Merkle_tree

9. https://en.wikipedia.org/wiki/SHA-2

10. https://en.wikipedia.org/wiki/Public-key_cryptography

11. https://en.wikipedia.org/wiki/Digital_signature

12. https://en.wikipedia.org/wiki/Proof_of_work

13. https://en.wikipedia.org/wiki/Quantum_cryptography

14. https://dci.mit.edu/bitcoin-security-initiative

15. https://dci.mit.edu/51-attacks

16. Genuinely Distributed Byzantine Machine Learning, El-Mahdi El-Mhamdi et al., 2020. ACM, New York, NY, https://doi.org/10.1145/3382734.3405695

Introduction

Markets rely on knowledge.

The internet provided practically endless knowledge and wisdom. Humanity has never seen such leverage. Technology's progress drives us to adapt to a changing world, changing our routines and behaviors.

In a digital age, people may struggle to live in the analogue world of their upbringing. Can those who can't adapt change their lives? I won't answer. We should teach those who are willing to learn, nevertheless. Unravel the modern world's riddles and give them wisdom.

Adapt or die . Accept the future or remain behind.

This essay will help you comprehend Bitcoin better than most market participants and the general public. Let's dig into Bitcoin.

Join me.

Ascension

Bitcoin.org was registered in August 2008. Bitcoin whitepaper was published on 31 October 2008. The document intrigued and motivated people around the world, including technical engineers and sovereignty seekers. Since then, Bitcoin's whitepaper has been read and researched to comprehend its essential concept.

I recommend reading the whitepaper yourself. You'll be able to say you read the Bitcoin whitepaper instead of simply Googling "what is Bitcoin" and reading the fundamental definition without knowing the revolution's scope. The article links to Bitcoin's whitepaper. To avoid being overwhelmed by the whitepaper, read the following article first.

Bitcoin isn't the first peer-to-peer digital currency. Hashcash or Bit Gold were once popular cryptocurrencies. These two Bitcoin precursors failed to gain traction and produce the network effect needed for general adoption. After many struggles, Bitcoin emerged as the most successful cryptocurrency, leading the way for others.

Satoshi Nakamoto, an active bitcointalk.org user, created Bitcoin. Satoshi's identity remains unknown. Satoshi's last bitcointalk.org login was 12 December 2010. Since then, he's officially disappeared. Thus, conspiracies and riddles surround Bitcoin's creators. I've heard many various theories, some insane and others well-thought-out.

It's not about who created it; it's about knowing its potential. Since its start, Satoshi's legacy has changed the world and will continue to.

Block-by-block blockchain

Bitcoin is a distributed ledger. What's the meaning?

Everyone can view all blockchain transactions, but no one can undo or delete them.

Imagine you and your friends routinely eat out, but only one pays. You're careful with money and what others owe you. How can everyone access the info without it being changed?

You'll keep a notebook of your evening's transactions. Everyone will take a page home. If one of you changed the page's data, the group would notice and reject it. The majority will establish consensus and offer official facts.

Miners add a new Bitcoin block to the main blockchain every 10 minutes. The appended block contains miner-verified transactions. Now that the next block has been added, the network will receive the next set of user transactions.

Bitcoin Proof of Work—prove you earned it

Any firm needs hardworking personnel to expand and serve clients. Bitcoin isn't that different.

Bitcoin's Proof of Work consensus system needs individuals to validate and create new blocks and check for malicious actors. I'll discuss Bitcoin's blockchain consensus method.

Proof of Work helps Bitcoin reach network consensus. The network is checked and safeguarded by CPU, GPU, or ASIC Bitcoin-mining machines (Application-Specific Integrated Circuit).

Every 10 minutes, miners are rewarded in Bitcoin for securing and verifying the network. It's unlikely you'll finish the block. Miners build pools to increase their chances of winning by combining their processing power.

In the early days of Bitcoin, individual mining systems were more popular due to high maintenance costs and larger earnings prospects. Over time, people created larger and larger Bitcoin mining facilities that required a lot of space and sophisticated cooling systems to keep machines from overheating.

Proof of Work is a vital part of the Bitcoin network, as network security requires the processing power of devices purchased with fiat currency. Miners must invest in mining facilities, which creates a new business branch, mining facilities ownership. Bitcoin mining is a topic for a future article.

More mining, less reward

Bitcoin is usually scarce.

Why is it rare? It all comes down to 21,000,000 Bitcoins.

