Learn these subtle cues to gain influence.

Hate being ignored?

As a 24-year-old, I struggled at work. Attention-getting tips How to avoid being judged by my size, gender, and lack of wrinkles or gray hair?

I've learned seniority hacks. Influence. Within two years as a product manager, I led a team. I'm a Stanford MBA student.

These communication hacks can make you look senior and influential.

1. Slowly speak

We speak quickly because we're afraid of being interrupted.

When I doubt my ideas, I speak quickly. How can we slow down? Jamie Chapman says speaking slowly saps our energy.

Chapman suggests emphasizing certain words and pausing.

2. Interrupted? Stop the stopper

Someone interrupt your speech?

Don't wait. "May I finish?" No pause needed. Stop interrupting. I first tried this in Leadership Laboratory at Stanford. How quickly I gained influence amazed me.

Next time, try “May I finish?” If that’s not enough, try these other tips from Wendy R.S. O’Connor.

3. Context

Others don't always see what's obvious to you.

Through explanation, you help others see the big picture. If a senior knows it, you help them see where your work fits.

4. Don't ask questions in statements

“Your statement lost its effect when you ended it on a high pitch,” a group member told me. Upspeak, it’s called. I do it when I feel uncertain.

Upspeak loses influence and credibility. Unneeded. When unsure, we can say "I think." We can even ask a proper question.

Someone else's boasting is no reason to be dismissive. As leaders and colleagues, we should listen to our colleagues even if they use this speech pattern.

Give your words impact.

5. Signpost structure

Signposts improve clarity by providing structure and transitions.

Communication coach Alexander Lyon explains how to use "first," "second," and "third" He explains classic and summary transitions to help the listener switch topics.

Signs clarify. Clarity matters.

6. Eliminate email fluff

“Fine. When will the report be ready? — Jeff.”

Notice how senior leaders write short, direct emails? I often use formalities like "dear," "hope you're well," and "kind regards"

Formality is (usually) unnecessary.

7. Replace exclamation marks with periods

See how junior an exclamation-filled email looks:

Hi, all!
Hope you’re as excited as I am for tomorrow! We’re celebrating our accomplishments with cake! Join us tomorrow at 2 pm!
See you soon!

Why the exclamation points? Why not just one?

Hi, all.
Hope you’re as excited as I am for tomorrow. We’re celebrating our accomplishments with cake. Join us tomorrow at 2 pm!
See you soon.

8. Take space

"Playing high" means having an open, relaxed body, says Stanford professor and author Deborah Gruenfield.

Crossed legs or looking small? Relax. Get bigger.

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

A must-read for everyone

Jobs is well-known. You probably know the tall, thin guy who wore the same clothing every day. His influence is unavoidable. In fewer than 40 years, Jobs' innovations have impacted computers, movies, cellphones, music, and communication.

Steve Jobs may be more imaginative than the typical person, but if we can use some of his ingenuity, ambition, and good traits, we'll be successful. This essay explains how to follow his guidance and success secrets.

1. Repetition is necessary for success.

Be patient and diligent to master something. Practice makes perfect. This is why older workers are often more skilled.

When should you repeat a task? When you're confident and excited to share your product. It's when to stop tweaking and repeating.

Jobs stated he'd make the crowd sh** their pants with an iChat demo.

Use this in your daily life.

• Start with the end in mind. You can put it in writing and be as detailed as you like with your plan's schedule and metrics. For instance, you have a goal of selling three coffee makers in a week.

• Break it down, break the goal down into particular tasks you must complete, and then repeat those tasks. To sell your coffee maker, you might need to make 50 phone calls.

• Be mindful of the amount of work necessary to produce the desired results. Continue doing this until you are happy with your product.

2. Acquire the ability to add and subtract.

How did Picasso invent cubism? Pablo Picasso was influenced by stylised, non-naturalistic African masks that depict a human figure.

Artists create. Constantly seeking inspiration. They think creatively about random objects. Jobs said creativity is linking things. Creative people feel terrible when asked how they achieved something unique because they didn't do it all. They saw innovation. They had mastered connecting and synthesizing experiences.

Use this in your daily life.

• On your phone, there is a note-taking app. Ideas for what you desire to learn should be written down. It may be learning a new language, calligraphy, or anything else that inspires or intrigues you.

• Note any ideas you have, quotations, or any information that strikes you as important.

• Spend time with smart individuals, that is the most important thing. Jim Rohn, a well-known motivational speaker, has observed that we are the average of the five people with whom we spend the most time.

• Learning alone won't get you very far. You need to put what you've learnt into practice. If you don't use your knowledge and skills, they are useless.

3. Develop the ability to refuse.

Steve Jobs deleted thousands of items when he created Apple's design ethic. Saying no to distractions meant upsetting customers and partners.

