Calmness is a vital life skill.

It aids communication. It boosts creativity and performance.

I've studied calm people's habits for years. Commonalities:

Have learned to laugh at themselves.

Those who have something to protect can’t help but make it a very serious business, which drains the energy out of the room.

They are fixated on positive pursuits like making cool things, building a strong physique, and having fun with others rather than on depressing influences like the news and gossip.

Every day, spend at least 20 minutes moving, whether it's walking, yoga, or lifting weights.

Discover ways to take pleasure in life's challenges.

Since perspective is malleable, they change their view.

Set your own needs first.

Stressed people neglect themselves and wonder why they struggle.

Prioritize self-care.

Don't ruin your life to please others.

Make something.

Calm people create more than react.

They love creating beautiful things—paintings, children, relationships, and projects.

Hold your breath, please.

If you're stressed or angry, you may be surprised how much time you spend holding your breath and tightening your belly.

Release, breathe, and relax to find calm.

Stopped rushing.

Rushing is disadvantageous.

Calm people handle life better.

Are attuned to their personal dietary needs.

They avoid junk food and eat foods that keep them healthy, happy, and calm.

Don’t take anything personally.

Stressed people control everything.

Self-conscious.

Calm people put others and their work first.

Keep their surroundings neat.

Maintaining an uplifting and clutter-free environment daily calms the mind.

Minimise negative people.

Calm people are ruthless with their boundaries and avoid negative and drama-prone people.

How to overcome public speaking fear and give a killer presentation

"Public speaking is people's biggest fear, according to studies. Death's second. The average person is better off in the casket than delivering the eulogy."  — American comedian, actor, writer, and producer Jerry Seinfeld

People fear public speaking, according to research. Public speaking can be intimidating.

Most professions require public speaking, whether to 5, 50, 500, or 5,000 people. Your career will require many presentations. In a small meeting, company update, or industry conference.

You can improve your public speaking skills. You can reduce your anxiety, improve your performance, and feel more comfortable speaking in public.

“If I returned to college, I'd focus on writing and public speaking. Effective communication is everything.” — 38th president Gerald R. Ford

You can deliver a great presentation despite your fear of public speaking. There are ways to stay calm while speaking and become a more effective public speaker.

Seven tips to improve your public speaking today. Let's help you overcome your fear (no pun intended).

Know your audience.

"You're not being judged; the audience is." — Entrepreneur, author, and speaker Seth Godin

Understand your audience before speaking publicly. Before preparing a presentation, know your audience. Learn what they care about and find useful.

Your presentation may depend on where you're speaking. A classroom is different from a company meeting.

Determine your audience before developing your main messages. Learn everything about them. Knowing your audience helps you choose the right words, information (thought leadership vs. technical), and motivational message.

2. Be Observant

Observe others' speeches to improve your own. Watching free TED Talks on education, business, science, technology, and creativity can teach you a lot about public speaking.

What worked and what didn't?

• What would you change?

• Their strengths

• How interesting or dull was the topic?

Note their techniques to learn more. Studying the best public speakers will amaze you.

Learn how their stage presence helped them communicate and captivated their audience. Please note their pauses, humor, and pacing.

3. Practice

"A speaker should prepare based on what he wants to learn, not say." — Author, speaker, and pastor Tod Stocker

Practice makes perfect when it comes to public speaking. By repeating your presentation, you can find your comfort zone.

When you've practiced your presentation many times, you'll feel natural and confident giving it. Preparation helps overcome fear and anxiety. Review notes and important messages.

When you know the material well, you can explain it better. Your presentation preparation starts before you go on stage.

Keep a notebook or journal of ideas, quotes, and examples. More content means better audience-targeting.

4. Self-record

Videotape your speeches. Check yourself. Body language, hands, pacing, and vocabulary should be reviewed.

Best public speakers evaluate their performance to improve.

Write down what you did best, what you could improve and what you should stop doing after watching a recording of yourself. Seeing yourself can be unsettling. This is how you improve.

5. Remove text from slides

"Humans can't read and comprehend screen text while listening to a speaker. Therefore, lots of text and long, complete sentences are bad, bad, bad.” —Communications expert Garr Reynolds

Presentation slides shouldn't have too much text. 100-slide presentations bore the audience. Your slides should preview what you'll say to the audience.

