But how does bitcoin actually work?

SUMMARY

In a 3Blue1Brown video, Grant Sanderson demystifies Bitcoin by guiding viewers through inventing a cryptocurrency, from communal ledgers and digital signatures to decentralized blockchains and proof-of-work mining, revealing the math powering trustless digital money.

STATEMENTS

Bitcoin is a fully digital currency without government issuance, bank management, or a known inventor, functioning as a ledger where transaction history constitutes the currency itself.
To understand Bitcoin, one can imagine inventing a simple communal ledger for tracking payments among friends, evolving it with cryptography to eliminate trust in centralized authorities.
Digital signatures use public-private key pairs to verify transactions, ensuring only the owner can approve a specific message, with signatures changing per message to prevent forgery.
A 256-bit signature space offers 2^256 possibilities, making forgery computationally infeasible, akin to guessing in an astronomically vast search.
To prevent overspending without cash settlement, the ledger tracks balances from initial deposits, rejecting transactions that exceed available funds, decoupling it from physical currency.
Decentralization requires everyone to maintain personal ledger copies and broadcast transactions, but consensus demands a protocol to agree on the valid history without a central authority.
Cryptographic hash functions like SHA-256 produce fixed-length, unpredictable outputs from any input, resisting reverse engineering and enabling proofs of computational effort.
Proof-of-work involves finding a nonce that makes a block's hash start with many zeros, requiring billions of guesses on average, verifiable quickly to confirm effort.
Blockchains chain blocks via hashes, ensuring alterations propagate and demand re-mining all subsequent blocks, fostering a tamper-evident structure.
Miners collect transactions into blocks, perform proof-of-work, and earn block rewards plus fees, introducing new currency while securing the network through competition.
Consensus favors the longest chain with the most work; to double-spend, an attacker needs over 50% of network computing power, making fraud probabilistically unlikely after confirmations.

IDEAS

Inventing a cryptocurrency starts with a simple ledger but evolves into a trustless system by replacing human trust with mathematical proofs, mirroring societal shifts from centralized to decentralized control.
Digital signatures aren't just copies of handwritten ones; their message-dependence creates a unique, non-reusable proof of intent, revolutionizing how ownership is asserted in digital realms.
The ledger itself becomes the currency, severing ties to physical money, allowing a global economy where value exists purely as verified transaction histories without fiat backing.
Decentralized consensus through proof-of-work turns computation into a form of "digital labor," where effort quantifies trustworthiness, inverting traditional authority based on reputation or institutions.
Hash functions' one-way nature means security relies on practical infeasibility rather than absolute proof, highlighting how much of modern tech trusts empirical hardness over theoretical guarantees.
Mining as a lottery democratizes currency creation, but it also centralizes power among those with hardware, raising questions about energy use and inequality in this supposedly egalitarian system.
Waiting for multiple confirmations before trusting a transaction quantifies risk in probabilistic terms, blending cryptography with game theory to build confidence in an anarchic network.
Bitcoin's halving mechanism ensures scarcity like digital gold, but transaction fees sustain miners long-term, evolving the system from reward-driven to service-based economics.
Block size limits create bottlenecks, contrasting Bitcoin's deliberate slowness with Visa's speed, underscoring trade-offs between security, decentralization, and scalability in protocol design.
Understanding Bitcoin's math empowers users beyond hype, revealing it as a protocol for verifiable scarcity and ownership, applicable to innovations like Ethereum's smart contracts.

INSIGHTS

Cryptocurrencies transform trust from interpersonal or institutional reliance into cryptographic primitives, enabling global, permissionless economies where math enforces fairness over authority.
Proof-of-work's genius lies in asymmetric verification: immense effort to create but trivial to check, creating a self-regulating network where honesty is the cheapest path.
By making the transaction history the money, Bitcoin decouples value from physical assets, fostering a paradigm where digital scarcity rivals natural resources in economic theory.
Decentralization isn't chaos but emergent order from incentives, where competing miners align on consensus through shared computational skin in the game.
The system's vulnerability to 51% attacks illustrates a profound balance: security scales with network participation, but growth introduces centralization risks via resource concentration.
Halvings and fees reveal an adaptive economy, where initial abundance bootstraps security, transitioning to sustainability, modeling how protocols can evolve without central planning.

QUOTES

"The history of transactions is the currency."
"You can verify that they went through a large amount of work, but without having to go through that same effort yourself."
"If everyone in the world was using this ledger, you could live your whole life just sending and receiving money on this ledger without ever having to convert to real US dollars."
"Trust whichever ledger has the most computational work put into it."
"All of this work is intrinsically tied to the list of transactions."

HABITS

Maintain a communal ledger for frequent small transactions among friends to avoid constant cash exchanges, settling balances monthly.
Generate and safeguard personal public-private key pairs for signing digital transactions, ensuring secrecy of the private key.
Broadcast signed transactions publicly while verifying full transaction history before acceptance to prevent overspending.
Listen for and update personal blockchain copies based on the longest proof-of-work chain, waiting for confirmations before trusting new payments.
Contribute to network security by mining blocks when possible, collecting transactions and solving hashes to earn rewards.

