How does the human brain normalise exponentials ?
The human brain normalizes exponentials poorly, but adapts with logarithmic intuition. Here's how it works:
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1. Logarithmic Perception Is Natural
Human senses—especially for sound (decibels), light (lumens), and numerosity—respond logarithmically:
Fechner's Law: Perceived intensity = k × log(stimulus)
This means we feel changes proportionally, not absolutely (e.g., +10 lumens feels the same whether it’s 10→20 or 100→200).
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2. We Normalize Exponentials by Compressing Them
Exponentials grow fast: , , etc.
The brain deals with this by mapping the exponential onto a logarithmic axis:
\log(f(x)) = x \log(2)
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3. Heuristics Help Cope with Fast Growth
Humans use rules of thumb:
“If it doubles every year, it explodes in a decade.”
“10 doublings = ~1000x growth.”
This is why many people struggle with:
Compound interest
Pandemic growth
Moore’s Law
Exponential AI capabilities
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4. Exponential Blindness
Evolution didn’t prepare us for exponential environments.
Our intuition underestimates them until it’s too late (e.g. “hockey stick” surprises).
Training, graphs, and logarithmic scales help make sense of them.
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TL;DR
The brain normalizes exponentials by compressing them into a logarithmic perception, but this creates blind spots in modern exponential contexts like finance, computing, and pandemics.
asyncmind
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2025-05-19 00:25:10
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"content": "How does the human brain normalise exponentials ?\n\nThe human brain normalizes exponentials poorly, but adapts with logarithmic intuition. Here's how it works:\n\n\n---\n\n1. Logarithmic Perception Is Natural\n\nHuman senses—especially for sound (decibels), light (lumens), and numerosity—respond logarithmically:\n\nFechner's Law: Perceived intensity = k × log(stimulus)\n\nThis means we feel changes proportionally, not absolutely (e.g., +10 lumens feels the same whether it’s 10→20 or 100→200).\n\n\n\n---\n\n2. We Normalize Exponentials by Compressing Them\n\nExponentials grow fast: , , etc.\n\nThe brain deals with this by mapping the exponential onto a logarithmic axis:\n\n\n\\log(f(x)) = x \\log(2)\n\n\n---\n\n3. Heuristics Help Cope with Fast Growth\n\nHumans use rules of thumb:\n\n“If it doubles every year, it explodes in a decade.”\n\n“10 doublings = ~1000x growth.”\n\n\nThis is why many people struggle with:\n\nCompound interest\n\nPandemic growth\n\nMoore’s Law\n\nExponential AI capabilities\n\n\n\n---\n\n4. Exponential Blindness\n\nEvolution didn’t prepare us for exponential environments.\n\nOur intuition underestimates them until it’s too late (e.g. “hockey stick” surprises).\n\nTraining, graphs, and logarithmic scales help make sense of them.\n\n\n\n---\n\nTL;DR\n\nThe brain normalizes exponentials by compressing them into a logarithmic perception, but this creates blind spots in modern exponential contexts like finance, computing, and pandemics.\n\n",
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