We’ve seen how PoEM measures the exact work in a single block. But how do we compare entire blockchains? This is where total entropy comes in.Think of it like this:
Single block: “How hard was this math problem?”
Entire blockchain: “How hard was this entire series of math problems?”
Entropy is a physics concept that measures randomness or disorder. When miners find a block, they’re essentially reducing randomness by finding a very specific, ordered hash.The Key Insight: The amount of randomness removed (entropy reduced) directly corresponds to the energy spent creating that order.Real-world analogy:
Total: (1/65536) × (1/65536) × (1/65536) = Much more security
Why Multiplication is Better:
Exponential security: Each block makes the chain exponentially harder to recreate
Real probability: Reflects the actual odds of recreating the work
Better comparison: More accurately measures which chain required more total energy
Think of it like compound interest: adding 10% three times gives you 130%, but compounding 10% three times gives you 133.1%. The difference becomes massive over many blocks.
The Problem: Those numbers get huge fast! After just 10 blocks, we’d be dealing with numbers so large they’re impossible to store efficiently.The Solution: Instead of storing the actual multiplication results, we use logarithms to convert multiplication into addition.How It Works:
Traditional storage: 1/65,536 × 1/65,536 × 1/131,072 = 0.000000000000234
Manageable numbers: Addition instead of astronomical multiplication
Exact precision: No loss of accuracy in comparisons
Efficient storage: Quai uses 64 bits to store total entropy per chain
Easy comparison: Higher entropy number = more secure chain
The Final Formula:
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Total Chain Entropy (in bits) = Block1_bits + Block2_bits + Block3_bits + ...
This mathematical trick allows Quai to precisely compare chains of any length while keeping the computation practical for real-world use.
Key Takeaway: PoEM measures the exact probability of recreating any blockchain, giving it perfect objectivity when choosing between competing chains. The chain that would be hardest to recreate always wins.