Use slides to emphasize your main point visually.

If you add text, use at least 40-point font. Your slides shouldn't require squinting to read. You want people to watch you, not your slides.

6. Body language

"Body language is powerful." We had body language before speech, and 80% of a conversation is read through the body, not the words." — Dancer, writer, and broadcaster Deborah Bull

Nonverbal communication dominates. Our bodies speak louder than words. Don't fidget, rock, lean, or pace.

Relax your body to communicate clearly and without distraction through nonverbal cues. Public speaking anxiety can cause tense body language.

Maintain posture and eye contact. Don’t put your hand in your pockets, cross your arms, or stare at your notes. Make purposeful hand gestures that match what you're saying.

7. Beginning/ending Strong

Beginning and end are memorable. Your presentation must start strong and end strongly. To engage your audience, don't sound robotic.

Begin with a story, stat, or quote. Conclude with a summary of key points. Focus on how you will start and end your speech.

You should memorize your presentation's opening and closing. Memorize something naturally. Excellent presentations start and end strong because people won't remember the middle.

Bringing It All Together

Seven simple yet powerful ways to improve public speaking. Know your audience, study others, prepare and rehearse, record yourself, remove as much text as possible from slides, and start and end strong.

Follow these tips to improve your speaking and audience communication. Prepare, practice, and learn from great speakers to reduce your fear of public speaking.

"Speaking to one person or a thousand is public speaking." — Vocal coach Roger Love

Non-technical talents can benefit data scientists in addition to statistics and programming.

As our article 5 Most In-Demand Skills for Data Scientists shows, being business-minded is useful. How can you get such a diverse skill set? We've compiled a list of helpful resources.

Data science, data analysis, programming, and business are covered. Even a few of these books will make you a better data scientist.

Ready? Let’s dive in.

Best books for data scientists

1. The Black Swan

Author: Nassim Taleb

First, a less obvious title. Nassim Nicholas Taleb's seminal series examines uncertainty, probability, risk, and decision-making.

Three characteristics define a black swan event:

• It is erratic.

• It has a significant impact.

• Many times, people try to come up with an explanation that makes it seem more predictable than it actually was.

People formerly believed all swans were white because they'd never seen otherwise. A black swan in Australia shattered their belief.

Taleb uses this incident to illustrate how human thinking mistakes affect decision-making. The book teaches readers to be aware of unpredictability in the ever-changing IT business.

Try multiple tactics and models because you may find the answer.

2. High Output Management

Author: Andrew Grove

Intel's former chairman and CEO provides his insights on developing a global firm in this business book. We think Grove would choose “management” to describe the talent needed to start and run a business.

That's a skill for CEOs, techies, and data scientists. Grove writes on developing productive teams, motivation, real-life business scenarios, and revolutionizing work.

Five lessons:

• Every action is a procedure.

• Meetings are a medium of work

• Manage short-term goals in accordance with long-term strategies.

• Mission-oriented teams accelerate while functional teams increase leverage.

• Utilize performance evaluations to enhance output.

So — if the above captures your imagination, it’s well worth getting stuck in.

3. The Hard Thing About Hard Things: Building a Business When There Are No Easy Answers

Author: Ben Horowitz

Few realize how difficult it is to run a business, even though many see it as a tremendous opportunity.

Business schools don't teach managers how to handle the toughest difficulties; they're usually on their own. So Ben Horowitz wrote this book.

It gives tips on creating and maintaining a new firm and analyzes the hurdles CEOs face.

Find suggestions on:

• create software

• Run a business.

• Promote a product

• Obtain resources

• Smart investment

• oversee daily operations

This book will help you cope with tough times.

4. Obviously Awesome: How to Nail Product Positioning

Author: April Dunford

Your job as a data scientist is a product. You should be able to sell what you do to clients. Even if your product is great, you must convince them.

How to? April Dunford's advice: Her book explains how to connect with customers by making your offering seem like a secret sauce.

You'll learn:

• Select the ideal market for your products.

• Connect an audience to the value of your goods right away.

• Take use of three positioning philosophies.

• Utilize market trends to aid purchasers

5. The Mom test

Author: Rob Fitzpatrick

The Mom Test improves communication. Client conversations are rarely predictable. The book emphasizes one of the most important communication rules: enquire about specific prior behaviors.

