In 8 months, I doubled my audience with them.

LinkedIn's buzz isn't over.

People dream of social proof every day. They want clients, interesting jobs, and field recognition.

LinkedIn coaches will benefit greatly. Sell learning? Probably. Can you use it?

Consistency has been key in my eight-month study of LinkedIn. However, I'll share seven of my tips. 700 to 4500 people followed me.

1. Communication, communication, communication

LinkedIn is a social network. I like to think of it as a cafe. Here, you can share your thoughts, meet friends, and discuss life and work.

Do not treat LinkedIn as if it were a board for your post-its.

More socializing improves relationships. It's about people, like any network.

Consider interactions. Three main areas:

• Respond to criticism left on your posts.

• Comment on other people's posts

• Start and maintain conversations through direct messages.

Engage people. You spend too much time on Facebook if you only read your wall. Keeping in touch and having meaningful conversations helps build your network.

Every day, start a new conversation to make new friends.

2. Stick with those you admire

Interact thoughtfully.

Choose your contacts. Build your tribe is a term. Respectful networking.

I only had past colleagues, family, and friends in my network at the start of this year. Not business-friendly. Since then, I've sought out people I admire or can learn from.

Finding a few will help you. As they connect you to their networks. Friendships can lead to clients.

Don't underestimate network power. Cafe-style. Meet people at each table. But avoid people who sell SEO, web redesign, VAs, mysterious job opportunities, etc.

3. Share eye-catching infographics

Daily infographics flood LinkedIn. Visuals are popular. Use Canva's free templates if you can't draw them.

Last week's:

It's a fun way to visualize your topic.

You can repost and comment on infographics. Involve your network. I prefer making my own because I build my brand around certain designs.

My friend posted infographics consistently for four months and grew his network to 30,000.

If you start, credit the authors. As you steal someone's work.

4. Invite some friends over.

LinkedIn alone can be lonely. Having a few friends who support your work daily will boost your growth.

I was lucky to be invited to a group of networkers. We share knowledge and advice.

Having a few regulars who can discuss your posts is helpful. It's artificial, but it works and engages others.

Consider who you'd support if they were in your shoes.

You can pay for an engagement group, but you risk supporting unrelated people with rubbish posts.

Help each other out.

5. Don't let your feed or algorithm divert you.

LinkedIn's algorithm is magical.

Which time is best? How fast do you need to comment? Which days are best?

Overemphasize algorithms. Consider the user. No need to worry about the best time.

Remember to spend time on LinkedIn actively. Not passively. That is what Facebook is for.

Surely someone would find a LinkedIn recipe. Don't beat the algorithm yet. Consider your audience.

6. The more personal, the better

Personalization isn't limited to selfies. Share your successes and failures.

The more personality you show, the better.

People relate to others, not theories or quotes. Why should they follow you? Everyone posts the same content?

Consider your friends. What's their appeal?

Because they show their work and identity. It's simple. Medium and Linkedin are your platforms. Find out what works.

You can copy others' hooks and structures. You decide how simple to make it, though.

7. Have fun with those who have various post structures.

I like writing, infographics, videos, and carousels. Because you can:

Repurpose your content!

Out of one blog post I make:

• Newsletter

• Infographics (positive and negative points of view)

• Carousel

• Personal stories

• Listicle

Create less but more variety. Since LinkedIn posts last 24 hours, you can rotate the same topics for weeks without anyone noticing.

Effective!

The final LI snippet to think about

LinkedIn is about consistency. Some say 15 minutes. If you're serious about networking, spend more time there.

The good news is that it is worth it. The bad news is that it takes time.

Move people with tiny words.

Apple fanboy here.

• Macs are awesome.

• Their iPhones rock.

• $19 cloths are great.

• $999 stands are amazing.

I love Apple's microcopy even more.

It's like the marketing goddess bit into the Apple logo and blessed the world with microcopy.

I took on a 30-day micro-stalking mission.

Every time I caught myself wasting time on YouTube, I had to visit Apple’s website to learn the secrets of the marketing goddess herself.

We've learned. Golden apples are calling.

Cut the friction

Benefit-first, not commitment-first.

Brands lose customers through friction.

Most brands don't think like customers.

• Brands want sales.

• Brands want newsletter signups.