Were all Bitcoins mined? Nope. Bitcoin's supply grows until it hits 21 million coins. Initially, 50BTC each block was mined, and each block took 10 minutes. Around 2140, the last Bitcoin will be mined.

But 50BTC every 10 minutes does not give me the year 2140. Indeed careful reader. So important is Bitcoin's halving process.

What is halving?

The block reward is halved every 210,000 blocks, which takes around 4 years. The initial payout was 50BTC per block and has been decreased to 25BTC after 210,000 blocks. First halving occurred on November 28, 2012, when 10,500,000 BTC (50%) had been mined. As of April 2022, the block reward is 6.25BTC and will be lowered to 3.125BTC by 19 March 2024.

The halving method is tied to Bitcoin's hashrate. Here's what "hashrate" means.

What if we increased the number of miners and hashrate they provide to produce a block every 10 minutes? Wouldn't we manufacture blocks faster?

Every 10 minutes, blocks are generated with little asymmetry. Due to the built-in adaptive difficulty algorithm, the overall hashrate does not affect block production time. With increased hashrate, it's harder to construct a block. We can estimate when the next halving will occur because 10 minutes per block is fixed.

Building with nodes and blocks

For someone new to crypto, the unusual terms and words may be overwhelming. You'll also find everyday words that are easy to guess or have a vague idea of what they mean, how they work, and what they do. Consider blockchain technology.

Nodes and blocks: Think about that for a moment. What is your first idea?

The blockchain is a chain of validated blocks added to the main chain. What's a "block"? What's inside?

The block is another page in the blockchain book that has been filled with transaction information and accepted by the majority.

We won't go into detail about what each block includes and how it's built, as long as you understand its purpose.

What about nodes?

Nodes, along with miners, verify the blockchain's state independently. But why?

To create a full blockchain node, you must download the whole Bitcoin blockchain and check every transaction against Bitcoin's consensus criteria.

What's Bitcoin's size? 

In April 2022, the Bitcoin blockchain was 389.72GB.

Bitcoin's blockchain has miners and node runners.

Let's revisit the US gold rush. Miners mine gold with their own power (physical and monetary resources) and are rewarded with gold (Bitcoin). All become richer with more gold, and so does the country.

Nodes are like sheriffs, ensuring everything is done according to consensus rules and that there are no rogue miners or network users.

Lost and held bitcoin

Does the Bitcoin exchange price match each coin's price? How many coins remain after 21,000,000? 21 million or less?

Common reason suggests a 21 million-coin supply.

What if I lost 1BTC from a cold wallet?

What if I saved 1000BTC on paper in 2010 and it was damaged?

What if I mined Bitcoin in 2010 and lost the keys?

Satoshi Nakamoto's coins? Since then, those coins haven't moved.

How many BTC are truly in circulation?

Many people are trying to answer this question, and you may discover a variety of studies and individual research on the topic. Be cautious of the findings because they can't be evaluated and the statistics are hazy guesses.

On the other hand, we have long-term investors who won't sell their Bitcoin or will sell little amounts to cover mining or living needs.

The price of Bitcoin is determined by supply and demand on exchanges using liquid BTC. How many BTC are left after subtracting lost and non-custodial BTC? 

We have significantly less Bitcoin in circulation than you think, thus the price may not reflect demand if we knew the exact quantity of coins available.

True HODLers and diamond-hand investors won't sell you their coins, no matter the market.

What's UTXO?

Unspent (U) Transaction (TX) Output (O)

Imagine taking a $100 bill to a store. After choosing a drink and munchies, you walk to the checkout to pay. The cashier takes your $100 bill and gives you $25.50 in change. It's in your wallet.

Is it simply 100$? No way.

The $25.50 in your wallet is unrelated to the $100 bill you used. Your wallet's $25.50 is just bills and coins. Your wallet may contain these coins and bills:

2x 10$ 1x 10$

1x 5$ or 3x 5$

1x 0.50$ 2x 0.25$

Any combination of coins and bills can equal $25.50. You don't care, and I'd wager you've never ever considered it.

That is UTXO. Now, I'll detail the Bitcoin blockchain and how UTXO works, as it's crucial to know what coins you have in your (hopefully) cold wallet.

You purchased 1BTC. Is it all? No. UTXOs equal 1BTC. Then send BTC to a cold wallet. Say you pay 0.001BTC and send 0.999BTC to your cold wallet. Is it the 1BTC you got before? Well, yes and no. The UTXOs are the same or comparable as before, but the blockchain address has changed. It's like if you handed someone a wallet, they removed the coins needed for a network charge, then returned the rest of the coins and notes.