Both ways work. If a client has suggestions or demands, listen carefully and ensure everyone understands. The book is packed with client-speaking tips.

6. Introduction to Machine Learning with Python: A Guide for Data Scientists

Authors: Andreas C. Müller, Sarah Guido

Now, technical documents.

This book is for Python-savvy data scientists who wish to learn machine learning. Authors explain how to use algorithms instead of math theory.

Their technique is ideal for developers who wish to study machine learning basics and use cases. Sci-kit-learn, NumPy, SciPy, pandas, and Jupyter Notebook are covered beyond Python.

If you know machine learning or artificial neural networks, skip this.

7. Python Data Science Handbook: Essential Tools for Working with Data

Author: Jake VanderPlas

Data work isn't easy. Data manipulation, transformation, cleansing, and visualization must be exact.

Python is a popular tool. The Python Data Science Handbook explains everything. The book describes how to utilize Pandas, Numpy, Matplotlib, Scikit-Learn, and Jupyter for beginners.

The only thing missing is a way to apply your learnings.

8. Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython

Author: Wes McKinney

The author leads you through manipulating, processing, cleaning, and analyzing Python datasets using NumPy, Pandas, and IPython.

The book's realistic case studies make it a great resource for Python or scientific computing beginners. Once accomplished, you'll uncover online analytics, finance, social science, and economics solutions.

9. Data Science from Scratch

Author: Joel Grus

Here's a title for data scientists with Python, stats, maths, and algebra skills (alongside a grasp of algorithms and machine learning). You'll learn data science's essential libraries, frameworks, modules, and toolkits.

The author works through all the key principles, providing you with the practical abilities to develop simple code. The book is appropriate for intermediate programmers interested in data science and machine learning.

Not that prior knowledge is required. The writing style matches all experience levels, but understanding will help you absorb more.

10. Machine Learning Yearning

Author: Andrew Ng

Andrew Ng is a machine learning expert. Co-founded and teaches at Stanford. This free book shows you how to structure an ML project, including recognizing mistakes and building in complex contexts.

The book delivers knowledge and teaches how to apply it, so you'll know how to:

• Determine the optimal course of action for your ML project.

• Create software that is more effective than people.

• Recognize when to use end-to-end, transfer, and multi-task learning, and how to do so.

• Identifying machine learning system flaws

Ng writes easy-to-read books. No rigorous math theory; just a terrific approach to understanding how to make technical machine learning decisions.

11. Deep Learning with PyTorch Step-by-Step

Author: Daniel Voigt Godoy

The last title is also the most recent. The book was revised on 23 January 2022 to discuss Deep Learning and PyTorch, a Python coding tool.

It comprises four parts:

1. Fundamentals (gradient descent, training linear and logistic regressions in PyTorch)

2. Machine Learning (deeper models and activation functions, convolutions, transfer learning, initialization schemes)

3. Sequences (RNN, GRU, LSTM, seq2seq models, attention, self-attention, transformers)

4. Automatic Language Recognition (tokenization, embeddings, contextual word embeddings, ELMo, BERT, GPT-2)

We admire the book's readability. The author avoids difficult mathematical concepts, making the material feel like a conversation.

Is every data scientist a humanist?

Even as a technological professional, you can't escape human interaction, especially with clients.

We hope these books will help you develop interpersonal skills.

The easiest online explanation.

Web3 is growing. Crypto companies are growing.

Instagram, Adidas, and Stripe adopted cryptocurrency.

Bitcoin and other cryptocurrencies made web3 famous.

Most don't know where to start. Cryptocurrency, DeFi, etc. are investments.

Since we don't understand web3, I'll help you today.

Let’s go.

1. Web3

It is the third generation of the web, and it is built on the decentralization idea which means no one can control it.

There are static webpages that we can only read on the first generation of the web (i.e. Web 1.0).

Web 2.0 websites are interactive. Twitter, Medium, and YouTube.

Each generation controlled the website owner. Simply put, the owner can block us. However, data breaches and selling user data to other companies are issues.

They can influence the audience's mind since they have control.

Assume Twitter's CEO endorses Donald Trump. Result? Twitter would have promoted Donald Trump with tweets and graphics, enhancing his chances of winning.