Here's their microcopy:

• “Buy it now.”

• “Sign up for our newsletter.”

Both are difficult. They ask for big commitments.

People are simple creatures. Want pleasure without commitment.

Apple nails this.

So, instead of highlighting the commitment, they highlight the benefit of the commitment.

Saving on the latest iPhone sounds easier than buying it. Everyone saves, but not everyone buys.

A subtle change in framing reduces friction.

Apple eliminates customer objections to reduce friction.

Less customer friction means simpler processes.

Apple's copy expertly reassures customers about shipping fees and not being home. Apple assures customers that returning faulty products is easy.

Apple knows that talking to a real person is the best way to reduce friction and improve their copy.

Always rhyme

Learn about fine rhyme.

Poets make things beautiful with rhyme.

Copywriters use rhyme to stand out.

Apple’s copywriters have mastered the art of corporate rhyme.

Two techniques are used.

1. Perfect rhyme

Here, rhymes are identical.

2. Imperfect rhyme

Here, rhyming sounds vary.

Apple prioritizes meaning over rhyme.

Apple never forces rhymes that don't fit.

It fits so well that the copy seems accidental.

Add alliteration

Alliteration always entertains.

Alliteration repeats initial sounds in nearby words.

Apple's copy uses alliteration like no other brand I've seen to create a rhyming effect or make the text more fun to read.

For example, in the sentence "Sam saw seven swans swimming," the initial "s" sound is repeated five times. This creates a pleasing rhythm.

Microcopy overuse is like pouring ketchup on a Michelin-star meal.

Alliteration creates a memorable phrase in copywriting. It's subtler than rhyme, and most people wouldn't notice; it simply resonates.

I love how Apple uses alliteration and contrast between "wonders" and "ease".

Assonance, or repeating vowels, isn't Apple's thing.

You ≠ Hero, Customer = Hero

Your brand shouldn't be the hero.

Because they'll be using your product or service, your customer should be the hero of your copywriting. With your help, they should feel like they can achieve their goals.

I love how Apple emphasizes what you can do with the machine in this microcopy.

It's divine how they position their tools as sidekicks to help below.

This one takes the cake:

Dialogue-style writing

Conversational copy engages.

Excellent copy Like sharing gum with a friend.

This helps build audience trust.

Apple does this by using natural connecting words like "so" and phrases like "But that's not all."

Snowclone-proof

The mother of all microcopy techniques.

A snowclone uses an existing phrase or sentence to create a new one. The new phrase or sentence uses the same structure but different words.

It’s usually a well know saying like:

To be or not to be.

This becomes a formula:

To _ or not to _.

Copywriters fill in the blanks with cause-related words. Example:

To click or not to click.

Apple turns "survival of the fittest" into "arrival of the fittest."

It's unexpected and surprises the reader.

So this was fun.

But my fun has just begun.

Microcopy is 21st-century poetry.

I came as an Apple fanboy.

I leave as an Apple fanatic.

Now I’m off to find an apple tree.

Cause you know how it goes.

(Apples, trees, etc.)

This post is a summary. Original post available here.

Unleash the power of persuasion and captivate your audience with compelling headlines.

As the old adage goes, "You never get a second chance to make a first impression."

In the world of content creation and social ads, headlines and titles play a critical role in making that first impression.

A well-crafted headline can make the difference between an article being read or ignored, a video being clicked on or bypassed, or a product being purchased or passed over.

To make an impact with your headlines, mastering the art of rhetoric is essential. In this post, we'll explore various rhetorical devices and techniques that can help you create headlines that captivate your audience and drive engagement.

tl;dr : Headline Magician will help you craft the ultimate headline titles powered by rhetoric devices

Example with a high-end luxury organic zero-waste skincare brand

✍️ The Power of Alliteration

Alliteration is the repetition of the same consonant sound at the beginning of words in close proximity. This rhetorical device lends itself well to headlines, as it creates a memorable, rhythmic quality that can catch a reader's attention.

By using alliteration, you can make your headlines more engaging and easier to remember.

Examples:

"Crafting Compelling Content: A Comprehensive Course"

"Mastering the Art of Memorable Marketing"

🔁 The Appeal of Anaphora

Anaphora is the repetition of a word or phrase at the beginning of successive clauses. This rhetorical device emphasizes a particular idea or theme, making it more memorable and persuasive.