John Sculley, the former CEO of Apple, said something like this. According to Sculley, Steve’s methodology differs from others as he always believed that the most critical decisions are things you choose not to do.

Use this in your daily life.

• Never be afraid to say "no," "I won't," or "I don't want to." Keep it simple. This method works well in some situations.

• Give a different option. For instance, X might be interested even if I won't be able to achieve it.

• Control your top priority. Before saying yes to anything, make sure your work schedule and priority list are up to date.

4. Follow your passion

“Follow your passion” is the worst advice people can give you. Steve Jobs didn't start Apple because he suddenly loved computers. He wanted to help others attain their maximum potential.

Great things take a lot of work, so quitting makes sense if you're not passionate. Jobs learned from history that successful people were passionate about their work and persisted through challenges.

Use this in your daily life.

• Stay away from your passion. Allow it to develop daily. Keep working at your 9-5-hour job while carefully gauging your level of desire and endurance. Less risk exists.

• The truth is that if you decide to work on a project by yourself rather than in a group, it will take you years to complete it instead of a week. Instead, network with others who have interests in common.

• Prepare a fallback strategy in case things go wrong.

Success, this small two-syllable word eventually gives your life meaning, a perspective. What is success?  For most, it's achieving their ambitions. However, there's a catch. Successful people aren't always happy.

Furthermore, where do people’s goals and achievements end? It’s a never-ending process. Success is a journey, not a destination. We wish you not to lose your way on this journey.

Technical books aren't like novels. We need a new approach to technical texts. I've spent years looking for a decent reading method. I tried numerous ways before finding one that worked. This post explains how I read technical books efficiently.

What Do I Mean When I Say Effective?

Effectiveness depends on the book. Effective implies I know where to find answers after reading a reference book. Effective implies I learned the book's knowledge after reading it.

I use reference books as tools in my toolkit. I won't carry all my tools; I'll merely need them. Non-reference books teach me techniques. I never have to make an effort to use them since I always have them.

Reference books I like:

• Design Patterns: Elements of Reusable Object-Oriented Software

• Refactoring: Improving the Design of Existing Code 
  You can also check My Top Takeaways from Refactoring here.

• Practical Object-Oriented Design in Ruby: An Agile Primer

Non-reference books I like:

• The Pragmatic Programmer: your journey to mastery

• Clean Code: A Handbook of Agile Software Craftsmans

The Approach

Technical books might be overwhelming to read in one sitting. Especially when you have no idea what is coming next as you read. When you don't know how deep the rabbit hole goes, you feel lost as you read. This is my years-long method for overcoming this difficulty.

Whether you follow the step-by-step guide or not, remember these:

• Understand the terminology. Make sure you get the meaning of any terms you come across more than once. The likelihood that a term will be significant increases as you encounter it more frequently.

• Know when to stop. I've always believed that in order to truly comprehend something, I must delve as deeply as possible into it. That, however, is not usually very effective. There are moments when you have to draw the line and start putting theory into practice (if applicable).

• Look over your notes. When reading technical books or documents, taking notes is a crucial habit to develop. Additionally, you must regularly examine your notes if you want to get the most out of them. This will assist you in internalizing the lessons you acquired from the book. And you'll see that the urge to review reduces with time.

Let's talk about how I read a technical book step by step.

0. Read the Foreword/Preface

These sections are crucial in technical books. They answer Who should read it, What each chapter discusses, and sometimes How to Read? This is helpful before reading the book. Who could know the ideal way to read the book better than the author, right?

1. Scanning

I scan the chapter. Fast scanning is needed.

• I review the headings.

• I scan the pictures quickly.

• I assess the chapter's length to determine whether I might divide it into more manageable sections.

2. Skimming

Skimming is faster than reading but slower than scanning.

• I focus more on the captions and subtitles for the photographs.

• I read each paragraph's opening and closing sentences.

• I examined the code samples.

• I attempt to grasp each section's basic points without getting bogged down in the specifics.

• Throughout the entire reading period, I make an effort to make mental notes of what may require additional attention and what may not. Because I don't want to spend time taking physical notes, kindly notice that I am using the term "mental" here. It is much simpler to recall. You may think that this is more significant than typing or writing “Pay attention to X.”

• I move on quickly. This is something I considered crucial because, when trying to skim, it is simple to start reading the entire thing.

3. Complete reading

Previous steps pay off.

• I finished reading the chapter.

• I concentrate on the passages that I mentally underlined when skimming.