We need a decentralized, uncontrollable system.

And then there’s Web3.0 to consider. As Bitcoin and Ethereum values climb, so has its popularity. Web3.0 is uncontrolled web evolution. It's good and bad.

Dapps, DeFi, and DAOs are here. It'll all be explained afterwards.

2. Cryptocurrencies:

No need to elaborate.

Bitcoin, Ethereum, Cardano, and Dogecoin are cryptocurrencies. It's digital money used for payments and other uses.

Programs must interact with cryptocurrencies.

3. Blockchain:

Blockchain facilitates bitcoin transactions, investments, and earnings.

This technology governs Web3. It underpins the web3 environment.

Let us delve much deeper.

Blockchain is simple. However, the name expresses the meaning.

Blockchain is a chain of blocks.

Let's use an image if you don't understand.

The graphic above explains blockchain. Think Blockchain. The block stores related data.

Here's more.

4. Smart contracts

Programmers and developers must write programs. Smart contracts are these blockchain apps.

That’s reasonable.

Decentralized web3.0 requires immutable smart contracts or programs.

5. NFTs

Blockchain art is NFT. Non-Fungible Tokens.

Explaining Non-Fungible Token may help.

Two sorts of tokens:

1. These tokens are fungible, meaning they can be changed. Think of Bitcoin or cash. The token won't change if you sell one Bitcoin and acquire another.

2. Non-Fungible Token: Since these tokens cannot be exchanged, they are exclusive. For instance, music, painting, and so forth.

Right now, Companies and even individuals are currently developing worthless NFTs.

The concept of NFTs is much improved when properly handled.

6. Dapp

Decentralized apps are Dapps. Instagram, Twitter, and Medium apps in the same way that there is a lot of decentralized blockchain app.

Curve, Yearn Finance, OpenSea, Axie Infinity, etc. are dapps.

7. DAOs

DAOs are member-owned and governed.

Consider it a company with a core group of contributors.

8. DeFi

We all utilize centrally regulated financial services. We fund these banks.

If you have $10,000 in your bank account, the bank can invest it and retain the majority of the profits.

We only get a penny back. Some banks offer poor returns. To secure a loan, we must trust the bank, divulge our information, and fill out lots of paperwork.

DeFi was built for such issues.

Decentralized banks are uncontrolled. Staking, liquidity, yield farming, and more can earn you money.

Web3 beginners should start with these resources.

If you think NFTs are awful, check out the art market.

The fervor around NFTs has subsided in recent months due to the crypto market crash and the media's short attention span. They were all anyone could talk about earlier this spring. Last semester, when passions were high and field luminaries were discussing "slurp juices," I asked my students and students from over 20 other universities what they thought of NFTs.

According to many, NFTs were either tasteless pyramid schemes or a new way for artists to make money. NFTs contributed to the climate crisis and harmed the environment, but so did air travel, fast fashion, and smartphones. Some students complained that NFTs were cheap, tasteless, algorithmically generated schlock, but others asked how this was different from other art.

I'm not sure what I expected, but the intensity of students' reactions surprised me. They had strong, emotional opinions about a technology I'd always considered administrative. NFTs address ownership and accounting, like most crypto/blockchain projects.

Art markets can be irrational, arbitrary, and subject to the same scams and schemes as any market. And maybe a few shenanigans that are unique to the art world.

The Fairness Question

Fairness, a deflating moral currency, was the general sentiment (the less of it in circulation, the more ardently we clamor for it.) These students, almost all of whom are artists, complained to the mismatch between the quality of the work in some notable NFT collections and the excessive amounts these items were fetching on the market. They can sketch a Bored Ape or Lazy Lion in their sleep. Why should they buy ramen with school loans while certain swindlers get rich?

I understand students. Art markets are unjust. They can be irrational, arbitrary, and governed by chance and circumstance, like any market. And art-world shenanigans.

Almost every mainstream critique leveled against NFTs applies just as easily to art markets

Over 50% of artworks in circulation are fake, say experts. Sincere art collectors and institutions are upset by the prevalence of fake goods on the market. Not everyone. Wealthy people and companies use art as investments. They can use cultural institutions like museums and galleries to increase the value of inherited art collections. People sometimes buy artworks and use family ties or connections to museums or other cultural taste-makers to hype the work in their collection, driving up the price and allowing them to sell for a profit. Money launderers can disguise capital flows by using market whims, hype, and fluctuating asset prices.