In headlines, anaphora can be used to create a sense of unity and coherence, which can draw readers in and pique their interest.

Examples:

"Create, Curate, Captivate: Your Guide to Social Media Success"

"Innovation, Inspiration, and Insight: The Future of AI"

🔄 The Intrigue of Inversion

Inversion is a rhetorical device where the normal order of words is reversed, often to create an emphasis or achieve a specific effect.

In headlines, inversion can generate curiosity and surprise, compelling readers to explore further.

Examples:

"Beneath the Surface: A Deep Dive into Ocean Conservation"

"Beyond the Stars: The Quest for Extraterrestrial Life"

⚖️ The Persuasive Power of Parallelism

Parallelism is a rhetorical device that involves using similar grammatical structures or patterns to create a sense of balance and symmetry.

In headlines, parallelism can make your message more memorable and impactful, as it creates a pleasing rhythm and flow that can resonate with readers.

Examples:

"Eat Well, Live Well, Be Well: The Ultimate Guide to Wellness"

"Learn, Lead, and Launch: A Blueprint for Entrepreneurial Success"

⏭️ The Emphasis of Ellipsis

Ellipsis is the omission of words, typically indicated by three periods (...), which suggests that there is more to the story.

In headlines, ellipses can create a sense of mystery and intrigue, enticing readers to click and discover what lies behind the headline.

Examples:

"The Secret to Success... Revealed"

"Unlocking the Power of Your Mind... A Step-by-Step Guide"

🎭 The Drama of Hyperbole

Hyperbole is a rhetorical device that involves exaggeration for emphasis or effect.

In headlines, hyperbole can grab the reader's attention by making bold, provocative claims that stand out from the competition. Be cautious with hyperbole, however, as overuse or excessive exaggeration can damage your credibility.

Examples:

"The Ultimate Guide to Mastering Any Skill in Record Time"

"Discover the Revolutionary Technique That Will Transform Your Life"

❓The Curiosity of Questions

Posing questions in your headlines can be an effective way to pique the reader's curiosity and encourage engagement.

Questions compel the reader to seek answers, making them more likely to click on your content. Additionally, questions can create a sense of connection between the content creator and the audience, fostering a sense of dialogue and discussion.

Examples:

"Are You Making These Common Mistakes in Your Marketing Strategy?"

"What's the Secret to Unlocking Your Creative Potential?"

💥 The Impact of Imperatives

Imperatives are commands or instructions that urge the reader to take action. By using imperatives in your headlines, you can create a sense of urgency and importance, making your content more compelling and actionable.

Examples:

"Master Your Time Management Skills Today"

"Transform Your Business with These Innovative Strategies"

💢 The Emotion of Exclamations

Exclamations are powerful rhetorical devices that can evoke strong emotions and convey a sense of excitement or urgency.

Including exclamations in your headlines can make them more attention-grabbing and shareable, increasing the chances of your content being read and circulated.

Examples:

"Unlock Your True Potential: Find Your Passion and Thrive!"

"Experience the Adventure of a Lifetime: Travel the World on a Budget!"

🎀 The Effectiveness of Euphemisms

Euphemisms are polite or indirect expressions used in place of harsher, more direct language.

In headlines, euphemisms can make your message more appealing and relatable, helping to soften potentially controversial or sensitive topics.

Examples:

"Navigating the Challenges of Modern Parenting"

"Redefining Success in a Fast-Paced World"

⚡Antithesis: The Power of Opposites

Antithesis involves placing two opposite words side-by-side, emphasizing their contrasts. This device can create a sense of tension and intrigue in headlines.

Examples:

"Once a day. Every day"

"Soft on skin. Kill germs"

"Mega power. Mini size."

To utilize antithesis, identify two opposing concepts related to your content and present them in a balanced manner.

🎨 Scesis Onomaton: The Art of Verbless Copy

Scesis onomaton is a rhetorical device that involves writing verbless copy, which quickens the pace and adds emphasis.

Example:

"7 days. 7 dollars. Full access."

To use scesis onomaton, remove verbs and focus on the essential elements of your headline.

🌟 Polyptoton: The Charm of Shared Roots

Polyptoton is the repeated use of words that share the same root, bewitching words into memorable phrases.