UTXO is a simple concept, but it's crucial to grasp how it works to comprehend dangers like dust attacks and how coins may be tracked.

Lightning Network: fast cash

You've probably heard of "Layer 2 blockchain" projects.

What does it mean?

Layer 2 on a blockchain is an additional layer that increases the speed and quantity of transactions per minute and reduces transaction fees.

Imagine going to an obsolete bank to transfer money to another account and having to pay a charge and wait. You can transfer funds via your bank account or a mobile app without paying a fee, or the fee is low, and the cash appear nearly quickly. Layer 1 and 2 payment systems are different.

Layer 1 is not obsolete; it merely has more essential things to focus on, including providing the blockchain with new, validated blocks, whereas Layer 2 solutions strive to offer Layer 1 with previously processed and verified transactions. The primary blockchain, Bitcoin, will only receive the wallets' final state. All channel transactions until shutting and balancing are irrelevant to the main chain.

Layer 2 and the Lightning Network's goal are now clear. Most Layer 2 solutions on multiple blockchains are created as blockchains, however Lightning Network is not. Remember the following remark, as it best describes Lightning.

Lightning Network connects public and private Bitcoin wallets.

Opening a private channel with another wallet notifies just two parties. The creation and opening of a public channel tells the network that anyone can use it.

Why create a public Lightning Network channel?

Every transaction through your channel generates fees.

Money, if you don't know.

See who benefits when in doubt.

Anonymity, huh?

Bitcoin anonymity? Bitcoin's anonymity was utilized to launder money.

Well… You've heard similar stories. When you ask why or how it permits people to remain anonymous, the conversation ends as if it were just a story someone heard.

Bitcoin isn't private. Pseudonymous.

What if someone tracks your transactions and discovers your wallet address? Where is your anonymity then?

Bitcoin is like bulletproof glass storage; you can't take or change the money. If you dig and analyze the data, you can see what's inside.

Every online action leaves a trace, and traces may be tracked. People often forget this guideline.

A tool like that can help you observe what the major players, or whales, are doing with their coins when the market is uncertain. Many people spend time analyzing on-chain data. Worth it?

Ask yourself a question. What are the big players' options?  Do you think they're letting you see their wallets for a small on-chain data fee?

Instead of short-term behaviors, focus on long-term trends.

More wallet transactions leave traces. Having nothing to conceal isn't a defect. Can it lead to regulating Bitcoin so every transaction is tracked like in banks today?

But wait. How can criminals pay out Bitcoin? They're doing it, aren't they?

Mixers can anonymize your coins, letting you to utilize them freely. This is not a guide on how to make your coins anonymous; it could do more harm than good if you don't know what you're doing.

Remember, being anonymous attracts greater attention.

Bitcoin isn't the only cryptocurrency we can use to buy things. Using cryptocurrency appropriately can provide usability and anonymity. Monero (XMR), Zcash (ZEC), and Litecoin (LTC) following the Mimblewimble upgrade are examples.

Summary

Congratulations! You've reached the conclusion of the article and learned about Bitcoin and cryptocurrency. You've entered the future.

You know what Bitcoin is, how its blockchain works, and why it's not anonymous. I bet you can explain Lightning Network and UTXO to your buddies.

Markets rely on knowledge. Prepare yourself for success before taking the first step. Let your expertise be your edge.

This article is a summary of this one.

Disclaimer : This is not financial advice for any investment.

TL;DR

• You might not have realized it, but as we move toward net zero carbon emissions, the globe is already at war.

• According to the Paris Agreement of COP26, 64% of nations have already declared net zero, and the issue of carbon reduction has already become so important for businesses that it affects their ability to survive. Furthermore, the time when carbon emission standards will be defined and controlled on an individual basis is becoming closer.

• Since 2017, the market for carbon credits has experienced extraordinary expansion as a result of widespread talks about carbon credits. The carbon credit market is predicted to expand much more once net zero is implemented and carbon emission rules inevitably tighten.

