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import React from 'react';
export default function PowerLaw() {
return (
<div className="space-y-6 font-mono text-sm leading-relaxed">
<p>
A <strong className="text-current">Power Law</strong> is a functional
relationship between two quantities, where a relative change in one
quantity results in a proportional relative change in the other
quantity, independent of the initial size of those quantities.
</p>
<p>
In statistics, it often manifests as a{' '}
<strong className="text-current">Long-Tail Distribution</strong>, where
a small number of events (the "head") occur with high frequency, while a
large number of events (the "tail") occur with low frequency.
</p>
<div className="space-y-8 my-6">
<div className="border border-emerald-500/20 p-4 bg-emerald-500/[0.02]">
<h4 className="text-xs font-bold text-emerald-400 uppercase tracking-widest mb-3">
The "Pizza Party" Analogy
</h4>
<p className="text-xs leading-relaxed opacity-80">
Imagine a party with 100 people and 100 slices of pizza.
</p>
<ul className="mt-3 space-y-2 text-xs">
<li className="flex gap-2">
<span className="text-emerald-500 font-bold">Normal:</span>
<span className="opacity-70">
Everyone gets exactly 1 slice. (Bell Curve)
</span>
</li>
<li className="flex gap-2">
<span className="text-emerald-500 font-bold">Power Law:</span>
<span>
1 person eats 80 slices, and the other 99 people have to share
the remaining 20 slices.
</span>
</li>
</ul>
<p className="mt-4 text-[10px] text-emerald-500/50 uppercase italic font-bold">
{'//'} This is why the "average" (1 slice per person) is useless
here.
</p>
</div>
<div className="border-l-2 border-yellow-500/50 pl-4 py-1">
<h4 className="text-xs font-bold text-yellow-400 uppercase tracking-widest mb-3">
Key Characteristics
</h4>
<ul className="space-y-3 text-xs opacity-90">
<li>
<strong className="text-current block mb-1">
Scale Invariance
</strong>
The distribution looks the same regardless of the scale at which
you observe it.
</li>
<li>
<strong className="text-current block mb-1">
Pareto Principle (80/20 Rule)
</strong>
A common manifestation where 80% of effects come from 20% of
causes.
</li>
<li>
<strong className="text-current block mb-1">
Lack of "Average"
</strong>
Unlike a Normal Distribution (Bell Curve), the "average" in a
power law is often misleading as it's heavily skewed by extreme
outliers.
</li>
</ul>
</div>
<div className="border-l-2 border-green-500/50 pl-4 py-1">
<h4 className="text-xs font-bold text-green-400 uppercase tracking-widest mb-3">
Real-World Examples
</h4>
<ul className="space-y-3 text-xs opacity-90">
<li>
<strong className="text-current">Wealth Distribution:</strong> A
small percentage of the population holds the majority of the
wealth.
</li>
<li>
<strong className="text-current">City Populations:</strong> A few
mega-cities vs. thousands of small towns.
</li>
<li>
<strong className="text-current">
Word Frequency (Zipf's Law):
</strong>{' '}
The most common words in a language appear significantly more
often than the rest.
</li>
<li>
<strong className="text-current">Internet Traffic:</strong> A few
websites (Google, YouTube) receive the vast majority of all
traffic.
</li>
</ul>
</div>
</div>
</div>
);
}