Examples:

"Real bread isn't made in factories. It's baked in bakeries"

"Lose your knack for losing things."

To employ polyptoton, identify words with shared roots that are relevant to your content.

✨ Asyndeton: The Elegance of Omission

Asyndeton involves the intentional omission of conjunctions, adding crispness, conviction, and elegance to your headlines.

Examples:

"You, Me, Sushi?"

"All the latte art, none of the environmental impact."

To use asyndeton, eliminate conjunctions and focus on the core message of your headline.

🔮 Tricolon: The Magic of Threes

Tricolon is a rhetorical device that uses the power of three, creating memorable and impactful headlines.

Examples:

"Show it, say it, send it"

"Eat Well, Live Well, Be Well."

To use tricolon, craft a headline with three key elements that emphasize your content's main message.

🔔 Epistrophe: The Chime of Repetition

Epistrophe involves the repetition of words or phrases at the end of successive clauses, adding a chime to your headlines.

Examples:

"Catch it. Bin it. Kill it."

"Joint friendly. Climate friendly. Family friendly."

To employ epistrophe, repeat a key phrase or word at the end of each clause.

If you waste time every day, even though you're ambitious, you're not alone.

Many of us could use some new time-management strategies, like these:

Focus on the following three.

You're thinking about everything at once.

You're overpowered.

It's mental. We just have what's in front of us. So savor the moment's beauty.

Prioritize 1-3 things.

To be one of the most productive people you and I know, follow these steps.

Get along with boredom.

Many of us grow bored, sweat, and turn on Netflix.

We shout, "I'm rarely bored!" Look at me! I'm happy.

Shut it, Sally.

You're not making wonderful things for the world. Boredom matters.

If you can sit with it for a second, you'll get insight. Boredom? Breathe.

Go blank.

Then watch your creativity grow.

Check your MacroVision once more.

We don't know what to do with our time, which contributes to time-wasting.

Nobody does, either. Jeff Bezos won't hand-deliver that crap to you.

Daily vision checks are required.

Also:

What are 5 things you'd love to create in the next 5 years?

You're soul-searching. It's food.

Return here regularly, and you'll adore the high you get from doing valuable work.

Improve your thinking.

What's Alex's latest nonsense?

I'm talking about overcoming our own thoughts. Worrying wastes so much time.

Too many of us are assaulted by lies, myths, and insecurity.

Stop letting your worries massage you into a worried coma like a Thai woman.

Optimizing your thoughts requires accepting what you can't control.

It means letting go of unhelpful thoughts and returning to the moment.

Keep your blood sugar level.

I gave up gluten, donuts, and sweets.

This has really boosted my energy.

Blood-sugar-spiking carbs make us irritable and tired.

These day-to-day ups and downs aren't productive. It's crucial.

Know how your diet affects insulin levels. Now I have more energy and can do more without clenching my teeth.

Reduce harmful carbs to boost energy.

Create a focused setting for yourself.

When we optimize the mind, we have more energy and use our time better because we're not tense.

Changing our environment can also help us focus. Disabling alerts is one example.

Too hot makes me procrastinate and irritable.

List five items that hinder your productivity.

You may be amazed at how much you may improve by removing distractions.

Be responsible.

Accountability is a time-saver.

Creating an emotional pull to finish things.

Writing down our goals makes us accountable.

We can engage a coach or work with an accountability partner to feel horrible if we don't show up and finish on time.

‘Hey Jake, I’m going to write 1000 words every day for 30 days — you need to make sure I do.’ ‘Sure thing, Nathan, I’ll be making sure you check in daily with me.’

Tick.

You might also blog about your ambitions to show your dedication.

Now you can't hide when you promised to appear.

Acquire a liking for bravery.

Boldness changes everything.

I sometimes feel lazy and wonder why. If my food and sleep are in order, I should assess my footing.

Most of us live backward. Doubtful. Uncertain. Feelings govern us.

Backfooting isn't living. It's lame, and you'll soon melt. Live boldly now.

Be assertive.

Get disgustingly into everything. Expand.

Even if it's hard, stop being a b*tch.

Those that make Mr. Bold Bear their spirit animal benefit. Save time to maximize your effect.