Hello! Ben here from Nonce Classic. Nonce Classic has recently confirmed the tremendous growth potential of the carbon credit market in the midst of a major trend towards the global goal of net zero (carbon emissions caused by humans — carbon reduction by humans = 0 ). Moreover, we too believed that the questions and issues the carbon credit market suffered from the last 30–40yrs could be perfectly answered through crypto technology and that is why we have added a carbon credit crypto project to the Nonce Classic portfolio. There have been many teams out there that have tried to solve environmental problems through crypto but very few that have measurable experience working in the carbon credit scene. Thus we have put in our efforts to find projects that are not crypto projects created for the sake of issuing tokens but projects that pragmatically use crypto technology to combat climate change by solving problems of the current carbon credit market. In that process, we came to hear of Climate Coin, a veritable carbon credit crypto project, and us Nonce Classic as an accelerator, have begun contributing to its growth and invested in its tokens. Starting with this article, we plan to publish a series of articles explaining why the carbon credit market is bullish, why we invested in Climate Coin, and what kind of project Climate Coin is specifically. In this first article let us understand the carbon credit market and look into its growth potential! Let’s begin :)

The Unavoidable Entry of the Net Zero Era

Net zero means... Human carbon emissions are balanced by carbon reduction efforts. A non-environmentalist may find it hard to accept that net zero is attainable by 2050. Global cooperation to save the earth is happening faster than we imagine.

In the Paris Agreement of COP26, concluded in Glasgow, UK on Oct. 31, 2021, nations pledged to reduce worldwide yearly greenhouse gas emissions by more than 50% by 2030 and attain net zero by 2050. Governments throughout the world have pledged net zero at the national level and are holding each other accountable by submitting Nationally Determined Contributions (NDC) every five years to assess implementation. 127 of 198 nations have declared net zero.

Each country's 1.5-degree reduction plans have led to carbon reduction obligations for companies. In places with the strictest environmental regulations, like the EU, companies often face bankruptcy because the cost of buying carbon credits to meet their carbon allowances exceeds their operating profits. In this day and age, minimizing carbon emissions and securing carbon credits are crucial.

Recent SEC actions on climate change may increase companies' concerns about reducing emissions. The SEC required all U.S. stock market companies to disclose their annual greenhouse gas emissions and climate change impact on March 21, 2022. The SEC prepared the proposed regulation through in-depth analysis and stakeholder input since last year. Three out of four SEC members agreed that it should pass without major changes. If the regulation passes, it will affect not only US companies, but also countless companies around the world, directly or indirectly.

Even companies not listed on the U.S. stock market will be affected and, in most cases, required to disclose emissions. Companies listed on the U.S. stock market with significant greenhouse gas emissions or specific targets are subject to stricter emission standards (Scope 3) and disclosure obligations, which will magnify investigations into all related companies. Greenhouse gas emissions can be calculated three ways. Scope 1 measures carbon emissions from a company's facilities and transportation. Scope 2 measures carbon emissions from energy purchases. Scope 3 covers all indirect emissions from a company's value chains.

The SEC's proposed carbon emission disclosure mandate and regulations are one example of how carbon credit policies can cross borders and affect all parties. As such incidents will continue throughout the implementation of net zero, even companies that are not immediately obligated to disclose their carbon emissions must be prepared to respond to changes in carbon emission laws and policies.

Carbon reduction obligations will soon become individual. Individual consumption has increased dramatically with improved quality of life and convenience, despite national and corporate efforts to reduce carbon emissions. Since consumption is directly related to carbon emissions, increasing consumption increases carbon emissions. Countries around the world have agreed that to achieve net zero, carbon emissions must be reduced on an individual level. Solutions to individual carbon reduction are being actively discussed and studied under the term Personal Carbon Trading (PCT).

PCT is a system that allows individuals to trade carbon emission quotas in the form of carbon credits. Individuals who emit more carbon than their allotment can buy carbon credits from those who emit less. European cities with well-established carbon credit markets are preparing for net zero by conducting early carbon reduction prototype projects. The era of checking product labels for carbon footprints, choosing low-emissions transportation, and worrying about hot shower emissions is closer than we think.

The Market for Carbon Credits Is Expanding Fearfully

Compliance and voluntary carbon markets make up the carbon credit market.

A Compliance Market enforces carbon emission allowances for actors. Companies in industries that previously emitted a lot of carbon are included in the mandatory carbon market, and each government receives carbon credits each year. If a company's emissions are less than the assigned cap and it has extra carbon credits, it can sell them to other companies that have larger emissions and require them (Cap and Trade). The annual number of free emission permits provided to companies is designed to decline, therefore companies' desire for carbon credits will increase. The compliance market's yearly trading volume will exceed $261B in 2020, five times its 2017 level.

