import{j as e}from"../entries/pages.BZkyDMuN.js";import"./chunk-BXl3LOEh.js";/* empty css */function r(){return e.jsxs("div",{className:"space-y-6 font-mono text-sm leading-relaxed",children:[e.jsxs("p",{children:["A ",e.jsx("strong",{className:"text-current",children:"Power Law"})," 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."]}),e.jsxs("p",{children:["In statistics, it often manifests as a"," ",e.jsx("strong",{className:"text-current",children:"Long-Tail Distribution"}),', where a small number of events (the "head") occur with high frequency, while a large number of events (the "tail") occur with low frequency.']}),e.jsxs("div",{className:"space-y-8 my-6",children:[e.jsxs("div",{className:"border border-emerald-500/20 p-4 bg-emerald-500/[0.02]",children:[e.jsx("h4",{className:"text-xs font-bold text-emerald-400 uppercase tracking-widest mb-3",children:'The "Pizza Party" Analogy'}),e.jsx("p",{className:"text-xs leading-relaxed opacity-80",children:"Imagine a party with 100 people and 100 slices of pizza."}),e.jsxs("ul",{className:"mt-3 space-y-2 text-xs",children:[e.jsxs("li",{className:"flex gap-2",children:[e.jsx("span",{className:"text-emerald-500 font-bold",children:"Normal:"}),e.jsx("span",{className:"opacity-70",children:"Everyone gets exactly 1 slice. (Bell Curve)"})]}),e.jsxs("li",{className:"flex gap-2",children:[e.jsx("span",{className:"text-emerald-500 font-bold",children:"Power Law:"}),e.jsx("span",{children:"1 person eats 80 slices, and the other 99 people have to share the remaining 20 slices."})]})]}),e.jsxs("p",{className:"mt-4 text-[10px] text-emerald-500/50 uppercase italic font-bold",children:["//",' This is why the "average" (1 slice per person) is useless here.']})]}),e.jsxs("div",{className:"border-l-2 border-yellow-500/50 pl-4 py-1",children:[e.jsx("h4",{className:"text-xs font-bold text-yellow-400 uppercase tracking-widest mb-3",children:"Key Characteristics"}),e.jsxs("ul",{className:"space-y-3 text-xs opacity-90",children:[e.jsxs("li",{children:[e.jsx("strong",{className:"text-current block mb-1",children:"Scale Invariance"}),"The distribution looks the same regardless of the scale at which you observe it."]}),e.jsxs("li",{children:[e.jsx("strong",{className:"text-current block mb-1",children:"Pareto Principle (80/20 Rule)"}),"A common manifestation where 80% of effects come from 20% of causes."]}),e.jsxs("li",{children:[e.jsx("strong",{className:"text-current block mb-1",children:'Lack of "Average"'}),`Unlike a Normal Distribution (Bell Curve), the "average" in a power law is often misleading as it's heavily skewed by extreme outliers.`]})]})]}),e.jsxs("div",{className:"border-l-2 border-green-500/50 pl-4 py-1",children:[e.jsx("h4",{className:"text-xs font-bold text-green-400 uppercase tracking-widest mb-3",children:"Real-World Examples"}),e.jsxs("ul",{className:"space-y-3 text-xs opacity-90",children:[e.jsxs("li",{children:[e.jsx("strong",{className:"text-current",children:"Wealth Distribution:"})," A small percentage of the population holds the majority of the wealth."]}),e.jsxs("li",{children:[e.jsx("strong",{className:"text-current",children:"City Populations:"})," A few mega-cities vs. thousands of small towns."]}),e.jsxs("li",{children:[e.jsx("strong",{className:"text-current",children:"Word Frequency (Zipf's Law):"})," ","The most common words in a language appear significantly more often than the rest."]}),e.jsxs("li",{children:[e.jsx("strong",{className:"text-current",children:"Internet Traffic:"})," A few websites (Google, YouTube) receive the vast majority of all traffic."]})]})]})]})]})}export{r as default};