Articles for tag: equation, infographic, future, prediction, meaning, mathematics, probability

1 January 2023

I have written much on predictions before. The following equation appeared in a different format in The arrogance of mathematics and Chaos Theory. I haven’t changed the content of it; only the layout. I’ll explain in a while. There are major problems with predictions. The first big one is that all predictions depend on ‘the ...

For those who want to spend their life understanding

The Analysis Tool (also called REPL) – is JavaScript code used by Claude.ai to perform the thermal calculations and generate the data. This was invoked using the repl command.

React Component – This is the visualization code Claude.ai created as an artifact using React and the Recharts library to display the temperature profiles. This was created with the identifier “temp-profile” and used the artifact type “application/vnd.ant.react”.

It now all makes perfect sense – right? 🤣😂

import React from 'react';
import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';

const TempProfile = () => {
  const [data, setData] = React.useState([]);

  React.useEffect(() => {
    // Using properties from Table 3
    const albumenFraction = 0.58;
    const shellFraction = 0.11;
    const yolkFraction = 1 - albumenFraction - shellFraction;
    
    const avgSpecificHeat = 
        albumenFraction * 3935 +
        yolkFraction * 3266 +
        shellFraction * 888;
    
    const eggMass = 0.06;
    const eggRadius = 0.025;
    const eggSurfaceArea = 4 * Math.PI * Math.pow(eggRadius, 2);
    
    const timePoints = [];
    const fridgeTemps = [];
    const eggTemps = [];
    const timeStep = 1;
    const totalTime = 7 * 60;
    
    for (let t = 0; t <= totalTime; t += timeStep) {
      let fridgeTemp;
      if (t <= 20) {
        fridgeTemp = 4 + (10 - 4) * (t / 20);
      } else {
        fridgeTemp = 4 + (10 - 4) * Math.exp(-0.01 * (t - 20));
      }
      
      const h = 10;
      const tempDiff = fridgeTemp - (eggTemps.length > 0 ? eggTemps[eggTemps.length - 1] : 4);
      const heatTransfer = h * eggSurfaceArea * tempDiff * timeStep;
      const tempChange = heatTransfer / (eggMass * avgSpecificHeat);
      
      const newEggTemp = (eggTemps.length > 0 ? eggTemps[eggTemps.length - 1] : 4) + tempChange;
      
      timePoints.push(t);
      fridgeTemps.push(fridgeTemp);
      eggTemps.push(newEggTemp);
    }
    
    const chartData = timePoints.map((t, i) => ({
      time: Math.round(t / 60 * 10) / 10,  // Convert to minutes with 1 decimal
      fridgeTemp: Math.round(fridgeTemps[i] * 1000) / 1000,
      eggTemp: Math.round(eggTemps[i] * 1000) / 1000
    }));
    
    // Sample every 3rd point to reduce data size
    setData(chartData.filter((_, i) => i % 3 === 0));
  }, []);

  return (
    <div className="w-full h-96 p-4">
      <ResponsiveContainer width="100%" height="100%">
        <LineChart data={data}>
          <CartesianGrid strokeDasharray="3 3" />
          <XAxis 
            label={{ value: 'Time (minutes)', position: 'bottom', offset: 0 }}
            dataKey="time"
          />
          <YAxis
            label={{ value: 'Temperature (°C)', angle: -90, position: 'insideLeft' }}
            domain={[3, 11]}
          />
          <Tooltip />
          <Legend />
          <Line 
            type="monotone" 
            dataKey="fridgeTemp" 
            stroke="#8884d8" 
            name="Fridge Temperature"
            dot={false}
          />
          <Line 
            type="monotone" 
            dataKey="eggTemp" 
            stroke="#82ca9d" 
            name="Egg Temperature"
            dot={false}
          />
        </LineChart>
      </ResponsiveContainer>
    </div>
  );
};

export default TempProfile;

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