In the Voluntary Market, carbon reduction is voluntary and carbon credits are sold for personal reasons or to build market participants' eco-friendly reputations. Even if not in the compliance market, it is typical for a corporation to be obliged to offset its carbon emissions by acquiring voluntary carbon credits. When a company seeks government or company investment, it may be denied because it is not net zero. If a significant shareholder declares net zero, the companies below it must execute it. As the world moves toward ESG management, becoming an eco-friendly company is no longer a strategic choice to gain a competitive edge, but an important precaution to not fall behind. Due to this eco-friendly trend, the annual market volume of voluntary emission credits will approach $1B by November 2021. The voluntary credit market is anticipated to reach $5B to $50B by 2030. (TSCVM 2021 Report)

In conclusion

This article analyzed how net zero, a target promised by countries around the world to combat climate change, has brought governmental, corporate, and human changes. We discussed how these shifts will become more obvious as we approach net zero, and how the carbon credit market would increase exponentially in response. In the following piece, let's analyze the hurdles impeding the carbon credit market's growth, how the project we invested in tries to tackle these issues, and why we chose Climate Coin. Wait! Jim Skea, co-chair of the IPCC working group, said,

“It’s now or never, if we want to limit global warming to 1.5°C” — Jim Skea

Join nonceClassic’s community:

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Mail us : general@nonceclassic.org

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.

Canonicalization and canonical URLs are essential for SEO, and improper implementation can negatively impact your site's performance.

Canonical tags were introduced in 2009 to help webmasters with duplicate or similar content on multiple URLs.

To use canonical tags properly, you must understand their purpose, operation, and implementation.

Canonical URLs and Tags

Canonical tags tell search engines that a certain URL is a page's master copy. They specify a page's canonical URL. Webmasters can avoid duplicate content by linking to the "canonical" or "preferred" version of a page.

How are canonical tags and URLs different? Can these be specified differently?

Tags

Canonical tags are found in an HTML page's head></head> section.

<link rel="canonical" href="https://www.website.com/page/" />

These can be self-referencing or reference another page's URL to consolidate signals.

Canonical tags and URLs are often used interchangeably, which is incorrect.

The rel="canonical" tag is the most common way to set canonical URLs, but it's not the only way.

Canonical URLs

What's a canonical link? Canonical link is the'master' URL for duplicate pages.

In Google's own words:

A canonical URL is the page Google thinks is most representative of duplicate pages on your site.

— Google Search Console Help

You can indicate your preferred canonical URL. For various reasons, Google may choose a different page than you.

When set correctly, the canonical URL is usually your specified URL.

Canonical URLs determine which page will be shown in search results (unless a duplicate is explicitly better for a user, like a mobile version).

Canonical URLs can be on different domains.

Other ways to specify canonical URLs

Canonical tags are the most common way to specify a canonical URL.

You can also set canonicals by:

• Setting the HTTP header rel=canonical.

• All pages listed in a sitemap are suggested as canonicals, but Google decides which pages are duplicates.

• Redirects 301.

Google recommends these methods, but they aren't all appropriate for every situation, as we'll see below. Each has its own recommended uses.

Setting canonical URLs isn't required; if you don't, Google will use other signals to determine the best page version.

To control how your site appears in search engines and to avoid duplicate content issues, you should use canonicalization effectively.

Why Duplicate Content Exists

Before we discuss why you should use canonical URLs and how to specify them in popular CMSs, we must first explain why duplicate content exists. Nobody intentionally duplicates website content.

Content management systems create multiple URLs when you launch a page, have indexable versions of your site, or use dynamic URLs.

Assume the following URLs display the same content to a user:

1. https://www.website.com/category/product-a/

2. https://www.website.com/product-a/

3. https://website.com/product-a/

4. http://www.website.com/product-a/

5. http://website.com/product-a/

6. https://m.website.com/product-a/

7. https://www.website.com/product-a

8. https://www.website.com/product-A/

A search engine sees eight duplicate pages, not one.

• URLs #1 and #2: the CMS saves product URLs with and without the category name.

• #3, #4, and #5 result from the site being accessible via HTTP, HTTPS, www, and non-www.

• #6 is a subdomain mobile-friendly URL.

• URL #7 lacks URL #2's trailing slash.

• URL #8 uses a capital "A" instead of a lowercase one.