• I put the book away and make my own notes. It is typically more difficult than it seems for me. But it's important to speak in your own words. You must choose the right words to adequately summarize what you have read. How do those words make you feel? Additionally, you must be able to summarize your notes while you are taking them. Sometimes as I'm writing my notes, I realize I have no words to convey what I'm thinking or, even worse, I start to doubt what I'm writing down. This is a good indication that I haven't internalized that idea thoroughly enough.

• I jot my inquiries down. Normally, I read on while compiling my questions in the hopes that I will learn the answers as I read. I'll explore those issues more if I wasn't able to find the answers to my inquiries while reading the book.

Bonus!

Best part: If you take lovely notes like I do, you can publish them as a blog post with a few tweaks.

Conclusion

This is my learning journey. I wanted to show you. This post may help someone with a similar learning style. You can alter the principles above for any technical material.

After viewing its insanity, I had to leave this platform.

I joined LinkedIn recently. That's how I aim to increase my readership and gain recognition. LinkedIn's premise appealed to me: a Facebook-like platform for professional networking.

I don't use Facebook since it's full of propaganda. It seems like a professional, apolitical space, right?

I expected people to:

• be more formal and respectful than on Facebook.

• Talk about the inclusiveness of the workplace. Studies consistently demonstrate that inclusive, progressive workplaces outperform those that adhere to established practices.

• Talk about business in their industry. Yep. I wanted to read articles with advice on how to write better and reach a wider audience.

Oh, sh*t. I hadn't anticipated that.

After posting and reading about inclusivity and pro-choice, I was startled by how many professionals acted unprofessionally. I've seen:

• Men have approached me in the DMs in a really aggressive manner. Yikes. huge yikes Not at all professional.

• I've heard pro-choice women referred to as infant killers by many people. If I were the CEO of a company and I witnessed one of my employees acting that poorly, I would immediately fire them.

• Many posts are anti-LGBTQIA+, as I've noticed. a lot, like, a lot. Some are subtly stating that the world doesn't need to know, while others are openly making fun of transgender persons like myself.

• Several medical professionals were posting explicitly racist comments. Even if you are as white as a sheet like me, you should be alarmed by this. Who's to guarantee a patient who is black won't unintentionally die?

• I won't even get into how many men in STEM I observed pushing for the exclusion of women from their fields. I shouldn't be surprised considering the majority of those men I've encountered have a passionate dislike for women, but goddamn, dude.

Many people appear entirely too at ease displaying their bigotry on their professional profiles.

As a white female, I'm always shocked by people's open hostility. Professional environments are very important.

I don't know if this is still true (people seem too politicized to care), but if I heard many of these statements in person, I'd suppose they feel ashamed. Really.

Are you not ashamed of being so mean? Are you so weak that competing with others terrifies you? Isn't this embarrassing?

LinkedIn isn't great at censoring offensive comments. These people aren't getting warnings. So they were safe while others were unsafe.

The CEO in me would want to know if I had placed a bigot on my staff.

I always wondered if people's employers knew about their online behavior. If they know how horrible they appear, they don't care.

As a manager, I was picky about hiring. Obviously. In most industries, it costs $1,000 or more to hire a full-time employee, so be sure it pays off.

Companies that embrace diversity and tolerance (and are intolerant of intolerance) are more profitable, likely to recruit top personnel, and successful.

People avoid businesses that alienate them. That's why I don't eat at Chic-Fil-A and why folks avoid MyPillow. Being inclusive is good business.

CEOs are harmed by online bigots. Image is an issue. If you're a business owner, you can fire staff who don't help you.

On the one hand, I'm delighted it makes it simpler to identify those with whom not to do business.

Don’t get me wrong. I'm glad I know who to avoid when hiring, getting references, or searching for a job. When people are bad, it saves me time.

What's up with professionalism?

Really. I need to know. I've crossed the boundary between acceptable and unacceptable behavior, but never on a professional platform. I got in trouble for not wearing bras even though it's not part of my gender expression.

If I behaved like that at my last two office jobs, my supervisors would have fired me immediately. Some of the behavior I've seen is so outrageous, I can't believe these people have employment. Some are even leaders.

Like…how? Is hatred now normalized?

Please pay attention whether you're seeking for a job or even simply a side gig.

Do not add to the tragedy that LinkedIn comments can be, or at least don't make uninformed comments. Even if you weren't banned, the site may still bite you.

Recruiters can and do look at your activity. Your writing goes on your résumé. The wrong comment might lose you a job.

Recruiters and CEOs might reject candidates whose principles contradict with their corporate culture. Bigotry will get you banned from many companies, especially if others report you.

If you want a high-paying job, avoid being a LinkedIn asshole. People care even if you think no one does. Before speaking, ponder. Is this how you want to be perceived?

Better advice:

If your politics might turn off an employer, stop posting about them online and ask yourself why you hold such objectionable ideas.

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