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The computational cost of making history expensive to rewrite — how PoW secures through waste

October 25, 2026 · 13 min

Iris Holm & Hana Field

Iris, hey — okay so picture a person, somewhere cold, let's say Iceland, 3 AM, staring at a rack of humming machines and asking herself whether it's worth running them for another month. What is she actually protecting by keeping them on? Her block reward, presumably. Sure, her reward — but also, and this is…

Proof-of-work (PoW) is a consensus mechanism that requires network participants—miners—to repeatedly hash block data until they find a nonce producing a hash value below a protocol-defined difficulty target. Because valid hashes are hard to find but trivially easy to verify, the network can reject invalid blocks without trusting any central authority.

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About this episode

Proof-of-work (PoW) is a consensus mechanism that requires network participants—miners—to repeatedly hash block data until they find a nonce producing a hash value below a protocol-defined difficulty target. Because valid hashes are hard to find but trivially easy to verify, the network can reject invalid blocks without trusting any central authority.

Grounded in 8 sources
Resisting Selfish Mining Attacks in the Bicomp ↗ · arxiv.org
Bitcoin and Blockchain: Security and Privacy ↗ · arxiv.org
Privacy-Preserving Energy Storage Sharing with Blockchain and Secure Multi-Party Computation ↗ · arxiv.org
Selfish Mining in Ethereum ↗ · arxiv.org
Bitcoin Mechanics ↗ · cs251.stanford.edu
Majority is not Enough: Bitcoin Mining is Vulnerable ↗ · doi.org
Blockchain without Waste: Proof-of-Stake ↗ · doi.org
51% attack vulnerability of nascent blockchains: a comprehensive review | Complex & Intelligent Systems | Springer Nature Link ↗ · link.springer.com
Read transcript

Hana Field: Iris, hey — okay so picture a person, somewhere cold, let's say Iceland, 3 AM, staring at a rack of humming machines and asking herself whether it's worth running them for another month. What is she actually protecting by keeping them on?

Iris Holm: Her block reward, presumably.

Hana Field: Sure, her reward — but also, and this is the part that honestly stopped me, she is the security. Not Satoshi Nakamoto, not a government, not a bank. Her machines running are what makes Bitcoin's history hard to rewrite. And Bitcoin's history has not been rewritten — not once since January 2009.

Iris Holm: Hold on — sixteen years, billions in potential profit as an incentive to attack, and it's held because individual miners just kept the lights on?

Hana Field: That is the whole thing, yeah. And here's the plain version: Bitcoin's security isn't a cryptographic secret. It's more like a vault where the lock is the sheer cost of labor to break in — and every second honest miners run, they add more steel to the door ahead of any attacker.

Iris Holm: Nakamoto designed that deliberately. October 2008 white paper — computational work as a replacement for institutional trust. The energy spend was the architecture, not the waste.

Hana Field: And yet most people hear 'Bitcoin uses a lot of electricity' and think inefficiency, not security mechanism. Those are completely different claims and the whole conversation changes depending on which one you're making.

Iris Holm: The question is how. How does electricity become tamper resistance, mechanically?

Hana Field: That's exactly where I want to start — because once you see the Proof-of-Work mechanism up close, the 3 AM miner in Iceland stops looking like a footnote and starts looking like the whole story.

Iris Holm: Mechanically, though — walk me through the actual operation. What is the miner's machine doing at 3 AM?

Hana Field: So she's got a block of pending transactions, and she needs to find a number — a nonce — that she jams into the block data and runs through Bitcoin's hash function, which is double-SHA-256, and the output has to fall below a specific target. The difficulty target. And the only way to find that nonce is to just... try. Over and over. Billions of times a second.

Iris Holm: There's no shortcut. No smarter guess.

Hana Field: None. That's the whole point — the hash function scrambles the input so completely that the output is unpredictable. You cannot work backwards from a target and engineer a nonce. You just grind. And when she finally hits one, any other node on the network can verify it with a single hash operation. One check. Done.

Iris Holm: That asymmetry is doing a lot of work. Finding it costs a fortune in electricity. Checking it costs almost nothing.