FACTS

Bitcoin's block rewards started at 50 BTC per block and halve every 210,000 blocks, roughly every four years, capping total supply at 21 million BTC.
SHA-256, Bitcoin's hash function, produces 256-bit outputs, with 2^256 possible values, making brute-force reversal equivalent to guessing among billions of times the atoms in the observable universe.
Bitcoin targets 10-minute block times by adjusting proof-of-work difficulty, contrasting with Visa's capacity for over 24,000 transactions per second.
Each Bitcoin block is limited to about 2,400 transactions, leading to higher fees during congestion as miners prioritize fee-paying ones.
The original Bitcoin blockchain's first blocks contain only the 50 BTC miner reward, with no other transactions, illustrating the system's bootstrapping phase.

REFERENCES

Original Bitcoin paper by Satoshi Nakamoto.
Block explorer tool for browsing the Bitcoin blockchain.
Michael Nielsen's blog post on Bitcoin transaction details.
CuriousInventor's video: "How Bitcoin Works Under the Hood."
Anders Brownworth's video: "Blockchain 101 - A Visual Demo."
Ethereum white paper.

HOW TO APPLY

Establish a shared digital ledger accessible to all participants, recording intended transactions like "Alice pays Bob $20" to track owed amounts without immediate cash exchanges.
Generate a public-private key pair for each user; sign transactions using the private key tied to the specific message, then broadcast the signed entry for public verification with the public key.
Initialize the ledger with equal deposits from participants (e.g., $100 each) to create starting balances, then validate new transactions by checking they don't exceed the sender's accumulated credits minus debits.
Organize transactions into blocks including a nonce for proof-of-work; compute SHA-256 hashes until the output starts with a target number of zeros (e.g., 60), chaining blocks via previous hash references.
When receiving a payment, wait for multiple subsequent blocks (confirmations) on the same chain before accepting, deferring to the longest chain if conflicts arise to ensure network consensus.

ONE-SENTENCE TAKEAWAY

Bitcoin's genius lies in using math to create trustless, decentralized money through ledgers secured by computational proof-of-work.

RECOMMENDATIONS

Study the original Bitcoin whitepaper before investing to grasp its trustless mechanics beyond market hype.
Use block explorers to trace real transactions, building intuition for how history forms the currency.
Wait for at least six confirmations on Bitcoin payments to minimize double-spending risks in practice.
Explore Ethereum's whitepaper next to understand smart contracts as an evolution of Bitcoin's ledger model.
Diversify cryptocurrency knowledge by watching visual demos like Anders Brownworth's to internalize blockchain chaining.

MEMO

In an era of skyrocketing cryptocurrency valuations, understanding Bitcoin isn't just prudent—it's essential. As 3Blue1Brown's Grant Sanderson explains in his animated deep dive, Bitcoin isn't magic or mere speculation; it's a meticulously engineered system born from cryptographic ingenuity. Imagine starting small: you and your friends maintain a shared ledger for splitting dinner bills, jotting down IOUs like "Alice pays Bob $20." This communal record, public and editable, evolves when trust erodes. Enter digital signatures—mathematical proofs using public-private key pairs that only the owner can generate, ensuring no forgeries. Each signature, a 256-bit string unique to the message, draws from a space so vast (2^256 possibilities) that guessing it rivals cosmic improbabilities.

But ledgers demand more than signatures; they need safeguards against overspending. By seeding the system with initial deposits and tracking balances in "ledger dollars," the protocol rejects invalid spends, untethering value from physical cash. Here, the ledger is the currency—a chain of verified history where Alice can "pay" Bob without ever touching dollars, exchangeable on open markets like any fiat pair. This abstraction hits Bitcoin's core: money as immutable transaction logs, not bank promises. Yet central ledgers invite tampering—who controls the website? Sanderson shifts to decentralization: everyone holds a copy, broadcasting signed transactions. Consensus emerges not from votes but from proof-of-work, where "miners" bundle transactions into blocks and hunt for a nonce making the SHA-256 hash start with zeros—a billion-guess lottery verifiable in seconds.

This proof-of-work chains blocks into a blockchain, each linking to the prior via hashes, rendering alterations a Herculean redo of all subsequent effort. Miners, racing to solve these puzzles every 10 minutes (Bitcoin's tuned average), earn fresh coins as rewards—50 BTC initially, now 12.5 after halvings every four years, capping supply at 21 million. Fraud, like double-spending, requires outpacing the network's collective compute, a 51% attack feasible only for state-like powers. Users wait for confirmations—six blocks atop a transaction—to trust it, as longer chains prevail. Sanderson demystifies mining: not picks and shovels, but hardware crunching hashes, fueled by electricity that critics decry as wasteful.

Bitcoin's limits shine through: blocks hold just 2,400 transactions, dwarfed by Visa's 24,000 per second, spiking fees during peaks as miners cherry-pick high payers. Yet this slowness bolsters security, prioritizing decentralization over speed. Newer coins tweak these—shorter blocks, varied consensus—but Bitcoin's blueprint endures, inspiring Ethereum's programmable ledgers. Sanderson urges: before hype-driven buys, know the math. It's not gold 2.0; it's a protocol for scarce, verifiable digital ownership, reshaping finance's foundations without kings or banks.

Ultimately, Bitcoin reveals technology's power to forge human flourishing through code, not coercion— a ledger where math ensures equity, if unevenly distributed. As investments pour in, this foundational grasp equips users to navigate evolutions, from fees sustaining miners post-halvings to global experiments in trustless trade.