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

How I monetized and sold an abandoned side project for $20,000

The Origin Story

I've always wanted to be an entrepreneur but never succeeded. I often had business ideas, made a landing page, and told my buddies. Never got customers.

In April 2021, I decided to try again with a new strategy. I noticed that I had trouble acquiring an initial set of customers, so I wanted to start by acquiring a product that had a small user base that I could grow.

I found a SaaS marketplace called MicroAcquire.com where you could buy and sell SaaS products. I liked Shareit.video, an online Loom-like screen recorder.

Shareit.video didn't generate revenue, but 50 people visited daily to record screencasts.

Purchasing a Failed Side Project

I eventually bought Shareit.video for $12,000 from its owner.

$12,000 was probably too much for a website without revenue or registered users.

I thought time was most important. I could have recreated the website, but it would take months. $12,000 would give me an organized code base and a working product with a few users to monetize.

I considered buying a screen recording website and trying to grow it versus buying a new car or investing in crypto with the $12K.

Buying the website would make me a real entrepreneur, which I wanted more than anything.

Putting down so much money would force me to commit to the project and prevent me from quitting too soon.

A Year of Development

I rebranded the website to be called RecordJoy and worked on it with my cousin for about a year. Within a year, we made $5000 and had 3000 users.

We spent $3500 on ads, hosting, and software to run the business.

AppSumo promoted our $120 Life Time Deal in exchange for 30% of the revenue.

We put RecordJoy on maintenance mode after 6 months because we couldn't find a scalable user acquisition channel.

We improved SEO and redesigned our landing page, but nothing worked.

Despite not being able to grow RecordJoy any further, I had already learned so much from working on the project so I was fine with putting it on maintenance mode. RecordJoy still made $500 a month, which was great lunch money.

Getting Taken Over

One of our customers emailed me asking for some feature requests and I replied that we weren’t going to add any more features in the near future. They asked if we'd sell.

We got on a call with the customer and I asked if he would be interested in buying RecordJoy for 15k. The customer wanted around $8k but would consider it.

Since we were negotiating with one buyer, we put RecordJoy on MicroAcquire to see if there were other offers.

We quickly received 10+ offers. We got 18.5k. There was also about $1000 in AppSumo that we could not withdraw, so we agreed to transfer that over for $600 since about 40% of our sales on AppSumo usually end up being refunded.

Lessons Learned

First, create an acquisition channel

We couldn't discover a scalable acquisition route for RecordJoy. If I had to start another project, I'd develop a robust acquisition channel first. It might be LinkedIn, Medium, or YouTube.

Purchase Power of the Buyer Affects Acquisition Price

Some of the buyers we spoke to were individuals looking to buy side projects, as well as companies looking to launch a new product category. Individual buyers had less budgets than organizations.

Customers of AppSumo vary.

AppSumo customers value lifetime deals and low prices, which may not be a good way to build a business with recurring revenue. Designed for AppSumo users, your product may not connect with other users.

Try to increase acquisition trust

Acquisition often fails. The buyer can go cold feet, cease communicating, or run away with your stuff. Trusting the buyer ensures a smooth asset exchange. First acquisition meeting was unpleasant and price negotiation was tight. In later meetings, we spent the first few minutes trying to get to know the buyer’s motivations and background before jumping into the negotiation, which helped build trust.

Operating expenses can reduce your earnings.

Monitor operating costs. We were really happy when we withdrew the $5000 we made from AppSumo and Stripe until we realized that we had spent $3500 in operating fees. Spend money on software and consultants to help you understand what to build.

Don't overspend on advertising

We invested $1500 on Google Ads but made little money. For a side project, it’s better to focus on organic traffic from SEO rather than paid ads unless you know your ads are going to have a positive ROI.

One-hour ebook sales, affiliate relationships, and more.

If you follow me, you may know I started a new ebook in August 2022.

Despite publishing on this platform, my website, and Quora, I'm not a writer.

My writing speed is slow, 2,000 words a day, and I struggle to communicate cohesively.

In April 2022, I wrote a successful guide on How to Write Google-Friendly Blog Posts.

I had no email list or social media presence. I've made $1,600+ selling ebooks.

Evidence:

My first digital offering isn't a book.

It's an actionable guide with my tried-and-true process for writing Google-friendly content.

I'm not bragging.

Established authors like Tim Denning make more from my ebook sales with one newsletter.

This experience taught me writing isn't a privilege.

Writing a book and making money online doesn't require expertise.

Many don't consult experts. They want someone approachable.

Two years passed before I realized my own limits.

I have a brain, two hands, and Internet to spread my message.

I wrote and published a second ebook after the first's success.

On Gumroad, I released my second digital product.

Here's my complete Gumroad evaluation.

Gumroad is a marketplace for content providers to develop and sell sales pages.

Gumroad handles payments and client requests. It's helpful when someone sends a bogus payment receipt requesting an ebook (actual story!).

You'll forget administrative concerns after your first ebook sale.

After my first ebook sale, I did this: I made additional cash!

After every sale, I tell myself, "I built a new semi-passive revenue source."

This thinking shift helps me become less busy while increasing my income and quality of life.

Besides helping others, folks sell evergreen digital things to earn passive money.

It's in my second ebook.

I explain how I built and sold 50+ copies of my SEO writing ebook without being an influencer.

I show how anyone can sell ebooks on Gumroad and automate their sales process.

This is my ebook.

After publicizing the ebook release, I sold three copies within an hour.

Wow, or meh?

I don’t know.

The answer is different for everyone.

These three sales came from a small email list of 40 motivated fans waiting for my ebook release.

I had bigger plans.

I'll market my ebook on Medium, my website, Quora, and email.

I'm testing affiliate partnerships this time.

One of my ebook buyers is now promoting it for 40% commission.

Become my affiliate if you think your readers would like my ebook.

My ebook is a few days old, but I'm interested to see where it goes.

My SEO writing book started without an email list, affiliates, or 4,000 website visitors. I've made four figures.

I'm slowly expanding my communication avenues to have more impact.

Even a small project can open doors you never knew existed.

So began my writing career.

In summary

If you dare, every concept can become a profitable trip.

Before, I couldn't conceive of creating an ebook.

How to Sell eBooks on Gumroad is my second digital product.

Marketing and writing taught me that anything can be sold online.

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.