What is Entropy (Information)?

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Entropy (Information)

Shannon Information Entropy

A measure of uncertainty or information content in a dataset, calculated as the negative sum of probabilities times their logarithms.

技術的詳細

Entropy (Information) answers 'to what power must the base be raised to produce this value?' Common bases: natural log (ln, base e ≈ 2.718), common log (log10), and binary log (log2, used in computing for bit-depth and information theory). Logarithmic scales are used for pH (chemistry), decibels (audio), Richter magnitude (seismology), and algorithm complexity analysis (O(log n)). The slide rule — the engineer's calculator before electronics — operated entirely on logarithmic principles.

例

```
Logarithm identities:

  log_b(x) = y  means  b^y = x

  log₁₀(1000) = 3   (10³ = 1000)
  log₂(256)   = 8   (2⁸ = 256)
  ln(e)       = 1   (e¹ = e ≈ 2.718)

  log(a × b) = log(a) + log(b)
  log(a / b) = log(a) - log(b)
  log(a^n)   = n × log(a)
```

Categories

Entropy (Information)

技術的詳細

例

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