Duplicate content may also exist in URLs like:

https://www.website.com
https://www.website.com/index.php

Duplicate content is easy to create.

Canonical URLs help search engines identify different page variations as a single URL on many sites.

SEO Canonical URLs

Canonical URLs help you manage duplicate content that could affect site performance.

Canonical URLs are a technical SEO focus area for many reasons.

Specify URL for search results

When you set a canonical URL, you tell Google which page version to display.

Which would you click?

https://www.domain.com/page-1/

https://www.domain.com/index.php?id=2

First, probably.

Canonicals tell search engines which URL to rank.

Consolidate link signals on similar pages

When you have duplicate or nearly identical pages on your site, the URLs may get external links.

Canonical URLs consolidate multiple pages' link signals into a single URL.

This helps your site rank because signals from multiple URLs are consolidated into one.

Syndication management

Content is often syndicated to reach new audiences.

Canonical URLs consolidate ranking signals to prevent duplicate pages from ranking and ensure the original content ranks.

Avoid Googlebot duplicate page crawling

Canonical URLs ensure that Googlebot crawls your new pages rather than duplicated versions of the same one across mobile and desktop versions, for example.

Crawl budgets aren't an issue for most sites unless they have 100,000+ pages.

How to Correctly Implement the rel=canonical Tag

Using the header tag rel="canonical" is the most common way to specify canonical URLs.

Adding tags and HTML code may seem daunting if you're not a developer, but most CMS platforms allow canonicals out-of-the-box.

These URLs each have one product.

How to Correctly Implement a rel="canonical" HTTP Header

A rel="canonical" HTTP header can replace canonical tags.

This is how to implement a canonical URL for PDFs or non-HTML documents.

You can specify a canonical URL in your site's.htaccess file using the code below.

<Files "file-to-canonicalize.pdf"> Header add Link "< http://www.website.com/canonical-page/>; rel=\"canonical\"" </Files>

301 redirects for canonical URLs

Google says 301 redirects can specify canonical URLs.

Only the canonical URL will exist if you use 301 redirects. This will redirect duplicates.

This is the best way to fix duplicate content across:

• HTTPS and HTTP

• Non-WWW and WWW

• Trailing-Slash and Non-Trailing Slash URLs

On a single page, you should use canonical tags unless you can confidently delete and redirect the page.

Sitemaps' canonical URLs

Google assumes sitemap URLs are canonical, so don't include non-canonical URLs.

This does not guarantee canonical URLs, but is a best practice for sitemaps.

Best-practice Canonical Tag

Once you understand a few simple best practices for canonical tags, spotting and cleaning up duplicate content becomes much easier.

Always include:

One canonical URL per page

If you specify multiple canonical URLs per page, they will likely be ignored.

Correct Domain Protocol

If your site uses HTTPS, use this as the canonical URL. It's easy to reference the wrong protocol, so check for it to catch it early.

Trailing slash or non-trailing slash URLs

Be sure to include trailing slashes in your canonical URL if your site uses them.

Specify URLs other than WWW

Search engines see non-WWW and WWW URLs as duplicate pages, so use the correct one.

Absolute URLs

To ensure proper interpretation, canonical tags should use absolute URLs.

So use:

<link rel="canonical" href="https://www.website.com/page-a/" />

And not:

<link rel="canonical" href="/page-a/" />

If not canonicalizing, use self-referential canonical URLs.

When a page isn't canonicalizing to another URL, use self-referencing canonical URLs.

Canonical tags refer to themselves here.

Common Canonical Tags Mistakes

Here are some common canonical tag mistakes.

301 Canonicalization

Set the canonical URL as the redirect target, not a redirected URL.

Incorrect Domain Canonicalization

If your site uses HTTPS, don't set canonical URLs to HTTP.

Irrelevant Canonicalization

Canonicalize URLs to duplicate or near-identical content only.

SEOs sometimes try to pass link signals via canonical tags from unrelated content to increase rank. This isn't how canonicalization should be used and should be avoided.

Multiple Canonical URLs

Only use one canonical tag or URL per page; otherwise, they may all be ignored.

When overriding defaults in some CMSs, you may accidentally include two canonical tags in your page's <head>.

Pagination vs. Canonicalization

Incorrect pagination can cause duplicate content. Canonicalizing URLs to the first page isn't always the best solution.

Canonicalize to a 'view all' page.

How to Audit Canonical Tags (and Fix Issues)

Audit your site's canonical tags to find canonicalization issues.