There’s a funny part of ‘Steve Jobs’ by Walter Isaacson where Jobs says that Bill Gates was more a copier than an innovator:

“Bill is basically unimaginative and has never invented anything, which is why I think he’s more comfortable now in philanthropy than technology. He just shamelessly ripped off other people’s ideas….He’d be a broader guy if he had dropped acid once or gone off to an ashram when he was younger.”

Gates lacked flavor. Nobody ever got excited about a Microsoft launch, despite their good products. Jobs had the world's best product taste. Apple vs. Microsoft.

A CEO's core job functions are all driven by taste: recruiting, vision, and company culture all require good taste. Depending on the type of company you want to build, know where you stand between Microsoft and Apple.

How can you improve your product judgment? How to acquire taste?

Test and refine

Product development follows two parallel paths: the ‘customer obsession’ path and the ‘taste and iterate’ path.

The customer obsession path involves solving customer problems. Lean Startup frameworks show you what to build at each step.

Taste-and-iterate doesn't involve the customer. You iterate internally and rely on product leaders' taste and judgment.

Creative Selection by Ken Kocienda explains this method. In Creative Selection, demos are iterated and presented to product leaders. Your boss presents to their boss, and so on up to Steve Jobs. If you have good product taste, you can be a panelist.

The iPhone follows this path. Before seeing an iPhone, consumers couldn't want one. Customer obsession wouldn't have gotten you far because iPhone buyers didn't know they wanted one.

In The Hard Thing About Hard Things, Ben Horowitz writes:

“It turns out that is exactly what product strategy is all about — figuring out the right product is the innovator’s job, not the customer’s job. The customer only knows what she thinks she wants based on her experience with the current product. The innovator can take into account everything that’s possible, but often must go against what she knows to be true. As a result, innovation requires a combination of knowledge, skill, and courage.“

One path solves a problem the customer knows they have, and the other doesn't. Instead of asking a person what they want, observe them and give them something they didn't know they needed.

It's much harder. Apple is the world's most valuable company because it's more valuable. It changes industries permanently.

If you want to build superior products, use the iPhone of your industry.

How to Improve Your Taste

I. Work for a company that has taste.

People with the best taste in products, markets, and people are rewarded for building great companies. Tasteful people know quality even when they can't describe it. Taste isn't writable. It's feel-based.

Moving into a community that's already doing what you want to do may be the best way to develop entrepreneurial taste. Most company-building knowledge is tacit.

Joining a company you want to emulate allows you to learn its inner workings. It reveals internal patterns intuitively. Many successful founders come from successful companies.

Consumption determines taste. Excellence will refine you. This is why restauranteurs visit the world's best restaurants and serious painters visit Paris or New York. Joining a company with good taste is beneficial.

2. Possess a wide range of interests

“Edwin Land of Polaroid talked about the intersection of the humanities and science. I like that intersection. There’s something magical about that place… The reason Apple resonates with people is that there’s a deep current of humanity in our innovation. I think great artists and great engineers are similar, in that they both have a desire to express themselves.” — Steve Jobs

I recently discovered Edwin Land. Jobs modeled much of his career after Land's. It makes sense that Apple was inspired by Land.

A Triumph of Genius: Edwin Land, Polaroid, and the Kodak Patent War notes:

“Land was introverted in person, but supremely confident when he came to his ideas… Alongside his scientific passions, lay knowledge of art, music, and literature. He was a cultured person growing even more so as he got older, and his interests filtered into the ethos of Polaroid.”

Founders' philosophies shape companies. Jobs and Land were invested. It showed in the products their companies made. Different. His obsession was spreading Microsoft software worldwide. Microsoft's success is why their products are bland and boring.

Experience is important. It's probably why startups are built by generalists and scaled by specialists.

Jobs combined design, typography, storytelling, and product taste at Apple. Some of the best original Mac developers were poets and musicians. Edwin Land liked broad-minded people, according to his biography. Physicist-musicians or physicist-photographers.

Da Vinci was a master of art, engineering, architecture, anatomy, and more. He wrote and drew at the same desk. His genius is remembered centuries after his death. Da Vinci's statue would stand at the intersection of humanities and science.

We find incredibly creative people here. Superhumans. Designers, creators, and world-improvers. These are the people we need to navigate technology and lead world-changing companies. Generalists lead.

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