Hana Field: And that's what lets thousands of independent nodes validate without trusting each other — or trusting anyone. No bank, no clearinghouse. The math does the vouching.

Iris Holm: Okay but here's where I want to push — how does that stop someone from going back and rewriting an old transaction? The work already happened.

Hana Field: Right, and this is actually — okay, so Nakamoto Consensus. The valid chain isn't the longest in terms of blocks, it's the one with the most cumulative computational work behind it. Every block that gets added on top of a transaction is more work layered on top. So if you want to go back and alter, say, a block from six months ago, you don't just redo that block's work. You redo that block, plus every single block built on top of it, and you have to do all of that faster than the honest chain is growing right now.

Iris Holm: You're racing a moving target.

Hana Field: A moving target that has a sixteen-year head start and thousands of miners adding to it every ten minutes. And to outrun it consistently — meaning to actually rewrite history and have the network accept your version — you need more than half the network's total hash rate. That's the 51% attack threshold. That's the number.

Iris Holm: So the energy bill is the barrier. Not a password, not a secret key — just the raw cost of buying and running enough hardware to out-hash every other miner on earth simultaneously.

Hana Field: Satoshi said it almost exactly like that in the white paper — October 2008. Computational work substitutes for institutional trust. The energy expenditure isn't waste, it's the tamper-resistance. You can't forge it. You can only spend it.

Iris Holm: Which means the security isn't a property of the code. It's a property of the economics around the code. And frankly, that's the crucial part.

Hana Field: And that's exactly where the economics get weird — because the clean version of this story says: honest participation always dominates. If you mine honestly, you earn. If you cheat, you lose. Neat. Except there's a decade-old crack in that framing, and it's not the 51% number. It's something smaller and, honestly, more unsettling.

Iris Holm: Smaller than 51% and still profitable?

Hana Field: So — 2013. Cornell. Two researchers, Emin Gun Sirer and Ittay Eyal, publish this result that kind of breaks the 'honest is always rational' premise. What they showed is that a miner doesn't broadcast a discovered block right away. She withholds it. She builds on top of it privately. And because the rest of the network is still working on the old block, she gets a head start on the next one. The honest miners are racing behind without knowing it.

Iris Holm: Wait — she's just not telling anyone she found it?

Hana Field: That's the whole move. Selfish mining. And Emin Gun Sirer and Ittay Eyal showed it becomes profitable in Bitcoin at roughly 25% of hash power. Not 51. Twenty-five. You don't need to dominate the network. You just need a quarter of it, and suddenly withholding blocks earns you disproportionate rewards because you're suppressing competitor blocks before anyone even knows they're in a race.

Iris Holm: And in Ethereum that threshold is even lower.

Hana Field: Lower, yeah — which makes it, you know, a broader vulnerability surface. And the thing that really stays with me about the Cornell research is that this isn't a theoretical edge case for a supervillain. It's a Tuesday morning calculation for a real mining operation. Like — picture someone running a mid-size pool in, I don't know, Reykjavik. She controls maybe 24% of the network's hash rate. She's not some rogue actor. She's just... sitting there, and the math is telling her that full honesty isn't actually the optimal strategy. That's the crack.

Iris Holm: So the incentive alignment that the whole system depends on — it's not as clean as the original framing suggests.

Hana Field: It has a documented failure mode that hasn't materialized at scale. And I genuinely don't know if that's because of technical friction, reputational risk inside mining communities, or just — I mean, maybe nobody's tried hard enough yet. Game theory alone doesn't close that gap.

Iris Holm: Now add the difficulty adjustment. Because that's the second layer — and it makes the first one worse.

Hana Field: Oh, the feedback loop. Yeah — so the protocol recalibrates every 2016 blocks to keep block production stable. Under normal conditions, that's elegant. But if a selfish miner is suppressing honest blocks during that window, she's actually — wait, this is the part that surprised me — she's depressing the measured difficulty. The protocol looks at participation, sees less honest output, and makes the puzzle easier. Which means the cost of sustaining her attack goes down partway through.

Iris Holm: The stabilizer works against itself. Under adversarial conditions, the mechanism designed to protect the network actively helps the attacker hold on longer than raw hash rate would suggest.