SEMrush Site Audit can help. You'll find canonical tag checks in your website's site audit report.

Let's examine these issues and their solutions.

No Canonical Tag on AMP

Site Audit will flag AMP pages without canonical tags.

Canonicalization between AMP and non-AMP pages is important.

Add a rel="canonical" tag to each AMP page's head>.

No HTTPS redirect or canonical from HTTP homepage

Duplicate content issues will be flagged in the Site Audit if your site is accessible via HTTPS and HTTP.

You can fix this by 301 redirecting or adding a canonical tag to HTTP pages that references HTTPS.

Broken canonical links

Broken canonical links won't be considered canonical URLs.

This error could mean your canonical links point to non-existent pages, complicating crawling and indexing.

Update broken canonical links to the correct URLs.

Multiple canonical URLs

This error occurs when a page has multiple canonical URLs.

Remove duplicate tags and leave one.

Canonicalization is a key SEO concept, and using it incorrectly can hurt your site's performance.

Once you understand how it works, what it does, and how to find and fix issues, you can use it effectively to remove duplicate content from your site.

Canonicalization SEO Myths

Prioritize big-ticket purchases

I've made several spending blunders. I get sick thinking about how much money I spent.

My financial mental model was poor back then.

Stoicism and mindfulness keep me from attaching to those feelings. It still hurts.

Until four or five years ago, I bought a new winter jacket every year.

Ten years ago, I spent twice as much. Now that I have a fantastic, warm winter parka, I don't even consider acquiring another one. No more spending. I'm not looking for jackets either.

Saving time and money by spending well is my thinking paradigm.

The philosophy is expressed in most languages. Cheap is expensive in the Netherlands. This applies beyond shopping.

In this essay, I will offer three examples of how this mental paradigm transformed my financial life.

Publishing books

In 2015, I presented and positioned my first book poorly.

I called the book Huge Life Success and made a funny Canva cover in 30 minutes. This:

That looks nothing like my present books. No logo or style. The book felt amateurish.

The book started bothering me a few weeks after publication. The advice was good, but it didn't appear professional. I studied the book business extensively.

I created a style for all my designs. Branding. Win Your Inner Wars was reissued a year later.

Title, cover, and description changed. Rearranging the chapters improved readability.

Seven years later, the book sells hundreds of copies a month. That taught me a lot.

Rushing to finish a project is enticing. Send it and move forward.

Avoid rushing everything. Relax. Develop your projects. Perform well. Perform the job well.

My first novel was underfunded and underworked. A bad book arrived. I then invested time and money in writing the greatest book I could.

That book still sells.

Traveling

I hate travel. Airports, flights, trains, and lines irritate me.

But, I enjoy traveling to beautiful areas.

I do it strangely. I make up travel rules. I never go to airports in summer. I hate being near airports on holidays. Unworthy.

No vacation packages for me. Those airline packages with a flight, shuttle, and hotel. I've had enough.

I try to avoid crowds and popular spots. July Paris? Nuts and bolts, please. Christmas in NYC? No, please keep me sane.

I fly business class behind. I accept upgrades upon check-in. I prefer driving. I drove from the Netherlands to southern Spain.

Thankfully, no lines. What if travel costs more? Thus? I enjoy it from the start. I start traveling then.

I rarely travel since I'm so difficult. One great excursion beats several average ones.

Personal effectiveness

New apps, tools, and strategies intrigue most productivity professionals.

No.

I researched years ago. I spent years investigating productivity in university.

I bought books, courses, applications, and tools. It was expensive and time-consuming.

Im finished. Productivity no longer costs me time or money. OK. I worked on it once and now follow my strategy.

I avoid new programs and systems. My stuff works. Why change winners?

Spending wisely saves time and money.

Spending wisely means spending once. Many people ignore productivity. It's understudied. No classes.

Some assume reading a few articles or a book is enough. Productivity is personal. You need a personal system.

Time invested is one-time. You can trust your system for life once you find it.

Concentrate on the expensive choices.

Life's short. Saving money quickly is enticing.

Spend less on groceries today. True. That won't fix your finances.

Adopt a lifestyle that makes you affluent over time. Consider major choices.

Are they causing long-term poverty? Are you richer?

Leasing cars comes to mind. The automobile costs a fortune today. The premium could accomplish a million nice things.

Focusing on important decisions makes life easier. Consider your future. You want to improve next year.