Almost every mainstream critique leveled against NFTs applies just as easily to art markets.

Art has always been this way. Edward Kienholz's 1989 print series satirized art markets. He stamped 395 identical pieces of paper from $1 to $395. Each piece was initially priced as indicated. Kienholz was joking about a strange feature of art markets: once the last print in a series sells for $395, all previous works are worth at least that much. The entire series is valued at its highest auction price. I don't know what a Kienholz print sells for today (inquire with the gallery), but it's more than $395.

I love Lee Lozano's 1969 "Real Money Piece." Lozano put cash in various denominations in a jar in her apartment and gave it to visitors. She wrote, "Offer guests coffee, diet pepsi, bourbon, half-and-half, ice water, grass, and money." "Offer real money as candy."

Lee Lozano kept track of who she gave money to, how much they took, if any, and how they reacted to the offer of free money without explanation. Diverse reactions. Some found it funny, others found it strange, and others didn't care. Lozano rarely says:

Apr 17 Keith Sonnier refused, later screws lid very tightly back on. Apr 27 Kaltenbach takes all the money out of the jar when I offer it, examines all the money & puts it all back in jar. Says he doesn’t need money now. Apr 28 David Parson refused, laughing. May 1 Warren C. Ingersoll refused. He got very upset about my “attitude towards money.” May 4 Keith Sonnier refused, but said he would take money if he needed it which he might in the near future. May 7 Dick Anderson barely glances at the money when I stick it under his nose and says “Oh no thanks, I intend to earn it on my own.” May 8 Billy Bryant Copley didn’t take any but then it was sort of spoiled because I had told him about this piece on the phone & he had time to think about it he said.

Smart Contracts (smart as in fair, not smart as in Blockchain)

Cornell University's Cheryl Finley has done a lot of research on secondary art markets. I first learned about her research when I met her at the University of Florida's Harn Museum, where she spoke about smart contracts (smart as in fair, not smart as in Blockchain) and new protocols that could help artists who are often left out of the economic benefits of their own work, including women and women of color.

Her talk included findings from her ArtNet op-ed with Lauren van Haaften-Schick, Christian Reeder, and Amy Whitaker.

NFTs allow us to think about and hack on formal contractual relationships outside a system of laws that is currently not set up to service our community.

The ArtNet article The Recent Sale of Amy Sherald's ‘Welfare Queen' Symbolizes the Urgent Need for Resale Royalties and Economic Equity for Artists discussed Sherald's 2012 portrait of a regal woman in a purple dress wearing a sparkling crown and elegant set of pearls against a vibrant red background.

Amy Sherald sold "Welfare Queen" to Princeton professor Imani Perry. Sherald agreed to a payment plan to accommodate Perry's budget.

Amy Sherald rose to fame for her 2016 portrait of Michelle Obama and her full-length portrait of Breonna Taylor, one of the most famous works of the past decade.

As is common, Sherald's rising star drove up the price of her earlier works. Perry's "Welfare Queen" sold for $3.9 million in 2021.

Imani Perry's early investment paid off big-time. Amy Sherald, whose work directly increased the painting's value and who was on an artist's shoestring budget when she agreed to sell "Welfare Queen" in 2012, did not see any of the 2021 auction money. Perry and the auction house got that money.

Sherald sold her Breonna Taylor portrait to the Smithsonian and Louisville's Speed Art Museum to fund a $1 million scholarship. This is a great example of what an artist can do for the community if they can amass wealth through their work.

NFTs haven't solved all of the art market's problems — fakes, money laundering, market manipulation — but they didn't create them. Blockchain and NFTs are credited with making these issues more transparent. More ideas emerge daily about what a smart contract should do for artists.

NFTs are a copyright solution. They allow us to hack formal contractual relationships outside a law system that doesn't serve our community.

Amy Sherald shows the good smart contracts can do (as in, well-considered, self-determined contracts, not necessarily blockchain contracts.) Giving back to our community, deciding where and how our work can be sold or displayed, and ensuring artists share in the equity of our work and the economy our labor creates.

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