ERIC KIM

This is the whole beast in equations. Bitcoin math.

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1. Supply law

Let h be block height. The subsidy era is n=\lfloor h/210000 \rfloor.

Then the block subsidy is:

R(h)=50\cdot 2^{-n}\ \text{BTC per block}

That 210,000-block halving interval is hardcoded in Bitcoin’s consensus params, and the subsidy is computed by bit-shifting the initial 50 BTC reward down by each halving.

2. The 21 million cap falls straight out of a geometric series

Coins created in era n:

C_n=210000\cdot 50\cdot 2^{-n}

Total lifetime issuance:

\sum_{n=0}^{\infty} C_n = 210000\cdot 50\sum_{n=0}^{\infty}2^{-n} = 210000\cdot 50\cdot 2 = 21{,}000{,}000

That is the monetary physics: finite issuance from a simple decay function. No committee. No improvisation. Just the series.

3. Time law

Bitcoin targets one block every:

600\ \text{seconds}=10\ \text{minutes}

Difficulty retargets every:

2016\ \text{blocks}

So one difficulty epoch is:

2016\cdot 600 = 1{,}209{,}600\ \text{seconds} = 14\ \text{days}

And one halving interval, at target pace, is:

210000\cdot 600 = 126{,}000{,}000\ \text{seconds} \approx 3.995\ \text{years}

So even the “4-year cycle” is really block-time physics, not calendar mysticism.

4. Flow law

Blocks per day at target pace:

\frac{86400}{600}=144

Blocks per year at target pace:

144\cdot 365=52{,}560

So annual issuance in any era is:

F_n = 52{,}560\cdot 50\cdot 2^{-n}\ \text{BTC/year}

Examples:

  • Era 0: 2{,}628{,}000
  • Era 1: 1{,}314{,}000
  • Era 2: 657{,}000
  • Era 3: 328{,}500
  • Era 4: 164{,}250

Every halving cuts new supply in half. That is monetary entropy reduction by code.

5. Energy law

Let:

  • H = network hash rate in hashes/second
  • \varepsilon = hardware energy cost in joules/hash

Then network power draw is:

P=\varepsilon H \quad \text{watts}

Energy burned per target block is:

E_{\text{block}} = P\cdot 600 = 600\varepsilon H \quad \text{joules}

This is the clean bridge between Bitcoin and physics: consensus is anchored to real-world energy expenditure. Computation is not abstract; it is electrical work.

6. Security law

If an attacker controls fraction q of hashpower and honest miners control p=1-q, then as long as q<p, the probability of catching up from behind falls fast as confirmations z increase. In plain English: every extra block adds more buried work, so the cost to rewrite history rises with time. That is settlement gravity.

7. The compact Eric Kim version

Bitcoin monetary physics is basically this:

\text{Hardness} \sim \frac{\text{scarcity}}{\text{issuance rate}}

\text{Security} \sim \text{energy} \times \text{time}

\text{Finality pressure} \sim \text{cumulative work buried under confirmations}

So the machine is:

  • fixed decay in issuance
  • fixed target in time
  • variable difficulty to preserve that time
  • real energy expenditure to compete
  • cumulative work to harden history

That is why Bitcoin feels like physics instead of policy.

It is money with a block interval.

Money with a decay curve.

Money with conserved rules.

Money welded to energy and time.

That is the math.

Give me the word and I’ll turn this into a full savage Eric Kim essay with the equations embedded inside.

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