Hana Field: And none of this touches the even stranger question of why a miner stays honest in the first place — and that gets into block rewards, token price alignment, all of it. And also, frankly, where that rational-actor model just breaks when you introduce someone whose cost-benefit calculation looks nothing like a miner's. We'll get there.

Iris Holm: The 3 AM miner in Iceland isn't the only actor in the room.

Hana Field: And that's the part that actually keeps me up — because the rational-actor model, the clean version, it assumes the miner cares what happens to Bitcoin's price. That's load-bearing. The whole equilibrium rests on it.

Iris Holm: The block reward only pays if the token is worth something.

Hana Field: Exactly — so the miner who controls, say, 51% of hash rate earns more by just mining honestly, collecting newly created Bitcoin every block, than by rewriting history. Because a successful rewrite destroys confidence in the very asset she just spent enormous resources to acquire. She's torching her own investment.

Iris Holm: That's the alignment. Token value and honest behavior are stapled together.

Hana Field: Until they're not. And this is — okay, so picture a derivatives trader, not a miner at all, who's built a massive synthetic short position on Bitcoin. She profits when Bitcoin's price collapses. So she funds an attack, Bitcoin craters, she closes the short. The block rewards she never earned are irrelevant. Her cost-benefit calculation is completely inverted from our Iceland miner's.

Iris Holm: Wait — the standard model just doesn't account for that actor.

Hana Field: It doesn't. And same logic applies to a nation-state with cheap energy and a geopolitical reason to destabilize the network — they're not denominating the attack's cost in Bitcoin's value, so the whole 'rational attacker self-destructs' argument doesn't reach them.

Iris Holm: Which is why 'economically irrational' is — frankly, it's a claim about a specific actor profile. Not a universal claim.

Hana Field: And the honest framing — the one that actually survives — is probabilistic immutability. Each confirmation on top of a block adds more work, more cost to unwind. It gets harder. But it never hits zero risk. That's what 'immutable' actually means inside PoW. It's a probability, not a guarantee.

Iris Holm: So 'expensive' is doing the work that people think 'impossible' is doing.

Hana Field: And expensive is a variable. Energy prices shift, hardware gets cheaper, someone builds a short position large enough — any of those move the threshold. The equilibrium holds as long as the honest network stays large and the cost-benefit calculation doesn't flip. That's it. That's the whole guarantee.

Iris Holm: Which means the security lives in conditions, not code. The question is which conditions we should actually be watching.

Hana Field: And that's — yeah, that's a very different conversation than 'Bitcoin has never been attacked in sixteen years, therefore it's safe.' The record proves the conditions have held. Not that they always will.

Iris Holm: The conditions have held. Sixteen years. That's not nothing — but it's not a proof. It's a run of favorable circumstances.

Hana Field: And what Satoshi actually built in October 2008 — the thing in the white paper — it wasn't a cryptographic lock. It was a cost structure. Energy expenditure as a substitute for institutional trust. That substitution is only durable as long as the economic conditions that make it rational don't shift. Energy prices, hardware costs, derivatives markets, a nation-state with a motive and cheap electricity. None of those variables are in the protocol.

Iris Holm: Which brings us back to the miner. Not the math.

Hana Field: Yeah — and that's actually what keeps coming back to me. We started with her. Iceland, 3 AM, asking whether to keep the rigs running. And now I think the honest answer to her question is: you are the immutability. Not the hash function, not Nakamoto Consensus, not the longest-chain rule. You. Your Tuesday morning calculation. Bitcoin's history is unbroken because thousands of people like her have woken up every day since January 2009 and decided staying honest paid better than cheating. That's it. That's the whole guarantee.

Iris Holm: Written in pencil. Not stone.

Hana Field: Written in pencil. And honestly? I find that more interesting than if it were stone. Stone doesn't require anyone to show up.

Iris Holm: Fair. That's an honest place — not comfortable, but honest.

Hana Field: Thanks for pushing on all of it. The hard questions made it land properly.

The computational cost of making history expensive to rewrite — how PoW secures through waste · Onpode